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C- STEADY-STATE PROCESSES INVOLVING LATTICE RE-ARRANGEMENT INTRODUCTORY PAPER BY J. H. DE BOER Central Laboratory, Staatsmijnen, Geleen, The Netherlands. Received 15th March, 1957 In a well-known, and deservedly well used, English text-book1 we read: " Crystals may be formed from solution, by cooling the molten material or by deposition from the vapour, and according to the conditions, single crystals or polycrystalline material may be obtained ". In the third part of this Discussion we shall deal with other methods by which crystals or polycrystalline material may be formed. Crystals may be formed from other crystals by lattice re-arrange- ment. The first sub-division of this section C is confined to transformation in solids. Many of our elements, metals as well as non-metals, may crystallize in various allotropic forms and we shall first deal with the transformations in the elements.THE FORMATION OF DIAMOND The most spectacular transformation in solids successfully performed in recent years, is, probably, the manufacture of diamond by a research team of the General Electric Laboratory at Schenectady (N.Y.), U.S.A. Little has been published in the scientific press, but an information booklet,2 published in 1955, reveals that the possibility of making diamonds lies in the region of 600,000 to 1,500,000 lb./sq. in. (40,000 to 100,000 atm) and 1350" F to 5000" F (700" C to 2750" C). The high-pressure part of the graphite-diamond diagram is moderately well- known from the work of Bridgman,3 who also tried to transform graphite into diamond. At the relatively low temperatures at which his experiments were performed, the rate of the transformation was negligibly small; at higher temperatures Bridgman could not maintain his pressure for more than one or two seconds.The secret of the success of the General Electric workers (e.g. A. L. Marshall, A. J. Nerad, F. P. Bundy, H. T. Hall, H. M. Strong and R. Wentorf) is that they can maintain high temperatures and high pressures simultaneously for sufficiently long times for the transformation to proceed despite the low rate of the process. Conversely, diamond does not change its stable form at normal pressures until the temperature is raised above 1700" C , a clear demonstration of the significance of a low rate of transformation. NUCLEATION The very low rate of transformation may be related to the strength of the covalent bonds between the carbon atoms, with the great difference in volume between the two phases and with the difference in arrangement between the two lattices.We may expect that the mechanism of transformation comprises the formation of nuclei and the subsequent growth of those nuclei. Various attempts have been made to derive mathematical equations describing the rate of such 171172 INTRODUCTION transformations. One of the relatively recent, successful, attempts by Avrami 4 may be mentioned here. He assumes that the formation of a new phase takes place by the growth of growth nuclei. These growth nuclei are generated at or from certain spots, called germs or potential nuclei (or embryos 5 9 6).There is always a certain number of these spots present ; they need not be preformed atomic ar- rangements of the new phase, but certain deformations, caused by stresses, surfaces of small crystals with sufficient surface energy, or foreign atoms or groups of atoms, may, probably suffice to serve as these starting points. Thermal fluctua- tions may cause a few atoms of the transforming phase to be arranged at those spots in a way as is prescribed by the lattice of the phase to be formed. If this activation is large enough the nuclei thus formed may exceed a critical size after which they may grow further to form the new phase. Those nuclei have then been turned into growth nuclei. The growth nuclei increase in size; the rate of this latter process is called the growth rate.A general expression results : 1 -f(t) = exp (- &), (1) wheref(t) is the fraction transformed, t the time, k is a constant, whilst A depends on the number of potential nuclei, on the rate of the formation of growth nuclei and on the rate of growth of those growth nuclei. The constant k may give some information about the mechanism of the process, as is explained in the fol- lowing article by Burgers and Groen.7 The rate of the formation of growth nuclei is governed by an activation energy, which depends on the critical size above which they may grow (this critical size depends also on temperature), and on the rate of the diffusion of the atoms to the forming nucleus.6s 8 THE GROWTH OF NUCLEI The growth rate, hence the rate of further increase of the size of the growth nuclei, has been the subject of separate studies of which we mention the treatment which Hartshorne published in a previous General Discussion.9 Assuming a thin transitional layer composed of molecules of high energy in a state of disorder to be present between the lattices of the two modifications, he visualizes molecules escaping from both lattices into this layer after having acquired a sufficiently great amount of energy.From this transition layer molecules are deposited on both lattices, the chances of being deposited being the same for both lattices. This view leads to the following equation for the linear rate of shift of the boundary between the two forms : where Vis the rate of advance of the interface when the unstable form a is trans- formed into the stable form p, below the transition point (above the transition point the sign changes). A , is a factor depending on the vibration frequencies of the molecules in the a-crystals, Ea is the activation energy of escape from the a-phase, q is the heat of transformation (q = E’ - Ed, TO is the absolute temper- ature of the transition point.If q is small-it is mostly small compared with E’ and Ea--and the temperature Tis not far from TO, an approximation may be used: Assuming q (and also Ea and Eg) to be independent of temperature we get d(T0 - T)/Tol =- AG, (4)J . H . DE BOER 173 Substituting where AG is the difference in free energy between the two phases. (4) in (3), Hartshorne obtains ( 5 ) where - AG is the “ driving force ” of the reaction.At the transition point AG = 0, hence V = 0. At lower temperatures (T < To), eqn. (4) shows that - AG increases with decreasing temperature ; the exponential term of eqn. (3) decreases at the same time. With decreasing temperatures, there- fore, Vrises from V = 0 to a maximum value, after which it decreases with falling temperature. As stated by Hartshorne9 similar expressions had already been derived by Akulov 10 and by Laurent.11 An expression similar to eqn. (5) was obtained by Frye, Stansbury and McElroy,l2 using Eyring’s theory of the transition state. Y = +AtL(- AG/RT) exp (- E,/RT) THE MAXIMUM IN THE RATE In all these conceptions the cause of a maximum rate of transformation at a certain temperature Tm < TO is the increasing tendency for the reverse transforma- tion to occur-the transformation from the stable to the unstable form-as the transition point is approached. In a discussion between Hartshorne and Dunning,l3 the latter assumes the deposition of atoms from the transition layer on the completed surface planes of the growing phase according to the mechanism of a two-dimensional nucleation to be the rate-determining step in the growth.If this is so, the reverse action, causing the observed maximum in the rate of trans- formation, results from the tendency-growing with increasing temperature-of sub-critical two-dimensional nuclei to disperse before they reach their critical size. The critical size of such nucleiwill be larger according as the temperatureis higher. INFLUENCE OF MOSAIC BLOCKS In re-crystallization processes the boundaries between the blocks of the mosaic structure of crystals play the role of transition layers.In these transition layers the deviations of the atoms from their normal positions are rather small.14 About 10 years ago W. G. Burgers 15 discussed the significance of the mosaic structure in the determination of the rate of recrystallization. The process of recrystallization, however, need not involve separate move- ments of individual atoms. Mechanisms by which whole rows or two- or three-dimensional arrangements of atoms make almost simultaneous shifts are possible. In a discussion with Mott 16 it was decided that the large value of the pre-exponential factor in the expression for the rate of recrystallization pointed towards a discontinuous mechanism by which whole blocks of the mosaic structure are transformed simultaneously.A mechanism of this kind now called a Burgers-Mott trigger mechanism, was introduced by Hartshorne to explain the very high value of A, (see eqn. (2) and (5)) which he found in the transformation of monoclinic into rhombic sulphur.9 In the subsequent discussion of Hartshorne’s paper, Garner,l7 referring to a similar case in the dehydration of chrome alum, suggests the rate of transformation within a mosaic block to be governed by an expression vN exp (- q/RT), where q is the free energy of transition. Since q is small, the transition within a mosaic block will be very rapid. The activation energy, Ea, measured by Hartshorne (eqn. (2) and (5)) would then be the energy required to form nuclei of rhombic sulphur between adjacent mosaic blocks.Since 1949, Hartshorne and Roberts 18 have found that, during transformation, the interface between the growing stable modification and the disappearing un- stable one, may cross a boundary between two differently oriented monoclinic crystals without a change in the orientation of the resulting rhombic phase. This fact would not be expected in view of the trigger mechanism discussed above. Private correspondence between Hartshorne and Garner 18 then led to the view that the reaction can proceed rapidly, with a small activation energy, over small homogeneous volume elements such as mosaic blocks.174 INTRODUCTION Periodically, however, the interface encounters obstacles which may be either cracks at mosaic block boundaries or growth cracks resulting from shrinkage.For the passage of such a crack a large activation energy is required (e.g. of the order of the heat of sublimation), which will determine the temperature coefficient of the whole reaction. The general idea, therefore, is still a process consisting of rapid sweeps over small elements of volume, interrupted by slower bridging processes. A similar mechanism may operate in the transformation of grey to white tin; according to Burgers and Groen7 the cracks result from the large difference in volume between the two modifications. THE TRANSFORMATIONS IN TIN AND IN SULPHUR The work of Burgers and Groen on tin and that of Briske and Hartshorne on sulphur, have some similarities.It had been decided not to include work on recrystallization and on metals in this Discussion. The contribution of Burgers and Groen, however, has been included on the grounds that one of the forms is non-metallic. It is, perhaps, for a similar reason that the authors themselves have decided to use the word '' allotropic" transformation in their title, just to show that, apart from the change in arrangement, there is a change in the character of the bond as well. The study of the rate of transformation of tin has a historic back- ground in this country, since E. Cohen started his research on the " tin-pest '' in 1899. Tin, also, offers an example of the beneficial results of a very low rate of transformation ; fortunately the addition of other metals, e.g.lead, even reduces the rate of conversion, so that the old pewter is relatively safe. Since Bragg 19 suggested the accumulation of foreign atoms at the boundaries of mosaic blocks, it would be interesting to know which influence foreign material has on the size of the domains which show a high rate of transformation. Briske and Hartshorne do not use the word '' allotropic " in their title. Ap- parently they wish to deal only with those transformations in which the molecular forms of the sulphur molecules do not change. The polymorphic behaviour of sulphur has been known since 1823, when Mitscherlich introduced the term poly- morphism. It is one of the oldest examples known in this field and it has played an important role in the classical investigations of Bakhuis Roozeboom and his pupils here in Amsterdam, at the beginning of this century.Recently, a thesis 20 on this element has been written, again in this country. As we are interested in lattice rearrangements, I may say something about the lattice arrangements. In the three " normal " modifications of crystalline sulphur, the element is present in the form of rings of 8 atoms. Rhombic sulphur (a- sulphur) is the only modification whose structure is known with sufficient certainty. The monoclinic form (p-sulphur), which is stable between 96" C and its melting point, also contains the Sg-rings and the transformation, the rate of which is low, comprises probably a rearrangement and perhaps also a small re-modelling of these rings. The transformation cc + p is slow in both directions, but mono- clinic sulphur is transformed quickly into the rhombic form when it is powdered at room temperature.Mechanical forces often strikingly accelerate these transformations. The metastable y-form of sulphur about which something was reported already in some of Hartshorne's reports on older investigations,Zl also contains Sg-rings. Other modifications may contain smaller rings, as e.g. s6-rings, probably present in the rhombohedra1 form (e-sulphur, also called p-sulphur), whilst longer or shorter chains of S-atoms present in the melt at elevated temperatures and in the amorphous modifications may persist in crystalline modifications derived herefrom, such as the w-sulphur, first described by Das.22 This w-sulphur seems to be metastable at all temperatures, though its transformation into a-sulphur proceeds very slowly at room temperature and only moderately fast at 110" C.23~ 20J.H . DE BOER 175 This transformation may here have special interest as it also involves the trans- formation of S-chains into S-rings. A rather slow cooling of viscous sulphur causes a certain degree of ordering, which Schenk 20 calls an embryonal crystallization, resulting in a form of colloidal dispersion (K-sulphur), found by Prins.24 Some years ago, Hartshorne,zs noted the significance of orientational effects in the transformations of sulphur. Above, we have already discussed how these effects can help to decide which mechanism is operating. Orientational effects seem also to be important in the transformations of tin, as we see from the work of Burgers and Groen.The molecular chain-form seems not to be stable in sulphur ; it is, however, the stable molecular form of selenium and tellurium. It is an interesting fact that the monoclinic ct- and P-modifications of selenium, which are built up of Seg-rings, transform themselves rather quickly into the stable hexagonal, metallic, modifica- tion of this element, which is built up of Se-chains. The black, amorphous, selenium obtained by cooling the liquid does not crystallize easily from its brittle glassy condition, nor from its highly viscous form above about 30" C. It is only at temperatures higher than 70" C that a slow ordering to the stable hexagonal crystalline phase takes place. It may be that the Se-chains partly disintegrate owing to the temperature movement and are built up again with the result that a more regular arrangement is produced at the same time.In these latter cases re-arrangement of the atoms constituting the molecules, and rearrangement in the lattices proceed simultaneously. TRANSFORMATIONS OF CHEMICAL COMPOUNDS Quite a number of polymorphic transformations of chemical compounds pro- ceed along the same laws as operate for the two elements discussed above. Avrami's eqn. (1) has been applied to several cases of recrystallization and transformation. Most of this work has been done with metals or alloys, but also some inorganic compounds have been investigated. In some cases it was found that the formation of nuclei was the rate-determining step, e.g. in the transformation of aragonite to calcite 26 and in the transformation of silver sulphate at 415" C.27 In the latter case the rate of the formation of nuclei depends also on time.The rate of growth of the stable phase from the unstable one, and its activation energy have also been investigated with several chemical compounds. The activa- tion energy (Ea, see eqn. (2) and (5)) is sometimes equal or nearly equal to the energy of sublimation, e.g. in the transformation of monoclinic to rhombic sulphur,Is of u- into /3-nitroaniline,28 of yellow to red mercuric iodide 29 and of azoxybenzene.30 As also the two-dimensional movement of mobile adsorbed molecules may play a role in such transformations and as the heat of transfer of a molecule from a crystal phase to an adsorbed phase is certainly lower than heat of evaporation,31 lower activation energies might be expected in some cases.Co-operative shifts of rows of molecules or quick conversions in domains of the crystals, e.g. in mosaic blocks, leading to a large pre-exponential factor of the rate equation, are certainly important in some transitions of chemical compounds. A jumpy displacement of the boundary of a growing crystal was observed by Muller 32 in the recrystallization of rocksalt. Schwab 33 observed such a phenom- enon in the transformation of potassium dichromate at 236-8" C ; the transforma- tion of the triclinic form into the monoclinic one, and the reverse effect when the specimen is cooled again, occur suddenly in relatively large pieces of crystal. In many cases the rate of transformation is largely dependent on the previous history of the samples.It may be asked if in such cases the sizes and the mutual arrangements of the blocks of the mosaic structure might play a dominant role. The mosaic character of a crystal is largely dependent on its mode of formation and also on its degree of purity. Very often a repeated transformation of an176 INTRODUCTION enantiomorphic substance from one form to the other and vice versa, has the result that the rate of transformation increases and also that the time of incubation for the formation of nuclei decreases. The crystal, so to say, gradually learns how to transform. The influence of foreign atoms on the rate of transformation could also be considered with respect to the sizes of mosaic blocks and to the nature of the transition layers between them.VARIOUS SORTS OF TRANSFORMATION One might have thought that a simultaneous shift of planes would rather easily result in transformations from the cubic to the hexagonal close-packed structures and vice versa. Such a shift resembles the sliding of planes which produces the rhombohedra1 form from normal graphite.34 Apart from many metals, there are some inorganic compounds showing two modifications, one having the cubic close-packed structure, and the other the hexagonal close-packed arrangement. For example, the S-atoms in zinc-blende are arranged according to the cubic close-packed system, those in wurtzite are hexagonally close-packed. The oxygen atoms (ions) in t~-Al203 are arranged according to the hexagonal close-packed system, those in y-Al2O3 to the cubic close-packed system.In both cases, how- ever, the distribution of the metal atoms (ions) is less simple and the rate of transformation may well depend on the movement of those metal atoms. The transformation of the tridymite form of SiO2 into the cristobalite form resembles that of wurtzite into zinc-blende. From this transformation and also from that of quartz into tridymite one may imagine that it will be necessary to break links between Si- and 0-atoms before SiO4 tetrahedra can be shifted and that after such shifts Si-0-links are re-established. Such transformations, con- sequently, do not proceed easily. All three forms of- SiO2, however, show a low temperature (a) and a high temperature @) modification. In these latter transformations only small alter- ations in the mutual orientation of SiO4 tetrahedra have to be made; they, con- sequently, take place at a far higher rate than the mutual conversions of the three main varieties. Tridymite and cristobalite may be converted innumerable times from their c( to their /3-modifications and vice versa, without being converted into the stable variety, quartz.Bernal35 pointed out that the rate of a transforma- tion is likely to be greater, according as the change in symmetry is smaller. A change in the mutual orientation in the lattice of molecules or of complex groups, without a change of the mutual arrangement of their centres, as takes place in the a + 6-transformations of the Si02-modifications, is of frequent occurrence. The possibility of such a transition was originally conceived as a transition from a fixed oriented position of such molecules or groups to a free rotational movement 34 in their lattice positions.The transformation of NaN03 observed in the temperature range of from 250-275" C was, consequently, described as a setting-in of the rotation of the NO3 ion.37 Many more examples of inorganic and of organic compounds, of ionic lattices, of layer lattices and of molecular lattices, have been described since. Zernike 38 pointed out that the observed phenomena may just as well be understood as a transition from ordered orientation to a disordered orientational arrangement. A free rotation in the lattice, therefore, is not strictly necessary and is, in many cases, certainly with many organic molecules, not likely.39 These orientational transformations, which involve an appreciably large in- crease in entropy, do not occur at a sharp transition point ; there is a transition range of temperatures, which, in some cases, however, may be rather narrow.When a certain number of molecules or groups have changed their fixed orientation into a free rotation or into another position leading to orientational disorder, it may, as far as energy is concerned, be easier for other molecules or groups to follow ; hence a co-operative shift is created by the first movements. A similar phenomenon may occur with other order-disorder transitions. TheJ . H . DE BOER 177 number of examples of order-disorder transitions of the distribution of one ionic species in a fixed lattice of the oppositely charged ion, is increasing immensely. In some cases the transition to an averaged structure of one of the ions coin- cides with a re-arrangement of the ions of the other species, such as in AgI, where two processes occur at the transition point.The iodine ions rearrange themselves into another lattice, whilst the silver ions take up averaged positions. The transition point is sharp, because of the rearrangement of the iodine-ion lattice. In Ag2HgI4 40 the iodine-ion lattice is not changed when the transition occurs from the fixed distribution of the cations to the averaged distribution of the silver and mercury ions ; the transition is rather gradual, occurring over a range of about 40” C to 50.7” C .Both these transitions show a high rate of conversion. In A1203, however, this is not the case. As mentioned above, the difference between a-Al203 (corun- dum) and y-Al203 comprises the two different forms of close-packed oxygen ion lattices and, moreover, the partially averaged structure of the A1 ions in the y-form. So many varieties of A1203 modifications are mentioned in literature that the Greek alphabet hardly has enough letters to indicate them. They may range from a completely random distribution of the Al-ions (in y’-A1203) to partially ordered distributions over the octahedron and tetrahedron holes in the oxygen lattice. All transitions, however, proceed rather slowly. The activation energies required for the movement of cations in the lattices are very much different in the AgI and the A1203 lattices This causes the large differences in transition rate in these two cases.FORMATION OF METASTABLE PHASES Some methods of electrolytic surface oxidation of aluminium produce y’-A1203, in which the A1 cations are distributed completely at random. The time of the formation of the lattice is, apparently, too short for the A1 ions to find their proper places. We may consider y’-Al2O3 to be a metastable phase under these con- ditions and the formation of this modification reminds us of the old rule of Wilhelm Ostwald, that metastable forms are often formed under such conditions that another form should be stable. For an averaged structure and low mobility of atoms (ions) in the lattice, this rule may be understood.In the paper by Burgers and Groen we are also reminded of this rule of “ step-wise formation ”, when they describe that electrodeposition of tin, even at temperatures lower than the transition point, always gives the white modification, which is not stable under those conditions. The reason for the adherence to the rule is less obvious in this case. - CHEMICAL REACTIONS IN SOLIDS The second sub-division of section C is confined to chemical reactions in solids. Here also, we have only a few papers and, consequently, the whole domain is not covered. Reactivity in solids was discussed last year in the Solvay-Conference at Brussels, and some problems will present themselves next week in the Purity Control Meeting under the auspices of the I.U.P.A.C. here in Amsterdam.At four-year intervals, moreover, the reactivity in solids has been discussed in other international meetings, created for this purpose, and there are plans to hold the fourth meeting of this kind, here in Amsterdam, in 1960. The molecular mechanism of rate processes has been studied in numerous cases. I shall make only a few remarks with respect to the formation of solid chemical compounds from other, simpler, solids and I shall deal with a few problems of the reverse reaction, the decomposition. THE FORMATION OF SOLIDS BY THE ACTION OF GASES ON OTHER SOLIDS Solids may be formed by reaction of a gas (or liquid) with other solids. The well-known tarnishing phenomena belong to this category. They have been178 INTRODUCTION studied intensively during the last decades.The rate of the reaction of oxygen, halogens or sulphur with metals is, mostly, governed by the rate of diffusion of one of the reacting species through the layer of oxide, halide or sulphide already formed. In many cases it is the metal species that moves through the layer and Wagner 41 suggested that metal ions and electrons diffuse separately. This view has been very successful and in many cases a quantitative agreement between the rate of diffusion, the rate of tarnishing and the ionic or electronic conducti- bility could be established. When the semiconductivity of the tarnishing layer has a dominantly electronic character, the rate of the reaction is governed by the diffusion of the metal ions, as, e.g., in the oxidation of copper.42 When the layer has an ionic conductance, the rate will be determined by the diffusion of the electrons, as, e.g.in the bromation of silver.43 When both the electronic and ionic conductances are low, the formation of the tarnishing layer comes to a standstill and the metal is protected from further attack, as, e.g., in the oxidations of aluminium or zirconium at moderate temperatures. REACTION BETWEEN TWO SOLID COMPOUNDS The formation of double salts or complex compounds from simpler salts may be successfully performed by reacting the compounds in the solid state. The diffusion of metal ions then governs the process. In accordance with what was seen above about transformation rates, the formation of Ag2HgI4 from AgI and HgI2 proceeds at a good speed at relatively low temperatures.* The formation of spinels seems to proceed along similar lines as far as reactions forming ferrites or chromites are concerned.The rate of formation of aluminates, however, seems not to be determined by the diffusion of both types of cations (e.g. Mg and Al, Zn and A1 or Ni and Al); the reaction is more complex and intermediate stages of unknown composition and character seem to play a role.45 The diffusion of oxygen ions may be one of the governing factors.46 An interesting reaction occurs when a small amount of cryolithe (Na3AIF6) acts on a-Al203 (corundum). The corundum is transformed into P-Al203, a hexagonal aluminium oxide which is stable only in the presence of a certain number of sodium ions.47 The rate of reaction of solids is, generally, increased in such temperature regions where one of the reacting solids suffers a transition (Hedvall effect).Definite orientational effects occur in this transformation. DOUBLE DECOMPOSITIONS In a reaction of the type Cu + AgCl -+ Ag + CuCl diffusion of copper and silver ions and electrons causes conditions that lead to the formation of nuclei of CuCl at the boundary between AgCl and Cu, while the resulting excess of Ag ions and electrons leads to the formation of Ag nuclei. These nuclei then grow larger, the material transport being covered by the ionic diffusion mechanism.48 DISSOCIATION OF SALT HYDRATES The decomposition of solids into simpler solids and gases often takes its course via nucleation and growth of nuclei. We have already mentioned the work of Garner on the dehydration of chrome alum, where quick dehydration of mosaic blocks interferes with the normal speed of the reaction.In normal cases of dehydration of salt hydrates, nuclei of the anhydrous material are formed on the surface of the crystals, whereupon these nuclei grow, layer by layer, while water is liberated. The rate is given by the expression Y = vN exp (- E/RT)J . H . D E BOER 179 where the frequency factor v has the normal value 1013 and N is the number of water molecules per sq. cm of interface. The activation energy E is equal to the heat of dissociation. With chrome alum, spherical nuclei are formed and layer growth does not occur; v has the abnormally high value of 1025 and E = 31 kcal/mole, which is nearly double the heat of dissociation (16 kcal/mole). The dehydration product of chrome alum, even when formed in vacuum is definitely crystalline.49 Such a behaviour is not always found.Many hydrated metal sulphates (Cu, Ni, Zn, Mn, Mg) when dehydrated in vacuum, yield an " active form ", with a high surface energy of the internal surface ; often these " active forms " are crypto-crystalline (X-ray amorphous).so On the admission of water vapour, above a certain limiting pressure (a few mm of mercury), they crystallize into the lattice of a lower hydrate. It appears that on dehydration a skeleton lattice is formed which collapses into either a crypto-crystalline state or a state of ionic disorder. The rate of dehydration often falls with increasing water vapour pressure to reach a minimum value at the limiting water vapour pressure mentioned above.From this minimum onwards the rate increases with increasing water vapour pressure, passes a maximum and decreases again. This effect has first been ob- served in the dehydration of manganous oxalate dehydrate 51 and was recently studied with sulphates by the Canadian workers.sos 52 Tt is a well-known fact that well-formed and well-shaped crystals of many salt hydrates do not easily lose their water. The nucleation with anhydrous (or lower hydrate) nuclei requires a long incubation time. Once it has started it proceeds at a quicker rate; the process has an autocatalytic character. Two of the hydrates of AlF3, viz. AlF3. H20 and AlF3.3H20 show very remarkable behaviour. The first of the two hydrates is converted into the " half" hydrate at roughly 210-250" C, whereas the last half-molecule of water is lost only at very high temperatures.Water-free AlF3 does not re-hydrate. Ketelaar 53 investigated this case and found that AlF3 and the two hydrates have exactly the same crystal structure and the same cell-dimensions. The water molecules are situated in holes between the F-ions and do not break up the lattice during dehydration. Actually, there is no lattice rearrangement in this case. DEHYDRATION OF HYDROXIDES It seems quite possible that in many cases of dehydration of metal hydroxides original lattice planes serve as a nucleus for the dehydration product ; no special nucleation seems to be necessary. The dehydration of brucite (Mg(0H)Z) leads to periclase (MgO) crystallites which are oriented with respect to the original lattice.The [111]- and [llO]-axis of the MgO crystals coincide with the [OOOl]- and [1010]-axis of the bmcite.54 The dehydration of the various aluminium trihydrates and monohydrates also leads to oriented anhydrous forms of alumina. When gibbsite (Al(OH)3) is dehydrated,sS water molecules are formed along its (001)-layers ; the lattice contracts and fissure-like pores are formed between plate-like particles of de- hydration product. When dehydration advances these plate-like particles are divided into rod-like particles, all of which lie parallel to each other in the cleavage plane including a second type of pore. All these particles are pretty well oriented, their octahedron planes lying parallel to the original (001)-plane of gibbsite.The dehydration product of gibbsite is x-A1203, but if the granules of the gibb- site are not too small, part of it is simultaneously converted into a well-crystallized boehmite (AlO(0H)). This conversion is caused by internal (intragranular) hydrothermal conditions during the dehydration process.56* 57 With fine granules this conversion takes place to a lesser extent, and small single crystals give the normal dehydration product only. The rate of dehydration and its change with - mperature and with time depend largely upon the proportion of normal de- - dration to intragranular hydrothermal conversion. The dehydration of the180 INTRODUCTION other modification of aluminium trihydroxide, viz. bayerite, is similar to that of gibbsite.56 It is interesting to note that various more or less anhydrous forms of A1203 result from the dehydration of aluminium hydroxides. According to the degree of crystallinity we may have, first, a completely amorphous Al2O3, secondly, the X-form as the dehydration product of gibbsite and the y-form (called the .?-form by others) as the dehydration product of bayerite, thirdly, the y-form as the dehydration product of boehmite, fourthly, the higher-temperature forms 8, K and 6, and fifthly, the cc-form (corundum). It may be that as has been stated above where the y'-form of A1203 was mentioned, all these forms, except a, have the same arrangement of the oxygen ions but that they differ in the degree of order- ing of the A1 ions.Due to the very low rate of diffusion of the A1 ions, some forms may well be metastable in the region where they are formed.DECOMPOSITION OF CARBONATES Orientation effects are also observed in the dissociation of carbonates. The dissociation of, e.g. dolomite crystals starts at the surface and proceeds gradually into the interior of the crystals. The first step involves the formation of MgO and CaC03 ; at relatively low temperatures (600-650" C) the calcite crystals are well oriented.58 A direct formation of the calcite crystals by an exchange mechanism of Ca and Mg ions, together with a small dilatation of the lattice, seems quite possible. The MgO crystals, however, show a random distribution. Apparently, the nuclei for the formation of the MgO crystals form statistically at those spots where a sufficient number of Mg ions has assembled by diffusion and where a sufficient number of carbonate ions has dissociated.It is an interesting fact that the calcite crystals formed in the dissociated dolomite seem to have a metastable existence under circumstances where they should dissociate quickly. On the other hand, they show during their formation a somewhat higher rate of C1302 exchange than does normal calcite. DECOMPOSITION OF AZIDES Like the dehydration of many salt hydrates the decomposition of inorganic azides has an autocatalytic character.59 The nuclei form both at the surface and in the interior of the crystals. Mott,60 inspired by theories on the latent image in photographic processes, suggested a mechanism for the formation of these nuclei. Later work by Thomas and Tompkins,sl however, showed that this theory did not explain all the facts.In our present meeting we are informed about the further work which Tompkins and Young have done in this field. They give definite attention to the formation of the germ nuclei (or potential nuclei as we called them above) and the growth of these nuclei to real growth nuclei. As metal atoms are formed inside metal salt crystals, it is obvious that colour centres (F-centres), electron movement and ionic movements play their roles. The properties are largely structure sensitive and, consequently, mosaic blocks and factors which influence them, are here also of great importance. RESTORATION AFTER DECOMPOSITION When in a lattice a local decomposition has been introduced, e.g.by an irradiation process, the rate of recombination, hence the rate of restoring the original lattice arrangement, may be studied. In such a case no nucleation phenomena need to be considered, because of the presence of the surrounding, undisturbed lattice. The rate may be determined by diffusion of the decomposi- tion products, which after they have been thrown apart have to meet again to recombine. In other cases it may be that, in the decomposition, such a serious change has taken place in the fragments that have been thrown apart that a straight-J . H . DE BOER 181 forward recombination cannot take place. It may then be that the recombina- tion is not a direct re-uniting of radicals, but that it represents a reaction involving an activation energy in itself. One of the modern ways to affect a local decomposition in a lattice, is the irradiation by neutrons.The fragments may be thrown apart over large distances, large compared with lattice dimensions. As we learn from the contribution by de Maine, Maddock and TaligbGl, this may mean that in some cases, the frag- ments do not find their way back at all. Another possibility, also discussed by the authors, is that the fragments, instead of diffusing back to recombine, may diffuse to the outer surface, where they either disappear by evaporating, or where they can be permanently fixed in another state of combination. The authors have performed many of their experiments in such a way that only recombination of fragments formed in one nuclear event need to be considered.One would not expect the mosaic structure to be a hindrance for the throwing apart of the fragments during this event but the mosaic structure may offer a serious obstacle for the return of fragments in order to recombine. The failure to obtain a complete recovery may perhaps also be caused by this irreversibility. The inclusion of this contribution in the present meeting is significant. The modern possibilities, offered by the nuclear processes, add new experimental techniques to the field of reactions in solids. They will undoubtedly, also largely increase the general interest in the chemistry and physics of the solid state. 1 Wells, Structural Inorganic Chemistry (Oxford, The Clarendon Press, 1945), p. 154. 2 Man-made Diamonds (Research Information Service, The Knolls, Schenectady, 3 Bridgman, J.Chem. Physics, 1947, 15, 92. 4 Avrami, J. Chem. Physics, 1939,7, 1103 ; 1940,8,212; 1941,9, 177. 5 Fisher, Hollomon and Turnbull, J. Appl. Physics, 1948, 19, 775. 6 Turnbull and Fisher, J. Chem. Physics, 1949, 17, 71. 7 Burgers and Groen, this Discussion. 8 For more details about the formation of nuclei, see Burke and Turnbull, Prog. 9 Hartshorne, Faraday Soc. Discussions, 1949, 5, 149. N.Y., 1955). Metal Physics, 1952. Smoluchowski, Znd. Eng. Chem., 1952,44, 1321. 10 Akulov, Compt. rend. U.R.S.S., 1941, 32, 340; 1943, 39, 268. 11 Laurent, Compt. rend., 1944, 219, 205 ; Rev. Me'tall., 1945, 42, 32. 12 Frye, Stansbury and McElroy, J. Metals, 1953, 5, 219. 13 Dunning, mentioned by Hartshorne, ref. (9), p. 156 ; see also p.194. 14Burgers, J. M., Proc. Physic. SOC., 194-0, 52, 23. Bragg, Proc. Physic. SOC., 1940, 15 Burgers, W. G., Proc. Kon. Ned. Ak. Wet., 1947, 50, 595, 719. 16 Mott, cp. Burgers, W. G., ref. (19, p. 726. 17 Garner, Faraday Soc. Discussions, 1949, 5, 194. 18 Hartshorne and Roberts, J. Chem. SOC., 1951, 1, 1097. 19 Bragg, W. L., Proc. Physic. SOC., 1940, 52, 105. 20 Schenk, J., Thesis (Delft, 1956). Prins, Schenk, J. and Hospel, Physica, 1956, 22, 21 Bradley, Hartshorne and Thackray, Nature, 1951, 173,400. 22 Das, Indian J. Physics, 1938, 12, 163 ; 1939, 13, 91. 23 Schenk, P. W., 2. anorg. Chem., 1955,280, 1. 24 Prins, Physica, 1954, 20, 124. 25 Elias, Hartshorne and Dennil James, J. Chem. Soc., 1940 (I), 588. 26 Chaudron, Mondange and Pruna, Proc. Znt.Symp. Reactivity in Solids, 1952, p. 9. 27 Johansson, Arkiv. Kemi, 1954, 8, 33. 28 Hartshorne, Walters and Williams, J. Chem. Soc., 1935, (2), 1860. 29 Eade and Hartshorne, J. Chem. SOC., 1938 (2), 1636. 30 Hodkin and Taylor, J. Chem. Soc., 1955, 489. 31 De Boer, J. H., The dynamical character of adsorption (Oxford, Clarendon Press, 32 Miiller, H. G., 2. Piiysik, 1935, 96, 279. 52, 54. 770 ; further articles to follow in Physica. 1953), p. 138 ff.182 I N T RO D IJ C T I 0 N 33 Schwab and Schwab-Agallidis, Naturwiss., 1941 , 29, 134. 34 Hofmann and Boehm, 2. anorg. Chem., 1955,278, 58. 35 Bernal, Trans. Faraday Soc., 1938,34, 834. 36 Pauling, Physic. Rev., 1930, 36,430. 37Kracek, J. Amer. Chem. Soc., 1931, 53, 2609. Kracek Posnjak and Hendricks, J. Amer. Chem. Soc., 1931, 53, 3339. Bijvoet and Ketelaar, J. Amer. Chem. Soc., 1932, 54, 625. Ketelaar and Stryk, Rec. traw. chim., 1945, 64, 174. 38 Zernike, Ned. Tijdschr. Natuurk., 1941, 8,66. 39 Perdok, W. G., Thesis (Groningen, 1942). Backer and Perdok, Rec. frav. chim., 1943, 62,533. Perdok and Terpstra, Rec. trav. chim., 1943, 62,687 ; 1946,65,493. 40 Ketelaar, 2. physik. Chem. By 1934, 26, 327 ; 1935, 30, 53 ; Trans. Faraday Soc., 1938,34,974. 41 Wagner, Z. physik. Chem. B, 1933,21,25 ; 1936,32,447. 42 Wagner and Griinewald, 2. physik. Chem. B, 1938,40,455. Castellan and Moore, J. 43 Wagner, Z. physik. Chem. B, 1936, 32,447. 44 Koch and Wagner, 2. physik. Chem. B, 1936,34, 317. 45 Lindner and Wkerstrom, 2. physik. Chem., 1956, 6, 162. Chem. Physics, 1949, 17, 41. Lindner, in Quelques probl2mes de chimie mintrale, Dixi2me Conseil de Chimie (Institut Solvay), 1956, Weyl, Quelques probl2mes ak chimie mine'rale, Dixizme Conseil Cie Chimie (Institut Solvay), 1956, p. 436. p. 472. 46 Bengtson and Jagitsch, Arkiv. Kemi, A, 1947,24, nr. 18. 47 Saalfeld, 2. anorg. Chem., 1956, 286, 174. 48 Wagner, 2. anorg. Chem., 1938, 236, 320. 49 Cooper and Garner, Proc. Roy. SOC. A, 1940,174,487. 50 Frost, Moon and Tompkins, E. H., Can. J. Chem., 1951, 29, 604. Quinn, Missen and Frost, Can. J. Chem., 1955,33,286. 51 Topley and Smith, J. Chem. SOC., 1935, 321. Vollmer and Seydel, 2. physik. Chem. A, 1937, 179, 153. 52 Wheeler and Frost, Can. J. Chem., 1955,33, 546. 53 Ketelaar, J. A. A., Thesis (Amsterdam, 1933) ; 2. Krist., 1933, 85, 119, 130. 54 Bussem and Korberich, 2. physik. Chem. B, 1932, 17, 310. Garrido, Compt. rend., 55De Boer, J. H., Steggerda and Zwietering, Proc. Kon. Ned. Ak. Wet., B, 1956, 56De Boer, J. H., Fortuin, J. M. H. and Steggerda, J. J., Proc. Kon. Ned. Ak. 57 PapCe and Tertian, Bull. SOC. Chim., 1955, 983. 58 Haul, Proc. Int. Symp. on the Reactivity of Solids (Gothenburg, 1952), p. 431. 59 Garner and Marks, J. Chem. Soc., 1936, 657. Garner and Maggs, Proc. Roy. Soc. 60 Mott, Proc. Roy. SOC. A, 1939, 172, 326. 61 Thomas and Tompkins, F. C., J. Chem. Physics, 1952, 20, 662. 1936, 203, 94. 59,435. Wet. By 1954,57, 170 and 434. A, 1939, 172,299.

