arXiv subjects

M. Widom

Publications and source records attributed to M. Widom.

At least 19 recordsLinked to original sources

arXiv2024

Simulated structure and thermodynamics of decagonal Al-Co-Cu quasicrystals

Atomic structures of Al-Co-Cu decagonal quasicrystals (QCs) are investigated using empirical oscillating pair potentials (EOPP) in molecular dynamic (MD) simulations that we enhance by Monte Carlo (MC) swapping of chemical species and replica exchange. Predicted structures exhibit planar decagonal tilin g patterns and are periodic along the perpendicular direction. We then recalculate the energies of promising structures using first-principles density functional theory (DFT), along with energies of competing phases. We find that our $\tau$-inflated sequence of QC approximants are energetically unstable a t low temperature by at least 3 meV/atom. Extending our study to finite temperatures by calculating harmonic vibrational entropy, as well as anharmonic contributions that include chemical species swaps and tile flips, our results suggest that the quasicrystal phase is entropically stabilized at temperatur es in the range 600-800K and above. It decomposes into ordinary (though complex) crystal phases at low temperatures, including a partially disordered B2-type phase. We discuss the influence of density and composition on QC phase stability; we compare the structural differences between Co-rich and Cu-rich quasicrystals; and we analyze the role of entropy in stabilizing the quasicrystal, concluding with a discussion of the possible existence of "high entropy" quasicrystals.

cond-mat.mtrl-sci↗

arXiv2018

Information entropy of liquid metals

Correlations reduce the configurational entropies of liquids below their ideal gas limits. By means of first principles molecular dynamics simulations, we obtain accurate pair correlation functions of liquid metals, then subtract the mutual information content of these correlations from the ideal gas entropies to predict the absolute entropies over a broad range of temperatures. We apply this method to liquid aluminum and copper and demonstrate good agreement with experimental measurements, then we apply it to predict the entropy of a liquid aluminum-copper alloy. Corrections due to electronic entropy and many-body correlations are discussed.

cond-mat.stat-mech↗

arXiv2017

Characterization of hexagonal boron nitride layers on nickel surfaces by low-energy electron microscopy

The thickness and interfacial geometry of hexagonal boron nitride (hBN) films grown by chemical vapor deposition on polycrystalline nickel foils is studied using low-energy electron microscopy (LEEM). The reflectivity of the electrons, measured over an energy range of 0 - 20 eV, reveals distinct minima and maxima. The measured data is compared with simulations based on a first-principles description of the electronic structure of the material. From this comparison, the number of hBN layers and the separation between the lowest hBN layer and the nickel surface is deduced. The coupling of interlayer states of the hBN to both image-potential and Shockley-type surface states of the nickel is discussed, and the dependence of the reflectivity spectra on the surface orientation of nickel grains is examined.

cond-mat.mes-hall↗

arXiv2017

Random tilings of high symmetry: II. Boundary conditions and numerical studies

We perform numerical studies including Monte Carlo simulations of high rotational symmetry random tilings. For computational convenience, our tilings obey fixed boundary conditions in regular polygons. Such tilings are put in correspondence with algorithms for sorting lists in computer science. We obtain statistics on path counting and vertex coordination which compare well with predictions of mean-field theory and allow estimation of the configurational entropy, which tends to the value 0.568 per vertex in the limit of continuous symmetry. Tilings with phason strain appear to share the same entropy as unstrained tilings, as predicted by mean-field theory. We consider the thermodynamic limit and argue that the limiting fixed boundary entropy equals the limiting free boundary entropy, although these differ for finite rotational symmetry.

cond-mat.stat-mech↗

arXiv2016

Frequency estimate for multicomponent crystalline compounds

Among crystal structures of N-component metal alloys, far fewer examples are known with N>=4 than with N=2 or 3, in apparent contradiction to the exponentially growing number of possible combinations of elements. Two effects contribute to this shortfall. Since the N-component composition space resides within a d-dimensional simplex with d=N-1, the vanishing volume in high dimensions reduces the distinct N-component compositions. Additionally, the increasing surface area makes it more probable that stable structures reside on the surface of the simplex (containing fewer than N components) as opposed to its interior. Despite their rarity, we propose that the actual number of N=4- and 5-component alloys greatly exceeds the number that are currently known. Specific estimates are developed through application of the empirical Miedema enthalpy model.

cond-mat.mtrl-sci↗

arXiv2015

Entropy and diffuse scattering: comparison of NbTiVZr and CrMoNbV

The chemical disorder intrinsic to high entropy alloys inevitably creates diffuse scattering in their x-ray or neutron diffraction patterns. Through first principles hybrid Monte Carlo/molecular dynamics simulations of two BCC high entropy alloy forming compounds, CrMoNbV and NbTiVZr, we identify the contributions of chemical disorder, atomic size and thermal fluctuations to the diffuse scattering. As a side benefit, we evaluate the reduction in entropy due to pair correlations within the framework of the cluster variation method. Finally, we note that the preference of Ti and Zr for HCP structures at low temperature leads to a mechanical instability reducing the local BCC character of NbTiVZr, while preserving global BCC symmetry.

