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Unified Perturbation Treatment for Phonons in Metallic Covalent and Ionic Crystals
Author(s) -
Eschrig H.
Publication year - 1973
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2220560118
Subject(s) - ionic bonding , crystal (programming language) , phonon , gaussian , tensor (intrinsic definition) , limit (mathematics) , physics , perturbation (astronomy) , quantum mechanics , matrix (chemical analysis) , ionic crystal , ion , perturbation theory (quantum mechanics) , statistical physics , condensed matter physics , chemistry , mathematics , mathematical analysis , computer science , programming language , chromatography , pure mathematics
An interpolation formula which interpolates the exact Hartree expression for the electronic part of the dynamical matrix between the limits of strong and weak crystal potentials and which becomes rigorous in the zero wave vector limit is used to avoid to the problems connected with the inversion of the screening tensor. In the ionic part of the dynamical matrix the Gaussian charge densities of the usual Ewald technique are replaced by the true charge densities around each ion in the unperturbed crystal. The arising expressions are transformed in such a way that the compensation with the corresponding terms in the electronic part can be done explicitely. As a result one gets an alternative formula for the dynamical matrix of simple metals, a practicable formula for transition and noble metals and covalent crystals, and a rather simple expression for ionic crystals which has some link to the physical picture of a shell model. It is shown that the given theory describes the qualitatively correct pressure dependence of the phonon frequencies.