ISSN:0366-9033    

DOI:10.1039/DF9572300171

出版商:RSC    

年代:1957

数据来源: RSC

摘要:

MECHANISM AND KINETICS OF THE ALLOTROPIC TRANSFORMATION OF TIN BY W. G. BURGERS AND L. J. GROEN Net herlands Laboratory of Physical Chemistry, Technological University, Delft, Received 21st January, 1957 The first part of the paper deals with X-ray and microscopic observations of the transformation of single and polycrystalline material, and discusses the question whether such observations allow conclusions regarding the atomic mechanism of processes under- lying nucleation and growth. It is put forward that unambiguous conclusions cannot be deduced from the experimental data, in particular not on the mechanism of nucleus formation. In the second part complete isothermal transformation curves for both transformations are given, deduced from dilatometric measurements, for tin samples of different purity.The influence of temperature has been considered. For the transformation white -+ grey the results comply with Avrami’s equation for the fraction transformed f ( t ) : 1 -f(t) = exp (- Ark), (1) with a value for k = 3. In agreement with the phenomenological aspect of the trans- formation, this result may be expected for three-dimensional growth of nuclei formed in the beginning of the transformation process. For the grey -+ white transformation the dilatometric measurements can also be described by an equation of type (l), with k-values varying from about 1 to 2-5. The interpretation of the equation, in this case, has to be different. Direct observation of the transforming grey modification shows the sudden formation of regions of the white phase, which grow in a few seconds to a limited size.Therefore, rate of nucleation, not rate of growth, determines the rate of transformation. For values of k about 1 the transformation is of the unimolecular reaction type ; k-values > 1 point to an autocatalytic reaction, spontaneously formed nuclei giving rise to induction of further nuclei in their neighbourhood. The problem of the mechanism of an allotropic transformation process in a solid would be solved if the exact atomic movements involved in the formation and growth of particles of the new phase at the cost of the existing modification were known. As these movements exempt themselves from immediate observa- tion one must have recourse to indirect experiments from which relevant con- clusions may be drawn.X-ray analysis may reveal the existence of definite crystal- lographic relationships between both phases, microscopic observation shows the way in which the new phase forms and grows on a “ visible ” scale. Furthermore the “ overall” course of the transformation can be studied, for example by determining the fraction transformed as function of time under isothermal con- ditions at various temperatures. One can then try to interpret the results obtained on the basis of an assumed model. This paper describes such investigations of the allotropic transformation of tin. Although this process has been the subject of much experimental work, in particular by Ernst Cohen and his co-workers in the years 1899-1937 (for extensive references of this and later work, see Groen *), this relates mainly to the white + grey transformation; the inverse process has been far less investig- ated.The study of the kinetics of the transformation has been restricted to 183184 ALLOTROPIC TRANSFORMATION OF TIN observations and calculations of the temperature-dependence of the linear growth-rate of the grey phase at the cost of a white matrix. Complete isothermal transformation curves have not, as yet, been measured. The paper is divided in two main parts. The first part deals with observations of different character : X-ray analysis, direct and microscopic observation, action of electrolytes on the rate of transformation. The results obtained are discussed in so far as they may bear on the processes of nucleation and growth, in particular regarding the question whether they take place by single atomic steps in a diffusion- like way, or by co-ordinated movements of larger groups of atoms, as in diffusion- less transformations.The second part discusses the isothermal transformation-curves deduced from dilatometric measurements for both the white -+ grey and the grey -+ white transformations. Combination of the evidence so obtained with data deduced from the phenomenological aspect of the transformation leads to definite con- clusions regarding the part played by nucleation and by growth in each of the two transformation processes. PART I MISCELLANEOUS OBSERVATIONS X-RAY ANALYSIS A diffusionless transformation leads in many cases to a definite crystallog- raphic relationship between the lattice orientations of the original and the new modification.Kuo and Burgers 2 investigated whether transformation of a single crystal of white tin gave rise to grey crystals with a definite orientation with regard to that of the mother crystal. Earlier experiments by Groen3 had shown that compact single crystals of the grey form could be obtained provided the white tin contains a small amount (about 0.1 weight %) of mercury. Of twenty trans- formed white crystals, twelve yielded single crystals of grey tin of sufficient size to determine their orientation by means of Laue photographs. Fig. 1 gives examples of partly transformed single crystals. Due to the large difference in specific volume (> 20 %), a considerable amount of transformation strain occurs close to the deformation front, resulting in fragmentation and rotation of the lattice of the white crystal over several degrees as was clear from the appearance of striae in the Laue photographs (cf.fig. 2). For this reason the orientation relationship could not be determined accurately. The fact, however, that the orientations for twelve pairs of white --f grey crystals showed a random scattering without any pronounced indication of preferred orientation (fig. 3), seems to point to the absence of a definite relationship between the lattices of the white crystals and of the grey crystals formed from it. However, it should be pointed out that only the absence of what may be called a " macro-orientation relationship " between the two modifications is shown in this way.The Laue method used is incapable of dealing with the existence of an eventual two-dimensional coherency over a few atomic layers. Hall4 and also Prasad and Wooster 5 have suggested, from purely structural considerations, the following orientation relationship : (100) white // (1 10) grey ; (001) white // (001) Fey. This would require a considerable lattice strain, which the " brittle " grey tin could not easily share, so that breakdown of the coherency would presumably occur after a few atomic layers (cf. Hall 4). MICROSCOPIC OBSERVATIONS In diffusionless transformations of the martensitic type one observes, on a polished section, the appearance of individual, often plate-shaped, lamellae whichFIG. 1.-Single crystals of white (,8) tin during transformation into grey ( x ) tin.FIG, 2.-Laue photographs of a single crystal of white tin during transformation : (a) far from the transformation front : undeformed white crystal ; (b) close to the transformation front : deformed white crystal (asterism) [To face page 184 and undeformed grey crystal (sharp spots).FIG. 4a. FIG. 4c. FIG. 4b. FIG. 4d. FIG. 4e. FIG. 4.-Formation of domains of white tin in grey tin powder (10 x) as seen in polarized light. Successive photographs were taken at intervals of 5-10 sec. (The white dotted lines are scratches on a brass plate serving as support for the powder.) [To face page 185W. G . BURGERS AND L . J . GROEN 185 " tilt " the surface due to the change in shape brought about by the co-operative displacement of a large group of atoms.The formation occurs either abruptly within very short times (of the order of 10-7 sec : Foster and Sclieil; 6 Mehl and Bunshah ; 7 true martensitic transformations according to Philibert *), or more gradually at a reasonable rate (0.5 mm/h in the isothermal transformation of uranium at room temperature (Holden ; 9 pseudo-martensitic transformation according to Philibert 8). The lamellae follow generally definite crystallographic crooy3 FIG. 3.-{100)-poles of twelve grey tin single crystals formed from twelve white tin single crystals. The orientations of the latter are rotated in the stereographic projection so as to coincide with the (001)-projection of the white tin. directions (habit planes). A process of this kind, in which a finite region of a crystal transforms at once, creates distortions and a stress field in its immediate neighbourhood.This in its turn may give rise to the formation of further plates, or induce growth of the lamellae. The above-mentioned characteristic features of diffusionless transformation processes are not encountered in this precise way in the transformation of tin. However, in particular the formation of white tin in a grey matrix shows in various respects an unmistakable resemblance to them. GREY -+ WHITE TIN The transformation in particles of grey tin (0.1-0.8 mm), each, as shown by X-rays, consisting of a large number of crystallites, was examined under a micro- scope in polarized light. This showed (fig. 4) a continuous sudden formation of small domains (0.04-0.2 mm) of white tin, growing to their final volume in a rela- tively short time (5-30 sec).In one individual grain of grey tin, 3-5 of such domains are formed, with intervals sometimes of a few minutes. The average volume of the domains was approximately constant during the process. During the rapid propagation of the phase boundary, which takes place fairly regularly, a shrinkage of the particles, due to the decrease in volume, was observed, together with changes in shape. The change in volume is accompanied by the formation of bursts and cracks, and sometimes the particles disintegrate into smaller186 ALLOTROPIC TRANSFORMATION OF TIN ones. It is suggested that the observed limited growth of the domains of white tin is due to the breaking-up of the grey modification. The linear rate of growth of the white phase in the grey phase could be measured in these experiments.It was found to be 0.003 mm/sec at 30" C and 0.022 mm/sec at 36" C, and is thus strongly temperature-dependenty increasing to high values at high temperatures (cf. fig. 7). This rate of growth is small compared with that in true martensitic processes, but high compared with that in the pseudo-marten- sitic transformation in uranium, and with that of the reverse white -+ grey tin- transformation. It is also large compared with the rate of growth of new crystals formed by recrystallization in cold-worked white tin. According to (unpublished) measurements of Barten in this laboratory these gave for crystals growing in a 15 %-stretched fine crystalline matrix of Banka tin about the same value (0.004 mm/sec) at 127" C.* The relatively high value might eventually be explained by assuming a co-ordinated movement of the atoms, but there is no further evidence to support this assumption.As will be discussed in part 11, the course of the transformation-time curves for the grey to white transformation requires " induction " of nuclei formation during the progress of the transformation. This effect, which is more pronounced at lower temperatures, is thought to be brought about by the deformation stress resulting from the volume decrease accompanying the formation of white regions. Again this feature of the transformation process is reminiscent of what is observed in martensite-type processes. However, it is well known that also in isothermal recrystallization of cold-worked metals the rate of nucleation is generally not constant.This is evident, e.g., from the work by Anderson and Mehl10 on the recrystallization of aluminium and in this laboratory by Barten (unpublished) on tin. This behaviour of the recrystallization process has been explained (Cahn 11) by assuming that the time for polygonization (i.e. the incubation period for nucleation) depends on the degree of deformation of the lattice region con- cerned. An arbitrary course of the rate of nucleation as a function of time of heating can then be attributed to a corresponding distribution of deformed regions in the cold-worked matrix. WHITE -+ GREY TIN The way in which the inverse transformation, of white into grey tin, takes place, gives no direct indication of a diffusionless process.When starting with a white polycrystalline plate the progression of the boundary of the grey nodules shows a certain resemblance to the growth of a large crystal in a recrystallizing polycrystalline plate. In both cases one observes the gradual extension ofap- proximately circular (spherical) regions (fig. 5). Although local differences in rate of growth certainly exist, there is no marked change in rate when the advancing boundary passes over from one matrix grain into another.? Also in a transforming white single crystal the shape of the phase boundary of a transformed grey region does not indicate a dependence of rate of growth on the relative orientations of growing grain and disappearing lattice.The considerable change in volume causes the formation of cracks and fissures between both modifications. On the other hand, continuous observation of grain growth in recrystallizing zinc (Brinson and Moore 12) and tin (Barten 13), made possible by use of polar- ized light, often revealed a jerky, discontinuous displacement of individual boun- daries (also earlier work, for example, on tin-antimony by Carpenter and Ela1n,14 using surface oxidation, showed similar features). This is an indication that, in * This latter value is of the order of magnitude estimated from the value of the co- efficient of self-diffusion as given by Fensham (Austral. J. Sci. Res. A, 1950,3, 91) divided by the atomic distance. t Even in a mass of filings of white tin a transforming region spreads spherically.FIG. 5.-Growth of grey tin in polycrystalline white material (1 X ).[To face page 186W. G . BURGERS AND L . J . GROEN 187 definite stages of the process of boundary displacement, co-operative movements of larger groups of atoms (which may have to do with the adjustment of coinciding boundaries) occur. In the case of a " simple " crystal boundary, made up of a series of edge-dislocations, as proposed by J. M. Burgers 15 and W. L. Bragg,l6 displacement of the boundary can actually be brought about by application of a suitable shear stress and be interpreted as a collective movement of the set of dislocations building it up (e.g. Parker 17 on zinc crystals). It remains doubtful whether a similar, possibly more complicated movement of dislocations, might also constitute the fundamental mechanism of boundary movement between two grains of arbitrary orientation, which in that case would possess a diffusionless character.It is of interest to note that the possibility of such a process during recrystallization was suggested by Dehlinger 18 as long ago as 1928. INFLUENCE OF SURFACE CONDITION ON THE NUCLEATION OF GREY TIN Cohen and Van Eyk19 observed that the transformation of white into grey tin is accelerated by immersion into a solution of pinksalt (NH4)2SnC16. Cohen ascribed this influence to " internal electrolysis " in local elements : white tin/ solution/grey tin. In such elements below the transformation point at 13.2" C, the unstable white modification would be dissolved and the grey modification precipitated.This explanation seems improbable (Groen ~ 2 0 ) , as electrolysis of a tin salt solution at a temperature below the transformation point deposits white tin on the cathode, even if this consists of grey tin. This result was found both with a 10 % solution of pinksalt in water at 0" C and with a 0.5 % solution of SnC12 in alcohol at - 50" C. Moreover, in a partially transformed white tin plate the displacement of the boundary between a grey region and the surrounding un- transformed white matrix is not influenced by immersion in pink-salt solution. Further an accelerating action is exerted by all electrolytes capable of dissolving tin or tin oxide; not only SnCIg--ions, but also Sn2+, Sn4+, HCl, H2S04 and NaOH, act as accelerators whereas Zn2f and Fe3+ have no influence.This latter result, combined with the fact already found by Bredie 21 and by Van Lieshout 12 that superficial oxidation of white tin exerts a pronounced retarding influence on the transformation, makes it probable that the acceleration finds its cause in the removal of a thin oxide layer at the surface of the specimen. In view of the considerable increase in specific volume, a mechanical obstruction of this kind would be immediately understandable if the formation of a grey nucleus were brought about by a coherent displacement of atoms in a lattice region, giving rise to a definite change in shape such as accompanies a martensite-type transformation process. In that case the accelerating effect would show a certain analogy with the increase in rate of creep of superficially oxidized cadmium single crystals when immersed in electrolytes capable of dissolving the oxide layer (Andrade and Randall 2 9 , the so-called Rehbinder effect.According to Andrade the formation of surface steps due to the glide lamellae meets with less obstruction at a clean crystal surface than at a slightly oxidized surface. However, also nucleation theories based on unit processes involving the addi- tion or removal of one atom at a time, as assumed in Becker and Doring's classical picture (cf. Hardy and Heal 2 9 , require a critical nucleus with a certain minimum size, depending, e.g., on the interfacial energy between the original and the new phase. Also such a process might be hindered by the presence of an obstructing oxide layer.In conclusion, one might say that neither from the X-ray investigation nor from the direct observation of the transformation process, conclusive arguments can be deduced for the assumption that nucleation and growth of the new phase,188 ALLOTROPIC TRANSFORMATION OF TIN be it white or grey tin, are diffusionless processes. The observations are, how- ever, not contradictory to this occurrence, only insufficiently sensitive for a decision to be made.* t 0 PART I1 e ' *' . -0, I I 1 -- KINETICS OF THE ALLOTROPIC TRANSFORMATION I N TIN# RATE OF GROWTH WHITE -+ GREY TRANSFORMATION Extensive measurements of the linear rate of growth of grey tin in a white matrix were performed by Tammann and Dreyer,27 who used a relatively impure Banka tin (99.95 %).They found, e.g., a maximum rate at - 40" C of 0.06 mm/24 h, and an acceleration or retardation by addition of various elements. C c m / 2 4 h t o c FIG. 6.-White to grey transformation. Linear rate of growth G at different temperatures for high-purity tin, as measured directly, and as calculated from dilatometer experiments (cf. fig. 8 and eqn. (3)). Cagle and Eyring 25 applied the absolute reaction rate theory ; the deviations between their theoretical values and the experiments are very large and the necessary constants are introduced such that only the maximum rate of growth for theory and experiment coincided. No definite conclusions can be deduced concerning a molecular mechanism. The same holds for similar efforts by Becker,28 who used a slightly different approach.A set of measurements of the linear rate of growth of white to grey tin was carried out in the present investigation on sheets of very pure tin (Vulcan De- * Cagle and Eyring,25 in an effort to apply the theory of absolute reaction rate to the transformation of white to grey tin, have assumed the simultaneous action, in growth, of activated complexes containing up to eight atoms. -f Dehlinger (p. 129, ref. (26)) mentions the tin transformation as an example of a pro- cess brought about by jumps of single atoms. The same author (p. lo), considered the effect of a progressive displacement of individual atoms in the lattice of grey tin into neighbouring positions of the lattice of white tin. It is shown that the stresses accom- panying the atomic displacements have to be taken into account in order to explain the existence of a sharp transformation point.2 For details of the investigations discussed in this part the reader is referred to Groen.1W. G . BURGERS A N D L . J . GROEN 189 tinning Co., 99-9978 %).* In this case, the maximum rate, appearing between - 35 and - 50" C, was found to be about 2.2 cm/24 h (fig. 6). The calculation of an activation energy by applying the usual treatments (Cagle and Eyring; 25 Frye, Stansbury and McElroy ; 29 Hartshorne 30) proved impossible. GREY --f WHITE TRANSFORMATION Hitherto no measurements concerning the growth-rate of this transformation are reported in literature. The values were measured here by the method already mentioned. For the same high-purity tin as was used in the reverse transformation experiments, values for the linear rate of growth were obtained in the range be- tween 30" and 36" C (fig.7). In this case an activation energy could be calculated C in O J I 1 I I 3 0 3 2 34 36 38 o c FIG. 7.-Grey to white transformation. Linear rate of growth G at different temperatures. from the results, being 50 kcal/mole, a rather high but not unreasonable value compared with those reported in recrystallization and transformation experiments (see Anderson and Mehl;lo Probst and Sinnott 31). RATE OF TRANSFORMATION For both transformations a large number of complete isothermal dilatometric measurements was made at various temperatures. The experiments were carried out with finely divided material : white filings, filings transformed into grey, powder formed by transformation of a white bar, and powder retransformed from grey to white.The glass dilatometer contained & 3 g tin ; the raising and lowering of the liquid level did not exceed 15 cm in a capillary tube with a diameter of 1 mm. The results allowed a plot of the transformed fraction as a function of log time for different samples and at various temperatures. All isothermal trans- formation curves obtained were S-shaped, some of them showing an incubation period (cf. fig. 8n and 9a). The differences between the individual curves were too large to allow of a simple uniform description, in terms of nucleation and growth, as given by Johnson and Mehl.32 In an effort to interpret the experimental course of the isothermal trans- formation curves, from the various formulae proposed in literature (Hardy and * put at our disposal by Dr.E. S. Hedges, Tin Research Institute, Greenford-190 ALLOTROPlC TRANSFORMATION OF TIN Heal; 24 Groen I), the relation given by Avrami 33 was considered to be the most general. 3 I00 200 FIG. &-White to grey transformation. (a) Isothermal transformation curves at different temperatures for high-purity tin, (b) Corresponding plots of loglo loglo l/(Z -f(t)) against loglo t ; the slope of the subjected to several preceding transformations. lines equals k in eqn. (1).W. G . BURGERS AND L . J . GROEN 191 0 FIG. 9a. I 2 loqmt FIG. 96. FIG. 9.-Grey to white transformation. (a) Isothermal transformation curves for high-purity tin at different temperatures.(b) Corresponding plots of loglo loglo 1/( -f(tZ)) against Joglo t ; the slope of the lines equals k in eqn. (1). In Avrami’s general formulation : 1 -f(t) = exp (- Ark) (1) in whichf(t) = fraction transformed, and t = time. The meaning of A and the value of k for some extreme cases are as follows : (a) Constant rate of nucleation N (number of nuclei formed per unit time per unit volume untransformed material) ; the nuclei extend in three dimensions with a constant linear rate of growth G : k = 4, A = uNG3, u = shape-factor.192 ALLOTROPIC TRANSFORMATION OF T I N (6) Nucleation takes place only at the beginning of the process, when a number of c nuclei per unit volume is formed ; three-dimensional growth follows : For two- and one-dimensional growth the value of k and the exponent of G decrease by 1 and 2 respectively.In order to find the value of k for each transformation curve, plots of loglo log10 l/(/ - f(t)) against log 1 were established : (2) In nearly all cases in both transformation directions, straight lines, the slope of which equals k, were obtained up to about 80 % transformation. k = 3 , A = acG3. loglo loglo I/(/- f(t)) = k loglo t + loglo (AP.3). WHITE -+ GREY TRANSFORMATION Microscopical and macroscopical observations on transforming specimens lead to the following picture. (i) In a hitherto untransformed white material, a small number of nuclei (d= 3/g tin) is formed at the beginning of the transformation after a long incubation period (some hours), and a transforming region spreads spherically around each nucleus.(ii) In a white material, already subjected to several transformations, in every particle a limited number (1-4) of grey nuclei is formed at the beginning of the transformation, each growing spherically. The nucleus formation is supposed to take place at the small regions of grey modification which remain after the preceding grey to white transformation. The presence of some grey tin in the specimen is indicated by the results of density measurements. * These phenomenological observations lead to a description of the transforma- tion in terms of nucleation and growth, and correspond to case (b) of the Avrami formula; thus one may expect k = 3 for the isothermal white to grey transform- ation. For some general curves, in which both cases (i) and (ii) are represented, the value of k varied between 1.45 and 2-4.This is not in accordance with expecta- tion; however, reasons for this deviation can easily be given (see ref. l), and are related, e.g. to the small number of nuclei and the small particle-size. In one series (gin fig, 8) carried out with a specimen of pure tin subjected to several preceding transformations (case (ii)), the k-values range from 2.65 to 3.55, thus giving good agreement with the expected value. The results allow of a calculation of G as a function of temperature. With 1 - f(t) = f (white), eqn. (2) becomes (3) from which (cccG3/2*3)* was calculated for 50 %-transformation. * From density measurements it would appear that neither the transformation of white into grey tin, nor the reverse transformation ever leads to completion of the process, but that about 1-2 % of the original phase remains untransformed.This is even SO for white tin formed from grey at 60” C. It is also found for grey formed from white which had been subjected to neutron bombardment (Fleeman and Dienes 34). This remarkable fact may be connected with a phenomenon observed during growth of new crystals at the cost of fine-grained material in a recrystallizing matrix of aluminium. In that case it is found that the growing crystal cannot consume those original crystallites of the matrix which have, within a few degrees, the same lattice orientation as the growing crystal, or occupy approximately a spinel-twin position with regard to it (Tiedema, May and Burgers ; 35 Lacombe and BerghCzan 36).In this case it means that the boundary be- tween two lattice regions with this mutual orientation relationship has a low mobility due to its particular “structure”. From this point of view one might envisage the possi- bility that also during the transformation of tin a special orientation relationship between the original and the new (grey or white) lattice may have an unfavourable “ structure ” for displacement and thus cause the presence of untransformed regions. loglo loglo l/f(white) = k loglo t + loglo cccG3/2*3W. G . BURGERS AND L . J . GROEN 193 By inserting in this expression the experimental G-value for -- 48" C (curve lg), the corresponding values were found for the other temperatures used ; considering the accuracy of the measurements, the agreement is satisfactory (fig.6). GREY -+ WHITE TRANSFORMATION The phenomenological observations, already described, lead to quite anotner interpretation for the isothermal transformation curves than in the foregoing case. The short time of growth of the white domains, compared with the total transformation time of the specimen, indicates that the rate of growth plays no specific part. The transformed fraction is determined only by the number of domains formed, i.e. by the rate of nucleation N. Fiti. lO.-Graphical plot of eqn. (7) for series (a) (cf. fig. 9) ; the value of p is given for the different experiments. Assuming a time-independent N , and an equal volume v for all white domains, the process can be interpreted as a " unimolecular reaction " df(t) == NU[ 1 - f(t)]dt, (4) lcading to 1 - f ( t ) = exp (- Nvr). ( 5 ) This formula has only a formal resemblance to the Avrami-formula with k ~ 1 , which is based on a different mechanism of the transformation process. It appeared that k is not equal to 1, but in many cases close to this value (0-70-1.30) ; for some specimens of high purity tin, however, k was larger, increasing up to 2-4 (series a, fig.9). Since the second assumption (constant volume v) is fairly near to reality, N must increase with time to obtain k > 1. This increase can be understood by introducing an " induction " of the nucleation, due to the transformation and the resulting deformation of surrounding lattice regions. This can be expressed by putting in (4) : N = c + af(0, (6) leading to log l-pf(t) t 13 - log - f(0l = M t , (7) in which p = a/c and in = (a + c)/2.3.In a number of cases, straight lines for definite p-values (fig. 10) are obtained when plotting the first term of this equation against t. The required values of p G194 ALLOTROPIC TRANSFORMATION OF TIN vary from 0-10. p = 0 means constant N, i.e. absence of induction; a large p - value corresponds to a large k. The fact that the lines do not pass through the origin can be interpreted as an indication that induction of nucleation does not start before the transformation has already proceeded to some extent in an “ initial period.” The parameter p (and thus also k ) appeared to increase with decreasing tem- peratures. This is understandable because at lower temperatures recovery is less effective, and so the disappearance of the distorted regions (potential nuclei) by this action is decreased.In one series (a in fig. 9), (high-purity tin), c was calculated for different tempera- tures for the corresponding values of p and of mv, parameter and slope of the graphical plot of eqn. (7), and assuming a mean value for v of 10-3 mm3. Fig. 11 10 10’ x % FIG. 1 1 .-Calculation of the activation energy for spontaneous nucleation, by plotting loglo c (eqn. (6) and (7)) against 1/T. shows the calculated values of loglo c as a function of l/T. The graph leads, for this particular specimen of high-purity tin, to an activation energy for the spon- taneous nucleation (spontaneous nucleation being represented by c in eqn. (6)) of 120 kcal/mole, a relatively high value (cf.e.g. White 37 ; Haeszner and Lucke 38). In a few experiments, carried out with 99.95 9; Merck’s tin, it appeared that k < 1, meaning that N decreases with time. Such a result is possible according to Cahn’s conception, if one assumes energetic non-equivalence of the potential nuclei, the most active nucleating first. For this relatively impure tin somewhat higher temperatures had to be applied to obtain a rate of transformation comparable with that of high-purity tin. There- fore, not only the presence of impurities but also recovery could have played a part in the decrease of /c in relation to the values obtained for pure tin. 1 Groen, Thesis (Delft, 1956). 2 Kuo and Burgers, Proc. K. Akad. Wet. Amsterdam B, 1956, 59, 288.3 Groen, Nature, 1954, 174, 1836. Groen and Burgers, Proc. K. Akad. Wet. Amster- 4Hal1, Symposium on the Mechanism of Phase Transformations in Metals, Znst. dam, B, 1954, 57, 79. Metals, 1955, p 87.195 W. G . BURGERS AND L . J . GROEN 5 Prasad and Wooster, Acta Cryst., 1956, 9, 35. 6 Foster and Scheil, Z. Metallkunde, 1940, 32, 165. 7 Bunshah and Mehl, Trans. Amer. Inst. Min. Met. Eng., 1953, 197, 1251. 8 Philibert, Publications de I'ltutitut de Recherches de la Sidkrurgie, IRSID, A, 1956, 9 Holden, Acta Metal., 1953, 1, 617. 10 Anderson and Mehl, Trans. Amer. Inst. Min. Met. Eng., 1945, 161, 140. 11 Cahn, Proc. Physic. Soc. B, 1950, 63, 323. 12 Brinson and Moore, J. Inst. Metals, 1951, 79, 429. 13 Barten, Ned. T. Natuurkuride, 1954, 20, 25. 14 Carpenter and Elam, J . Inst. Metals, 1920, 24 [2], 83. 15 Burgers, J. M., Proc. Physic. Soc. B, 1940, 52, 23. 16Bragg, W. L., Proc. Physic. Soc. B, 1940, 52, 54. 17 Choh, Edwards, Washburn and Parker, Acta Metal, 1953, 1, 223. 18 Dehlinger, Ann. Physik., 1929, 2, 784 ; 2. Metallkunde, 1930, 22, 221 ; cf. Burgers, 97. 19 Cohen and Van Eyk, 2. physik. Chem., 1899 30, 601. 2@Groen, Proc. K. Akad. Wet. Amsterdam B, 1954, 57, 122. 21 BredCe, Thesis (Utrecht, 1928). 22 Van Lieshout, Thesis (Utrecht), 1934. 23 Andrade and Randall, Proc. Physic. Soc. B, 1952, 65, 445. 24 Hardy and Heal, Symposium on the Mechanism of Phase Transformations in 25 Cagle and Eyring, J. Physic. Chem., 1953, 57, 942. 26 Dehlinger, Chemische Physik der Metalle und Legierungen (Leipzig, 1939). 27 Tamann and Dreyer, Z. anorg. Chem., 1931, 199, 97. 28 Becker, Bull. Ameu. Physic. Soc., 1956, p. 45. 29 Frye, Stansbury and McElroy, J. Metals, 1953, 5, 219. 30 Hartshorne, Faraday Soc. Discussions, 1949, 5, 149. 31 Probst and Sinnott, J . Metals, 1955, 7, 215. 32 Johnson and Mehl, Trans. Amer. Inst. Min. Met. Eng., 1939, 135, 416. 33 Avrami, J . Chem. Physics, 1939, 7, 1103 ; 1940, 8, 212. 34 Fleeman and Dienes, J. Appl. Physics, 1955, 26, 652. 35 Tiedema, May and Burgers, Acta Cryst., 1949, 2, 151. 36 Lacombe and BerghCzan, Me'taux et Corrosion, 1949. 37 White, J . Metals, 1955, 7, 1221. 38 Haeszner and Lucke, 2. Metaffkunde, 1955, 46, 110. 139. Handbuch Metallphysik, 1941, 3, (2), Metals, Inst. Metals, 1955, p. 1 ; Prog. Metal Physics, 1954, 5, 143.

ISSN:0366-9033    

DOI:10.1039/DF9572300183

出版商:RSC    

年代:1957

数据来源: RSC

摘要:

