Electron-phonon based local mode descriptions of displacive transformations

  • PDF / 751,189 Bytes
  • 7 Pages / 613 x 788.28 pts Page_size
  • 39 Downloads / 245 Views

DOWNLOAD

REPORT


I.

INTRODUCTION

M E T A L L I C alloys with very strong electron-phonon coupling may require a theoretical approach quite different from the conventional one based on the concept of separable electrons and phonons. This concept must be recognized as an approximation, which is usually justified in terms of Migdal's theorem. ~ However, Anderson has argued 2 that for the A-15 compounds and other strong-coupling superconductors, Migdal's theorem breaks down, and that the usual zeroth order description based on free electrons and phonons is an improper starting point in these cases. An alternative description, based on a local phonon approach, models these systems in zeroth order as follows: a certain fraction of the vibrational modes are taken to be noninteracting Einstein oscillators strongly coupled to the electron states. (Most of the vibrational modes are still ordinary phonons.) A key feature of local phonon models, as described here, is the existence of a double-well potential function for each oscillator, which is a consequence of the strong electron-phonon coupling. Displacive transformations are therefore implicitly a part of these models. In this article, we will review the local phonon approach as it has been developed by Abell 3 to qualitatively model amorphous metals, and by Yu and Anderson 2 to describe, semi-quantitatively, properties of strong-coupling superconductors, especially from the A-15 family. Precursive phenomena in the A-15 compounds V3Si and Nb3Sn have been widely studied. Finlayson4 has argued that some type of defect theory offers the best chance for understanding these phenomena in the A-15's and other martensitic alloys. One goal of the present article is to encourage a closer look at local phonon models as a basis for understanding premartensitic effects, especially in strong-coupling alloys such as the A-15's and TiNi. It is also hoped that the study of premartensitic phenomena will be broadened to include the temperature dependence of characteristic electronic properties, such as resistivity and magnetic susceptibility. Indeed, G.C. ABELL is Research Specialist with Monsanto Research Corporation, MRC-Mound, Miamisburg, OH 45342. This paper is based on a presentation made in the symposium "Pretransformation Behavior Related to Displacive Transformations in Alloys" presented at the 1986 annual AIME meeting in New Orleans, March 2-6, 1986, under the auspices of the ASM-MSD Structures Committee. METALLURGICAL TRANSACTIONS A

a few recent studies 5 argue that electron-phonon coupling is fundamental to displacive transformations in at least some metallic systems; but, generally speaking, the focus seems to be very much on phonon properties.

II.

BASIS FOR LOCAL PHONON MODELS

What is the basis for considering local phonon models? McMillan 6 has shown that standard charge density wave (CDW) theory cannot explain the properties of the dichalogenide, TaSe2. If the correlation length of the CDW is long compared to the lattice spacing, phonon frequencies are modified only over a small region o

Data Loading...