Bulbul Chakraborty

Brandeis University

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Nigel Goldenfeld

University of Illinois Urbana-Champaign

K. R. Elder

Oakland University

Zhigang Xi

Brandeis University

Dapeng Bi

Northeastern University

Philip B. Allen

University of Notre Dame

Oana Malis

Purdue University West Lafayette

Karl Ludwig

Boston University

Warren E. Pickett

University of California, Davis

Robert Behringer

Duke University

Jie Zhang

Shanghai Jiao Tong University

Cooperative Institutions

Brandeis University

Northeastern University

Boston University

University of Illinois Urbana-Champaign

University of California, San Diego

Purdue University West Lafayette

University of California, Davis

Czech Academy of Sciences, Institute of Physics

University of Florida

United States Naval Research Laboratory

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Monte Carlo study of short-range order and displacement effects in disordered CuAu

Philosophical Magazine B (1999)

Oana Malis Karl Ludwig David L. Olmsted Bulbul Chakraborty

The correlation between local chemical environment and atomic displacements in disordered CuAu alloy has been studied using Monte Carlo simulations based on the effective medium theory (EMT) of metallic cohesion. These simulations correctly reproduce the chemically-specific nearest-neighbor distances in the random alloy across the entire Cu\$_x\$Au\$_{1-x}\$ concentration range. In the random equiatomic CuAu alloy, the chemically specific pair distances depend strongly on the local atomic environment (i.e. fraction of like/unlike nearest neighbors). In CuAu alloy with short-range order, the relationship between local environment and displacements remains qualitatively similar. However the increase in short-range order causes the average Cu-Au distance to decrease below the average Cu-Cu distance, as it does in the ordered CuAuI phase. Many of these trends can be understood qualitatively from the different neutral sphere radii and compressibilities of the Cu and Au atoms.

Short range order

Atomic radius

Cohesion (chemistry)

10.1080/13642819908214846

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Citations (3)

An X-ray scattering and simulation study of the ordering kinetics in CuAu

EPL (Europhysics Letters) (1998)

K. R. Elder Oana Malis Karl Ludwig Bulbul Chakraborty Nigel Goldenfeld

A detailed numerical and experimental study of the ordering of the low-temperat ure 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.

Tetragonal crystal system

Metastability

10.1209/epl/i1998-00409-9

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Citations (4)

Infrared and dc conductivity in metals with strong scattering: Nonclassical behavior from a generalized Boltzmann equation containing band-mixing effects

Physical review. B, Condensed matter (1981)

Philip B. Allen Bulbul Chakraborty

Metals with high resistivity (\ensuremath{\sim} 100 \ensuremath{\mu}\ensuremath{\Omega} cm) seem to show weaker variation of resistivity (as a function of temperature and perhaps also static disorder) than predicted by semiclassical (Bloch-Boltzmann) theory (SBT). We argue that the effect is not closely related to Anderson localization, and therefore does not necessarily signify a failure of the independent collision approximation. Instead we propose a failure of the semiclassical acceleration and conduction approximations. A generalization of Boltzmann theory is made which includes quantum (interband) acceleration and conduction, as well as a complete treatment of interband-collision effects (within the independent-collision approximation). The interband terms enhance short-time response to $\stackrel{\ensuremath{\rightarrow}}{\mathrm{E}}$ fields (because the theory satisfies the exact $f$-sum rule instead of the semiclassical approximation to it). This suggests that the additional conductivity, as expressed phenomenologically by the shunt resistor model, is explained by interband effects. The scattering operator is complex, its imaginary parts being related to energy-band renormalization caused by the disorder. Charge conservation is respected and thermal equilibrium is restored by the collision operator. The theory is formally solved for the leading corrections to SBT, which have the form of a shunt resistor model. At infrared frequencies, the conductivity mostly obeys the Drude law $\ensuremath{\sigma}(\ensuremath{\omega})\ensuremath{\sim}\ensuremath{\sigma}(0){(1\ensuremath{-}i\ensuremath{\omega}\ensuremath{\tau})}^{\ensuremath{-}1}$, except for one term which goes as ${(1\ensuremath{-}i\ensuremath{\omega}\ensuremath{\tau})}^{\ensuremath{-}2}$.

