Showing 1–50 of 100 results for author: Widom, M

First-Principles Investigation of the Al-V Phase Diagram

Authors: AKM Sadman Mahmud, Hassan Albuhairan, Marek Mihalkovic, Michael Widom

Abstract: The Al-V alloy system contains a number of phases including several with complex structures and at least two exhibiting sites of partial occupation. Through electronic density functional theory-based total energy calculations combined with methods of statistical mechanics, we examine the relative stability of phases at finite temperatures. We construct composition-continuous free energy models for… ▽ More The Al-V alloy system contains a number of phases including several with complex structures and at least two exhibiting sites of partial occupation. Through electronic density functional theory-based total energy calculations combined with methods of statistical mechanics, we examine the relative stability of phases at finite temperatures. We construct composition-continuous free energy models for the V-rich solid solution and for one of the complex intermetallic phases. In the V-rich region, we identify three ground states that transform to the solid solution at elevated temperatures. We also suggest that \phase{Al}{V_3} takes the Al15 structure as an intermediate-temperature phase stabilized by anharmonic vibrational free energy. △ Less

Submitted 7 July, 2026; originally announced July 2026.

Reversible non-equilibrium phase transformation in amorphous germanium

Authors: Yang Huang, Marek Mihalkovič, Michael Widom

Abstract: First principles molecular dynamics simulations of germanium reveal a reversible liquid-glass transition below the equilibrium melting point with a wide hysteresis loop. Direct calculation of the liquid and amorphous state free energies, enabled by absolute entropy calculations, verify that the transition is first order in character between two metastable phases. These results lend credence to mod… ▽ More First principles molecular dynamics simulations of germanium reveal a reversible liquid-glass transition below the equilibrium melting point with a wide hysteresis loop. Direct calculation of the liquid and amorphous state free energies, enabled by absolute entropy calculations, verify that the transition is first order in character between two metastable phases. These results lend credence to models of explosive recrystallization from amorphous Ge thin films, through a metastable liquid state and finally reaching the low temperature crystalline structure. △ Less

Submitted 22 June, 2026; originally announced June 2026.

Computational Design of Ductile Additively Manufactured Tungsten-Based Refractory Alloys

Authors: Kareem Abdelmaqsoud, Daniel Sinclair, Venkata Satya Surya Amaranth Karra, S. Mohadeseh Taheri-Mousavi, Michael Widom, Bryan A. Webler, John R. Kitchin

Abstract: Tungsten exhibits exceptional temperature and radiation resistance, making it well-suited for applications in extreme environments such as nuclear fusion reactors. Additive manufacturing offers geometrical design freedom and rapid prototyping capabilities for these applications, provided the intrinsic brittleness and low printability of tungsten can be overcome. Designing tungsten alloys with impr… ▽ More Tungsten exhibits exceptional temperature and radiation resistance, making it well-suited for applications in extreme environments such as nuclear fusion reactors. Additive manufacturing offers geometrical design freedom and rapid prototyping capabilities for these applications, provided the intrinsic brittleness and low printability of tungsten can be overcome. Designing tungsten alloys with improved ductility, and thus printability in additive manufacturing, can be accelerated using a computationally derived performance predictor to screen out brittle compositions. Calculations of the Pugh ratio using density functional theory may serve this purpose, given its correlation with ductility. This process can be made more efficient through the use of machine learning interatomic potentials to accelerate density functional theory calculations. Here, we demonstrate that machine learning interatomic potentials can effectively identify optimal alloy compositions in the W-Ta-Nb system along the melting point-Pugh ratio Pareto front. The trend in Pugh ratio as a function of tungsten fraction is explained in terms of the electronic density of states at the Fermi level. Experimental validation reveals a strong correlation between the computed Pugh ratio and the observed crack fractions in additively manufactured alloys. Notably, the two alloys predicted to have the highest Pugh ratio values, W20Ta70Nb10 and W30Ta60Nb10, exhibit no intergranular microcracking in experiments. △ Less

Submitted 16 January, 2026; originally announced January 2026.

