arXiv subjects

Michael Widom

Publications and source records attributed to Michael Widom.

At least 37 records · Page 2Linked to original sources

arXiv2022

Nonlinear deformation and elasticity of BCC refractory metals and alloys

Application of isotropic pressure or uniaxial strain alters the elastic properties of materials; sufficiently large strains can drive structural transformations. Linear elasticity describes stability against infinitesimal strains, while nonlinear elasticity describes the response to finite deformations. It was previously shown that uniaxial strain along [100] drives refractory metals and alloys towards mechanical instabilities. These include an extensional instability, and a symmetry-breaking orthorhombic distortion caused by a Jahn-Teller-Peierls instability that splays the cubic lattice vectors. Here, we analyze these transitions in depth. Eigenvalues and eigenvectors of the Wallace tensor identify and classify linear instabilities in the presence of strain. We show that both instabilities are discontinuous, leading to discrete jumps in the lattice parameters. We provide physical intuition for the instabilities by analyzing the changes in first principles energy, stress, bond lengths and angles upon application of strain. Electronic band structure calculations show differential occupation of bonding and anti-bonding orbitals, driven by the changing bond lengths and leading to the structural transformations. Strain thresholds for these instabilities depend on the valence electron count.

cond-mat.mtrl-sci↗

arXiv2022

Vibrational entropy of crystalline solids from covariance of atomic displacements

The vibrational entropy of a solid at finite temperature is investigated from the perspective of information theory. Ab initio molecular dynamics (AIMD) simulations generate ensembles of atomic configurations at finite temperature from which we obtain the $N$-body distribution of atomic displacements, $ρ_N$. We calculate the information-theoretic entropy from the expectation value of $\ln{ρ_N}$. At a first level of approximation, treating individual atomic displacements independently, our method may be applied using Debye-Waller B-factors, allowing diffraction experiments to obtain an upper bound on the thermodynamic entropy. At the next level of approximation we correct the overestimation through inclusion of displacement covariances. We apply this approach to elemental body-centered cubic sodium and face-centered cubic aluminum, showing good agreement with experimental values above the Debye temperatures of the metals. Below the Debye temperatures we extract an effective vibrational density of states from eigenvalues of the covariance matrix, and then evaluate the entropy quantum mechanically, again yielding good agreement with experiment down to low temperatures. Our method readily generalizes to complex solids, as we demonstrate for a high entropy alloy. Further, our method applies in cases where the quasiharmonic approximation fails, as we demonstrate by calculating the HCP/BCC transition in Ti.

cond-mat.stat-mech↗

arXiv2021

An investigation of high entropy alloy conductivity using first-principles calculations

The Kubo-Greenwood equation, in combination with the first-principles Korringa-Kohn-Rostoker Coherent Potential Approximation (KKR-CPA) can be used to calculate the DC residual resistivity of random alloys at T = 0 K. We implemented this method in a multiple scattering theory based ab initio package, MuST, and applied it to the ab initio study of the residual resistivity of the high entropy alloy Al$_x$CoCrFeNi as a function of $x$. The calculated resistivities are compared with experimental data. We also predict the residual resistivity of refractory high entropy alloy MoNbTaV$_x$W. The calculated resistivity trends are also explained using theoretical arguments.

cond-mat.mtrl-sci↗

arXiv2021

Ab-initio free energies of liquid metal alloys: application to the phase diagrams of Li-Na and K-Na

Comparison of free energies between different phases and different compositions underlies the prediction of alloy phase diagrams. To allow direct comparison, consistent reference points for the energies or enthalpies are required, and the entropy must be placed on an absolute scale, yielding absolute free energies. Here we derive absolute free energies of liquids from ab-initio molecular dynamics (AIMD) by combining the directly simulated enthalpies with an entropy derived from simulated densities and pair correlation functions. As an example of the power of this method we calculate the phase diagrams of two binary alkali metal alloys, Li-Na and K-Na, revealing a critical point and liquid-liquid phase separation in the former case, and a deep eutectic in the latter. Good agreement with experimental data demonstrates the power of this simple method.

cond-mat.mtrl-sci↗

arXiv2020

Edge Dislocations Can Control Yield Strength in Refractory Body-Centered-Cubic High Entropy Alloys

