POINT DEFECTS IN THE SILVER HALIDES

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POINT DEFECTS IN THE SILVER HALIDES

A. Batra, L. Slifkin

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POINT DEFECTS IN THE SILVER HALIDES(*)

A. BATRA and L. SLIFKIN

Department of Physics and Astronomy, University of North Carolina, Chapel Hill, N. C , 27514, U. S. A.

Résumé. — On décrit les résultats de trois expériences sur les défauts ponctuels dans AgCl. (1) L'énergie d'activation de la diffusion des cations divalents de la première série de transition est expliquée quantitativement au moyen des effets du champ électrique cristallin. (Recherche en colla-boration avec J. Hernandez). (2) On utilise la diffusivité de N a+ comme sonde pour la concentration des lacunes. On établit que la variation de l'énergie de formation avec la température est conforme à celle proposée par Aboagye et Friauf. (3) L'agglomération des dipôles Mn2+-lacune, étudiée par TTC et RPE, montre que la cinétique est soit du 2e ordre, soit du 3 e ordre, selon le degré de la sursaturation initiale. (Recherche faite par J. Dutta et D. Golopentia.)

Abstract. — The results of three experiments on point defects in AgCl are described. (1) For the diffusion of tracers of the divalent cations of the first transition row, the variation of the activation energy is quantitatively accounted for by the effects of the crystalline electric field. (Research in collaboration with J. Hernandez). (2) Using the diffusivity of Na+ tracer as a probe for the concen-tration of vacancies in AgCl, the temperature-dependence of the Frenkel defect formation energy is determined and found to agree with that proposed by Aboagye and Friauf. (3) The aggregation of Mn2+-vacancy dipoles in AgCl is studied by both ITC and EPR, and is found to proceed by either 2nd or 3rd order kinetics, depending on the initial supersaturation. (Research performed by J. Dutta and D. Golopentia).

1. Introduction. — Crystals of silver chloride and

bromide have many aspects of interest to the solid state scientist. The best-known of these, of course, is the photographic process, which depends upon a fortuitous combination of unexpected properties [1]. In comparison with the more frequently studied alkali halides, the silver halides are also of interest because here the dominant defect is of the cation Frenkel type and because these defects occur with very high con-centrations (about 1 % near the melting point). Moreover, polarization effects are much more in evi-dence in the silver halides. The present discussion outlines the results of three experiments on point defects in AgCl which were recently completed of the University of North Carolina.

2. Crystal field effects on diffusion. — For solute diffusion in simple, free-electron metals the variations in activation energy can be largely understood in terms of the Lazarus electrostatic screening theory, but for ionic crystals there is no comparable general model. In this latter case, of course, there is no screen-ing by free electrons, and the solute-vacancy associa-tion energy is not necessarily simply related to H2,

the activation energy for the solute-vacancy exchange (*) This research was supported by NSF Grant No. DMR 72-03212-AO1, and by the Materials Research Center, Univ. of NC, under NSF Grant No. DMR-7500806. The manuscript was prepared while one of the authors (LS) was a collaborates etranger at SRMP, C. E. N. Saclay, France.

jump. Recently, however, there has been some indi-cation that one might to able to correlate the migra-tion properties of a solute in an ionic crystal with its electronic structure. Varotsos and Miliotis [2], for example, have shown that the dielectric loss due to rotation of solute-vacancy complexes in alkali halides has properties, such as the breadth of the loss peak, which depend on the presence or absence of d-elec-trons on the solute ion. In particular, the activa-tion energy was found to be sensitive to the ionic radius for alkaline earth ions, but not for transi-tion ions.

A somewhat different type of experiment has recen-tly been carried out [3], in which the diffusion of a set of six consecutive divalent cations from the first row of transition metals was studied in AgCl. The activa-tion energy for diffusion was found to vary systema-tically with atomic number, dropping from 2.08 eV for V2 + to a minimum value of 1.18 eV for M n2 +, and then rising again to 1.88 eV for N i2 +. In addition, one knows the solute-vacancy binding energies for most of these impurities ; they are apparently all within about 0.01 eV of 0.25-0.26 eV [4-6]. And finally, for such solutes which have relatively small frequencies of exchange with a vacancy, the correla-tion factor is near to unity and hence is independent of the temperature. Combining all of this information, and comparing the other solutes with Mn2 + , it then follows that g(solute)-£)(Mn2+) is very nearly equal to AH2 = H2(soMe) - i /2( M n2 +) , where Q is the

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POINT DEFECTS I N THE SILVER HALIDES C7-397

activation energy for tracer diffusion and H, is that for the solute-vacancy exchange.

