摘要:

144 GROWTH OF FACES OF SODIUM CHLORATE CRYSTALS THE GROWTH OF INDIVIDUAL FACES OF CUBIC SODIUM CHLORATE CRYSTALS FROM AQUEOUS SOLUTION BY S. P. F. HUMPHREYS-OWEN Received 29th December, 1948 Bunn, in hitherto unpublished work, and Berg grew crystals of NaC10, alone in a thin film of aqueous solution between optically-plane glass plates. Growth was constrained to the four faces in the plane of the film. The rates of advance of these faces were measured together with the concentration 1 Berg, Proc. Roy. SOC. A , 1938, 164, 79.S. P. F. HUMPHREYS-OWEN I45 contiguous to them, the latter being deduced by means of interference fringes formed in the solution surrounding the crystal. The results obtained were unexpectedly complex. (i) the concentration was not uniform along a face, but was lowest a t its centre, rising on each side to the corners ; (ii) the component of the concentration gradient normal to the face (hereafter called the normal gradient), which is proportional to the exit of solute per unit area from the solution, was also not uniform.It was highest at the centre and fell towards the corners ; (iii) faces of one crystal, though all of the same type and initially in contact with solution of the same strength, usually grew at different rates and sometimes stopped growing altogether ; (iv) there was a tendency for the slower growing faces of one crystal to be in contact with solution of higher concentration. Berg suggested that (ii) implied the existence of a transport of solute laterally along the face in a layer too thin to be observed.For without such a transport the growth of the face as a plane would be inexplicable. The present author has obtained some new results with NaClO,, using the same technique, which are reviewed and discussed in this paper. It was found that : Predictions from Diffusion Theory With a given supersaturation far from the crystal as one boundary condition, and some selected boundary condition at the crystal surface, the diffusion of solute to the crystal is determined and its rate of growth can be approximately calculated and compared with experiment. In order to render the treatment mathematically practicable two approximations were made ; the polygonal perimeter of the crystal was replaced by a circular perimeter (under the experimental conditions the diffusion field is two- dimensional).Secondly, the difficulty caused by the non-existence of a stationary state was overcome by neglecting the first moments of rapid growth and treating only subsequent periods, in which the increase in size of the crystal and of the surrounding zone of non-uniform concentration was regarded as slow. Let p = density of the solid crystal, a = radius of the crystal, t = time, c, = concentration at the crystal, assumed uniform, c, = solubility. The diffusion constant, D, of the solute was defined from Fick’s law: mass of solute transported per second across unit area equals the product of D and the concentration gradient normal to that area. Since it appeared from Bunn’s results that differently growing faces of one crystal were associated with different values of the contiguous concentration, Berthoud’s equation was employed as the boundary condition at the crystal surface, namely G = K ( c ~ - c,), .where G is the mass per second per unit area incorporated into the crystal, and k is a constant of the surface which can be different for different faces. c, takes a value dependent simultaneously on k and on the external diffusive environment. For the far boundary condition it was assumed that a constant, uniform Humphreys-Owen, PYOC. Roy. SOC. A , 1949, 197, 218. Berthoud, J . Chim. Physique, 1912, 10, 625.146 GROWTH OF FACES OF SODIUM CHLORATE CRYSTALS concentration, c,, existed at and beyond a radius r0 measured from the centre of the crystal. It was found experimentally that, except for the first moments of growth, Y, increased slowly at a rate such that its ratio to the diagonal of the crystal remained constant.The ratio ro/a was therefore taken as constant in the calculation, and the disturbance of the stationary state caused by the time-dependence of yo and a was ignored. With this assumption and the above boundary conditions it can be shown that : p.da/dt = k(ca - c~), . * (4 The radial rate of advance declines with time as a increases, and depends on the ratio Dlk. If k is large compared with D , (4) becomes ca = c,, and (3) becomes adaldt a (c, - c,). This is the historical assumption of Nernst for growth from solution, in which the concentration at the crystal surface is brought down effectively to the saturation value and the facial rate of advance depends only on the diffusion geometry.In this case, ( z ) , which represents the dependence of the rate of advance on the crystallographic factor R, then becomes indeterminate with (Ca - cs) tending to zero as k tends to infinity. For comparison with experiment a face is regarded as the arc of a circle, and the non-uniformity of concentration along it observed by Bunn is neglected. Of course, it is implicit that central symmetry be preserved; when faces of one crystal grow at different rates and are in contact with different concentrations there will be a redistribution of lines of flow round the crystal and the above equations will lose some of their validity. Experimental and Results Bunn’s observation of different facial rates of growth in one crystal was confirmed, but it was found that certain faces did sometimes grow in accordance with the Nernst assumption.In these cases the distance y advanced by a face (made equivalent to a by a suitable numerical factor) obeyed (3) quantitatively for the case G, = cs, where c, was taken as the concentration at the face centre. This indicated that the centre concentration, to be called cw$ hereafter, is the important one, and that Bunn’s distribution of concentration along the face is a “ fine structure ” effect of the growth mechanism and can be replaced by c,,, when calculating rate of advance. Often, however, faces were found which grew a t rates less than calculated under the Nernst assumption. In these cases the value of c, was not that corresponding to saturation but higher.This is qualitatively in accordance with (3) ; for, with a given G,, it predicts an inverse correlation between ydy/dt and c,. The quanti- tative agreement was not good, because crystals with all four faces with the same rate of advance and concentration distribution were never encountered, and the distortion of the concentration field caused by differently behaving faces modified the concentration a t each face. The other prediction, the time-depen- dence of G, by reason of the term I/U in (4), would be falsified both by lack of central symmetry and by the only partially justified assumption of a stationary state, and was not observed. But these results, as far as they go, are of interest in their demonstration that the Nernst mode of growth is observed only with certain faces of a crystal bounded by faces all of the same type.Other faces appear to have a smaller value of the Berthoud constant k , and behave as if they were “ hindered ” in some way. It is still possible that they obey the condition (I), but to test this rigorously i t will be necessary to isolate one face from the others of the sameS. P. F. HUMPHREYS-OWEN I47 crystal, and also to confine the inflow to one dimension so that the true diffusion equation in bc/bt can be solved. Nevertheless, it will be convenient in the discussion to assume the truth of (I) and to say that the hindered faces have a smaller value of K than others. Faces did not always preserve the same K during an experiment. Sometimes it changed, and when this happened the change was observed to be sudden and discontinuous. The concentration at the face would suddenly rearrange itself to a new distribution.This points to a definite, abrupt event at the crystal surface and will have important bearing on any physical hypothesis put forward to interpret ‘‘ hindrance.” The variation of concentration in the vicinity of a face was studied quanti- tatively, and both the concentration and its normal gradient g were expressed empirically in terms of x , the distance along the face from its centre, R the rate of advance of the face, and other observables. Neglecting distortion caused by adjacent faces having different behaviour, i t was found that g could be expressed by the parabola : where I is the half-length and q is an experimentally observed constant.and typical values were : g = R((p/o) f iIq - (p/-D)I [I - 3(X2/1’))1) 2 * * ( 5 ) Units R = 10-5 cm./sec. (typical), I = 0.015 cm. (typical), D = 1.7 x IO-’ g./cm. sec., q = 1-62 x 10’ sec./cm 2, p = 2.5 g . / ~ m . ~ . g was expressed in change of concentration per cm., where concentration is g . solute per IOO g. solution. If there is a lateral flow of solute along the face, as suggested by Berg, its value a t any point can be derived from (5) as long as (a proviso pointed out by F. C. Frank) the diffusion of solvent down the gradient bc/bx is neglected. With the above figures the flow is such that a t the face centre about g yo of the intake from outside does not crystallize locally. For an estimate of the physical signi- ficance of this lateral flow the magnitude of the transport across unit area must be known.This requires knowledge of the thickness of the layer in which the flow takes place. The layer is not thick enough to cause any discontinuity in the interference fringes terminating a t the crystal, but nevertheless the upper limit to the thickness is uncertain within wide limits because refraction effects a t the crystal edge prevented observation much closer than I O - ~ cm. from the face. Berg (loc. cit.) suggested that the layer might be a Volmer adsorbed phase. If the thickness is taken to be, say, 10-7 cm., on the assumption of a Volmer layer one molecule thick, the transport of solute across unit area works out a t about 6000 times the diffusive transport in the outside solution.This indicates a very high coefficient of diffusion in the layer. Of course, a lower coefficient of diffusion is derived if a greater layer thickness is assumed, but it is difficult to find grounds for postulating a mobile layer many molecules thick. The absolute gradient, normal to lines of equal concentration, was found to be uniform along a face, and this fact can be used in conjunction with (5) to derive an expression for the concentration, G, as a function of x . This is : where cc = 2413, and p = q -pp/D. Eqn. (6) represents a very large effect, as can be seen from the fact that the concentration difference between the face centre and the corners is about 1/4 of the supersaturation of the solution far from the crystal. Some x-dependent property of the face is required to explain (6), and if, as suggested by Frank, an intermediate layer between the face and the solution is not acceptable as a source of such a property, something must be put in its place.Bunn has favoured the existence of vicinal planes on a growing face as an explanation, but it is doubtful whether such a hypothesis can be found capable of dealing quantitatively with (6).148 GROWTH OF FACES OF SODIUM CHLORATE CRYSTALS The non-uniformity of concentration is observed whether or not hindrance is present, but the latter effect does modify (6) since both c , ~ and R are affected by hindrance. The separate effect of hindrance can be extracted by the use of (3), and i t can be shown that the rise of concentration during hindrance is rela- tively greater a t the centre than a t the corners.On three occasions the restart of growth of a completely inert face was observed, and it was seen that there was then a sudden fall of concentration at a single point, not at a corner, on the face. From this point the change of concentration spread rapidly to either side, until, after about two seconds, the usual Bunn distribution was re-established. Discussion Only one type of face, the (IOO), was investigated, and we have seen that this type, in NaClO,, is capable of growing a t the maximum rate permitted by diffusive presentation of material (for the Nernst condition amounts to this). It would be interesting to investigate other types of face by this optical technique, in order to see what values of concentration are in contact with such faces.At first sight it is puzzling how less stable types of face could succeed in obtaining the additional supply of material necessary for their higher rates of advance. This might be achieved by dendritic growth in which a face, in broad terms, does not ‘wait for’ the presentation of solute by diffusion. Or it might be found, despite thermodynamical objections, that less stable types of face have a lower solubility, Regarding the ‘ hindrance ’ effect, there seems no doubt that this is caused by some process at the face itself. Previously the fact that simple (100)- bounded crystals rarely grow as perfect cubes has been ascribed to irregu- larities in the supply of material caused by imperfect stirring or by the presence of other crystals in the neighbourhood. Some more directly crystallo- graphic explanation is now necessary.The three salient facts are, firstly, the discontinuous change from one degree of hindrance to another, secondly, the long periods, i.e., during the deposition of many new crystal planes, of its operation, and thirdly the rise of contiguous concentration accompanying it. The blockage of the nucleation point by a foreign adsorption is adequate as an explanation of the rarer event of complete stoppage of growth. It is probable that the observation mentioned at the end of the previous section represented either the restart of nucleation after ejection of an impurity or the start of nucleation at some new point. But explanations of hindrance in terms of impurities are not satisfactory.If impurities are sufficiently common to cause the very general hindrance effect, how could some faces remain unhindered, as they do, for long periods 1 Again, how could the impurity continue to have effect during the deposition of many new crystal planes ? The sudden changes point to some event, nevertheless, at the nucleation point ; neither the discontinuity of change nor the selection of certain faces is consistent with a non-localized change on the face, say, in its topography or in a Volmer adsorbed phase. But no facile explanation comes to mind, and the effect must remain temporarily obscure and open to discussion. Turning to the non-uniformity of concentration and normal gradient along the face, the author favours the acceptance of an intermediate layer, perhaps a Volmer phase, with properties dependent on position on the face. Although a flow in such a layer has not, perhaps, been conclusively demon- strated, it is reasonable to postulate its existence. It could well arise by interaction between the layer and the advancing growth sheets of the face, and non-uniformity of density, or perhaps concentration, would be expected in it which would give rise to non-uniformity in the concentration of the external solution contiguous to it and to non-uniformity of intake from outside. If desired, part of the non-uniformity in the layer could be ascribedS. P. F. HUMPHREYS-OWEN I49 to the existence of vicinal planes on the underlying surface. For Volmer has said that the surface free energy of the underlying surface would affect the density of his phase. But, as said in the previous section, it is unlikely that surface topography alone could account for the large contiguous non-uniformities observed. Birkbeck College, Uiziversity of London.

ISSN:0366-9033    

DOI:10.1039/DF9490500144

出版商:RSC    

年代:1949

数据来源: RSC

摘要:

S. P. F. HUMPHREYS-OWEN I49 THE LINEAR VELOCITY OF POLYMORPHIC TRANSFORMATIONS BY N. H. HARTSHORNE Received 31st January, 1949 In an earlier paper on the transformation of cc- to P-o-nitroaniline it was suggested that the linear rate of advance of the interface was determined by the difference between the rates of escape of molecules from the two crystal lattices, these rates being assumed to be the same, or at least to have the same dependence on temperature, as the rates of evaporation of the crystals into a vacuum. This picture, involving molecules travelling in both directions across the interface instead of only from the unstable t o the stable lattice, seemed to be demanded by general kinetic considerations such as are applied to other types of phase boundaries. The suggestion of equality between the rates of escape and rates of evaporation into a vacuum arose from the fact that the apparent activation energy of the transformation (i.e., the value deduced from the slope of the graph of log rate against I/T) was found to be of the same order as the internal latent heat of sublimation of the p-form.In transformations studied later (yellow to red mercuric iodide, monoclinic to rhombic sulphur 3), the apparent activation energy was found to be less than the heat of sublimation (though very much greater than the heat of fusion), suggesting that in these cases the energy required to surmount the potential barrier at the interface was less than that involved in evaporation into a free vapour space. (A more recent study of the sulphur trans- formation, to be described later in this paper, has cast doubt on this interpretation as far as this substance is concerned.) The form of the expression giving the rate of escape of molecules from a lattice will not be affected by the question as to whether the activation energy is equal to or less than the heat of sublimation.In either case the probability of a molecule acquiring this energy will be given to a close approximation by the simple exponential factor e-EIRT. We can therefore proceed to derive a general expression for the linear rate on the basis of the above ideas as follows. Let it be assumed that there exists at the interface between the two lattices a thin transitional layer of the order of one molecule in thickness, composed of molecules of high energy in a state of disorder.Molecules escape from each lattice into this layer as they acquire sufficient energy. Hartshorne, Walters and Williams, J. Chem. Soc., 1935, 1860. Eade and Hartshorne, J. Chem. Soc., 1938, 1636. 3 Elias, Hartshorne and James, J . Chem. Soc., 1940, 588.150 VELOCITY OF POLYMORPHIC TRANSFORMATIONS They then stand an equal chance of either returning to their parent lattice or of condensing on the opposite lattice, i.e., the probability that a molecule which breaks free from one crystal modification will contribute to the growth of the other is 4. Consider first the transformation of an enantiotropic substance below the transition point. If v, is the rate of escape of molecules from the unstable form, and q that from the stable form, both multiplied by the appropriate factor to convert them to linear rates of recession of the crystal surfaces, we have that V , the linear rate of advance of the interface, is given by V = +(va - vS) = *(A,e-E,lRT - A S O e-E IRT * (1) where Eu and E, are the activation energies of escape, and A, and A@ are factors which depend on the vibration frequencies of the molecules in the crystals and which to a first approximation may be taken as independent of temperature. where q is the heat of transformation.Now E , = E a + 4, Substituting for E, in (I), we obtain V = le-E,/RT (Aa - Ase-4/RT) . ' (2) But at the transition point, To, V = 0. Therefore A , = AB e-qlRTo, or Ap = A,eqIRTo. Substituting for A , in (z), we obtain It is assumed that q, E,, and E, are independent of temperature.According to this equation, V passes through a maximum value, as is observed in practice. We may obtain a value for the temperature, Tmax., at which the velocity has this maximum value by differentiating V with respect to T and equating to zero, whence Now if E, approaches the value of the heat of sublimation, the ratio q/Ea will, in general, be small, since the heats of transformation of polymorphs are usually small. Thus Within this approximation, therefore, the interval between To and T,,,. increases as E, decreases, and is practically independent of the value of q. Eqn. (3) may be put in the following logarithmic form : From this it is seen that the plot of the difference between In V and In ( I - eR(T, T ) ) is a straight line with a slope of -E,/R.In addition, * This expression in a slightly different form was first deduced by the author in 1938. and in its present form in 1942. It has not previously been published because until recently there has seemed to be no trustworthy data covering a sufficiently wide range of temperature by which i t could be tested. 1 L - _ LN. H. HARTSHORNE 151 inspection of the equation shows that the plot of In V against I/T, at temperatures below Tmax., will have a slope which tends more and more nearly to --E,/R as T decreases. For example, suppose that E, = 22,500 cal., q = 730 cal., and To = 369" K, whence T,,,. (from (5)) is 354" K. The mean slope of the graph of In V against I/T then corresponds to the following E values (apparent activation energies) for the temperature ranges given : 313 - 293" K, 19,400 cal.; 293 - 273" K, 20,500 cal. ; 273 - 253" K, 21,100 cal. These figures show that, provided that eqn. (3) is valid, the apparent activation energy for a temperature range sufficiently far below T,,,. (say, 50" or more) may be taken as an indication of the order of the true activation energy, E,, for the process of transfer of molecules from the unstable to the stable lattice. This will also apply in general to the apparent activation energy in monotropic transformations, such as the a- to p- change in o-nitroaniline mentioned above, for in these cases the (theoretical) transition point lies above the melting point, and Tmax. also may be expected to be in this region. Eqn. (3) may be modified to apply to an enantiotropic transformation above the transition point simply by changing the sign of the quantity in the brackets, thus : The subscript a still refers to the form which is unstable below the transition point, now the stable form, and T is now greater than To. The equation corresponds to a continuous increase of the linear rate Y' with rise of temperature.By expanding the exponential term inside the brackets in eqn. (3) and neglecting all but the first two terms of the expansion, we obtain This approximation is a close one only if is a small fraction, i.e., if q is small and T is not too far below To. From the general thermodynamic relation G = H - T S , where G is the free energy, H the heat content, and S the entropy, it follows, since we have assumed that q (= -AH) is constant, that q ( y ) = -AG.Substituting in (8) we obtain This form of the velocity equation is interesting in bringing out the influence of the difference between the free energies of the two modifications as the " driving force " of the reaction. Equations similar to (8) and (9) have been derived independently by Akulov and by L a ~ r e n t . ~ Akulov's argument is briefly as follows. He expresses the work done by a molecule in moving from one side of the inter- face to the other as qv6, where q is the coefficient of the internal resistance (arising from the collisions suffered by the molecule in its passage through the boundary layer), v is the average velocity of the molecule, and 6 the Akulov, Compt. rend. U.R.S.S., 1941, 32, 340 ; 1943, 39, 268.Laurent, Rev. Mktall., 1945, 42, 22.152 VELOCITY OF POLYMORPHIC TRANSFORMATIONS average path covered. free energies of the molecule in its initial and final positions. This work is equated to the difference between the Thus where q, To and T have the same significance as above. In addition, it is necessary that a molecule shall possess sufficient kinetic energy to sunnount the potential barrier at the interface, and the probability of this is e-EIRT, where E is the height of the barrier, or in the general case a certain function of this. The number of molecules crossing unit area of the interface in unit time, and therefore the linear rate, will be proportional to Laurent has used very similar arguments to those on which eqn. (3) is based, the main differences being that he expresses the activation energy in terms of quantum theory, the molecules in the lattice being assumed to behave as simple harmonic oscillators, and that, despite this refinement, he adopts the same approximation as we have used here to obtain eqn.(8) and (9). His equation may be put in the form- (--AG) ? ( ! - E ) Linear rate = A ___ .eT = R , RT hv where A is a constant, 8 = - the Einstein characteristic temperature, k' and E is the height of the potential barrier. Since O/zT is sma.11 compared with -E/RT, the exponential factor will be of the same order as e-EIRT. TABLE I Temp. (" C) 0 I 0 20 30 40 5 0 60 70 80 Mean linear rate, V (mm./hr.) 0.029 0' I 30 0.36* 0.86* 0.94 1.98* 3.60 5.16 5'30 1-60 Standard deviation ( S ) 0.007 0.032 0'2 7 0.17 0'73 0.97 1-47 1-56 0.60 0'10 Coefficient of variation ( S / V ) 0.24 0.2 5 0'2 8 0.32 0'1 8 0.3 7 0.2 7 0'2 8 0.29 0'37 * Results of Elias, Hartshorne and James.The author, with M. H. Roberts, has now completed measurements of the linear rate of transformation of monoclinic to rhombic sulphur over a sufficiently wide range of temperatures (0" to 80" C) for eqn. (3) to be tested. Polycrystalline films of monoclinic sulphur between glass surfaces, prepared under controlled conditions and 0.06 to 0.1 mm. thick, were maintained at constant temperature, and after the reaction had been started by inocula- ting the edge of the film with rhombic sulphur, the position of the interface was observed at fixed intervals of time by projecting an enlarged image of the film on to a grid drawn on a white screen.The time taken for the interface to traverse each rectangle of the grid (corresponding to an advance of 0.25 mm.) was noted, about 1200 such readings being taken at eachN. H. HARTSHORNE I53 temperature. From these readings the average rate, standard deviation, and coefficient of variation were calculated. This is similar to the method used by Elias, Hartshorne and James (loc. cit.), whose work, interrupted by the war, only covered the range 20" to 40" C. Somewhat different methods were used at 10" and oo, where the interface movement was too slow to be conveniently followed in this way. The work will be fully described elsewhere. The results, together with those of Elias, Hartshorne and James, are given in Table I, and in Fig.I (curve A), log V is plotted against r/T. The short strokes above and below each point on the graph represent the standard deviation. The variance is considerable, but the means lie very nearly on a smooth curve, which shows a maximum at about 65" (To = 95.6"). It is 036 - I FIG. I.-Results of Elias, Hartshornc and James indicated by broken lines. particularly satisractory mat tne earlier results, wnlcn were obtained w m a different sample of sulphur and using a different apparatus, agree well with the later ones. It will also be seen that the coefficients of variation (Table I) remain fairly constant throughout the whole range, which may perhaps be taken to indicate that there is no essential change in the character of the reaction with change of temperature. The third column of Table I1 gives the values of log V - log \ I - eR(T.b)) (which we will now write as log (I - "x) for brevity), taking q to be 730 cal./mol. (SJ. This is the mean, to the nearest 10 cal. of Bronsted's value of 616 cal. at o", determined directly for the transition temperature from measurements of the vapour pressures of the two modifications, namely, 840 cal. The change of q with temperature q L- and that calculated by Neumann 6 Bronsted, 2. playsik. Chern., 1906, 55, 371. 7 Neumann, 2. physik. Chem., 1934, 171, 416.154 VELOCITY OF POLYMORPHIC TRANSFORMATIONS represented by these figures agrees well with that calculated from heat i r7 \ capacity data.* In Fig. I, log ( is shown plotted against I / T (curve B).I-x The plot is not a straight line & demanded by eqn. (6), and at first sight the deviation from this requirement seems very great, for the curve passes through a maximum. Similar deviations are found when the equations of Akulov and Laurent (above), put into the logarithmic form, are applied. It must be noted, however, that the value of (I - x) in the higher temperature range (70" to 80") is extremely sensitive to small changes in x . An increase in x of only a few per cent. in this region is sufficient to abolish the maximum V in the curve completely since it sharply elevates the values of log - On the other hand, a similar change in the lower temperature region has a comparatively small effect on the values of log (I - _" x), and practically none on the slope of the curve.It is thus possible by making appropriate (,I - z). TABLE I1 q= 730 cal./mol. Temp. (" C ) -_I___ 0 I0 20 30 40 50 Go 70 80 (I - x)* 0.295 0.260 0.22 7 . 0.194 0- I 62 0.131 0.071 0.043 0'10 I - 1'010 - 0.30 I 0.203 0.644 0.684 1.086 1.437 1.708 1.871 1.571 E, = 22,500 cal./mol. 1-02 0.98 1.04 1-08 1.07 1.08 1-09 1-08 1-07 1-04 (p25.5= 1-10 1'1 I 1-07 1-10 1-12 1'1 I 1-11 1-10 1-09 1-07 1.04 1'2 I 1-16 1-16 1-16 1-15 1-14 1-12 1-10 1-07 1-04 t Results of Elias, Hartshorne and James. but quite minor adjustments to the value of x to convert curve B into a straight line. It has therefore seemed worth while to consider whether there is any factor, not taken into account in deriving eqn. (6), which would act so as to increase slightly the values of x.A possibility is suggested by the marked difference which is observed in the appearance of the interface under the microscope at the lower temperatures from that at temperatures around and above T,,,,.. In the former case the advancing front of the rhombic phase is finely serrated, indicating that the particle size is small; in the latter it consists of quite large crystals with well-developed faces. We may suppose that at the lowest temperatures the rhombic phase forms as a finely divided mass which does not recrystallize, or only very slowly. Rise of temperature will favour recrystallization, but up to the region of Tmax. this will be offset, as far as conditions at the actual interface are concerned, by the increase in the linear rate, which will act so that recrystal- lization will be effectively confined to the material in rear of the advancing 8 Lewis and Randall, J .Amer. Chem. Soc., 1914, 36, 2468.N. H. HARTSHORNE I55 front. Above Tmax., however, the linear rate progressively slackens and with rise of temperature conditions will become more and more favourable for the formation of large, well-ordered crystal planes at the interface itself. We may further suppose that owing to the fine state of division at temperatures up to Tma,., the rate of escape of molecules from the rhombic form into the transition layer will be greater than the normal value for large crystals because of increased surface energy, but that above Tmax. the rate of escape will tend towards the normal value as the transition point, To, is approached.On this view, eqn. (I) becomes V = +(A,e-E,lRT - 'p . A,e-Eg/Rl-), where cp is greater than unity and is approximately constant up to Tmax,, and then decreases to become unity at T,. From this we obtain the ea uation : Since, as stated above, small increases in x make very little difference to the slope of curve B at the low temperature end, we may use this part of the curve to obtain a value for E,, and in this way we find that it lies between 22,ooo and 23,000 cal./mol. Now the internal latent heat of sublimation of monoclinic sulphur as given by Neumann's vapour pressure results (loc. cit.) is 22,500 cal./mol. to the nearest IOO cal. The slope of line c in Fig. I corresponds to this value. It thus appears that E, is the same, or nearly the same, as the energy which the molecules must acquire to escape completely from the monoclinic lattice into a free vapour space.Taking it to be 22,500 cal., ~e may test the applicability of eqn. (10). Bearing in mind the argument on which this equation is based, the problem is to see whether it is possible to find a value for 'p, not much greater than unity, which is constant over the range from 0" to the region of Tmax,, and which gives a straight line plot of log ~ against r/T with a slope corre- sponding to 22,500 cal. The method which has been adopted is to assume different values of 'p for a temperature of 25.5" which lies midway between oo and Tn,ax. on the reciprocal scale, and then work out values for other temperatures on the assumption that the above linear relationship holds.The last three columns of Table I1 show the results obtained taking 'p at 25.5" as 1-05, 1-10 and 1.15 respectively. It will be seen that up to 50" there is an upward trend in the first case, a downward one in the last, but that at 1-10 the values show no trend. (The variation from strict constancy may be attributed to errors in the value of V. If we reverse the calculation by assuming a constant value of 1-10 for cp, and work out the corresponding values of V , we obtain results which are very close to the experimental ones, and well inside the standard deviation limits for these.) From 60" onwards the 'p values decline in all cases. The requirements of the theory are thus satisfied by cp = 1.10, and this is a not improbable figure. The real meaning of the rp factor is that the activation energy for the escape of molecules from the rhombic form is reduced below the normal value applicable to large crystals.(1 - 9%) Thus we may write : 'p e-EpIRT = e-E$RT, where E i is this reduced activation energy. For 'p = 1.10 andEP = 23,230 cal. = (E, + q), Ei has the mean value of 23,173 cal. for the range oo to Soo, which is only 57 cal., or 0.25 yo, less than E,. This corresponds to an increase of 57 cal. in q as the temperature rises from 50" to To. In the156 VELOCITY OF POLYMORPHIC TRANSFORMATIONS light of this we can say that the deviations of curve B from the requirements of (6), if expressed as percentage variations of E,, are quite small. From eqn. (IO), the temperature-independent factor A , may be cal- culated.Taking E, as 22,500 cal. and cp in the lower temperature range as 1-10, the value obtained is 2.0 x 1017 mm./hr. or 0.56 x 1013 cm./sec. This is greater than the speed of light. An even higher factor ( 1 0 ~ ~ to 1o16 cm./sec.) was obtained by Anderson and Mehl from measurements of the linear rate of recrystallization of cold-rolled aluminium. Burgers lo and N. F. Mott have suggested that this very high value indicates that some process which depends on temperature through an exponential factor e-E/RT triggers the change of crystal form of a whole mosaic block without the intervention of any other thermally activated process, though Mott has also given an alternative explanation.ll On the basis of this theory we may equate A , to Bvd, where v is the vibration frequency of the molecules, and d the average spacing between them, in the monoclinic crystal, and B is the number of molecules whose rearrangement is initiated by the thermal activation of one molecule.Taking v as 1o12 - 1013, and d (from the density) as 6 x 10-* cm., B works out to the order of 10’. The volume occupied by this number of molecules in monoclinic sulphur is about 10-l~ CM.~, which is within the range of the usual estimates of the size of a mosaic block. In showing that the deviations of the experimental results from eqn. (6) can be accounted for by means of the cp factor, it has not been forgotten that this equation was deduced on the assumption that A,, A,, E,, Eg, and therefore q, were all independent of temperature, whereas at best this can only be an approximation.The increase of q with temperature given by the results of Bronsted and Neumann, and calculated from the heat capacities recorded by Lewis and Randall (see above), is in fact greater than that corresponding to the introduction of the cp factor, and this suggests that the deviations may be due to the approximations inherent in the equation rather than to changes in surface energy. We cannot, of course, consider this possibility solely on the basis of the thermodynamic variation of q, i.e., without regard to the temperature dependence of the other four ‘constants,’ and unfortunately q appears to be the only one whose tem- perature dependence can be assessed with any certainty. It is, however, intended to look further into this question.It has also been suggested to the author by Prof. E. G. Cox that the average size of the mosaic blocks of the monoclinic phase may vary with temperature as a result of the way in which the films are prepared. This would result in corresponding changes in A,, if the Burgers-Mott trigger mechanism be accepted. ADDENDUM. (Received 13th May, 1949.) Since the above paper was presented, it has been pointed out to the author by Dr. W. J. Dunning that the temperature coefficient of the reaction can be accounted for on the basis of Volmer’s equation for the linear rate of growth of a crystal from its vapour.12 Applied to a solid-solid reaction Dunning’s treatment assumes that the transitional layer between the two lattices behaves as a true vapour (in which case it will have to be somewhat thicker than one molecule) and that the rate of advance of the interface depends not only on the supersaturation of the vapour with respect to the stable phase, but also on the probability of formation of two-dimensional nuclei on the completed surface planes of molecules of this phase.Anderson and Mehl, Trans. Amer. Inst. Min. Met. Efzg., 1945, Tech. Pub. No. 1805. lo Burgers, K . Ned. Ak. Wet., 1947, 50, 719. l1 Mott, Proc. Physic. SOC., 1948, 60, 391. l2 Volmer, Kinetik der Phasenbildzmng, 1939, p, 174.N. H. HARTSHORNE I57 For this case Volmer's equation can be put in the simplified form : Y . * (11) V = K . e-E/RT . e-A"/RT where E is the activation energy for the escape of molecules from the unstable lattice (i-e., the internal latent heat of sublimation), and A" is that for the formation of two-dimensional nuclei.Now A" wMp2NT, - const. -- RT - 2qdSRT(To - T ) - T(T0-T) ' where o is a shape factor, M is the molecular weight, p the edge free energy, N the Avogadro number, q the heat of transformation, d the density, 6 the spacing between lattice planes and the other symbols have the usual signi- ficance. Substituting for A"/RT and taking logarithms, eqn. (11) becomes : const. - (13) E In F' = In K - -~ - RT T(To- T ) ' * Dunning finds that this equation fits the results given in Table I very well, when In K = 38-77, E = ZO,ZOO cal., and the constant in the third term is 3.5 x lo4. (K is of the same order of magnitude as the author's A,, so that this treatment does not throw any light on the reason for the large pre- exponential fact or.) This contribution to the problem is most interesting and important, and the possibility that surface nucleation is a rate-determining factor will receive serious consideration in future work carried out by the author on solid-solid transformations.For the present, however, the following objec- tions to the theory, at least in its present form, and as applied to the case of sulphur, may be raised. (I) The marked difference, mentioned in the paper, between the surface contour of the rhombic phase above and below T,,,. suggests strongly that if surface nucleation is necessary at all, it is not equally so over the whole range of temperature; that is to say, the effect cannot be expressed by the simple factor e-*"IRT as defined above.At temperatures below 50" the advancing front exhibits numerous rounded promontories of the order of I O - ~ cm. or less in diameter, and it is difficult to reconcile these with the Volmer picture of the successive laying down of extended plane layers of molecules. Possibly surface nucleation only becomes necessary at the higher temperatures, and if so, this could account for the negative deviations from eqn. (3) in this region. (2) R. S. Bradley l3 has found from measurements of the rate of evaporation of single crystals of rhombic sulphur between 15' and 32-5" C that the accommodation coefficient, i.e., the fraction of molecules which on striking the surface condense, is constant at 0.7. This could be interpreted as indi- cating that an activation energy of about zoo cal.is required for surface nucleation (by equating 0.7 to e-A"IRT), but this is very much less than the value calculated from eqn. (12) for this temperature range, viz., 700-1000 cal. Alternatively the deviation of the coefficient from unity may be due to an orientation requirement, i.e., that molecules approaching the surface must have orientations within a certain solid angle if they are to condense. (3) The value 3-5 x 104 for the constant in the third term of eqn. (13) corresponds to an edge free energy (p) of 2.4 x I O - ~ erglcm. (taking o as m), from which the surface free energy may be calculated to be of the order of 4 ergs/cm.2. Bearing in mind that, according to the theory, the growing surface is supposed to be in contact with vapour, this value is far too small.The surface free energy of liquid sulphur just above the melting point is 13 Private communication.158 BOUNDARY MIGRATION AND GRAIN GROWTH 60 ergs/cm.a and that for the solid must be somewhat greater. If the g value corresponding to this is inserted in eqn. (13)~ the constant is increased by a factor of about zoo, and the equation no longer fits the experimental results. (4) The picture of a fairly thick transitional layer of vapour between the two lattices introduces difficulties. Owing to the increase of density accom- panying the transformation, the vapour gap would progressively widen as the reaction proceeded, and it can be shown that this would result in a concomitant decline of the linear rate. Such a decline was in fact observed by the author with o-nitroaniline and mercuric iodide (loc. cit.) and the theory of a progressively widening gap was invoked to explain it. In the case of sulphur, however, the rate is constant at constant temperature. This is probably due to the fact that, as can be seen under the microscope, the shrinkage accompanying the transformation is continuously accommo- dated by the formation of short cracks at, or just behind, the interface. This shows that solid-solid contact is never completely lost. Against all this, however, must be set the fact that both by Dunning’s and the author’s treatments the activation energy for escape of molecules comes out to be of the same order as the heat of sublimation. Further, if the linear rate is calculated on the assumption that it is given by the difference between the rates of evaporation of the two forms (using the , the result is of the order of I O - ~ to I O - ~ of the observed rate, i.e., the discrepancy between theory and observation is much less than when, as in the paper, the temperature independent factor is expressed as the product of the vibration frequency and the lattice spacing. From the above discussion it is very evident that much remains to be discovered about the mechanism of solid-solid transformations. The author desires to thank the Council of the Chemical Society for a Research Grant in connection with the investigation of the sulphur trans- formation and to acknowledge his indebtedness to Mr. R. S. Bradley, with whom he has had much stimulating discussion of problems raised in this paper. I usual equation, v = a$ Z/zxMRT) University College of Swansea , University of Wales , and The University, Leeds.