cond-mat.mtrl-sci↗

arXiv2014

Inelastic Effects in Low-Energy Electron Reflectivity of Two-dimensional Materials

A simple method is proposed for inclusion of inelastic effects (electron absorption) in computations of low-energy electron reflectivity (LEER) spectra. The theoretical spectra are formulated by matching of electron wavefunctions obtained from first-principles computations in a repeated vacuum-slab-vacuum geometry. Inelastic effects are included by allowing these states to decay in time in accordance with an imaginary term in the potential of the slab, and by mixing of the slab states in accordance with the same type of distribution as occurs in a free-electron model. LEER spectra are computed for various two-dimensional materials, including free-standing multilayer graphene, graphene on copper substrates, and hexagonal boron nitride (h-BN) on cobalt substrates.

cond-mat.mes-hall↗

arXiv2014

Phase Transitions of Boron Carbide: Pair Interaction Model of High Carbon Limit

Boron Carbide exhibits a broad composition range, implying a degree of intrinsic substitutional disorder. While the observed phase has rhombohedral symmetry (space group R3(bar)m), the enthalpy minimizing structure has lower, monoclinic, symmetry (space group Cm). The crystallographic primitive cell consists of a 12-atom icosahedron placed at the vertex of a rhombohedral lattice, together with a 3-atom chain along the 3-fold axis. In the limit of high carbon content, approaching 20% carbon, the icosahedra are usually of type B11Cp, where the p indicates the carbon resides on a polar site, while the chains are of type C-B-C. We establish an atomic interaction model for this composition limit, fit to density functional theory total energies, that allows us to investigate the substitutional disorder using Monte Carlo simulations augmented by multiple histogram analysis. We find that the low temperature monoclinic Cm structure disorders through a pair of phase transitions, first via a 3-state Potts-like transition to space group R3m, then via an Ising-like transition to the experimentally observed R3(bar)m symmetry. The R3m and Cm phases are electrically polarized, while the high temperature R3(bar)m phase is nonpolar.

cond-mat.mtrl-sci↗

arXiv2013

Low-Energy Electron Reflectivity of Graphene on Copper and other Substrates

The reflectivity of low energy electrons from graphene on copper substrates is studied both experimentally and theoretically. Well-known oscillations in the reflectivity of electrons with energies 0 - 8 eV above the vacuum level are observed in the experiment. These oscillations are reproduced in theory, based on a first-principles density functional description of interlayer states forming for various thicknesses of multilayer graphene. It is demonstrated that n layers of graphene produce a regular series of n-1 minima in the reflectance spectra, together with a possible additional minimum associated with an interlayer state forming between the graphene and the substrate. Both (111) and (001) orientations of the copper substrates are studied. Similarities in their reflectivity spectra arise from the interlayer states, whereas differences are found because of the different Cu band structures along those orientations. Results for graphene on other substrates, including Pt(111) and Ir(111), are also discussed.

cond-mat.mes-hall↗

arXiv2013

Low-energy Electron Reflectivity from Graphene

Low-energy reflectivity of electrons from single- and multi-layer graphene is examined both theoretically and experimentally. A series of minima in the reflectivity over the energy range of 0 - 8 eV are found, with the number of minima depending on the number of graphene layers. Using first-principles computations, it is demonstrated that a free standing n-layer graphene slab produces n-1 reflectivity minima. This same result is also found experimentally for graphene supported on SiO2. For graphene bonded onto other substrates it is argued that a similar series of reflectivity minima is expected, although in certain cases an additional minimum occurs, at an energy that depends on the graphene-substrate separation and the effective potential in that space.

cond-mat.mes-hall↗

arXiv2013

Prediction of stable insulating intermetallic compounds

We explore the stability of structure exhibiting hybridization gaps across a broad range of binary and ternary intermetallic compositions by means of band structure and total energy calculations. This search reveals previously unknown metal-based insulators, some with large gaps exceeding 1 eV, such as Al2Fe and Al4IrRe. We confirm large gaps using a hybrid density functional including exact exchange, and predict a gap of 2.2 eV for AlMnSi in the Pearson type tP6 structure, which is a chemically ordered ternary variant of the prototype MoSi2 (Pearson type tI6) structure.

cond-mat.mtrl-sci↗

arXiv2012

Low-energy Electron Reflectivity from Graphene: First-Principles Computations and Approximate Models

A computational method is developed whereby the reflectivity of low-energy electrons from a surface can be obtained from a first-principles solution of the electronic structure of the system. The method is applied to multilayer graphene. Two bands of reflectivity minima are found, one at 0 - 8 eV and the other at 14 - 22 eV above the vacuum level. For a free-standing slab with n layers of graphene, each band contains n-1 zeroes in the reflectivity. Two additional image-potential type states form at the ends of the graphene slab, with energies just below the vacuum level, hence producing a total of 2n states. A tight-binding model is developed, with basis functions localized in the spaces between the graphene planes (and at the ends of the slab). The spectrum of states produced by the tight-binding model is found to be in good agreement with the zeros of reflectivity (i.e. transmission resonances) of the first-principles results.

