Studies of Ion Transport in AgCl and AgBr
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MRS BULLETIN/MAY 1989
dispersion and judged to be of equal importance to the quadrupolar E g (r 12 + ) coupling. These calculations predicted the lowering of the frequencies of the optic mode phonons, which results in an exchange of wave vectors between the TO and TA phonons at the L point in AgBr. This was subsequently verified experimentally. 4 However, Kleppman and Weber15 have shown that an excellent representation of phonon dispersion in AgCl and AgBr results from a m o d e l which i n c l u d e s l o n g i t u d i n a l E„(r 12 + ) and transverse T 2g (r 2 5 + ) couplings, but without the T lg (ri 5 + ) contribution included by Fischer et al. 3 The Eg force constants are about seven times larger than their T2g counterparts. The calculations by Kleppman and Weber13 clearly demonstrate the importance of the quadrupolar deformation of Ag + , and particularly the longitudinal (Eg) coupling, as well as the relative unimportance of covalency in these silver halides. The cohesive energy of AgCl and AgBr is well accounted for by a fully ionic model. It might be supposed that covalency was in fact being masked by the particular choice of parameters used in the short-range interaction but it w o u l d then be r a t h e r unlikely that the C n elastic constant, which depends primarily on the curvature of the n potential-energy curve, would also be reproduced so precisely. 10 Moreover, Fischer et al. 3 found that even when the T lg coupling was included, the phonon dispersion w a s fitted w i t h an ionic charge Z of 0.934 for AgCl; 0.96 was used in the AgBr calculations. These values are in line with the values of Z that emerge from the fitting of phonon dispersion (and other properties) of alkali h a l i d e s which are u s u a l l y
regarded as fully ionic materials. There is thus no doubt about the suitability of the ionic model for AgCl and AgBr. Ionic Transport in AgCl and AgBr The ionic conductivity of AgCl and AgBr is much higher than that of the corresponding sodium salts at the same TITm where Tm is the melting temperature and attains values of 10"1 S cm"1 and 1 S cm"1, respectively, at T/Tms=l. The latter is a remarkably high value and, b u t for t h e r a t h e r h i g h A r r h e n i u s energy of ~0.9 eV, would result in AgBr being classified as a superionic instead of a conventional ionic conductor. This high ionic conductivity is due to two factors — the relatively low formation energy of cation Frenkel defects and the extremely low activation energy for the motion of interstitial Ag + ions. Information on the mechanism of Ag + ion transport can be obtained from the Haven ratio for a defect species r, H,=
DtNqtVkT 05
-0'--
0 =
_--o---~
^'AF
-•——•-.
I
49
48
I
i
51
v/A 3
Figure 3. Calculated (—) enthalpy of formation of a Frenkel defect in AgBr at constant pressure, hf, and Helmholtz energy of formation of a Frenkel defect at constant volume f", compared with experimental (—) values of hf and the Gibbs energy of formation of a Frenkel defect at constant pressure, g>', respectively. AF = Aboa
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