Electronic structure and elasticity of the Ta-W solid solution

Authors: Kareem Abdelmaqsoud, John R. Kitchin, Michael Widom

Abstract: The brittleness or ductility of metals has long been attributed to their elastic constants, with high Poisson ratio, or equivalently high Pugh ratio, favoring greater ductility. Growing evidence links ductility with their electronic structure. Consequently, it is desirable to understand how the electronic structure affects the elastic constants. Here, we examine the Ta-W binary alloy system, which… ▽ More The brittleness or ductility of metals has long been attributed to their elastic constants, with high Poisson ratio, or equivalently high Pugh ratio, favoring greater ductility. Growing evidence links ductility with their electronic structure. Consequently, it is desirable to understand how the electronic structure affects the elastic constants. Here, we examine the Ta-W binary alloy system, which evolves from ductile character at Ta-rich compositions to brittleness at high W. We show that a change in slope of the composition-dependent shear modulus near the equiatomic composition coincides with an abrupt change in the Fermi level density of states. We relate the behaviors of the elastic constants to the characters of occupied electronic orbitals close to the Fermi level. Finally, we consider additional alloy systems from groups V and VI and show that qualitatively similar behavior occurs more broadly. △ Less

Submitted 14 January, 2026; originally announced January 2026.

First-Principles Thermodynamics of Al$_{10}$V: An Analytical Treatment of Localized Anharmonic Modes

Authors: Hassan Y. Albuhairan, Marek Mihalkovič, Michael Widom

Abstract: Many complex intermetallic structures possess cage-like environments that can host additional guest atoms. In Al$_{10}$V, these atoms give rise to low-frequency, localized vibrations (Einstein modes) that dominate the thermodynamic response at low temperature. They become imaginary under volume expansion as temperature rises, invalidating the harmonic approximation. We develop a framework to incor… ▽ More Many complex intermetallic structures possess cage-like environments that can host additional guest atoms. In Al$_{10}$V, these atoms give rise to low-frequency, localized vibrations (Einstein modes) that dominate the thermodynamic response at low temperature. They become imaginary under volume expansion as temperature rises, invalidating the harmonic approximation. We develop a framework to incorporate these strongly anharmonic vibrational modes into first-principles thermodynamic calculations. By explicitly modeling the cage potential and solving the associated Schrödinger equation numerically, we compute the full anharmonic free energy contribution and demonstrate its impact on thermodynamic phase stability. Our results reproduce key experimental signatures, including the anomalous rise in the thermal expansion coefficient and specific heat at low temperatures, and reveal that the presence of guest atoms is essential to stabilizing the Al$_{10}$V phase at elevated temperatures. △ Less

Submitted 18 June, 2025; originally announced June 2025.

X-Ray and neutron diffraction patterns of the AlCrTiV high entropy alloy and quaternary Heusler structures

Authors: Nedjma Kalliney, Michael Widom

Abstract: The quaternary alloy AlCrTiV has been proposed as both a lightweight high entropy alloy and also a functional spin filter material based on the Heusler structure. Experimental investigations to-date, based on X-ray diffraction, offer conflicting interpretations of the structure. Here we simulate diffraction patterns of the various proposed structures to show that neutron diffraction, in particular… ▽ More The quaternary alloy AlCrTiV has been proposed as both a lightweight high entropy alloy and also a functional spin filter material based on the Heusler structure. Experimental investigations to-date, based on X-ray diffraction, offer conflicting interpretations of the structure. Here we simulate diffraction patterns of the various proposed structures to show that neutron diffraction, in particular, can reveal the nature of long-range chemical order and discriminate among distributions of the refractory transition metals. Magnetic contributions to the neutron diffraction are also discussed. △ Less

Submitted 12 May, 2025; originally announced May 2025.

First principles investigation of phase stability in the B-Pt alloy system

Authors: Michael Widom

Abstract: The B-Pt alloy system contains several Pt-rich phases exhibiting complex structures, many with partial site occupation. It also exhibits a deep (nearly 1000 degrees C) eutectic. We evaluate the ab-initio total energies of the crystalline solids to clarify the identity and character of the phases. Our work identifies inconsistencies in materials databases such as the Inorganic Crystallographic Stru… ▽ More The B-Pt alloy system contains several Pt-rich phases exhibiting complex structures, many with partial site occupation. It also exhibits a deep (nearly 1000 degrees C) eutectic. We evaluate the ab-initio total energies of the crystalline solids to clarify the identity and character of the phases. Our work identifies inconsistencies in materials databases such as the Inorganic Crystallographic Structure Database and the ASM Phase Diagram Database, but our total energy calculations allow us to match up experimentally reported stable phases with specific structures. High temperature Gibbs free energy calculations in the liquid and solid states at the composition Pt$_2$B reveal that the depth of the eutectic arises from the low energy and high entropy of the liquid state. △ Less

Submitted 15 November, 2024; originally announced November 2024.