cond-mat.mes-hall↗

arXiv2011

Structure and stability of Al$_2$Fe

We employ first principles total energy and phonon calculations to address the structure and stability of Al$_2$Fe. This structure, which is reported as stable in the assessed Al-Fe phase diagram, is distinguished by an unusually low triclinic symmetry. The initial crystallographic structure determination additionally featured an unusual hole large enough to accommodate an additional atom. Our calculations indicate the hole must be filled, but predict the triclinic structure is unstable relative to a simpler structure based on the prototype MoSi$_2$. This MoSi$_2$ structure is interesting because it is predicted to be nonmagnetic, electrically insulating and high density, while the triclinic structure is magnetic, metallic and low density. We reconcile this seeming contradiction by demonstrating a high vibrational entropy that explains why the triclinic structure is stable at high temperatures. Finally, we note that Al$_5$Fe$_2$ poses a similar problem of unexplained stability.

cond-mat.mtrl-sci↗

arXiv2008

Liquid-liquid transition in supercooled silicon determined by first-principles simulation

First principles molecular dynamics simulations reveal a liquid-liquid phase transition in supercooled elemental silicon. Two phases coexist below $T_c\approx 1232K$. The low density phase is nearly tetra-coordinated, with a pseudogap at the Fermi surface, while the high density phase is more highly coordinated and metallic in nature. The transition is observed through the formation of van der Waals loops in pressure-volume isotherms below $T_c$.

cond-mat.mtrl-sci↗

arXiv2008

Empirical oscillating potentials for alloys from ab-initio fits

By fitting to a database of ab-initio forces and energies, we can extract pair potentials for alloys, with a simple six-parameter analytic form including Friedel oscillations, which give a remarkably faithful account of many complex intermetallic compounds. As examples we show results for (crystal or quasicrystal) structure prediction and phonon spectrum for three systems: Fe--B, Al--Mg--Zn, and Al--Cu--Fe.

cond-mat.mtrl-sci↗

arXiv2007

Symmetry-broken crystal structure of elemental boron at low temperature

The crystal structure of boron is unique among chemical elements, highly complex, and imperfectly known. Experimentalists report the beta-rhombohedral (black) form is stable over all temperatures from absolute zero to melting. However, early calculations found its energy to be greater than the energy of the alpha-rhombohedral (red) form, implying beta cannot be stable at low temperatures. Furthermore, beta exhibits partially occupied sites, seemingly in conflict with the thermodynamic requirement that entropy vanish at low temperature. Using electronic density functional theory methods and an extensive search of the configuration space we find a unique, energy minimizing pattern of occupied and vacant sites that can be stable at low temperatures but that breaks the beta-rhombohedral symmetry. Even lower energies occur within larger unit cells. Alternative configurations lie nearby in energy, allowing the entropy of partial occupancy to stabilize the beta-rhombohedral structure through a phase transition at moderate temperature.

cond-mat.mtrl-sci↗

arXiv2007

Soft modes near the buckling transition of icosahedral shells

Icosahedral shells undergo a buckling transition as the ratio of Young's modulus to bending stiffness increases. Strong bending stiffness favors smooth, nearly spherical shapes, while weak bending stiffness leads to a sharply faceted icosahedral shape. Based on the phonon spectrum of a simplified mass-and-spring model of the shell, we interpret the transition from smooth to faceted as a soft-mode transition. In contrast to the case of a disclinated planar network where the transition is sharply defined, the mean curvature of the sphere smooths the transitition. We define elastic susceptibilities as the response to forces applied at vertices, edges and faces of an icosahedron. At the soft-mode transition the vertex susceptibility is the largest, but as the shell becomes more faceted the edge and face susceptibilities greatly exceed the vertex susceptibility. Limiting behaviors of the susceptibilities are analyzed and related to the ridge-scaling behavior of elastic sheets. Our results apply to virus capsids, liposomes with crystalline order and other shell-like structures with icosahedral symmetry.

physics.bio-ph↗

arXiv2007

Geometrical Frustration in Liquid Fe and Fe-Based Metallic Glass

We investigate short rane order in liquid and supercooled liquid Fe and Fe-based metallic glass using ab-initio simulation methods. We analyze the data to quantify the degree of local icosahedral and polytetrahedral order and to understand the role of alloying in controlling the degree of geometric frustration . Comparing elemental Fe to Cu we find that the degree of icosahedral order is greater in Fe than in Cu, possibly because icosahedral disclination line defects are more easily incorporated into BCC environments than FCC. In Fe-based metallic glass-forming alloys (FeB and FeZrB) we find that introducing small concentrations of small B atoms and large Zr atoms controls the frustration of local icosahedral order.

cond-mat.mtrl-sci↗