Mean Field Theory of enhanced defect formation in AgCl and AgBr

Abstract

The large conductivity anomaly observed at high temperatures indicates substantial enhancement of defect formation near the melting point T,. Since neither Debye-Hiickel corrections nor the classical continuum theory yield a suitable temperature dependence, a mean field theory is introduced in which the formation energy is reduced by an amount directly proportional to the defect concentration. The simple MFT does gives a rapid rise in defect concentration at high T, but when the strength constant is chosen to match T, the predicted concentrations are too small at lower temperatures. 1. Defect model. 1 .1 NORMAL TEMPERATURE DEPENDENCE. The ionic conductivity is dominated by cation Frenkel defects, with transport by silver ion vacancies and by two kinds of interstitialcy jumps [I]. Careful fitting of conductivity curves in an intermediate intrinsic temperature range (1500 to 280 OC for AgCl and 150° to 2200 for AgBr) gives the activation enthalpies in table I [2]. Table I. Fornzation and migration enthalpies (eV) for AgCl and AgBr. Mechanism Ag Cl AgBr Formation of Frenkel defects 1.49 + 0.02 1.16 & 0.02 Cation vacancy migration 0.31 + 0.01 0.32 f 0.01 Coliinear interstitialcy 0.02 & 0.01 0.04 + 0.01 Non-collinear interstitialcy 0.14 + 0.01 0.28 + 0.01 1 . 2 HIGH TEMPERATURE ANOMALY. At higher temperatures the measured conductivity becomes considerably larger than the extrapolated value, assuming all formation and jump enthalpies are independent of temperature. The excess appears at least 150 OC below T, and rises to more than 100 % near T;, (see Fig. 4). Since evidence from diffusion of Na in AgCl and AgBr [3] indicates that most of the effect is due to an increase in defect concentration (rather than enhanced mobilities), we measure the anomaly by Thus we obtain AgToT directly from experimental measurements, and then calculate the final concentration x, from the extrapolated value x, without any defect interactions. 2. Defect interactions. 2 . 1 DEBYE-HUCKEL CORRECTIONS. The sizable Coulomb interactions between charged defects at large concentrations are represented by the usual first order theory [4]. We find that the formation energy of a Frenkel pair is lowered by Ag,,, which varies approximately as the square root of x,. Since AgDH cannot account for all of the observed anomaly expressed by AgToT in figure 1, we are forced to introduce some extra defect interaction AgEX lo make up the difference. The expla-