ORIENTATIONAL EFFECTS IN THE POLYMORPHIC TRANSFORMATIONS OF SULPHUR BY C. BRISKE AKD N. H. HARTSHORNE Dept. of Inorganic and Structural Chemistry, The University, Leeds, 2 Received 31st January, 1957 When films of y-sulphur are inoculated with cc-sulphur, or mechanically by scratching, certain relative orientations of the two forms are preferred, and there is a pronounced tendency to preserve these orientations as growth of the a-phase proceeds. The implica- tions of these results as regards the mechanism of the transformation process are discussed. Earlier work on the transformation of /3-(monoclinic) to a-(rhombic) sulphur 1 9 2 has shown that the activation energy (as deduced from the temperature coefficient at temperatures far below the transition point) is equal to the internal latent heat of sublimation of the /3-form, or nearly so, suggesting that the process is analogous to that of crystal growth from a vapour phase. This is consistent with the ob- servation that when an a-crystal advances across the boundary between two differently orientated /3-crystals, it does so without apparent change of orientation (ref.(l), fig. 9), indicating that the transition layer between the two forms is com- pletely disordered. The observed rate of advance of the interface is, however, at least lo3 times greater than that calculated on this basis at temperatures between - 15" (the lowest temperature at which the rate has been measured) and 20°, though the discrepancy decreases with rise of temperature, and near to the transi- tion point (95.5"), there is agreement between the observed and calculated rates to within a power of ten.2 Similar considerations apply to the monotropic transformation of ?-(mono- clinic) to a-sulphur at low temperatures.Between - 15" and 20" the rate of advance of the interface is of the same order as that for p- to cc-sulphur,3 and measurements of the temperature coefficient so far made correspond to an activa- tion energy of between 20 and 26 kcal/mole, within which range the internal latent heat of sublimation of y-sulphur almost certainly lies. (The values for a- and @-sulphur are 23.2 and 22.6 kcal/mole respectively, and that for y-sulphur cannot be very different.) Furthermore, there is no apparent change of orientation when an a-crystal crosses the boundary between two differently orientated y- crystals.Assuming that the vapour pressure of y-sulphur is not more than about twice that of p-sulphur, the discrepancy between the observed and calculated rates is again of the order of 103. The calculated rates just referred to are those given by the product of the supersaturation x and the vacuum rate of evaporation of a-sulphur calculated from the Langmuir expression m = ap/(2nMRT)*, where rn is the rate in moles cm-2 sec-1, a is the condensation coefficient (taken here as unity), p is the vapour pressure, and the other symbols have their usual significance, This product is multiplied by Nd3 (N is the Avogadro number, and d the mean lattice spacing) to give the linear rate of advance of the interface? Now Bradley4 has shown that the rates given by the Langmuir expression agree with those actually observed for a-sulphur over the range 15" to 32.5", if the condensation coefficient is taken as 0-7, i.e. -unity, and making the reasonable assumption that this agreement holds over a wider range of temperature, it seems clear that the above method of calculation must give the maximum rate of advance of the interface for a mechan- 196FIG. 1.-Typical spherulite of y-sulphur FIG.2.-Film shown in fig. 1 after between crossed polars (vibration direc- transformation to a-sulphur between tions of polars parallel to edges of crossed polars (vibration directions of [To face page 197 figure). polars parallel to edges of figure).C . BRISKE A N D N . H . HARTSHORNE 197 ism consisting simply of the evaporation of molecules from one form and their condensation on the other.The large discrepancy between the observed and calculated rates therefore suggests that some secondary mechanism associated with an activation energy lower than the heat of sublimation is involved in the transformation, i.e. a displacive process, and, if so, the possibility arises that the orientation of the unstable phase will have some influence on that of the stable phase. The results reported in this paper show that such an effect does in fact exist in the transformation of y- to a-sulphur in thin films, though it is not per- ceptible in the crossing of a single crystal boundary by the a-phase. This trans- formation is a particularly favourable case to study, since the y-form habitually crystallizes as spherulites, the axis of elongation of the individual crystals being c, and (OlO), the optic axial plane, commonly lying in the plane of the section, so that growth of the a-sulphur across a spherulite encounters a progressively changing orientation of the y-form.EXPERIMENTAL The sulphur used was purified by the method of Bacon and Fanelli,s the starting material being B.D.H. crystalline sulphur. The films were prepared between 3 in. by 1 in. micro- scope slides and 2 in. square cover slips (no. 1). A slide with a cover slip laid on it was heated to a temperature just above the melting point of the sulphur, which was placed at the edge of the cover slip, and ran underneath by capillary action on melting. The slide was then transferred to a cold aluminium plate, and this usually resulted in the crystallization of the y-form, often as a single spherulite. In some cases the /3-form, or a mixture of the p- and y-forms appeared.The film was then re-melted and chilled as before, and the process repeated if necessary. Slides which failed to give a suitable y-film after three meltings were rejected. A typical y-film is shown in fig. 1. The slides and cover slips had been previously cleaned by prolonged immersion in hot chromic acid, followed by boiling distilled water, and then washed with conductivity water and dried at 160". In some of the experiments described below, the y-films were uncovered by stripping off the cover slip, and were then inoculated with either a single crystal, or a polycrystalline bead, of the or-form.The stripping was effected by prising up the cover slip at a corner with a razor blade, and since the slip was very thin it bent easily, leaving the sulphur attached to the slide. The inoculation was done on the stage of a polarizing microscope, and was watched with a low-power objective. The inoculating crystal or bead was mounted on a horizontal arm overhanging the stage. This arm was pivoted on jewel bearings carried in a stirrup support attached to the stage bracket of the microscope, and was counterpoised so that the crystal or bead could be lowered into very light contact with the film without splintering it. The slide was moved to the required position by means of a mechanical stage. By this method any selected point on the film could be inoculated.For the subsequent study of the orientations of the a-crystals resulting from the inoculation, the inoculating device could be swung aside, thus permitting the use of high-power objectives. RESULTS AND DISCUSSION The following experiments were carried out : (a) inoculation of uncovered y-films with (i) a single a-crystal, (ii) a polycrystalline bead, as above, followed by determination of the orientations of the resulting cc-crystals near to the site of inoculation, in relation to the c-axis of the y-form and the plane of the section; (6) inoculation of covered y-films by scratching along one edge of the cover slip with a razor blade, followed, after transformation of the whole film was complete, by determination of the orientations of the a-crystals as above in randomly dis- tributed areas mostly situated some distance from the edge inoculated.Some determinations were also made of the orientations of the a-crystals immediately adjacent to the edge inoculated, but these determinations were limited by the shattering of the film which had occurred as a result of the action of the razor blade.198 POLYMORPHIC TRANSFORMATIONS OF SULPHUR The orientations of the cc-crystals were determined from their interference figures, using the optical crystallographic data given in Groth’s Chemische Kristul- lugraphie.6 Stereographic projections of the principal low-index sections, showing the orientation of the optic axes, traces of the cleavage planes, and the true angular diameter of the interference figure given by the objective used (4 mm, N.A., 0-85), helped in identifying the sections presented.As a further aid to identification, the birefringences for these sections were calculated from the well-known relation (Ng’ - Np’) = sin 8 sin 8’(Ng - Np), where Ng’, Np’ are the greater and smaller indices of the section respectively, Ng, Np the greatest and smallest indices of the crystal, and 8, 8’ the angles made by the normal to the section with the two optic axes. From these birefringences it was often possible to confirm the identity of a section by comparing its birefringence with that of a neighbouring one whose identity was in no doubt, by using a calibrated graduated quartz wedge. c FIG. 3.-(a) Net used to plot orientations of a-crystals ; (b) optic orientation of y-sulphur, showing presumed orientation of s8 rings.By these means it was possible to determine the orientations of the axes of the optical indicatrix in relation to the c axis of the original y-crystals and the plane of the section to within say k 10”. The distributions of these orientations were then found by plotting two axes of the optical indicatrix, namely, those correspond- ing respectively to the principal refractive indices Np (see above) and N,,, (the principal intermediate refractive index) * on the stereographic quarter net shown in fig. 3(a). The NS (north-south) diameter of the net represents the c-axis of the y-form, and the primitive quarter circle the plane of the section. All results plotted were pooled in this one quadrant of the usual circle, since it was assumed that two poles in different quadrants but making the same angles with the NS diameter and with the centre of the projection represented structurally equivalent relative orienta- tions of the two forms.Thus, for example, poles actually plotting at P’ and P” (see figure), which are both at an angle w to the NS diameter and 4 from the centre, were placed at P. The justification for this procedure was that (i) a-sulphur is orthorhombic and the indicatrix axes and crystallographic axes therefore * The symbols Np, Nm and Ng have been used for the principal refractive indices instead of the more usual a, and y, to avoid confusion with the designations of the three forms of sulphur.C . BRISKE AND N . H . HARTSHORNE 199 coincide (Np = a, Nm = 6, Ng = c).Moreover it belongs to the highest sym- metry class, so that all sections having the same indices are structurally equivalent ; (ii) y-sulphur is pseudo-orthorhombic, for its p-angle is 8 8 r and the extinction angle N p : c is only ly (hence the parallel extinction cross seen in fig. 1).6*7 Furthermore the birefringence of y-sulphur is strong and negative, which shows that the Sg rings must be arranged parallel to one another with their planes normal to c, or approximately so, as shown in fig. 3(b). The sections of the net, numbered 1 to 7, are projections of equal areas on the surface of the sphere in the corresponding spherical projection. If therefore the orientations of the cc-crystals had been quite random, these areas should have TABLE PERCENTAGES OF a-CRYSTALS HAVING (i) THE Np AXIS, (ii) THE Nnl AXIS, OF THE OPTICAL INDICATRIX IN THE DIFFERENT SECTIONS OF THE NET IN FIG.3 exDeriment and total number of crystals studied (in brackets) section of net inocn. by crystal (332) inocn. by bead (241) inocn. of covered films at edge crystals at edge (65) crystals in randomly situated areas (272) Np Nm 23.8 56.6 3.9 7.5 4.5 7.5 1.5 0 2.4 0 6.1 0 57.8 28.3 N p N m 28.2 63.1 2.9 2.9 2.5 5-4 0 2.1 0-8 1.2 7.9 1.2 57.7 24.1 Np N", 40-0 46.1 0 6.2 23.1 15.4 4.6 0 3.1 0 3.1 0 26.2 32.3 Np Nm 22-8 54.0 2.9 6.3 19-9 21.7 6.3 0 0.7 0 8.1 0 39.3 18.0 been approximately equally populated with poles representing any one axis of the indicatrix, since the number of crystals studied in each experiment was quite large. The actual distributions, given in table 1, show that this was far from being the case.In all experiments, the percentage of crystals with the N7,L axis plotting in section 1 was high (46.1 to 63-1 %), indicating a strong tendency for the NgNp plane, i.e. the optic axial plane, to become orientated approximately normally or at a large angle to the c axis of the original y-phase. In the first two experi- ments (inoculation by crystal and bead respectively) the figures indicate also a marked tendency for the Np axis to orientate vertically, or at a small angle (< 31") to the vertical (section 7 ) . The fairly close correspondence between these distribu- tions will be noted, and is discussed later. In the last two experiments (inoculation of covered films at the edge), the percentages of crystals with the ATp axis in section 7 are much smaller, but there is an increase in the population of section 3, both by this axis and by the N,,, axis.It will also be noted that sections 2,4, 5 , and 6, i.e. those corresponding to large angles with the c ( y ) axis and the plane of the section are either sparsely populated, or avoided altogether. Table 2 shows the distribution of cc-crystals having one of the two axes Nm and Np in section I , i.e. parallel or at a small angle to c(y), and the other in either section 3 or section 7. Such crystals present " centred " interference figures (two optical symmetry planes vertical), or are inclined at small angles, i.e. up to the angular limits of these net sections, to these centred positions.cc-Sulphur is optically positive, and so the Np axis is the obtuse bisectrix. The indicatrix axis normal to the centred section is given in brackets in each column heading of the table. The totals in the penultimate column show that the majority of the crystals are distributed among these categories. A striking consequence of this tendency to adopt orientations so simply related to that of the y-form is demon- strated by fig. 2, which shows the film in fig. 1 after having been completely trans- formed to cc-sulphur. The film still displays a marked extinction cross with arms parallel to the vibration directions of the polars. On rotating the polars in unison200 POLYMORPHIC TRANSFORMATIONS OF SULPHUR the cross rotated in sympathy, though it was not as complete throughout the operation as that shown in the figure, since not all the crystals had achieved the same degree of conformity with the general tendencies expressed in table 2.This persistence of the parallel extinction cross has been observed on a number of transformed films. TABLE 2.-PERCENTAGE DISTRIBUTIONS OF a-CRYSTALS SHOWING CENTRED, OR APPROXIMATELY CENTRED INTERFERENCE FIGURES, WITH ONE VIBRATION DIRECTION PARALLEL TO C(y) crystals crystals crystals crystals with with with with N,,, in 1, N,,, in I, N,,, in 7, N,,, in 3. total crystals Npin7 Nph3 Npin 1 Npinl Ngin 1 (obtuse (acute (optic (acute bisectrix) bisectn'x); normal) bisectrix) 0' with expt. inoculation by crystal 48.2 2.1 23-2 0.3 73.8 6.6 inoculation by bead 53.5 2.1 22.4 4-1 82.1 0.8 inoculation at edge: crystals at edge 21.6 21.6 30.8 9.2 83.2 1.5 random areas 26.5 19.5 14.7 8.1 68.8 7.7 In the last column of table 2 are the percentages of crystals having the Ng axis in section 1.These of course differ from those just discussed in having Nm and Np normal to c(y). The percentages are all small, and so there is evidently a tendency to avoid this orientation. An explanation of this is suggested by the structure of cc-sulphur determined by Warren and Burwell.8 In this structure the planes of the s8 rings are all parallel to the N, axis, but are near 45" to the N,,, and Np axes. Therefore if the Ng axis were aligned with the c-axis of the y-form (see fig. 3(6)), the rings would have to turn through about 90" to fit on to the a-structure, whereas a much smaller rotation would be involved if either the N,,, or Np axis were parallel to c(y).The tendency to preserve the orientations established on inoculation, in particular the parallelism between the Nm axis and the c(y) axis which is shown by the figures for the last two experiments in tables 1 and 2, and by the persistence of the extinction cross (fig. 1 and 2), shows that a-crystals advancing across a y-spherulite and encountering a progressively changing orientation of the y- crystals are subjected to what may be described as a " steering " effect by the y-crystals. A detailed example, one of several observations, is shown in fig. 4. In this, an area of cc-crystals, all showing a centred acute bisectrix figure with N,,, parallel to c(y), maintains this relationship over a change of direction of the y-needles of more than 90". Detailed microscopic examination of the area has shown that the change in the orientation of the a-phase is partly continuous and partly discontinuous, i.e.it consists of a series of slightly misaligned blocks, some of which are curved crystals, showing a wave of extinction passing from one end to the other as the section is rotated between crossed polars. This steering effect is imperceptible in the crossing of a single y - y crystal boundary, even when there is a very marked change in the orientation of the y-phase, as for example, at the boundary between two spherulites. Table 2 shows that the crystals produced by inoculation with a crystal or bead at single points included very few which presented acute bisectrix type sections (columns 3 and 5), as compared with those resulting from inoculation by scratching at the edge, and that these contained far fewer obtuse bisectrix type sections (column 2) than the former. Whether this is fortuitous, or due to the different methods of inoculation is not known.It may be noted, however, that the fully transformed films resulting from point inoculation by crystal or bead developed many crystals showing acute bisectrix type figures at places distant from the sitesC . BRISKE AND N . € I . HARTSHORNE 20 1 of inoculation, but it has not yet been possible to ascertain whether they resulted from spontaneous nucleation, or as the result of a gradual change in the orientation of the original crystals. B 0 FIG. 4.-" Steering * ' effect, showing change of orientation of a-crystals in sympathy with change in direction of c(y). 0 = centre of original y-spherulite, OA, OB, OC = original y-needles. Finally the correspondence between the distributions of the orientations re- sulting from the crystal and bead inoculations may be noted with some interest (tables 1 and 2). In the former the crystals used were bipyramids bounded by { 11 11, and they were mounted on the inoculating device so that when in contact with the y-film, the c axis of the crystal made an angle of about 65" with the film. Now this axis is the acute bisectrix of a-sulphur, so that if the orientation of the crystal had any effect on the mechanism of the inoculation, a large proportion of inclined acute bisectrix figures was to be expected. As already stated, these were almost completely absent, and the results were very similar to those obtained with a polycrystalline bead. This raises the question as to how exactly a crystalline inoculant acts in a solid-solid transformation. 1 Hartshorne and Roberts, J. Clzern. SOC., 1951, 1097. 2 Hartshorne and Thackray, J. Chern. SOC., 1957, 212. 3 Bradley, Hartshorne and Thackray, Nature, 1954, 173,400. 4 Bradley, Proc. Roy. Soc., A, 1951, 205, 553. 5 Bacon and Fanelli, Ind. Eng. Chem., 1942,34, 1043. 6 Groth, Clzernische Kristallographie (W. Engelmann, Leipzig, 1906), vol. I. 7 Sekanina, Z. Krist., 1931, 80, 174. 8 Warren and Burwell, J, Chern. Physics, 1934, 89, 195. G*

ISSN:0366-9033    

DOI:10.1039/DF9572300196

出版商:RSC    

年代:1957

数据来源: RSC

摘要:

