D. Roy’s research while affiliated with Presidency College and other places

From a careful analysis of the energy expression of the second-order pseudopotential theory, the reason for the breakdown of the consistency condition is pointed out. The problem is resolved by introducing the concept of local volume strain which introduces some modifications in the dynamical matrix and leads to the equality of static and dynamic elastic constants. A unified study of the alkali metals with the Heine-Abarenkov model pseudopotential in conjunction with Taylor's dielectric function, and taking proper care of the consistency condition, yields satisfactory results for both the static and dynamic properties of these metals. One interesting feature of the present investigation is that the theory satisfying the consistency condition reproduces the crossing of the longitudinal and transverse branches in the (100) direction for Li, while reproducing the normal behaviour for the dispersion curve of other metals.

Unified study of the different properties of metals clearly reveals the inadequacy of the empty-core Ashcroft pseudopotential even in the case of simple metals. In the present paper we propose a modification of the one-parameter Ashcroft pseudopotential by assuming the parameterr c to be wave vector-dependent. This introduces a simple modification of the electron-ion pseudopotential in the reciprocal space. The corresponding potential in the configuration space shows that the abrupt change in the Coulomb potential atr=r c is replaced by a continuous change spread over a small region near the core boundary. The present model has been used to make a unified study of Al and is found to be a significant improvement over the simple Ashcroft model. The agreement between the calculated and experimental values is found to be quite satisfactory.

The consistency condition for the energy expression of a metal obtained from the pseudopotential theory is found to be equivalent to the statement that the static and dynamic elastic constants must agree. If the band-structure energy and the coupling parameter are both confined to the second order of the perturbation theory then this consistency condition is violated. It is pointed out that the reason for this violation lies in the fact that the homogeneous deformation theory takes note of the change in the dielectric function due to strain, while the long wave theory partly ignores it. It is shown that by suitably coupling the local strain to the ionic coordinates one can get the missing terms in the long-wave theory and the consistency condition is satisfied. The effect of these terms on the phonon dispersion curves for Al is analyzed.

Ashcroft’s empty core pseudopotential is applied to the substitutional alloy (K-CS) to calculate the heat of formation and lattice parameter over the entire concentration range. At any concentration the defect crystal is considered to be equivalent to a perfect crystal with a modified lattice parameter and the potential parameter for the defect crystal is calculated by using some suitable interpolation formula. The calculated results agree well with the available experimental results.

Experimentally observed deviations of the lattice parameter from Vegards' law in alkali halide solid solutions are predicted from the boundary condition on the equation for the heat of formation. This also simultaneously makes the latter consistent with experimental results. The theory uses no experimental information of the solid solution and only the perfect crystal information is sufficient. The model is employed here to calculate the lattice parameter and heat of formation of ten alkali halide solid solutions over the entire concentration range. The agreement with the experimental results is quite satisfactory. Experimentell beobachtete Abweichungen des Gitterparameters von der Vegardschen Regel in Alkalihalogenidmischkristallen werden aus den Randwertbedingungen der Gleichung für die Bildungswärme vorhergesagt. Dies macht die letztere konsistent mit experimentellen Ergebnissen. Die Theorie benutzt keine experimentellen Informationen der Mischkristalle, und es genügen allein die Informationen der perfekten Kristalle. Das Modell wird benutzt, um den Gitterparameter und die Bildungswärme von zehn Alkalihalogenidmischkristallen über den gesamten Konzentrationsbereich zu berechnen. Die Übereinstimmung mit den experimentellen Ergebnissen ist befriedigend.

The heat of formation of rare gas crystals is calculated using a relatively simple approach. As the difference in the values of heat of formation and cohesive energy depend entirely upon the relaxation and many‐body effects, the contribution of these terms to the heat of formation is examined critically. It is found that the relaxation effect is quite negligible. Though three‐body interaction other than triple‐dipole approximately cancels with the higher many‐body effects in the case of cohesive energy, the cancellation is not at all complete in the case of heat of formation, and the many‐body effects other than the triple‐dipole is found to contribute significantly to the difference between the energy of the perfect and imperfect crystal. The differences in the values of heat of formation and cohesive energy are calculated for the rare gas solids using a very simple approach and compared with experimental results and also with those obtained from more sophisticated calculation. The present calculation is found to reasonably reproduce the experimental results. It is emphasised that an accurate determination of this difference is necessary as this serves as a direct test of the role of many‐body forces in rare gas solids.

A model expression is developed for the energy in a metal with the help of which one may calculate a fairly large number of different properties of the metal with much greater facility than in a strictly pseudopotential calculation. The model is applied to calculate the phonon frequencies of the b. c. c. metal W and the f. c. c. metals Cu, Ag, and Ni. With a suitable expression for the two-body central interaction the model can be easily extended to calculate a fairly large number of both static and dynamic properties of metals.

An electron fluid model is proposed for the lattice dynamics of metals which satisfies the requirement of translational invariance and the lattice is in equilibrium without recourse to external forces. The model is applied to calculate the phonon dispersion of sodium in the symmetry directions.