• T V Ramakrishnan

Articles written in Bulletin of Materials Science

• Relevance of liquid state to solid state properties

We outline in this talk the beginning of a new programme to study physical properties of crystalline solids. It is based on considering the latter, a broken symmetry phase, in terms of the higher symmetry liquid phase. The solid is a calculable perturbation on the fluid. This is exactly opposite to the standard approach which relates mechanical properties to the behaviour of defects (mainly dislocations) etc., in an otherwise perfect crystalline solid. However, most other broken symmetry phases (e.g. ferromagnets) are discussed starting from a symmetric Hamiltonian or a free energy functional, and earlier work by one of the authors shows that the liquid-solid transition is well described, qualitatively and quantitatively, by this approach. On the other hand, defect theories of melting have a long record of nonsuccess. In the first part of the talk, the density wave theory of freezing will be outlined, and it will be shown how properties such as Debye Waller factor, entropy change of freezing etc. can be calculated with no or one free parameter. The problem of calculating shear elastic constants and dislocation core structures as well as energies in terms only of observable liquid state properties will be set up, and results presented. The method will be contrasted with zero temperature ‘atomistic’ models which obscure the essential dependence on structure and flounder in a mass of detail. The concluding part will describe further proposed applications, some suggestive experimental results extant in the literature, and some speculations.

• Topological defects in crystals: A density-wave theory

A new approach for describing dislocations and other topological defects in crystals, based on the density wave theory of Ramakrishnan and Yussouff is presented. Quantitative calculations are discussed in brief for the order parameter profiles, the atomic configuration and the free energy of a screw dislocation with Burgers vector$$\overset{\lower0.5em\hbox{\smash{\scriptscriptstyle\rightharpoonup}}} {b} = (a/2, a/2,a/2 )$$ in a bcc solid. Our results for the free energy of the dislocation in a crystal of sizeR, when expressed as (λb2/4π) ln (αR/|b|) whereλ is the shear elastic constant, yield, for example, the valueα ⋍ 1·85 for sodium at its freezing temperature (371°K). The density distribution in the presence of the dislocation shows that the dislocation core has a columnar character. To our knowledge, this study represents the first calculation of dislocation structure, including the core, within the framework of an order parameter theory incorporating thermal effects.

• # Bulletin of Materials Science

Volume 44, 2021
All articles
Continuous Article Publishing mode

• # Dr Shanti Swarup Bhatnagar for Science and Technology

Posted on October 12, 2020

Prof. Subi Jacob George — Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bengaluru
Chemical Sciences 2020