AZIDE DECOMPOSITIONS BY F. C. TOMPKINS AND D. A. YOUNG Chemistry Dept., lmperial College of Science and Technology, London, S . W.7 Receiwed 30th January, 1957 Some aspects of the mechanism of decomposition of azides have been considered in relation to the physical properties of real crystals. Particular attention has been given to the information provided by conductance and absorption spectra measurements in characterizing some of the processes occurring in both the decomposition and in the ageing, or annealing, of azide crystals. Some tentative suggestions are made to account for the differences observed in the decomposition of barium, calcium and potassium azide in terms of the conditions necessary for germ nuclei formation and their subsequent growth. Many metallic azides can be prepared in a state of high purity and decompose practically stoichiometrically to the metal and nitrogen in convenient temperature ranges ; they are therefore particularly suitable for investigating processes of the general type (1) Much of our earlier work 1 was concentrated on the kinetic analysis of the rate of nitrogen evolution and the general characteristics of the overall process.This approach is limited because such results are not sufficiently definitive. Thus, move recent work2 has shown that different rate expressions may be obtained with a particular compound due to slight variations in the method of its prepara- tion or to different degrees of ageing of samples of the same preparation. Indeed, we may conclude that the divergences between the results of various workers are largely attributable to the different physical nature of the reactant, whereas impurities in the chemical sense often contribute relatively minor effects.This conclusion has been clearly demonstrated in the decomposition of silver oxalate 3 and mercury fulminate.4 Further, the interpretation of an overall equation in terms of nucleation and nucleus growth is not without ambiguity; thus, for the dehydration of calcium carbonate hexahydrate 5 it is not possible to decide be- tween a mechanism based on (i) instantaneous nucleation, one nucleus per par- ticle, and absence of any abnormal surface growth and (ii) a random nucleation of particles followed by an infinitely fast surface growth. Additional independent information is therefore essential in order to make progress in the understanding of the main details of the mechanism.One approach, largely developed by Garner and his co-workers,6 is the direct measurement under a low-power microscope of the rates of nucleus formation and growth ; in particular, Wischin’s observations 7 with barium azide left little doubt that, for the preparation used in that investigation, the pressure of nitrogen evolved increased as the sixth power of the time. This work led to a detailed theory of the mechanism of the decomposition by Mott 8 in terms of isolated lattice imper- fections, but it has since become increasingly evident that the whole array of imperfections present in real crystals should be considered in any discussion on solid decompositions.We shall therefore consider, in summary fashion, some properties of real crystals in order to assist in formulating more detailed mechanisms for particular decompositions. 202 AM -+ B(4 4 C(d.P . C . TOMPKINS A N D D . A . YOUNG 203 THE NATURE OF REAL CRYSTALS In the practical case, crystals are prepared by precipitation or crystallization from aqueous solution and in our work vary in linear dimensions from 10 to lO4p.. Crystals prepared by these methods at room temperature some 3-400' below their melting point, are certainly not in thermodynamic equilibrium. We shall therefore assume the validity for ionic crystals of the model for real crystals which was first described by metallurgists. Many features of this model have recently received confirmation in the elegant work of Mitchell and co-workers arid by Dekeyser,lo and Amelinckx.10 It now seems probable that crystals greater than 100 p in linear dimensions are traversed by twin and grain boundaries which separate grossly disoriented regions of the crystal. The grains so delineated are the particles of micro-crystalline preparations. These grain boundaries, prob- ably about lop apart, contain impurities adsorbed during growth.They are sites of mechanical weakness and such crystals will undergo intercrystalline brittle fracture on stressing. In large (200-mg), carefully grown, single crystals the dis- orientation of neighbouring grains is less and it is probably better to describe the crystals as being traversed by interlocking systems of low-angle grain boundaries, again about 10 p apart.Each grain or particle, as defined above, is itself traversed by a random net- work of single dislocations which delineate irregular mosaic blocks of dimensions < 1 p, and contains isolated and clustered lattice vacancies in excess of the equili- brium concentration. These crystals may be expected to change their proper ties on storage and to show characteristic annealing phenomena. Thus below 0.25 Twt ( T , = m.p.), the temperature at which surface ionic conductance becomes sig- nificant, it should be possible to observe the effects of the motion of those vacancies near the surface which are in energetically special positions, for example, in steep stress or coulombic fields. Pairs of vacancies of opposite sign separated by a few unit cells, isolated vacancies near edge dislocations and more especially vacancies near jogs in dislocations are in the most favourable positions energetic- ally and will move first.Phenomena of this type are believed to occur in potas- sium and calcium azides below 100" C. The next stage of annealing, which becomes marked in the range 0.25 to 0.3 T,,, is complex. It consists of the motion towards dislocations of vacant sites derived from clusters or grain boundaries in such a way that the dislocations become straighter and are enabled to climb, as suggested by Seitz 11 and Mott.12 This process is an essential preliminary to polygonization which, being largely a motion of dislocations in mutual stress fields, requires only a small activation energy. Polygonization succeeds climb and cannot be separated from it experimentally by adjustment of temperature.Simultaneously, the energies of high-angle grain boundaries will be somewhat reduced by grain boundary diffusion of lattice de- fects in such a way that the overlap between the compressive and dilatational strain fields of the dislocations forming the grain boundary is increased. The surface free energy is thus reduced : in micro-crystalline specimens this is probably the superficial sintering observed by Goodman and Gregg.13 At higher temperatures, above 0.5 to 0.6 T,, bulk ionic conduction predomin- ates. In this range intergranular adhesion and grain growth become possible. Such behaviour has only been observed in silver-azide of the systems studied to date. CONDUCTANCE DATA In Mott's theory of the decomposition of barium azide, only isolated single imperfections were considered, and since these can be subject to independent investigations involving diffusion and conductance measurements, it is possible in principle to make a quantitative assessment of the part they Play in Solid deo mpositions.Thus, with barium azide, Wischin's measurements allow a204 AZIDE DECOMPOSITIONS calculation of the rate of addition of barium atoms to the nuclei of barium metal and consequently one possible mechanism 7-the trapping of electrons by the nucleus which, by electrostatic attraction, then attracts mobile interstitial barium ions-may be tested experimentally. Subsequent measurements 14 of the ionic conductance of the barium azide showed that the maximum rate of ionic move- ment is about 106 times too slow to account for the directly observed growth rate.It was therefore argued that the growth reaction was restricted to the metal/azide interface and involved the discharge of lattice barium ions adjacent to it. Initially, the metal atoms are formed in an expanded lattice for which the barium-barium distance is equal to that in the azide but as growth proceeds recrystallization to the normal metal lattice takes place. It remains a problem whether or not the interface remains coherent or incoherent under different conditions of treat- ment. We might note, however, that these arguments, for an interface mechanism take no account of the possible migration of neutral entities. A conceivable alternative is the thermal production of F-centres at the surface of the crystal and their migration along the surface and dislocations to traps where they can contribute to the growth of the metallic nucleus.Indeed, our work on KN3 suggests that germ nuclei are formed only at imperfections at which the coulombic distortion is sufficiently large to trap migrating F-centres and that nucleus formation (as distinct from growth) can occur only at sites not already occupied by trapped electrons or holes. In calcium and strontium azides, where nucleus formation appears to be largely complete before thermal decomposition is commenced, there is complete occupation. In the barium salt this is not so, probably because the anhydrous pseudomorph of the monohydrate undergoes some lattice collapse and recrystallization in localized regions when it is heated. Nevertheless, although the original model used for barium azide was idealized, it remains true for the azides of the alkali and alkaline earth metals, that measure- ments of ionic conductance prove that migration of current carriers do not play an important part in the mechanism of decomposition, whence we conclude that conductance data are unlikely to further the quantitative formulation of the decomposition of these salts.The higher ionic conductivity of the azides of the heavy metals, e.g. silver azide, permits a Mott mechanism to be operative at low degrees of decomposition. With silver azide, which we have investigated in some detail, the interpretation of the conductance results is particularly difficult and it has been essential to study the photoconductance, the thermo-electric power and Hall effect on specimens in different degrees of aggregation in order to separate the contributions in partially decomposed material of surface and bulk ionic conductance from the electronic conductance. The detailed results are being published elsewhere ; we note here that the specific conductance of interstitial silver ions is about 10-6 ohm-1 cm-1 at 190" C and that of the (n-type) electronic contribution is around 10-5 ohm-1 cm-1 at the same temperature.Our results are consistent with the theory that thermal electronic excitation of anions giving positive holes and electrons can proceed along the whole length of a dislocation (and not merely at singular points, such as jogs) since the spectra suggest that sufficient relaxation of the selection rules for electronic excitation takes place.15 Tnterstitial silver ions are discharged and deposited only at specific sites along the dislocations but, by reason of the mobility of the metal atoms, these eventually occupy all available sites in the dislocation network.Subsequently, excitation and deposi- tion occur at the same site and an interface mechanism becomes operative. A different situation arises with the alkaline earth azides because relaxation sufficient to cause an adequate decrease in the activation energy for thermal ex- citation of the anion occurs only at singular points in the dislocations (jogs) and moreover it is only at singular points that the colour centres are efficiently trapped.Consequently, in barium azide, discrete nuclei are formed.F . C. TOMPKINS AND D . A . YOUNG 205 SPECTROPHOTOMETRIC MEASUREMENTS From the foregoing, it is evident that the main experimental problem is to devise sufficiently definitive methods for investigating the role of the various imperfections in a particular decomposition. One approach which has given us further insight into the initial stages of nucleus formation in potassium azide has been the study of absorption spectra. Advantage here is taken of the fact that vacancies, and various aggregates of these, trap electrons which then undergo transitions and so give rise to characteristic absorption bands in or near the visible part of the spectrum. It proved possible by comparison with appropriate results obtained with alkali halides to make tentative identifications of the probable structures of these colour centres, to estimate their concentration, and to follow certain processes, such as impurity-centre aggregation. Freshly prepared potassium azide was coloured by radiation with light of h 2537 A at liquid-nitrogen temperature and the change of concentration of colour centres followed as a function of temperature, incident intensity, particle size and age of the azide.We shall merely state the main conclusions of our work,16 giving emphasis to those processes involving mass transfer or rearrangement since it is not possible to consider these without reference to electronic processes occurring at the same time. At - 196O C, absorption bands due to the presence of F-centres (single electrons trapped at isolated anion vacancies) and V-centres [positive holes (azide radicals) trapped at isolated cation vacancies] are observed.They are formed in the well-crystalline mosaics by interaction of excitons with isolated vacancies. Simultaneously, nitrogen is evolved at a rate proportional to the square of the intensity of the incident radiation by a bimolecular process involving, for example, a mobile positive hole and an exciton trapped at a jog (J) in an edge dislocation, which itself may form one of an array constituting a low-angle grain boundary. A complex colour centre of the R-type, e.g. J results with a corresponding V-centre deficit. On warming to - 78" C all the V-centres are annihilated by reaction with F-centres, and the remaining F-centres migrate to grain boundaries where they interact to form R'-centres.The R'-centre is considered by us to be an array of interacting F- and R-type centres precipitated along dislocations in such concentration that the individual centres have lost their separate identities; such a centre is a probable precursor to the precipitation of sodium on the grain boundaries of sodium chloride in Amelinckx's work.10 In terms of the band theory the R'-centre confers an impurity band on the crystal. At 60" C , these centres are thermally bleached and a new weak band centred at 440 mp appears. This is at a wavelength expected for selective photo-emission of electrons from metallic potassium into the conduction band of the azide, a conclusion which is supported by a 100-fold increase of photoconductance when it is irradiated in the blue end of the spectrum.We therefore consider that potassium atoms have been precipitated along the dislocation network of the azide. If now the temperature is raised to 270" C a strong, narrow, temperature- independent band at 725-730 m p appears, which arises from light-scattering by colloidal particles of metallic potassium. Such bands are well known in the alkali halides 17 where the particles are estimated to contain, on average, 100-400 potassium atoms.l* A calculation by the method employed by Scott, Smith and Thompson 19 places the band in potassium azide at 740 mp. We suggest that these colloidal centres are formed by movement of potassium atoms along dis- locations to nodes which act as deeper traps.The movement involves simul- taneous transport of anion vacancies as F-centres and of cation vacancies as well because the atomic volume of metallic potassium is greater than the molecular volume of the azide ; without such transport there would be insufficient space to form the colloidal centre. The low ionic conductance of potassium azide, and206 AZIDE DECOMPOSITIONS the low temperature (- 25" C ) at which the R'-band begins to form, suggests that movement of unionized F-centres rather than of anion vacancies and free electrons OCCUTS. We believe the colloidal particles to be essentially similar to the metallic nuclei observed in the thermal decomposition. Different results are obtained with the same sample of potassium azide which has been aged, i.e.stored for 3 months in a vacuum desiccator at room temperature or maintained at 100" C for an hour. Irradiation at - 196" C or - 78" C gives no absorption bands except possibly of the R-type, but production of the bands found with fresh material after irradiation at room temperature is unimpaired. Hence one mechanism of ageing probably involves the formation of anion-cation vacancy pairs ; these, however, can be dissociated by combined interaction with an exciton and phonons ( E ) (where = anion vacancy, 0 = cation vacancy, [N3-]* = exciton, F- centre) to give an F-centre and a positive hole trapped at the cation vacancy. These centres then undergo the usual reactions to form nitrogen gas, R'-centres, etc., thus accounting for the retention of colorability at room temperature.THE AGEING OR ANNEALING PROCESS Freshly prepared azides, in particular the potassium and calcium salts con- sidered below, undoubtedly contain vacancies in excess of their equilibrium con- centration and their behaviour on heating depends in large measure on the rate of increase of temperature to which they have been subjected. PHYSICAL AGEING We shall now consider the changes of conductivity that take place on first heating a pellet formed from fresh material (KN3 and CaN6) and previously outgassed (< 10-6 mm Hg) for 3 days at room temperature. The results are summarized in fig. la, b; they are similar in form to those recently obtained by Leiserzo with P-AgI. We ascribe the conductance wholly to the motion of vacancies since our specimens displayed no photoconductance even when ir- radiated at A 365 mp.There is a fairly abrupt irreversible decrease in conduc- tivity at about 60" C for KN3 and at 97" C for caN6 if, as is the case for the results shown in fig. lb, the rate of temperature increase is not greater than about 5 deg./min; this decrease we ascribe largely to the formation of neutral vacancy pairs. The lattice instability accompanying this pair formation promotes the conversion of R'-centres to the metal, as has been observed for potassium azide at 60" C. True colloidal particles are, however, not formed until the temperature is sufficiently high to cause electron emission from the potassium into the azide where the electrons are trapped by anion vacancies in the mosaics.This occurs around 270" C. During this process the filamentary metal acquires a net positive charge and attracts cation vacancies ; these assist the " dissociation " of the fila- ment and the migration of the potassium atoms to form larger colloidal particles of metal of smaller specific surface area for which the change in potential per electron emitted is smaller. The abrupt onset of colloidal centre formation arises from the co-operation between the increased production of vacancies of both signs and the increased electron emission above 270" C. Normally, when studying the thermal decomposition of an azide the rate of temperature rise is deliberately made rapid, e.g. an increase of 100-200 deg. to the reaction temperature in 10-30 sec.When the crystals are heated slowly, vacancy pair and aggregate formation take place predominantly at grain boun- daries already present in the crystals ; the vacancies are therefore effectively eliminated and the total decrease in free energy resulting from these processes is a maximum under these conditions. But on rapid heating, vacancy aggregationF . C. TOMPKINS AND D. A . YOUNG 207 also proceeds in the mosaic to form small clusters which may collapse to give dislocation rings in the relatively perfect parts of the crystal; the free energy decrease is therefore less with rapid than with the slower rate of heating. Con- sequently, depending on whether the elimination of excess vacancies from the system (in presence of R'antres) is slow or fast, the number of germ nuclei formed Fiti.la.-The electrical conductivity of freshly prepared KN3 heated for the first time. FIG. 1b.-The electrical conductivity of freshly prepared CaN6 heated for the first time. 0 rising temperature ; 0 rising temperature ; falling temperature and subsequent measurements. A falling temperature and subsequent measurements. 1 . 1 I L I I I 1 0 2 0 4 0 6 0 a 0 I00 T i m e ( d a y s ) FIG. 2.-The initial rate of decomposition of KN3 at 271" C plotted as loglo rate against the age of the sample. The rate is in arbitrary units, -A-gives the value for material heated to 100" C for 1 h. will vary. In slow heating, the pattern is largely determined by the original crystal topography ; with rapid heating vacancy aggregation leads to a higher jog density and the number of germ nuclei formed is higher.Preliminary gentle annealing before rapidly raising the temperature of KN3 to that for measurable decomposi- tion thus causes the rate of decomposition to be slower than for the fresh material which has had no pretreatment, the decrease being greater, the longer the annealing period (fig. 2). The differences found for the effect of ageing on the potassium and the calcium salts are due to the fkct that vacancy aggregation is complete in KN3 before the208 AZIDE DECOMPOSITIONS minimum temperature for thermal decomposition is reached (as is evidenced by the effect of annealing on the ionic conductance and the colorability at - 196" C). Calcium azide, however, decomposes at a much lower temperature.Thus the rate of decomposition is measurable above 78" C whereas rapid vacancy aggrega- tion, as shown by the decrease in conductance, becomes marked only above 97" C. This continuation of the annealing process between these two temperatures is reflected in the anomalous rates of decomposition of CaN6 found below 97' C. Thus, an apparent " activation energy " of 35 kcal/mole for the decomposition is obtained using samples of fresh CaN6 in individual runs at different temperatures. If, however, the rate is measured at one temperature below 97" C and then the temperature is changed to a new value below 97" C, with or without intermediate quenching to room temperature, and the rate then remeasured (" split runs "), an activation energy of 18 kcal/mole is found from the family of curves at the different temperatures.In the split runs, as for individual runs on well-aged samples the simple kinetic expression (2) p = k3(t - to)3 is applicable, but the value of the pre-exponential factor in the Arrhenius equation is dependent on the temperature used in the first run of the series. We therefore conclude that the 35 kcal/mole is not a true activation energy for decomposition since the temperature coefficient of the velocity constant includes the temperature dependence of the pre-exponential factor. If, however, the temperature in the split runs is raised above 97" C, the kinetic law (eqn. (2)) is not valid for the first 20-30 min, and after this period values of log k are first obtained in the region X (fig. 3), which may be crossed in two or three stages provided the temperature does not exceed 105" C.Subsequently, the values fall on the line ,6 whose slope again corresponds to 18 kcal/mole. With aged or well-annealed material, how- ever, the log k values always fall close to the line /I no matter whether these were obtained in split or individual runs. We recall that the region X is that in which the conductivity decreases, consequently in the regions cy. and p, it appears that imperfections are not in equilibrium with the parent matrix although the annealing processes appropriate to these two temperature ranges are virtually complete. When fresh material is heated at a rapid rate for the first time to a temperature not greater than 97" C, a minority of vacancies condense at the dislocations resulting in a form of partial annealing.There is, however, little aggregation of vacancies in the bulk. The number of growing nuclei is therefore predominantly determined by the original crystal topography and is substantially constant. The activation energy of 18 kcal/mole thus refers to that required for linear growth of the nuclei. When, however, the temperature is raised above 97" C , aggregation of bulk vacancies takes place by a mechanism similar to that which is effective in dis- persing filamentary potassium. This dispersal occurs in a matrix which is simul- taneously having its jog density (or node density) artificially increased by aggrega- tion of excess vacancies and the subsequent collapse of these clusters. Conse- quently the number of growing nuclei is increased and the rate of decomposition is higher, but the activation energy of growth (18 kcal/mole) is the same.Fresh and aged material also behave differently when pre-irradiated. The thermal rate constant in eqn. (2) increases for aged calcium azide with pre- irradiation dose up to about 1014 photons/cm2 and then remains substantially constant. The quantum efficiency is around 0.01 for X 2537 8, and hence about 1012 nuclei/crnz of the projected area are formed at a limited number of nodes in the dislocation network, this maximum number being determined by the crystal topography. The number of nodes, however, can be increased by cross-slip pro- duced by cold-working, i.e. by gently grinding, thus the saturation number of germ nuclei is increased about 100-fold but the general behaviour during decom- We therefore interpret these results in the following manner.F .C . TOMPKINS AND D. A . YOUNG 209 position is otherwise unchanged. With fresh calcium azide, k rises with increasing dose similarly to but to a somewhat higher value than the maximum for aged material and then more slowly to a value of about 1017 photons/cmZ. This is attributed to production, under ultra-violet irradiation, of R'-centres which are I000 . 4 " c , FIG. 3.--Arrhenius plot for the thermal decomposition of CaN6. k is the rate constant x individual runs on fresh material. 8, 0, D, three series of " split runs " on fresh material commenced below 97" C. B individual and split runs on fresh material which had been annealed at 60" C for two 0 individual and split runs on aged material (5 months old).in p = k3(t - to)3. days. dispersed to form colloidal centres during the vacancy aggregation process which occurs on hcating. A saturation effect on prolonged irradiation would be expected but this has, as yet, not been observed. With barium azide, the exponent IZ = 6 in the rate equation p == C(t - for fresh material falls to 3 for anhydrous material aged at room temperature for several months, and the number of nuclei, which is proportional to C, is reduced. Evidently, certain sites which previously were thermally transformed to germ nuclei have been removed by annealing. Prolonged pre-irradiation of fresh material has the same effect on the exponent but the number of nuclei formed is much larger ; under these conditions, all possible sites become germ nuclei without the requirement of thermal development.CHEMICAL AGEING In the azides the ageing processes have been termed physical, that is, they are not accompanied by any chemical decomposition as far as we can ascertain. The ageing of mercury fulminate, on the other hand, is an example of the effects210 AZIDE DECOMPOSITIONS of chemical deterioration during storage. Pure freshly prepared fulminate is white; it decomposes after a long induction period according to an exponential law with an activation energy of 27 kcal/mole, but if it is crushed, pre-irradiated with ultra-violet light, or allowed to stand for about 2 years, the decomposition proceeds according to a cube law after a shorter induction period.Because the activation energy remains at 27 kcal/mole it is concluded that the change in kinetics is concerned with changes not in the chemical act but rather with the topochemistry. Closer examination shows that in the decomposition of aged material the induc- tion period commences with a unimolecular evolution of gas with a low activation energy (cn. 5 kcal/mole), this effect being absent from the decomposition of crushed or pre-irradiated material. Furthermore pre-irradiation of fresh material in- duces cracks in the reactant matrix. It is therefore concluded that the exponential law is associated with a matrix in which the reactant sub-grains are contiguous whereas the cube law applies in a matrix in which the sub-grains have been separated from each other by some means.During ageing sufficient decomposition occurs in the sub-grain boundaries to separate the reactant into non-contiguous domains; the gas evolution at the commencement of the decomposition of aged material is therefore merely the desorption of the gaseous products of this decomposition. The cracks which appear in pre-irradiated fulminate are propagated down sub-boundaries by the stresses set up at the misfitting interface between the solid product of the photo- lysis and the parent reactant. On this basis if a solvent for mercury fulminate could be introduced into these cracks or into the partially decomposed grain boundaries of the aged material then it might be possible to " reconnect " the sub- grains of the reactant matrix with undecomposed fulminate and obtain material which decomposed according to an exponential law. This was in fact found to be experimentally possible. Even exposures of only a few minutes to damp ammonia vapour which condensed in the pores of the solid were sufficient to con- vert " cubic '' to " exponential " fulminate. The details are more fully discussed in a previous paper4 and the fragmentation of mercury fulminate has been de- scribed in a later paper by Singh.21 1 Thomas and Tompkins, Proc. Roy. SOC. A, 1951,210, 11 1 ; 1951,209, 550. 2 Bartlett, Tompkins and Young, unpublished. 3 Benton and Cunningham, J. Amer. Chem. SOC., 1935, 57, 2227. Tompkins, Trans. Faraday Soc., 1948, 44, 206. Finch, Jacobs and Tompkins, J. Chem. SOC., 1954, 2053. Szabo and Biro-Sugar, Z. Elektrochem., 1956, 60, 869. 4 Bartlett, Tompkins and Young, J. Chem. SOC., 1956, 3323. 5 Topley and Hume, Proc. Roy. SOC. A, 1928, 120, 210. 6 for example, Acock, Garner, Milsted and Willavoys, Proc. Roy. SOC. A, 1947, 189, 7 Wischin, Proc. Roy. SOC. A , 1939. 172, 314. 8 Mott, Proc. Roy. SOC. A , 1939, 172, 325. 9 Mitchell, e.g. see chap. 13 of Garner, Chemistry of the Solid State. 10 Amelinckx, Phil. Mag., 1956, 50, 269. Bontinck and Dekeyser, Physica, 1956, 22, 11 for example, Seitz, Adv. Physics, 1952, 1, 43. 12 Mott, Proc. Physic. SOC. B, 1951, 64, 729. 13 Goodman and Gregg, J. Chem. SOC., 1956, 3612. 14 Thomas and Tompkins, J. Chem. Physics, 1952, 20, 662. 15 cp. Seitz, Rev. Mod. Physics, 1951, 21, 327. 16 Tompkins and Young, Proc. Roy. SOC. A, 1956,236, 10. 17 e.g. Seitz, Rev. Mod. Physics, 1954, 26, 7. 18 Scott, Phil. Mag., 1954, 48, 610. 19 Scott, Smith and Thomson, J. Physic. Chem., 1953, 57, 757. 20 Leiser, Z. physik. Chem., 1956, 9, 308. ** Singh, Trans. Faraday SOC., 1956, 52, 1623. 508. Cooper and Garner, Proc. Roy. SOC. A , 1940, 174,487. 595.

