Nonequivalence of De Launay and Clark, Gazis, and Wallis Angular Force Models

Abstract

The angular force models of De Launay and Clark, Gazis, and Wallis are analysed by resolving the atomic displacements along three mutually perpendicular directions. It is shown that the CGW model which neglects a two-body force component perpendicular to the plane of the triangle is not equivalent t o the DAF model which neglects the three-body forces confined to the plane, for :my crystal structure and all the earlier claims regarding their equivalence are therefore spurious. The equivalence between the angular force constants of these models, the relations between these and other force constant models as well as the role played by the axially symmetric forces, in the case of b.c.c. and f.c.c. structures are discussed.

Angular Force Models in the Lattice Dynamics of Cubic Systems

“…metals in the DL and CGW models and found that the CGW model gives better dispersion results. We have also pointed out that in a recent work Ramamurthy [7] has given some erroneous statements, especially in relation to the work of Moore and Upadhyaya [6]. Further, we have shown that the interaction system and dynamical matrix for ion-ion part of Thakur and Singh [22] for the f.c.c.…”

“…[7]. If a l , a, are identified to central force constants and a;, a; to the angular force constants of the de Launay model [3] for second nearest neighbour interaction, we obtain (by putting c13 = a; = = 0) from (1) the dynamical matrix due to the DL angular force model.…”

“…For the first time, Moore and Upadhyaya [6] developed a systematic procedure to examine the CGW model beyond second nearest neighbours. Recently Ramamurthy [7] has put an effort to analyse the DL and CGW angular force models for cubic metals but limiting the interaction system only up to second nearest neighbours. The central conclusion of his analysis is that the DL and CGW models are not equivalent to each other for any crystal structure.…”

“…The central conclusion of his analysis is that the DL and CGW models are not equivalent to each other for any crystal structure. Basically the analysis of Ramamurthy [7] is contained in the work of Moore and Upadhyaya [6]. However, Ramamurthy has given erroneous statements relevant to the two angular force models and more specifically in relation to the work of Moore and Upadhyaya [6].…”

“…Therefore, it seems useful that a fresh interpretation of the facts is to be put before the readers. In order to have a comparative study with the work of Ramamurthy [7] and others, we shall deduce expressions for the dynamical matrix using the CGW angular force model for three sets of nearest neighbours.…”