For the purposes of calculation, assume that the saddle point is near the interstitial site lying at the center of the cube formed by 4 cation sites and 4 anion sites

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when the jumping solute ion is at this position, of course, two of the cation sites will be vacant, thereby lowering the local symmetry. Now, the experimental minimum in H, is at Mn2+, which has the spherically symmetric d5 configuration. Hence, for this ion the crystalline electric field makes no contribution to the energy required to take the solute from the substi- tutional to the interstitial site. The experimental results thus suggest that the variation of AH, with the number of electrons in the d-shell may well be a manifestation of the effects of the crystal field on the electronic energy levels of the solute in the two different sites.

Such a calculation has been made by J. Hernan- dez [3]. Because of uncertainties in the crystal field for the activated site, one employs the value appropriate to a point ion model, but corrected by a single adjus- table parameter which is constrained to have the same value for the entire set of solute ions. It is then found that the best choice of this parameter permits a detailed fitting of the experimental results. Not only is the general trend of AH, versus atomic number (with its deep minimum) reproduced, but the numerical agree ment is quantitative : the average value of the magni tude of AH2(theory)-AH2(expt) is less than 0.04 eV, and in no case does theory differ from experiment by more than 0.05 eV, all of this over a range of AH, of 0.9 eV. This excellent agreement thus appears to demonstrate a significant systematic effect of electronic structure on mass transport in ionic crystals.

3. Temperature-dependent formation energies. -

For AgCl and AgBr, the Arrhenius plot of the ionic conductivity (log o T us. 1/T) shows a pronounced upward curvature at high temperatures, within about 100 degrees of the melting point. In fact, just below the melting point, the conductivity is about three times larger than the value extrapolated from the lower temperature portion of the intrinsic region. The Lidiard-Debye-Huckel screening can account for only half, or less, of this anomaly. The remainder has been variously attributed either to the onset of one or more additional types of interstitialcy process [4, 7, 81 or to a decrease in the Frenkel defect formation energy at high temperatures [9, 101.

A test of these two alternatives has recently been carried out by means of a detailed measurement of the diffusion of Naf in AgCl 1111. The sodium ion diffuses in the silver halides only by the vacancy mechanism [12] ; moreover, because it is singly charged and not oversized, it is not expected to have a substantial energy of association with a vacancy. Hence, the diffusivity of Na+ represents a probe of the concentration of cation vacancies, and is insensitive to the onset of an

additional interstitialcy mechanism by the host silver ion.

The results of this diffusion experiment show an anomaly at high temperatures which quantitatively replicates that displayed by the ionic conductivity. This excellent agreement argues rather convincingly that the high-temperature anomaly in both phenomena is indeed a result of a supplementary increase in Fren- kel defect concentration, an excess which may be expressed in terms of a decrease Ag,, in the defect formation energy, as had been proposed by Mul- ler [9] and by Aboagye and Friauf [lo]. At the melting point, this decrease (which includes the effect of Lidiard-Debye-Hiickel screening) amounts to approxi- matively 0.1 eV, or about 7

%

of the low-temperature value of the enthalpy of formation of the Frenkel defect.

A similar experiment has also been performed on diffusion of Na' in silver bromide (A. Batra and L. Slif- kin, to be published). Here, the comparison with the conductivity anomaly is more difficult because the curvature of the Arrhenius plot is greater and sets in at lower temperatures, thus making more difficult the determination of the low-temperature values for the free energy of formation of the Frenkel defects. Never- theless, in this case also, the behavior of the diffusion results is found to parallel that of the ionic conductivity analysis of Aboagye and Friauf [lo]. Quantita- tively, the high-temperature values of Ag,, as deduced from the diffusion experiment, are somewhat smaller than originally proposed by Aboagye and Friauf ; for example, at 400 OC, the present experiment gives Ag, = 0.16 eV, as compared to 0.19 eV from the conductivity analysis.

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vacancies, but recent evidence 117, 181 indicates that in the alkali halides the migration energies for the two types of vacancy are almost identical. In view of the results presented here for AgX, one is tempted to suggest that the high-temperature anomaly in the alkali halides may also be due to a decrease in formation energy, although on a much smaller scale.

4. Aggregation of solute-vacancy con~plexes. -

When an ionic crystal containing solute-vacancy dipolar complexes is stored at a relatively low temperature, the complexes are observed to disappear from solution, first forming higher-order aggregates, and eventually producing one or more new phases. In the alkali halides, the initial aggregation process has been studied by a number of researchers, seeking to answer the following question : do the dipoles disappear by a second-order process, forming dimers, or by a third- order process to form trimers ? One might expect a straightforward resolution of this problem, from measurement of the order of the kinetics or from the activation energy of the process (which, for the trimer case is predicted to be lower than the diffusion energy of the complex by just the binding energy of a presumably metastable dimer [19]). In fact, however, the results have instead given rise to a lively debate (see for example, 1201 and [21]).

