Formation Volume of Vacancies in Elements and the Defect Formation Mechanism of Melting

The formation volume V_v of vacancies is given by V_v = (h_v/L) ΔV_f with h_v = 8L (formation enthalpy h_v of vacancies and heat L of fusion given in same units; ΔV_f = change of volume due to melting). If there are phase transitions within the solid, L and ΔV_f must be replaced by (L + Δ H_t) and by (ΔV_f + ΔV_t), respectively (Δ H_t and Δ V_t refer to the heat (s) of transition (s) and to the volume change(s) due to transition(s), resp.). The pressure dependence of the melting point is dT_m/dp = (T_mV_v)/h_v. Independent of the sign of V_v any increase of the vacancy concentration above the maximum concentration possible within the solid decreases the melting point thus resulting in the observed surface melting. The melting point is fixed by the characteristics of vacancy formation (h_v, S_v, V_v) and by the bulk modulus of the solid (S_v = formation entropy of vacancies).