Angular Force Models in the Lattice Dynamics of Cubic Systems

Abstract

Angular force models of de Launay (DL) and Clark-Gazis-Wallis (CGW), as applied to study the lattice dynamics of b.c.c. and f.c.c. systems, are analysed and discussed. Removal of the deficiencies from the DL angular force model results in a scheme identical to the central pairwise potential procedure. As far as the calculation of phonon frequencies in cubic metals is concerned, the CGW model gives dispersion results identical to those obtained by applying the general tensor force (GTF) model. It is observed that the GTF constants are composite quantities, expressible in terms of elementary CGW force constants. The two schemes are applied in the calculation of phonon dispersion curves of some b.c.c. and f.c.c. metals and numerical results are discussed. Finally the stability of the lattice is discussed.Die fur die Untersuchung der Gitterdynamik von k.r.2.-und k.f.2.-Systemen benutzten Winkelkraftmodelle von de Launay (DL) und Clark-Gazis-Wallis (CGW) werden analysiert und diskutiert. Die Beseitigung der Mange1 des DL-Winkelkraftmodells fuhrt zu einer Form, die mit der Paar-Zentralpotentialmethode identisch ist. Insoweit die Berechnung der Phononenfrequenzen in kubischen Metallen betrachtet wird, liefert das CGW-Modell Dispersionsergebnisse, die mit denen aus dem allgemeinen Tensor-Kraftmodell (GTF) identisch sind. Es wird beobachtet, daB die GTF-Konstanten zusammengesetzte GroDen sind, die sich mit elementaren CGW-Kraftkonstanten ausdrucken lassen. Beide Methoden werden fur die Berechnung der Phonondispersionskurven einiger k.r.2. -und k.f.z.-Metalle benutzt, und die numerischen Ergebnisse werden diskutiert. Schliemich wird auch die Gitterstabilitat diskutiert.

Lattice Dynamical Study of Titanium (Ti) by Using CGW-VTBFS Model

“…The present work is the second theoretical and the first Angular Force model application on the lattice dynamics of bcc Ti. In this work, an angular force model (CGW), originally proposed by Clark-Gazis-Wallis [6] and later improved by Moore [7]& Upadhyaya et al [8], is used to reproduce the phonon frequencies of bcc Ti. According to this model the angular forces arise due to a change in the angle included between the pair of bonds connecting two neighbours.…”