Investigation of the equilibrium concentration of lattice vacancies in silver and dilute silver-tin alloys with a differential dilatometer

Abstract

The difference between relative changes in macroscopic length Delta L/L and X-ray lattice parameter Delta a/a has been measured over a wide temperature range from room temperature to 25 K below the respective melting point in pure silver and in some dilute silver-tin alloys between 0.25 and 8.60 at.% Sn. At higher temperatures, Delta L/L- Delta a/a increases, showing an Arrhenius behaviour due to vacancy formation. The absolute vacancy concentration at the melting point increases continuously from 5.2*10-4 for pure silver to 2.5*10-3 for a Ag-8.6 at.% Sn alloy. The vacancy formation enthalpy decreases from 1.05 to 0.74 eV simultaneously. The binding enthalpy and entropy for the first vacancy-impurity complex were found to be hBI=0.15+or-0.02 eV and sBI=-(0.5+or-0.2)kB. The impurity-impurity interaction is repulsive and of the order of 1/10 eV, similar to other noble metal alloys with positive excess charge. The binding Gibbs free energy of the first complex was determined as gBI=0.20+or-0.02 eV in good agreement with earlier measurements of resistivity and silver self-diffusion enhancement in silver-tin alloys but without some of their constraints since the vacancy concentration has been determined directly. All results can be interpreted within the framework of the model of Berces and Kovacs (1983).