The true and the experimental entropy values of vacancies

2014 The formation enthalpy and entropy of a Schottky defect in alkali halides depend on temperature due to anharmonic effects. Thus the experimental values of these parameters obtained at high temperatures do not coincide with the true ones. In the case of NaCl the experimental value of the formation enthalpy exceeds by 7 % the real formation enthalpy at absolute zero. The experimental value of the formation entropy is different from the true value. This is due to a term that depends on the temperature derivative of the formation enthalpy. The calculation shows that the experimental value should be 13 K in adequate agreement with the published values. LE JOURNAL DE PHYSIQUE LETTRES TOME 38, 1er AOUT 1977, Classification Physics Abstracts 61.70 63.70 In ~ former paper [1] ] we indicated a method for calculating hlho and slso from elastic constants of materials with bulk moduli B falling linearly with temperature. h and s are the enthalpy and the entropy for the formation of vacancies and the subscript zero indicates values at T = 0. The method disregarded the entropy svib’due to the change of frequency of the vibrators surrounding the vacancy. The influence of expansivity was investigated separately [2]. Taking both effects into consideration one obtains where # is the bulk thermal expansivity and Although both parameters h and s change with temperature, in the analysis of conductivity or diffusion experiments they are assumed to be constants and are labelled as hexp and sexp. The present letter will compare these parameters for NaCI with the values of h and s in the region where experiments are usually carried out. Using published data for the bulk modulus [3] and expansivity [4] we have calculated and plotted in figure 1 hlho and (s svib)lho as a function of temperature. We have refrained from giving s/ho directly because Svib can only be calculated in the approximation of an Einstein model [5]. We note that the bulk FIG. 1. Temperature dependence of formation parameters for NaCl. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyslet:019770038015032900 L-330 JOURNAL DE PHYSIQUE LETTRES modulus has only been measured up to 700 K. In this region it falls linearly with temperature; we assume that it continues in the same way up to 1 073 K thus fulfilling the condition for the validity of eqs. (1). The following simple numerical expressions fit these plots in the region 750 to 1 073 K