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