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

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 252K below the respective melting point in pure Ag and in some dilute Ag--Sn alloys between 0.25-8.60 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 x 10 exp --4 for pure Ag to 2.5 x 10 exp --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 h sub B1 = 0.15 plus /minus 0.02 eV and s sub B1 = --(0.5 plus/minus 0.2)k sub B . The impurity--impurity interaction is repulsive and of the order of 0.1 eV, similar to other noble metal alloys with positive excess charge. The binding Gibbs free energy of the first complex was determined as g sub B1 = 0.20 plus/minus 0.02 eV, in good agreement with earlier measurements of resistivity and Ag self-diffusion enhancement in Ag--Sn 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.