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

The low-temperature anomalous properties of amorphous solids have been explained by the two-level-system (TLS) model. But there are some disagreements between thermal and acoustic experimental results. An anisotropic structure for these TLS’s has been proposed, but no investigation has been made to date into the possibility of any specific structure. This paper considers a generalized distribution of the TLS parameters, takes into account all variations with external strain, and investigates the property of amorphous materials for specific symmetry in the structure of the TLS’s. It is found that the present model with a single set of five parameters is capable of providing a unified description of about eleven different observed physical properties of vitreous silica, including phonon-echo experiments at low temperatures. The model indicates that all experiments are consistent with one another and reduces the disagreement regarding the number of TLS’s taking part in acoustic and specific-heat experiments.

Using EXAFS technique it is possible to measure the relaxation of the nearest neighbours around a substitutional defect and at a finite concentration one obtains distinctly two types of nearest-neighbour distances in a binary solid solution. A relation is derived containing a single parameter for the variation of these two types of nearest-neighbour distances with concentration which predicts the results successfully both, for alkali halide solid solutions and covalently bonded tetrahedral solid solutions of zincblende structure. The parameter is calculated for alkali halide solid solutions using information of the perfect crystals only. Mittels EXAFS-Technik ist es möglich, die Relaxation der nächsten Nachbarn um einen Substitutionsdefekt zu messen und bei einer endlichen Konzentration erhält man getrennt zwei Arten von Abstände nächster Nachbarn in einem binären Mischkristall. Es wird eine Beziehung abgeleitet, die einen einzigen Parameter für die Änderung dieser beiden Typen der Abstände nächster Nachbarn mit der Konzentration enthält und die Ergebnisse sowohl für Alkalihalogenidmischkristalle als auch kovalent gebundene tetraedrisch koordinierte Mischkristalle mit Zinkblendestruktur vorhersagt. Der Parameter wird für Alkalihalogenidmischkristalle berechnet, wobei nur Informationen des perfekten Kristalls benutzt werden.

The assumption of the existence of an aggregate of two-level systems (TLS's) in an amorphous dielectric leads to a satisfactory understanding of their unusual low-temperature properties, but a detailed mechanism of response of the TLS to an external strain has not yet been formulated. In this work we have developed the general mechanics of interaction of a TLS in amorphous solids and an external strain field. The model is able to predict the temperature dependence of static elastic constants arising from TLS interaction. It also successfully explains the experimentally observed relation between the deformation potentials Ml and Mt and between Dl and Dt for longitudinal and transverse waves. Another new feature is that the Bloch equations are solved by a perturbation technique which is considerably simpler and straightforward compared with earlier methods.

Uptil now it has not been possible to explain the different physical properties of amorphous polymers using a model based on a single conceptual scheme. In this paper, a phenomenological model is proposed which tries to explain the mechanical, optical and thermal properties (both thermal conductivity and expansivity) of amorphous polymers. The model has similarities with the composite model, proposed by the present authors, which has proved to be successful in interpreting the different physical properties of semicrystalline polymers. The present model considers the bulk form of the polymer as an aggregate of microscopic units possessing intrinsic physical properties. On drawing, the development of anisotropy in different physical properties is supposed to be due to the development of preferred orientation of these units. The development of the preferred orientation has been estimated directly from birefringence data. The agreement between the calculated and experimental values of the elastic modulus, thermal conductivity and thermal expansivity of PVC, PMMA and PS is found to be reasonable good.

A manifestation of ‘antipiezoelectricity’ in the ionic crystals with fluorite structure is the development of a macroscopic volume distribution of electrostatic quadrupole moment under mechanical strain. We give here microscopic expressions and numerical estimates for the moment and find that it is too feeble to be measured by electrostatic experiments.

The authors deal with a subtle logical mistake in the standard theory of lattice dynamics for molecular crystals. Thus, usually one writes down the vibration energy up to terms quadratic in displacement of the atoms and then expresses it in terms of translation and infinitesimal rotation vectors. But since the displacement cannot be uniquely described up to quadratic terms in a rotation vector, this scheme seems to be erroneous. The correct procedure would be to start from the force and torque equations which are linear in the rotation vector. They develop this scheme to obtain the expressions for molecular force constants (in terms of atomic force constants), first retaining the coupling between internal and external vibrations and then passing over to the rigid-molecule approximation. The translational and rotational invariance conditions are also derived. However, the results are found to be identical with the existing ones derived from energy considerations. The root of this seemingly fortuitous agreement is traced to the interesting fact that up to quadratic terms in the rotation vector, the energy is indeed uniquely specified, though the displacement field is not.

Starting from a Lippmann–Schwinger-type equation, which is very similar to that of quantum mechanical multiple scattering theory, Zeller and Dederichs [Phys. Status Solidi B 55, 831 (1973)] have developed the effective medium theory. This theory has found wide application in understanding the mechanical behavior of disordered solids. However, unlike the problem in quantum mechanics, this equation of the random elasticity is only approximate since this is a linear response theory. So, it is proposed in this work for the first time to go beyond this approximation to treat nonlinear properties of such solids of which the third-order elastic constant is a generic. Again, so far as the nonlinear elastic behavior of these solids is concerned, no work has been done except the simple Voigt- and Reuss-type averaging. Both are extreme approximations and are, moreover, known to lead to violation of the equilibrium condition. The salient feature of the present calculation is to get an exact formal solution of the problem in terms of an appropriate Green’s function in a closed form. The result obtained is quite general and may be adopted to treat nonlinearity in any tensor property of disordered materials. Finally several approximations, including a self-consistent solution, have been discussed for obtaining the effective nonlinear static mechanical susceptibility.

A Unified study of lattice-mechanical properties of lead using energy-dependent pseudopotential is carried out. Energy dependence in pseudopotential is considered through the effective mass approximation; the pseudopotential model chosen is the local Heine-Abarenkov model potential. Properties studied include cohesive energy, equilibrium lattice parameter, second-order elastic constants, pressure derivative of second-order elastic constants, equation of state (atT=0 K), phonon-dispersion and effective two-body interaction. The results show fairly good agreement with experiment especially with a modified Heine-Abarenkov potential.

The computation of the orientational averages is a great problem in the case of semicrystalline polymers. In a previous communication [1] it has been shown that sin?=f(?) sin?' describes the orientational changes satisfactorily for a certain class of polymers. In this paper some alternative deformation schemes are also discussed. It has been concluded that birefringence provides a useful guideline in the choice of a deformation scheme.