arXiv subjects

Michael Widom

Publications and source records attributed to Michael Widom.

At least 55 records · Page 3Linked to original sources

arXiv2015

Machine Learning methods for interatomic potentials: application to boron carbide

Total energies of crystal structures can be calculated to high precision using quantum-based density functional theory (DFT) methods, but the calculations can be time consuming and scale badly with system size. Cluster expansions of total energy as a linear superposition of pair, triplet and higher interactions can efficiently approximate the total energies but are best suited to simple lattice structures. To model the total energy of boron carbide, with a complex crystal structure, we explore the utility of machine learning methods ($L_1$-penalized regression, neural network, Gaussian process and support vector regression) that capture certain non-linear effects associated with many-body interactions despite requiring only pair frequencies as input. Our interaction models are combined with Monte Carlo simulations to evaluate the thermodynamics of chemical ordering.

cond-mat.mtrl-sci↗

arXiv2015

Predicted phase diagram of B-C-N

Noting the structural relationships between phases of carbon and boron carbide with phases of boron nitride and boron subnitride, we investigate their mutual solubilities using a combination of first principles total energies supplemented with statistical mechanics to address finite temperatures. Owing to large energy costs of substitution, we find the mutual solubilities of the ultra hard materials diamond and cubic boron nitride are negligible, and the same for the quasi-two dimensional materials graphite and hexagonal boron nitride. In contrast, we find a continuous range of solubility connecting boron carbide to boron subnitride at elevated temperatures. The electron precise compound B$_{13}$CN consisting of B$_{12}$ icosahedra with NBC chains is found to be stable at all temperatures up to melting. It exhibits an order-disorder transition in the orientation of NBC chains at approximately T=500K.

cond-mat.mtrl-sci↗

arXiv2015

Elastic Instability of the Orthorhombic Antiferromagnetic Phase of 122-Pnictides Under Pressure

A-122 pnictides (A an alkaline earth element) possess striped antiferromagnetic states of orthorhombic (OR) symmetry and nonmagnetic states of tetragonal (T) symmetry. Based on total energy calculations, we show that the T = 0K pressure-driven transition from OR to T states occurs at a pressure, $P_H$, where the tetragonal enthalpy drops below the orthorhombic. The OR state remains metastable up to a higher pressure, $P_M$ > $P_H$. We find anomalies in magnetism and orthorhombicity as $P \rightarrow P_M$, and a trend towards elastic instability.

cond-mat.str-el↗

arXiv2015

Enumeration of octagonal tilings

Random tilings are interesting as idealizations of atomistic models of quasicrystals and for their connection to problems in combinatorics and algorithms. Of particular interest is the tiling entropy density, which measures the relation of the number of distinct tilings to the number of constituent tiles. Tilings by squares and 45 degree rhombi receive special attention as presumably the simplest model that has not yet been solved exactly in the thermodynamic limit. However, an exact enumeration formula can be evaluated for tilings in finite regions with fixed boundaries. We implement this algorithm in an efficient manner, enabling the investigation of larger regions of parameter space than previously were possible. Our new results appear to yield monotone increasing and decreasing lower and upper bounds on the fixed boundary entropy density that converge toward S = 0.36021(3).

math.CO↗

arXiv2014

First Principles Modeling of the Temperature Dependent Ternary Phase Diagram for the Cu-Pd-S System

As an aid to the development of hydrogen separation membranes, we predict the temperature dependent phase diagrams using first principles calculations combined with thermodynamic principles. Our method models the phase diagram without empirical fitting parameters. By applying thermodynamic principles and solid solution models, temperature-dependent features of the Cu-Pd-S system can be explained, specifically solubility ranges for substitutions in select crystalline phases. Electronic densities of states calculations explain the relative favorability of certain chemical substitutions. In addition, we calculate sulfidization thresholds for the Pd-S2 system and activities for the Cu-Pd binary in temperature regimes where the phase diagram contains multiple solid phases.

cond-mat.mtrl-sci↗

arXiv2014

First Principles Calculation of Elastic Moduli of Early-Late Transition Metal Alloys

Motivated by interest in the elastic properties of high strength amorphous metals, we examine the elastic properties of select crystalline phases. Using first principles methods, we calculate elastic moduli in various chemical systems containing transition metals, specifically early (Ta,W) and late (Co,Ni). Theoretically predicted alloy elastic properties are verified for Ni-Ta by comparison with experimental measurements using resonant ultrasound spectroscopy. Comparison of our computed elastic moduli with effective medium theories shows that alloying leads to enhancement of bulk moduli relative to averages of the pure elements, and considerable deviation of predicted and computed shear moduli. Specifically, we find an enhancement of bulk modulus relative to effective medium theory and propose a candidate system for high strength, ductile amorphous alloys. Trends in the elastic properties of chemical systems are analyzed using force constants, electronic densities of state and Crystal Overlap Hamilton Populations. We interpret our findings in terms of the electronic structure of the alloys.

cond-mat.mtrl-sci↗

arXiv2014

Hybrid Monte Carlo/molecular dynamics simulation of a refractory metal high entropy alloy