ISSN:0366-9033    

DOI:10.1039/DF9572300202

出版商:RSC    

年代:1957

数据来源: RSC

摘要:

THE CHEMICAL EFFECTS OF RADIATIVE THERMAL NEUTRON CAPTURE PART 4.-THE KINETICS OF A RADICAL RECOMBINATION PROCESS IN SOLIDS BY M. M. DE MAINE, A. G. MADDOCK AND K. T A ~ G B ~ L * University Chemical Laboratory, Lensfield Road, Cambridge, England Received 25th February, 1957 The kinetics of the slower stage of the recombination of the fragments produced by neutron capture in potassium chromate have been studied. The results indicate a surprisingly small activation energy for the process. The earlier stages of the process have been studied in solid solutions of potassium chromate in potassium fluoberyllate and in an entirely different type of compound, hexabromo-ethane. In both cases the essential features of the recombination resemble those in potassium chromate, but the recombination can be studied at much lower temperatures in hexabromo-ethane. The results are discussed in terms of a mechanism suggested in a previous paper. Of the chemical processes that take place in crystalline substances, one of the more convenient for kinetic study is the recombination of fragments formed by radiative thermal neutron capture by atoms combined in the molecules or molecular ions forming the crystal lattice.Provided that the compounds of elements that show strong resonance absorptions are avoided, the events pro- ducing the fragments are randomly distributed throughout the crystals. The rupture of the molecule following neutron capture may be due to one or both of the following causes : (i) recoil from the emission of the photon or photons which carry away the excitation energy of the compound nucleus, or (ii) ionization of valence electrons following internal conversion of one or more of the photons. In solid substances, the former process must be more important since it will gener- ally lead to some separation of the fragments in the lattice.For an isolated molecule or molecular ion, it can be shown that there is only a very small chance of the molecule surviving rupture by this mechanism.l.2 However, when solids are irradiated, it is often found upon chemical analysis that a substantial proportion of the radioactive atoms formed by neutron capture are present in molecules of the target species. It must be admitted that the analytical procedures used are themselves sometimes capable of converting closely related molecular species into the target species,3 but the influence of the analytical procedure can often be assessed by comparing results from different procedures. If the neutron-irradiated solid is heated before analysis, the fraction of radio-active atoms found in the target species increases and the process in the solid takes place sufficiently slowly for a kinetic study.5 49 5 The principal features of the kinetics have been described in an earlier paper relating to a study of irradiated potassium chromate.6 It has been shown that the data can be explained neither in terms of a combination of uni- or bimolecular processes with a limited number of energies of activation, nor by competitive reactions.The latter possibility has been excluded by the results obtained on heating a sample at one temperature and subsequently at a higher temperature. * present address : Joint Establishment for Nuclear Energy Research, Box 87, Lillestrqm, Norway.21 1212 RADICAL RECOMBINATION PROCESS A simple power law dependence on the time of heating, as is characteristic of a number of diffusion-controlled processes, was also found to be inadequate. The kinetics appeared to be very similar to those that have been found for the formation of a very thin oxide film on metals such as copper.7~ 8 The rapid increase in the retention to a value which subsequently changes only very slowly corresponds to the formation of a nearly constant thickness oxide film by cor- rosion at any given temperature. This behaviour can be predicted for any system where an inverse power law attraction force between the reacting fragments or particles is superimposed on a unimolecular recombination process.In the earlier paper it was suggested that the attractive force might be electro- static attraction between charged fragments. Unfortunately, the nature of the actual fragments is by no means certain. For the oxyanions of the transition metals, Libby et. af. 9 have argued that the recoil ruptures bonds without changing the valence state of the central atom, so that oxygen ions are split off. On this basis, CrO42- produces CrO3, Cr022+, CrO4+ and possibly Cr6+. The first two members of this series hydrate to chromate ions upon solution of the irradiated chromate prior to the analytical separation. It is only the third and last members that can oxidize the water and become reduced to the separable trivalent state. It seems doubtful whether the bare chromium ion could persist in the lattice at room temperature until the irradiated salt was investigated, which was usually not less than a week after the neutron irradiation had ended, in order to allow time for the decay of the potassium activity.Therefore the recombina- tion process must primarily concern the Cr04-’ species. There are two obvious mechanisms whereby this ion can be converted into one of the earlier members of the series ; (i) reaction with one of the oxygen ions in the lattice formed in the same or another nuclear event, or (ii) reaction with a nearby inactive chromate ion, :TrO4+ -$- CrO42- -+ *Cr02+ + Cr03.The conditions of neutron irradiation chosen for these experiments are such that about 2 chromium atoms in 109 are converted to the radioactive species, but about five times as many suffer radiation capture to produce inactive, and therefore, at present, undetected, fragments. At the same time, about as many potassium atoms and a very much smaller number of oxygen atoms suffer a recoil. The fragmenting events are thus generally widely separated. Unfortun- ately, insufficient data are available regarding the capture of gamma radiation spectra to permit the average recoil energy to be calculated (the maximum energy is - 500 eV). For this reason, it is not yet possible to calculate the average separation of chromium-containing fragments with much precision, but it appears probable that it will amount to about a hundred lattice units under these con- ditions of neutron irradiation. It seemed possible to distinguish between the two mechanisms described above by studying the behaviour of irradiated solid solutions of potassium chromate in potassium fluoberyllate.In these solutions, the second mechanism is far less likely to occur and if it were important the thermal recombination process should not be very noticeable in irradiated solid solutions. In the earlier paper a state- ment of the result of such an experiment was made. In this paper more detailed quantitative results are presented. Since the recombination process appears to take place in much the same way as in the pure chromate the first mechanism for the process is considered more likely.This mechanism predicts electrostatic attraction between the fragments, which are CrO4+ and 02-. The low con- centration of the species suggests that the recombination will generally take place between CrO4+ and 0 2 - fragments formed in the same nuclear event. Other work10 has shown that recombination processes of this kind are by no means restricted to relatively simple ionic crystals. It was decided to deter- mine whether the same kinetic features were to be found in some of these systems. A number of organic bromine compounds have been investigated and some results for hexabromo-ethane are reported.M. M . DE MAINE, A . G . MADDOCK AND K . T A U G B ~ L 21 3 EXPERIMENTAL MATERIALs.-Analytical reagent quality potassium chromate was used without further purification.Potassium fluoberyllate was made by dissolving the purest beryllium carbonate in reagent quality hydrofluoric acid, evaporating to dryness and recrystallizing the product from water twice. The mixed crystals were prepared by heating a potassium chromate solution, 97 % saturated at 20" C, to the boiling point, saturating with potas- sium fluoberyllate and allowing the hot solution to crystallize slowly. The crystals were separated, washed quickly with ice-cold water, dried on an absorbent plate and finally in uacuo. The crystals were examined for homogeneity under the microscope and the chromate found to be uniformly incorporated. Spectrophotometric analysis showed the crystals contained 0.9 mole % of chromate. Hexabromo-ethane was synthesized by the method of Mouneyrat.11 It was re- crystallized a number of times from carbon disulphide before use.IRRADIATIoNS.-The chromate and mixed crystals were sealed in uaem in silica ampoules for irradiation. The hexabromo-ethane was irradiated in air in snap closure polythene ampoules, after preliminary experiments showed no difference in behaviour from samples irradiated in uacuo. ANALYTICAL PRocEDuRES.-With the pure and solid solutions of the potassium chromate, after solution of the irradiated crystals the radioactive chromium is found either as chromate or as chromic ions. The chromic-chromate separation used has been described in part 2.3 An arbitrary quantity of the substance was dissolved in carbon tetrachloride, containing a trace of free bromine, in a 5-ml standard flask.The total activity was determined by removing a 1-ml aliquot and diluting with 25 ml of alcohol in the counting cup. Another 1-ml aliquot was shaken with 5 ml of an approximately millimolar solution of sodium bisulphite and potassium bromide. The activity of an aliquot of the aqueous extract was determined after dilution with 25 ml of alcohol in the counting cup. DETERMINATION OF THE ACTIVITY.-The activities available in the experiments with the mixed crystals were very small and quantitative studies would have been impossible without the use of a heavily screened scintillation counter with a one-channel pulse analyser. Even with the hexabromo-ethane the low solubility of the compound precludes the use of a counter with too high a background rate.A cylindrical thallium activated sodium iodide crystal detector was used, 35mm high and 25mm diameter. The solutions to be measured were placed in one of a series of interchangeable polythene annular vessels which could be fitted over the crystal in a reproducible fashion. The vessels and the crystal holder were constructed so that none of the beta particles from the annular space would penetrate to the crystal. By means of the pulse analyser only the photo-absorption pulses from the 0-32 MeV y-ray of the 5lCr or the 0.78 MeV y-ray of 82Br were recorded. In this way interference was avoided from the small amounts of the 8oBr isomers that were sometimes still present when the measurements were made. Essentially the whole of the photo-peak from the 51Cr y-radiation could be collected in a channel in which the background was only 6 counts per min.The usual corrections for the background were made. Related measurements were always made quickly enough for corrections for h a y to be unnecessary. It was verified that the counter was not liable to any short-term variations in sensitivity. In both series of experiments it was found that appreciably larger changes in the density of the sample solutions than occurred during the measure- ments were without effect on the recorded activity. Self-absorption corrections were therefore unnecessary. The absence of absorption of activity on the walls of the counting cups was demon- strated in both series of experiments by observing that neither did the counting rate change with the time elapsed since the cup was filled, nor was an abnormal proportion of the activity retained on simply pouring out its contents and draining the cup. Although various organic solutions containing free bromine were used in the second series of experi- ments, the polythene counting cups were seldom contaminated or attacked.chromic-chromate separation have already been described.3 With the hexabromo- ethane it was necessary to demonstrate that exchange was unimportant during the time taken for the separation. In addition it was desirable to determine the relation of the retention, measured as described above, to the true value ; that is, to what extent other water insoluble organic bromine compounds are included in the retention. The retention in the hexabromo-ethane was determined as follows.OBSERVATIONS ON THE EXPERIMENTAL TECHNIQUES.-TeStS On the reliability Of the214 RADICAL RECOMBINATION PROCESS Exchange with free bromine in carbon tetrachloride was shown to be unimportant by demonstrating that negligible exchange occurred between active bromine and in- active hexabromo-ethane in 10 times the usual period elapsing before examination of the solution (1 h). A more rapid exchange, or at least fixation of activity in the organic layer, took place if the system was strongly illuminated or if a wet solution of bromine in carbon tetrachloride was used. These conditions were carefully avoided in the actual separation. It was found also that radioactive pure hexabromo-ethane slowly gave up its bromine to a warm solution of sodium bisulphite and potassium bromide, either by exchange or more likely by hydrolysis.However, the reaction was not complete in 2 days at 82" and does not imply any correction for the usual period of contact of the carbon tetrachloride solution and the aqueous extractant (10 min). The reproducibility of the results obtained under varying conditions of extraction confirms that exchange or similar reactions are unimportant. Hexabromo-ethane was chosen for study because there appeared to be relatively few products in which the radioactive bromine might be found. However, the method of analysis used would record most other organic bromine compounds in the retention. It was proved that these do not in fact represent a very substantial fraction of the retention by comparing the specific activity of the hexabromo-ethane immediately after the aqueous extraction and after a series of fractional crystallizations.1 g of inactive hexabromo- ethane was added to the washed carbon tetrachloride solution and the volume made up to 50ml. A 10-ml portion was removed to provide a reference sample showing the initial specific activity. The remainder was evaporated to dryness and fractionally crystal- lized from ether thrice. A portion of the product was weighed and dissolved and the specific activity compared with initial sample. The change indicated that about 85 "/D of the measured retention was due to hexabromo-ethane. RESULTS PURE POTASSIUM CHROMATE The slower part of the recombination process has now been studied for periods up to 35 days' heating. The experiments were conducted on samples from a single irradiation of 1 week at a nominal neutron flux of 1010 neutrons/cm sec.Since previous experi- ments 6 showed no difference between samples heated for short periods in air and in z)ucuo, Time of heotinq, days FIG. 1 .-The slow recombination process in potassium chromate crystals. (Chromate all irradiated 1 week at pile factor 0.1.) 0 no heating, 0 heated at 439" K, (> heated at 455" K, 0 heated at 465" K, heated at 497" K, 0 heated at 508" K. these experiments were made with samples heated in air in thermostatically controlled ovens (& 1" C). In a control experiment it was shown that the same retention was reached on heating samples for 16 days in an open tube and in an evacuated tube.All the points are the means of at least duplicate determinations, and two or more aliquots of the chromic and chromate fractions were counted in each determination. The results are shown in fig. 1. It is apparent that the retention always reaches 100 % after a long enough period of heating.M . M . DE M A I N E , A . G . MADDOCK AND K . T A ~ G B ~ L 215 THE MIXED CRYSTALS The mixed crystals were found even more susceptible to the radiation dose received during irradiation than the pure chromate.3 Table 1 records the mean values of the initial retention. Each sample was irradiated for one week. Samples I and I1 were entirely separate irradiations. TABLE 1 pile factor sample I sample I I u.1 ( s 1011 neutron cmz/sec) nominal flux 26-2 f 0-3 1.0 28.7 -1: 0.4 28-7 f 0.7 4.5 YY Y Y 9 ) 28-2 6-0 9 , ,Y Y Y 43.9 25.7 & 0-5 $ 9 9 , > Y - - Time of heatinq, hours FIG.2.-Change of retention with heating of potassium chromate-fluoberyllate (irradiated 1 week at pile factor 0.1). 9 heated at 468" K, 0 heated at 508" K, 0 heated at 433" K. Time of heatinq. h o u r s FIG. 3.-Change of retention with heating of potassium chromate-fluoberyllate (irradiated 1 week at pile factor 1). 0 heated at 468" K, 0 heated at 508" K.216 R A D I C A L RECOMBINATION PROCESS The kinetics of the recombination process were studied in the samples irradiated at pile factors of 01, 1.0 and 45, the last two being examined rather less thoroughly. The results are shown in fig. 2, 3 and 4 respectively. The relation of the difference between the initial and " plateau " values of the retention and the temperature of heating was determined in the same way as for the pure chromate.Time of heatinq, bows FIG. 4.-Change in retention on heating potassium chromate-fluoberyllate (irradiated 1 week at pile factor 4.5). 0 heated at 468" K, 0 heated at 508" K. Because the whole process takes place more quickly in the mixed crystals the slope of the retention plateau is more noticeable. Hence it was decided to measure the values R1 and R20 of the retention at I h and 20 h at various temperatures of heating of the mixed crystals irradiated at the lowest pile factor. The results are displayed in fig. 5. FIG. 5.-Difference between initial and " plateau " retentions for irradiated mixed potassium chromate-fluoberyllate crystals (irradiated 1 week at pile factor 0.1).0 using R1 - Ro (R1 retention after 1 h heating) 0 using R20 - Ro (R20 retention after 1 h heating). HEXABROMO-ETHANE Like most organic compounds hexabromo-ethane is susceptible to gross radiolysis Conditions were chosen so that this radiolysis, releasing inactive bromine, However, traces of pure bromine formed during some irradi- in the pile. was kept to a minimum,M . M . DE MAINE, A . G . MADDOCK AND K . T A ~ G B ~ L 217 ation did not appear to influence the behaviour of the irradiated product. The initial retention, as usual, proved to be dependent on the dose of ionizing radiation received during the neutron irradiation. All irradiations lasted 2 days. Mean retentions at 3 nominal pile fluxes are given below.nominal pile flux (x 10-11 n/cm* sec) 0.002 005 0 1 R 70.6 79.1 820 These measurements were made on samples stored at the temperature of solid carbon dioxide from a few hours after withdrawal from the pile. When samples were stored at room temperature it was found that the retention increased gradually. Results are shown in fig. 6. For all subsequent investigations the I 2 3 4 days Time of heatinq FIG. 6.-The recombination process in hexabromo-ethane crystals (all irradiated two days at pile factor 0.1). Upper time scale : 0 heated at 339" K, Lower time scale : 0 heated at 355" K, 9 heated at 327" K. 0 stored at room temperature. 5 FIG. 7.-Dif€erence between initial and " plateau " retentions AR, as a function of the temperature of heating T.21 8 R A D I C A L RECOMBINATION PROCESS material was stored at solid carbon dioxide temperature except when deliberately under- going heat treatment.It was verified that no measurable changes occurred during 4 days' storage under these conditions. The general kinetic features of the thermal re- combination process were found to be the same as with the chromates. Results at 3 temperatures are shown in fig. 6. All measurements were made on material with essenti- ally the same initial retention. All values are the means of a number of determinations. The earlier stages of the process are over more quickly and the plateaux slope even more noticeably than for the mixed crystals. The retention changes after 3-h heating were therefore determined at a number of temperatures on samples of material with the same initial retention.The results are shown in fig. 7. In the same way as for other chromates, it was shown that the effect of raising the temperature, after heating until the plateau value has been reached at some lower tem- perature, was to increase the retention to the same value as it would have had if the whole period of heating had taken place at the higher temperature. Some results are shown below. sample (a) 5 h at 54" C 6 h at 82" R = 97.1 + R = 96.6 3.5 h at 82" sample (6) 3hat44" 3 h at 66" R = 94.2 + R = 94.0 2-25 h at 66" sample (c) 24 h at 42" 3 h at loOO R = 97.2 + R = 97-0 3 h at 100" Sample (c) had a different initial retention from (a) and (b). The previous experiments were all conducted by heating the irradiated solid in a glass tube.Longer periods of heating appeared to give somewhat erratic results, and it seemed desirable to determine if some new process was involved. Some crystals were heated for three days at 66" in a closed tube attached to a vessel containing wet glycerol with a trace of sodium sulphite and potassium bromide. The activity found in the distillate, which was retained by the glycerol, consisted largely of bromine. Thus the retention determined after long periods of heating in an open tube would be erroneously high because of the diffusion of active bromine out of the irradiated crystals. This supposition was verified in the following experiment in which the retention of samples heated in a closed tube was compared with that of samples heated in an open tube.In the former case the entire contents of the tube were dissolved for the determination. At 66" the contents of the open tube show a mean R = 97.3 ; those of the closed tube show R = 96.0 ; and the 3-h plateau value is R = 93-5. Superimposed on the recom- bination process is a slow diffusion of active free bromine out of the crystals. DISCUSSION The behaviour of the mixed crystals and of the hexabromo-ethane indicates that the mechanism of the recombination process in both cases is essentially similar to that in the pure chromate. In the mixed crystals the process seems limited to a maximum recombination of about 83 % of the fragments. The remaining 17 % might represent the fraction of chromium fragments that are so greatly separated from their partners by the recoil that it is impossible for them to re- combine.Alternatively, it might represent the fraction permanently reduced to the chromic state by some reaction with the surrounding fluoberyllate. With the hexabromo-ethane some small fraction of the radioactive bromine can escape by diffusing out of the crystal. Thus there is set a limit to the ultimate maximum retention which possibly depends on the size of the crystallites. It must be observed that if chromium fragments diffuse to the surface in the same way, it is most likely that they would also end up in the " unretained " or chromicM . M . DE MAINE, A . G . MADDOCK AND K . T A ~ G B ~ L 21 9 fraction. The fact that nearly all the radioactive chromium can return to the chromate state upon dissolution in water after a sufficiently long period of heating the crystals, suggests that diffusion is unimportant in the chromates.Earlier experiments have failed to reveal a connection between the retention and the crystal size for a variety of chromate samples.; FIG. 8.-Activation energy for the slow process in potassium chromate. The data on the effect of continued heating of the pure chromate allow an estimate to be made of the energy of activation of the recombination process. The points are rather scattered (fig. S), but they indicate an energy of activation between 1 and 4 kcal with a best value of about 2 kcal. This value is very much smaller than would be expected on the basis of the theory outlined in the previous paper.6 Indeed, it is unusually small for any process taking place in a solid. The authors would like to acknowledge the sympathetic assistance of the Isotope Division, A.E.R.E., during their studies. One of us, M. M. de M., wishes to thank the Commissioners of the Exhibition of 1851 for a science over- seas scholarship held during the period this work was carried out. Another, K. H. T., wishes to thank the Royal Norwegian Council for Scientific and Industrial Research for a Fellowship and the Joint Establishment for Nuclear Energy Research for leave of absence during this work. 1 McCallum and Maddock, Trans. Faraday SOC., 1953, 49, 1150. 2 Cobble and Boyd, J. Amer. Chem. SOC., 1952,74, 1282. 3 Green, Harbottle and Maddock, Trans. Faraday SOC., 1953, 49, 1413. 4 Green and Maddock, Nature, 1949, 164,788. 5 Rieder, Broda and Erber, Monatsch., 1950, 81, 657. 6 Maddock and de Maine, Can. J. Chem., 1956,34,275, 7 Mott, Trans. Faraday SOC., 1947, 43, 429. 8 Cabrera and Mott, Reports Prog. Physics, 1948, 12, 163. 9 Libby, J. Amer. Chem. SOC., 1947, 69, 2523. 10 Maddock and Sutin, Trans. Faraday SOC., 1955, 51, 184. 1 1 Mouneyrat, Bull. SOC. Chim., 1898, 19, 177.