ISSN:0366-9033    

DOI:10.1039/DF9490500149

出版商:RSC    

年代:1949

数据来源: RSC

摘要:

158 BOUNDARY MIGRATION AND GRAIN GROWTH BOUNDARY MIGRATION AND GRAIN GROWTH * BY WALTER C. MCCRONE Received 8th February, 1949 It has long been known that metals will show grain growth and that this growth involves a reorientation of metal atoms across grain boundaries in such a way that many grains disappear entirely. This movement of * Contribution of Armour Research Foundation of Illinois Institute of Technolo,T.a b FIG. I.--TNT during boundary migration a t So” C (a after I min. ; b after 4 min.) ( Y roo) crossed Nicols. a b FIG. 2.-DDT showing secondary crystallization due to boundary migration (b is an enlargement ( x 100) of part of a ) . ( x 40) crossed Nicols. T o face page 1591WALTER C. McCRONE I59 grain boundaries led to the term " boundary migration" which will be used here as a synonym for grain growth.In 1929 Tammann2 published data showing that certain compounds (camphor, pinene hydrochloride and ice) show a behaviour very similar to that observed in metals. showed that some minerals (e.g., anhydrite, fluorite, periclase and corundum) when compressed and heated to temperatures well below the melting point would also show boundary migration similar to metals. In 1949 the study of octachloropropane was suggested as a means of studying boundary migration in metals. During the past several yeus a number of organic compounds quite dissimilar to octachloropropane in lattice properties have been shown to exhibit boundary migration. For example, Kofler reported in I941 that an organic compound, TNT, shows a somewhat similar behaviour in that crystals once formed undergo a further recrystallization in the solid phase so that one crystal grows into and through its neighbour (Fig.I). DDT has been reported and several other organic compounds (unreported) have been observed to show similar behaviour (Fig. 2). In each of these cases and in contrast with the metals, camphor, fluorite, octachloropropane, etc., it is apparent that these materials show boundary migration in which direction is dependent on the orientation of the crystal lattice within the grains. Metals, octachloropropane, camphor, pinene hydrochloride, ice, fluorite, anhydrite, etc., show migration of one crystal into another in such a way that the orientation of the lattice cannot be an important factor. On the other hand, boundary migration by TNT, DDT, Vitamin K, etc., is definitely dependent on orientation of the crystals.The crystals will grow in a direction which can be predicted for a given compound from the known relative orientations. The two types will be described throughout as the DDT type, in which orientation controls the direction of boundary migration ; and the octachloropropane type, in which orientation has little or no effect on the direction of boundary migration. The DDT type of boundary migration is of particular interest since as stated above the direction of growth is dependent on lattice orientation. Any theory covering the mechanism of boundary migration must take into account, for crystals of this type, the effect of difference in orientation of the two lattices in contact.DDT, for example, grows in such a way that the (001) face will penetrate either the (roo) or (010) planes of adjacent crystals. If, on the other hand, crystals of this type are aligned parallel to each other no growth will occur. Maximum growth will occur, therefore, when crystals elongated parallel to c intersect at 90° angles (Fig. 2). TNT shows a very similar behaviour although it does not grow as rapidly during boundary migration. It does, however, grow in much the same manner and in such a way that the direction of migration can always be predicted from the orientation of the crystals. In this case the (010) face will always grow into the (001) and (roo) faces (Fig. I). During the past 20 or 30 years there has been considerable discussion regarding the possible mechanism by which boundary migration occurs.In 1946 Buerger and Washken Two different types of boundary migration are therefore recognized. 1 Carpenter and Elam, J . I n s t . Metals, 1920, 24, 133. 2 Tammann, 2. anorg. Chem., 1929, 182, 289. 3 Buerger and Washken, Amer. Miner., 1947, 32, 296. 4 McCrone, J . A@Z. Physics, 1949, 20 (Feb.). Kofler, 2. physik. Chem. A , 1941, 188, 201. 6 McCrone, Anal. Chem., 1948,20,274.160 BOUNDARY MIGRATION AND GRAIN GROWTH Most of this discussion has been on boundary migration of the octachloro- propane type and most of it has concerned metals. Harker and Parker 7 have advanced the argument that grain shape governs the extent and direction of boundary migration. This results in movement of the grain boundaries in such a way that straight boundaries meet at angles of IZOO.By this criterion little or no grain growth should occur when these conditions are satisfied. The effect of lattice deformation on boundary migration is not discussed by them, although presumably it would at least affect the angles between grain boundaries. Most other investigators have assumed that strain energy, due to cold-working and resultant plastic deformation, is the driving force. Two hypothetical questions can be posed as a result of irreconciliation of these two ideas- I. Can grain growth occur in a sample whose grains meet throughout at 120' angles with straight boundaries but in which the grains possess residual strain energy ? 2. Can grain growth occur in a sample whose grains show curved boundaries and many angles not equal to 120' but in which the grains are strain-free ? Unfortunately the first of these questions cannot be answered in an un- equivocal fashion.A close approximation to a final answer to the second can, however, be obtained. This is done by comparing the rate of growth in two samples : one with, and the other as nearly as possible without, strain. Experimental data to answer this question are presented below. A broader problem, however, and one of great interest and importance is to find a more definite relation between boundary migration in metals and in the octachloropropane type of organic compound. It is obvious on examination of photomicrographs showing boundary migration in systems of these two kinds that in superficial appearance there is no difference between the two cases.There is a striking similarity between growth in metals and in octachloropropane and the resulting structures are amazingly similar in appearance before, during and after boundary migration. Furthermore, octachloropropane and other organic compounds of this type show a final structure which agrees entirely with the ideas presented by Harker and Parker. Octachloropropane, for example, during annealing changes progressively toward an ultimate appearance in which all grain boundaries are straight and meet only at angles of 120' (Fig. 3). An additional effort has been made to relate boundary migration of octachloropropane to that of metals. This is being done by studying the rate of growth at different temperatures and comparing these data with corresponding data for metals systems.Unfortunately little data of the latter type are available and it appears very difficult to accumulate large amounts of such data because of the experimental difficulties. It is possible, on the other hand, to follow boundary migration in organic compounds during annealing of a thin transparent section using polarized light under controlled temperature conditions and to obtain a complete curve with as many experi- mental points as desirable in a few hours. Some data taken in this way are summarized in Table I. These data were obtained by the following procedures. Expt. 1-4: A small quantity (5-10 mg.) of octachloropropane (purified by sublimation to a melting point of 168" C) was melted between a cover glass and slide.The fused preparation was quenched quickly to room temperature by placing i t cover-glass side down on a metal block. This preparation was then placed in a previously heated hot-stage set a t the desired temperature. About 10 sec. was required for the slide to become heated and from 3-60 sec. to find 7 Harker and Parker, Trans. Amer. SOC. Metals, 1g45,34, 156.FIG. 3.-Boundary migration in octachloropropane, the numbers refer to the same crystal as i t appears at successive times. ( x 100) crossed Nicols. [To faccpagc 160Time (min.) 5 6 7 I 3 16 27 32 41 54 64 I 0 22 I 2 3 5 7 15 28 45 80 140 I 0 I 30 60 I80 240 300 I20 I I 0 20 I 040 1485 2 I00 3390 F WALTER C, McCRONE TABLE I ISOTHERMAL TIME-RATE DATA FOR OCTACHLOROPROPANE Expt.I : 136' C Log Time 0.70 0.78 0.85 1-15 1-34 1'43 1-5 I 1-61 1-73 1.8 I I '00 1'20 0'00 0.30 0.48 0.60 0.85 1-17 "45 1-65 1-90 2-15 1'00 0'00 1.48 1.78 2-08 2.26 2-38 2.48 0'00 1-00 1.30 3-02 3-18 3'32 3'5 3 Rate Log Rate 0'010 0.007 0.006 0.005 0.004 0.004 0.004 0.004 0.004 0.003 0.003 0.003 8.00-10 7-85-10 7' 7 8- I o 7'70-10 7'60-10 7-60-10 7-60-10 7.60-10 7-60-10 7.4 8- 10 7-4 8-1 0 7'48-10 Expt. 2 : 123'C - - 0'0022 7-34-10 7.20-10 0.00 I 6 0.00 I 5 7-18-10 0'00 I I 7.04- I 0 0'00 I0 7-00-10 0.0008 6*90-10 - - 0.ooog 6.95-10 Expt. 3 : 115" C 0*0008 6.90-10 0*0007 6-85-10 0.00055 6-74-10 0~00035 6-54-10 0.00025 6-40-10 0'00020 6.30-10 0'00020 6.30-10 Expt. 4 : 103°C 0*00056 6-75-10 0.00033 6052-10 0'00022 6'34-10 0'000 I3 5'1 1-10 0-000 I 3 5-1 1-10 0-000 I 3 5-1 1-10 0~000 I 3 5.1 1-10 161 Log Diam.2-06 2-07 2-16 2.18 2.29 2.32 2'34 2-42 2-40 2-46 2'54 2-11 2.32 2-36 2.36 2'37 2.38 2-38 2-39 2-42 2'44 2.50 2-58 2'20 2-28 2-30 2'37 2'37 2-41 2.4 I 2.29 2-30 2-3 I 2-38 2-42 2-41 2-45162 BOUNDARY MIGRATION AND GRAIN GROWTH TABLE I-(Continued) Expt. 5 : 136' C Time Log Time Rate Log Rate Diam. Log Diam. (min.) (micron) I 1'5 2.5 4'5 5'5 7'5 I 0 I 5 27 40 60 90 140 I 60 I20 4 9 I3 18 23 0'00 0.18 0.40 0.65 0'74 0.88 1-18 1-43 1-60 1-78 1-95 2-08 2-15 1-00 2'20 0.015 0.013 0.0065 0.0055 0.0050 0.0038 0.003 8 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0'010 8.18-10 8.1 1-10 8. I O- I o 7-81-10 7-74-10 7-70-1 0 7-58-10 7 -5 8-1 0 7.5 8-10 7'5 8-10 7'5 8-10 7-58-10 7058-1 o 7.58- 10 7'5 8-1 o 1-77 1-83 1-89 2-06 2-13 2-16 2-18 2-32 2-42 2.52 2'55 2-64 2-80 2.89 2'10 Expt.6 : 159' C 0.60 0.006 7-78-10 185 2-2 7 0.95 0.006 7'78-10 188 2.2 7 1'1 I 0.006 7'7 8- 10 204 2.3 I 1-26 0.006 7.78-10 231 2'36 1-36 0.006 7-78-10 287 2-46 Expt. 7 : 145'C I 0'00 o.oo08 6.90-10 171 2.23 40 I -60 o*ooo8 6.90- I 0 203 2-3 I an appropriate field of view. In all experiments zero time indicates the time a t which the preparation was placed in the hot-stage. Most of the readings were started at M = I mjn. A carefully calibrated Kofler hot-stage was used with a Sola constant voltage transformer. The temperature data are accurate to &I" C and accurately represent the temperature of the field under observation. The data were taken by means of photomjcrography using a Leica with a Speed-O-Copy attachment.The 35 mm. negatives were enlarged to a convenient magnification and the average grain size was determined by measuring the intersections of grain boundaries on a linear scale during a number of regularly spaced linear traverses of the entire field (Fig. 3). Expt. 5 : A small quantity (5-10 mg.) of octachloropropane (purified as above) was placed between a slide and cover-glass and subjected to 500 psi pressure. This preparation was then placed in a previously heated hot-stage as for Expt. 1-4. Expt. 6 and 7 : In these two experiments 5-10 mg. of octachloropropane was melted in the usual way between a slide and cover-glass. The preparation was then, however, placed immediately in the previously heated hot-stage so that the temperature of the preparation a t no time fell below 145" C (Expt.7) or 159" C (Expt. 6). The average diameters were then determined in the same manner as described above. Fig. 4 shows these average diameters as a function of time for each experiment. These data were then smoothed from these curves and rate of growth data were calculated from the slopes of these smoothed curves. Fig. 5 shows log rate against log time for each experiment. Fig. 6 shows log rate against temperature with a vertical line for each experiment covering the time variable. The actual data points fall on the vertical lines with increasing time downward.WALTER C. McCRONE 40 30 10' IC 1 9-10 FIG. +-Grain growth curves for octachloropropane. 0 STRAINED T H E R M 0 COLD-WORKED 4 UNSTRAINED )-103k I 2 3 FIG.5.-Rate-time curves for grain growth in octachloropropane.164 BOUNDARY MIGRATION AND GRAIN GROWTH 9 - I C a-ic 7- 10 6-10 5 - IC A 0 B 9 I 0 - - u fl I TEMPERATURE rC) I I I I I I I I10 120 130 140 150 160 FIG. 6.-Rate-temperature curves for grain growth in octachloropropane. Discussion Fig. 4 shows that the slope of the rate curve plotted against time is constant after an initial period and that the slope increases with increasing temperature. The equations for the linear portions are : 136" C : D = 3.2M + 130 . (1) 123' C : D = I-IM + 230 . (4 115' C : D = o28M + 189 . * (3) 103" C : D = o-ozgM + 205 . (3) where D is the average grain diameter in microns and M is the time in minutes. The constant in each relation is, of course, fortuitous and depends only on the grain size of the original preparation.These equations are equivalent to the expression given by Beck : D = K(tg + A)". where K is the slope and A the imaginary time required for the grains to grow by boundary migration to an average size D at tg. In either case, however, the question is whether K is independent of A or, in the other case, whether S is independent of Di, the intercept on the grain diameter ordinate. The fact that the slope is a linear function of temperature (shown below) as well as the fact that the D against time curves are also linear is strong evidence for the belief that AD/AM is independent of initial grain size. A plot of the log slope against temperature is also very nearly linear and follows the relation, where S is the slope, AD/AT, and T is the temperature in O C.to the same phenomenon in octachloropropane. log S = 0.063 T + (Z.IO-IO), (5) These relations show that boundary migration in metals is closely related 8 Beck, J . Appl. Physics, 1948, 19. 507.WALTER C. McCRONE Expt. Fig. 4 also shows that two different preparations, one strained thermally (Expt. I) and a second strained mechanically (Expt. 5 ) , show little difference in rate of increase of grain diameter as a function of time. This may have been coincidental in that the amount of strain induced by these two means may have been nearly equal. The two Expt. 6 and 7 made on nearly unstrained crystals show that these two preparations grew at rates far below those predicted by eqn. (5) on the basis of Expt 1-5.It is believed that the growth which occurred in Expt. 6 and 7 is partly the result of residual strain and partly of the tendency of the grains to form straight boundaries meeting at 120" angles. Since the interboundary angles for the preparations used in Expt. 6 and 7 are no nearer 120O than those used in Expt. 1-5, the decreased growth in Expt. 6 and 7 must be due to lack of lattice strain. In other words, lattice strain must be the most important factor causing boundary migration in octachloropropane. TABLE I1 COMPARISON OF OBSERVED AND CALCULATED SLOPES Temperature 0.8 7'2 7 1 145°C I S 126 I Slope Fig. 5 shows the smoothed rate data plotted in log form as a function of log time. These curves illustrate again that the rate is higher in the early stage of annealing and decreases quickly to a constant value.The constant rate is, of course, reached more rapidly the higher the temperature. These curves show again that Expt. 6 and 7, at 159' C and 145O C respectively, are lower than would be expected from an extrapolation of rates in Expt. 1-5. This figure shows the separate curves for Expt. I and 5 which were combined by smoothing in Fig. 4. These data show that boundary migration in octachloropropane is very similar mathematically to boundary migration in metals. It is suggested that the mechanism by which boundary migration occurs in lattices of these two types is therefore similar and that boundary migration in metals can be studied to great advantage using the much simpler technique involved in studying octachloropropane.As a result of the above work on octachloropropane it was decided to attempt to determine the effect of lattice strain on boundary migration in compounds of the DDT type. Unfortunately DDT itself could not be used since the crystal habit changes drastically with temperature of crystalliza- tion. However, TNT can be crystallized as broad rods over a wide tempera- ture range. Accordingly an attempt was made to determine the effect of thermally induced lattice strain on boundary migration in TNT. First a small sample (5-10 mg.) of TNT was melted and cooled to about 50°C before crystallization. This preparation was then placed in an already heated hot-stage at 78" C and observed for a period of 40 min. During this time the crystals grew into adjacent crystals a distance of 0.5 mm.Fig. I shows two photomicrographs in this series, one taken at the end of I min., the second at the end of 4 min.166 CRYSTAL GROWTH AT HIGH TEMPERATURES A second preparation of TNT was then melted and placed in the hot-stage at 80" C before crystallization occurred. On seeding, crystals of TNT were made to grow slowly into contact at right-angles. Observation of this and similar preparations over a period of 60 min. showed no sign of boundary migration. The conclusion from this information is that boundary migration in TNT and presumably in DDT and other compounds of this type is entirely due to lattice strain. Conclusion .-Boundary migration in the octachloropropane and DDT types of crystal lattice is similar in the sense that lattice strain due either to cold working or temperature changes seems to be the principal motivating influence.The two differ, however, in two respects : (i) relative orientations of the neighbouring crystals are important for the DDT type and have little or no effect on compounds of the octachloropropane type; (ii) grain shape is important in controlling grain growth in compounds of the octachloro- propane type and not important in compounds of the DDT type. This dependence of boundary migration in crystals of the DDT type on relative orientation of the two crystals is more difficult to explain. This, however, has been resolved by the thought that all compounds of the octachloropropane type possess crystal lattices which are either cubic or, at least approximately plastically isotropic. On the other hand, crystals of the DDT type which show boundary migration are highly anisotropic compounds and must be elastically anisotropic. In other words, when crystals of this type, such as DDT, are subjected to pressure or to large temperature changes the resulting strain must be distributed anisotropically throughout the lattice and in such a way that the crystals grow most readily parallel to one definite direction, depending on the anisotropy of elasticity for that lattice. This work was supported jointly by the Armour Research Foundation and the Research Corporation. Percy T. Cheng made some of these measurements. This help is gratefully acknowledged. Armour Research Foundation, Illinois Institute of Technology, Technology Center, Chicago 16, U.S.A.

ISSN:0366-9033    

DOI:10.1039/DF9490500158

出版商:RSC    

年代:1949

数据来源: RSC

摘要:

166 CRYSTAL GROWTH AT HIGH TEMPERATURES CRYSTAL GROWTH AT HIGH TEMPERATURES BY S. ZERFOSS, L. R. JOHNSON AND P. H. EGLI Received 18th March, 1949 Large single crystals can be grown from water solution, eg., of K-alum or NH,H,PO,, near room temperature because of ready solubility of the salts in water and their large temperature coefficient of solubility. For many other materials which possess low solubility in water or other solvents, some other technique involving higher temperatures must be used. The selection of the ideal growth technique depends naturally on the properties of the substance, particularly its melting point, the stability of its melt, and the possible occurrences of lower temperature inversions. Although single-crystal growth can be effected from melts of polynary composition, the most successful growth to date has been achieved with mono-mineralic melts.When a substance exhibits polymorphism, as quartz or nephelite, where theS. ZERFOSS, L. R. JOHNSON AND P. H. EGLI 167 desirable phases are not in equilibrium with the melt, the crystal must be grown from a binary or ternary melt, eg., the ternary system Na,O-Si0,-H,O in the case of quartz and the system LiF-Na,O-Al,O,-SiO, in the case of nephelite. Similar subterfuges are available for growth of other polymorphous substances ; for example, the water-insoluble HgI, (red form) can be grown successfully from a solution of K2HgI, saturated with HgI, by lowering the temperature of the solution. The growth of crystals from anhydrous melts or vapours can be accom- plished in a variety of ways providing the substance melts congruently and has no lower temperature inversions : (I) THE MOVING CRUCIBLE TECHNIQUE.A crucible containing the melt is slowly lowered through a fixed thermal gradient.12 (2) THE STATIONARY CRUCIBLE A crucible containing the melt is cooled in a slowly changing thermal gradient. This variation of (I) was used successfully by Stober,5 Stockbarger and Phelps6 It does not appear to have any advantage over (I). (3) THE KYROPOULOS TECHNIQUE.' A crystal seed is lowered into the melt and then slowly withdrawn through a gradient provided by cooling the seed. This technique has been used to grow crystals up to 30 cm. diam. (NaCl). It might have special advantages for those crystals that show one strong directional-growth tendency.Through the use of fluxes a low-temperature phase may be induced to appear on the liquidus of the phase diagram and hence make growth of the phase possible, e.g., nephelite from a LiF-NaA1Si04 melt, whereas growth from a mono-mineralic melt of the same phase would yield the undesired high-temperature modification, carnegieite. By cooling a melt, of which the desired substance is the primary phase, the resultant solid would consist of crystals of the primary phase in an eutectic matrix. Winkler has discussed the relationship between the degree of supercooling and the size and number of the nephelite crystals. The difficulties of obtaining large single crystals by this technique appear enormous because of inability to prevent multiple nucleation.(5) THE VERNEUIL TECHNIQUE.^^ Melting is accomplished by passing the powdered substance through one tube of an oxyhydrogen torch into the flame. The molten material is collected on a refractory rod and by suitable manipulation is converted into a single crystal. (4) EUTECTIC MELT GROWTH TECHNIQUE.^ * IBridgman, Proc. Amer. Acad. Arts Sci., 1925, 60, 305. 2 Stockbarger, OSRD Report, No. 4690 (1944). Rev. Scz. Instr., 1936, 7, 133. J . Opt. 3 Tuttle and Egli, J . Chem. Physics. 1946, 14, 571. 4 Strong, Physic. Rev., 1930, 36, 663. Stober, 2. Krist., 1923-4, 61, zgg. 6 Phelps, Chem. Eng. News, 1948, 26, 2453. 7 Kyropoulos, 2. anorg. Chem., 1926, 154, 308. See also B.I.O.S. Final Report 8 Winkler, Amer. Miner., 1947, 32, 131 ; Heidelberger Beitrage zur Miner.u 9 Matthias, Physic. Rev., 1948, 73, 808. fOVerneuil, Compt. rend., 1902, 135, 791. Ann. Chim. Phys., 1904, 3, 20. SOC. Amer., 1937, 27, 416. Rev. Sci. Instr., 1939, 10, 205. No. 468, No. 21, 22. Petrographie, 1947, I, 86. * Small single crystals of BaTiO, have been grown 51 by a similar operation (using an excess of BaCl,, etc.) although the phase relationships are not known. Such " mineral- ization " is standard practice for the recrystallization of high-melting, slightly soluble materials.168 CRYSTAL GROWTH AT HIGH TEMPERATURES (6) GROWTH FROM THE VAPOUR PHASE. (a) “ Chemical reaction ” in the gaseous state is carried out in a suitable thermal gradient, e.g., Cd vapour + H2S yields CdS (greenockite) + H2.11 (b) Volatilization of a pure substance and condensation in a gradient into single crystals, eg., Se, 12.12 This technique is undeveloped but has been used to produce small crystals (up to 5 x 5 x 10 mm.) for a variety of substances.The difficulties of the technique lie in the impossibilities of setting a gradient of the proper character in a gas stream and providing a suitable heat sink for deposition of single-crystal material from a super- saturated gas. The Crystal Section has extended Frerichs’ work in producing crystals of CdS having small amounts of luminescent-active additives. TABLE I Name Halide . . .. .. Villiaumite .. .. Sylvite . . .. .. Nantockite . . .. Cerargyrite . . . . Bromyrite .. .. KRS6 .. .. .. KRS 5 . . .. .. Fluorite .. .. Scheelite .. .. Composition NaCl NaBr NaF KCl (K,Rb) C1 KBr KI LiF CUCl AgCl AgBr TlCl TlBr T1 (C1,Br) T1 (Br,I) CaF, BaF, MnF, PbC1, PbB;, PbI, CdI, CaWO, ZnWO, CdWO, NaNO, NaNO, AsI, Size Boule Available * (in.) Source ** C L ( N W ; ; ( N W L (NRL) C L (NRL) C L (NRL) L (ERDL) (NRL) L (ERDL) (NRL) L (ERDL) (NRL) L (ERDL) (NRL) L L L L (NRL) L (NRL) L (NRL) CL (NRL) CL (NRL) L (NRL) L (NRL) L L (NRL) L ( N W * Size available-diameter of cylindrical boules of 2 in.-4 in.length. ** Abbreviations : C - Commercially produced. L - Academic laboratories. (NRL) - Crystal Section, Naval Research Laboratory. (ERDL) - Engineer Research and Development Laboratory, Ft. Belvoir. The Crystal Section of the Naval Research Laboratory has been using techniques ((I) , moving crucible), ((51, Verneuil) and ((6), vapour growth) to produce a variety of small single crystals for research purposes (see Table I).In this paper an attempt will be made to correlate the various factors influencing growth. Table I is a summary list of crystals grown by various industrial and academic laboratories based on information available to US. Of the six techniques, only (I), (2) and (5) are in current industrial use for 11 Frerichs, Physic. Rev., 1947, 72, 594. 12 Vasko, SKEarske ruzhledy, 1946, 6 7 , 98.S. ZERFOSS, L. R. JOHNSON AND P. H. EGLI 169 the mass production of single crystals. The other techniques have been little used because of inherent difficulties in control of single-crystal growth but are potential techniques for unexplored materials. If none of the melt techniques is suitable because of the existence of lower temperature inversions in a substance, there is a method of last resort- that of growth under hydrothermal conditions-in the presence of water at elevated temperatures and pressures in a closed system.Despite theoretical and experimental difficulties much attention is being paid to this technique but it is outside the scope of this report. Experiment a1 Technique No. 1. By far the most popular technique is that of moving a crucible through a fixed gradient.* It is capable of producjng much larger crystals because of the ease of gradient control. A cylindrical crucible with a cone-shaped tip containing the melt is slowly lowered from some temperature above the liquidus temperature down through the fixed gradient of the furnace. Presumably, when the tip of the crucible reaches the liquidus temperature, the small volume of the tip favours the incidence and development of one nucleus a t the expense of all others and thereafter conditions are so maintained that this initial crystal will grow vertically and assume the shape of the crucible. For this purpose ideal conditions obtain when the isotherms are horizontal. Their distribution of spacing will characterize the gradient.Naturally, the control of the gradient, speed of lowering and the purity and composition of the crystal are important factors. If adequate controls are not imposed, several nuclei will be competing for the material from the freezing liquid thereby yielding a polycrystalline boule. THE CONDITIONS OF CRYSTALLIZATION. The conditions for producing a single crystal, though dominated by the purity of the charge, depend upon the rate a t which heat is withdrawn from the melt.The heat sink is provided in two ways-the thermal gradient and the speed a t which the crucible passes through the gradient. Too small a gradient or too rapid lowering of the crucible favour the growth of many nuclei leading to polycrystalline boules. The gradients available for growth are limited by furnace design and by the temperature of operation. Numerous unsuccessful attempts have been made to systematize these data and reduce them to an equation. The difficulties lie in the inability to specify the exact conditions for obtaining single crystallinity. The furnace used in technique No. I has been described.2 It consists of an upper and lower section separately wound and controlled.The gradient along the furnace length can be modified by adjusting the heat input into the separate sections. By supplying heat to the upper section only, one obtains a temperature distribution with the high point near the bottom of the upper section and a sharp gradient. This gradient can be reduced by supplying heat to the lower section. It can be intensified by the use of a baffle between the two furnace sections. The baffle is a thin, flat annulus of metal or ceramic material, the inner diameter of which is large enough to permit passage of the crucible. Typical data on the effect of the baffle are given as follows : NRL furnace 6-1948, 28 in. high, inner tube diameter = 4 in. Temp. at 14 in. level = 464O C.Thermal gradient at 14 in. level with baffle = 74O/in. without baffle = 44O/in. The question of whether or not the baffle has any particular efficacy in favouring single-crystal growth over the plain furnace has not been settled since it involves the question of the optimum gradient. Any of the crystals mentioned can be grown without a baffle, and we can report no detectable improvement from the use of a baffle. * This gradient is somewhat modified by the change of position of the crucible during lowering but this factor is probably small, provided the heat capacity of the crystal is small compared to that of the whole system. F*170 CRYSTAL GROWTH AT HIGH TEMPERATURES It is apparent from our experience that the diameter of the muffle does not play a role in the gradient providing i t exceeds the crucible diameter by a factor of 1.5.The isotherms within the crucible for this condition axe flat as shown by the freezing surface of the single-crystal part of several incompletely crystallized boules. This temperature control can be accomplished by any of a variety of constant-temperature regulators,13 but we have found the use of a constant- voltage transformer (saturable-reactor type) sufficient to maintain the temperature & 1.0" C in the range 300°-10000 C for crucibles up to I& in. diam. For larger crucibles more elaborate controls are required ( f. 0 . 2 ~ C). Typical gradients used for successful growth in our laboratory are as follows : Melting Point " C Gradient " C/in. Expt. No. AgCl 55 NRL 20-6 TlCl 45 NRL 22-6 NaF 45 NRL 63-1 KI 64 NRL 114-7 In our experience gradients larger than 75" C/in.can be used if available. The lower limit for successful growth of medium-sized crystals is 35' C/in. The higher temperature runs operate under higher gradients because of normal furnace design. The lowering of the crucible is accomplished by a gear assemblage attached to the support rod and operated by a constant-speed motor. The effect of the speed of lowering is related to the gradient since both perform the same heat-sink operation on the melt but the relationship is not a simple one and has not been worked out. For medium-sized crucibles (up to 13 in. diam.) a speed of 0.12 in./hr. or 0.32 cm./hr. is optimum. Slower speeds are not detrimental providing tempera- ture control is adequate. The stability of the furnace assemblage, i.e., the amount of vibration suffered by the crystal during growth, is apparently not significant.In fact, some vibration may be essential to the prevention of extreme supercooling with subsequent multiple crystallization, To test the effect of excessive vibration, crystals of AgCl were grown with a buzzer attached loosely to the support rod. Satisfactory single crystals resulted in two runs. The shape of the crucible commonly used by the various investigators is a cylinder with a 60*-135" conical tip. However, there appears to be nothing critical about the angle of the conical tip. Successful single crystals Q in. to 16 in. djam. of AgCl, TlC1, and TlBr were grown in flat-bottomed crucibles at lowering speeds of 0.12 in./hr. in a gradient of 45" C/in.The choice of crucible material depends on the nature of the crystal to be grown, its chemical reaction with the crucible, and the temperature of operation. The following crucible materials have been used in our laboratory or reported in the literature. TYPICAL CRUCIBLE MATERIALS CRYSTAL CRUCIBLE REMARKS MATERIAL Alkali halides Platinum * Some adherence Lead halides Silica glass Sealed crucible Thallous halides Pyrex glass Little adherence Silver halides Pyrex glass Some adherence ** Divalent tungstates Platinum *** Fluorite Carbon * Strong used an iron crucible for alkali halides (in an H, atrnosphere).I ** It is known that AgCl or other silver salts react with alkali glasses exchanging AgCl adheres strongly to such altered glasses.** * Considerable difficulty was experienced in preparing leak-free crucibles Ag for Na ions a t the surface. for these temperatures. 13 Temperature, Its Measurement and Control in Science and Industry, Amer. Inst. Physics (Reinhold, N.Y., 1941).S. ZERFOSS, L. R. JOHNSON AND P. H. EGLI 171 As far as temperature stability goes, Pyrex glass is suitable up to 500' C , silica glass can be used up to 1 x 0 0 ~ C and platinum is suitable up to its melting point, Most single crystals can be grown in open crucibles in air. Some exceptions are easily oxidized substances like the lead halides. Fluorite is reported to hydrolyze in air during growth. In the case of the glass crucibles the support rod i s an extension of the tip of the crucible.The metal crucibles are supported on metal cone supports. The removal of the crystal from the crucible has been done by inverting the crucible immediately after crystallization is complete and raising the temperature rapidly above the liquidus whereupon a thin layer of the crystal melts and the crystal drops out of the crucible. For medium-sized crucibles with proper annealing of the crystal, this is not necessary. The crystal can be removed by cracking the crucible ; in fact, the crucible is usually fractured during annealing. The factor of purity of the initial charge is a complex and im- portant one since it probably dominates all other factors in determining the final single crystallinity of the boule. An impurity in the charge is foreign both to the composition of the melt and to the lattice of the crystal. It is usually insoluble in the crystal and hence does not favour single-crystal growth but leads to multiple crystals and cloudy boules.For example, TlCl is completely soluble in TlBr in the melt and crystal, and good single crystals of solid solutions can be had. However, the presence of more than 0.1 yo TlCl in AgCl (in which i t is sparingly soluble) yields cloudy polycrystalline boules. Hence, in the latter case i t is a definite impurity. In fact, a melt containing 0.5 yo TlCl in AgCl can be converted to a poor single crystal containing less than 0.1 yo, the remainder having been rejected during growth. Generally speaking, the usual C.P. chemicals are not suitable. For each chemical a purification scheme must be worked out to provide sufficient purity for the growth technique, and in some cases additional purification must be carried out to satisfy more rigid specifications for a particular material.However, it is slowly being recognized, for crystals grown from the melt or from water solution, that extreme purity is not always desirable and often leads to poor growth. The degree of perfection of many crystals can be improved through the use of small amounts of additives, e.g., Pbff in NaCl or Tlf in KI. No correlation can be made between the chemical nature of the additive and its effectiveness in improving crystal quality beyond the statement that most effective additives are large, easily polarizable cations. The difficulties in obtaining a single-crystal boule of a variety of materials vary with the chemical nature of the material, in a manner as yet not determined.For example, rather extreme controls are required, on matters of purity, etc., for such materials as PbC1, and CaW04, while on the other extreme AgCl can be converted into single-crystal material under almost any conditions. On the basis of general phase-rule considerations, the crystallization of a solid solution by the melt technique should yield a fractionated boule with the tip material richer in the higher melting component. For normal, solid-solution behaviour one might predict that a homogeneous, solid-solution single crystal could not be grown. For example, a crystal (2 in. x $ in. diam.) grown from a melt of AgCl and NaCl (NRL-13-X) the top of the boule analyzed 76 mol-% AgCl while the tip of the boule analyzed 72 yo AgC1.A similar situation obtained during the growth of solid solutions in the system KC1-KBr (in this latter the fractionation was detected by refractive index measurements rather than chemical analysis). The solid solution 42 mol-yo TlBr-58 mol-yo T1I may show some fractionation during growth. McFee l4 has given quantitative data on the self-purification of impure crystals of NaCl during growth. The available crucible materials limit the crucible-melt technique to temperatures below 1700' C . Crucibles are available for higher temperatures but they are readily attacked by the various melts and hence usually unsuitable. In 1891 a Swiss worker, Verneuil, developed a method for growth of crystals THE CHARGE.Technique No. 5 . I4McFee, J. Ckem. Physics, 1947, 15, 856.172 THE GROWTH OF QUARTZ CRYSTALS of highly refractory materials by fusing the material in the flame of an oxygen- hydrogen torch.1° In this process, fine powder is introduced into the oxygen tube of the burner. As the powder enters the flame i t is melted and is collected on a refractory rod. By suitable manipulation this melted material can be caused to grow into a single crystal. Initially the powder is allowed to accumulate as a cone of semi-melted material on the support and then the tip of this cone is melted by adjusting the gases, and the flow of powder is increased. If this initial melting operation is carried out under proper control, a single crystal results which may be extended by smooth addition of more material as the rod is lowered.Some operators use oriented seeds attached to the rod as the original material to which additional material is added through the flame. The successful growth operation depends upon the skill of the operator in manipulating the flame and feed and in initiating the single-crystal tip. Further growth proceeds continuously as the feed material melts and is assimilated into the growing crystal. The purity of the starting material must be quite high. The same concepts apply to the question of piirity in this material as in the melt- crucible growth. For example, in the growth of sapphire boules the A1,0, is prepared by calcining a twice-recrystallized ammonium alum. The growing crystal purifies itself by ‘‘ scumming-off ” impurities to the liquid surface of the boule. If the feed material is too impure, this scum covers the surface, and growth is interrupted.15 In the past, the crystals grown by this technique have been limited to corundum (sapphire), corundum coloured by small amounts of other oxides (ruby , alexandrite, etc.) and a spinel solid solution (MgA1,0, + excess Al,03). In the past year, several new crystals have been added of which we can list : This crystal, grown up to 75 carats, emerges from the furnace as a black, oxygen-deficient boule which can be bleached in 0, into a clear, light-yellow material with rather unusual optical and electrical properties. This material (of interest as the light emitter in scintillation counters) has been grown up to t in. diam. with little difficulty. The published literature on the details of this process is quite scanty. (I) RUTILE.~~ ( 2 ) SCHEELITE-C~WO.~~ Crystal Section, Naval Research Laboratory, Washington, D . C. l5 Moore, Jr., private communication, 1948. l6 Titanium Division, National Lead Co., Sci. Newsletter, Oct. 1947. l7 Linde Air Products Corp., Chem. Eng. News, 1949, 27, 48. l8 Zerfoss, Johnson and Imber, Physic. Rev., 1949, 75, 320.