The high entropy alloy containing refractory metals Mo-Nb-Ta-W has a body centered cubic structure, which is not surprising given the complete mutual solubility in BCC solid solutions of all pairs of the constituent elements. However, first principles total energy calculations for the binaries reveal a set of distinct energy minimizing structures implying the likelihood of chemically ordered low temperature phases. We apply a hybrid Monte Carlo and molecular dynamics method to evaluate the temperature-dependent chemical order. At 300K a cesium-chloride ordering emerges between mixed (Nb,Ta) sites and mixed (Mo,W) sites. This order is lost at elevated temperatures.

cond-mat.mtrl-sci↗

arXiv2014

Lifshitz Transitions in 122-Pnictides Under Pressure

We demonstrate, using $T=0$ first principles total energy calculations, that observed pressure-driven anomalies in the entire 122-pnictides family ($A$Fe$_2$As$_2$; $A$ = alkali earth element Ca, Sr, Ba) can be understood as consequences of Lifshitz transitions (LTs) \cite{Lifshitz60}. Our results for energy band dispersions and spectra, lattice parameters, enthalpies, magnetism, and elastic constants over a wide range of hydrostatic pressure provide a coherent understanding of multiple transitions in these compounds, namely, enthalpic, magnetic and tetragonal (T) - collapsed tetragonal (cT) transitions. In particular, the T-cT transition and anomalies in lattice parameters and elastic properties, observed at finite temperatures, are interpreted as arising from proximity to $T=0$ Lifshitz transitions, wherein pressure causes non-trivial changes in the Fermi surface topology in these materials.

cond-mat.supr-con↗

arXiv2013

First Principles Study of Bismuth Films at Transition Metal Grain Boundaries

Recent experiments suggest that Bi impurities segregate to form bilayer films on Ni and Cu grain boundaries but do not segregate in Fe. To explain these phenomena, we study the total energies of Bi films on transition metal (TM) $Σ$3(111) and $Σ$5(012) GBs using density functional theory. Our results agree with the observed stabilities. We propose a model to predict Bi bilayer stability at Ni GBs which suggests that Bi bilayer is not stable on (111) twist CSL GBs but is stable in most (100) twist CSL GBs. We investigate the interaction and bonding character between Bi and TMs to explain the differences among TMs based on localization of orbitals and magnetism.

cond-mat.mes-hall↗

arXiv2013

Folding Kinetics of Riboswitch Transcriptional Terminators and Sequesterers

To function as gene regulatory elements in response to environmental signals, riboswitches must adopt specific secondary structures on appropriate time scales. We employ kinetic Monte Carlo simulation to model the time-dependent folding during transcription of TPP riboswitch expression platforms. According to our simulations, riboswitch transcriptional terminators, which must adopt a specific hairpin configuration by the time they have been transcribed, fold with higher efficiency than Shine-Dalgarno sequesterers, whose proper structure is required only at the time of ribosomal binding. Our findings suggest both that riboswitch transcriptional terminator sequences have been naturally selected for high folding efficiency, and that sequesterers can maintain their function even in the presence of significant misfolding.

q-bio.BM↗

arXiv2013

Prediction of A2 to B2 Phase Transition in the High Entropy Alloy MoNbTaW

In this paper we show that an effective Hamiltonian fit with first principles calculations predicts an order/disorder transition occurs in the high entropy alloy MoNbTaW. Using the Alloy Theoretic Automated Toolset, we find T=0K enthalpies of formation for all binaries containing Mo, Nb, Ta, and W, and in particular we find the stable structures for binaries at equiatomic concentrations are close in energy to the associated B2 structure, suggesting that at intermediate temperatures a B2 phase is stabilized in MoNbTaW. Our previously published hybrid Monte Carlo/molecular dynamics results for the MoNbTaW system are analyzed to identify certain preferred chemical bonding types. A mean field free energy model incorporating nearest neighbor bonds is derived, allowing us to predict the mechanism of the order/disorder transition. We find the temperature evolution of the system is driven by strong Mo-Ta bonding. Comparison of the free energy model and our hybrid Monte Carlo/molecular dynamics results suggest the existence of additional low-temperature phase transitions in the system likely ending with phase segregation into binary phases.

cond-mat.mtrl-sci↗

arXiv2013

First Principles Study of Bismuth Films on the Nickel(111) Surface

A recent experiment(Bollmann11) suggested that bismuth forms hexagonal close packed (HCP) films on the Ni(111) surface, of heights 3, 5 and 7 layers. A quantum size effect based on free electrons was proposed in explanation. To test this idea, we calculate the total energies of Bi on the Ni(111) surface using density functional theory. We find that HCP film stabilities disagree with the observed odd layer preferences, and the structures are mechanically destabilized by adding capping atoms which pucker the HCP layers. Furthermore, we find that rhombohedral films based on the bulk Bi structure are energetically more favorable than the proposed HCP films. These structures also favor odd numbers of layers, but owing to covalent chemical bonding rather than confinement of free electrons. Specifically, a strongly bound adsorbed surface monolayer forms, followed by bulk-like rhombohedral bilayers.