ISSN:0366-9033    

DOI:10.1039/DF9572300211

出版商:RSC    

年代:1957

数据来源: RSC

摘要:

GENERAL DISCUSSION Dr. P. W. M. Jacobs (Imperial College London) said As a typical example of a steady-state process involving lattice rearrangement Prof. de Boer has men-mentioned the oxidation of metals. I would like to draw attention to some recent work on the anodic oxidation of tantalum which is relevant to the existing theories of oxide formation. Cabrera and Mott 1 considered that every ion escaping from the metal into the oxide is swept right through the oxide by the high field applied across it. Thus a single barrier located at the metal/oxide interface is supposed to control the current and therefore the rate of oxide formation. It is readily shown that for any theory based on current control by a single barrier the dependence of field E on current i is given by where q is the charge on the mobile species and b the barrier half-width.Experi-mentally however Vermilyea,2 Young3 and Bray4 have found that the Tafel slope 7 is independent of T between 0 and 90" C for oxide films formed on niobium and tantalum. We 5 have recently extended this work to - 63" C by forming oxide films in non-aqueous media and found that the Tafel slope does fall off with temperature below 0" C. T = 1.86 x 104 V cm-1 at 300" K and 1.55 x 105 V cm-1 at 210" K. This is consistent with the theory proposed by Dewald6 in which allowance is made for the space charge in the film caused by ions in transit. The effect of this space charge is to cause a change over from entrance-control to migration-control as Tincreases so that although at both low and high temperatures respec-tively r should be proportional to T at intermediate temperatures (O-lOOo C) its variation with Tis too slight to be detected experimentally.Our results thus support the view that in steady-state formations of oxide films the rate of oxide growth is determined not by a single entrance barrier but by two barriers one controlling migration within the film and the other located at or near the metal-oxide boundary. Dr. K. H. Lieser (Darmstadt) said The transition of AgI discussed in the paper of Prof. de Boer also turns out to be more complex if considered in detail. Before the transition occurs we have relatively high disorder in the low tem-perature /?-phase. Therefore we find a rather high specific heat below the transi-tion temperature.7 The properties of the /?-modification lead to the conclusion that the disordered silver ions prefer the octahedral interstitial sites within the hexagonal lattices At about 10 % disorder the relatively big iodine ions rearrange and we find a sharp transition point.In a freshly prepared compact sample we find in vacuo values up to about 153" C. After the AgI has passed through several transitions the values fall to about 148' C.0 The transition temperature itself depends on the history of the sample. 1 Cabrera and Mott Rep Prog. Physics 1948 12 163. 2 Vermilyea Acta Metallurgica 1953 1 282. 3 Young Trans. Faraday Soc. 1956 52 502. 4 Bray Thesis (University of London 1957). 5 Bray Jacobs and Young to be published. 6 Dewald J. Electrochem. SOC. 1955 102 1.7 Lieser 2. physik. Chem. 1954,2,238. 8 Lieser 2. physik. Chem. 1956 9 216 302. 9 Lieser unpubhhed measurements. 22 GENERAL DISCUSSION 22 1 In powdered samples even lower values have been measured. The pressure de-pendence of the transition temperature seems to show irregularities with respect to the Clausius-Clapeyron equation. Both effects may depend on the retardation of equilibrium. Kokhanenko and Gol'tsev 1 found that cr.-AgI may take up an excess of silver, P-AgI not. They ascribe the variation of the transition point to this excess of silver. In every case the transition temperature of AgI is not a good standard for thermometric calibration as proposed sometimes in the literature.2 Dr. J. Meinnel (Rennes) said Dielectric measurements are very interesting for the study of the lattice rearrangements accompanying the order-disorder transitions in some ionic crystals like ammonium halides alkali metal nitrates, cyanides etc.We have found that the NaCl (or I1 > I) transition of ammonium halides was characterized by a very large increase of the dielectric constant (up to 100 %). The transition at 401" K of KNO3 showed a similar increase while for NaN03 the raising of E' began 100" C before the transition. Traces of moisture influences the results very much. Consequently the study of dielectric constant variations for these products by varying the circumstances of measurements (dry or wet powders pressed powders single crystals) may give valuable information on the kinetics of the transformation. Dr.R. P. Rastogi (Lucknow University) said I want to make a brief remark about the phase transformation of tin. Any theory of phase transformation must take into account the kinetics of nucleus formation and growth of nuclei simul-taneously since both are competing processes ; in practice it is difficult to separate the two. From this point of view Avrami's formalism seems to be a step in the right direction. Incidentally it explains why we do not have constant rate of isothermal transformation examples of which we also come across in phase trans-formation in solutions.3 Since only a functional relationship has been tested for Avrami's equation a complete test has not been achieved and the conclusions about the mechanism of nucleation should be treated with caution. Theoretically, Avrami's equation does not seem to be completely sound since it does not take into account the presence and number of dislocations in crystals.4 Dr.L. J. Groen (Velsen-N.) (communicated) In our attempt to describe the kinetics of the transformation of grey to white tin we found k - 1 in the general formula. (1) Following our observations this means that a first-order reaction applies to this transformation. In the Avrami relationship however k = 1 should mean nucleation at t = 0 and unidimensional growth an interpretation that certainly does not hold in this tin transformation. This makes clear again that the application of any overall relationship for the rate of transformation is useless as long as rate of nucleation and rate of growth are not treated independently.The Avrami formula however is a general one that can be adapted to fit a certain problem. It does take into account the separate role of nucleation and growth. As to nucleation the underlying principle of the relationship is the existence of germ nuclei be it impurities dislocations or residual particles of the unstable modification that might eventually become active nuclei. The time-lag found in the grey to white transformation is still more pronounced in the white to grey transformation where in some cases incubation periods of several hours were observed. Its appearance is related to the necessary formation of nuclei of critical size as was suggested by Turnbull and Fisher,6 or in terms of Avrami to the time needed for the formation of growth nuclei out of germ nuclei.In the interpretation of the factor p (fig. 10) it was supposed that any growing 1 Kokhanenko and Gol'tsev Doklady Akad. Nauk S.S.R. 1952,85 543. 2 e.g. by Barshad Amer. Miner. 1952,37 667. 3 Rastogi and Chatterji J. Physic. Chem. 1955 59 I . 4 Burton Cabrera and Frank Phil. Trans. A 1951 243 299. 6 Turnbull and Fisher J. Chem. Physics 1949 17 71 222 GENERAL DISCUSSION N - 4 .c c L u D i+ taken for the initial distribution of embryos (fig. l a ) to adjust itself to a steady-state distribution (fig. lb). The rate of nucleation then follows the relation J ( t ) = JO exp (- ~ / t ) , where J(t) is the rate of nucleation at time t and Jo is the rate of nucleation at t = CO the time constant T is given by 'A. -1 where O, and v are the cross-sectional area and volume per atom cr is the inter-facial free energy between the nucleus and the parent phase Ap the differ-ence in chemical potentials of the stable and unstable phases and AGA the free energy of activation for transport of an atom across the interface.If this relation is applied to the transformation of grey to white tin we have where EA is the activation energy for transport across the interface and ATis the superheating. According to this expression T will be very large near the transformation temperature and will decrease rapidly as ATincreases. In fig. 9a of Burgers and Groen the time which elapses before any transformation is perceptible may be taken as proportional to T. Then by plotting log T ( A T ) ~ against 1/Twe can obtain a value of 13 ltcal for EA.It is interesting to note that the data given in fig. 7 expt. temp. "C AT T (expt.) T (AT)4 a1 25 6 60 8.8 x 104 a2 27.5 8.5 8 4.2 x 104 a3 30 11 1 1.5 x 104 1 Zeldovich Acta physicochim. 1943 18 1. 2Turnbul1 Trans. Amer. Inst. Min. Met. Eng. 1948 175 774. 3 Kantrowitz J. Chem. Physics 1951 19 1097. 4 Probstein J. Chem. Physics. 1951 19 619 GENERAL DISCUSSION 223 per atom then the " driving force " towards transformation .: is A p - AG and is therefore less than it would be in the absence of strain energy. A distribution of strained em-bryos (fig. 2) is built up during the initial time-lag and 5 some reach the critical size containing k atoms; k is 9' given by I< 1 6.rru3vr1 + n 3(Ap - AGe)' f ;\ and clearly k < k,.From fig. 2 we see that some embryos hitherto subcritical may now become critical and even supercritical. The number of nuclei capable of free growth has therefore increased. Since AG per atom is effectively inde-pendent of temperature its removal will have a far greater effect when L$L is small (i.e. close to the transformation temperature) than when Ap is large (i.e. far from the transformation temperature). This is in accordance with values of y = 10 at 25" and p = 0 at 3.5". The higher the temperature the smaller are the nuclei in the neighbourhood of the critical size and presumably the probability of inter-action with moving dislocations will also be smaller; this effect would operate in a sense to reduce the values of p at high temperatures relative to the values at low temperatures.A further eKect which would be expected is that AGA would be reduced owing to the interface becoming more disordered and thus the process of accretion on to the growing nucleus would occur more readily. In the above it has been assumed that the nucleation is homogeneous this is not a restriction however. With modifications the interpretation can be applied when the nucleation is heterogeneous and takes place on structural imperfections. Suppose the embryos form coherently at an edge dislocation. The smaller atomic volume of the white tin would favour a location on the compressive side of the dislocation but the lattice spacings would not have necessarily their equilibrium values ; the atnount of strain and the magnitude of AG are likely to be less than they would be in the homogeneous case.The release of the strain energy on plastic flow would have a similar effect as before though it would be smaller and might even be negative (in the sense that the driving force again falls below Ap). It is conceivable that in some cases the embryos remain coherent and that following deformation the dislocation at which they were formed glides away from the embryo; this would result in the opposite effect in that the rate of nucleation would decrease with plastic flow 224 GENERAL DISCUSSION It seems that the " induction effect " found by Burgers and Groen cannot be due simply to a multiplication of dislocations following deformation. This would merely affect the value of n the number of sites at which nucleation is -a 0.0 -favoured in the equation for the nucleation rate J, J = (nk* kT/h) exp (- AGA/kT) exp (- AGk/kT), and would not account for the effect of temperature on p. In fig. 10 the lines do not pass through the origin. We suggest that during this second time-lag nuclei are growing and straining the lattice; the elastic limit is I i reached and plastic flow occurs at the end of this second time-lag. 1 / ~ Finally the large value (120 kcal) found for the acti-vation energy of spontaneous nucleation may be due to FIG. 3 the observations being taken too near to the trans-formation temperature. The expected form of the curve for log J against 1/T is shown in fig. 3 and we see that the curve is asymptotic to the ordinate corresponding to the transformation temperature.Dr. N. H. Hartshorne (Leeds University) (communicated) We have reported that the observed rates for the sulphur transformations at low temperatures are much larger than those calculated for an evaporation-condensation mechanism, and that in the 18 -+ a transformation this discrepancy declines and finally dis-appears or at least becomes very small as the transition point TO is approached.1 Since writing our paper it has occurred to me that an explanation of these and other facts might be found along the following lines. Let us suppose as in the earlier " crack-block " or " gap-block " theory 2 that the interface proceeds by a series of rapid sweeps over small elements of volume (low activation energy " surges ") interspersed with slower steps due to the formation of gaps resulting from the shrinkage attending the transformation.The earlier theory required that these gaps be bridged in some way and it was always difficult to visualize just how this could happen. It is now proposed that the gaps are not bridged at all but that after a lapse of time during which the a-surface and of course the gap with it is advancing at the evaporation-condensa-tion rate a nucleus of the a-form is formed on the /3- (or y-) side of the gap and that this initiates a new surge which proceeds until another gap is formed and so on. It is further proposed that the formation of these nuclei on the unstable wall is triggered off by the impact of those molecules in the return stream from the a-form which possess more than the activation energy for nucleation.The average time elapsing before a nucleus appears will thus be inversely proportional to the rate of evaporation of the ct-form and proportional to exp (AIRT) where A is the activation energy for nucleation. A will increase rapidly as TO is approached. Let w be the average distance over which the interface advances between surges at the evaporation-condensation rate v and W the average distance of advance in a surge the surge velocity being V. Then the time to travel the total distance (w + W) is w/v + W/V and V = (W + W)/(W/U + W/V) = Bv (0 where v is the measured mean rate and B is the factor by which this is greater than the evaporation-condensation rate. From (i) B = (w/v + W/v)/(w/v + W/V) 1 -t (l/v - l/V)/(w/Wv + 1/Y).1 Briske and Hartshorne this Discussion. 2 Hartshorne and Roberts J. Chern Soc. 1951 1097 GENERAL DISCUSSION 225 If V is very large we can neglect 1/ V in comparison with l/v and also in com-parison with w/Wv unless w / W is very small which it is only likely to be at very high supersaturations. Thus the equation simplifies to B = 1 + w/w (ii) and from (i) we get G = v + (W/w)v. (iii) Now the time required to advance over the distance w equals the time elapsing before the appearance of a nucleus which equals [l/(rate of evaporation of the a-form)] exp A/RT = K exp (L,/RT) exp (A/RT) = w/v, where K is a constant (to a sufficient approximation) and mation of a-sulphur. is the heat of subli-(iv) If we take A to be an activation energy for two-dimensional nucleation the second term in this equation is nearly the same as Dunning's expression proposed in 1949,l which was based on the idea that two-dimensional nucleation of the advancing a-surface assumed to be in contact with a vapour-type transition layer, was necessary to sustain growth.The only difference is that in the first exponential L appears instead of the somewhat smaller LIr the heat of sublimation of the unstable form. Dunning's expression is known to fit the temperature coefficient of the /? -+ a transformation over the range - 15" to 80° but between 80" and TO the rates show a strong positive deviation and near To become approximately equal to the evaporation-condensation rate as mentioned above.2 Eqn. (iv) fits this behaviour at least qualitatively because at low temperatures v the evaporation-condensation rate will be negligible in comparison with that given by the second term for A is then small ; but as TO is approached A increases rapidly and the second term becomes negligible so that U -v.The basic idea underlying eqn. (iv) would also meet one of the main objections to Dunning's theory namely that the value of A deduced from the experimental results corresponded to an edge free energy which appeared to be far too low for a solid-vapour interface and of the order to be expected for a solid-solid inter-face. According to the new approach the edge free energy involved in the forma-tion of the nucleus would in fact be that for a solid-solid interface. Dr. W. J. Dunning (Bristol) (communicated) Hartshorne's 3 theory of the transformation kinetics of a- to /l-sulphur assumes the presence of a thin disordered layer of molecules resembling a vapour lying between the two phases.The experiments on the transformation of y- to a-sulphur4 suggest that in this case solid-solid contact is maintained throughout. On this view the spherulitic struc-ture of the y-phase would be considered as a succession of tilt boundaries com-posed of edge dislocations. If the lattice of the new phase were continuous with that of the old phase the steering effect could be accounted for. The assumption of an interface with the properties of a quasi-vapour seems foreign to such a view and it is necessary to consider the consequences of replacing the quasi-vapour by a coherent interface.In sketching the discussion a number of assumptions are made to simplify the treatment. Both the stable a- and unstable y-phases are considered to be simple cubic Kossel crystals with the same lattice. The interface between them consists of two semi-infinite cc and 7-001 layers meeting in a 10 line (" step ") and on this Substituting for w/v in (iii) we obtain 5 = v + ( w/K) exp (- L,/RT) exp (- A/RT). H 1 Dunning Faraahy SOC. Discussions 1949 5 157. 2 Hartshorne and Thackray J. Chern. Soc. 1957,212. 3 Hartshorne Faruduy SOC. Discussions 1949 5 149. 4 Hartshorne this Discussion 226 GENERAL DISCUSSION line is a kink. Fig. 1 shows a section parallel to the interface. Transformation is assumed to occur in the following manner; site 1 adjacent to the kink becomes vacant the molecule of phase y on site 2 moves to site 1 becoming a molecule of phase a and transferring the vacancy to site 2.This last assumption is closely analogous to the diffusion process discussed by Bardeen and Herring 1 and we shall adapt their procedure for deriving the kinetics of this process. Suppose each phase can be treated as an ideal dilute solid solution in which vacancies play the role of solute. If NA and NV are the numbers and and p v are the chemical potentials of molecules and vacancies then the free energy G of such a phase at equilib-rium with its vacancies is given by FIG. 1 and p v = 0 . 2 The concentrations of molecules and vacancies are given by 3 5 - - 7 exp (-@ N where N = NA + NV is the total number of sites t is the Nth root of the grand partition function and the ratio KA/KV is the change in the partition function of the crystal (in a given configuration) when a molecule is placed in a vacant lattice site.(3) (4) The forms of K A and K V may be taken as KA = ZA exp ( X A / k T ) , KV = zv exp (XvlkT), where X A - X V is the energy required to extract a molecule into the vapour and leave a vacant site. The probability P V l A 2 that site 1 is vacant and that there is a molecule on site 2 is given by, and the probability P A 1 v 2 that site 1 is occupied and site 2 vacant is given by where superscripts distinguish the phases. on site 2 jumping to site 1 is The net probability of the molecules = k f P V l A 2 - k b p A l V 2 - (7) At the transformation temperature TO there is equilibrium and on assuming in this approximation that the ks are independent of temperature 1 Bardeen and Herring Imperfections in Nearly Perfect Crystals (John Wiley and ZHerring The Physics of Powder Metallurgy (ed.Kingston) (McGraw Hill New 3 Fowler and Guggenheim Statistical Thermodynamics (Cambridge 1939) p. 242. Sons Chapman and Hall London 1952) p. 261. York 1950) GENERAL DISCUSSION From (7) and (8) the net probability of transformation is By using eqn. (1) to (6) eqn. (9) becomes t ) } 7 where = ZQ v z y A ZYe v zue A/(Z?/yz5 zy zy), Ax = x; - x; - (XY - x;, - qAT/To 1 /L - /.L - (/LY - py). The dependence of P v ~ A ~ on temperature can be approximated by the expression A exp (- Ev/kT) where A is a constant and Ev is the energy to form a vacancy in the crystal For homopolar crystals EV will be similar in magnitude to the heat of sublimation of a molecule.Thus the final result for the rate of trans-formation in this unit process will be of the same form as Hartshorne’s equation 1 v = +A exp (- g){ 1 - exp R 14- (L To - :)}. The discussion so far has been confined to two sites. After the jump from site 2 to site 1 there is a vacancy at site 2 into which the molecule on site 3 can move leaving a vacancy on site 3 and so on. Thus the vacancy which appeared initially at site 1 diffuses along the step. The overall process is analogous to a chain reaction ; the initiating step is the appearance of a vacancy at site 1 and the propagating steps are V1A2 -f A1 v2 V2A3 -f A2V3 etc.The chain-terminating step would be the diffusion of the vacancy away from the step into the bulk of the crystal for example when the reaction VxAz -f AxYz takes place instead of the reaction VxAy -+ AxVy. The relative probabilities of the chain-propagating and chain terminating steps could be computed for a Kossel crystal. If as assumed the adhesion between the y-and a-phases is high and the interface remains coherent during the epitaxial transformation, it seems that some interesting situations might arise. For example (fig. 2) an edge disloca-tion c in the y-phase could resist the passage of a growing a step b across it. Subsequent stepsfand e would then pile up on b forming a surface bfe and this surface normally will be liberated by the transformation of the obstacle plane c which will occur from the right.However it is possible that c will be an isolated plane having no connection with any transformed planes ; such island planes might originate during the crystallization of the y-phase from L-shaped dislocations by movement of the screw segment across a loop of the edge segment.2 The transformation of 8 d FIG. 2 1 Hartshorne Faraday Soc. Discussion 1949 5 149. 2Amelinkx et al. Phil. Mag. 1957 2 94 355. H 228 GENERAL DISCUSSION such an island plane would require nucleation and nucleation would be achieved more readily at the bounding dislocation than in the interior of the plane. The simplest picture would be of a plane lenticular nucleus (fig. 3a) on the dislocation. ( b) FIG.3 If the edges of the nucleus and the dislocation are represented approximately as circles the free energy AG, of formation of such a nucleus would be where f ( 0 ) = (0 - sin 6’ cos 69/77 if the radius of curvature of the dislocation line is very much greater than the radius of curvature of the boundary of the nucleus and 8 is the contact angle. It is interesting to note that the free enegry to form a critical two-dimensional nucleus could be quite different according to whether the nucleus is v. in p or /3 in ‘J( (fig. 3b). Dr. N. H. Hartshorne (Leeds University) (communicated) Dunning’s new theory is stimulating but it appears to lead to the observed value for the tcm-perature coefficient at low temperatures (namely that corresponding to the heat of sublimation) only because it neglects the activation energy involved in the jump of a molecule into the vacancy from an adjacent site.Dunning’s picture really reduces to that of a coherent interface with a small fraction of interface sites unoccupied this fraction being proportional to exp (- L/RT) where L may be taken as somewhere between the heats of sub-limation of the two forms. The contribution of any one vacancy to the advance of the interface as a whole will be given by the net rate at which molecules from the y side jump into it and this can be expressed as (0 where nr and ca are the activation energies for molecules to jump into the vacancy from the y and a sides respectively and the A’s are constants containing the vibra-tion frequencies. By equating v to 0 at To the transition temperature,and solving for Aa and multiplying by the number of vacancies in the area of interface under consideration i.e.by K exp (- L/RT) where K is a constant we obtain for the rate of advance of the interface V = KAY exp - ((L + ay)/RT) (1 - exp (q/RTo - q/RT)) (ii) where q = oa - a, the heat of transformation. It is difficult to estimate the values of ar and a, but they would be far from negligible. On the simple cubic model they would be equal at least to L/3 since the jump requires virtually a complete break-away from the cube on the side opposite to the vacancy. In the actual structures consisting of Ss rings the situ-ation would of course be far more complex but it seems clear that the average jump energy would be equal to a considerable fraction of the heat of sublimation.Eqn. (ii) would therefore predict an appreciably greater temperature coefficient for the rate at low temperatures (where the change in the last factor in the ex-pression is small) than that corresponding to L and this is not found. v = A exp (- a,/RT) - A exp (- u,/RT) GENERAL DISCUSSION 229 It seems rather unlikely that our sulphur films did in fact contain an equilibrium concentration of vacancies. Crystallization of the y-form began at various tem-peratures between the melting point and room temperature during rapid cooling to the latter and measurements of the rate were then made at - 15" O" and 20" to determine the temperature coefficient. The same films were used at all these temperatures and it seems improbable that the number of vacancies would have kept pace with these temperature changes so far below the melting point.One further point-why should it be thought that a true solid-solid transfornia-tion i n a structure built up of molecules shaped as are the &3 rings requires the presence of a complete molecular vacancy-a " whole hole " in fact? Surely all that may be needed is a little " elbow room " to permit the molecules to take up their positions on the new lattice by executing small rotational movements. Dr. G. Salomon (Devt) said Formation and structure of spherulites from crystalline polymers have been extensively studied by Keller and by Schuur. These authors assume a specific mechanism depending on the polymeric nature of the material. The phenomena discussed by Briske and Hartshorne are very similar to those observed with polymers.It seems likely therefore that some of the factors determining spherulite formation are independent of the size of the molecule. One possibility would be a stress field produced by localized differ-ences in heat content. Has the influence of external stresses on spherulite formation of sulphur been studied ? Prof. J. H. de Boer (Geleen) said Concerning the paper by Tompkins and Young is any nitride formed during the decomposition of calcium azide by a direct or an indirect process ? Dr. F. C. Tompkins and Dr. D. A. Young (Imperial College) (communicated): In answer to Prof. de Boer some calcium nitride is always formed during the decomposition of the azide. When the azide is decomposed in high vacuum, the presence of nitride is scarcely detectable whereas if the nitrogen pressure is allowed to rise to say 100 p at the inflexion point up to 20 % of the theoretical amount of nitride may be formed.These results suggest that the nitride is formed by the combination of metallic calcium with gaseous nitrogen produced in the decomposition reaction and does not arise as an intermediate in the azide decomposition. We assume however that Prof. de Boer is more concerned as we were with the composition of the product nuclei at the actual reactant/product interface. Recognizing that mere analysis of reaction products gives no information on the nitride formation reaction we argued that were the nitride formed at the interface the electrical conductivity of the reaction matrix after coalescence of product nuclei would be characteristic of an ionic or semi-conductor whereas if no nitride was formed at the interface the conductivity would be metallic.We therefore measured the electrical conductivity of 5 mm thick pellets of calcium azide during decomposition at 95" C,1 with (a) the pressure of nitrogen always less than l/lOp and (b) allowing the nitrogen pressure to build up to 1 mm during the early stages of the reaction. In the former case (a) the conductivity remained substantially constant at 1013 ohm from the commencement to the inflexion point (120 min) when it fell within 2 min to about 300 ohm. The tem-perature coefficient of resistivity at this stage was small and positive i.e. character-istic of metallic conduction.In the latter case (b) the resistance fell at the inflexion point to values between lo5 and 107 ohm in different runs the temperature co-efficient of resistance in this state being large and negative i.e. characteristic of ionic or semi-conduction. We therefore concluded that in our normal decomposi-tion runs carried out at low pressures the reactant product interface was essentially not contaminated with nitride. 1 Gamer and Reeves have also conducted this experiment though with a different end in view 230 GENERAL DISCUSSION Dr. J. Y. Macdonald (St. Andrew) said Some of the reactions mentioned by Tompkins and Young are highly exothermic and the heat liberated may affect the mechanism. For example Thomas and Tompkins 1 estimate - AH for the reaction 2N3 = 3N2 at 151 kcal while the energy of activation of the barium azide decomposition is only 25 kcal.Formerly the idea of energy chains was rejected,2 as it was thought that any reaction would take place within a very few molecular vibrations after the absorption of energy and this leads to rates of reaction far in excess of what is found. The exiton theory which has been developed by Tompkins for these reactions however allows for the retention of the energy for an appreciable time before reaction and overcomes this difficulty. But even if energy chains are not formed there must be a very considerable thermal shock at the point where two azide radicals react and this might trigger off the decomposition of quite a number of radicles say some tens thus bridging that rather awkward gap between what simply amounts to two atoms in proximity and what can genuinely be considered as a tiny speck of the metallic product.It would be of interest to know whether any of the reactions studied by Tompkins and Young give any evidence of either of these effects. Each of the decompositions in question can be broken down into two series of steps one involving the anion and the other the cation and it seems that some features of the silver oxalate decomposition may help to determine which of these steps is rate-determining. It is not necessarily the same in all cases. For silver oxalate the following equation 5 may be written : C2O42- -+ 2C02 + 2e (oxidation) (1) Ag+ + e +Ag (reduction) (2) Ag + Agtl -+ Ag(n+l) (lattice growth).(3) Eqn. (1) is a summary of a number of steps such as those suggested by Tompkins et aZ.,5 and is chemically an oxidation process. Eqn. (2) the production of free silver atoms is a reduction; while (3) represents the aggregation of these atoms into a silver lattice. Now the interesting thing is that the decomposition of silver oxalate is retarded by oxygen and oxidizing agents,3 and is accelerated by hydrogen 4 and reducing agents? This points strongly to the equilibrium represented in eqn. (2) as being a rate-determining one in the normal thermal decomposition. This decomposi-tion moreover is autocatalytic in character and this seems to indicate that eqn. (3) which represents nuclear growth is also rate-determining. Now Tompkins et al.5 have shown conclusively that in the photochenzical decomposition of silver oxalate the steps summarized in eqn.(1) are the important ones and it is note-worthy that in this case the reaction is not appreciably autocatalytic. Now, the oxygen-retarded decomposition also shows no acceleration (after perhaps the initial 1 % or so) and I suggest that in this case reactions (2) and (3) have been retarded to such an extent that eqn. (1) becomes rate determining. It is significant that when silver oxalate is allowed to decompose in air for some 10 % to 15 %, it subsequently decomposes in a vacuum in just the same way as a specimen which has been pre-irradiated with u.-v. light. In each case the vacuum reaction starts 1 Thomas and Tompkins Proc. Roy. SOC. A 1951,209 550. 2 Furuduy SOC.Discussion (Chemical Reactions Involving Solids) 1938. 3 Macdonald J. Chem. SOC. 1936 832. 4 Szab6 and Bir6-Sug$r 2. Elektrochem. 1956 60 869. 5 Tompkins Trans. Furuduy SOC. 1948 44 206. Finch Jacobs and Tompkins, Macdonald and Sandison Trans. Faruduy SOC. 1938 34 589. J. Chem. Soc. 1954 2053 GENERAL DISCUSSION 23 1 at a very low rate indicating a virtual absence of interface but it accelerates more rapidly than the untreated specimens indicating that centres for the growth of nuclei have been formed (see figure which may be compared with fig. 1 in ref. (3a)). The following explanation of the " normal " decomposition of silver oxalate may perhaps be applicable with suitable modifications to other substances. A piece -of silver in contact with silver oxalate will acquire a contact potential by 0" U 0 c 0 -8-.- c 3 - 0 > c - 0 .I 0 OL c FIG.1 .