ISSN:0366-9033    

DOI:10.1039/DF9490500166

出版商:RSC    

年代:1949

数据来源: RSC

摘要:

THE GROWTH OF QUARTZ CRYSTALS SOME ASPECTS OF THE GROWTH OF QUARTZ CRYSTALS* BY A. C. SWINNERTON, G. E. OWEN AND J. F. CORWIN Received 25th Febmary, 1949 The aspects of laboratory quartz research discussed in this paper are three- (I) Quantitative growth results and observations related to growth Growth was obtained in dilute alkali halide fold. experiments are presented. * The results and interpretations presented here are derived from work supported on contract between Antioch College and the US. Army Signal Corps through its Signal Corps Engineering Laboratories a t Fort Monmouth, New Jersey. The senior author is Professor of Geology at Antioch College ; from 1943 to 1946 he was associated with the U.S. Army Signal Corps in the research and development activities related to quartz oscillator units.In late 1945 he participated in the interrogation of German scientists, among them Rickard Nacken, who had worked in the search for alternatives to natural quartz. Dr. Owen is Professor of Physics and Dr. Corwin is Associate Professor of Chemistry, both at Antioch College.A. C. SWINNERTON, G. E. OWEN AND J. F. CORWIN 173 solutions at 400' C with a nominal zero thermal gradient, utilizing vitreous silica as source material and crystalline seed plates. ( 2 ) In supplementary experiments designed to investigate the nature of the solutions in the critical state apparatus was developed to record automatically the impedances of the liquid and vapour phases as they approach and pass into the super- critical state. The current results of these investigations are described since the impedance technique gives promise of having both practical and theoretical value.(3) Finally, certain tentative, theoretical interpretations regarding the nature of the Si0,-H,O-metal ion relationships, based in part on X-ray analysis, are outlined. This paper is in the nature of a progress report of work which is continuing. It represents data and conclusions as of approximately 1st February, 1949. Growth in Alkali Halide Sdutions The selection of the alkali halide solutions as the solvents in laboratory quartz experiments resulted from a survey of the analyses of the liquid inclusions in natural quartz. Na and C1 were found to be the commonest components reported. Early results in this project gave growth when fused silica, rather than quartz, was used as source material ; fused silica has been consistently, although not exclusively, used for this purpose.Seed plates are natural quartz, either AT-cut oscillator blanks or plates cut parallel to the minor rhombohedra1 face, approximately 0.5 x 0.6 x 0.030 in. in size and weighing close to 0.400 g. The autoclave equipment consists of several 250 ml. bombs made by the Parr Instrument Company from stainless steels 347 and 316. Some difficulty has been experienced in obtaining steel free from defects. The interior of the bomb is a cylindrical cavity 34 in. deep by 24 in. in diameter. The centre of the lid has a small eyelet for suspending the seed plate. Just off centre a thermowell tube extends 2 in. into the cavity. Accessory equip- ment includes a junction block above the lid with a blow-out safety disc, a needle valve outlet and a tubing connection to a 0-10,ooo psi Bourdon- type gauge.The closure gasket is copper. The heater is a vertical insulated cvlinder with two Calrod units coiled one above the other ; each is controlled by its own variable transformer. Thus the heat is supplied through the walls of the autoclave rather than at the bottom. Temperature control is supplied by Leeds and Northrup proportioning controllers through mechanical relays. Temperature observa- tions are recorded automatically from two thermocouples , one placed in the thennowell in the lid and the second inserted in a copper block insulated from the furnace wall but supporting the bottom of the autoclave.The thermal gradient in the autoclave is controlled in two ways : (I) the input to the lower and upper heating coils may be varied by adjusting the variable transformers ; ( 2 ) the radiation from the upper surface can be varied by piling on, or removing, loose insulation. An operating temperature of 400" C was selected for the reasons that i t was sufficiently above the critical temperature to ensure the existence of the supercritical state within the autoclaves and for all degrees of filling under 65 yo was within the safe limits of the equipment. The thermal gradient, although controlled closely, is probably not less than I' C, or more than 5" C, warmer at the bottom than at the top. Several concentrations of sodium chloride and several degrees of filling or " charge " were systematically explored in series.In the first series the solutions were " neutral," i.e., the NaCl was dissolved in distilled water of pH ranging around 6. At least two experiments were done for each set of conditions. The single figures in Table I represent the averages ofI74 THE GROWTH OF QUARTZ CRYSTALS 2 1.5 3 consistent results. nominal period. Forty-eight hours a t temperature was the standard TABLE I AVERAGE yo INCREASE IN WEIGHT OF SEED PLATE. SODIUM CHLORIDE PH 6-7. 48 HR. AT 4oo0C, oo THERMAL GRADIENT. AVERAGE WEIGHT OF SEED PLATE 0.400 G. 3-5 2.5 2-5 2 2 1.5 2 -3 3 2 4'5 3 5 I 0 % Charge 50 40 30 20 Solution Growth yo I 0.65 KCl 66 1-35 1.80 2.60 NaBr I03 KBr 58 52'4 80.7 I 29.0 I 11'0 N - 40 -13 4 7 A second series of experiments was undertaken in which the initial pH of the solution was adjusted to 10 & 0.5 by the addition of a few drops of concentrated NaOH.A slightly different range of concentrations was used for the second series. Otherwise the conditions of experimentation shown in Table I1 are the same as those shown in Table I. The contrast in results between the two Tables indicates the effectiveness of the increased alkalinity. In every case the terminal pH had a value in the range of 7 to 5 . TABLE I1 AVERAGE yo INCREASE I N WEIGHT OF SEED PLATE. NACL ADJUSTED TO PH 10 WITH NAOH 48 HR. AT 400°C, oo THERMAL GRADIENT. AVERAGE WEIGHT OF SEED PLATE 0.400 G. ~ %Charge: N/40 1 N/IO N/2 1 3N/4 ~ N -- -- 40 5 30 6 I0 I 0A. C. SWINNERTON, G. E. OWEN AND J. F. CORWIN 175 - Solution I Time (hr.) 1 Growth % NaCl 48 1 120 NaCl 72 25 KC1 63'5 KCl :i ~ 66 KC1 96 I 73'9 KBr 48 58-2 KBr 96 1 58'4 source yield small growth.But source material in excess of 2.6 g. shows little or no more growth on the seed plate than when 2.6 g. of fused silica is used as a source. The source residue of the first run (0.65 g . ) showed in X-ray analysis to be entirely quartz, whereas the residues from the last two (15.1 and 16.1 g.) shewed some cristobalite present with quartz. The relation of amount of growth to length of time represents a confused picture. Experiments continued in excess of 48 hr. tend to give less growth than those of the two-day period. Remarks Average of several runs Average of several runs One run with leakage Average of two runs Average of two runs Average of two runs Average of two runs A striking characteristic of the process is the contrast between the initial alkalinity, adjusted in several series of experiments to a nominal pH 10, and the terminal pH which invariably shows less alkalinity and may even be on the acid side.The factors causing the variability in the terminal pH have not been identified with certainty. It does not bear a direct relationship either to time or to amount of growth. Devitrification of the fused silica source is pronounced and is another characteristic of the process. The fused material becomes either granular quartz or a mixture of quartz and cristobalite. It has not been possible to observe if the change in alkalinity is related to the devitrification. Attempts have been made to counteract both changes.To maintain alkalinity, buffered solutions have been tried. Injection of alkali and manual regeneration of the solutions have been attempted. None of these has given substantial success as yet. The devitrification of fused silica led to the experimentation with other solutions and with other source materials. This phase of the investigation is still in progress. In summary it should be pointed out that the method pursued here is dependent on the difference in solubilities of the solid forms of silica, particularly fused silica, and quartz. I t is distinctly different from the techniques which utilize large thermal gradients and circulation from an under-sa turated source zone to a supersaturated locus of crystallization.The phase-solubility transfer method yields rapid growth of good quality but is limited by a time factor which is associated with decreasing alkalinity and devitrification of fused silica source material. Impedance Studies The introduction of an insulated electrical lead into the internal cavity of a stainless steel bomb has made it possible to observe certain changes in the liquid and vapour phases with temperature. The electrical lead is an airplane-type spark plug furnished by the AC Spark Plug Division of General Motors Corp. It consists of an electrode centred in a core of fused A1,0,. The core in turn is gasketed with copper in a threaded metal jacket which screws into the bomb. Another copper gasket is used to seal the176 THE GROWTH OF QUARTZ CRYSTALS plug to the bomb.The outer end of the electrode is provided with a screw connector for one wire. The circuit is completed by a second wire attached to the wall of the bomb. Best results have been obtained in a special 5 in. long 18 ml. tubular stainless steel bomb. One end is solid ; a spark plug serves as the closure for the other end. The bomb is heated in a furnace which can be inverted so that readings may be taken alternately in the liquid and vapour phases. This method is preferred at present to the use of a two-plug bomb because the incidence of leakage is less with one plug than with two, and because there is no question of variation in impedance due to the presence of two plugs. I ' FIG. 1.-N/40 NaCl40 %. Scale IOO ohms. A voltage regulated signal generator supplies a I KC current to the spark plug circuit.The impedance is compared with a known value in a branch circuit. This voltage is rectified and, after suitable amplification, is applied to a potentiometer-type recorder of the kind ordinarily used for thermo- couple temperature records. The ordinary temperature scale on the pa.per chart can be calibrated by substituting known resistances in place of the bomb. The instrumental and recording arrangement yields printed records of impedance and bomb-wall temperature on the same time chart. Investigations are in progress to discover the basic patterns of various concentrations of NaCl and other alkali halides, with and without the alkalinity adjusted, with and without silica present, in several degrees of filling. Enough consistent data have been secured to permit certain comments and conclusions.A. C.SWINNERTON, G. E. OWEN AND J. F. CORWIN 177 (I) The technique is successful in showing changes in the impedance-related properties of both the liquid and gas phases of the solutions so far used, as they approach and enter the supercritical state. (2) The records of the top phase of the bomb clearly distinguish between different degrees of filling. The variations in bottom readings are small with differences in filling. (3) So far variations in alkalinity have not been identified. (4) The presence of silica has shown distinctive but anomalous behaviour, not subject to repetition in detail, but predictable as to general character. In particular, the impedance of the top phase seems to be lowered by the presence of silica.Fig. I is The nature of the patterns obtained is shown in Fig. I and 2 . the tracing of a chari of temperature and impedance jor a 40 yo charge of -4CO- FIG. z.-N/40 NaCl 40 yo. Scale IOO ohms. N/4o NaC1. The record begins at the right with a rapidly rising tempera- ture curve. The high impedance of the top electrode (vapour phase) appears at the upper right. The nature of the apparatus is such that the scale as used for this record places IOO ohms near the top ; very high values are not distinguishable. When the temperature reaches 375" & IO the top impedance drops abruptly and levels off at 55 ohms as the temperature levels off at 400OC. The break in the record indicates that the furnace and bomb were inverted.The bottom impedance drops abruptly and then curves downwards, apparently approach- ing a firm value. The reading which the first (right-hand) down curve thus approaches assymptotically is 35 ohms. When the furnace and bomb are reinverted, so that the electrode measures top impedance, the break is sharp, the impedance returning to its previous value. Fig. z shows the same conditions except that the record begins with the electrode at the bottom (liquid phase). The times when the furnace and bomb were inverted are apparent from the impedance shifts. The curves show Below IOO ohms the scale is reasonably linear.178 THE GROWTH OF QUARTZ CRYSTALS the response of impedance to temperature changes particularly at the bottom position. It also shows the abrupt break in top impedance when the cooling temperature curve passes through 375" C.The remarkable contrast in the variation of top impedance with charge and the absence of variation of bottom impedance with charge is shown in Table VI. TABLE VI IMPEDANCE (2) VARIATION WITH BOMB CHARGE N/40 NACL AT 400°C. VOLUME OF BOMB 18 ML. Charge (ml.) 8 6.4 6.0 5'4 5'0 4'0 Bottom 2 (ohms) 35 35 38 36 -* -* Top Z (ohms) 55 80 235 330 I20 1000 * I n these records the downward curve was not permitted to continue to the point where a satis- factory reading could subsequently be made: in both cases the number can bc said certainly to be less than 50 and probably less than 40. The consistency of readings is shown by Table VII in which are tabulated the impedance readings for several 40 yo charges of N/4o NaCl.TABLE VII IMPEDANCE CHARACTERISTICS OF 40 yo CHARGE, N/4O NACL Minimum 2 (ohms) 1 Temp. Min. 2 1 Bottom 2 400" C ! Top 2 400" C 25 25 29 27 28 308" C 320 340 336 312 33 33 35 35 38 54 51 50 58 57 Measurements made with bombs from which air has been evacuated give curves which are very similar to those already described. Since the bombs were not designed to be evacuated the numerical results obtained are not precise enough for direct comparison. The same is true of experi- ments made with water with no sodium chloride, from which the air has been removed, The difference between top and bottom impedances remains and the general forms of the curves are similar. Space does not permit discussion of the implications of the data in regard to the nature of the critical state. The possible applications to the observa- tions and control of quartz growth appear promising.But much more work must be done before that step can be taken. Chemical Theory In addition to the several series of growth experiments and the impedance studies, investigations have been made for the express purpose of establishing a hypothetical interpretation of the growth process. These include : (I) several 250 ml. autoclave runs using buffered solutions either as the growth medium or as the alkalizing agent; (2) 250 ml. autoclave trials of several different source materials ; (3) X-ray examinations of the residual source materials and of the residual solutions after evaporation to dryness.A. C. SWINNERTON, G.E. OWEN AND J. F. CORWIN 179 A summary of the pertinent facts follows: (I) the maximum growth occurs with fused silica in 48 hr. or less followed by cessation of growth and in some cases by resolution ; (2) a decrease in the alkalinity shows a depletion in the available OH- ion even when buffered solutions are used; (3) fused silica as source material gives excellent growth but devitrifies, becoming either quartz or a mixture of quartz and cristobalite ; (4) quartz used as source does not transfer quartz to the seed plate, chalcedony promotes very slight growth, natural cristobalite yields a moderate increase in seed plate weight ; (5) quartz, chalcedony and cristobalite remain unchanged, i.e., do not show modification like the change of fused silica to quartz and cristobalite ; (6) the solution residuals when analyzed by X-ray indicate the presence of NaCl (in the NaCl experiments) together with non-crystalline silica.The conclusions, which must be regarded as tentative, are not readily summarized and require more elaboration and explanation than space permits. (I) The growth which occurs when fused silica and cristobalite are used as source material, together with the small or negative results with quartz and chalcedony, emphasizes the conclusion that the process is essentially based on the solubility differences of the several forms of silica. This state- ment is consistent with the generally accepted values of the vapour pressure .of the several forms. Both solubilities and vapour pressures reflect the internal energies of the several forms.(2) The solution of silica in dilute NaC1, pH 10 (NaOH) is probably not simple solution in the sense of the dispersal of 50, ions in the solvent. Disintegrative reaction is involved, more likely a series of such reactions, in which Na silicates are formed. Silicon tetrafluoride is a gas at ordinary temperatures. Arguing from the similarity in size and weight of OH and F, it seems possible that Si(OH),, particularly a t high temperature, may be a gas ; likewise for SO, ions. These solution-reaction products are assumed to be less stable in the presence of quartz than in the presence of fused silica. Growth on the seed plate should return OH- ions to the solution, maintaining the alkalinity. The process of growth, moreover, should leave some residual silicates in the solution.This residual does not appear in the X-ray data as crystalline silicates but as amorphous silica. (3) The solution of the fused silica source is considered as occurring by the replacement one at a time of the oxygen atoms on the apexes of the silica tetrahedra by OH and ONa groups, thus breaking the bonds to the adjacent tetrahedra. During this process the alkalinity is depleted because of distribution of OH groups over the increasing surfaces. It is possible that this process also brings about the devitrification of the fused silica by giving opportunity for any vague structural nuclei of cristobalite and quartz in the fused silica to orient and complete their structures. Although the tentative nature of these conclusions should be repeatedly emphasized, several lines of investigation are clearly suggested. (I) Devitrification of fused silica must be regulated or inhibited either by solutions or other operating conditions which discourage it, This answer is probably not easy. As an alternative to a direct answer, suspended fused silica might be injected into the autoclave to renew the source supply. ( 2 ) Source material which does not suffer modification can be sought. Cristo- balite gives some promise and is currently under investigation. (3) The alkaline level may need to be maintained by injection to keep the transfer active. In general it can be said that : General Conclusions The process of quartz growth by differential phase solubility gives rapid Its growth of excellent quality at temperatures above the critical point.180 DIFFUSION POTENTIALS AND GROWTH limitation is the cessation of growth after a short period. The stoppage is related apparently to a series of complex silicate solution reactions which result in diminished alkalinity and devitrification of vitreous source material. The impedance studies show promise as a means of developing a technique for observing and controlling the progress of the reactions. Since the quality of product is good and the process is rapid, investigations are continu- ing in an effort to overcome the limitations. Antioch College, Yellow Springs, Ohio.

ISSN:0366-9033    

DOI:10.1039/DF9490500172

出版商:RSC    

年代:1949

数据来源: RSC

摘要:

180 DIFFUSION POTENTIALS AND GROWTH THE ROLE OF DIFFUSION POTENTIALS IN THE GROWTH OF IONIC CRYSTALS BY A. R. UBBELOHDE Received 29th April, 1949 The object of this paper is to draw attention t o certain electrical effects which appear to be significant for the growth of crystals. Experimental study of these effects is still in too early a stage to permit a fully connected account of all the phenomena. Nevertheless some discussion of the role of electrical effects in the growth of ionic and polar crystals is desirable in reviewing the field of crystal growth as a whole. Diffusion Potentials in the Neighbourhood of Ionic Crystals. -The different mobilities in solution of the positive and negative ions which go t o form an ionic crystal must normally lead to the establishment of diffusion potentials in the neighbourhood of the crystals.Such diffusion potentials can have a notable effect on the migration of the ions. The following cases are selected to illustrate some of the various possibilities which can arise. (A) DIFFUSION POTENTIALS DUE TO CONCENTRATION GRADIENTS IN THE SOLUTION IN THE NEIGHBOURHOOD OF THE CRYSTAL.-It follows from the Nernst argument that any concentration gradient dc/dx in solution is accom- panied by a potential gradient dEldx in the solution if the ionic mobilities U+ and U- differ. When a solution of a pure ionic crystal is considered with ions of equal valency ne, the well-known expression is obtained for the potential gradient : RT dc dx Such a potential gradient in the body of the solution can be substantially modified by the presence of foreign ions whose valency and ionic mobility are very different from n, and U+ or U - .Three types of ionic impurity may be quoted which may be expected to have a substantial effect in modifying concentration gradient potentials in solution, and which may in consequence modify crystal growth. (i) The H+ ion when the anion is common, and to a less degree the (ii) Ions of high valency as an impurity in a solution of ions of low (iii) Colloids capable of acting as ions with very low mobility. OH- when the cation is common.l valency . 1 cf. Abegg and Bose, 2. physik. Chem., 1899, 30, 545.A. R. UBBELOHDE I81 Before an assessment can be made of the role of such impurities in modifying crystal growth by modifymg concentration gradient potentials, it would be of value to have an experimental technique which would reveal the equipotential surfaces around an ionic crystal growing in solution. Such a technique does not seem to be available a t present.But studies of the effects of the deliberate addition of impurities such as (i), (ii) or (iii) may be useful in indicating the kind of distribution over a plane face, and around edges and corners of a growing crystal. Alterations of the viscosity of the solution would also modify the con- centration gradient potentials around a crystal, by affecting the values of U+ and U-. Probably this effect is subsidiary in aqueous solutions until the change in ionic mobilities is substantial. (B) THE POTENTIAL GRADIENT ACROSS THE INTERFACE BETWEEN THE LATTICE AND THE SOLUTION.-Even under conditions where growth rates are negligible, and concentration gradient potentials in the bulk of the solution can be neglected, a potential difference should normally persist across the interface between the crystal and the solution.For example, such potential differences should persist in saturated solution in equilibrium with a crystal surface. Unequivocal theoretical calculations of the magnitude of this potential difference do not appear to be available.2 The various physical factors contributing to this potential difference have not been fully elucidated, but its origin can be grasped by considering an ionic crystal in equilibrium with its very dilute vapour in vacuo. The steady state is somewhat more complicated for an ionic crystal than for a homopolar crystal in equilibrium with a monatomic vapour, owing to the fact that the work done against the crystal lattice forces on removing isolated positive ions is usually not quite the same as the work done in removing isolated negative ions, on account of differences in the polarizabilities and van der Waals’ attractions.A potential difference between the interior of the solid and the vapour must be built up till the rate of vaporization of the two ions becomes equal. The way in which this potential difference is established need not be particularized here. One process would be a displacement of the ions near the surface of the crystal from their normal equilibrium positions. A similar potential difference may normally be expected for crystals in contact with solution. Although the calculation of the magnitude of this potential difference in solution is not finally solved, it is important to consider how it would be modified at various crystal faces by the presence of foreign ions of the type considered under (A) above.Foreign ions especially of the types (ii) and (iii) are well known t o influence streaming potentials and will have a corresponding effect on the surfaces of an ionic crystal in aqueous solution. (c) CATAPHORESIS OF CRYSTAL NUCLEI IN SOLUTION.-under conditions such that potentials described under (B) are sufficiently large, it should be possible to cause the crystal nuclei which are formed in solution to migrate to the electrodes by applying a potential gradient. It should be noted that such cataphoresis will be sensitive to factors which affect the surface potentials of the nuclei.Reference may be made to experiments to test this p~ssibility.~ In these experiments, by applying a potential difference across a pair of copper electrodes dipping in a supersaturated solution of copper sulphate, all the nuclei grow as crystals adhering firmly to the anode. * cf. Faraday SOC. Discussions, 1947, I, 3, 43. Ubbelohde, Trans. Faraday SOC., 1940, 36, 863.I82 DIFFUSION POTENTIALS AND GROWTH Owing to the incidence of the war, it has not yet proved possible t o extend this experimental work. Some further discussion may, however, be given here in view of the statement that such directed nucleation is merely due to the concentration differences at the two electrodes, arising from a passage of the current.In a typical experiment (Ubbelohde, loc. cit., p. 864) the initial concentration of copper sulphate corresponded with 66 g. CuS0,.5H,O in IOO g. water at 20’ C. The equilibrium concentration at the same temperature was approximately 32 g. CuSO,.5H,O in IOO g. With electrodes of surface area 2.4 sq. cm., preferred nucleation on the anode was still definitely detectable after the passage of 0-2 mA flowing for 15 min., i.e., 0.18 coulomb. This quantity of electricity would lead to an ultimate gain of CuSO, in the anode region of 0.18 x 124.8 x 0.625 = 1.45 x IO-, g. 96,500 calculated as pentahydrate, using the transport number 0.625 for the anion. Questions which arise are whether the gain of CuSO, in the anode region can make a significant difference to the degree of supersaturation, and why all the crystals are found firmly adhering to the electrode, with evidence of preferred but not unique orientation. The increase in concentration around the anode depends on the volume in which the gain of CuSO, is contained.Considering this volume as a cylindrical sheath of thickness x around the anode, the increase in concen- tration is approximately 6.0 x IO-~/X g./ml. For this increase to be an appreciable fraction of the supersaturation in the bulk of the solution (approx. 0.3 g./ml.) x must be of the order of IO-, cm. This thickness of anode layer is physically not unreasonable and the increased probability of nucleation in the anode region may well be attributed to the increased concentration resulting from the transport of electricity.But mere increase in probability of nucleation does not explain why the crystals are found to adhere firmly to the anode, and with preferred but not unique orientation. This appears to be a significant observation for the mechanism of growth of ionic crystals. One explanation could be (Ubbelohde, loc. cit., p. 866) that the SO,” ions discharged at the surface of the copper electrode can act as two-dimensional nuclei for the growth of CuS04.5H,0. The preferred but not unique orientation observed for the crystals would be analogous with oriented overgrowths in other cases. An alternative explanation is that the increased concentration due t o the transport of electricity leads to a higher probability of nucleus formation in the anode region, and that these nuclei are swept to the anode by cata- phoresis as soon as they are formed. Since the streaming potentials at different crystal faces are not the same, there would be a tendency to turn the nuclei in the current flow, which would explain preferred orientation. Whatever the explanation, the phenomenon of the electrolytic growth of ionic crystals offers one of the problems of crystal growth which appear to be related with the potential distribution around ionic crystals. The Queeds University, Belfast. Boerboom, Nutwe, 1947, 159, 230.