Energy efficiency is motivating the search for new high-temperature metals. Some new body-centered-cubic random multicomponent "high entropy alloys (HEAs)" based on refractory elements (Cr-Mo-Nb-Ta-V-W-Hf-Ti-Zr) possess exceptional strengths at high temperatures but the physical origins of this outstanding behavior are not known. Here we show, using integrated neutron-diffraction (ND), high-resolution transmission electron microscopy (HRTEM), and theory, that the high strength and strength retention of a NbTaVTi alloy and a new high-strength/low-density CrMoNbV alloy are attributable to edge dislocations. This is surprising because plastic-flow in BCC elemental metals and dilute alloys is universally accepted to be controlled by screw dislocations. We use the insight and theory to perform a computationally-guided search over $10^7$ BCC HEAs and identify over $10^6$ possible ultra-strong high-temperature alloy compositions for future exploration.

cond-mat.mtrl-sci↗

arXiv2020

An averaged cluster approach to including chemical short range order in KKR-CPA

The single-site Korringa-Kohn-Rostoker Coherent Potential Approximation (KKR-CPA) ignores short range ordering present in disordered metallic systems. In this paper, we establish a new technique to fix this shortcoming by embedding an averaged cluster that displays chemical short range order (SRO). The degree of SRO can be tuned by externally defined order parameters. This averaged cluster can be embedded in the single site CPA medium, or a self-consistently obtained effective medium that contains SRO information. The validity of this method is demonstrated by applying it to two alloy systems - the CuZn body centered cubic (BCC) solid solution, and AlCrTiV, a four-element BCC high entropy alloy. A comparison between the non-self-consistent and self-consistent modes is also provided for the two above mentioned systems. We make the code available on the internet. Planned extensions to this work are discussed.

cond-mat.mtrl-sci↗

arXiv2020

Cluster variation method analysis of correlations and entropy in BCC solid solutions

Solid solutions occur when multiple chemical species share sites of a common crystal lattice. Although the single site occupation is random, chemical interaction preferences bias the occupation probabilities of neighboring sites, and this bias reduced the entropy of mixing below its ideal value. Sufficiently strong bias leads to symmetry-breaking phase transitions. We apply the cluster variation method to explore solid solutions on body centered cubic lattices in the context of two specific compounds that exhibit opposite ordering trends. Employing density functional theory to model the energetics, we show that CuZn exhibits an order-disorder transition to the CsCl prototype structure, while AlLi instead takes the NaTl prototype structure, and we evaluate their temperature-dependent order parameters, correlations and entropies.

cond-mat.mtrl-sci↗

arXiv2019

Formation of Graphene atop a Si adlayer on the C-face of SiC

The structure of the SiC(000-1) surface, the C-face of the {0001} SiC surfaces, is studied as a function of temperature and of pressure in a gaseous environment of disilane (Si2H6). Various surface reconstructions are observed, both with and without the presence of an overlying graphene layer (which spontaneously forms at sufficiently high temperatures). Based on cross-sectional scanning transmission electron microscopy measurements, the interface structure that forms in the presence of the graphene is found to contain 1.4 - 1.7 monolayers (ML) of Si, a somewhat counter-intuitive result since, when the graphene forms, the system is actually under C-rich conditions. Using ab initio thermodynamics, it is demonstrated that there exists a class of Si-rich surfaces containing about 1.3 ML of Si that are stable on the surface (even under C-rich conditions) at temperatures above about 400 K. The structures that thus form consist of Si adatoms atop a Si adlayer on the C-face of SiC, with or without the presence of overlying graphene.

cond-mat.mes-hall↗

arXiv2019

Spontaneous formation of thermodynamically stable Al--Cu--Fe icosahedral quasicrystal from realistic atomistic simulations

Icosahedral quasicrystals spontaneously form from the melt in simulations of Al--Cu--Fe alloys. We model the interatomic interactions using oscillating pair potentials tuned to the specific alloy system based on a database of density functional theory (DFT)-derived energies and forces. Favored interatomic separations align with the geometry of icosahedral motifs that overlap to create face-centered icosahedral order on a hierarchy of length scales. Molecular dynamics simulations, supplemented with Monte Carlo steps to swap chemical species, efficiently sample the configuration space of our models, which reach up to 9846 atoms. Exchanging temperatures of independent trajectories (replica exchange) allows us to achieve thermal equilibrium at low temperatures. By optimizing structure and composition we create structures whose DFT energies reach to within $\sim$2 meV/atom of the energies of competing crystal phases. Free energies obtained by adding contributions due to harmonic and anharmonic vibrations, chemical substitution disorder, phasons, and electronic excitations, show that the quasicrystal becomes stable against competing phases at temperatures above 600K. The average structure can be described succinctly as a cut through atomic surfaces in six-dimensional space that reveal specific patterns of preferred chemical occupancy. Atomic surface regions of mixed chemical occupation demonstrate the proliferation of phason fluctuations, which can be observed in real space through the formation, dissolution and reformation of large scale icosahedral motifs -- a picture that is hidden from diffraction refinements due to averaging over the disorder and consequent loss of information concerning occupancy correlations.

