Relation between the formation energy of a vacancy and the nearest neighbor interactions in pure metals and liquid metals

The nearest neighbor interaction model was used to describe pure metals and liquid metals. The interaction was assumed to be independent of the distance between atoms for small changes near the solid spacing. Two interaction models are considered. For one, the potential of atoms infinitely separated is taken to be zero (uniform dilatation method). For the other, the electron density is kept constant (constant volume method). For constant dilatation method, ''ghost'' bonds are considered. The relation between the interaction energy between atoms, E/sub AA/, the cohesive energy E/sub coh/ and the ''ghost'' bond between a vacancy and an atom E/sub AV/ is clarified. E/sub AV/ approximately 0.35 E/sub AA/ approximately 0.7 E/sub coh//Z/sub s/. Z/sub s/ is the coordination number. The formation energy of a vacancy E/sub V//sup F/ approximately -0.29 E/sub coh/ = Z/sub s/ RT/sub m//(Z/sub s/ -- Z/sub l/). R is the gas constant, T/sub m/ melting temperature, Z/sub l/ is the average number of nearest neighbors in liquid state. These relations are valid for all metals independent of crystal structures