Crystal Electrostatic Energy

TL;DR

This paper investigates the electrostatic energy of ion crystals, demonstrating that local ions suffice for calculations in alkali halides and proposing a delta-function electron density model to explain metallic properties.

Contribution

It introduces a localized electron density model to reconcile electrostatic calculations with observed properties in metals, extending beyond simple ion lattice considerations.

Findings

Ion lattice electrostatic energy agrees with experiments in alkali halides.

Electron density localization explains metallic properties not accounted for by ion lattice energy alone.

Localized electron model aligns theoretical predictions with observed melting temperatures and shear moduli.

Abstract

It has been shown that to calculate the parameters of the electrostatic field of the ion crystal lattice it sufficient to take into account ions located at a distance of 1-2 lattice spacings. More distant ions make insignificant contribution. As a result, the electrostatic energy of the ion lattice in the alkaline halide crystal produced by both positive and negative ions is in good agreement with experiment when the melting temperature and the shear modulus are calculated. For fcc and bcc metals the ion lattice electrostatic energy is not sufficient to obtain the observed values of these parameters. It is possible to resolve the contradiction if one assumes that the electron density is strongly localized and has a crystal structure described by the lattice delta - function. As a result, positive charges alternate with negative ones as in the alkaline halide crystal. Such delta-like localization of the electron density is known as a model of nearly free electrons.