Role of thermal vibrations in alloy phase transitions

Abstract

All theoretical models (Heisenberg, Ising etc.) assume a negligible role for thermal vibrations in alloy and magnetic phase transitions. Analysis of diffraction data conclusively proves that this assumption is incorrect. A simple criterion emerges that theoretical models can ignore the role of thermal vibrations only if the Debye-Waller Factor is ignored in the analysis of diffraction data. Diffraction data constrain all theoretical models to incorporate the role of thermal vibrations. This conclusion is also supported by other experimental results, the effect of thermal vibrations on ordering energy that is of the same order of magnitude as ordering energy and an isotope effect on magnetic phase transitions. An electron-phonon interaction (EPI) formalism that incorporates the Debye-Waller Factor in electronic structure calculations already exists and must be adopted for a correct understanding of phase transitions as it can account for all the different experimental results mentioned above. The discrepancy between experimental and theoretical ordering energy in Ni 3 V is direct evidence for the role of thermal vibrations in altering ordering energy. The inter-nuclear potential energy term converges if zero point vibrations are incorporated and this method can replace the Ewald sum method. The three dimensional Ising model cannot represent order-disorder transition in beta brass, CuZn. An isotope effect is predicted for magnetic phase transitions if the transition temperature is below Debye temperature. The long range order parameter obtained from diffraction data can only be compared with predictions of models that incorporate the role of thermal vibrations and not otherwise.

Physical meaning of the Ewald sum method

“…We have recently shown that diffraction data impose severe constraints on theoretical models for order-disorder phase transitions in alloys [19]. It is essential to incorporate the role of thermal vibrations for a correct understanding of order-disorder phase transitions.…”

“…The simplest mean-field Bragg-Williams model was modified to make the ordering energy temperature dependent so as to enable its predictions to be compared with diffraction data. In order to obtain a simple form for the temperature dependence of the ordering energy for the simplest Modified Bragg-Williams model, we had in passing identified the Gaussian in the Ewald sum method with thermal vibrations [19].…”

Role of thermal vibrations in magnetic phase transitions

“…Recently, we have addressed [7] a similar contradiction in order-disorder alloy phase transitions and shown that diffraction data impose severe constraints on all theoretical models. It is essential to incorporate thermal vibrations for a correct understanding of order-disorder transitions.…”

“…It is essential to incorporate thermal vibrations for a correct understanding of order-disorder transitions. In particular, all existing models must be modified to explicitly include a temperature dependent interaction parameter before their predictions can be compared with diffraction data [7].…”