Surajit Sengupta

The liquid-solid transition of hard discs: first-order transition or Kosterlitz-Thouless-Halperin-Nelson-Young scenario?

We consider the question of whether a two-dimensional hard-disc fluid has a first-order transition from the liquid state to the solid state as in the three-dimensional melting-crystallization transition or whether one has two subsequent continuous transitions, from the liquid to the hexatic phase and then to the solid phase, as proposed by Kosterlitz, Thouless, Halperin, Nelson and Young (KTHNY). Monte Carlo (MC) simulations of the fluid that study the growth of the bond orientational correlation length, and of the crystal are discussed. The emphasis is on a recent consistency test of the KTHNY renormalization group (RG) scenario, where MC simulations are used to estimate the bare elastic constants and dislocation fugacities in the solid, as a function of density, which then are used as starting values for the RG flow. This approach was validated earlier for the XY model as well.

Elastic Properties of 2D Colloidal Crystals from Video Microscopy

Elastic constants of two-dimensional (2D) colloidal crystals are determined by measuring strain fluctuations induced by Brownian motion of particles. Paramagnetic colloids confined to an air-water interface of a pendant drop are crystallized under the action of a magnetic field, which is applied perpendicular to the 2D layer. Using video microscopy and digital image processing we measure fluctuations of the microscopic strain obtained from random displacements of the colloidal particles from their mean (reference) positions. From these we calculate system-size dependent elastic constants, which are extrapolated using finite-size scaling to obtain their values in the thermodynamic limit. The data are found to agree rather well with zero-temperature calculations.

Nonaffine displacements in crystalline solids in the harmonic limit

A systematic coarse graining of microscopic atomic displacements generates a local elastic deformation tensor D as well as a positive definite scalar χ measuring nonaffinity, i.e., the extent to which the displacements are not representable as affine deformations of a reference crystal. We perform an exact calculation of the statistics of χ and D and their spatial correlations for solids at low temperatures, within a harmonic approximation and in one and two dimensions. We obtain the joint distribution P(χ,D) and the two-point spatial correlation functions for χ and D. We show that nonaffine and affine deformations are coupled even in a harmonic solid, with a strength that depends on the size of the coarse-graining volume Ω and dimensionality. As a corollary to our work, we identify the field h(χ) conjugate to χ and show that this field may be tuned to produce a transition to a state where the ensemble average and the correlation length of χ diverge. Our work should be useful as a template for understanding nonaffine displacements in realistic systems with or without disorder and as a means for developing computational tools for studying the effects of nonaffine displacements in melting, plastic flow, and the glass transition.

Non-monotonic crossover from single-file to regular diffusion in micro-channels

The diffusion behavior of interacting particles determines the behavior of a large number of systems ranging from pedestrians crossing a road to ions passing through channels in living cells. Here we present a system in which the nature of the diffusion process varies with changes in the external conditions. We find this special behavior in a colloidal model system, consisting of micron sized particles which are confined to narrow channels and interact via induced magnetic dipoles. When the density of these particles is changed, diffusion alternates between normal Fickian behavior and single-file diffusion. This anomalous behavior is induced by the order of the particles in the restricted geometry and does not depend on the exact nature of the inter-particle interactions.

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 Neel order. As a function of filling factor ν and Lande factor g, the Skyrmion crystal undergoes a triangle → square → triangle transition at zero temperature. We argue that this structural transition is driven by a change in the shape of the individual Skyrmions and may be probed experimentally. Quantum fluctuations lead to an orientationally disordered phase at low Skyrmion densities.