ISSN:0366-9033    

DOI:10.1039/DF9490500180

出版商:RSC    

年代:1949

数据来源: RSC

摘要:

GENERAL DISCUSSION Dr. M. H. R. J. Plusjh (Geleen) said : I should like to make a comment on the paper of Dr. Dunning concerning the kinetics of crystallization in solution. Dr. Dunning has grown crystals in a continuous manner under steady conditions. This is the way in which crystallization is carried out in practice on a large scale, and I am particularly interested in crystallization as a unit operation. Dr. Dunning has found that the rate of linear crystal growth is a function of the supersaturation and Table I of his paper proves that small deviations in the supersaturation have a marked influence on the rate of growth. In my opinion, however, the figure he uses for the supersaturation is not the actual supersaturation under which the crystals were growing, even after the correction made for the somewhat higher temperature of the solution caused by the heat of mixing.To find the supersaturation he has taken the difference between the actual concentration, determined by immediate filtration, and the concentration after a prolonged time of mixing, the last concentration after a correction for a small difference in temperature due to the heat of mixing. In determining the supersaturation he has supposed that the last-named concen- tration is the equilibrium concentration a t the surface of the crystal. The reason is that the temperature of a growing crystal is higher than the temperature of the solution in which i t grows. This is caused by the heat of crystallization, which is released a t the surface of the crystal. When crystallizing in a continuous manner under steady conditions the crystals reach a certain fixed temperature, which remains constant during the growing process.Therefore, there is a constant flow of heat (the heat of crystallization) from the crystals to the solution and from the solution through the wall of the container to the cooling medium (heat of crystallization plus heat of the solution). We have tried to determine this difference between the temperature of growing crystals and the temperature of the solution. With an indirect method we found for Ca(N03),.4H,0 in an aqueous solution a difference of about I / I O O C : the exact value depending on the ratio between the total crystal surface and the surface of the cooled vessel. The actual concentration of the solution at the surface of a growing crystal is therefore never the equilibrium concentration a t the temperature of the solution, but somewhat higher.Because small differences in the supersaturation have such marked influences on the rate of growth, I think it absolutely necessary to take the ‘‘ crystal temperature ’’ and the heat flow into account in order to obtain a real picture of the kinetics of crystallization in solution. Dr. W. J. Dunning (Bristol) (communicated) : Dr. Plusj6 reminds us that the temperature of the growing crystal is higher than that of the solution. An estimate of this temperature difference is readily obtained if certain assumptions are made. As he says, under steady conditions of continuous crystallization the crystals reach a fixed temperature T’ and if in addition the suspension is adequately stirred, the temperature To of the solution is also constant up to a small distance 6 from the surface.If the crystal is growing at a constant linear rate g, the rate of heat production at the surface can be derived. Part of this heat raises the temperature of the new growth to T’ and the rest is conducted away down the temperature gradient (T’ - To)/& My opinion is that this is not correct. This model gives where A H is the heat of crystallization per mole, g the linear rate of growth, M the molecular weight, c the specific heat, K the thermal conductivity, and d the density. If we take the largest value of g in Table I (8.6p/min.), and assume K N I O - ~ cal. cm.2/cm.o C, by using the Neumann-Kopp rule a value of c-0-2 can be estimated, we then find that with 6 = 10-4 cm., T’ - To is of the order 1 0 - d o C.184 GENERAL DISCUSSION The figure of 0.1~ C found by Dr.Plusjk can be explained if i t is assumed that his stirring is less efficient than we have assumed to be the case in the discussion above. This would be consistent with his finding that the temperature difference depends upon the ratio of the areas of the crystal surface and the cooling surface. In this connection we might mention again that particular attention was paid to stirring efficiency in our experiments. The efficiency used was such that on halving the speed of rotation of the stirrer no significant effect was noted. Burton and Cabrera comment that i t would be very interesting to develop experiments directed to avoid all possible foreign nuclei which could facilitate nucleation.Our continuous method does not lend itself to exhaustive elimination of growth nuclei, but the batch method does allow operation in a closed system by which nuclei can be progressively eliminated to an isolated part of the apparatus. Work is in hand on this latter technique but all the experimental problems have not yet been solved. In connection with our results for the continuous method, i t is easy to show that since the reagents were drawn from the same bulks in all but the first three experiments of Table I and if it is assumed that the rate of introduction of foreign nuclei is proportional to the rate of introduction of the reagents (i.e., the number of foreign nuclei per unit volume of reagents is constant), then if the nucleation is not homogeneous but solely due to foreign nuclei, the product of no and the time of passage should be a constant. This is certainly not the case as inspection of Table I will show, and this lends support to the view that in these experiments the nucleation was homogeneous. Mr.W. K. Burton and Dr. N. Cabrera (Bristol) (communicated) : With reference to the papers by Dunning and others it seems to us worth while to point out again the essential quantitative disagreement between theory and experiment, in three-dimensional nucleation from solution. The theoretically expected critical supersaturations, for which nucleation should occur, are always of the order of a hundred times bigger than those experimentally observed.Of course, the theory requires the knowledge of the surface energy between nucleus and solution ; the theoretical estimates are made taking some fraction of the heat of solution for this surface energy. The disagreement with experiment would disappear if the surface energy is assumed to be 20 or 30 times smaller than the estimate above.1 We do not think that this estimate can be wrong by this factor. This is essentially the same situation as that occurring in the surface nucleation. We tried several possible explanations (entropy factors, influence of the mobility of the adsorbed layer), but none changes the disagreement by an appreciable amount.2 The difficulty has now been overcome by the dislocation mechanism proposed by Frank.It would be very interesting to develop experiments directed to avoid all possible foreign nuclei, which could facilitate nucleation ; it is possible that real three-dimensional nucleation has not yet been observed. Dr. R. F. Strickland-Constable (London) said : Bransom, Dunning and Millard find that the rate of crystal growth appears to approximate to a linear function of the supersaturation. It is believed that this result can be rendered very probable on the basis of some rather general considerations which have no relation to any particular mechanism. For this purpose it is necessary to remember that crystal growth involves a balance between two other processes, namely, deposition and solution. Then the growth rate can be expressed as : where g = net rate of growth ; In nucleation from solution no explanation has been found.g = F(c) - K , . * (1) F(c) = gross rate of deposition of solute. It is expressed as an entirely unknown function of the total concentration (not as a function oi the supersaturation) ; 1 Amsler, HeZv. physic. Acta, 1942, 15, 699 ; see also Dunning and others, This 2 Burton and Cabrera, This Discussion. Discussion.GENERAL DISCUSSION G = concentration of the solution in contact with the crystal face ; K = gross rate of solution, which is a constant, independent of the In the Figure the curve F(c) representing deposition rate and the straight line corresponding to the constant rate of solution K intersect a t the point where c = Csat.. The rate of crystal growth is shown as the difference in height of the two curves.It is clear from the small triangle that (F(c) - K ) is directly proportional to (G - Csat.) to a close degree of approximation provided that : concentration.* (I) F(G) is continuous in the neighbourhood of c = csat.; ( 2 ) G - Csat. is small compared to Csat.. The former condition is most probably fulfilled since there is no reason why the rate of deposition, which is here looked on as a property of the solution, should behave in a special manner a t the point of crossing the solubility curve. The second condition is normally fulfilled for practical reasons. It is therefore possible to write : g G K ( c - Gsat.), true for c - Csat. < Csat. . ’ ( 2 ) This principle has an important application in experiments such as those of Bentivog1io.s This author found that in the case of a number of crystals the relative rates of growth of the different faces were constant, in spite of a variable degree of supersaturation.The most general form of growth law which would express this result, con- sidered by itself, is where g, = net rate of growth of face A ; g A = h A ( f ( ~ ) --f(csat.> 1, * (3) k , = constant appropriate to face A ; f(c) = unknown function of the concentration of the solution in contact This function must be the same function for each with similar expressions for the other faces B, C . . . etc., whence - = - = etc. with the face. face of the crystal, g, gB k A k B Bentivoglio, Proc. Roy. SOC. A , 1927, 115, 58. * Since the growth rate is known to be sensitive to small quantities of impurities the above equation must hold only for a given state of the solution containing a definite constant amount of such impurities.In order that the condition, g = o for G = cat., may be fulfilled, where csst. is the concentration of the saturated solution, K must be equal to F(caat.), and eqn. (I) can therefore also be written as : g= F(G) - F(c,,t.).186 GENERAL DISCUSSION Eqn. (2) is a special case of (3), in which the arbitrary function f ( c ) is placed equal to KG. If therefore the law expressed in (2) is a general law, the results of Bentivoglio are accounted for. At the same time the expression ( 3 ) has been written down in order to show that Bentivoglio’s results are, considered by themselves, consistent with a more general law which allows the growth rate to depend on an arbitrary function of the concentration which, however, must be the same for each face.It seems more likely, however, that Bentivoglio’s results are, in fact, due to the general validity of eqn. ( 2 ) . Dr. W. J. Dunning (Bristol) (communicated) : Regarding some remarks of Prof. Juliard, I would make the following suggestion. Even in the case of homogeneous nucleation the crystals finally obtained are of approximately the same size, if as is usually the case the rate of nucleation depends on a higher power of the supersaturation than the rate of growth does. Then the nuclei born earliest when the supersaturation is greatest are not only the most frequent but become the largest crystals, hence a high proportion of the weight of the precipitate will be in this size group.Casual observation (as distinct from number distribution analysis) will give an impression of size homogeneity. Again the sigmoid shape is not solely a characteristic of the presence of foreign nuclei. With homogeneous nucleation, the rate dSe/dO = o a t the beginning and the end of the precipitation, but it is finite during crystallization, hence there must be an inflection point. If growth occurs only on foreign nuclei and homogeneous nucleation does not occur, the eqn. (7a) in Bransom and Dunning’s paper takes a simple form, from which the relation can be obtained, where no is the number of foreign nuclei per unit volume. In a series of experiments of different initial So and no, the left-hand side can be obtained for each and plotted against So.Then the ratios of the ordinates for all So values ought to be constant and equal to the ratios of the no’s. From these plots the functional dependence of f(S6) can be obtained apart from a constant factor. Dr. S . Fordham (Stevenston, Ayrshire) said : The results in my paper showed that there was a strong probability that strained crystals of ammonium nitrate had an initially increased rate of growth. More recently the surfaces of typical crystals have been examined by a replica technique with the electron microscope. Fig. I shows the surface of an unstrained crystal characterized by what appear t o be cracks parallel to the (001) plane of the crystal. Fig. 2 shows that straining of the crystal causes small areas to be raised above the general level, thus producing irregularities of finite size.The two photographs were taken by Mr. J. Ames. Dr. F. C. Frank (Bristol) (partly communicated) : With reference to Dr. Fordham’s observations, for reasons given, I should not expect the change in dislocation content produced by straining the crystals to cause a significant change in the rate of growth (though it could affect the critical supersaturation for growth, if one were found). In this case, I think the transient extra growth is to be explained more on Prof. Stranski’s lines, by completion of layers from the steps produced by slip. This remains true although the slip steps are shown by electron-micrography to be of a rather complex character. Fordham refers to them as “ dislocations.” The word “ dislocation ” has acquired a very definite meaning in the theory of the solid state, and ought not to be applied freely to any sort of derangement of a crystal: though various sorts of derangement can be analyzed into systems of dislocations.Prof. Stranski has mentioned the high rate of growth of twin crystals having faces which meet in the composition plane so as to make a re-entrant angle with each other. A notable mineralogical example of this is fluorite. The great majority of large fluorite crystals exceeding, say, I cm. in size, especially those of Weardale which make up the principal exhibits of fluorite in British museums, are interpenetrating twins, with a twin emergent on every face. Exceptions toI’IG. I . FIG. 2. [To face page 186GENERAL DISCUSSION 187 this rule always have visible disoriented blocks.Sometimes the corner of the twin is just on the point of being submerged-evidently growth then ceases. Each face of these twin crystals shows a pronounced growth pyramid of unusually steep vicinal faces centred on the common line of the twin faces which meet on the composition plane. In a typical example (of which a lantern slide was shown) the inclination of these faces to the (100) face is 3*0°, in contrast with zo’, which is the most which is usually observed for growth pyramids centred on some ordinary point in the face of a crystal, as observed on alums, for example, by Sir Henry Miers. This unusually steep growth-pyramid signifies an unusually high rate of emission of growth fronts from the initiating centre (in this case the junction with the twin) compared with their rate of travel over the surface- of the order 10 times as great as when the initiating centre is a simple dislocation or group of dislocations.Another admirably simple example to be seen in collections of minerals is provided by calcite ; the “ heart-shaped ” or “ butterfly-shaped ” twins of calcite on (I 10) are characteristically 10 times as large, linearly, as the accompany- ing population of single crystals. With regard to the visible growth steps or layers to which Dr. Bunn draws attention, I certainly think that a t least in some cases they arise in a manner which Prof. Becker aptly likens to the formation of shock-waves ; i.e., that for some reason molecular steps bunch together.We have then to find the influence which leads to this bunching. This must be a “ second-order ” effect : for if deposition occurs a t equal rates on every molecular step-line, the surface profile is conserved, travelling with the steps ; while if there is competition between the steps so that their rate of accretion is proportional to the distance between them the profile is conserved in the mean, while the molecular steps travel through. Neither of these extreme conditions, nor any simple linear combina- tion of them, gives rise to an accentuation of irregularities in the profile ; this requires that the leading members of a group should travel slower than the rest. This will tend to occur in a stirred or convecting medium once the height of the multiple step becomes an appreciable fraction of thickness of the laminar diffusion layer at the surface of the crystal ; but this effect will be very slight until a substantial bunching has occurred, and I would attribute the initial bunching to fluctuations in concentration at the initiating centre.The most important point to notice, however, is that with this sort of inter- pretation there are no layers, only a stepped profile. I suppose that there are also other types of crystal growth with a genuine lamination; but one must avoid confusing the two, taking the visible steps as certain evidence of real layers. In particular, steps which increase in height as they spread outwards cannot correspond to layers. Dr. S . Fordham (Stevenston, Ayrshire) said : Dr. Frank has suggested that my results were due to crystallization on slip planes in the strained ammonium nitrate crystals.Neither optical nor electron microscopic examination indicated the presence of regular slip along glide planes. On the contrary, crystals had irregularities in their surface which were of finite size and in appearance seemed to be very similar to the dislocations discussed by Dr. Frank although they were, of course, on a larger scale. While willing to avoid the use of the term dislocation in describing these irregularities, I think this is a matter of nomenclature which does not affect the interpretation of the results. Prof. W. E. Garner (Bristol) said : The films of Dr. Bunn and Emmett showed the spread of crystallization as a series of waves starting a t some point near the centre of the crystal surface.Crystal growth therefore appears to be a periodic phenomenon. In these experiments the supersaturation was probably high, and a t high supersaturations the formation of a two-dimensional nucleus at the centre of a crystal face will have a high probability, even if no dislocations be present. The supersaturation at the centre of a face will decrease when a nucleus is formed, and increase again as the nucleus grows away from its point of origin. Therefore a periodic formation of nuclei implies a periodic change in supersaturation. Likewise the probability of nuclei formation will vary periodi- Phil. Trans. A , 1904, 2o2, 459.I88 GENERAL DISCUSSION cally as the supersaturation fluctuates. It is possible, therefore, that the phenomena observed are due to the interrelationship between the probability of nuclei formation and the supersaturation.It appears to be important to work out the dynamics of such processes. In crystallization from melts, a periodic fluctuation in the temperature of the melt in the neighbourhood of the crystal surface is probably the effective agent in creating the wave motion. Dr. K. G . Denbigh (Cambridge) said : I would draw attention to the fact that crystals are occasionally found in which there are a number of liquor inclusions situated symmetrically with respect to the centre of the crystal. During the war this had been observed both in R.D.X. and in hexamine. It seems that the mechanism depends on the formation of a symmetrical dendrite at an early stage of growth.The process by which R.D.X. crystals are formed had been carried out under the microscope and i t was seen, a few seconds after initiation, that minute cross-shaped dendrites were formed. A t a later stage of growth these developed into crystals of a more regular shape and the symmetrical inclusions were due to the trapping of mother liquor at the angles of the cross. In a particular case there were twelve liquor inclusions in a hexamine crystal situated with almost perfect symmetry about its centre. I t was of interest that these inclusions were almost spherical and did not show the plane faces of the crystal. During a hard winter I have observed an ice crystal growing on the surface of still water in a bath. Over a period of a few days the dendritic crystal grew to the size of a plate, and its intricate pattern was perfectly symmetrical about the centre, like a greatly magnified snowflake.It had the usual hexagonal form and the question arose how it came about that each of the six spikes of the structure had exactly the same fernlike pattern. It was known that between one snowflake and another there were a great variety of patterns and i t was therefore surprising that each of the spikes, in any one crystal, should develop in the same way. It seemed as if the pattern was controlled from the centre, as a chromosome controls the structure of a cell. It was perhaps related to Prof. Garner’s point concerning periodic waves of crystallization radiating from a central point. Dr. W. A. Wooster (Cambridge) said : Dr.Bunn has pointed out that some faces of a given crystal grow quickly while others grow more slowly or not a t all. The concentration is greater near the non-growing surface than i t is near the rapidly growing one. It may, therefore, be necessary to look for a cause which arises within the crystal rather than in the solution. I wish to put forward tentatively a suggestion based on the thermal motion of the atoms. For an ionic crystal such as NaCl the amplitude of vibration of the ionic centres at room temperature is of the order of 1/10 A, i.e., a small, but not negligible, fraction of the distance apart of neighbouring atoms. At a growing surface this amplitude of vibration may be greater owing to the unsymmetrical nature of the environment-solvent molecules on one side and regularly arranged atoms on the other.This atomic movement may determine the ease with which atoms can be attached to the surface. The study of diffuse thermally scattered X-rays has shown that atomic move- ments, though random so far as any one atom is concerned, may be resolved into a series of waves of different frequencies travelling with the speed of sound. These waves constantly passing to and fro in the crystal will be reflected from the boundaries, and the amplitude of vibration at any corner, step or other dis- continuity will be greater than on a corresponding flat surface. Thus if a crystal face has grown perfectly flat, and has no growing centres or steps, the elastic waves will be reflected but not scattered and the vibration of an individual atom in the surface may therefore be a minimum.On the other hand, if a crystal face has a step there may be a concentration of elastic vibrational energy just within the step which may keep the amplitude of atomic vibration gi-eater than normal. This condition may favour further deposition and keep the step advancing. A feature of growth, which, though not fully established for ionic crystals growing in solution, is certainly established for growth from the vapour, is the migration of atoms from the centre of a face to the growing edge. May it be Why is the structure of snowflakes so remarkably symmetrical ?GENERAL DISCUSSION that this feature is also explained by the thermally generated elastic waves ? If a step occurs on a surface there is a possibility that if vibrational energy is concentrated within the step it may act like a pulsating membrane and pump the liquid along the surface from the centre of the face towards the edge. The question was also raised as to what mechanism could determine the symmetrical nature of the pattern of an ice crystal growing in still water, i.e., why all the branches arise on the opposite sides of a given stem a t just the same distance from the centre.In a stem growing out in opposite directions from a centre, there will be elastic waves which will have the same vibrational pattern a t the same distance from the centre on either side. If the nodes and antinodes of the elastic vibration pattern determine the generation of the branches, then the branches would occur a t the same distance from the centre. Dr.D. R. Hale (Cleveland, Ohio) (communicated) : Bunn and Emmett call attention to the rounded surfaces of growth on high-index faces. The (001) face or basal plane in quartz is not a natural face and would thus be the equivalent, so far as growth is concerned, of a high-index face on, e.g., sodium chloride. In the work a t The Brush Development Co., Cleveland, Ohio, on quartz crystal growing we have noted a high rate of growth, yielding rounded surfaces, on the artificial (001) face obtained by sawing the ~ r y s t a l . ~ The rate of growth is about an order of magnitude faster than that on a rhombohedral face. These observations may be added to those mentioned in the paper as evidence of the indiscriminate, high-rate deposition on high-index surfaces.A further common type of deposition observed on the artificial (001) face of quartz is an assemblage of minute, oriented trigonal crystals growing in the c-direction and fused with their neighbours a t sufficient edges so that a porous structure results. The separate crystals in this growth generally terminate in trigonal caps, and no rounded points or areas are produced. Thirty synthetic quartz crystals have been examined for evidence of layer formation. About a third of them do not have sufficiently plane faces to show unmistakable evidence of layer growth. On a few of the reasonably flat surfaces a, regular pattern of fine and closely spaced concentric lines is evidence of the growth mechanism described by Bunn and Emmett.Many of the well-developed crystalline faces, particularly the rhombohedral faces, exhibit low rounded domes frequently outlined in a number of what seem to be contour lines, so that the appearance from above is that of looking a t a map and seeing a hill marked on by lines of constant level. These lines are assumed to be the steps from one growing level to another, but in these quartz crystals the edge seems always to fall away in a sharp concave surface which hardly levels out before the next contour fine is reached. This appearance seems to indicate that growth is taking place on faces of high index. Dr. F. C. Frank (Bristol) (partly communicated) : Bunn and Humphreys- owen have produced some delightful experiments demonstrating that crystal growth is a structure-sensitive process.I am disappointed that they should finish their accounts of these phenomena by saying they are puzzling. Such things as a sudden change in growth rate are to be expected. They could arise from a sudden rearrangement of dislocations (since the ability of dislocations to move under small stresses is one of their fundamental properties). They can also be produced by adsorption of a very small amount of impurity on the step-line connecting a dominant pair of dislocations. These observations do Seem to suggest, however, that in these particular experiments the number of dislocations influencing growth may be quite small. Let me now deal with the " Berg effect," firstly pointing out what a very odd effect it is. It is not a t all similar to what was observed by Volmer and Ester- mann.In their experiment a crystal of mercury grows in the form of a very thin plate from the vapour at low temperature in a vacuum. The mean free path is about 10,000 times the size of the crystal. I t is found that every molecule which strikes the crystal anywhere on its surface sticks, but migrates and is built into the crystal only a t the edge of the plate. This surface migration is entirely understandable and just what we ought to expect. 5 Hale, Science, 1948, 107, 393.190 GENERAL DISCUSSION In the experiment of Berg, Bunn and Humphreys-Owen, on the other hand, we have a crystal growing from solution and its size is about 10,000 times the mean free path in the surrounding medium. Ions migrating over the surface of the crystal will suffer jostling from the molecules of the surrounding medium.It appears quite possible, in the circumstances, that migration over the surface will not be observable in comparison with diffusion in the solution. But suppose i t were : if there were a very mobile layer a t the crystal surface, the boundary condition at that surface would be an “ equipotential ” one, and, like electro- static lines of force, the lines of diffusion flow would be most concentrated a t the crystal corners. If there is no special surface migration, a crystal preserving its form must have uniform deposition over the surface. But what is supposed to be observed by Berg and Humphreys-Owen is an excess of flux in the middle of each face. It has a negative resistance.Diffusing matter goes out of its way, through a longer path in the ordinary medium, so as to reach the corners roundabout through this surface layer. This is not impossible, but is sufficiently odd to demand very good evidence before it is accepted. A test which he only used qualitatively, in which he used the angles a t which optical fringes met the crystal boundary to show that the normal gradient of concentration of solute (3~,/3n) was not constant (as he supposed i t should be in uniform deposition without surface migration) ; and the more elaborate method of calculating concentration at many points in the medium, constructing a concentration map, and deriving (3ca/3n) a t the boundary from this. He was wrong to suppose (3~~13%) would be constant in the simple case.This would be true in dilute solution, but in more concentrated solution it is obviously necessary to allow for the fact that a part of the material required to build the crystal is there already, and a larger flux is needed where the solution is weakest. One may alternatively think of the necessary diffusion of solvent away from the crystal, which must also be greatest where the solution is weak. This is (as Berg knew) no ordinary layer of high mobility. Berg’s evidence was two fold. Then the boundary condition is (3Ga/W = ( W I D ) @Alp3 (pa - 4 where w is the rate of advance of a crystal face (cm./sec.), D the diffusion coefficient (cm.t/sec.), p A the crystal density (g./~m.~), pa the effective density of the solute in solution (= p A if there is no change of volume on solution) and ca is the concentration of solute in the solution in contact with the crystal surface.Since the latter is about half the crystal density, and varies by 5 yo or so over the crystal face, the correction is not negligible. However, according to data with which Dr. Humphreys-Owen provided me, it only accounts for about 20 yo of the observed variation of (3ca/3n) across a crystal face. Some uncertainty arises from the possibly illusory position of the crystal boundary, since lateral resolution in the microscope is necessarily sacrificed in compromising with the “ parallel light ” requirement for multiple-beam inter- ference fringes. But the chief source of error is probably convection, the presence of which will invalidate the assumption that the flux of solute is simply pro- portional to the concentration gradient.Convection must occur because of the large gradient of density associated with the concentration gradient near the growing crystal. One may readily show that the ratio of the resulting convective transport to the diffusive transport is proportional to where g is the acceleration due to gravity, h is the thickness of the cell in which the observations are made, p is the density and q the viscosity of the solution and D the diffusion coefficient of solute. By a rather crude estimation of the numerical factors involved it is found that the convective transport and diffusive transports are of similar order of magnitude when this dimensionless quantity is about 2000. In the experiments of Berg, Bunn and Humphreys-Owen we have typically : grad p = 5 g ./ ~ m . ~ per cm., q = I O - ~ and D = I O - ~ c.g.s. unit, while h = I to 2 x I O - ~ cm. ; so that the above number varies from 500 to 8000. The effect of convection is thus never negligible in the experiments as conducted up to now, but since the fourth power of the cell thickness appears in the criterion, i t is relatively easy to make the convection negligible by using sh4 I grad p I /TOGENERAL DISCUSSION 191 a thinner cell : let us say, 10 times thinner. Dr. Humphreys-Owen tells me it is practicable to use a supersaturation ten times as large as in most of his experi- ments so that the optical sensitivity remains the same. We shall then be able to see whether the Berg experiment really does exist.It is perhaps worth making a few more comments on the design of the experi- ment. Time and expense appear to be the only considerations really favouring a micro-experiment. Removal of heat and suppression of convection are both achieved by using a thin cell, which is also advantageous for optical resolution. An increase of the lateral dimensions of the crystal and field of view is purely advantageous so far as these considerations are concerned, provided that half- silvered optical flats of sufficient area are available, but can only be achieved by growing the crystal in situ, which takes a time proportional to the area, or longer. Prof. A. Juliard (Brussels) said : May I suggest that if there were any impurities in either solution or in the gas phase from which a crystal is formed this crystal may not grow a t all ? (4 (4 FIG.I.-Perturbation of the crystal structure due to the imbedding of a single foreign particle : (a) local dislocation : ( b ) centre of a helix molecular terrace for- mation ( \k ) ; (c) twinning formation ; (d) mosaic structure formation. Foreign particles adsorbed on the surface of a crystal may exercise different effects. (i) I f these particles are strongly adsorbed and are present a t a relatively high surface concentration they may prevent a further aggregation of the con- stituents of the crystal and so stop the growth of this surface. When this action is exercised on each surface of the crystal, the presence of this impurity can com- pletely inhibit the precipitation. When this inhibiting action is only effective on certain surfaces, the impurity may simply modify the habit of the crystal.(ii) If the particles are strongly adsorbed but present a t a relatively low surface concentration they may be embedded in the crystal by its later growth. The presence of these foreign particles in the lattice may distort the lattice or introduce dislocations on a molecular scale which may be the origin of helix molecular terraces, of the twinning habit, or of the mosaic structure of certain crystals (Fig. I).192 GENERAL DISCUSSION (iii) If the particles are weakly adsorbed they may act as mineralizers in the broad sense of the word. With convenient geometrical and chemical conditions these particles can initiate on a crystal surface an active spot which acts as a step from which a new molecular layer of the crystal may grow.When, in addition, these particles are easily expelled from the newly formed layer, one can imagine that these growing particles may be pushed ahead on a step-shape protuberance on the surface of the crystal. Such protuberances could be the origin of those “ multi-growth ” layers whose existence was evidenced by the remarkable film on crystal growth shown by Dr. Bunn and Emmett. Mr. A. E. Robinson (Holton Heath, Poole) said : The crystal habit of Li,SO, has been found to be considerably influenced by pH of the growing solution : a t pH above 7 growth along x and y axes is encouraged : at pH below 5 growth along the z axis is encouraged. The growth appears to be somewhat slower at low pH.There is another effect of pH which may throw some light on the anomalies of the adsorption effects discussed in the previous section. Small amounts of phosphate ( 5 parts per million) have been found to inhibit growth at one polar end of the crystal. At the higher pH this ion is deposited on the crystal ; a t the lower pH it remains in the solution. The addition of a surface-active agent to this solution is an attractive idea as one of the problems is the adherence of air bubbles to the growing crystal. These may persist throughout growth and result in a hole through the crystal. One wetting agent used prevented this effect, but crystal growth was rather slower and two extra faces parallel to the y axis were developed. Mr. L. J. Griffin (Egham) said : It may be relevant to mention the part which can be played by the study of the surface topography of crystals using multiple-beam interferometric techniques as developed by Tolansky .By this means one can study natural and cleavage faces, and also synthetic growths on either of these types of faces, with a “ resolution ” in depth approaching molecular dimensions. One is thus enabled to arrive a t a picture of the mechanism of growth of many crystals, and in particular many minerals, which are not otherwise amenable to study. In order to illustrate the possibilities of the technique I should like to mention some work I have done on beryl with particular relation to Bunn’s results given earlier in the Discussion. Such naturally occurring crystals have grown under unknown conditions, possibly with several complicating factors influencing their growth.Therefore in all work of this nature a guiding principle has been that several, and preferably many, crystals should show the same type of behaviour before any general type of behaviour is claimed. Several specimens have been found to show an extensive layer structure, the thickness of the layers varying between some hundreds down to three or four unit cells. These layers tend toward perfect conformity with the symmetry of the face, the conformity in general becoming more rigorous as the layers become very thin. It may be mentioned that the outline of these very thin layers shows no trace of the presence of dislocations of the type proposed by Frank. The importance of the nature of the layer edges has already been stressed by Bunn and it is worthy of note that multiple-beam interferometry provides a means, with beryl, of indexing the edges of the thickest layers.Some data have already been obtained but have not yet been numerically evaluated. Bunn’s thesis of high index edges would, however, seem to be borne out. The nature of the layer edges on beryl is actually such as to produce a diffraction effect rendering them visible, under the micro- scope, even when only some four or five unit cells high, The limit of sensitivity of this surprising effect has not yet been capable of determination although evidence has been obtained for the observation of layers three unit cells thick. By utilizing this diffraction effect and interferometric methods, direct experi- mental proof has been obtained that the vicinal faces of beryl consist of extensive series of stepped layers.The growing points are sited, in general, towards the centre of the face and away from edges or corners. The observations on this point are not yet sufficiently extensive as compared with Bunn’s to enable one to claim a general behaviour. In conclusion, it may be mentioned that the existence of layers has been observed on a number of other crystals, and in fact there seems little doubt that many crystals do grow by layer deposition.GENERAL DISCUSSION I93 Prof. I . N. Stranski (Berlin) said : The problem of the occurrence of visibly thick layers on growing crystals has two aspects. It is not sufficient to show that the thicker layers (or multimolecular lattice planes) extend more slowly than the elementary lattice faces (which are afterwards caught up by the lattice faces which begin later).I t must also be explained why the thicker layers may not become thinner by escape of individual lattice planes from the base. A special mechanism of coarsening which sometimes occurs on single faces of metal crystals and which is obviously connected with the edges of the faces may be mentioned in this connection. I should also like to point out the fundamental difference between the growth and reduction of crystals of urotropine at low and high temperatures and also the remarkable variation shown by layer growth on faces of Cd or Zn crystals according to whether they are surrounded by the fused liquid or the gas phase (EisenZoeffeZ) . Dr.C. W. Bum (I.C.I., PZastics) said : In answer to Dr. U. €3. Evans' remarks on dendrite formation, I would like to give some additional details of the calculations of the diffusion process round a square crystal plate which are mentioned in my second paper. Only the results of long-continued diffusion (i.e., arrival of excess solute a t face centres) are mentioned in the paper, because these appear relevant to the phenomenon of layer formation at face centres. But at the beginning of the process, corresponding to the early growth of a crystal nucleus, the reverse result is obtained-more solute arrives a t corners than at face centres. This is the expected result, and may be regarded as due to the convergent diffusion flow to the corners, when diffusion has just started and the diffusion field does not extend far from the crystal.It is natural to suppose that dendrite formation may be due to this excess arrival of material at the corners of a polyhedral crystal nucleus-excessive deposition takes place on the corners, which begin to shoot outwards. But I should like to point out that the effect might be due either to this convergent diffusion effect, or to the fact that the supersaturation is higher a t the corners than elsewhere ; we ought to distinguish carefully between these two possible causes. I do not know of any evidence on the question which is the dominant effect ; but since both work out in the same direction, we do not lack an explanation of dendrite formation! Moreover, once dendritic growth has started, not only does the growing tip retain the advantage of being in contact with the most highly supersaturated solution, but also the diffusion field will become organized to supply solute so as to continue the process by very convergent diffusion flow to the growing point.In fact, the difficulty is to explain why any crystals ever avoid dendrite formation and grow as polyhedra. That many of them do is presumably due, as Dr. Evans says, to the tendency towards the setting up of surfaces of lower surface energy-" healing," as I have called it. The results in my paper are those which follow if it is assumed that the crystal does avoid dendritic growth and that the diffusion field extends far out into the solution. Dr. Wooster's suggestions on the possible influence of the thermal wave-pattern in the crystal on the growth of layers are very interesting and worth bearing in mind ; but I do not agree that to explain the remarkable variations in growth rate of NaC10, crystal faces it is necessary to look for a cause which arises in the crystal rather than in the solution ; the cause may be either in the crystal or the solution, and in my paper I have suggested particular solution conditions -i.e., variations .of concentration gradient (not concentration itself) brought about by convection currents or other effects.Dr. Wooster states that " the gradient of concentration is greater near to the non-growing surface than it is to the rapidly growing one '' ; but, as far as our measurements go, this is not so-the actual concentration is greater a t the non-growing surface, but the gradient normal to the face is less steep than a t the rapidly growing surface, as one would expect; the normal gradients are roughly proportional to the rates of growth.It is true that we can only measure concentrations up to within, say, 10-3cm. of the face, and there might be sudden changes a t very small distances from the face ; but any sharp bend in the concentration-distance GI94 GENERAL DISCUSSION curve would only be persistent if there is a big change of diffusion constant near the face ; this would mean a change of structure of the solution near the face. The ordered structure of the crystal might well affect the strgcture of the solution and its diffusion constant a t very short distances (say, 10 A) ; but i t does not seem possible to measure concentrations at such small distances.For the present all we can do is to measure concentrations as close to the face as we can get, and draw what conclusions we can on the provisional assumption that these measurements represent concentrations " a t the face." Prof. W. E. Garner (Bristol) said : With reference to Hartshorne's paper, and particularly to the high-temperature independent factor required (eqn. (10)) to account for this factor, the author, adopting a theory of Xott's, suggests that approximately 10 molecules of monoclinic sulphur, forming a mosaic block, are converted to rhombic sulphur by a trigger action. Discrepancies in the temperature independent factor of a similar character are found in certain solid reactions of the type A(solid)+B(solid) + nH,O, where nuclei of B are formed in the surface of crystals of A simultaneously with the liberation of water.Where the nuclei of B have pseudo-crystalline shapes and presumably grow layer by layer, as in crystallization from the melt or from solution, the Polanyi-Wigner equation, rate = v N e-EIRT, gives the normal value for v of 1olS and E is the same as Q, the heat of dissociation of the solid. N is the number of water molecules per sq. cm. of interface. In these cases there is very close coupling between the formation of the new and the destruction of the old phase, no activation energy being needed in excess of the heat of dissociation. On the other hand, chrome alum gives spherical nuclei and layer growth obviously does not occur.In this case the rate of growth of nuclei of solid B is given by y = 1026N e-3IWdRT. There is thus a discrepancy of 10'~ in the frequency factor and a further anomaly is found, namely, that E is no longer the same as Q, which is 16 kcal. These abnormalities can be accounted for if chrome alum possesses a mosaic structure and if the reaction spreads at the normal rate within a mosaic block, but needs a high activation energy to penetrate adjacent blocks. In parallel with the case of chrome alum, it is suggested that for rhombic sulphur the rate of conversion within a mosaic block might be given by vN e-dRT, where q is the free energy of transition from monoclinic to rhombic sulphur. Since q is small, transition within a mosaic block will be very rapid.The E that is measured would then be the activation energy required to form nuclei of rhombic sulphur between adjacent mosaic blocks. Dr. W. J. Dunning (Bristol) (cornmwnicated) : Dr. Hartshorne has given an interesting interpretation of his experimental results, but there is another point of view worth considering. Accepting his model that there is a thin layer one molecule thick which has properties similar to a gas, and which is situated between the two crystalline forms, the rate of growth of the lower temperature form should be given by Volmer's equation. The process would then be very similar to the growth of a crystal from a supersaturated vapour of pressure PI, this vapour pressure would be given by p , = Ce-EvikT, where C is a constant and I?,, the latent heat of evaporation of the high tem- perature form. Crystal growth from the vapour requires two-dimensional nucleation which contributes another term to the activation energy.With -6 I4--PIICa where g is the rate of growth ; putting x = in A', we have , and neglecting the term g = const, e-Eu/kT e-A"/kT,GENERAL DISCUSSION I95 but 4 and pI-pII, =y ( T o - f ) , we obtain Applying this equation to Dr. Hartshorne’s results, it is found that 20 200 35,oco log v = 38.77 --+ ---- Rf l ( l o - - - l - ) fits them quite well. Mr. Y. Haven (EimUzoveu) said : I would propose ail alternative mechanism for polymorphic transformations and recrystallization processes which avoids the conception that one atom catalyzes, e.g., 10‘ other atoms, as has been proposed to account for the large pre-exponential factor.Between the two phases a boundary region showing a certain amount of disorder is assumed. At a given moment only some of the atoms in this region are in a position to move ; the equilibrium concentration is given by A’ e-E‘ikT (E’ = energy of disorder) and the mobility by A” e-U/kT ( U = activation energy for transition). So the transformation velocity may be written as (apart from other factors) y = Lg e-E/kT = L-l‘ e-E’/kT . ,4” e-U/kT, where E = L;’ + U . Both A’ and A” may contain large entropy factors e+SIK. An entropy factor of 102 in A” may be a reasonable one, so if the pre-exponential factor is 10‘ times greater than has been expected A’ should contain an entropy factor of the order of magnitude 105. This may be compared with ionic crystals where an entropy factor of 104 in the expression for the degree of disorder is very common, e.g., the number of vacant lattice sites in LiF is given by n/h; = 104.e-I6,mo/T, where 1V and 12 = number of lattice sites and vacancies per ~ m . ~ respectively. Dr. W. J. Dunning (Bristol) (communicated) : Prof. Davies and Mr. Jones interpret the turning points on the curves in their Fig. 3 as giving the concentra- tion of the metastable limit. That this is correct can be seen from the following argument. The equation e e e gives 0 t dSe/dO is their ordinate ( y ) in Fig. 3 and -So is their abscissae (x). Hence 0 0 t Their turning point is presumably where dx/dy is changing very rapidly.The only quantity- on the right-hand side which is changing rapidly is F(S,) and the point where it is changing is the metastable limit. Mr. E. 0. Hall (Cambridge) said : I should like to draw Dr. McCrone’s atten- tion to similar results in two papers by Boas and Honeycornbe where similar grain boundary migration problems are studied in non-cubic metals, and the cause is traced to the strain set u p in the matrix by anisotropic expansion during the thermal cycles. 7 Boasand Honeycombe, Proc. Roy. SOC. A , 1946, ~ 8 6 , 57 ; 1948, 188, 427.196 GENERAL DISCUSSION Dr. H. K. Hardy ( S f o h e Poges) said : Reference has been made to some experiments on crystal growth as influenced by an electric potential. The same principle has been applied to organic liquids.8 Crystallization of piperiiol occurred preferentially about one electrode after being held molten with a potential of 5000 V between the electrodes. The effect was reversed when the electrodes were interchanged and was interpreted as evidence that the ultra-nuclei were foreign bodies. Mr. E. 0. Hall (Cambridge) said : The adherence of silver halides to glass, noted in the paper of Zerfoss, Johnson and Egli, is, of course, widely known. However, a t the Cavendish Laboratory we have grown single crystals of the silver halides in rod form by the method of Andrade and Roscoe using Pyrex tubes coated with a thin film of silicone grease. The rods are cast in these coated tubes, from the melt, and from the resulting polycrystalline rods single crystals may be grown in exactly the same manner as metal crystals, although, of course, coated tubes must again be used.Mr. H. E. E. Powers (London) said : The phenomenon of the luminosity caused by crushing of sucrose is well known under the name of triboluminescence and can easily be demonstrated by crushing sucrose crystals between sheets of plate-glass in the dark. It is generally considered to be due to electrical effects and these may be part of the cause of some of our caking phenomena. Other speakers have spoken of the symmetry of “fault intrusions” into crystals. Many years ago I carried out some work on the production of large candy crystals coloured with caramel. In the course of this work a very large number of crystals of one to two inches in length was examined and in very many cases the coloration thijugh geometric was far from symmetric. May I, in conclusion, say that in our industry we have a wealth of interesting material and problems, and I should welcome contact and collaboration with any who feel interested in sucrose.Dr. K. G. Denbigh (Cambridge) said : In reply to Mr. Powers, I agree that symmetrical inclusions were somewhat rare. The trapping of mother liquor in the angles of a dendritic structure was probably not the only mechanism of the formation of inclusions. I have obtained some evidence that an alternative mechanism depended on the deposition of a speck of solid impurity on the surface of the growing crystal. Fresh crystalline material could not deposit directly on this impurity and the face therefore moved outwards with a fairly wide radius of curvature, creating a pocket of mother liquor with the impurity at the bottom.Crystals were sometimes seen in which there were cavities which had not completely sealed across. Dr. A. F. Wells (I.C.I., Dyestuffs) said : In his earlier remarks Dr. Denbigh drew attention to the symmetrical shape of an ice crystal growing on still water. I would suggest that it would be more remarkable if the development were not symmetrical. The growing crystal possesses certain symmetry, and it would be expected that the environment of the crystal (in this case, the water) would develop the same symmetry as regards diffusion currents, etc. In the absence of disturbances, therefore, a symmetrical development will occur. With regard to the experiments of Bunn, Berg and Humphreys-Owen, i t would seem dangerous to assume that the phenomena associated with the thick layers observed on crystals growing in supersaturated solution are closely related to the mechanism of slow growth. Many abnormalities are observed in rapid growth from highly supersaturated solutions, particularly the development of faces which do not appear on crystals grown slowly and continuously. The frequent occurrence of inclusions in crystals grown rapidly and the observa- tion that a crystal with obvious internal imperfections often grows more rapidly in the same solution than a clear crystal suggest that the process of desolvation may become an important factor in rapid growth. Before a sodium ion becomes 8 Hammer, Ann. Physik, 1938 ( 5 ) , 33, 445. B Andrade and Roscoe, Proc. Physic. SOL, 1937, 49, 152.GENERAL DISCUSSION I97 incorporated in the surface of a sodium chlorate crystal i t must be half-dehydrated, but before the next layer can be deposited the remaining water molecules must be removed. Thus the spreading of the thick layers observed in some of Bunn’s experiments might not correspond to the actual process of incorporation of ions in the crystal direct from the solution but, for example, to some secondary process of ordering in a disordered surface layer containing partially desolvated ions. Prof. A. R. Ubbelohde (Bevast) said : I would like to ask Sir John Lennard- Jones how far the contraction he calculated a t the surface of ionic crystals would be modified when the crystals are dipped in a medium of high dielectric constant. Under certain circumstances i t seems likely that the effect of the high dielectric constant must be to reduce surface strain. In the absence of such reduced surface strain, when a sheet of ions grows outwards over a crystal face there must be a comparatively large discontinuity in the arrangement of ions a t the surface region where the uppermost layer terminates, and this discontinuity must travel outwards as the uppermost layer extends. Sir John Lennard-Jones (Cambridge) said : I have not calculated the effect on a crystal surface of a highly polarizable medium surrounding it, but i t seems clear that for ionic crystals such a medium would produce forces attract- ing the surface ions outwards. The forces would partly counterbalance the attraction of the rest of the crystal on its surface layer and so tend to eliminate (or reduce) the contraction a t the surface.