Recently, Strutt and Lilley [22] have demonstrated, by means of a theoretical analysis, that the system generally has a choice of several possible reaction paths. And experimentally, these conclusions are corro- borated by recent work of Dutta [23] and Golopen- tia [24] on AgCI containing ~ n ~ ' - v a c a n c y complexes. Dutta used EPR techniques to monitor the loss of complexes during annealing, after quenching to temperatures in the range of - 20 OC to

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50OC. In these studies, the experimental procedure produced only rather small supersaturations, and all observa- tions were consistent with a 2nd order dimer formation until a plateau is reached in the annealing curve :

a) the annealing curves were well-fit by Unger and Perlman's equations [25] for 2nd order kinetics with a dissociative back-reaction ;

b) the activation energy of 0.70 f 0.04 eV agrees

well with the 0.72 eV found for diffusion of the Mn2+

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vacancy complex [26] ;

c) comparing specimens with different concentra- tions of manganese, the time scale for the decay was found to vary inversely with the initial concentration of complexes, as expected for a 2nd order process. Golopentia, on the other hand, followed the aggregation process by means of ionic thermoconductivity techniques. In this work, the quenched specimens contained quite large supersaturations, and over the measured range of

+

400 to

-

80 OC the decay of the concentration of dipoles was accurately described by 3rd order kinetics. Moreover, as expected for a process in which trimers are formed, the half-time for the decay varied as the reciprocal of the square of the initial concentration of complexes. And finally, the aggregation process was found to have an activation energy of 0.55 f 0.04 eV, which is lower than that for diffusion by about the expected magnitude. Thus, in contrast to Dutta's results on systems with low supersaturation, Golopentia's high-supersaturation samples are seen to aggregate by means of very well- defined 3rd-order kinetics, presumably forming pri- marily trimers.

One is thus led to conclude that, as argued by Strutt and Lilley, the aggregation phenomenon is realy a complex superposition of possible mecha- nisms. Which particular process dominates is determined by such initial conditions as the supersaturation of dipolar complexes.

Acknowledgments.

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One of the authors (L. S . ) is extremely grateful to Dr Y. Adda and his colleagues

at C . E. N. Saclay for their warm and generous hos-

pitality during the preparation of this manuscript.

References [I] SLIFKIN, L., Science Progress (Oxford) 60 (1972) 151 ;

see also The Photographic Process, in Radiation Damage

Processes in Materials, ed. by Dupuy (Noordhoff, Leyden) 1975, p. 405.

[21 VAROTSOS, P. and MILIOTIS, D., J. Phys. & Chem. Solids 35

(1974) 927.

I31 BATRA, A., HERNANDEZ, J. and SLIFKIN, L., Phys. Rev.

Lett. 36 (1976) 876.

[41 CORISH, J. and JACOBS, P., J. Phys. & Chem. Solids 33

(1972) 1799.

[ S ] GERLACH, J., Ph. D. Thesis, University of North Carolina (1974).

[61 LE~B, R., Thesis, Univ. of N. C. (1976).

171 CORISH, J. and JACOBS, P., Phys. Status Solidi B 67 (1975) 263.

181 LANSIART, S., J. Phys. & Chem. Solids 36 (1975) 543. [9] MULLER, P., Phys. Status Solidi 21 (1967) 693.

[lo] ABOAGYE, J. and FRIAUF, R., Phys. Rev. B 11 (1975) 1654 [ll] BATRA, A. and SLIFKIN, L., Phys. Rev. B 12 (1975) 3473. [12] SUPTITZ, P., Phys. Status Solidi 12 (1965) 555.

[13] TANNHAUSER, D., J. Phys. & Chem. Solids 5 (1958) 224. [14] BATRA, A. and SLIFKIN, L., J. Phys. C : Solid State 9 (1976)

947.

[l5] HANLON, J., J. Chem. Phys. 32 (1960) 1492.

[16] S U P ~ T Z , P. and WEIDMANN, R., Phys. Status Solidi 27 (1968) 631.

[17] DILLER, K., AERE-Harwell Rept. T. P. 642 (1975). [18] BEN&RE, M., CHEMLA, M., BENIBRE, F. and CATLOW, C.,

J. Phys. & Chem. Solids, to be published. [I91 CRAWFORD, J., J. Phys. & Chem. Solids 31 (1970) 399. [20] COOK, J. and DRYDEN, J., Phys. Rev. B 12 (1975) 5995. [21] UNGER, S. and PERLMAN, M., Phys. Rev. B 12 (1975) 5997. [22] STRUTT, J. and LILLEY, E., Phys. Status Solidi A 33 (1976)

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POINT DEFECTS IN THE SILVER HALIDES C7-399 D ~ A , J., Ph. D. Thesis, University of North Carolina [25] UNGER, S. and PERLMAN, M., Phys. Rev. B 10 (1974)

(1975). 3692.

GOLOPENTIA, D., Ph. D. Thesis, University of North [26] BATRA, A. and SLIFKIN, L., J. Phys. C : Solid State 8

Carolina (1975). (1975) 2911.

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