Paper
On Calculation of Lattice Energy in Spatially Confined Domains

Authors:

Yevgen Bilotsky

Abstract

Evaluation of internal energy and the interatomic or ionic interactions in a crystal lattice usually requires precise calculation of lattice sums. This in the case of small nanoparticles (as spacelimited domains) presents several challenges, as conventional methods are usually valid only for infinite lattices, tailored for a specific potential. In this work, a new method has been developed for calculation of atomic interactions based on the radial density function with the geometric probability approach, extended to arbitrary fixed lattices and potentials in a nanoparticle.
The derived radial density function (RDF) combines terms for a uniform particles distribution, for nonuniform spherical symmetry and the last one for an additional, angledependent term. The second term originates from Walfiszlike formula for lattice sums. The RDF with these three terms is explicitly integrated for spherical lattice domains resulting in the internal energy of the system with a prescribed interaction potential. The application of the method was demonstrated for Wigner model of electrons lattice interacting with compensating positive jelly in finite lattice sphere, which interacting energy between lattice and jelly was evaluated. The excess of this energy caused by spacelimitation of the lattice was explicitly expressed in the terms of absolutely convergent lattice sums.

Keywords

Nanocrystals; Energy; Geometric Probability; Surface; Convergent Lattice Sums

StartPage

127

EndPage

137

Doi

10.5963/AMSA0204001