-Decomposition of specimen Q in a vacuum at 130". I was maintained at 130" in air for 233 min prior to evacuation during which time about 15 % decomposition had taken place the rate falling from about 7 units to about 1 unit. I1 is the control, decomposed entirely in a vacuum. either gaining or losing electrons. If the metal loses some electrons it will become positively charged and will trap the corresponding negative charges in the neigh-bourhood of the interface forming a double layer. These charges being localized, will not confer general conductivity on the crystal. Chemically the presence of electrons is equivalent to having a certain concentration of metal atoms in the crystal lattice close to the interface.These atoms will join the metal lattice when they receive the required thermal activation. The rate of growth of the nuclei will be proportional to the number of these atoms and this in turn will depend on the area of the interface on the metal-salt contact potential and the presence of a reducing or oxidizing medium which will act as a source or sink of electrons. Variations in these conditions may alter considerably the rate of de-composition without however affecting the temperature coefficient which will be controlled by the activation energy of eqn. (3) above. The manner in which the concentration of charges (free atoms) at the inter-face will vary with the size of the metallic speck is not quite clear but it seems evident that with very small nuclei it will increase with the size of the speck for the work required to remove an electron from a single atom of silver is 7.5 eV and from a large piece of silver is 4.7 eV ; that from a group of a small number of atoms will lie in between.This may account for the so-called exponential kinetic equation which Tompkins has shown tends to disappear with the ageing of the crystal. On the above theory the behaviour of the fresh crystal would be repre-sented by the growth of a very large number of small nuclei that of an aged one, by the growth of a relatively small number of larger nuclei 232 GENERAL DISCUSSION The above analysis refers only to the growth of nuclei which have once been formed. The mechanisms suggested by Tompkins and Young adequately explain the initiation of nuclear growth and the whole course of the reaction in those cases where growth is suppressed.Dr. F. C. Tompkins and Dr. D. A. Young (Imperial College) (communicated): Although it is true as Dr. Macdonald has pointed out that the recombination of azide radicals to form nitrogen molecules is highly exothermic it is nevertheless the case that in solid state decompositions much of this energy is utilized in trans-ferring valence electrons to the cation ground state forming metal atoms and eventually specks. The work for this transfer as several authors starting with de Boer have pointed out may be considerable. Thus we find that the overall heat of reaction for the alkali and alkaline earth azides is almost certainly below 10 kcal/mole.For these azides we know of no evidence for energy chains in decomposition processes. On the other hand the heats of reaction for most heavy metal azides are large and it may well be that even in the slow thermal decomposition which precedes superheating leading to detonation energy chain processes may play a part. Dr. Macdonald’s suggestion regarding the influence of oxidizing and reducing agents is most interesting. In many respects the model which Dr. Macdonald has set up is similar to one proposed by one of us (D. A. Y.) for the donor states in partially decomposed AgN3 in which the conduction electrons are assumed to arise from energy levels in a barrier layer round positively charged Ag-colloids. Experience with this model leads us to suggest that the oxidizing and reducing agents described by Dr.Macdonald can be regarded as precisely analogous to the electron acceptor and electron donor states of standard semi-conductor theory respectively; in which case we know that for them to be effective the electrons trapped round the Ag-product colloids must be able to move from the region of the colloid to the site at which the acceptor molecule is adsorbed. It therefore seems essential to examine the semi- and photo-conduction of pure and partially decomposed silver oxalate in various atmospheres (H2 or 0 2 ) before Dr. Macdonald’s suggestion can be further developed. Dr. T. C. Waddington (Cambridge) and Dr. Peter Gray (Leeds) (communicated) : Tompkins and Young discuss the origins of differences observed in the decom-positions of members of the divalent- and univalent-metal azide families.We should like to draw attention to the regularities within the family of alkali metal azides. The thermal stability as manifested by the steady lowering in the de-composition temperatures,l decreases in the order CsN3 RbN3 KN3 NaN3, LiN3 despite the fact that the stability of the ionic lattice as indicated by the lattice energy,2 increases steadily in the same order. If for these azides the overall activation energy of thermal decomposition is close to the energy Es required in the thermal formation of an exciton then the activation energies in this series may be estimated numerically and compared. We proceed as follows : (i) Es can be determined in terms of Eo the energy needed in optical formation of an exciton and the static and optical dielectric constants eS and EO = n2.The relation is Es = (EO/Es)EO. (1) (ii) EO can be calculated by the methods of J o s ~ ~ Mott and Gurney4 and Mott and Littleton 5 in terms of the lattice energies WL the electron affinity of the azide ion E the work of removal of an electron from the conduction band to 1 Elovich Roginskii and Shuelk Izvesf. Akad. Nauk. S.S.R. 1950 469. 2 Gray and Waddington Proc. Roy. SOC. A 1956 235 481. 3 Jost J. Chem. Physics 1933 1 466. 4 Mott and Gurney Electronic Processes in Ionic Crystals (Oxford 1948). 5 Mott and Littleton Trans. Furuduy SOC. 1938 34 485 GENERAL DISCUSSION 23 3 infinity Y the (optical) depth of the stablest exciton level beneath the conduction band R&$ and the potential @ at an uncharged anion site produced by the polarization of its surroundings.The equation is These equations lead to diminishing activation energies in the azide series CsN3 . . . LiN3 (for example calculated values of E for KN3 and LiN3 are 54 and 46 kcal mole-1 respectively) and thus they offer an interpretation of the observed order of thermal stabilities. The method of comparison used here includes all the relevant magnitudes on which E depends and is clearly the true basis of the two successful empirical correlations-between stability and heat of formation 1 and between stability and ionization potential 2-previously made. Dr. F. C. Tompkins and Dr. D. A. Young (Imperial College) (communicated): If we have correctly interpreted eqn.(2) in the discussion remarks of Dr. Waddington and Dr. Gray they have equated the energies required (1) to remove an NP ion from the lattice to infinity i.e. WL -(2) to remove an electron from the azide ion to infinity EO 4 &/E$ 4- N$, then to remove the azide radical (zero energy) and finally to combine the electron with the azide radical at infinity (- E). However there is confusion here between optical and thermal excitation energies or alternatively one might say that the crystal in process (1) has been allowed to relax whereas in (2) it has not. The correct equation appears to be and in consequence their calculations require modification In this respect we should certainly value information on how the magnitudes of Eo W’ EO and were obtained for LiN3.We believe in any event little cdn be done with their theoretical evaluation since the calculated values of 54 and 46 kcal/mole from KN3 and LiN3 bear little resemblance to the experimental values of 41 and 19 kcal/mole. We would also like to give credit to de Boer who noted some 20 years ago the close correlation between ionization potential and the stability of the azides. This work was reviewed by Thomas (Thesis London,. 1951). Would the authors please show how this correlation arises from eqn. (2)? Dr. Peter Gray (Leeds) and Dr. T. C. Waddington (Cambridge) (communicated) : Dr. Tompkins and Dr. Young appear to have misunderstood the derivation of the equation we gave. ( 1 ) An azide ion is removed from the crystal W - +Ne!D.If this could be done “ instantaneously ” the energy required would be W,. The energy re-quired will however decrease in two stages. After a period corresponding to the electronic binding frequencies (10-15 sec) the electron clouds on the surrounding ions will adjust themselves to compensate for part of this energy. This stage can be termed the electronic polarization of the lattice. Then after a period of the order of nuclear vibration periods in the lattice (10-11 to 10-12 sec) the nuclei of the ions themselves will shift into new positions compensating for more of the energy expended. Since optical processes are not “ instantaneous ” we must allow for the electronic polarization of the lattice and this is the +Ne$ term cal-culated using the optical dielectric constant of the lattice.EO = WL + E - N Y - RH/EO - +Ne@. (2) ; EO = WL + E - N$ - R H / E ; , It is derived as follows. (2) An electron is removed from the free azide ion + E. (3) The azide radical is replaced in the lattice to produce a positive hole zero (4) The electron is replaced in the conduction band of the crystal - N Y . (5) The electron and the positive hole are combined to produce an exciton, energy. - RH/€02. Gray and Waddington Proc. Roy. SOC. A 4956 235 106. 2 Evans and Yoffe Proc. Roy. SOC. A 1957,238 568 234 GENERAL DISCUSSION Therefore the optical energy EO required is given by Eo= W L - & N e @ + E - N Y - R & $ . (2) For LiN3 W has been calculated the values of EO and Y appropriate to LiBr have been taken and hence EO has been found using the above equation.The thermal activation energy calculated in this way refers to the uncatalyzed decom-position not to the reaction at an azide/potassium interface and therefore the figure 41 kcal mole-1 found by Tompkins and Jacobs should be taken as the experimental reference. We would be interested to know the source of the ex-perimental figure of 19 kcal mole-1 quoted for LiN3 and the kinetic equation used to derive it. The two most important qualitative empirical correlations noted for the alkali metal azides are between their stability and (i) the ionization potential of the metal and (ii) the polarizing power (e/r) of the cation. The ionization potential of the metal and the polarizing power of the metal cation are of course connected and both can be related to eqn.(2). (For KN3 WL = 204 kcal mole-1 as compared with the next largest term E = 81 kcal mole-1.) Now by the Born-Haber cycle The only terms here which vary in the alkali metal series are of course IM+ SM+ and AH,"MN3 (cryst.) and since IM+ is the largest and varies most an obvious correlation exists between it and W and hence between it and Eo. Again it may be shown that WL is roughly proportional to e/rM+ for a series of salts either by considering hydration heats or from the Kapustinsky equation, and hence EO depends on e/rM+ the polarizing power of the cation. Dr. F. C. Tompkins and Dr. D. A. Young (Znzperial College) (conzmunicated) : In reply to Dr. Gray and Dr. Waddington their more detailed derivation con-vinces us that our criticism is valid; their electronic polarization is recovered on replacing the electron in the lattice.The experimental value of 19 kcal/mole for LiN3 was obtained by Dr. B. E. Bartlett in these laboratories; the value is independent as it should be of the kinetic equation used. Dr. A. B. Lidiard (Harwell) (communicated) Concerning the paper by Tompkins and Young there are some features of the authors' interpretation of the low-temperature conductivity (particularly of KN3) which are not clear to me. The authors suggest that freshly prepared KN3 at room temperature contains a non-equilibrium number of mobile lattice defects and that these are responsible for a large part of the conductivity as measured for the first time (circles in fig. 1).The dip in conductivity at around 60" C is interpreted as due to the disappearance of these excess defects by migration to grain boundaries and possibly formation of neutral vacancy pairs. But this explana-tion seems to me rather doubtful. The activation energy for this initial con-ductivity is about 0.2 eV and in the authors' picture this is also the activation energy for movement of the defects. Hence their diffusion coefficient is D = DO exp (- 0.2 eV/kT) where DO will almost certainly not be smaller than 0.01 cm2/sec. The time for the defects to migrate to dislocation sinks in the sub-boundaries (assumed lO-4cm apart) is thus of the order of (10-4)2/60 which, at room temperature I find to be about 10-3 sec. The postulate of a non-equili-brium defect concentration cannot therefore give a consistent picture.Instead I would suggest surface conductivity as the explanation. The dip at about 60" C for KN3 is then very possibly due to a sintering process which reduces the total surface area of the particles in the specimen pellet. There is insufficient description of the specimens however for me to wish to be very definite on this point although a very similar effect in AgBr was studied in detail by Shapiro and Kolthoff 1 and seems quite unambiguously associated with surface conduction. 1 Shapiro and Kolthoff J. Chem. P/zysics 1947 15 41. First the largest term by far in eqn. (2) is W,. W = AH; N3(g) - E - 2RT + ZM+ + SM+ - AH; MN3 (cryst.) GENERAL DISCUSSION 235 Dr. F. C. Tompkins and Dr. D. A. Young (Imperial College) (cornnzunicated): Dr.Lidiard's uncertainty as to the correctness of the interpretation of our results arises solely we believe from the brevity with which we described them. We have little doubt that the low activation energy of 0.2eV observed with freshly prepared KN3 crystals refers to surface conductance. However we would suggest there is some danger in drawing too close an analogy between the ageing (anneal-ing) of freshly prepared salts in the two groups KBr KN3 and AgBr AgN3. Thus the low-temperature colorability of the former group is much enhanced when the salts are fresh recently quenched or cold-worked whereas the corresponding efTect in the second group is much less pronounced if indeed observable; we ascribe the difference to the greater mobility of lattice defects in the silver salts than in the alkali-metal salts which thus mitigates against the retention of vacancies in the crystals during growth.With regard to the stability of isolated lattice vacancies in excess of the thermo-dynamic value in KN3 we believe these vacancies are present within the sub-stantially perfect crystalline regions consequently it is incorrect to calculate their contribution to the sintering process using the activation energy for surface con-ductance. The activation energy of diffusion of isolated vacancies through the bulk, estimated as 1.3 eV or that of neutral vacancy pairs (experimentally inaccessible at present but probably 0.6-0.8 eV) should be used ; substituted in the equation quoted by Lidiard these give annealing times of the order of months.This result encouraged us to develop this model of excess vacancies which has also helped us in explaining the thermal decomposition results. Following Wyon and Lacombe and others, we assumed the existence of a marginal depletion zone adjacent to grain boundaries as observed in precipitation from supersaturated solid solutions. We then argued that the excess vacancies act as a supersaturated solute capable of precipitating heterogeneously on dislocations and grain boundaries or in certain circumstances of precipitating homogeneously as voids (discs) which may collapse to give general dislocation rings. The surface exhibits marked departures from equilibrium conditions which enhance the pre-exponential factor for surface conductance and receives mobile isolated and pair vacancies on slow heating from that part of the crystal which is to become the marginal depletion zone.The condensation of these vacancies facilitates the sintering of the surface. At the same time the remaining vacancies within the crystal bulk being nearer to " block-traversing " dislocations than to the crystal surface precipitate out on these dislocations. The extra conditions imposed during rapid heating are that small vacancy precipitates (voids) are formed on the dislocations and homogeneous nucleation of voids may occur thus accounting for the enhanced reaction nucleus density. One would expect that the marginal depletion zone would be deeper on slow than on rapid heating. Dr. Peter Gray (University ofLeeds) said I should like to comment on two aspects of the valuable survey by Tompkins and Young on the problems of charac-terizing processes occurring during azide decompositions (i) the value in solid decompositions of the stationary state hypotheses and (ii) the value of supple-mentary information from the use of artificially incorporated defects in the azide lattice.Dr. Waddington and I have recently applied these ideas to silver azide. There is no induction period and the azide is insensitive to pre-irradiation. The kinetics normally follow a two-thirds power law. Silver azide decomposes exothermally.1 These features 2 are also found by other workers 3 AgN3 -+ Ag + 1.5 N2 AH = - 74.15 kcal mole-1, E = 36 5 5 kcal mole-1. d"2lldt = k[AgN31*, 1 Gray and Waddington Proc.Roy. SOC. A 1956,235 106 487. 2 Gray and Waddington Chem. and Ind. 1955 1255. 3 Audubert J . Chim. Phys. 1952 49 275. Yoffe Proc. Roy. Soc. A 1951 208 188. Garner and Haycock 1955 personal communication 236 GENERAL DISCUSSION The following mechanism 1 (in Rees' notation) explains the behaviour of silver azides (N3 [ DA) -+ (N3 I OA) + e production of an electron and a positive hole (1) formation of nitrogen (2) reverse of (1). (3) trapping of an electron. (4) On this mechanism (2) is the step leading to the final product nitrogen. Both positive holes and electrons are mobile in the crystal. The stationary-state hypothesis may be applied and when (3) predominates over (4) i.e. when most of the electrons formed recombine with positive holes to re-form azide ions the rate of decomposition is That is if the number of traps remains effectively constant during reaction this mechanism leads to a reaction of kinetic order two-thirds as observed experi-mentally.The experimental velocity constant k and the activation energy E are thus composite quantities (E = %El + QE2 - 8E3 + 8E4). A theoretical value of 40 kcal mole-1 for E concordant with the experimental 1 value 36 f 5 may be derived from estimates of the activation energies of the individual steps (1) to (4). The second aspect is the sensitization of decomposition by introducing artificial lattice defects. The cyanamide ion CN8- has been incorporated in the silver azide lattice-probably on an azide ion site and with an associated interstitial Ag+ to preserve electroneutrality.Specimens incorporating such defects 2 show dramat-ically enhanced reactivity and we hope this technique may provide another means of examining the details of azide decompositions. Dr. F. C. Tompkins and Dr. D. A. Young (Imperial College) (communicated): Dr. Gray is apparently unaware that over the past five or six years the steady-state approach to azide decompositions has been extensively exploited in papers by Thomas Jacobs and Groocock with one of us (F. C. T.) where the pitfalls of employing this method when only few kinetic data are available have been stressed. Our own investigations on the thermal and photochemical decomposition of AgN3 its photo-response electronic and ionic conductance absorption spectra, themo-electric power etc. convince us that the very simple approach of Dr.Gray cannot be sustained. Thus from general studies of photoconductivity it is normally accepted that recombination of a free electron with a free positive hole is an improbable occurrence. Furthermore one would anticipate that the number of electron traps would increase during decomposition unless some further special hypothesis were proposed. Dr. Gray however proposes that recombination is predominant and the trap density constant. Since sufficient details of his experi-mental work have not been published it is difficult to assess how well his kinetic data fit his analysis; we would however note that a great majority of solid de-compositions can be fitted with some success with two-thirds power law over a large part of the decay period and one need not do more than say that this is simply explained as a rate proportional to the surface (interface) area of the solid, as Garner pointed out some 25 years ago.Obedience to this law is thus in no way discriminatory. Moreover with single crystals of AgN3 the rate accelerates over the first 25-30 % decomposition indicating that the topographical features of the solid as we have shown for Ag oxalate and Hg fulminate may be a dominating influence in characterizing the kinetics. We further find that our rates with AgN3 agree substantially with those obtained by Audubert but both differ almost 50-fold from those reported by Gray and Waddington ; their rather uncertain activa-tion energy of 36 + 5 kcal/mole might well be some " average " value since AgN3 1 Gray and Waddington Chem.and Ind. 1955 1255. 2(N3 I OA) -+ 20,4 -k 3N2 (N3 I O A ) + e + "3 I O A ) T + e -+ Ag (eventually) d("21)idt = (k?k2k42T/k5>Wi I OA)I* GENERAL DISCUSSION 237 exists in two allotropic modifications (transition temperature 190" C) which have different activation energies for decomposition our values are < 190" C , 45 i 1 kcal/mole; It is difficult therefore to ap-preciate the value of his theoretical estimate. In that connection we would welcome information on the theoretical estimation of E2 E3 E-+; presumably E3 and E4 are assumed to be zero but E2 is thought by some workers to be large and thus to explain some features of the rather similar decomposition of PbN6. The energy El seems to require a knowledge of WL $ 60 for the high-temperature modification and we would value information on these magnitudes and the argu-ments by which they were estimated.Dr. Peter Gray (Leeds) (communicated) Dr. Tompkins and Dr. Young suggest that to explain silver azide decomposition kinetics one need not do more t!iaii say this is a rate proportional to the interfacial area of the solids. However this does not offer any explanation of the three striking instances of sensitizatioii of silver azide decomposition (i) by metallic gold (Evans) (ii) by cyanamidc anions (Gray and Waddington) and (iii) by cadmium cations from lloAg (Deb Evans and Yoffe). Since to be acceptable a reaction scheme should contain the basis of all aspects of decomposition and not only overall kinetic order recognition of the important role of topography does not remove the need to examine the detailed mechanism.The basic features of the scheme put forward are three-fold. They are the suggestions that (i) production of an electron and an azide radical is of prime importance (ii) that both electrons and azide radicals may be removed in more than one way and (iii) that molecular nitrogen arises from the combination of pairs of azide radicals. Fitting reaction schemes to kinetic data even of homo-geneous systems is notoriously ambiguous and it would be rash to claim more than that adoption of this scheme is in accord with the experimental data and is physically realistic. A more detailed account both of experimental methods and of theory is in the press 1 at present and should be published by the time this Discussion is published.I think the most welcome developments since our experiments were performed are the investigations by Dr. Bowden's group in Cambridge of the thermal photo-chemical and explosive decompositions and of the photoconductivity and ab-sorption spectra of silver azide. Their published results have been of the greatest value in providing direct experimental values for some of the chief physical pro-perties required and in reducing our dependence on theoretical calculations which too often involve crude approximations. Dr. Tompkins and Dr. Young's data on these lines should give us equal assistance. Dr. F. C. Tompkins and Dr. D. A. Young (Imperial College) (conzmunicared) : We did not suggest that the silver azide decomposition was explained by a rate proportional to the interfacial area; we merely pointed out that such a " geo-metric" hypothesis also gave the Qrd power-law derived by Dr.Gray from a particular reaction scheme and was therefore completely non-discriminatory-more so than in homogeneous systems where as he points out the fitting of such schemes particularly simple ones is a '- notoriously ambiguous " procedure. Dr. Gray has taken over Mott's original suggestions of 1938 which we analysed in detail in 1952; the position is that we find that irt crddition to taking rzgard of isolated defects we must also make our model physically realistic by including other properties of real crystals which we have termed topographical. Such inclusion helps to explain the important results of the Cambridge school and also to make us doubt the validity of the theoretical calculations which Dr.Gray and Dr. Waddington have sought to revive. Furthermore the kinetic scheme is not in accord w*th the experimental data on single crystals of AgN3 where it would be expected to be more valid than for the decomposition of a mass of polycrystalline material. 1 Proc. Roy. SOC. A . > 190" C 32 f 1 kcal/mole 238 GENERAL DISCUSSION Dr. T. C. Waddington (Cambridge University) said In their extensive survey of azide decompositions Tompkins and Young point out the great differences in decomposition behaviour shown by different azides. I would like to stress the great effect that the gross physical properties of the salts have on their thermal decomposition and in particular the effect of the dielectric constant.This is very well illustrated by a comparison of the behaviour of cuprous silver and thallous azide on the one hand and the behaviour of the alkali metal azides on the other. A summary is given in tabular form below. COMPARISON OF THE PROPERTIES OF THE AZIDES AZIDES OF Cu Ag T1 AZIDES OF THE ALKALI METALS The decomposition has normally no in-duction period and is insensitive to pre-irradiation. by pre-irradiation. The decomposition has a marked induc-tion period which can be greatly shortened The salts photoconduct. The salts have a relatively high ionic The salts do not photoconduct. The salts have a low ionic conductivity conductivity and are probably cation and are probably anion conductors.conductors. The decomposition has not been sensit-by divalent anions. Volatility of the alkali metal does not not increase in size but increase in density permit the observation of nuclei in the as the reaction proceeds. The primary process in the decomposition of the alkali and alkaline earth azides has been identified by Tompkins 1 2 as the creation of an exciton from an azide ion and a satisfactory explanation of the behaviour of potassium and barium azides has been given on this basis. Wannier3 has pointed out that the depth below the conduction band of the exciton levels in a crystal may be calculated by assuming that an exciton is an electron from the conduction band trapped in a hydrogen-like orbit by the Coulombic field round a positive hole.The energy difference is then given by U = &/E2n2 where Rn is the Rydberg constant, E is the dielectric constant of the medium and n is the quantum number of the exciton energy level. For the difference in themzal energies E will be the static dielectric constant es. Thus the thermal depth of the stablest exciton level is given by U1 = R&f. The actual static dielectric constants of only a few azides are known,4 and they are close to the values for the corresponding bromides. For KN3 U1 - 13 kcal mole-1 for AgN3 U1 - 2 kcal mole-1 for TlN3 U1 - 1-5 kcal mole-1 ; these values refer to thermal energies. The conclusion is obvious ; any exciton formed in the silver and thallium salts will readily dissociate into an electron in the conduction band and a free positive hole ; free electrons will not be generated in the alkali metal or alkaline earth azides whose dielectric constants will be much lower than those of the corresponding silver and thallium salts.Dr. F. C. Tompkins and Dr. D. A. Young (Imperial College) (cornmunicated) : Dr. Waddington’s generalizations are stimulating but quite misleading particularly since the impression is gained that the differences are throughout dominated by bulk properties such as the dielectric constant of the salt. Thus in the decom-position of sodium and potassium azide the reaction rate initially decreases then accelerates and it is difficult to speak of an induction period ; moreover as shown by Jacobs preirradiation with u.-v. light does not accelerate the subsequent thermal decomposition of these salts.In any case it is not the induction period The decomposition has been sensitized Nuclei in AgN3 are very small and do ized by divalent anions. thermal decomposition. 1 Jacobs and Tompkins Proc. Roy. Sue. A 1952,215,265. 2 Thomas and Tompkins Proc. Roy. SOC. A. 1951 210 11 1. 3 Wannier Physic. Rev. 1937 52 91. 4 McLaren private communication GENERAL DISCUSSION 239 which is important but rather the kinetics of the acceleratory period and the degree of decomposition at which the maximum rate is attained. With silver azide the reaction appears to be propagated rapidly through the sub-grain boundaries at the commencement of the reaction whereas in the more electropositive metal azides the reaction is concentrated in a number of discrete nuclei-it is this topochemical difference which may be the key to the true classification.We further note that single crystals of AgN3 do in fact decompose with an induction period. Again it is rather sweeping to state that the alkali azides do not photoconduct ; KN3 for example does so when irradiated with a hydrogen lamp i.e. at wave-lengths well within the fundamental absorption edge. The difference is merely that the optical excitation required is much higher consequently the corresponding thermal energy (-hv~O/c) is not accessible at temperatures at which the azide remains substantially undecomposed. We are unaware of any experimental evidence for the sign of the mobile (ionic) species in azides except our own recent work on AgN3; this suggests that inter-stitial silver ions are mobile.In our view it is most unlikely that the alkali azides are anionic conductors though there is no experimental evidence on this point. Again the only outstanding example of sensitization by divalent ions is that of the cyanamide ion found by Gray and Waddington and is in our experience unique. Where we have observed effects of “ doping ” with divalent ions they have been confined to the very earliest stages of decomposition and with both AgN3 and the more ionic azides anions accelerate and cations retard the rate of decomposition. It is true that Dr. Sawkill observed with AgN3 the increase in density of nuclei but this effect was brought about with high-velocity electron bombardment and the topochemistry revealed in this manner does not apply when AgN3 is thermally decomposed.The Wannier calculation of exciton energies in the manner used by Dr. Waddington is also open to grave objections. First his concept of the thermal creation of an exciton appears not to have any theoretical justification (although Thomas and Tompkins originally put forward a similar idea); secondly the order of approximation is quite different with compounds differing in dielectric constant as much as do the T1 and K salts; thirdly the calculation neglects the great departure from the coulombic field within the unit cell and moreover, in the case of group 5 impurity atoms in germanium there is evidence that the non-coulombic contribution to the radial field largely determines the ground-state energy whereas this is not considered in Waddington’s calculation ; fourthly some decompositions undoubtedly proceed at the metal/azide interface after nucleus formation and the Fermi energies of the different metals are important parameters which have no place in his treatment.Waddington’s estimates seem to refer to nucleus formation which is substantially complete for some azides but not for others. Finally Waddington’s remarks surely have relevance only for photoconductance and the relation of conductance to the mechanism of thermal decomposition is by no means clear. In our view the errors in reasoning arise from a total rejection of the topochemistry of the salts e.g. Herzfeld some 30 years ago showed that electron transfer from say a negative to a positive ion is about 3 eV (12 kcal) less at the surface of an internal “ crack ” than that for transfer in bulk.Point line and planar imperfections create new energy states, in addition to which optically forbidden transitions in the perfect lattice can take place there as a result of relaxation of selection rules. It therefore would appear that the final “ obvious ” conclusion cannot be substantiated along the simple lines suggested. Dr. T. C. Waddington (Canzbridge) (communicated) Dr. Tompkins and Dr. Young appear to be dubious as to the applicability of the Wannier calculation to the thermal stability of excitons in the azides. To reply to the points they raise one by one : (i) If exciton energy levels exist in the azides (there is good evidence that the 240 GENERAL DISCUSSION do at least at low temperatures in AgN3 and analogy with the alkali metal halides would suggest that they do in the metal azides) then they will be excited thermally unless there are a large number of thermally lower energy levels which can lead to decomposition.(ii) I cannot see why the order of approximation should differ so much in KN3 and TIN3 when their dielectric constants change by less than a factor of three. (iii) It is quite true that the hydrogen-like orbit calculation neglects the de-parture from the coulombic field within the unit cell but this is not necessarily a source of great error as many simple models neglecting a periodic field are in reasonably good quantitative agreement with the experimental values. No doubt a more refined model would take this into account but I doubt very much whether it would alter the striking difference in the exciton stabilities in the alkali metal and heavy monovalent metal azides.(iv) 1 would agree that my remarks would not apply to a nietal/azide interface reaction. (v) It is true that the relations between photoconduction photolysis and thermal decomposition are by no means as clear as one could wish. However, I think my final remark about exciton stabilities still stands. This is borne out by the experimental evidence for AgN3. Here a band appears in the absorption spectrum of the crystal at low temperatures that is absent at room temperatures. At these low temperatures the photoconductivity disappears suggesting strongly that this band is an exciton band.Dr. F. C. Tompkins and Dr. D. A. Young (Imperial College) (commurzicntcd) : In reply to Dr. Waddington the problem of the thermal production of exciton has clearly not been considered by him and he merely accepts this without question. Similarly if the decomposition occurs at the metal/azide interface-and with many azides there is adequate experimental confirmation for this-his calculations are not relevant to activation energies for decomposition, Dr. F. S. Stone (Bristol) (communicated) By condensing at sufficiently low temperatures the products of an electric discharge through peroxide (or water) vapour it is possible to prepare under controlled conditions deposits of amorphous ice which evolve oxygen on warming. There is now good evidence that the oxygen evolution is due to the recombination of trapped OH and HO2 radicals and this relatively simple system is therefore well suited to the study of the kinetics of recombination processes in solids. Dr. R. L. Allen and I have recently been investigating the rates of recombination (as measured by the rate of oxygen evolu-tion) in deposits of this kind. The kinetics frequently conform to the general type of behaviour reported by Dr. Maddock and his co-workers and it would seem that an initial very rapid reaction followed by a slow stage the " ceiling " being dependent on temperature is a general characteristic of radical recom-bination processes in solids. There is of course no charge separation in our system so that one must look for an alternative explanation to that based on the Mott-Cabrera model. The idea however of a mechanism involving complete depletion of radicals or fragments within finite volumes of the solid these volumes increasing as the temperature is raised remains valid and it is possible that one should consider the volumes surrounding grain boundaries and line imperfections as the ones operative in the rapid process. Phase transitions and recrystallization processes within the solid certainly have a marked effect on recombination. Indeed, for the case to which I have referred internal recombination is absent below - 120" but is first triggered by the transition from amorphous to cubic ice which occurs at that temperature. Another indication that the process is overlaid by structure-sensitive factors is that whilst it has been relatively easy to make the initial concentration of the reacting species in the deposits the same in separate experiments the extent of the rapid initial reaction obtainable at any chosen temperature below the melting point is frequently not reproducible

