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