S. Sengupta’s research while affiliated with Jadavpur University and other places

The extensivity property of entropy is clarified in the light of a critical examination of the entropy formula based on quantum statistics and the relevant thermodynamic requirement. The modern form of the Gibbs paradox, related to the discontinuous jump in entropy due to identity or non-identity of particles, is critically investigated. Qualitative framework of a new resolution of this paradox, which analyses the general effect of distinction mark on the Hamiltonian of a system of identical particles, is outlined.

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.

The nature of the dependence of the Heine-Abarenkov model pseudopotential parameters rc and u for different alkali metals, obtained through a comprehensive unified study of the metals, on the atomic number, Z, is investigated, leading to simple empirical relations between Z and the parameters. The product of Z1/2 and the dynamical matrix, D, calculated using the parameters yielded by these relations is found to satisfy a relation of the form DZ1/2 = C1(q, e) for various Z-values, C1(q, e) being a constant depending on the phonon wave vector q and the polarization e. This at once leads to the relation m1/2Z1/4v = C2(q, e) which is verified empirically and thus implies that the lattice vibrations of alkali metals are homologous. The relations obtained are used for a comprehensive unified study of Cs and for predicting its dispersion relation. The importance of the approach lies in the fact that knowing only Z, a unified study of a large number of lattice static, dynamic, and electronic properties of any alkali metal can be carried out within the framework of the pseudopotential theory.

The silver halide crystals have many peculiarities in their physical properties which are uncommon among the simple ionic solids. The different theoretical models used to calculate the properties of this group of solids have concentrated on explaining one or the other of them. But these calculations have one major difficulty common to all. It has not been possible to give a consistent description of the dielectric properties and the dispersion of phonons in the framework of a single model. We have shown from a microscopic analysis of the energy expression of a system of ions occupying arbitrary positions that there exist two types of short-range polarization mechanisms, one arising out of the overlap of the unperturbed wave functions and another due to the perturbation of the wave function. These two effects taken together resolve the incompatibility mentioned above. Based on this analysis we have proposed a model in terms of which we have correlated the cohesion, the stability, the phase-transition properties, the elastic and the dielectric properties, and the phonon dispersion of the AgCl crystal. It is seen that the present model broadly reproduces all the characteristic features of this crystal. Moreover, we have tried to assess in a rough way the relative importance of the different interactions envisaged and their relation to the typicalities of this solid. Finally, some of the limitations of the present calculation are also pointed out.

An attempt is made for a unified study of the lattice statics and dynamics of the LiH–LiD crystals. So far it has not been possible to obtain a unified description of the different properties of this crystal on the basis of a single model and with a single set of model parameters. All the previous calculations suffer from this inadequacy and their results show that there are certain problems regarding the stability of the static lattice structure, the cohesive energy, and a consistent description of the dielectric properties and the dispersion of phonons for this crystal. The present calculation based on the extended deformable shell model removes the earlier difficulties and provides a good overall description of the lattice mechanical properties of this crystal with a single set of parameters. Another salient feature of the present investigation is to indicate the effect of the quadrupolar distortion of the charge cloud, in particular, of the hydrogen ion which has been neglected in all the earlier investigations of the lattice mechanics of these crystals. The calculation clearly points out that without including this effect it is not possible to obtain a coherent description of the lattice mechanics in all its totality. Some qualitative justification for this effect being significant for the crystals under consideration is also presented.

The authors point out a logical fallacy in Robinson's analysis (ibid., vol.13, p.877, 1980) of a thought experiment purporting to show violation of Heisenberg's uncertainty principle. The real problem concerning the interpretation of Heisenberg's principle is precisely stated.

The importance of the three‐body interaction in the study of simple ionic solids with centrosymmetric structure is both, theoretically and empirically well established. But so far there is no attempt to investigate its significance in the properties of ionic crystals belonging to fluorite and antifluorite structures. In contrast to said alkali halides the absence of the centre of symmetry for this structure implies complications which make a direct estimate of this effect quite difficult. From an analysis of the elastic data the inadequacy of a two‐body central interaction to describe the elastic constants of such crystals is demonstrated. An order of estimate is made of the three‐body interaction in the elastic properties of the calcium fluorite crystal from the HF wavefunctions of the ions. For the other crystals where the Clementi wavefunctions for the ions are not available the estimate is done directly from the elastic constants. The order of magnitude of this interaction obtained for the different crystals is comparable and lies in the range observed for other ionic solids. Further this investigation apart from indicating the importance of the three‐body interaction also accounts for the anomalies in the previous calculations. Finally some of the limitations of the present calculation are pointed out.

A perturbation‐theoretic model calculation is developed in the point‐dipole approximation for the study of ionic crystals from a knowledge of the Hartree‐Fock wave functions of the free ions that constitute the solid. The salient features of the present calculation are that it a) provides a method for calculating the different lattice static and dynamic properties of a crystal directly from the free ion wave functions without using any crystal property; b) clearly gives an empirical justification for the major assumption of the phenomenological shell model; c) develops a new method for evaluating the Coulomb overlap interaction; d) suggests a modified short‐range polarisation mechanism; and lastly e) shows how far actually the free ion wave functions are realistic as a starting point. The method is applied to calculate a number of lattice mechanical properties of the two ionic crystals namely, NaCl and KCl. Despite the simplicity of the approach the agreement, with observation for both the crystals is quite impressive. The source of the remaining discrepancy is discussed.