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) DELTA-V(f) with h(v) = 8L (formation enthalpy h(v) of vacancies and heat L of fusion given in same units; A V(f) = change of volume due to melting). If there are phase transitions within the solid, L and DELTA-V(f) must be replaced by (L + DELTA-H(t)) and by (DELTA-V(f) + DELTA-V(t)), respectively (DELTA-H(t) and DELTA-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(m)V(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).