ISSN:0366-9033    

DOI:10.1039/DF9490500183

出版商:RSC    

年代:1949

数据来源: RSC

摘要:

GENERAL DISCUSSION I97 111. ABNORMAL AND MODIFIED CRYSTAL GROWTH Introductory Paper BY A. F. WELLS Received 4th March, 1949 The discussion of abnormal crystal growth implies that we know what is meant by normal growth, but this is far from being true. A crystal grows by the deposition, layer by layer, of new material on its faces, and the growth on faces of different kinds (i.e., different crystallographic foims) is measured as the perpendicular displacement of the face parallel to itself. One object of theoretical treatments of crystal growth is to calculate these rates of growth on the various faces of a crystal in terms of the atomic structure of the crystal and the concentration of material around the crystal. A partial solution of this problem, the calculation of relative rates of growth, would answer the purely morphological question : why does a crystal of a particular substance grown under specified conditions develop certain faces ? This, however, raises another question : to what extent is the face-develop- men t of crystals of a substance constant, external conditions remaining the same ? Although it is known that certain face-developments are character- istic of certain crystals, it has never been established experimentally that a crystal with faces of more than one form does in fact maintain exactly the same shape during growth, i.e., that the relative rates of deposition on the different faces remain the same.For the present we shall assume that by normal growth is meant the development of a nucleus into a single crystal with plane faces, the relative rates of growth on which are maintained the same throughout growth.We can then classify the various possible types of abnormal growth. Before this is done, however, one other point deserves mention.198 ABKORMAL AND MODIFIED CRYSTAL GROWTH All artificial crystals, and most natural ones, are not ideal crystals in the sense that a particular atomic arrangement extends without inter- ruption throughout the whole crystal. Instead, the crystal consists of mosaic blocks (within which the structure may be regarded as ideal) which are inclined to one another at small angles. The development of mosaic structure seems such an inevitable feature of crystal growth that it would appear necessary for any theoretical treatment of crystal growth to account for its appearance.(The fact that a few minerals attain, or approach, the ideal state does not necessarily mean that they grew as ideal crystals ; they may have been annealed subsequently.) It is known that gross imperfections in internal structure can radically affect the rate of growth of crystals. For example, it is sometimes observed that if two seed crystals, grown in the same way, are grown in the same solution under apparently identical conditions, one may grow very much faster than the other if it has visible internal imperfections. It is tempting to extend this idea of dependence of rate of growth on perfection of internal (and therefore surface) structure, and to suggest that an ideal crystal would not grow a t a measurable rate.The numerous anomalies observed in interferometric studies of crystal growth, for example, the cessation of growth on one half of a growing face of a crystal of sodium chlorate while growth proceeds normally on the other half, might then be associated with the perfection of the faces. It may be that if one part of a face accidentally attains an abnormally high degree of perfection, then growth is thereby slowed down. This would appear as reasonable as other explanations, for example, that minute (undetectable) amounts of an unknown impurity settle preferentially on one half of a crystal face. (Alternatively there might be delay in the initiation of an ordering process in a surface layer of randomly oriented, partially solvated, solute.) This complication in experimental studies of crystal growth is one which has not received enough attention, and it may be necessary to ascertain the degree of mosaic structure when comparing growth rates of diferent crystals.The more important types of abnormal crystal growth are set out below. and I propose to mention briefly some of the problems they raise. TYPES OF ABNORMAL CRYSTAL GROWTH Dendrites, hopper and other skeletal growths crystals, Single crystals with S p Jzerzdites (no crystallographic relation between the individual crystals) impurities, etc. Contact twins Penetration twins Crystals with (individuals related by (small number of twin vicinal faces, definite crystallographic components or repeated curved faces, laws, i.e., continuity of twinning to give etc. crystal structure) pseudo-symmetrical lamellar twins) The account of the morphology of crystals as described, for example, in Groth's Chemische Krystallographie is in some cases very misleading, for two main reasons.(I) The face-developments illustrated for many crystals are much more complex than those of crystals grown slowly and continuouslyA. F. WELLS I99 from pure solutions. They obviously represent, in many cases, crystals which had grown in dishes on laboratory benches and had been subjected to tem- perature fluctuations leading to alternate partial dissolution and regrowth, and hence to complex face-developments. Crystallographers have always tended to be interested in crystals showing complex face-developments because of the diagnostic value of complex forms, quite apart from the intrinsic beauty of the crystals.(2) Inorganic salts are usually soluble only in water, but many organic compounds are soluble in a variety of solvents, and there is often a crystal habit characteristic of a particular solvent (or set of chemically related solvents). In such cases a single illustration should be replaced by a set of drawings showing these different face-developments. a b c d FIG. I.-Variation of crystal habit with solvent. Above : crystals of a, aniline, b, cyclohexane. Below : crystals of anthranilic acid alcohol, d , glacial acetic acid. iodoform from from t, ethyl Fig. I shows examples of crystals which grow with different face- developments from different solvents. Elucidation of habit changes of this type calls for the development of a new branch of surface chemistry involving a study of the interactions of molecules (of solute and solvent) in solution with those in the various crystal faces.Unfortunately, little progress towards even qualitative explanations can be made until the crystal structures of the solutes are known. An exception is provided by resorcinol (m-dihydroxy-benzene) , which shows some interesting differences in behaviour when grown from different solvents, differences which can to some extent be related to its crystal structure. In the polar crystal of resorcinol (low- temperature form) all the molecules are similarly oriented with respect to the200 ABNORMAL AND MODIFIED CRYSTAL GROWTH c axis, as shown in Fig. 2, which shows in projection the surface structure of a crystal of the type illustrated in Fig. 3 a.The inclusions in such a crystal show that no deposition has taken place on the lower end of the crystal. This is presumably due to the strong interaction of this hydroxylic face with water molecules. If such a crystal is transferred to benzene solution, growth takes place on both ends of the crystal (Fig. 3 b). In this solution there is no preferential interaction between solvent molecules and a hydroxylic as compared with a benzenoid face. Unidirectional growth also takes place in certain other solvents, and from ethyl acetate a remarkable shape develops (Fig. 3 c). This is a conical crystal terminated by two normal plane (o??) and (oIZ) faces, and growth takes place only on these faces. No deposition occurs on the lower (conical) end of the crystal.No explanation has yet been found for this extraordinary crystal shape, which is the normal develop- ment from ethyl acetate solution. FIG. 2.-Projection of the structure of resorcinol on (100) showing the surface structure of (011) and (on) faces. The shaded circles represent OH groups and the broken lines, 0-H-0 bonds. Closely related to the effect on crystal habit of change of solvent is the effect of impurities in solution. Preferential interaction between the atoms or groups in certain crystal faces with either solvent or impurity alters the relative rates of growth on faces of different types, resulting in change of habit. Much of the experimental work on the effect of adsorbed impurities has been carried out with complex dyes and, as might be expected, it is difficult to account for the remarkably specific action of many of these complex molecules in terms of the structures of the adsorbed molecule and of the crystal surfaces. This is emphasized in the papers of Buckley, and of Butchart and Whetstone, which follow.An interesting application of this kind of habit change is described by Whetstone, who has found that caking of certain soluble salts is due to the formation of intergranular bridges, the mechanical strength of which can be considerably reduced by modifying the habit of the recrystallized material formed between the granules.FIG. 3.-Crystals of resorcinol (low-temperature form) : a, crystal from water, showing inclusions ; 0 , crystal of type a, grown larger in benzene solution ; c, crystal from ethyl acetate.[To face page 200A. F. WELLS 201 The unidirectional growth of resorcinol in water and some other solvents shows in a striking way the importance of interaction between molecules in the surface of a crystal and solvent molecules. It suggests that even in cases where this interaction is less powerful, desolvation of the solute mole- cules may be an important factor to be considered in the growth of crystals from solution. Even when a solute molecule (or ion) has settled on a crystal face it has been only half-desolvated, and before the next layer can be laid down the remaining solvent must be removed. Under certain conditions, particularly during rapid growth, all this solvent is not removed and inclu- sions are formed in the crystal.In a similar way, adsorbed molecules may be trapped in the growing crystal, as in the case of coloured crystals of inorganic salts mentioned by Buckley. In some cases included molecules or crystallites are oriented in the host-crystal and give rise to pleochroism. A phenomenon closely allied to the deposition of oriented crystallites on the surface of a growing crystal is the formation of oriented overgrowths on crystal faces, The literature of this field is very extensive, and much of the interpretation of the experimental facts has been concerned primarily with the geometrical aspect, i.e., the fitting of the overgrowth to the substrate. Two papers in this section deal with the energetics of the formation of oriented overgrowths. Rhodin deals with thin aluminium films deposited on the surfaces of inorganic crystals, mostly ionic in character, and van der Merwe has made a valuable survey of the literature in connection with a theoretical study of the conditions which must be satisfied for the formation of an oriented, crystal- line, overgrowth. A third paper in this field, by Hocart, describes observations on oriented overgrowths of ammonium nitrate on mica made in connection with a study of the stabilization of the high-temperature forms of the salt by incorporation of small amounts of other salts with suitable lat tice-cons t an ts. Research Laboratories, Imperial Chemical Industries, Ltd., Hexagon House, Blackiey , Manchester, 9.

ISSN:0366-9033    

DOI:10.1039/DF9490500197

出版商:RSC    

年代:1949

数据来源: RSC

摘要:

A. F. WELLS 201 MISFITTING MONOLAYERS AND ORIENTED OVERGROWTH BY J. H. VAN DER MERWE Received 3rd February, 1949 Crystal orientations are not in general determined by long-range forces, but by forces between one atomic layer and the next. Hence, in order that there shall be a definite orientation in a crystalline overgrowth on a crystalline substrate, there must be formed, as the initial stage, an immobile monolayer of regular atomic pattern, to be called an “ embryo.” If the formation of a monolayer is regarded as a process of adding atom to atom, it is possible, if the influence of the substrate is strong, for these (foreign) atoms to take up the same positions on the substrate as would atoms belonging to the same substance as the substrate. The resulting monolayer is therefore homogeneously deformed to fit on the substrate, thus forming an embryo. “ Oriented overgrowth ” is then obtained when the atomic pattern (unchanged, when the final overgrowth is pseudomorphic, or homogeneously deformed, when the abnormal strain is released, at some G*202 MONOLAYERS AND ORIENTED OVERGROWTH stage, by lateral expansion or contraction) and orientation of the embryo are preserved throughout the entire lattice of the overgrowth.A theory has been developed1 which led to predictions regarding the necessary conditions under which an embryo can be formed. The theory is based on the properties of a one-dimensional dislocation model, consisting of a row of identical balls, connected by identical springs (force constant <) ; the balls at the same time being acted on by a force, which varies periodically with the position on the substrate.The first harmonic term (amplitude &W) in a Fourier series is taken to represent the corresponding potential energy. There may be a difference between the natural spacing b of the balls and the wavelength a of the substrate field. In the application to embryo formation the configuration of balls and springs is taken to represent the monolayer, and the periodic force to represent the substrate’s influence on the deposit atoms; this extension from one to two dimensions can be shown to be justified. FIG. 1.-Graph of ZJP = ZQ@/a - I) against ZJP0 = Z,(b/a - I). A. Lowest energy state. (N.B. Z,/P= o for o 1 lo/Po 1 2/7r.) B. Spontaneous generation of dislocations.It is found that with this model the fit or misfit of the monolayers and substrate is naturally described in terms of “ dislocations.” Thus, if there is misfit so that gg or IOI atoms in a row lie over IOO potential troughs, the majority of the atoms actually lie nearly at the bottom of their troughs, while there is a small region where the atoms ride over the crests, to miss a trough or squeeze an extra atom in. This region of misfit we call a surface dislocation : if a perfect crystal is built above it, it will develop into an ordinary crystal dislocation of the kind originally proposed by Orowan and Taylor to account for the mechanical properties of solids. The mathematical theory of our model shows that when the natural spacing b differs from that, a, of the substrate, the lowest energy state of the system remains one with no dislocations up to a certain critical value of the misfit r/Po defined by 1/P0 z= (b/a - 1)critical = z/d,, where I, (pa2/2W)*.Calculation with Lennard- Jones forces, assuming the interactions with Frank and van der Merwe, Proc. Roy. SOC. A (in press).J. H. VAN DER MERWE 203 other atoms of the deposit and with the substrate atoms are similar, shows that I, is about 7. Thus the critical misfit should be about g yo in an average case. There will, however, in general be a large variation about this average value, depending on the relative forces exerted by deposit atoms on each other (giving p) and on the substrate (giving W ) , respectively. This is not the only critical condition of importance, for there still remains an activation energy for the generation of dislocations,* which only falls to zero a t a larger degree of misfit I/Z, (equal to 14 yo in the average case). Hence, below this critical misfit, it is also possible at low temperatures for the monolayer to be deposited in fit with the substrate, thus producing an embryo in a metastable state.Fig. I shows that the density of dislocations F/a - I, where b' is the average spacing of deposit atoms, rises abruptly to a large value on passing either of the critical misfit conditions, the lower of which is probably significant for high, and the higher for low, temperatures. Once there is a high density of dislocations (at which incidentally the spacing of the deposit layer becomes B FIG. 2.-Graph of ZJP0 against w/W.A. Lowest energy state. generation of dislocations. B. Spontaneous of that of the surface, free to an embryo for be a preferred practically equal to its natural spacing and independent substrate) the monolayer should be quite mobile on the rotate as well as to glide. Such a monolayer cannot be fully oriented overgrowth, though, of course, there may axis normal to the surface, as also occurs on amorphous substrates. It is unlikely that the variation of potential energy in an actual case will be represented accurately by a single sinusoidal term. The corresponding curve is expected to have in general a maximum which is flatter and wider than its minimum. This can be attained by introducing into the potential representation a second harmonic term of small amplitude &I.Increasing w/W beyond 1/4 makes the potential curve change its nature ; it develops a second minimum. Thus the introduction of a second harmonic term was found to be convenient in investigating the influence of the shape of the potential curve on the critical properties of the system. The outcome of the investigation It is seen that the limiting misfit corresponding to spontaneous generation of complete disloca- is represented graphically in Fig. 2. * This spontaneous generation is only possible a t the edge of the layer, and, of course, becomes impossible when any flat region of the surface is cornPZeteZy covered.204 MONOLAYERS AND ORIENTED OVERGROWTH tions (displacement vector 2) does not depend at all on the actual shape of the potential curve, but only on its maximum variation Wo, according to the formula I/P, = I / Z ~ , where I , = (pa2/zW,)+. This result was shown to be completely general, holding for any shape of periodic potential curve of wavelength a.The effect on the critical misfit corresponding to the state of lowest energy of the system is to increase this misfit ; the increase having a maximum value of approximately 1-2 times the original value at w = 0. This corresponds to a shift of the critical value of g % to approximately 11 yo (assuming W, to remain constant). We may therefore conclude that the actual shape of the potential curve is of secondary importance in embryo formation, and that it is its maximum variation W , which is the important factor. Note that W always occurs in the ratio Wo/y.We shall come back to the significance of W , and W,/p when we discuss the experimental evidence. Q FIG. 3. 0 denotes troughs of potential field. + denotes suitable troughs for fitting of deposit units. o denotes natural positions of deposit units. 0 =angle through which the monolayer must be sheared to fit on the substrate. Having described the conditions necessary for the formation of an embryo, the next step is to explain how an oriented deposit can grow from it. This embryo is a suitable substrate for the formation of another embryo on it, provided the binding between deposit atoms is not weaker than their binding on to the substrate. If the atomic pattern of the embryo, and hence that of the substrate, resembles the atomic pattern of a plane in the normal lattice of the deposit (e.g., when the two lattices are isomorphic), it is possible for a stable, macroscopically thick, oriented film to grow by repetition of this process of embryo formation. This assumes, of course, that any flat region of the surface is completely covered by the first monolayer before the second layer is appreciable (see below).Since the formation of a monolayer is really a process of adsorption on the substrate, it is the pattern of potential troughs, i.e., positions of minimum potential energy, of the deposit atoms in the substrate field, rather than the atomic pattern of the substrate surface, which must resemble the atomic pattern in a plane of the deposit structure. To realize the need of this distinction it is only necessary to consider the case of a neutral argon atomJ. H.VAN DER MERWE 205 on the (001) face of NaC1, for which the potential troughs are a t the centres of the small squares having alternately Na+ ions and C1- ions at their corners,2 as compared with the case of a K+ ion on the same substrate for which the potential troughs are presumably on top of C1- ions. This example also shows that, for the sake of generality, it is convenient to speak of deposit or substrate “ units,” since these can be atoms, molecules, ions, etc. An illustration of a more general case of fitting deposition units in substrate potential troughs is shown in Fig. 3. Note therefore that a difference in the shapes of corresponding patterns, e.g., a shear as in the Fig. 3 , also represents “ misfit,” measured by tan 8.This case is in fact covered by the the0ry.l The orientation of alkali halides on NaNO, with tan 8 = o m is an example. The thickening of films will, however, certainly cause the generation of dislocations at free boundaries of an initially undislocated film, since the energy to compress the thick film will be much greater. For example, a double layer will have a critical misfit of the order of (z)-t times that of a monolayer (taking t,c for a double layer to be twice that for a monolayer). However, once the embryo covers the whole flat area, it no longer has “ free boundaries on a flat substrate,” since it will also be completed around corners and edges, thus pinning the boundaries to the substrate. It is therefore possible for a stable oriented film to grow pseudomorphically with the substrate.Even if, during the early stages of growth, spontaneous generation of dislocations does take place at free boundaries in planes parallel to the substrate, the initial orientation will be preserved in subsequent layers provided the dislocated layer is at least a few (say, of the order of four) monolayers thick, for the irregularities in the atomic pattern existing at the centres of dislocations will be largely smoothed out over this thickness. We know, on the other hand (if spontaneous dislocation does not take place during the early stages of growth), that the large strain, permissible in thin layers, cannot persist into films of indefinite thickness; a fact also well established in experiments showing that pseudomorphic growth was no longer observed in sufficiently thick film~.3~ It will be impossible to grow macroscopically thick films with more than, say, 0.1 yo of strain, corresponding to the yield stress of the bulk material. Hence thickening of films must necessarily be accompanied by transition processes which make the bulk of thick deposits strain free.These theoretical ideas are in good general agreement with experimental observations. The fact that pseudomorphic overgrowth is observed seems to show that there are cases in which slip does not take place during the early stages of growth. Amongst the most striking examples are the cases of A1 on Pt 3 b and ZnO on Zn.SUlb Similar tendencies were observed in over- growths of MgO on Mg,Sb Ni and Co on C U , ~ ~ and in the experiments of Finch and Sun,5 where the abnormal crystal orientations of very thin films were in general such that the atomic population density in the orientation plane of the deposit approached that in the substrate surface.More experi- mental observations on very thin films would be very useful. In all cases, whatever the mechanism of the slip process, some residual stresses are likely to remain. There is plenty of experimental evidence for this from the behaviour of stripped films, though one must always consider the possibility of strains caused by the stripping process. Orr, Trans. Faraday Soc., 1939, 35, 1247. 3 Finch and Quarrell, (a) Proc. Physic. SOC., 1934, 46, 148 ; (b) Proc. Roy. soc. A , 1939, 141, 398 ; (c) Trans.Faraday Soc., 1935, 31, 1051. 4 Menzer, (a) Naturwiss., 1938, 26, 385 ; (b) 2. Krist., 1938, gg, 378 ; (c) 1938,g9,410. Finch and Sun, Trans. Faraday Soc., 1936, 32, 852. * Goche and Wilman, Proc. Physic. Soc., 1939, 51, 625.206 MONOLAYERS AND ORIENTED OVERGROWTH The most important effect of the strain transition process is the possibility of a loss or change in the initial orientation. If this process takes place through slip in planes parallel to the substrate, as we assume is the case in experiments 7 8 where the orientations of the small deposit crystals are determined under the microscope, such a loss is not very likely. If, however, the slip takes place simultaneously in planes inclined to each other, a loss is likely to occur. This was presumably the case in the experiments of Finch and Sun ; the initial regular orientation became almost random with sufficient film thickness.The transition process can, however, also take place through the growth of an unstrained bulk film on the thin strained part of the overgrowth at the contact surface. Detailed calculations by Menzer 4 {confirmed by Goche and Wilman in the case of Ag) on observations of Ag and Ni films on NaCl showed that the bases of the deposits consisted of small crystallites (in four orientations rotated through go”) having (221) faces in contact with the substrates. The bulk of the film, growing on these crystallites, is twinned on the (111) faces with respect to the crystallites and has an orientation parallel to that of NaC1. The corresponding misfits {g 7’ for Ag, 7 yo for Ni) in the contact plane thus also lie within the tolerance limit, which is not the case for the misfits (-27 yo for Ag, -38 yo for Ni) suggested by the orientation of the bulk of the overgrowths.Many of the orientations of metallic overgrowths on ionic crystals are likely to belong to similar types, and are therefore given in a separate table (Table 11). These orientations are in general such that better fit can be achieved by other orientations, as was shown by Thomson10 for some cases. These con- siderations, together with the fact that deposits on a random substrate have a tendency to expose a definite plane, show that one cannot be certain that the orientation of an overgrowth is the same as that of the initial embryo. If we assume that strong adsorption of the overgrowth on to the substrate can in general be expressed by a large W,, then it is in agreement with the theory that strong adsorption is an essential condition for preferred orientation, as has been established by various workers l1 l2 l3 l4 l5 as a result of experiments on “ partners’’ (combination of deposit and substrate) which yielded no oriented overgrowth in spite of ideal geometrical conditions.The binding in the adsorption processes was of various types, eg., through a hydrogen bond, 8d through dipoles, 7 g etc. Willems, having drawn the general conclusion that, for oriented overgrowth to take place, there must exist the possibility of a strong chemical bond between the units of the overgrowth and the corresponding units of the substrate, confirmed it experimentally. 7 Neuhaus, 2.Krist. A , (a) 1941, 103, 297 ; (21) 1943, 105, 187 ; Nuturwiss., ( G ) 1943. 31, 33 ; (4 1943, 31, 387 ; ( 8 ) 1944, 32, 34 ; (fl 1948, 35, 27 ; (9) 2. Phvsik. Chem. A , 1943, 191, 359 ; ( h ) 1943, 192, 309 ; (2) News. Jb. Mzner., Geol., Paloort, 1943, 78, 189 ; ( 3 ) 2. Elektrochem., 1944 (in press). (b) 1943, 105, 53 ; (c) 1943, 105, 144 ; 31, 146; ( A ) 1943, 31, 203 ; (if 1943, 3.1. 232 ; (i) 1943, 31, 301 ; ( k ) 1944, 32, 324 ; (I) Ber., 1943 (in press) ; (m) Kollozd-Z., 1940, go, 298. 1 0 Thomson, Pvoc. Physic SOC., 1948, 61, 403. 11 Sloat and Menzies, .J. Physic. Chem., 1931, 35, 2005. 12 Seifert, Fortsch. Miner., (a) 1935, 19, 103; 8 Willems, 2. Kvist. A , (u) 1938, 100, 272 ; (4 1943, 105, 149; ( 8 ) 1943, 105, 155; Naturwzss., ( f ) 1941, 29, 319; (9) 1943.9 Bruck, Ann. Plzysik, 1936, 26 (5), 233. (b) 1936, 20, 324; (c) 1937, 22, 185; 2. Krist. A , (d) 1937, 96, 111 ; (e) 1938, 99, 16 ; (f) 1939, 100, 120 ; (g) 1940, 102, 183. 13 Heintze, Z. Krist., 1937, 97, 241. l4 Royer, Bull. SOC. franc. Migier., ( a ) 1928, 51, 7 ; Cow@t. yend., (b) 1925, s80, 2050; (c) 1932, 194, 620 ; (4 1932, 194, 1088 ; (e) 1933, 196, 282 ; (f) 1933, 196, 552 ; 1 5 Vineyard, Physic. Rev., 1942, 61, 100. (g) 1937, 205, 1418.J. H. VAN DER MERWE 207 Amongst the most interesting experiments for the present theory, from the point of view of binding, are those on ionic partners. These experiments show that the limiting misfits, in cases where both partners are ionic, are much greater than when one of the partners is not ionic.This indicates that the electrostatic forces are the important binding components in these cases. These experiments provide special opportunities to test conclusions from the present theory, if we make the following assumptions- (i) The electrostatic binding is' the important factor in the adsorption energy. (ii) Stronger adsorption, and hence larger W,, can be attained by (a) using solvents (from which to deposit overgrowth) of lower dielectric constant and (b) closer approach of deposit units to the substrate, which will be the case if the ionic radii of the deposit units and/or those of the substrate, are small. Hence preferred orientation for partners, having misfits in the region of the tolerance limit, will be sensitive to small variations in W,, i.e., partners which do not orientate under certain conditions will do so under conditions for which Wo is greater.Thus Willem, 8 b Sloat and Menzies l1 established that the tolerance limit could be increased by using solvents of lower dielectric constants. In the case of Sloat and Menzies, this was as much as 7 yo. They also showed that NaCl had an appreciably greater orientating ability than KCL. This is to be expected since the ionic radii are 0.98 ,& for Na+ and 1-33 In the preceding we have assumed that the properties of the original simple model (identical balls, i.e., a single Wo) also apply for compound overgrowths (non-identical balls). Only the fact that the deposition units (ions in a special case) are of different size is-sufficient justification for the use of W , = W,, for the one unit, and W, = W,, for the other unit, where W , * W,.This problem has been solved l6 by using parabolic arcs in the potential representation, since it could not be solve'd for a Fourier repre- sentation. The resulting expressions show that the corresponding limiting misfits increase with (IT, + W,)/p. It is also in agreement with the theory that the limiting misfits in the case of ionic overgrowths should be greater than that for metallic overgrowths (assuming the adsorption is not much different), since the compressibilities of the former are much greater than those of the latter. In particular, oriented overgrowth with very large misfits is observed in the case of oxides and iodides-a fact which we can connect with the particularly high com- pressibilities of these large anions.The general problem of oriented overgrowth of a non-isomorphic deposit on various surfaces of a substrate is exceedingly complicated, but from similar theoretical considerations as those above one may anticipate that a preferred orientation can exist when there is a similarity in spacing in one row of closely packed units in- each lattice, as concluded by various workers.6 l3 l4 Seifert,12 in his work on oriented overgrowth of ionic partners, came to the conclucion that one-dimensional lattice fitting for a row of closely spaced ions of a b .mating sign is sufficient to give rise to oriented overgrowth. I am indebted to Dr. F. C. Frank and Prof. N. F. Mott for their keen interest in this work and their many valuable suggestions.I also have to thank the South African €ouncil for Scientific and Industrial Research for a grant and special leave, which rendered it possible to perform this research. for K+, thus making W, (for NaC1) greater than Wo (for KC1). H . H . Wills Physical Laboratory, University of Bristot. 16 van der Merwe (to be published elsewhere).208 MONOLAYERS AND ORIENTED OVERGROWTH Tables In Tables I to III- Column I gives the substrate material, the exposed crystal face and a reference axis lying in this face. Column z gives the material deposited, the crystal face in contact with the substrate, and the crystal axis parallel to the reference axis in column I . Where the face and/or axis in either column I or 2 is missing it is supposed tobe that just above it.Column 3 gives the percentage excess of the lattice spacing of the deposit, relative to the substrate ; in the case of non-isomorphic relationship, the misfits in two orthogonal directions are given. Column 4 gives the literature by number, and remarks by numbers with asterisks. The underlined entries give a few of the numerous cases in which oriented overgrowth was not observed under conditions closely comparable with the preceding analogous cases. The misfit is calculated in these cases for the orientation given. No attempt has been made to give an eshaustive list of negative cases. TABLE I CASES IN MOST OF WHICH NORMAL ORIENTED OVERGROWTH IS BELIEVED TO OCCUR Substrate Pt Pt - c u cu Au I’d At3 c u a-Fe 2 (111) [~io] (110) [OOI] (111) [~io] (110) [rio].(111) [~io] (111) (100) [OII] (roo) [oro] (111) [ITO]. (100) [OII] (111) [rio). (100) [OOI] [or I1 (110) [~io] (001) [roo] Deposit Al* AU & ME cu co Ni Cr co* Ni Ag Zn g A U Fe L co Ni 2 c u Fe Au c u Fe Au cu,o FeO MgO PdO (111) TITO] ( 1 1 0 ) [OOI] (111) [ITO] (110) [~io] (100) [OIO] (110) [OOI] (100) [OIO] (111) [~io] (100) [OIO] (111) [ITO] (100) [OOI] (110) [~io] (100) [OOI] (001) y1001 [I 101 (111) C~io] (001) [IOO] 3 4 -4 I G -8 I 0 I1 2 -1 -3 13 4 16 13 12, -9 0, 18 -13 -14 24 6, 24 -4 - I3 -7 4 3 1.5, -19 1 8 0 0 I2 0 6 -7 I1 3b; I* 3b 3 b 3c 5 5 5 I8 18; 2* 18; 3*, z* I8 18 I8 5 5 5 5 5 5 ; 4* 5 5 ; 5* 5 , 9 5 5 5 5 5 5 5 9 9, ~ g a , 2 0 , ax, 22, z 3 , 24; 6*, 2 19 a, b 3 b ; 2 * 24 [Cont.Substrate NaCl KCI KC1 TlCl TlBr AgCl T1C1 7 1Br T Z (0001) [ ~ o i o ] (00I)t [I0011 ( 0 0 1 ) [ I I O ] [I001 [I io] (111) (001) [OIO] II 1001 (001) [IOO] J.H. VAN DER MERWE TABLE I (Continued) 209 Deposit ZnO 4 2 0 AgBr AgCl 491 a r igc1 :u I :uBr :u,s* JaC1 JH ,Br :sc1 {H,Cl GaBr qaCN ?a1 <F iC1 i C N iBr <I iC1 ,iBr 9gc1 4gBr 9gCN RbI YH,Cl YH,Br YH ,I PbS uc1 NaF E l KCN KBr KI NaCl NaBr NaCN NaI AgCN AgCl AgBr LiBr NH,C1 N H ,Br NH ,I RbCl RbBr RbI PbS KF ‘1 1Ur T1I AgBr AgBr - AgCl T& AgCl ( 1 1 1 ) [ITO] [ i i z ] [ITO] (001) [ I I O ] L 1001 (001) [IOO] [I101 ____ Misfit % ’ Literature + ~ Remarks 0 2 -4 3 , -14 -41 -17 -3 -9 2 -3 -1 I I 5 -5 6 7 :5 -9 -3 I 1 $0 r6 !3 -18 [7 1 5 2 r !9 I2 - I 0 -5 -5 3 -8 -8 - I3 4 15 5 9 17 5 -15 4 6 4 3 - 4 - I2 I0 -2 I0 , 3 a, b ; I * 25 17, 2 5 I 7 7 7 7 7 2 2 2 ; 2 * , ’* 1 9 I I I I, 14 I, ‘4 1 , I4 1, 14 I, ‘4 I, 14 I , I4 1, ‘4 1 , ‘4 4? 14 4 48 ‘4 .4 :4 !4 [ 4 [4 [4 ~ 4 , 14 a r4, ‘4 a [4 [ I , 14 a [ I , 14 a 11, 14 a [ I , 1 4 a 11, I4U 11, 14a 11, 1 4 a I I I 1 I 1 I1 I 1 1 1 , 1 4 a 11, 1 4 a I 1 11 I1 26 d 26 d 26 b 26 d 26 d 26 d 26 d [Cont.210 MONOLAYERS AND ORIENTED OVERGROWTH Substrate AgBr PbS PbS - MgO MgO FeO Fe304 ZnS u-Al,O, CaCo, - CaCO, NaNO, KC10: XH,C 1 NH ,Br KC1 NaCl K Z ZnS PbS NaCl NaNO, (111) [ITO] (001) [IOO] (001) [IOO] ( I IYO) [ooo I] (100) [or01 (110) j i I o j (105’1) [r-e*] (001) [IOO] (III) [ ~ i - o ] (001) [IOO] (111) [I-io] [OOII (001) [IIO] (001) [IIO] (100) [ O I I ] (110) [ ~ i o ] Siderite Rhodochrosite Zincspar Magnesite TABLE I (Continued) Deposit NaBr NaCK NaI KC1 KCN KBr K I AgRr RbCl IibBr NH,I NaF LiF Fe,04 FeO Zno NiO NaNO, NaCl hTaBr NaI KCl IIBr K I RbCl RbBr NaCl NaBr NaI KC1 KBr K I LiCl LiBr KMnO, Iirea AgC 1 L Z N* R X Urea Thiourea - A* a-H * CC-H a-H p-H* p-EI (001) [IOO] (001) [roo] (111) [I131 (100) [OIO] (roi3) [OIOO] (110) [ ~ i o ] (001) [IIO] (111) [~io] (1 10) (010) [OOI] (101) [OIO] (001) [IOO] (100) [OOI] (010) [OOI] (111) [I+o] (Ioio) [ooo I] Misfit yb 13 -6 --I -1 8 5 I 0 I 0 I8 -7 -4 Ia 1.5 -3 21 I 0 -5 -3 3 16 - 7* 0, 16* -12, t* = 21 -7 I0 I I -2 3 3 7 14, t = 21 -13, t = 23 -8, t= 23 0 , 1 = 23 -3, t = 23 I0 Literature + Remarks 26 G I I , 14 a 11, 14 a II, 14 a 11, 14 a TI, 14 a 11, 1 4 a 11, 1 4 a 11, 14 a 11, 1 4 a 11, 1 4 a I r , 1 4 a 11 I1 I1 15 I5 I5 19 b 19 1 2 9 ; 8* 2 7 ; 9* 2 7 ; IO* 28 14 f 14 f I4 f I4 f I4 f I4 f I4 f I4 f 13, 1 4 J ; II* 133 I4f 13, ‘4f 13, I 4 f 14f9 I I * -21, t= 23 -15 -3 4 I 10, -17 1, -7 1, 1 5 14.2 1 12, 2 0, -6 1, 0 -1, 23 10, I1 7 , -2 10, I 3 11, I 2 , 19 2 , 19 0, 21 2, 21 3 , -8 13 I3 71 29 29 29 29 29 29 7 f 7 f 14d 7 f 8 f ; I2* 8 b ; 12* 1 4 d ; 12* 8 b 8 b 8 b 8 b 8 b 14d [Cotzt.J. H. VAN DER MERWE d s (b-G) [c-axis] - S-a NH,Cl (001) [I001 NH,Br 211 31 3 3 , -12 61 7 6, -16 -8, o -4 O J 4 - 1 TABLE I (Continued) KClO , NH4C10, a-H (1130) [ooor] Thiourea (010) [001] MgS04.7H,0 (roo) [oor] MnS04-7H,0 NiS0,.7H20 Urotropins (110) [ITO] LiCl ( 1 1 1 ) [ ~ i o ] LiBr NaCl NaBr KC1 KBr Substrate I 7) -4 9 9 0 g, 6 8 , 7, t= 0 I 0 0 I, 8, t = 14 , -6 0 3 8 I4 -4, 6 2 1 Dolomite (roo) [o I I] Baryte Celestite (roo) (001') (00 1) Urea [ I 101 Mica [ 1001 (Muscovite) Chloritc Mica (Muscovite) [~io] [OIOI Mica (001) [I201 {Muscovite) Gypsum (010) [ ~ o I ] CaF, (111) [ITO] Deposit Misfit 1 Literature + j Remarks ' 33 ~ 33 1 33 33 33 1 33 I *.Pseudomorphic overgrowth. z*. Pseudomorphic tendencies. 3". Orientation does not persist in thick films. 4*. Direction on plane denoted by t is not given by the authors, and thus assumed to be that given. 5*. All potential troughs (face-centred cubic and hexagonal) are assumed to be occupied by deposit units. 6". Cu,O has tendency to expose (110) face. 7". Cu,S deposit has cubic symmetry, thus differing from normal structure. (Pseudomorphism ?) 8*. Author explains types of orientations on different faces of ZnS.g*. " Fit " oxygen atoms against each other. lo*. Half of deposit units (when deformed for " fit ") are on potential crests. I I*. t = tan 8 (in yo), where 8 = angle through which to shear deposit pattern in order that i t might resemble the substrate pattern. Two orientations differing by 8. 12*. A = anthraquinone ; a-H = a-hydroquinone ; (3-H = (3-hydroquinone. 13". d-G d-glucose ; S-a. = salicylic acid ; (b-G) = plane through b- and c-axes ; dl G long face-diagonal. 14*. Of the deposit units (when "fitted ") 1/3 are on potential crests, 1/3 on intermediate positions and 1/3 in troughs. Y-C* e rhombohedra1 edge.212 TABLE I1 CASES, IN MANY OF WHICH A VARIETY OF ORIENTATIONS OCCUR, IN WHICH IT IS SUSPECTED THAT THE FINAL ORIENTATION IS ESTABLISHED THROUGH INTERMEDIATE LAYERS O F DIFFERENT ORIENTATION, ANALOGOUS TO THE CASES ANALYSED BY ~ ~ E N Z E R ~ Substrate Deposit NaClt t NaCltt KClt t KBrt t K I t t NaClt t KClt t M O S , ZnS PbS FeS, Mica* * (00 I (001) [IOO] Au A1 c u c o Pd Fe Cr Cr Mo Fe Mo Ag Pd Ni (001) [roo] (221)* (001) [IOO] (111) [TIO] (221)* [ I ~ o ] (111) [ I ~ o ] (001) [IOO] ("1 (c) (61 (110) [iro] (001) [IOO] (111) [Ti21 (210) [ i z f ] (110) [OOI] (111) [ii~] (210) [OOI] (111) [ I ~ o ] (331) (001) [IOO] (111) [ i ~ o ] (001) rI001 Ag* * (111) [ITO] (110) (100) [OOI] Au (111) [ ~ i o ] Ag Pd Au Ag Pd -27 26, -27 9, 9** 9 ; t t I 9 4, 6 ; 2 * , 3** 3 -38 or 24* 4 9 ; 4* -7, -7** I 4 ; 2*, 3** -12 4 25, -28 9 24, -28 -36 or 28* -31 -3 -28 I , -28* -28 2, -12* 2, x* -11 I 2, -28 3 4 c : 9 2.-12* 3 4 c ; 4* -19, -28 2 ; -28; 2 , 1 1 ; -21; 11, - 9 ; 29 ; -9, -12; 2 3 ; -19; 1 5 ; 12, x -21, x 30 -8, 13 24 I5 9 25 32 24 IO* -4* IO* -4* 7* 7* -28 -21 29 -12, 23 -19. 15 -5, x -.5. x - 1 0 , x 34 c 3 4 c ; 5* 34 d : 5* 3 4 a : 5* 3 4 a : 5* 3 4 a ; 5* 3 4 d ; 6* 3 4 d ; 6* 9 -9 -9 -9 3 5 ; j** 35 35 35 3 6 ; 4*, 7** 3 6 ; 4' 3 6 ; 4* 3 6 ; 4* 3 6 ; 4* 3 6 ; 4* 3 6 ; 7** 36 34 t t I . The potential troughs of the ionic crystals are assumed to be at the centres of the small squares (parallelograms for CaCO,) having at their corners alternately negative and positive ions. 2*. This was shown to be the true orientation of deposit a t the contact surface. 3*. Three Ag (or Ni) atoms are fitted against two Na+ ions. 4*.Half of deposit units on potential crests. 5 * . The first misfit, eg., -9, corresponds to orientation (a) the second, 6*. x = bad pattern and bad fit for a direction perpendicular to that for which 7*. There are indications that the orientation towards the contact surface is e.g., 29, to (b) and the third, eg., -9, 29, to (c). the misfit is given. different from that in thc bulk deposit. See Fe on NaCl.J. H. VAN DER MERWE 213 TABLE I11 CASES OF ORIENTED OVERGROWTH IN WHICH THERE APPEARS TO BE FIT IN ONE DIRECTION ONLY One-Dimensional “ Fitting ” Substrate Au (110) [OOI] (001) [IOO] [IOO] Pd [TIO] 2 C l I1 101 Mica io 101 NaNO, (100) [&I** [@I** NaNO, Deposit Fe (100) [OOI] PdO [OIOl /Thio- (010) [IOO] 1 urea (100) [OOI] NaCl (111) [ITO] Urea NaCl (111) [ITO] KC1 LiCl KBr KI NaI (See also Tables I and I1 Nisfit 0, 30 11, 36 -3, 69 8, 40 -4, 5 0 8, -50 - I , x 10, x -10, x -I, x 10, x -a, x Literature + Remarks 5 24 9 7 f 7 f 7 f 13; I*, 2** I 3 I3 13; 2** I3 I3 I * .z * . x = bad fit, bad pattern. ds = short face-diagonal, dl = long face-diagonal. TABLE IV RECORDED CASES OF ORIENTED OVERGROWTH FOR WHICH DETAILS ARE LACKING Oriented overgrowth in the following cases has also been established : Royer C NH,C1, NH,Br, LiNO,, KNOs, K,Zn(CN) ,, K,Cd(CN) ,, KPF6, RbPF6, CsPF,, NH,PF, on mica. Willems * A A. Organic compounds on organic compounds. Pentachlorphenol, aniline, pentabromphenol and anthracene on (001) of chloranil.8 z P-naphthol, P-naphthylamine, benzidine, anthracene, phenanthrene, fluorene, pyrene in molecular compound with hexachlornaphthoquinone on hexa- chlornaphthoquinone (unpublished).Coronene (uncertain whether in compound with picric acid) on (010) of picric acid.8 g Anthracene on (010) of aminophenol.8i 3-hydroxypyrene, p-nitrophenol, pentachlorphenol on ( I 10) of urea, and pentachlorphenol on (010) of dioxopiperazine. 8 i Organic compounds on metallic salts (and hydrates of metallic salts). Succinic acid, p-aminobenzoic acid, pentachlorbenzoic acid on (roo) of alkali halides, e.g., NaC1.8i Hexamethylenetetramine on (010) of gypsum.Sg,d Pentachlorphenol, pentabromphenol on (100) of alkali halides. i a-hydroquinone, P-hydroxydiphenyl, p,P’-dihydroxydiphenyl, 3-hydroxy- pyrene, pentachlorphenol on (100) of the carbonates of the calcspar series and NaNO,.sb,f> k a-hydroquinone and pentachlorphenol on a series of micas.Pentachlorphenol on (001) of Pennin and on KC103, gypsum, anhydrite, bournonite. * i B.214 MONOLAYERS AND ORIENTED OVERGROWTH Neuhaus 7 g A. Planar-shaped molecules (organic overgrowths) . 5 : 7-dibrom-8-hydroxyquinoline on NaCl, baryte, calcite, mica, fluorite, PbS. Sb,S,. I I " I-, 4 : I-, 5 : 2-, 7-dihydroxynaphthalene on (001) of NaCl (with needle- axis parallel to [IIO] of NaCl and on (1011) of NaNO,. P-naphthoquinone on NaC1, baryte, XaNO,, Sb,S,, PbS. Succinic anhydride on NaCl, XaNO,, ZnS. I : 4-hydroxyquinone, I-nitronaphthalene, 3-methylindol, isatin, fluorescein, benzoquinone, hexachlorbenzene on sucrose. C, k B. Linear-shaped molecules (organic overgrowths) . p-arninophenol on NaC1, baryte, mica, NaNO,.p-aminobenzoic acid on NaCl, KCl. 9-nitrobenzoic acid on mica, ZnS. m-nitro-o-chlorobenzoic acid on NaC1, PbS, NaNO,. m-phenylene diamine on NaCl, KC1, CaCO,, NaNO,. p-nitrophenol, 9-aminobenzoic acid, p-succinic acid, I-hydroxyanthracene on sucrose. According to the author corresponding planes contained a set of atomic rows of closest packing (misfit 3 yo) together with another set of less close packing (misfit 10 yo). Binding is due to dipoles, which orientates in general perpen- dicular to the substrate. Neuhaus 7: Methyl Red, p-amino-, nz-, o-methylazobenzene ; I : z : 4-triamino-anthra- quinone ; I : z-diamino-anthraquinone ; methylamjno-anthraquinone, pron- tosil rubrum and helianthin on (100) meconic acid. Prontosil rubrum, Methyl Red, $-amino-, m-, o-methylazobenzol on (010) of phthalic acid. (He established that the " built-in " mixed crystals, which tend to form with same partners, had the same orientation as the oriented overgrowth.) 17Wilman, Proc. Physic. SOC., 1940, 52, 323. 18 Cochrane, PYOG. Physic. SOG,, 1936, 48, 723. 19 Mehl, McCandles and Rhines, Nature, (a) 1934, 134, 1009 ; (b) 1936, 137, 702. 2 0 Thessen and Schutza, 2. anorg. Chem., 1937, 233, 35. g1 Frisby, Comfit. rend., 1947, 224, 1003. 22 Usmani, Phil. Mug.. 1941, 32, 89. 23 Yamaguti, PTOG. Physic. Math. SOL, Japan, (a) 1935, 17, 443; (b) 1938, 20, 230. z 4 Fordham and Kalsa, J . Chem. SOC., 1939, 406. 25 Tiapkina and Dankov, Comfit. rend., U.S.S.R., 1946, 54, 41 j. z 6 Schwab, (a) 2. fihysik. Chem. B, 1942, 51, 245 ; Trans. Faraduy Soc., (c) 1947, 43, 715 : ( d ) 1947, 43, 724. 27 Thirsk and Whitmore, Trans. Faraday SOG., 1940, 36, 565. 28 Finch, J . Chem. SOL, 1938, 1137. 2 9 Bum, Proc. Roy. SOC. A , 1933, 141, 567. 30West, J. 09t. SOC. Amer., 1945, 35, 26. Buckley, 2. Krist., 1937, 97, 370. 32 Spangenberg and Neuhaus, Chem. Erde, 1930, 5, 437. ss Krastanow and Stranski, 2. Krist., 1939, gg, 444. 3 4 Shirai, Proc. Physic. Math. SOC., Japa.iz, (u) 1937, 19, 937 ; ( b ) 1938, 20, 8j j ; (6) 1939, 36 Uyeda, Proc. Physic. Math. SOL, Japan, (a) 1938, 20, 656 ; (b) 1940, 22, 1023. 36 Riidiger, Ann. Physzk, 1937, 30 (5), 505. (b) Kolloid-Z., 1942, 101, 204; 21, 800 ; ( d ) 1941, 23, 12.

ISSN:0366-9033    

DOI:10.1039/DF9490500201

出版商:RSC    

年代:1949

数据来源: RSC

摘要:

