Liquid Madelung energy and Schottky defect energy related to liquid structure and melting temperature for alkali halides

Motivated by the work of Reiss et al in which the melting temperature T_m of alkali halides is correlated with Coulomb energy, we consider the cohesive energy W of ionic melts and Schottky defect energy E_s in the hot crystal, relative to the thermal energy k_BT_m It is shown here that W is accurately approximated by the liquid Madelung energy and hence that Wk_BT_m relates to the charge-charge direct correlation function c_QQ(r) at r = 0 The existence of a “Madelung constant” for the liquid at T_m is thereby demonstrated through the alkali halide series An estimate of the ratio E_s/k_BT_m then considered, the basic additional ingredient being argued to be the static dielectric constant of the solid The BarrDawson-Lidiard empirical correlation between E_s, and k_BT_m can be understood in this way.