Semiclassical physics

Boltzmann constant

Scattering rate

Collision frequency

10.1103/physrevb.23.4815

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Citations (65)

Jamming by shear

Nature (2011)

Dapeng Bi Jie Zhang Bulbul Chakraborty Robert Behringer

10.1038/nature10667

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Citations (603)

Density of states, optical mass, and dc electrical resistance of Ta, W, Nb, and Mo using Slater-Koster interpolation

Physical review. B, Solid state (1976)

Bulbul Chakraborty Warren E. Pickett Philip B. Allen

Slater-Koster interpolation has been used to fit the nonrelativistic augmented-plane-wave (APW) band calculations of Petroff and Viswanathan for Ta and W. The resulting Slater-Koster parameters have been used to calculate the density of states and optical mass. The density of states compares well with the original APW calculation, but the optical masses which have not been calculated before, seem to differ appreciably from presently available experimental data. The dc electrical resistances, which have been calculated using our values of the optical mass, agree well with experiment if an empirical coupling constant similar to McMillan's is assumed.

Interpolation

Coupling constant

Constant (computer programming)

10.1103/physrevb.14.3227

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Citations (104)

Microscopic modeling of the growth of order in an alloy: Nucleated and continuous ordering

Physical review. B, Condensed matter (1996)

Bulbul Chakraborty Zhigang Xi

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

Microscopic theory

Hamiltonian (control theory)

Cohesion (chemistry)

10.1103/physrevb.53.5063

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Citations (5)

Rheology of granular materials: dynamics in a stress landscape

Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences (2009)

Dapeng Bi Bulbul Chakraborty

We present a framework for analysing the rheology of dense driven granular materials, based on a recent proposal of a stress-based ensemble. In this ensemble, fluctuations in a granular system near jamming are controlled by a temperature-like parameter, the angoricity, which is conjugate to the stress of the system. In this paper, we develop a model for slowly driven granular materials based on the stress ensemble and the idea of a landscape in stress space. The idea of an activated process driven by the angoricity has been shown by Behringer et al. (Behringer et al. 2008 Phys. Rev. Lett. 101, 268301) to describe the logarithmic strengthening of granular materials. Just as in the soft glassy rheology (SGR) picture, our model represents the evolution of a small patch of granular material (a mesoscopic region) in a stress-based trap landscape. The angoricity plays the role of the fluctuation temperature in the SGR. We determine (i) the constitutive equation, (ii) the yield stress, and (iii) the distribution of stress dissipated during granular shearing experiments, and compare these predictions with the experiments of Hartley & Behringer (Hartley & Behringer 2003 Nature 421, 928-931.).

Mesoscopic physics

Shearing (physics)

Stress space

10.1098/rsta.2009.0193

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Citations (16)

Dynamics of ordering in alloys with modulated phases

Physical review. B, Condensed matter (1994)

Bulbul Chakraborty

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 nonconserved 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 nonlinearities on the growth kinetics are discussed qualitatively and it is shown that the presence of an underlying elastic lattice introduces qualitatively interesting effects. A lattice Hamiltonian capable of describing these effects and suitable for carrying out simulations of the growth kinetics is also constructed.

Lattice (music)

Hamiltonian (control theory)

Dynamics

10.1103/physrevb.49.8608

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Citations (2)

Kinetics of Ordering in Cu₃Au : An Atomistic Approach

MRS Proceedings (1992)

Zhigang Xi Bulbul Chakraborty

Hamiltonian (control theory)

Kinetic Monte Carlo

10.1557/proc-291-165