ORIENTED ARRANGEMENTS OF THIN ALUMINIUM FILMS FORMED ON IONIC SUBSTRATES BY T. N. RHODIN JR. Methods Principles and Data Received 1st February 1949 There can be two types of films on solids those which are stable in mono- layers and those which tend to aggregate into three-dimensional structures. A great number of metal films formed by condensation on to a solid base are unstable in the sense that they will aggregate into crystals providing the atoms possess sufficient surface mobility. The crystalline structure of the film is strongly influenced by the base in many systems and in some cases a single orientation prevails when the force fields around the atoms in the supporting crystal are sufficiently strong.1 Relatively little is available in the literature about the nature of these forces and the role they play in promoting a preferred orientation of the atoms arriving at the substrate surface.An understanding of their periodicity and magnitude relative to the surface forces characteristic of the film itself should provide insight into the critical dependence of film orientation on the nature and temperature of the substrate. In addition this effect may be very useful in preparing samples for surface studies. The study of the physical and chemical characteristics of pure metal surfaces has been severely handicapped by the presence of strongly adherent foreign films. Furthermore the randomness of the surface orientation has obscured interpretation of experimental results. Evaporation of metals in high vacuum on to carefully selected substrates under ideal conditions for preferred orientation appears suited to the preparation of flat oxide-free oriented films for surface reaction studies.Many factors influence their structure and some understanding of the mechanism of their formation is a necessary prerequisite for obtaining satisfactory surfaces for study. The dominant factors in defining film structure are film thickness and growth rate and the nature condition and temperature of the substrate. Experimental Procedure GENERAL ASSEMBLY.-The system was enclosed in an 18-in. bell- jar which rested on an L-shaped neoprene gasket on a ground steel plate as indicated in Fig. I. Rapid evacuation of the system to I O - ~ mm. mercury was facilitated by a 4-in.manifold 2-in. packless valve and an extra large diffusion pump. Suitable arrangement of valves on a secondary manifold permitted one to introduce purified gases readily into the chamber. Outgassing of the entire internal surface in a glow discharge was greatly expedited by a 5000 V copper cathode mounted at the top of the bell-jar. The entire frame was carefnlly shock-mounted to isolate the microbalance from building vibration. The lead-ins for control and power were situated in the steel base. Pressures from 10 to I O - ~ mm. mercury could be measured and temperatures of the substrate and crucible couId be independently controlled and measured. Atmosphere pressure seated the bell-jar hard on the gasket when the latter was evacuated. When i t was filled with dry nitrogen at one atmosphere it could be readily elevated out of reach.FORMATION OF THE FILM.-The film was produced by evaporating high purity (99.99 ?(,) aluminium from a microcrucible in a good vacuum ( I O - ~ mm.) and 1 Barrett Structure of Metals-Crystallographic (McGraw-Hill New York 1g43) p. 441. 215 216 THIN ALUMINIUM FILMS ON IONIC SUBSTRATES condensing it on an independently heated substrate. With a suitable slit system a uniform concentrated direct molecular beam resulted. The arrangement of the source slits and substrate is indicated by items 2 and I in Fig. I. The substrate (item I) was mounted 25 mm. above the source in a copper frame which held i t in place against an externally heated copper block. In this manner the lower face was exposed to the beam and maintained a t the desired temperature by heating from the upper face.The temperature was regulated to I yo by a proportionating potentiometer controller. The substrate consisted of a square plate of an ionic salt approximately 5 mm. on the side and I mm. thick. A freshly cleaved face was exposed just prior to a run. A thermocouple probe in contact with the lower face of the substrate indicated the film temperatures. Two additional platinum probes 2-0 mm. apart were in contact with the surface. The appearance of the first few layers of the film was indicated by the sudden decrease in resistance measured between the probes. FIG. 1.-Vacuum evaporator (I) Substrate ; (2) Molecular beam source ; (3) Furnace (4) 18-in.glass bell-jar ; (5) Right-angle neoprene gasket ; (6) Polished steel plate ; (7) High-voltage cathode-5000 V ; (8) 4-in. packless valve ; (9) 2-in. packless valve ; (10) Manifold ; (11) Purified gases ; (12) Holding pumps ; (13) High-capacity diffusion pump ; (14) Shock mount ; (15) 200-lb. weights ; (I 6) Thermocouple pressure gauge ; ( I 7) Ionization gauge ; (18) Temperature controller ; (19) Electronic heater ; (20) Electrical ground. The source (item 2) of the beam was a small tantalum crucible located directly below the substrate. The microcrucible held a charge of IOO mg. The inside diameter of the crucible was 3 mm. but the beam was actually emitted through a 0.1 mm. orifice in a tantalum cap placed over the top of the microcrucible.The cap prevented splattering and also promoted thermal equilibrium of the atoms before they were emitted. The charge was outgassed by prefusing in sitzt before evaporating during which time the substrate was protected by an externally manipulated shield. The heating of the crucible was very satisfactorily effected by an arrangement for direct electron heating indicated in Fig. 2 . The crucible is shown with the lid off as item I. Electrons emitted from an incandescent 30 mil. tungsten filament T. N. RHODIN (7) Stainless steel ; (8) Mykroy spacer ; (9) Filament electrodes. 217 (item 2) around the crucible are accelerated by a positive potential towards it. A tantalum shield (item 3) around the assembly reduced heat losses and another tantalum lid (item 4) shielded the substrate from direct exposure to the filament.The temperature of the microcrucible could be accurately adjusted and main- tained a t any temperature up to 1 5 0 0 ~ C within 2-3 yo by regulating the filament emission and the accelerating potential. This high fidelity temperature control is necessary in the determination of the substrate temperature-condensation pressure relationship for various substrates. The substrate was tied in at the same potential as the crucible to eliminate the possibility that metal ions formed in or around the crucible may be spuriously accelerated towards the substrate. FIG. 2.-Electronic heater (I) Tantalum crucible ; (2) Tungsten filament ; ( 3 ) Tantalum shield ; (4) Tantalum lid ; ( 5 ) Nickel leads ; (6) Crucible electrode ; In the measurement of critical condensation pressures the crucible tem- perature was slowly increased until the rate of evaporation of the aluminium was just enough to cause condensation on the substrate for a given base tem- perature.The rapid decrease in the film resistance between the probes was used to indicate the formation of the initial layer. The process was reversible that is a small increase in base temperature for a critical pressure caused the film to evaporate. The microcrucible could be readily removed from the crucible electrode (item 6) for replacement and the position could be easily lined up by adjusting the eccentric a t the base. The crucible temperature was measured by a Chromel-Alumel thermocouple mounted in the bottom.218 THIN ALUMINIUM FILMS ON IONIC SUBSTRATES RATE OF CoNDENsATIoN.-The condensation rate for a given crucible and sub- strate temperature was determined by weighing in situ a thin glass slide hanging on a quartz fibre over the molecular beam as indicated in Fig. 3. A sensitive quartz torsion microbalance facilitated accurate and quick measurements in vacuum. The torsion fibre was rotated by magnetic coupling through the glass wall. The sensitivity of the weighing was I O - ~ g. with a 23 mp quartz torsion fibre (item 5 ) . The thickness corresponding to weight increments was calculated for a constant area assuming the film to be flat and continuous and the film density to be comparable to the mass density. A microgram corre- sponding to a hundred Angstroms thick layer of aluminium for the film was used.The condensation rates for various substrate and crucible temperatures were calibrated in this manner. FIG. 3.-Quartz torsion microbalance (I) Bow fibre ; (2) Static; (3) %am; (4) Hang-up ; ( 5 ) Torsion fibre; (6) Hang-down; (7) Image of index; (8) Graduated wheel ; (9) Single field image ; (10) Substrate ; (I I) Molecular beam ; (12) Collimating slit ; (13) Source. EXAMINATION OF THE FILM MetuZZogruphy.-Upon completion of the run the substrate was cooled in situ and removed for examination. Reflectivity of the surface varied from very mirror-like to cloudy as the film thickness and substrate temperature increased. Metallographic examination of the samples was con- siderably hampered by their fragility.Where i t was possible to observe grains without destroying the film the average grain size was two to five thousand Angstroms for a film of the same thickness. Structure Determinatioa.-The film structure was determined with X-ray diffraction using a surface reflection pinhole technique in a vacuum camera as indicated in Fig. 4. A Picker-Waite diffraction unit was used with a water- cooled chromium target. The exposure time varied from 2 to 15 hr. for film thicknesses from 5000 to 500 A with an accelerating potential of 50 kV and a space current of 10 mA. The sample (item 6) was anchored flat on the turntable (item 7) and rotated around an axis (item 19) normal to the surface of the sample. The axis of rotation was inclined away from the incident beam an amount corresponding to the Bragg angle for reflection from the plane of preferred orientation.The camera was particularly designed to suit the geometry and orientation unique to the samples studied. The simplicity of the film patterns indicated in Fig. 5 a and Fig. 5 b clearly show the advantage obtained. Preferred orientation is characterized by segmentation of the lines into local marks as shown by the heavy marks of five degrees length on the dashed reflection lines in Fig. 5 b . The vertical distance from the centre line measures the orientation azimuths T. N. RHODIN * where cos p = cos p sin 0 + sin p cos 0 cos 'p p = angle between oriented plane and reflecting plane 0 = Bragg angle for reflection from reflecting plane 'p = orientation azimuth for oriented plane.2=9 characteristic of a preferred orientation. The value of the Orientation azirnnths (9) can be calculated for any preferred orientation.2 (1) p = angle between normal to oriented plane and incident beam Some values of cp calculated for reflection of K and Kp chromium radiation from the (III) (zoo) and (311) planes of aluminium for (111) (100) or (110) FIG. 4.-X-ray vacuum camera (I) End plates ; (2) Film case ; (3) Entrance beam ; (4) Beryllium window ; (5) Pinholes ; (6) Specimen ; (7) Lucite spacer ; (8) Lock- n u t ; (9) Rotor assembly ; (10) Drive-wheel shaft; (11) Rotor vacuum seal; (12) Lead-glass window; (13) Vacuum outlet; (14) Plate nuts; (15) Motor; (16) Track clamp (17) Exit beam; (IS) Neoprene gaskets; (19) Axis of specimen rotation.I00 Axis of Spectrnen Rotation \ 29 7 5 50 25 -& 50 251 0 75 Cones of reflection from low indce plones (4 100 - Pottern of (111) Fibre mis oriented within? five degrees. b'l - - FIG. 5.-Diagram of X-ray pattern from oriented film. 2 Barrett Sfructure of Metals-Crystallo~~uphic Methods Principles am? Data (McGra~-Hill New York 1943) p. 156. THIN ALUMINIUM FILMS ON IONIC SUBSTRATES TABLE I BRAGG ANGLES AND ORIENTATION AZIMUTHS CHROMIUM RADIATION ON ALUMINIUM Plane Orientation Azimuths ( y Angle 220 orientation are listed in Table I. The kind of orientation can be readily deter- mined from the pattern defined by the characteristic values of 9.A semi- quantitative value for the degree of orientation with a maximum error of 10 yo in this determination can be obtained by measuring the opaqueness of the spot relative to the integrated opaqueness of the whole line with a Leeds and Northrup recording microphotometer. The error is introduced by the assumption that the intensity at any one spot on the film is linearly proportional to the amount of radiation reflected to that point and is the same for all azimuth angles. Radiation CrK (110) 0 83 0 80 29'5 26.8 34'7 3 1-0 68 65 64 62 0 119 0 I11 82 68 89 63 52 95 58,142 54'4 47'0 70.0 59'2 50 Results Orientation Results GENERAL.-A quantitative dependence of degree of preferred orientation on film thickness and substrate temperatures was found over a considerable range of thickness and temperature for eleven aluminium- substrate pairs.It was necessary however to make a preliminary evaluation of four other factors sufficiently well so as to minimize their influence. The pertinent results of the preliminary survey is herewith presented in condensed form as a background against which the significance of the quantitative aspects can be more intelligently considered. Film Growth Rate.-Foremost is the important influence of film growth rate on structure. Since the experimental system was not propitiously suited for studying this aspect it was maintained a t a constant value in all experiments. The evaporation rate was adjusted for each substrate temperature corresponding to an effective film growth rate of ten to thirty monolayers of aluminium per second.In the case of the binding energy determinations however the film growth rate was not controlled since it was only desired to determine the condition for minimum condensation. Heat Treatment.-Heat treating of the substrates with or without adherent metal film caused no striking change in the resulting orientation. The films were therefore usually kept a t constant temperature during formation and then permitted to cool by radiation in a vacuum. Annealing a randomly oriented film at elevated temperatures (up to 600° C) in helium resulted only in grain growth. Likewise oriented structures were not markedly altered by annealing under similar conditions.This temperature stability of the structure is in con- trast to the temperature sensitive orientations of thinner aluminium films (400 A) previously reported .3 Gas Atmosflhere Eflects.-The influence of gases present even a t I O - ~ mm. pressure was also considered. The pressure of purified quantities of helium oxygen nitrogen and hydrogen a t low pressures ( I O - ~ mm.) decreased the orientation to a relatively small extent. The effect was not unique to any one gas or substrate and appeared solely to hamper the steady evolution of aluminium Dixit Phil. Mag. 1933 16 1049. T. N. RHODIN 221 vapour. In no case mas a gas such as helium observed to improve the film orientation as reported by others for thinner films.* Substrate Condition.-The contamination of the substrate surface itself by the gases previously listed was not considered to be critical.Oriented films could be formed on freshly cleaved rocksalt which had been preheated in oxygen and hydrogen atmospheres. In all cases however the cleanliness of the sub- strate was a critical requirement and best results were always obtained with freshly cleaved ionic surfaces whose lattices had an arrangement of ions the geometry and dimensions of which showed a certain correlation to that of aluminium. The limited number of such salts emphasized the preparation of oriented substrates by other means. Even after repeated polishing etching and annealing use of NaCl and LiF surfaces obtained in this manner was only moderately successful.Successful techniques for exposing any desired sub- strate orientation in a suitably clean and flat condition would be most useful for further studies. 5 4 3 4 3 3 2 I BASE TEMPERATURE IN HUNDREDS OF DEGREES CENTIGRADE I00 - 5 4 m o x 103 FIG. 6.-Approximate film thicknesses in %ngstroms. Orientation of aluminium film deposited on cleavage face of sodium chloride. Each column indicates I 2 5 x 103 average values for four samples. Dev. f 10 %. SPECIFIC FACTORS FzErn Thickness.-Initial studies made it evident that degree of orientation was very dependent on film thickness for all film-substrate pairs. This characteristic will be described first since it depended only on temperature and film thickness and was general to all substrates.The %-orienta- tion for films on the (100) face of rocksalt for various thicknesses and base temperatures is plotted in Fig. 6 as an illustration. An exponential dependence of orientation on film thickness was observed and the data plotted in Fig. 7 is a typical case. It is interesting to note that a critical film thickness for perfect orientation at each temperature is suggested by extrapolation of the straight line to small film thicknesses. A striking temperature dependence is also indicated by the distinctly small slope of Curve 2 compared to Curve 3 in Fig. 7. The validity of a strong base temperature dependence of %-orientation is also indicated in Fig. 8 for a variety of film-substrate pairs. Discussion of the temperature dependence is however temporarily postponed until right after the discussion of the thickness effect.4 Beeck Smith and Wheeler Proc. Roy. Soc. A . 1940 62 177. 222 y 10‘ I- - THIN ALUMINIUM FILMS ON IONIC SUBSTRATES I 0’ A E fn MI C K N E SSSR IE N TAT1 ON 1 @ 200oc i @ 4OOOC c tl .z tn 0 I I J LL lo3 lo2 10 I o6 lo5 I I a 300% --y ,5000c ,ir 20 300 I i 103 60 40 80 ! W a I Glass Slide I 700 FIG. ./.-Per cent. orientation. ORIEr*;TtlTl@N AND SUBSTRATE TEMPERATURE 500 -I- 0 FIG. &-Substrate temperature-centigrade. - __- Binding Enrrqy 600 8 33 T. N. RHODIN t T 0 where 223 The thickness dependence may mean that the oriented arrangement is constant at all points in the film and merely decreases as the film thickens.It seems more reasonable to assume that the orientation is strongly dependent on the substrate and produces an orientation large at the inner film surface and decreasing towards the outer film surface. The latter possibility is in agreement with the surface reflection characteristics of X-rays. In this case a disproportionately large fraction of the radiation producing the pinhole pattern is reflected from the outer planes of the film. A quantitative illustration of this can be presented by calculating the intensity of radiation reflected from successive layers of metal atoms as follows.5 The intensity (It) reflected from a thickness ( t ) relative to the intensity ( I d ) reflected from an infinitely thick film can be expressed I d td 6 I 1 ' 9 24 25 depth of penetration (A) ; column 2 thickness penetrated relative to limit- ing thickness; and column 3 the corresponding O/,-intensity for that 5 x I02 5 x 103 5 x IO* 53 6 Hess (Institute for the Study of Metals) (private communication to the author).THIN ALUMINIUM FILMS ON IONIC SUBSTRATES TABLE I11 STRUCTURE CHARACTERISTICS O F THIN ALUMINIUM FILMS Pressurt Ec Temp. Orient. kc.lm. kc./m. Orient. kc./m. kc./m. cm.Hg. " C A - A 22 x 104 0-007 A 42 28 I 8 % 87 75 80 1'52 0.003 31 2 1 16 I1 13 50 55 22 20 I8 I2 I0 I 0 I 0 0.024 0'022 0'0 I2 0'0 I2 224 the orientation of the outer surface was essentially observed.The orientation is greatest in the region nearest to the substrate-film interface. Szrbstrnte Tem@mztztre .-A base temperature dependence in which orientation of the film increased rapidly a t some characteristic temperature for each sub- strate illustrated in Fig. 8 was typical of all substrates. The less the maximum orientation however the smaller the dependence on the characteristic tem- perature This is illustrated by the contrast in the curves for (100) orientation on rocksalt and glass. The temperature dependence may mean that the metal atoms must possess a minimum kinetic energy corresponding to the observed temperature for maximum orientation for them to take up the preferred positions suggested by the substrate.The transition of a (110) orientation of the film on mica at low temperatures to a (111) orientation at higher temperatures indi- cates that a higher minimum mobility is required for formation of the second configuration. In all cases the rate at which orientation increased with base temperature as well as the maximum value i t approached was typical of the substrate. I t indicates that production of ordered arrangements is governed not only by the interaction of the substrate and metal but by a relatively slow temperature-dependent surface diffusion process as well. Calculation of activa- tion energies for the rate process involved seems premature until the mechanism of arrangement is better defined. The characteristic values of base temperature and maximum observed orientation are plotted in Fig.8 for rocksalt mica and glass and listed for eleven substrates in columns z and 4 of Table 111. Substrate Mica . . Mica . . NaCl NaCl LiF LiF CaCO Glass . . A 20 I 0 I5 I 0 20 15 20 I5 20 20 20 . . CaF . . ZnS Sodalite 33 25 25 I5 20 21 2 1 50 I5 I 0 I 0 I 0 I 0 5 0 0 I I - 5 2 4 2 6000 760 700 700 Experimental data for mica in the temperature region intermediate between the (110) and (111) orientations were inconclusive. I t is noteworthy that the most oriented configurations corresponded to the higher orientation temperatures. This characteristic is a general one for all the substrates studied.It is illus- trated by the dashed curve in Fig. 8 in which the orientation temperature as abscissa is plotted against the substrate binding energy as ordinate on the right. The substrate binding energy heretofore undefined is described in a subsequent section and shown to be proportional to the percentage of the observed film orientation. Nature of Substrate.-From the facts presented so far it seems clear that the nature and degree of the observed orientation was critically dependent on the This dependence held in general for all the substrates studied. In substrate. every case there was a correlation of some kind between the geometry and dimensions of the underlying lattice and that plane of aluminium preferentially oriented parallel to it.For example the (100) face of aluminium was the only orientation observed on the (100) face of the alkali halide substrates. Similarly the (111) planes of aluminium tended to be preferentially oriented parallel to substrates with hexagonal cleavage or hexagonal-polished faces providing the base temperature and film thickness were favourable. In other cases (110) ( b ) Aluminium on (TOO) sodium chloride 80 yo (100) orientation ( a ) Aluminium on glass random orientation. 104 A thick. 1-2 x 103 A thick. (c) Aluminium on (111) mica 87 ”/ (111) orientation. 1.3 x 1 0 3 1 ( d ) Aluminium on glass 10 yo (100) orientation. 103 A thick. thick. FIG. 9. To face page 2253 T. N. RHODIN I FIG. 10.-Aluminium unit cell.Discussion 225 orientation was observed to occur on (110) oriented substrates. This is not a general effect however since cases occur where substrates stabilize preferred film orientations other than their own but in most cases that orientation of aluminium occurred for which the geometry and spacing of the metal atoms yielded the best fit on the substrate. The data are summarized in columns I 2 3 4 of Table I11 in order of decreasing orientation. The direction of orientation in the film listed in the third column is the same as that of the substrate for the first seven items. A small orientation was observed on glass which of course possesses no definable surface arrangement. The small degree of orientation on fluorite was barely measurable.The (111) orientation on zinc blende and sodalite was also very small. The last two substrates possess cubic lattices with good (I 10) cleavage faces and are examples of film o ientation differing from that of the substrate. Some typical surface reflection X-ray film patterns are illustrated in Fig. 9. The interpretation is handicapped by the poor contrast of the aluminium lines the strong and complex pattern caused by reflection from the substrate and the poor reproduction but the over-all pattern analysis is quantitatively unique for each orientation. Continuous reflection from all the low indice reflection planes indicate complete randomness in Fig. g a. The sharply defined orientation of a (100) aluminium film on rocksalt is illustrated in Fig.9 b. Fig. g G is greatly complicated by the mica pattern but arrows indicate the discrete aluminium reflections corresponding to (I I I) orientation. A poorly oriented film on glass tending towards (100) orientation is included for comparison (Fig. g d). Geometric Considerations.-The good correlation between substrate and film orientation is in accord with the excellent matching between the oriented aluminium plane and the geometry and dimensions of the surface lattice upon which it forms. Similar results have been reported for thinner films.6 The striking geometric kinship among the three low indice planar arrangements (IOO) (IIO) (111) of aluminium in Fig. 10 and the geometry of the corresponding planes in sodium chloride and lithium fluoride in Fig.II suggests that such correspondence between film and substrate pro- motes a related orientation in the former. This hypothesis is suggested by the Bruck Ann. Physik 1936 26 233. Rudiger Ann. PhysiR 1937 30 505. Finch Quarrel1 and Wilman Trans. Faraday SOC. 1935 31 1051. H 226 THIN ALUMINIUM FILMS ON IONIC SUBSTRATES Table of lattice distances summarized in Fig. 11. They agree within a few yo in each case except for the (111) sodium chloride face for which the lattice spacing is 40 yo greater than the corresponding spacing in the (111) aluminium plane. It is doubtful whether this correlation is generally essential for substrate-metal interaction but it is significant that no (111) orientation of aluminium was ever observed on a (111) sodium chloride surface.Corre- sponding orientations were observed in every other case. @CATION Lattice parameters (A) NaCl 0 ANION FIG. I I .-Unit cell of alkali halide. A1 (110) c 4-04 . . 3.98 . . 4-01 I.iF (roo) a . . 2-85 . . 2.83 . . 2-84 (111) b 2-85 . . 3-98 . . 2-84 Substrates with hexagonal cleavage faces of atomic dimensions corre- sponding to the (111) face of aluminium yielded (111) oriented aluminium films. The fairly complicated surface structure of mica accommodated (110) arrangement of aluminium as well. The arrangement of the atoms in the hexagonal cleavage faces of mica calcite and fluorite are drawn to scale in Fig. 12. The matching of lattice distances was poorer than for the cubic face cleavage substrates and the observed degree of orientation was also correspondingly poorer with the exception of mica.The (110) cleavage faces of cubic zinc blende and sodalite are not indicated but the matching was relatively poor for both substrates and they are unsatisfactory as (110) directing surfaces. In all cases studied the nature and degree of the observed film orientation bore a close relationship to the geometry and dimensions of the underlying substrate. It appears that directing forces are geometrically distributed on the substrate surfaces in close correspondence to the atomic distribution in the substrate plane. An interpretation based on this approach will be discussed in the next section. T. N. RHODIN 227 Characterization of Substrate.-In an effort to characterize the substrates an effect discovered by Wood and studied by Estermann,* was used in a modified form.When a beam of metal vapour is directed at a heated substrate condensation will occur if the pressure is sufficiently high or the substrate temperature sufficiently low. Whether most of the atoms bounce off the surface losing none or relatively little of their kinetic energy or whether they are accommodated on the surface depends on the relative values of the aforementioned variables plus a third the attraction of the substrate for the metal atoms. Since the relationship between these factors can be quantitatively expressed the attraction of the substrate may be determined providing the corresponding pressures and base temperatures can be measured. This pressure-temperature dependence was determined for all the substrate-metal pairs at those substrate temperatures at which maximum orientation was known to occur in each case.The substrate temperature was measured with a thermocouple probe on the surface. The metal pressure was not measured directly but calculated from the crucible where FIG. 12.-Crystal substrates with hexagonal cleavage. temperature using the free energy of vaporization values for aluminium.9 The minimum vapour pressure was accurately determined for each base temperature at which condensation of the first layers took place. The formation of the first layer was indicated by measuring the sudden drop in film resistance between two probes on the surface. The corresponding values of pressure and base temperature for a group of typical runs are plotted in Fig.13. The pressure-temperature relationship can be expressed as $I = pressure of metal vapour a = constant insensitive to temperature T = absolute temperature of the substrate A = an energy term characteristic of the film and the substrate. 7 Wood Phil. Mag. 1916 32 (6) 365. 8 Estermann 2. Elektrochem. 1926 31 441. 9 Kelley The Free Energies of Vaporization and Vapour Pressures of Inorganic Substances (Bulletin 383 Bureau of Mines 1935). 228 THIN ALUMINIUM FILMS ON IONIC SUBSTRATES The values of a could be interpolated from the intercept on the pressure axis of the curves plotted in Fig. 13. It is insensitive to the nature of the substrate and to the base temperature for the conditions observed.Hence it was of little use for characterizing the substrates on a relative basis. It however includes at least three significant terms describing (a) geometry of the system (b) size of the condensing particles (c) a linear temperature correction. Hence an interpretation of the mechanism of condensation would eventually require an analysis of a into its component terms . 6 .f W E 0 I- LL. 0 W a v W 3 v) a P 0 0 1 The values of A could be readily interpolated from the slopes of the straight lines plotted in Fig. 13. Some typical values are listed there in order of decreasing magnitude. Corresponding values of temperature pressure and A are more completely listed in columns 2 5 and 6 of Table 111.A definite trend of A in Table I11 from 42 kc./m. to 20 kc./m. is evident. This trend corresponds to decreasing observed orientation. It is significant that the values of A are smallest for the ionic substrates at the end of the Table for which the orientation was poorer. The smaller surface-free energy of the (111) arrangement corresponds to the observation that the A values for (111) substrate-film orientations are somewhat greater than those for (110) and (100) orientations for each substrate-metal pair. An interpretation of A as describing the heat of condensation of the FIG. 13. I/T x 103 degrees (absolute). 229 T. N. RHODIN first layer of metal atoms on the substrate is indicated by the temperature- dependence relationship established by the straight lines in Fig.13 and by the empirical findings of Wood and Estermann. A theoretical analysis of their work by Semenoff l o applied to these results indicates that where - (5) E = the adhesive energy of binding of the metal and substrate A = the energy of binding of the aluminium atoms in the first layer eg. the surface energy characteristic of the metal film itself. If the first term is large the substrate is likely to influence strongly the A = E + A formation and arrangement of the atoms in the first layer providing the atoms possess sufficient mobility to assume those positions on the surface of lowest potential energy. If it is small relative to the second term that is the adhesive forces between metal and substrate are negligible compared to the cohesive binding between metal atoms the film formation will be relatively independent of the substrate and should any orientation occur it will be that arrangement for which the surface-free energy is smallest.Formation of an oriented first layer under the first condition would facilitate the occurrence of the same orientation for subsequent layers. The degree of observed orientation should increase with the value of E providing other factors are also favourable e.g. mobile atoms and relatively thin films. Formation of an oriented layer under the second condition may also occur but the degree of orientation will likely be considerably less. I t is note- worthy that the values of A varied from 42 kc./m. for aluminium on mica to 15 kc./m.for aluminium on glass (column 6 Table 111). In the latter case one might consider the interaction between the glass and the metal to exert a relatively small influence on the film structure and the measured heat of condensation to correspond mainly to the cohesive forces in the (100) plane of aluminium. Since there are about one-third the number of bonds in this configuration compared to that of massive aluminium the surface energy can be roughly approximated to be one-third of the molar heat of vaporization or 22 kc./m. For this crude approximation the order of magnitude agrees with the experimentally determined value measured on an amorphous substance like glass. Neglecting the entropy correction the substrate binding energy for the other substrate-metal pairs may be similarly approximated by subtracting an energy A corre- sponding to the cohesive binding energy of the film from A the total energy of condensation.In view of the assumptions involved the values obtained are speculative but the resulting values (E) listed in column 8 of Table I11 are of the right order of magnitude. These approximations compare favourably with values calculated on the same basis as van der Waals’ inter- action. The trend of the experimental values of E is in qualitative accord with the trend of observed orientations for each metal-substrate pair. This is indicated by the data on the maximum orientation and the substrate binding energies listed in columns 4 and 8 in Table 111. The correlation is also evident in Fig.14 in which the maximum observed orientation is plotted as ordinate against the substrate binding energy as abscissa. The calculated values included for comparison are now discussed. Van der Waals’ 1nteraction.-Understanding of the binding between a metal and an ionic surface would provide considerable insight as to the nature of the metal-substrate interaction. A rigorous attempt to define the binding is well beyond the scope of this paper but some speculation in this direction seems justified. The characteristic of the binding namely 10 Semenoff 2. physik. Claem. B 1930 7 471. THIN ALUMINIUM FILMS ON IONIC SUBSTRATES 230 its relative magnitude and non-specificness suggests the validity of an approach based on van der Waals’ interaction between the first layer of metal and the substrate.An analysis similar to a certain extent to the calculation of heats of adsorption of gases physically adsorbed on ionic surfaces near the boiling point of the gas seems justified. I t is obvious that the chief distinguishing characteristic between metal and physically adsorbed gas films other than the different temperature range in which they form is the marked importance of the cohesive forces in the former case. It is conceivable nevertheless that a strong periodicity in the potential energy surface of the substrate towards the metal atom may be sufficient to start the condensation in a favoured direction. The energy of van der Waals’ binding of aluminium on each of the substrates was calculated on this basis.Q [IiO] Li I Experimrntol (A-A) Substrate binding energy (kc./m.). FIG r+-Substrate orientation. Van der Waals’ interaction between non-polar molecules has three important constituent parts (I) the attraction between fluctuating dipole and induced dipole (dispersion effect) varying inversely as the sixth power of the distance (2) the attraction between fluctuating quadruple and induced dipole varying inversely as the eighth power of the distance and (3) the repulsion energy decreasing exponentially with the distance. A fourth con- stituent part is unique to ionic surfaces the so-called influence effect. The latter is due to the fact that the charged ions of the substrate induce a dipole moment in the metal atom which results in an attraction between the ions and the induced dipole.At the equilibrium distances characteristic of the metal films the first of the four terms is by far the most important. The calculations were made on an approach similar to 0rr1l in which he calculated heats of physical adsorption of argon on potassium chloride. l1 Orr Trans. Faraday SOC. 1939 35 1247. T. N. RHODIN and an ion of the substrate can be written where 231 The dispersion effect was introduced by London l2 in the calculation of heats of adsorption. The dispersion potential cp between an atom of metal (6) where Y is the equilibrium distance and C the dispersion constant is given by (9) ’ (10) ‘p = - c p . a’ polarizability < = = characteristic of energy the ion of the metal a = polarizability of the metal J = characteristic energy of the ion.The interaction between an atom and the entire surface of the substrate can be very simply calculated if one assumes that the distance between atom and ion is not smaller than the distance between ions. In this case the summation over the ions of the substrate can be replaced by an integration. For alkali halide substrates this approximation will yield values that are too low by 25 yo to 30 yo. For the mutual dispersion energy of an infinitely large surface and an isolated atom where N = number of ions per ~ m . ~ and dv is the volume element. Sub- stituting expression (6) for the dispersion constant JJ’ Nx uu’ 9=---- 4 9 J+J” An exact evaluation from eqn.(8) is not possible because some of the experi- mental data are missing particularly the value of J for aluminium. Never- theless to show the order of magnitude calculations were made using the first ionization potential. The value of N for the substrates other than the alkali halides was calculated from the density. The distance r between an ion and an aluminium atom was assumed to be made up of two parts after London,13 viz. + d2f2 . . r = For d l / z half the distance between ions in the substrate was used and for d,/2 half the interplanar distance for that plane of aluminium observed to be preferentially oriented. The identity and geometry of the important ions in the substrate were not always definitely established and a choice had to be made in some cases.The ion was chosen whose arrangement on the surface best fitted the observed aluminium orientation. For example the oxygen ions were chosen instead of the silicon ions in mica. The calculated binding energy for both is listed in Table IV for comparison. The atomic polarizabilities were taken from Van Vleck l4 if possible or calculated from where v is the characteristic frequency of the atom and the other symbols have the customary significance. The polarizability and characteristic energies l a London 2. physik. Chew. B 1930 11 222. l3 London 2. physik. Chew. B 1930 11 222. 1 4 Van Vleck EZectric and Magnetic Susceptibilities (Oxford University Press 1932) p. 225. THIN ALUMINIUM FILMS ON IONIC SUBSTRATES 232 for the ions of the alkali halides were taken from Mayer’s l 5 analytical treat- ment of the lattice energy characteristics of alkali halides.The validity of the physical constants in this case warranted more extended consideration. A potential energy surface for the system (100) aluminium-sodium chloride was constructed after Orr.16 It is schematically represented in Fig. 15. The potential hole in the centre represents a position of the aluminium in which the potential energy is 7 kc./m. lower than a position over the cation. The position over the anion corresponds to the highest potential energy on the surface. For this system it is evident that the central site is relatively large but is deeper by 7 kc./m. than the next most favourable site and corre- sponds to a binding energy of approximately 18 kc./m.It is noteworthy that the atoms of the (100) aluminium plane could be laid over the grid ANION 0 CATION X MOST PROBABLE ALUMINUM SITE FIG. ~g.-Potential energy surface (100) face sodium chloride unit cell. formed by the potential energy holes with negligible distortion. The calcula- tions are summarized in Table IV in which the atom positions the ionic polarizabilities the characteristic energies the dispersion constants and the calculated substrate binding energies are tabulated for thirteen substrate- metal pairs in columns I to 7. Considering the approximations involved in the theory and the uncer- tainties in the assumed values of J and Y one cannot expect in general more than an agreement in the order of magnitude between calculated and experi- mental values.The calculated values (E,) in column 9 Table 111 should be evaluated on that basis. It is considered fortuitous that the calculated values other than for the alkali halides agree as well as they do with the experimental values (column 8). It is significant however that the highest values correspond to the substrates upon which the best oriented aluminium films were formed and that the trend definitely agrees with that characteristic 15Mayer J . Chem. Physics 1933 I 270. l6 Orr Trans. Faraday SOC. 1939 35 1247. of the %-orientation for all eleven substrates and with the indirectly deter- mined substrate binding energies. It is evident that the periodicity of the potential energy surface of the substrate-atom pair is a very important factor in defining the arrangement of the metal atoms.233 Calcite (CaCO,) Fluorite VnS) DISPERSION EFFECT. ALUMINIUM ON IONIC SUBSTRATES Plane Substrate Sodium Chloride . . (NaC1) Lithium Fluoride . . (LiF) Mica ( KAI,Si,Ol*,~OH) *j ' Charac- teristic Energy Ionic Position Polariza- bility x I012 Centre of face ergs/ molecule Two ions Two ions Two ions Two ions Two ions Two ions Oxygen ion Oxygen ion Silicon ion Oxygen ion Fluorine ion Sulphur ion Oxygen ion 7 x 1060 Disper- Binding sion Energy Constant F; x 10-3 cal./ :rgs cm.6 molecule . . (CaF,) Zinc Blende . . Sodalite (Na4A1,Si,0,,C1) .. Conclusions .