cond-mat.mes-hall↗

arXiv2013

Generalized Potentials for a Mean-field Density Functional Theory of a Three-Phase Contact Line

We investigate generalized potentials for a mean-field density functional theory of a three-phase contact line. Compared to the symmetrical potential introduced in our previous article [1], the three minima of these potentials form a small triangle located arbitrarily within the Gibbs triangle, which is more realistic for ternary fluid systems. We multiply linear functions that vanish at edges and vertices of the small triangle, yielding potentials in the form of quartic polynomials. We find that a subset of such potentials has simple analytic far-field solutions, and is a linear transformation of our original potential. By scaling, we can relate their solutions to those of our original potential. For special cases, the lengths of the sides of the small triangle are proportional to the corresponding interfacial tensions. For the case of equal interfacial tensions, we calculate a line tension that is proportional to the area of the small triangle.

cond-mat.stat-mech↗

arXiv2012

A Free Energy Model of Boron Carbide

The assessed phase diagram of the boron-carbon system contains a single non-stoichiometric boron-carbide phase of rhombohedral symmetry with a broad, thermodynamically improbable, low temperature composition range. We combine first principles total energy calculations with phenomenological thermodynamic modeling to propose a revised low temperature phase diagram that contains two boron-carbide phases of differing symmetries and compositions. One structure has composition B4C and consists of B11C icosahedra and C-B-C chains, with the placement of carbon on the icosahedron breaking rhombohedral symmetry. This phase is destabilized above 600K by the configurational entropy of alternate carbon substitutions. The other structure, of ideal composition B13C2, has a broad composition range at high temperature, with rhombohedral symmetry throughout, as observed experimentally.

cond-mat.mtrl-sci↗

arXiv2012

First Principles Study of CaFe2As2 "Collapse" Under Pressure

We perform first principles calculations on CaFe2As2 under hydrostatic pressure. Our total energy calculations show that though the striped antiferromagnetic (AFM) orthorhombic (OR) phase is favored at P=0, a non-magnetic collapsed tetragonal (cT) phase with diminished c-parameter is favored for P > 0.36 GPa, in agreement with experiments. Rather than a mechanical instability, this is an enthalpically driven transition from the higher volume OR phase to the lower volume cT phase. Calculations of electronic density of states reveal pseudogaps in both OR and cT phases, though As(p) hybridization with Fe(d) is more pronounced in the OR phase. We provide an estimate for the inter-planar magnetic coupling. Phonon entropy considerations provide an interpretation of the finite temperature phase boundaries of the cT phase.

cond-mat.str-el↗

arXiv2011

Mean-field Density Functional Theory of a Three-Phase Contact Line

A three-phase contact line in a three-phase fluid system is modeled by a mean-field density functional theory. We use a variational approach to find the Euler-Lagrange equations. Analytic solutions are obtained in the two-phase regions at large distances from the contact line. We employ a triangular grid and use a successive over-relaxation method to find numerical solutions in the entire domain for the special case of equal interfacial tensions for the two-phase interfaces. We use the Kerins-Boiteux formula to obtain a line tension associated with the contact line. This line tension turns out to be negative. We associate line adsorption with the change of line tension as the governing potentials change.

cond-mat.other↗

arXiv2011

Prediction of Orientational Phase Transition in Boron Carbide

The assessed binary phase diagram of boron-carbon exhibits a single alloy phase designated "B4C" with rhombohedral symmetry occupying a broad composition range that falls just short of the nominal carbon content of 20%. As this composition range is nearly temperature independent, the phase diagram suggests a violation of the third law of thermodynamics, which typically requires compounds to achieve a definite stoichiometry at low temperatures. By means of first principles total energy calculations we predict the existence of two stoichiometric phases at T=0K: one of composition B4C with monoclinic symmetry; the other of composition B13C2 with rhombohedral symmetry. Using statistical mechanics to extend to finite temperatures, we demonstrate that the monoclinic phase reverts to the rhombohedral phase above T=600K, along with a slight reduction on carbon content.

cond-mat.mtrl-sci↗

arXiv2011

VASP on a GPU: application to exact-exchange calculations of the stability of elemental boron

General purpose graphical processing units (GPU's) offer high processing speeds for certain classes of highly parallelizable computations, such as matrix operations and Fourier transforms, that lie at the heart of first-principles electronic structure calculations. Inclusion of exact-exchange increases the cost of density functional theory by orders of magnitude, motivating the use of GPU's. Porting the widely used electronic density functional code VASP to run on a GPU results in a 5-20 fold performance boost of exact-exchange compared with a traditional CPU. We analyze performance bottlenecks and discuss classes of problems that will benefit from the GPU. As an illustration of the capabilities of this implementation, we calculate the lattice stability α- and β-rhombohedral boron structures utilizing exact-exchange. Our results confirm the energetic preference for symmetry-breaking partial occupation of the β-rhombohedral structure at low temperatures, but does not resolve the stability of α relative to β.

cond-mat.mtrl-sci↗