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A Study in the Homology of Lattice Mechanical Properties of Alkali Metals
Author(s) -
Sarkar S. K.,
Sen D.,
Sengupta S.
Publication year - 1981
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.2221050110
Subject(s) - pseudopotential , alkali metal , dispersion relation , phonon , lattice (music) , lattice vibration , physics , condensed matter physics , chemistry , thermodynamics , quantum mechanics , acoustics
The nature of the dependence of the Heine‐Abarenkov model pseudopotential parameters r c and u for different alkali metals, obtained through a comprehensive unified study of the metals, on the atomic number, Z , is investigated, leading to simple empirical relations between Z and the parameters. The product of Z 1/2 and the dynamical matrix, D , calculated using the parameters yielded by these relations is found to satisfy a relation of the form DZ 1/2 = C 1 ( q, e ) for various Z ‐values, C 1 ( q, e ) being a constant depending on the phonon wave vector q and the polarization e . This at once leads to the relation m 1/2 Z 1/4 v = C 2 ( q, e ) which is verified empirically and thus implies that the lattice vibrations of alkali metals are homologous. The relations obtained are used for a comprehensive unified study of C s and for predicting its dispersion relation. The importance of the approach lies in the fact that knowing only Z , a unified study of a large number of lattice static, dynamic, and electronic properties of any alkali metal can be carried out within the framework of the pseudopotential theory.