-The structure of thin aluminium films condensed in vacuum on clean ionic substrates is strongly influenced by the nature geo- metry and temperature of the ions in the base. The degree of orientation of the film with respect to the base can be semi-quantitatively correlated with a binding energy characteristic of the substrate. The values of the substrate binding energy are of the same order of magnitude as van der Waals' binding between a single atom and an infinite ionic surface. The characteristics of the film structure show this method to be effective for the preparation of oxide-free oriented aluminium surfaces for studying surface react ions. The writer is indebted to many of the research faculty for opportunities to discuss the subject and particularly to Prof.Charles Barrett Prof. Clarence Zener and Prof. Cyril Smith of the Institute for the Study of Metals and to Prof. Joseph Mayer of the Institute for Nuclear Studies. In addition all the structure determinations were made in Prof. Barrett's X-ray diffraction laboratory by his kind permission with the assistance of Messrs. Donald Clifton and John Hess whose assistance is gratefully acknowledged. Institute for the Study of Metals li'9aiversity of Chicago H* Chicago . T. N. RHODIN TABLE IV x 1oZ4 cm.3 0.93 16.4 I 6.4 16-4 24'3 24'3 24'3 20.5 20.5 2'0 20.5 19'4 3'27 3'27 3'27 0-93 0.93 3.88 3.88 0.17 3.88 1-04 10'2 17'5 3.88 20.5 251 251 18 I2 6 251 80.8 80.8 80.8 321 I 0 I0 I0 20 22'0 2 5 2 4 2 321 3'6 321 84'4 544 321 ORIENTED ARRANGEMENTS OF THIN ALUMINIUM FILMS FORMED ON IONIC SUBSTRATES BY T.N. RHODIN JR. Received 1st February 1949 There can be two types of films on solids those which are stable in mono-layers and those which tend to aggregate into three-dimensional structures. A great number of metal films formed by condensation on to a solid base are unstable in the sense that they will aggregate into crystals providing the atoms possess sufficient surface mobility. The crystalline structure of the film is strongly influenced by the base in many systems and in some cases, a single orientation prevails when the force fields around the atoms in the supporting crystal are sufficiently strong.1 Relatively little is available in the literature about the nature of these forces and the role they play in promoting a preferred orientation of the atoms arriving at the substrate surface.An understanding of their periodicity and magnitude relative to the surface forces characteristic of the film itself should provide insight into the critical dependence of film orientation on the nature and temperature of the substrate. In addition this effect may be very useful in preparing samples for surface studies. The study of the physical and chemical characteristics of pure metal surfaces has been severely handicapped by the presence of strongly adherent foreign films.Furthermore the randomness of the surface orientation has obscured interpretation of experimental results. Evaporation of metals in high vacuum on to carefully selected substrates under ideal conditions for preferred orientation appears suited to the preparation of flat oxide-free oriented films for surface reaction studies. Many factors influence their structure and some understanding of the mechanism of their formation is a necessary prerequisite for obtaining satisfactory surfaces for study. The dominant factors in defining film structure are film thickness and growth rate and the nature condition and temperature of the substrate. Experimental Procedure GENERAL ASSEMBLY.-The system was enclosed in an 18-in. bell-jar which rested on an L-shaped neoprene gasket on a ground steel plate as indicated in Fig.I. Rapid evacuation of the system to I O - ~ mm. mercury was facilitated by a 4-in. manifold 2-in. packless valve and an extra large diffusion pump. Suitable arrangement of valves on a secondary manifold permitted one to introduce purified gases readily into the chamber. Outgassing of the entire internal surface in a glow discharge was greatly expedited by a 5000 V copper cathode mounted at the top of the bell-jar. The entire frame was carefnlly shock-mounted to isolate the microbalance from building vibration. The lead-ins for control and power were situated in the steel base. Pressures from 10 to I O - ~ mm. mercury could be measured and temperatures of the substrate and crucible couId be independently controlled and measured.Atmosphere pressure seated the bell-jar hard on the gasket when the latter was evacuated. When i t was filled with dry nitrogen at one atmosphere it could be readily elevated out of reach. FORMATION OF THE FILM.-The film was produced by evaporating high purity (99.99 ?(,) aluminium from a microcrucible in a good vacuum ( I O - ~ mm.) and 1 Barrett Structure of Metals-Crystallographic Methods Principles and Data (McGraw-Hill New York 1g43) p. 441. 21 216 THIN ALUMINIUM FILMS ON IONIC SUBSTRATES condensing it on an independently heated substrate. With a suitable slit system a uniform concentrated direct molecular beam resulted. The arrangement of the source slits and substrate is indicated by items 2 and I in Fig. I. The substrate (item I) was mounted 25 mm.above the source in a copper frame which held i t in place against an externally heated copper block. In this manner the lower face was exposed to the beam and maintained a t the desired temperature by heating from the upper face. The temperature was regulated to I yo by a proportionating potentiometer controller. The substrate consisted of a square plate of an ionic salt approximately 5 mm. on the side and I mm. thick. A thermocouple probe in contact with the lower face of the substrate indicated the film temperatures. Two additional platinum probes 2-0 mm. apart were in contact with the surface. The appearance of the first few layers of the film was indicated by the sudden decrease in resistance measured between the probes. A freshly cleaved face was exposed just prior to a run.FIG. 1.-Vacuum evaporator (I) Substrate ; (2) Molecular beam source ; (3) Furnace : (4) 18-in. glass bell-jar ; (5) Right-angle neoprene gasket ; (6) Polished steel plate ; (7) High-voltage cathode-5000 V ; (8) 4-in. packless valve ; (9) 2-in. packless valve ; (10) Manifold ; (11) Purified gases ; (12) Holding pumps ; (13) High-capacity diffusion pump ; (14) Shock mount ; (15) 200-lb. weights ; (I 6) Thermocouple pressure gauge ; ( I 7) Ionization gauge ; (18) Temperature controller ; (19) Electronic heater ; (20) Electrical ground. The source (item 2) of the beam was a small tantalum crucible located directly below the substrate. The inside diameter of the crucible was 3 mm. but the beam was actually emitted through a 0.1 mm.orifice in a tantalum cap placed over the top of the microcrucible. The cap prevented splattering and also promoted thermal equilibrium of the atoms before they were emitted. The charge was outgassed by prefusing in sitzt before evaporating during which time the substrate was protected by an externally manipulated shield. The heating of the crucible was very satisfactorily effected by an arrangement for direct electron heating indicated in Fig. 2 . The crucible is shown with the lid off as item I. Electrons emitted from an incandescent 30 mil. tungsten filament The microcrucible held a charge of IOO mg T. N. RHODIN 217 (item 2) around the crucible are accelerated by a positive potential towards it. A tantalum shield (item 3) around the assembly reduced heat losses and another tantalum lid (item 4) shielded the substrate from direct exposure to the filament.The temperature of the microcrucible could be accurately adjusted and main-tained a t any temperature up to 1 5 0 0 ~ C within 2-3 yo by regulating the filament emission and the accelerating potential. This high fidelity temperature control is necessary in the determination of the substrate temperature-condensation pressure relationship for various substrates. The substrate was tied in at the same potential as the crucible to eliminate the possibility that metal ions formed in or around the crucible may be spuriously accelerated towards the substrate. FIG. 2.-Electronic heater (I) Tantalum crucible ; (2) Tungsten filament ; ( 3 ) Tantalum shield ; (4) Tantalum lid ; ( 5 ) Nickel leads ; (6) Crucible electrode ; (7) Stainless steel ; (8) Mykroy spacer ; (9) Filament electrodes.In the measurement of critical condensation pressures the crucible tem-perature was slowly increased until the rate of evaporation of the aluminium was just enough to cause condensation on the substrate for a given base tem-perature. The rapid decrease in the film resistance between the probes was used to indicate the formation of the initial layer. The process was reversible, that is a small increase in base temperature for a critical pressure caused the film to evaporate. The microcrucible could be readily removed from the crucible electrode (item 6) for replacement and the position could be easily lined up by adjusting the eccentric a t the base.The crucible temperature was measured by a Chromel-Alumel thermocouple mounted in the bottom 218 THIN ALUMINIUM FILMS ON IONIC SUBSTRATES RATE OF CoNDENsATIoN.-The condensation rate for a given crucible and sub-strate temperature was determined by weighing in situ a thin glass slide hanging on a quartz fibre over the molecular beam as indicated in Fig. 3. A sensitive quartz torsion microbalance facilitated accurate and quick measurements in vacuum. The torsion fibre was rotated by magnetic coupling through the glass wall. The sensitivity of the weighing was I O - ~ g. with a 23 mp quartz torsion fibre (item 5 ) . The thickness corresponding to weight increments was calculated for a constant area assuming the film to be flat and continuous and the film density to be comparable to the mass density.A microgram corre-sponding to a hundred Angstroms thick layer of aluminium for the film was used. The condensation rates for various substrate and crucible temperatures were calibrated in this manner. FIG. 3.-Quartz torsion (8) Graduated wheel ; (12) Collimating slit ; (4) Hang-up ; ( 5 ) EXAMINATION OF THE substrate was cooled in microbalance (I) Bow fibre ; (2) Static; (3) %am; Torsion fibre; (6) Hang-down; (7) Image of index; (9) Single field image ; (10) Substrate ; (I I) Molecular beam ; (13) Source. FILM MetuZZogruphy.-Upon completion of the run the situ and removed for examination. Reflectivity of the surface varied from very mirror-like to cloudy as the film thickness and substrate temperature increased.Metallographic examination of the samples was con-siderably hampered by their fragility. Where i t was possible to observe grains without destroying the film the average grain size was two to five thousand Angstroms for a film of the same thickness. Structure Determinatioa.-The film structure was determined with X-ray diffraction using a surface reflection pinhole technique in a vacuum camera as indicated in Fig. 4. A Picker-Waite diffraction unit was used with a water-cooled chromium target. The exposure time varied from 2 to 15 hr. for film thicknesses from 5000 to 500 A with an accelerating potential of 50 kV and a space current of 10 mA. The sample (item 6) was anchored flat on the turntable (item 7) and rotated around an axis (item 19) normal to the surface of the sample.The axis of rotation was inclined away from the incident beam an amount corresponding to the Bragg angle for reflection from the plane of preferred orientation. The camera was particularly designed to suit the geometry and orientation unique to the samples studied. The simplicity of the film patterns indicated in Fig. 5 a and Fig. 5 b clearly show the advantage obtained. Preferred orientation is characterized by segmentation of the lines into local marks as shown by the heavy marks of five degrees length on the dashed reflection lines in Fig. 5 b . The vertical distance from the centre line measures the orientation azimuth T. N. RHODIN 2=9 characteristic of a preferred orientation. The value of the Orientation azirnnths (9) can be calculated for any preferred orientation.2 cos p = cos p sin 0 + sin p cos 0 cos 'p where * (1) , p = angle between oriented plane and reflecting plane, p = angle between normal to oriented plane and incident beam, 0 = Bragg angle for reflection from reflecting plane, 'p = orientation azimuth for oriented plane.Some values of cp calculated for reflection of K and Kp chromium radiation from the (III) (zoo) and (311) planes of aluminium for (111) (100) or (110) FIG. 4.-X-ray vacuum camera (I) End plates ; (2) Film case ; (3) Entrance beam ; (4) Beryllium window ; (5) Pinholes ; (6) Specimen ; (7) Lucite spacer ; (8) Lock-n u t ; (9) Rotor assembly ; (10) Drive-wheel shaft; (11) Rotor vacuum seal; (12) Lead-glass window; (13) Vacuum outlet; (14) Plate nuts; (15) Motor; (16) Track clamp (17) Exit beam; (IS) Neoprene gaskets; (19) Axis of specimen rotation.Axis of Spectrnen Rotation \ 29 Cones of reflection from low indce plones (4 I00 7 5 50 25 -& 251 0 50 75 100 -Pottern of (111) Fibre mis oriented within? five degrees. b'l - -FIG. 5.-Diagram of X-ray pattern from oriented film. 2 Barrett Sfructure of Metals-Crystallo~~uphic Methods Principles am? Data (McGra~-Hill New York 1943) p. 156 220 THIN ALUMINIUM FILMS ON IONIC SUBSTRATES orientation are listed in Table I. The kind of orientation can be readily deter-mined from the pattern defined by the characteristic values of 9. A semi-quantitative value for the degree of orientation with a maximum error of 10 yo in this determination can be obtained by measuring the opaqueness of the spot relative to the integrated opaqueness of the whole line with a Leeds and Northrup recording microphotometer.The error is introduced by the assumption that the intensity at any one spot on the film is linearly proportional to the amount of radiation reflected to that point and is the same for all azimuth angles. TABLE I BRAGG ANGLES AND ORIENTATION AZIMUTHS CHROMIUM RADIATION ON ALUMINIUM Radiation CrK Plane Angle 29'5 26.8 34'7 3 1-0 54'4 47'0 70.0 59'2 0 83 0 80 68 65 63 52 95 58,142 Orientation Azimuths ( y (110) 64 62 0 119 0 I11 82 68 50 89 Results Orientation Results GENERAL.-A quantitative dependence of degree of preferred orientation on film thickness and substrate temperatures was found over a considerable range of thickness and temperature for eleven aluminium-substrate pairs.It was necessary however to make a preliminary evaluation of four other factors sufficiently well so as to minimize their influence. The pertinent results of the preliminary survey is herewith presented in condensed form as a background against which the significance of the quantitative aspects can be more intelligently considered. Film Growth Rate.-Foremost is the important influence of film growth rate on structure. Since the experimental system was not propitiously suited for studying this aspect it was maintained a t a constant value in all experiments. The evaporation rate was adjusted for each substrate temperature corresponding to an effective film growth rate of ten to thirty monolayers of aluminium per second.In the case of the binding energy determinations however the film growth rate was not controlled since it was only desired to determine the condition for minimum condensation. Heat Treatment.-Heat treating of the substrates with or without adherent metal film caused no striking change in the resulting orientation. The films were therefore usually kept a t constant temperature during formation and then permitted to cool by radiation in a vacuum. Annealing a randomly oriented film at elevated temperatures (up to 600° C) in helium resulted only in grain growth. Likewise oriented structures were not markedly altered by annealing under similar conditions. This temperature stability of the structure is in con-trast to the temperature sensitive orientations of thinner aluminium films (400 A) previously reported .3 Gas Atmosflhere Eflects.-The influence of gases present even a t I O - ~ mm.pressure was also considered. The pressure of purified quantities of helium, oxygen nitrogen and hydrogen a t low pressures ( I O - ~ mm.) decreased the orientation to a relatively small extent. The effect was not unique to any one gas or substrate and appeared solely to hamper the steady evolution of aluminium Dixit Phil. Mag. 1933 16 1049 T. N. RHODIN 221 vapour. In no case mas a gas such as helium observed to improve the film orientation as reported by others for thinner films.* Substrate Condition.-The contamination of the substrate surface itself by the gases previously listed was not considered to be critical.Oriented films could be formed on freshly cleaved rocksalt which had been preheated in oxygen and hydrogen atmospheres. In all cases however the cleanliness of the sub-strate was a critical requirement and best results were always obtained with freshly cleaved ionic surfaces whose lattices had an arrangement of ions the geometry and dimensions of which showed a certain correlation to that of aluminium. The limited number of such salts emphasized the preparation of oriented substrates by other means. Even after repeated polishing etching and annealing use of NaCl and LiF surfaces obtained in this manner was only moderately successful. Successful techniques for exposing any desired sub-strate orientation in a suitably clean and flat condition would be most useful for further studies.BASE TEMPERATURE IN HUNDREDS OF DEGREES CENTIGRADE 5 4 3 I00 - 5 4 3 2 I I 2 5 x 103 4 3 m o x 103 FIG. 6.-Approximate film thicknesses in %ngstroms. Orientation of aluminium film deposited on cleavage face of sodium chloride. Each column indicates average values for four samples. Dev. f 10 %. SPECIFIC FACTORS FzErn Thickness.-Initial studies made it evident that degree of orientation was very dependent on film thickness for all film-substrate pairs. This characteristic will be described first since it depended only on temperature and film thickness and was general to all substrates. The %-orienta-tion for films on the (100) face of rocksalt for various thicknesses and base temperatures is plotted in Fig.6 as an illustration. An exponential dependence of orientation on film thickness was observed and the data plotted in Fig. 7 is a typical case. It is interesting to note that a critical film thickness for perfect orientation at each temperature is suggested by extrapolation of the straight line to small film thicknesses. A striking temperature dependence is also indicated by the distinctly small slope of Curve 2 compared to Curve 3 in Fig. 7. The validity of a strong base temperature dependence of %-orientation is also indicated in Fig. 8 for a variety of film-substrate pairs. Discussion of the temperature dependence is however temporarily postponed until right after the discussion of the thickness effect. 4 Beeck Smith and Wheeler Proc.Roy. Soc. A . 1940 62 177 222 THIN ALUMINIUM FILMS ON IONIC SUBSTRATES I 0’ I o6 A E .z lo5 tl c tn fn y 10‘ 0 I I-I J -LL lo3 lo2 10 I MI C K N E SSSR IE N TAT1 ON 1 @ 200oc a 300% @ 4OOOC i --y ,5000c ,ir I i 20 40 60 80 103 FIG. ./.-Per cent. orientation. ORIEr*;TtlTl@N AND SUBSTRATE TEMPERATURE I 300 -I-! W a __- Binding Enrrqy - I Glass Slide I 0 500 600 700 8 33 FIG. &-Substrate temperature-centigrade 223 T. N. RHODIN depth of penetration (A) ; column 2, thickness penetrated relative to limit-ing thickness; and column 3 the corresponding O/,-intensity for that 5 x I02 5 x 103 5 x IO* The thickness dependence may mean that the oriented arrangement is constant at all points in the film and merely decreases as the film thickens.It seems more reasonable to assume that the orientation is strongly dependent on the substrate and produces an orientation large at the inner film surface and decreasing towards the outer film surface. The latter possibility is in agreement with the surface reflection characteristics of X-rays. In this case a disproportionately large fraction of the radiation producing the pinhole pattern is reflected from the outer planes of the film. A quantitative illustration of this can be presented by calculating the intensity of radiation reflected from successive layers of metal atoms as follows.5 The intensity (It) reflected from a thickness ( t ) relative to the intensity ( I d ) reflected from an infinitely thick film can be expressed : t td I d , 1 ' 9 6 24 25 I 53 T 0 where 6 Hess (Institute for the Study of Metals) (private communication to the author) 224 THIN ALUMINIUM FILMS ON IONIC SUBSTRATES the orientation of the outer surface was essentially observed.The orientation is greatest in the region nearest to the substrate-film interface. Szrbstrnte Tem@mztztre .-A base temperature dependence in which orientation of the film increased rapidly a t some characteristic temperature for each sub-strate illustrated in Fig. 8 was typical of all substrates. The less the maximum orientation however the smaller the dependence on the characteristic tem-perature This is illustrated by the contrast in the curves for (100) orientation on rocksalt and glass.The temperature dependence may mean that the metal atoms must possess a minimum kinetic energy corresponding to the observed temperature for maximum orientation for them to take up the preferred positions suggested by the substrate. The transition of a (110) orientation of the film on mica at low temperatures to a (111) orientation at higher temperatures indi-cates that a higher minimum mobility is required for formation of the second configuration. In all cases the rate at which orientation increased with base temperature as well as the maximum value i t approached was typical of the substrate. I t indicates that production of ordered arrangements is governed not only by the interaction of the substrate and metal but by a relatively slow temperature-dependent surface diffusion process as well.Calculation of activa-tion energies for the rate process involved seems premature until the mechanism of arrangement is better defined. The characteristic values of base temperature and maximum observed orientation are plotted in Fig. 8 for rocksalt mica and glass and listed for eleven substrates in columns z and 4 of Table 111. TABLE I11 STRUCTURE CHARACTERISTICS O F THIN ALUMINIUM FILMS Substrate Mica . . Mica . . NaCl NaCl LiF . . LiF CaCO Glass . . CaF . . ZnS Sodalite Temp. Orient. " C % Orient. 87 75 80 50 55 50 I5 I 0 I 0 I 0 I 0 Pressurt x 104 cm.Hg. 0-007 1'52 0.003 0.024 0'022 0'0 I2 0'0 I2 6000 760 700 700 A kc./m. 42 28 31 33 25 25 I5 2 1 20 21 2 1 A kc.lm.20 I 0 I5 I 0 20 20 20 20 20 15 I5 A - A kc./m. 22 I 8 16 13 5 I1 I 0 0 0 I I Ec kc./m. 22 20 I8 I2 I0 I 0 5 -2 4 2 Experimental data for mica in the temperature region intermediate between the (110) and (111) orientations were inconclusive. I t is noteworthy that the most oriented configurations corresponded to the higher orientation temperatures. This characteristic is a general one for all the substrates studied. It is illus-trated by the dashed curve in Fig. 8 in which the orientation temperature as abscissa is plotted against the substrate binding energy as ordinate on the right. The substrate binding energy heretofore undefined is described in a subsequent section and shown to be proportional to the percentage of the observed film orientation.Nature of Substrate.-From the facts presented so far it seems clear that the nature and degree of the observed orientation was critically dependent on the substrate. In every case there was a correlation of some kind between the geometry and dimensions of the underlying lattice and that plane of aluminium preferentially oriented parallel to it. For example the (100) face of aluminium was the only orientation observed on the (100) face of the alkali halide substrates. Similarly the (111) planes of aluminium tended to be preferentially oriented parallel to substrates with hexagonal cleavage or hexagonal-polished faces providing the base temperature and film thickness were favourable.In other cases (110) This dependence held in general for all the substrates studied ( a ) Aluminium on glass random ( b ) Aluminium on (TOO) sodium orientation. 104 A thick. chloride 80 yo (100) orientation 1-2 x 103 A thick. (c) Aluminium on (111) mica 87 ”/ ( d ) Aluminium on glass 10 yo (100) (111) orientation. 1.3 x 1 0 3 1 orientation. 103 A thick. thick. FIG. 9. To face page 225 225 T. N. RHODIN orientation was observed to occur on (110) oriented substrates. This is not a general effect however since cases occur where substrates stabilize preferred film orientations other than their own but in most cases that orientation of aluminium occurred for which the geometry and spacing of the metal atoms yielded the best fit on the substrate.The data are summarized in columns I 2, 3 4 of Table I11 in order of decreasing orientation. The direction of orientation in the film listed in the third column is the same as that of the substrate for the first seven items. A small orientation was observed on glass which of course, possesses no definable surface arrangement. The small degree of orientation on fluorite was barely measurable. The (111) orientation on zinc blende and sodalite was also very small. The last two substrates possess cubic lattices with good (I 10) cleavage faces and are examples of film o ientation differing from that of the substrate. I FIG. 10.-Aluminium unit cell. Some typical surface reflection X-ray film patterns are illustrated in Fig. 9. The interpretation is handicapped by the poor contrast of the aluminium lines, the strong and complex pattern caused by reflection from the substrate and the poor reproduction but the over-all pattern analysis is quantitatively unique for each orientation.Continuous reflection from all the low indice reflection planes indicate complete randomness in Fig. g a. The sharply defined orientation of a (100) aluminium film on rocksalt is illustrated in Fig. 9 b. Fig. g G is greatly complicated by the mica pattern but arrows indicate the discrete aluminium reflections corresponding to (I I I) orientation. A poorly oriented film on glass tending towards (100) orientation is included for comparison (Fig. g d). Discussion Geometric Considerations.-The good correlation between substrate and film orientation is in accord with the excellent matching between the oriented aluminium plane and the geometry and dimensions of the surface lattice upon which it forms.Similar results have been reported for thinner films.6 The striking geometric kinship among the three low indice planar arrangements (IOO) (IIO) (111) of aluminium in Fig. 10 and the geometry of the corresponding planes in sodium chloride and lithium fluoride in Fig. II suggests that such correspondence between film and substrate pro-motes a related orientation in the former. This hypothesis is suggested by the Bruck Ann. Physik 1936 26 233. Rudiger Ann. PhysiR 1937 30 505. Finch, Quarrel1 and Wilman Trans. Faraday SOC. 1935 31 1051. 226 THIN ALUMINIUM FILMS ON IONIC SUBSTRATES Table of lattice distances summarized in Fig.11. They agree within a few yo in each case except for the (111) sodium chloride face for which the lattice spacing is 40 yo greater than the corresponding spacing in the (111) aluminium plane. It is doubtful whether this correlation is generally essential for substrate-metal interaction but it is significant that no (111) orientation of aluminium was ever observed on a (111) sodium chloride surface. Corre-sponding orientations were observed in every other case. 0 ANION @CATION FIG. I I .-Unit cell of alkali halide. Lattice parameters (A) (roo) a . . (111) b (110) c Substrates with hexagonal sponding to the (111) face of A1 NaCl I.iF 2-85 . . 2.83 . . 2-84 2-85 . . 3-98 . . 2-84 4-04 . . 3.98 . . 4-01 cleavage faces of atomic dimensions corre-aluminium yielded (111) oriented aluminium films.The fairly complicated surface structure of mica accommodated (110) arrangement of aluminium as well. The arrangement of the atoms in the hexagonal cleavage faces of mica calcite and fluorite are drawn to scale in Fig. 12. The matching of lattice distances was poorer than for the cubic face cleavage substrates and the observed degree of orientation was also correspondingly poorer with the exception of mica. The (110) cleavage faces of cubic zinc blende and sodalite are not indicated but the matching was relatively poor for both substrates and they are unsatisfactory as (110) directing surfaces. In all cases studied the nature and degree of the observed film orientation bore a close relationship to the geometry and dimensions of the underlying substrate.It appears that directing forces are geometrically distributed on the substrate surfaces in close correspondence to the atomic distribution in the substrate plane. An interpretation based on this approach will be discussed in the next section T. N. RHODIN 227 Characterization of Substrate.-In an effort to characterize the substrates an effect discovered by Wood and studied by Estermann,* was used in a modified form. When a beam of metal vapour is directed at a heated substrate condensation will occur if the pressure is sufficiently high or the substrate temperature sufficiently low. Whether most of the atoms bounce off the surface losing none or relatively little of their kinetic energy or whether they are accommodated on the surface depends on the relative values of the aforementioned variables plus a third the attraction of the substrate for the metal atoms.Since the relationship between these factors can be quantitatively expressed the attraction of the substrate may be determined providing the corresponding pressures and base temperatures can be measured. This pressure-temperature dependence was determined for all the substrate-metal pairs at those substrate temperatures at which maximum orientation was known to occur in each case. The substrate temperature was measured with a thermocouple probe on the surface. The metal pressure was not measured directly but calculated from the crucible FIG. 12.-Crystal substrates with hexagonal cleavage.temperature using the free energy of vaporization values for aluminium.9 The minimum vapour pressure was accurately determined for each base temperature at which condensation of the first layers took place. The formation of the first layer was indicated by measuring the sudden drop in film resistance between two probes on the surface. The corresponding values of pressure and base temperature for a group of typical runs are plotted in Fig. 13. The pressure-temperature relationship can be expressed as where $I = pressure of metal vapour, a = constant insensitive to temperature, T = absolute temperature of the substrate, A = an energy term characteristic of the film and the substrate. 7 Wood Phil. Mag. 1916 32 (6) 365. 8 Estermann 2. Elektrochem. 1926 31 441.9 Kelley The Free Energies of Vaporization and Vapour Pressures of Inorganic Substances (Bulletin 383 Bureau of Mines 1935) 228 THIN ALUMINIUM FILMS ON IONIC SUBSTRATES The values of a could be interpolated from the intercept on the pressure axis of the curves plotted in Fig. 13. It is insensitive to the nature of the substrate and to the base temperature for the conditions observed. Hence it was of little use for characterizing the substrates on a relative basis. It however includes at least three significant terms describing : (a) geometry of the system (b) size of the condensing particles (c) a linear temperature correction. Hence an interpretation of the mechanism of condensation would eventually require an analysis of a into its component terms .6 .f W E 0 I-LL. 0 W 3 v, v) W P a a 0 0 1 FIG. 13. I/T x 103 degrees (absolute). The values of A could be readily interpolated from the slopes of the straight lines plotted in Fig. 13. Some typical values are listed there in order of decreasing magnitude. Corresponding values of temperature, pressure and A are more completely listed in columns 2 5 and 6 of Table 111. A definite trend of A in Table I11 from 42 kc./m. to 20 kc./m. is evident. This trend corresponds to decreasing observed orientation. It is significant that the values of A are smallest for the ionic substrates at the end of the Table for which the orientation was poorer. The smaller surface-free energy of the (111) arrangement corresponds to the observation that the A values for (111) substrate-film orientations are somewhat greater than those for (110) and (100) orientations for each substrate-metal pair.An interpretation of A as describing the heat of condensation of th T. N. RHODIN 229 first layer of metal atoms on the substrate is indicated by the temperature-dependence relationship established by the straight lines in Fig. 13 and by the empirical findings of Wood and Estermann. A theoretical analysis of their work by Semenoff l o applied to these results indicates that where A = E + A - (5) E = the adhesive energy of binding of the metal and substrate, A = the energy of binding of the aluminium atoms in the first layer eg. the surface energy characteristic of the metal film itself. If the first term is large the substrate is likely to influence strongly the formation and arrangement of the atoms in the first layer providing the atoms possess sufficient mobility to assume those positions on the surface of lowest potential energy.If it is small relative to the second term, that is the adhesive forces between metal and substrate are negligible compared to the cohesive binding between metal atoms the film formation will be relatively independent of the substrate and should any orientation occur it will be that arrangement for which the surface-free energy is smallest. Formation of an oriented first layer under the first condition would facilitate the occurrence of the same orientation for subsequent layers. The degree of observed orientation should increase with the value of E providing other factors are also favourable e.g.mobile atoms and relatively thin films. Formation of an oriented layer under the second condition may also occur but the degree of orientation will likely be considerably less. I t is note-worthy that the values of A varied from 42 kc./m. for aluminium on mica to 15 kc./m. for aluminium on glass (column 6 Table 111). In the latter case one might consider the interaction between the glass and the metal to exert a relatively small influence on the film structure and the measured heat of condensation to correspond mainly to the cohesive forces in the (100) plane of aluminium. Since there are about one-third the number of bonds in this configuration compared to that of massive aluminium, the surface energy can be roughly approximated to be one-third of the molar heat of vaporization or 22 kc./m.For this crude approximation the order of magnitude agrees with the experimentally determined value measured on an amorphous substance like glass. Neglecting the entropy correction the substrate binding energy for the other substrate-metal pairs may be similarly approximated by subtracting an energy A corre-sponding to the cohesive binding energy of the film from A the total energy of condensation. In view of the assumptions involved the values obtained are speculative but the resulting values (E) listed in column 8 of Table I11 are of the right order of magnitude. These approximations compare favourably with values calculated on the same basis as van der Waals’ inter-action.The trend of the experimental values of E is in qualitative accord with the trend of observed orientations for each metal-substrate pair. This is indicated by the data on the maximum orientation and the substrate binding energies listed in columns 4 and 8 in Table 111. The correlation is also evident in Fig. 14 in which the maximum observed orientation is plotted as ordinate against the substrate binding energy as abscissa. The calculated values included for comparison are now discussed. Van der Waals’ 1nteraction.-Understanding of the binding between a metal and an ionic surface would provide considerable insight as to the nature of the metal-substrate interaction. A rigorous attempt to define the binding is well beyond the scope of this paper but some speculation in this direction seems justified.The characteristic of the binding namely, 10 Semenoff 2. physik. Claem. B 1930 7 471 230 THIN ALUMINIUM FILMS ON IONIC SUBSTRATES its relative magnitude and non-specificness suggests the validity of an approach based on van der Waals’ interaction between the first layer of metal and the substrate. An analysis similar to a certain extent to the calculation of heats of adsorption of gases physically adsorbed on ionic surfaces near the boiling point of the gas seems justified. I t is obvious that the chief distinguishing characteristic between metal and physically adsorbed gas films other than the different temperature range in which they form is the marked importance of the cohesive forces in the former case. It is conceivable nevertheless that a strong periodicity in the potential energy surface of the substrate towards the metal atom may be sufficient to start the condensation in a favoured direction.The energy of van der Waals’ binding of aluminium on each of the substrates was calculated on this basis. Q [IiO] Li I Experimrntol (A-A) Substrate binding energy (kc./m.). FIG r+-Substrate orientation. Van der Waals’ interaction between non-polar molecules has three important constituent parts (I) the attraction between fluctuating dipole and induced dipole (dispersion effect) varying inversely as the sixth power of the distance (2) the attraction between fluctuating quadruple and induced dipole varying inversely as the eighth power of the distance and (3) the repulsion energy decreasing exponentially with the distance.A fourth con-stituent part is unique to ionic surfaces the so-called influence effect. The latter is due to the fact that the charged ions of the substrate induce a dipole moment in the metal atom which results in an attraction between the ions and the induced dipole. At the equilibrium distances characteristic of the metal films the first of the four terms is by far the most important. The calculations were made on an approach similar to 0rr1l in which he calculated heats of physical adsorption of argon on potassium chloride. l1 Orr Trans. Faraday SOC. 1939 35 1247 T. N. RHODIN 231 The dispersion effect was introduced by London l2 in the calculation of heats of adsorption. The dispersion potential cp between an atom of metal and an ion of the substrate can be written where Y is the equilibrium distance and C the dispersion constant is given by ‘p = - c p .(6) where a = polarizability of the metal, a’ = polarizability of the ion < = characteristic energy of the metal, J = characteristic energy of the ion. The interaction between an atom and the entire surface of the substrate can be very simply calculated if one assumes that the distance between atom and ion is not smaller than the distance between ions. In this case the summation over the ions of the substrate can be replaced by an integration. For alkali halide substrates this approximation will yield values that are too low by 25 yo to 30 yo. For the mutual dispersion energy of an infinitely large surface and an isolated atom, where N = number of ions per ~ m .~ and dv is the volume element. stituting expression (6) for the dispersion constant, Sub-Nx uu’ JJ’ 9=---- (9) 4 9 J+J” An exact evaluation from eqn. (8) is not possible because some of the experi-mental data are missing particularly the value of J for aluminium. Never-theless to show the order of magnitude calculations were made using the first ionization potential. The value of N for the substrates other than the alkali halides was calculated from the density. The distance r between an ion and an aluminium atom was assumed to be made up of two parts after London,13 viz., r = + d2f2 . . ’ (10) For d l / z half the distance between ions in the substrate was used and for d,/2 half the interplanar distance for that plane of aluminium observed to be preferentially oriented.The identity and geometry of the important ions in the substrate were not always definitely established and a choice had to be made in some cases. The ion was chosen whose arrangement on the surface best fitted the observed aluminium orientation. For example, the oxygen ions were chosen instead of the silicon ions in mica. The calculated binding energy for both is listed in Table IV for comparison. The atomic polarizabilities were taken from Van Vleck l4 if possible or calculated from where v is the characteristic frequency of the atom and the other symbols have the customary significance. The polarizability and characteristic energies l a London 2. physik. Chew. B 1930 11 222. l3 London 2.physik. Chew. B 1930 11 222. 1 4 Van Vleck EZectric and Magnetic Susceptibilities (Oxford University Press 1932), p. 225 232 THIN ALUMINIUM FILMS ON IONIC SUBSTRATES for the ions of the alkali halides were taken from Mayer’s l 5 analytical treat-ment of the lattice energy characteristics of alkali halides. The validity of the physical constants in this case warranted more extended consideration. A potential energy surface for the system (100) aluminium-sodium chloride was constructed after Orr.16 It is schematically represented in Fig. 15. The potential hole in the centre represents a position of the aluminium in which the potential energy is 7 kc./m. lower than a position over the cation. The position over the anion corresponds to the highest potential energy on the surface.For this system it is evident that the central site is relatively large but is deeper by 7 kc./m. than the next most favourable site and corre-sponds to a binding energy of approximately 18 kc./m. It is noteworthy that the atoms of the (100) aluminium plane could be laid over the grid ANION 0 CATION X MOST PROBABLE ALUMINUM SITE FIG. ~g.-Potential energy surface (100) face sodium chloride unit cell. formed by the potential energy holes with negligible distortion. The calcula-tions are summarized in Table IV in which the atom positions the ionic polarizabilities the characteristic energies the dispersion constants and the calculated substrate binding energies are tabulated for thirteen substrate-metal pairs in columns I to 7. Considering the approximations involved in the theory and the uncer-tainties in the assumed values of J and Y one cannot expect in general more than an agreement in the order of magnitude between calculated and experi-mental values.The calculated values (E,) in column 9 Table 111 should be evaluated on that basis. It is considered fortuitous that the calculated values other than for the alkali halides agree as well as they do with the experimental values (column 8). It is significant however that the highest values correspond to the substrates upon which the best oriented aluminium films were formed and that the trend definitely agrees with that characteristic 15Mayer J . Chem. Physics 1933 I 270. l6 Orr Trans. Faraday SOC. 1939 35 1247 T. N. RHODIN 233 of the %-orientation for all eleven substrates and with the indirectly deter-mined substrate binding energies. It is evident that the periodicity of the potential energy surface of the substrate-atom pair is a very important factor in defining the arrangement of the metal atoms. TABLE IV DISPERSION EFFECT. ALUMINIUM ON IONIC SUBSTRATES Substrate Sodium Chloride . . (NaC1) Lithium Fluoride . . (LiF) ( KAI,Si,Ol*,~OH) *j ' Mica Calcite . . (CaCO,) Fluorite . . (CaF,) Zinc Blende VnS) Sodalite . . (Na4A1,Si,0,,C1) Plane Position Centre of face Two ions Two ions Two ions Two ions Two ions Two ions Oxygen ion Oxygen ion Silicon ion Oxygen ion Fluorine ion Sulphur ion Oxygen ion Ionic Polariza-bility x 1oZ4 cm.3 3'27 3'27 3'27 0.93 0-93 0.93 3.88 3.88 0.17 3.88 1-04 10'2 3.88 Charac-teristic Energy x I012 ergs/ molecule 16.4 I 6.4 16-4 24'3 24'3 24'3 20.5 20.5 2'0 20.5 19'4 17'5 20.5 Disper-sion Constant 7 x 1060 :rgs cm.6 251 251 251 80.8 80.8 80.8 321 321 3'6 321 84'4 544 321 Binding Energy F; x 10-3 cal./ molecule 18 6 I2 I 0 I0 I0 20 22'0 2 5 2 4 2 Conclusions .-The structure of thin aluminium films condensed in vacuum on clean ionic substrates is strongly influenced by the nature geo-metry and temperature of the ions in the base. The degree of orientation of the film with respect to the base can be semi-quantitatively correlated with a binding energy characteristic of the substrate. The values of the substrate binding energy are of the same order of magnitude as van der Waals' binding between a single atom and an infinite ionic surface. The characteristics of the film structure show this method to be effective for the preparation of oxide-free oriented aluminium surfaces for studying surface react ions. The writer is indebted to many of the research faculty for opportunities to discuss the subject and particularly to Prof. Charles Barrett Prof. Clarence Zener and Prof. Cyril Smith of the Institute for the Study of Metals and to Prof. Joseph Mayer of the Institute for Nuclear Studies. In addition all the structure determinations were made in Prof. Barrett's X-ray diffraction laboratory by his kind permission with the assistance of Messrs. Donald Clifton and John Hess whose assistance is gratefully acknowledged. Institute for the Study of Metals, li'9aiversity of Chicago, Chicago . H

ISSN:0366-9033    

DOI:10.1039/DF9490500215

出版商:RSC    

年代:1949

数据来源: RSC