Droplet fluctuations in the morphology and kinetics of martensites

Material Science Division, Indira Gandhi Centre for Atomic Research, Kalpakkam 603102, India(February 1, 2008)We derive a coarse grained, free-energy functional whichdescribes droplet configurations arising on nucleation of aproduct crystal within a parent. This involves a new ‘slow’vacancy mode that lives at the parent-product interface. Amode-coupling theory suggests that a slow quench from theparent phase produces an equilibrium product, while a fastquench produces a metastable martensite. In two dimensions,the martensite nuclei grow as ‘lens-shaped’ strips having alter-nating twin domains, with well-defined front velocities. Sev-eral empirically known structural and kinetic relations dropout naturally from our theory.PACS: 81.30.Kf, 81.30.-t, 64.70.Kb, 64.60.Qb, 63.75.+z

Anomalous structural and mechanical properties of solids confined in quasi one dimensional strips

We show using computer simulations and mean field theory that a system of particles in two dimensions, when laterally confined by a pair of parallel hard walls within a quasi-one-dimensional channel, possesses several anomalous structural and mechanical properties not observed in the bulk. Depending on the density rho and the distance between the walls Ly, the system shows structural characteristics analogous to a weakly modulated liquid, a strongly modulated smectic, a triangular solid, or a buckled phase. At fixed rho, a change in Ly leads to many re-entrant discontinuous transitions involving changes in the number of layers parallel to the confining walls depending crucially on the commensurability of interlayer spacing with Ly. The solid shows resistance to elongation but not to shear. When strained beyond the elastic limit, it fails undergoing plastic deformation but surprisingly, as the strain is reversed, the material completely recovers and returns to its original undeformed state. We obtain the phase diagram from mean field theory and finite size simulations and discuss the effect of fluctuations.

Heat conduction through a trapped solid: the effect of structural changes on the thermal conductance

We study the conduction of heat across a narrow solid strip trapped by an external potential and in contact with its own liquid. Structural changes, consisting of addition and deletion of crystal layers in the trapped solid, are produced by altering the depth of the confining potential. Nonequilibrium molecular dynamics simulations and, wherever possible, simple analytical calculations are used to obtain the thermal resistance in the liquid, solid and interfacial regions (Kapitza or contact resistance). We show that these layering transitions are accompanied by sharp jumps in the contact thermal resistance. Dislocations, if present, are shown to increase the thermal resistance of the strip drastically.

Field-induced ordering phenomena and non-local elastic compliance in two-dimensional colloidal crystals

Ordering phenomena in colloidal dispersions exposed to external one-dimensional, periodic fields or under confinement are studied systematically by Monte Carlo computer simulations. Such systems are useful models for the study of monolayers on a substrate. We find that the interaction with a substrate potential completely changes the miscibility of a binary, hard disc mixture at low external field amplitudes. The underlying ordering mechanisms leading to this laser-induced de-mixing differ, depending on which components interact with the substrate potential. Generic effects of confinement on crystalline order in two dimensions are studied in a model system of point particles interacting via a potential ∝ r −12 . The state of the system (a strip of width D) depends very sensitively on the precise boundary conditions at the two confining walls. Commensurate, corrugated boundary conditions enhance both orientational order and positional order. In contrast, smooth repulsive boundaries enhance only the orientational order and destroy positional (quasi-)long range order. As external fields have a strong impact on the elastic behaviour of colloidal crystals there is a need to analyse the elastic response in such systems for the field-free case first. To this aim we study the strain–strain correlation functions in a two-dimensional crystal formed by super-paramagnetic colloids, as monitored by standard video microscopy. (Some figures in this article are in colour only in the electronic version)

Non-affine deformation in microstructure selection in solids: I. Molecular dynamics

We study the nucleation dynamics and microstructure selection in a model two-dimensional solid undergoing a square to rhombic transformation, using coarse-grained molecular dynamics (MD) simulations. We find a range of microstructures depending on the depth of quench. The transformations are accompanied by the creation of transient and localized non-affine zones (NAZ), which evolve with the rapidly moving parent-product interface. These plastic regions are created beyond a threshold stress, at a rate proportional to the local stress. We show that the dynamics of NAZs determines the selection of microstructure, including the ferrite and martensite.