Simplified forms of the Fielek model for bcc transition metals

Abstract

Two simple forms of theFielek [1] model are developed to infer about the nature of the interactions among neighbouringd-shells, characterising the transition metals. The first model expresses this interaction as the sum of first two terms of the Taylor’s expansion for energy, while the second model describes this interaction to be three body (angular or unpaired) type. Both of these models obey the equilibrium condition and represent core-core interactions to be central pairwise extending to immediate neighbours only. Volume interactions among core and conduction electrons and also amongd-shells and conduction electrons follow the modifiedBhatia Scheme [5]. The theoretical findings given by these models on phonon dispersion in bcc zirconium and niobium are compared with the experimental data. Further these findings are also compared with those of the originalFielek model which is simplified by substituting the saidBhatia scheme for that due toKrebs [3].