arXiv subjects

Surajit Sengupta

Publications and source records attributed to Surajit Sengupta.

61 records · Page 4Linked to original sources

arXiv1999

Elastic constants from microscopic strain fluctuations

Fluctuations of the instantaneous local Lagrangian strain $ε_{ij}(\bf{r},t)$, measured with respect to a static ``reference'' lattice, are used to obtain accurate estimates of the elastic constants of model solids from atomistic computer simulations. The measured strains are systematically coarse- grained by averaging them within subsystems (of size $L_b$) of a system (of total size $L$) in the canonical ensemble. Using a simple finite size scaling theory we predict the behaviour of the fluctuations $<ε_{ij}ε_{kl}>$ as a function of $L_b/L$ and extract elastic constants of the system {\em in the thermodynamic limit} at nonzero temperature. Our method is simple to implement, efficient and general enough to be able to handle a wide class of model systems including those with singular potentials without any essential modification. We illustrate the technique by computing isothermal elastic constants of the ``soft'' and the hard disk triangular solids in two dimensions from molecular dynamics and Monte Carlo simulations. We compare our results with those from earlier simulations and density functional theory.

cond-mat↗

arXiv1999

Arrested States of Solids

Solids produced as a result of a fast quench across a freezing or a structural transition get stuck in long-lived metastable configurations of distinct morphology, sensitively dependent on the processing history. {\it Martensites} are particularly well studied examples of nonequilibrium solid-solid transformations. Since there are some excellent reviews on the subject, we shall, in this brief article, mainly present a summary of our work on the nonequilibrium statistical mechanics of Martensites.

cond-mat.stat-mech↗

arXiv1998

Low temperature hcp to monoclinic structural transition in solid C$_{70}$ : Is there an intermediate phase?"

We follow the structural transformation in solid C$_{70}$ from the high temperature hcp to a low temperature monoclinic phase using x-ray diffraction studies at controlled cooling-rates from 0.0033 to 0.42 K/min. Rapid cooling of the sample gives the signature of a two-step transformation which disappears when the system is transformaed quasi-statically. These experimental results can be rationalised using a simple mean field, Langevin dynamical theory using a free energy functional with minima corresponding to the parent and two competing product phases such that one of these product phases remains metastable throughout. The implication of our results on the existence of the intermediate phase in the sequence, hcp-dhcp-monoclinic, of structural transitions in solid C$_{70}$ with the lowering of temperature is discussed.

cond-mat.mtrl-sci↗

arXiv1997

First Passage Times and Time-Temperature-Transformation curves for Martensites

Martensites are long-lived nonequilibrium structures produced following a quench across a solid state structural transition. In a recent paper (Phys. Rev. Lett. 78, 2168 (1997)), we had described a mode-coupling theory for the morphology and nucleation kinetics of the equilibrium ferrite phase and twinned martensites. Here we calculate nucleation rates within a first-passage time formalism, and derive the time-temperature-transformation (TTT) diagram of the ferrite-martensite system for athermal and isothermal martensites. Empirically obtained TTT curves are extensively used by metallurgists to design heat treatment cycles in real materials.

cond-mat↗

arXiv1997

Shape Deformation driven Structural Transitions in Quantum Hall Skyrmions

The Quantum Hall ground state away from $ν= 1$ can be described by a collection of interacting skyrmions. We show within the context of a nonlinear sigma model, that the classical ground state away from $ν= 1$ is a skyrmion crystal with a generalized Néel order. We show that as a function of filling $ν$, the skyrmion crystal undergoes a triangle to square to triangle transition at zero temperature. We argue that this structural transition, driven by a change in the shape of the individual skyrmions, is stable to thermal and quantum fluctuations and may be probed experimentally.

cond-mat.mes-hall↗

arXiv1996

Droplet Fluctuations in the Morphology and Kinetics of Martensites

We derive a coarse grained, free-energy functional which describes droplet configurations arising on nucleation of a product crystal within a parent. This involves a new `slow' vacancy mode that lives at the parent-product interface. A mode-coupling theory suggests that a {\it slow} quench from the parent phase produces an equilibrium product, while a {\it fast} quench produces a metastable martensite. In two dimensions, the martensite nuclei grow as `lens-shaped' strips having alternating twin domains, with well-defined front velocities. Several empirically known structural and kinetic relations drop out naturally from our theory.

cond-mat↗

arXiv1996

Droplet Free Energy Functional for the Morphology of Martensites

Martensites are metastable phases, possessing a characteristic morphology, usually formed during a fast quench accross a structural transition. We attempt to understand these morphological features using a coarsegrained free energy functional ${\cal F}[ε; Φ]$ which contains, in addition to the usual strain fields $ε_{ij}$ (the `` order parameter'' for the transition), the ``vacancy'' field $ϕ$ which arises due to the geometric mismatch at a parent-product interface. The relaxation of this mismatch is slow compared to typical front propagation times and hence $ϕ$ is essentially frozen in the reference frame of the growing martensite front. Minimisation of ${\cal F}$ then automatically yeilds typical martensite morphologies. We demonstrate this in two dimensions for the square to rhombus transformation and obtain internally twinned martensites, which grow as thin strips, for ``hard'' martensites (e.g., Fe-based alloys) or with a `single-interface', for ``soft'' martensites (e.g., In-Tl alloys).

cond-mat↗