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. 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