arXiv subjects
Publications and source records attributed to Bulbul Chakraborty.
In an effort to understand the glass transition, the kinetics of a spin model with frustration but no quenched randomness has been analyzed. The phenomenology of the spin model is remarkably similiar to that of structural glasses. Analysis of the model suggests that defects play a major role in dictating the dynamics as the glass transition is approached.
Many systems where interactions compete with each other or with constraints are well described by a model first introduced by Brazovskii. Such systems include block copolymers, alloys with modulated phases, Rayleigh-Benard Cells and type-I superconductors. The hallmark of this model is that the fluctuation spectrum is isotropic and has a minimum at a nonzero wave vector represented by the surface of a d-dimensional hyper-sphere. It was shown by Brazovskii that the fluctuations change the free energy structure from a $ ϕ^{4}$ to a $ϕ^{6}$ form with the disordered state metastable for all quench depths. The transition from the disordered to the periodic, lamellar structure changes from second order to first order and suggests that the dynamics is governed by nucleation. Using numerical simulations we have confirmed that the equilibrium free energy function is indeed of a $ ϕ^{6}$ form. A study of the dynamics, however, shows that, following a deep quench, the dynamics is described by unstable growth rather than nucleation. A dynamical calculation, based on a generalization of the Brazovskii calculations shows that the disordered state can remain unstable for a long time following the quench.
Using a Monte Carlo coarse-graining technique introduced by Binder et al., we have explicitly constructed the continuum field theory for the zero-temperature triangular Ising antiferromagnet. We verify the conjecture that this is a gaussian theory of the height variable in the interface representation of the spin model. We also measure the height-height correlation function and deduce the stiffness constant. In addition, we investigate the nature of defect-defect interactions at finite temperatures, and find that the two-dimensional Coulomb gas scenario applies at low temperatures.
A detailed numerical and experimental study of the ordering of the low temperature tetragonal phase of CuAu is presented. The numerical simulations are based on a coarse-grained free energy derived from electronic structure calculations of CuAu, while the experimental results are obtained from in situ x-ray scattering. Both theoretical and experimental work indicate a subtle kinetic competition between the ordered tetragonal phase and the metastable modulated phase.
We propose a simple dynamical model for a glass transition. The dynamics is described by a Langevin equation in a piecewise parabolic free energy landscape, modulated by a temperature dependent overall curvature. The zero-curvature point marks a transition to a phase with broken ergodicity which we identify as the glass transition. Our analysis shows a connection between the high and low frequency response of systems approaching this transition.
We propose a simple dynamical model of the glass transition based on the results from a non-randomly frustrated spin model which is known to form a glassy state below a characteristic quench temperature. The model is characterized by a multi-valleyed free-energy surface which is modulated by an overall curvature. The transition associated with the vanishing of this overall curvature is reminiscent of the glass transition. In particular, the frequency-dependent response evolves from a Debye relaxation peak to a function whose high-frequency behavior is characterized by a non-trivial power law. We present both an analytical form for the response function and numerical results from Langevin simulations.
We have analyzed a non-randomly frustrated spin model which exhibits behavior remarkably similar to the phenomenology of structural glasses. The high-temperature disordered phase undergoes a strong first-order transition to a long-range ordered structure. Using Monte Carlo simulations, we have studied the behavior of the supercooled state by quenching to temperatures below this transition temperature. For a range of supercooling, the system remains ergodic and exhibits dynamics characteristic of supercooled liquids. Below a certain characteristic temperature, however, the system freezes into a "glassy" phase. In this phase, the system is non-ergodic and evolves through a distribution of traps characterized by a power-law distribution of trapping times. This change in the dynamic behavior is concurrent with the appearance of a shear instability.
A continuum model derived from an atomistic Hamiltonian is used to examine the ordering kinetics in CuAu. A detailed description of the formation of the low and high temperature ordered and modulated superlattice states is given. The metastability of the modulated phase at low temperatures is shown to severely hinder creation of the ordered superlattice. Formation of the modulated superlattice is shown to results in interesting lamellar and labyrinthine structures.
We study the early-stages of ordering in $Cu_3 Au$ using a model Hamiltonian derived from the effective medium theory of cohesion in metals: an approach providing a microscopic description of interatomic interactions in alloys. Our simulations show a crossover from a nucleated growth regime to a region where the ordering does not follow any simple growth laws. This mirrors the experimental observations in $Cu_3 Au$. The kinetics of growth, obtained from the simulations, is in semi-quantitative agreement with experiments. The real-space structures observed in our simulations offer some insight into the nature of early-stage kinetics
Recent experiments in metallic solid solutions have revealed interesting correlations between static pair-displacements and the ordering behavior of these alloys. This paper discusses a simple theoretical model which successfully explains these observations and which provides a natural framework for analyzing experimental measurements of pair-displacements and chemical correlations in solid solutions. The utility and scope of this model is demonstrated by analyzing results of experiments on $Ni-Fe$ and $Cr-Fe$ alloys and results of simulations of $Cu-Au$ and $Cu-Ag$ alloys.
This paper presents a theoretical model for studying the dynamics of ordering in alloys which exhibit modulated phases. The model is different from the standard time-dependent Ginzburg-Landau description of the evolution of a non-conserved order parameter and resembles the Swift-Hohenberg model. The early-stage growth kinetics is analyzed and compared to the Cahn-Hilliard theory of continuous ordering. The effects of non-linearities on the growth kinetics are discussed qualitatively and it is shown that the presence of an underlying elastic lattice introduces qualitatively new effects. A lattice Hamiltonian capable of describing these effects and suitable for carrying out simulations of the growth kinetics is also constructed.
We study the kinetics of ordering in Cu3Au using a model Hamiltonian derived from the effective medium theory of chemical bonding. Monte Carlo simulations are used to investigate universal and non-universal features of the growth kinetics. Anisotropic scaling of the structure factor is observed in late-stage growth of ordered domains. The anisotropy is a non-universal feature determined by details of the microscopic model, and we find that the anisotropy observed in the simulations is in excellent agreement with experiments on Cu3Au. The simulations are discussed in the context of theories of unstable growth. To our knowledge, this is the first study of kinetics in a realistic model Hamiltonian describing the material-specific properties of Cu3Au.