ISSN:0366-9033    

DOI:10.1039/DF9572300220

出版商:RSC    

年代:1957

数据来源: RSC

摘要:

AUTHOR INDEX * Akerstrom, A., 133. Barrer, R. M., 79, 155, 156, 161. Boer, de, J. H., 76, 164, 171, 229. Bottcher, C. J. F., 7. Brinkman, H. C., 11, 72. Briske, C., 196. Burgers, W. G., 183. Clarke, F. P., 141, 169. Cole, X. H., 31. Compaan, K., 105. Crank, J., 99, 156. Donth, H., 19. Dryden, J. S., 39, 75, 76, 78. Dunning, W. J., 222, 225. Eigen, M., 80. Frank, F. C., 73, 78, 82, 122, 159, 165. Granicher, M., 50, 76, 82, 83. Gray, P., 232, 233, 235, 237. Groen, L. J., 183,221. Hartshorne, N. K., 196, 224, 228. Haul, K. A. W., 156, 164. Haven, Y., 72, 76, 77, 80, 105, 158. Havriliak, S., Jr., 31. Howard, R. E., 113. Jaccard, C., 50. Jacobs, P. W. M., 220. Jost, W., 137, 162, 165. Koehler, J. S., 74, 85, 159. Laurent, J. F., 165. Lidiard, A. B., 77, 83, 113, 162, 234. Lieser, K. H., 220. Lindner, R., 133. Macdonald, J. Y., 230. Maddock, A. G., 168,211. Maine, de M. M., 211. Meakins, R. J., 39. Meijering, J. L., 82. Meinnel, J., 84, 221. Oel, J. J., 137. Pfaff, F., 19. Rastogi, R. P., 221. Roberts, L. E. J., 156, 163. Ruetschi, P., 159. Sack, R. A., 78. Salomon, G., 165, 229. Scherrer, P., 50. Schwarzl, F., 11, 72. Seeger, A., 19, 74, 75, 158. Seitz, F., 85. Steinemann, A., 50, 79, 81. Stone, F. S., 240. Suddaby, A., 72. Taiigb61, K., 2 1 1. Tompkins, F. C., 202, 229, 232, 233, 234, Tosi, M. P., 92. Ubbelohde, A. R., 73, 128, 163. Volger, J., 63, 75. Waddington, T. C., 232, 233, 238, 239. Walton, G. N., 169. Wood, J., 72. Young, D. A., 167, 202, 229, 232, 233, 234, 235, 236, 237, 238, 240. 235, 236, 237, 238, 240. * The references in heavy type indicate papers submitted for discussion. 24 1

ISSN:0366-9033    

DOI:10.1039/DF9572300241

出版商:RSC    

年代:1957

数据来源: RSC