cond-mat.mtrl-sci↗

arXiv2019

Proximity-induced superconducting gap in the quantum spin Hall edge state of monolayer WTe$_2$

The quantum spin Hall (QSH) state was recently demonstrated in monolayers of the transition metal dichalcogenide 1T'-WTe$_2$ and is characterized by a band gap in the two-dimensional (2D) interior and helical one-dimensional (1D) edge states. Inducing superconductivity in the helical edge states would result in a 1D topological superconductor, a highly sought-after state of matter. In the present study, we use a novel dry-transfer flip technique to place atomically-thin layers of WTe$_2$ on a van der Waals superconductor, NbSe$_2$. Using scanning tunneling microscopy and spectroscopy (STM/STS), we demonstrate atomically clean surfaces and interfaces and the presence of a proximity-induced superconducting gap in the WTe$_2$ for thicknesses from a monolayer up to 7 crystalline layers. At the edge of the WTe$_2$ monolayer, we show that the superconducting gap coexists with the characteristic spectroscopic signature of the QSH edge state. Taken together, these observations provide conclusive evidence for proximity-induced superconductivity in the QSH edge state in WTe$_2$, a crucial step towards realizing 1D topological superconductivity and Majorana bound states in this van der Waals material platform.

cond-mat.mes-hall↗

arXiv2019

First Principles Study of Electronic Structure and Fermi Surface in Rare-earth Filled Skutterudites RPt4Ge12

Experiments on rare-earth filled skutterudites demonstrate an intriguing array of thermodynamic, transport and superconducting properties, and bring to fore theoretical challenges posed by f-electron systems. First principle calculations based density functional theory and its extensions for strongly correlated systems such as the Hubbard U correction, provide valuable information about electronic structure that can be used to understand experiments. We present a comprehensive study of the electronic structure and Fermi surface of a series of rare earth filled skutterudites, RPt4Ge12 (where R = La, Ce, Pr), aimed at shedding light on: consequences of progressive increase of f-orbital occupancy in the series; the effects of the Hubbard parameter U; the Fermi surfaces, band structures and densities of states. The calculated Fermi surfaces may be relevant to the question of multi-band versus single-band superconductivity. Computed densities of states qualitatively explain the available resonant photoemission spectroscopy experiments, and (together with available specific heat measurements) provide estimates of the effective masses. We also show the existence of pseudogaps in the total density of states which may be relevant for the thermoelectric properties of these systems.

cond-mat.str-el↗

arXiv2018

Band Structure Theory of the BCC to HCP Burgers Distortion

The Burgers distortion is a two-stage transition between body centered cubic (BCC) and hexagonal close-packed (HCP) structures. Refractory metal elements from the Sc and Ti columns of the periodic table (BCC/HCP elements) form BCC structures at high temperatures but transition to HCP at low temperatures via the Burgers distortion. Elements of the V and Cr columns, in contrast, remain BCC at all temperatures. The energy landscape of BCC/HCP elements exhibits an alternating slide instability, while the normal BCC elements remain stable as BCC structures. This instability is verified by the presence of unstable elastic constants and vibrational modes for BCC/HCP elements, while those elastic constants and modes are stable in BCC elements. We show that a pseudogap opening in the density of states at the Fermi level drives the Burgers distortion in BCC/HCP elements, suggesting the transition is of the Jahn-Teller-Peierls type. The pseudogap lies below the Fermi level for regular BCC elements in the V and Cr columns of the periodic table. The wave vector $k_S$ when the gap opens relates to the reciprocal lattice vector G=(1 $\frac{1}{2}$ $\frac{1}{2}$) of the distorted BCC structure as $k_S$=$\frac{1}{2}$G. BCC binary alloys containing both BCC/HCP and BCC elements exhibit a similar instability but stabilize part way through the BCC to HCP transition.

cond-mat.mtrl-sci↗

arXiv2017

First-principles prediction of high-entropy-alloy stability

High entropy alloys (HEAs) are multicomponent compounds whose high configurational entropy allows them to solidify into a single phase, with a simple crystal lattice structure. Some HEA's exhibit desirable properties, such as high specific strength, ductility, and corrosion resistance, while challenging the scientist to make confident predictions in the face of multiple competing phases. We demonstrate phase stability in the multicomponent alloy system of Cr-Mo-Nb-V, for which some of its binary subsystems are subject to phase separation and complex intermetallic-phase formation. Our first-principles calculation of free energy predicts that the configurational entropy stabilizes a single body-centered cubic (BCC) phase from T = 1,700K up to melting, while precipitation of a complex intermetallic is favored at lower temperatures. We form the compound experimentally and confirm that it forms as a single BCC phase from the melt, but that it transforms reversibly at lower temperatures.

cond-mat.mtrl-sci↗

arXiv2017

Phase Diagram of Carbon Nickel Tungsten: Superatom Model

Carbon solubility in face-centered cubic Ni-W alloys and the phase diagram of C-Ni-W are investigated by means of first principle calculations and semi-grand canonical Monte Carlo simulations. With density functional theory (DFT) total energies as fitting data, we build a superatom model for efficient simulation. Multi-histogram analysis is utilized to predict free energies for different compositions and temperatures. By comparing free energies of competing phases, we are able to predict carbon solubility and phase diagrams of C-Ni-W at different temperatures. A simple ideal mixing approximation gives qualitatively similar predictions.

cond-mat.mtrl-sci↗

arXiv2017

Elastic stability and lattice distortion of refractory high entropy alloys

Refractory high entropy alloys containing elements from the Ti, V and Cr columns of the periodic table form body centered cubic (BCC) structures. Elements from the Ti column are noteworthy because they take the BCC structure at high temperature but undergo a shear instability and transform to the hexagonal (HCP) structure at low temperature. We show that the instability of these elements impacts the properties of the HEAs that contain them. In particular, the shear moduli are greatly reduced, causing increased dynamic contributions to lattice distortion. Relatively large size differences between elements of the BCC/HCP column compared with the regular BCC columns create additional static contributions to lattice distortion. These findings are supported by direct evaluation of elastic constants and lattice distortion in four representative HEAs. Comparing moduli of HEAs with those of compositionally averaged pure elements verifies the impact of BCC/HCP elements and allows us to estimate the compositions at which the BCC phases become elastically unstable, predictions that could be useful in material design.

cond-mat.mtrl-sci↗

arXiv2016

Phase Diagram of Boron Carbide With Variable Carbon Composition

Boron carbide exhibits intrinsic substitutional disorder over a broad composition range. The structure consists of 12-atom icosahedra placed at the vertices of a rhombohedral lattice, together with a 3-atom chain along the 3-fold axis. In the high carbon limit, one or two carbons can replace borons on the icosahedra while the chains are primarily of type C-B-C. We fit an interatomic pair interaction model to density functional theory total energies to investigate the substitutional carbon disorder. Monte Carlo simulations with sampling improved by replica exchange and augmented by 2d multiple histogram analysis, predicts three phases. The low temperature, high carbon composition monoclinic Cm "tilted polar" structure disorders through a pair of phase transitions, first via an Ising-like transition to a "bipolar" state with space group C2/m, then via a first order 3-state Potts-like transition to the experimentally observed "nonpolar" \bar{R}3m symmetry.

cond-mat.mtrl-sci↗

arXiv2016

Thickness characterization of atomically-thin WSe$_2$ on epitaxial graphene by low-energy electron reflectivity oscillations

In this work, low-energy electron microscopy is employed to probe structural as well as electronic information in few-layer WSe$_2$ on epitaxial graphene on SiC. The emergence of unoccupied states in the WSe$_2$--graphene heterostructures are studied using spectroscopic low-energy electron reflectivity. Reflectivity minima corresponding to specific WSe$_2$ states that are localized between the monolayers of each vertical heterostructure are shown to reveal the number of layers for each point on the surface. A theory for the origin of these states is developed and utilized to explain the experimentally observed featured in the WSe$_2$ electron reflectivity.

cond-mat.mes-hall↗

arXiv2016

A microscopic continuum model for defect dynamics in metallic glasses

Motivated by results of the topological theory of glasses accounting for geometric frustration, we develop the simplest possible continuum mechanical model of defect dynamics in metallic glasses that accounts for topological, energetic, and kinetic ideas. The model is aimed towards the development of a microscopic understanding of the plasticity of such materials. We discuss the expected predictive capabilities of the model vis-a-vis some observed physical behaviors of metallic glasses.

cond-mat.mtrl-sci↗