Comments: Proceedings of ISBB 2024

First-principles study of the order-disorder transition in the AlCrTiV high entropy alloy

Authors: Michael Widom

Abstract: The AlCrTiV high entropy alloy undergoes an order-disorder transition from body centered cubic (Strukturbericht A2) at high temperatures to the CsCl structure (B2) at intermediate temperatures. We model this transition using first principles Monte Carlo/molecular dynamics simulations. Simulation results yield the temperature-dependent energy, entropy, heat capacity, occupancy fluctuations, and dif… ▽ More The AlCrTiV high entropy alloy undergoes an order-disorder transition from body centered cubic (Strukturbericht A2) at high temperatures to the CsCl structure (B2) at intermediate temperatures. We model this transition using first principles Monte Carlo/molecular dynamics simulations. Simulation results yield the temperature-dependent energy, entropy, heat capacity, occupancy fluctuations, and diffraction patterns. The contribution of chemical disorder to the entropy is calculated on the basis of point and pair cluster frequencies. The simulated structures exhibit compensated ferrimagnetism, and the Fermi level lies in a pseudogap. Sensitivity of structure and magnetism to the exchange-correlation functional is discussed, and neutron diffraction experiments are proposed to help resolve the true chemical order. △ Less

Submitted 30 June, 2024; originally announced July 2024.

Vibrational Entropy and Free Energy of Solid Lithium using Covariance of Atomic Displacements Enabled by Machine Learning

Authors: Mgcini Keith Phuthi, Yang Huang, Michael Widom, Venkatasubramanian Viswanathan

Abstract: Vibrational properties of solids are key to determining stability, response and functionality. However, they are challenging to computationally predict at Ab-Initio accuracy, even for elemental systems. Ab-Initio methods for modeling atomic interactions are limited in the system sizes and simulation times that can be achieved. Due to these limitations, Machine Learning Interatomic Potentials (MLIP… ▽ More Vibrational properties of solids are key to determining stability, response and functionality. However, they are challenging to computationally predict at Ab-Initio accuracy, even for elemental systems. Ab-Initio methods for modeling atomic interactions are limited in the system sizes and simulation times that can be achieved. Due to these limitations, Machine Learning Interatomic Potentials (MLIPs) are gaining popularity and success as a faster, more scalable approach for modeling atomic interactions, potentially at Ab-Initio accuracy. Even with faster potentials, methodologies for predicting entropy, free energy and vibrational properties vary in accuracy, cost and difficulty to implement. Using the Covariance of Atomic Displacements (CAD) to predict entropy, free energy and finite-temperature phonon dispersions is a promising approach but thorough benchmarking has been hampered by the cost of Ab-Initio methods for sampling. In this work, we use a MLIP and the CAD to characterize the convergence of the predicted properties and determine optimal sampling strategies. We focus on solid lithium at zero pressure, showing that the MLIP-CAD approach reproduces experimental entropy, phonon dispersions and the martensitic transition while also comparing to more established methods. △ Less

Submitted 18 June, 2024; originally announced June 2024.

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

Authors: Y. Huang, M. Widom, M. Mihalkovič

Abstract: 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… ▽ More 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 $τ$-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. △ Less

Submitted 22 April, 2024; originally announced April 2024.

First principles evaluation of phase stability in the In-Sn binary system

Authors: Michael Widom

Abstract: The In-Sn binary alloy system exhibits several unusual features that challenge crystallographic and thermodynamic expectations. We combine first principles total energy calculation with simple thermodynamic modeling to address two key points. First, we evaluate energies along the Bain path to interpret the discontinuous transition between the phases $α$-In (Pearson type tI2) and $β$--In$_3$Sn (als… ▽ More The In-Sn binary alloy system exhibits several unusual features that challenge crystallographic and thermodynamic expectations. We combine first principles total energy calculation with simple thermodynamic modeling to address two key points. First, we evaluate energies along the Bain path to interpret the discontinuous transition between the phases $α$-In (Pearson type tI2) and $β$--In$_3$Sn (also Pearson type tI2) that are identical in symmetry. Second, we demonstrate that the solid solution phases $β$-In$_3$Sn and $γ$-InSn$_4$ (Pearson type hP1) exist at high temperatures only, and they exhibit eutectoid decompositions at low temperatures. △ Less

Submitted 5 February, 2024; originally announced February 2024.

Entropy approximations for simple fluids

Authors: Yang Huang, Michael Widom

Abstract: Liquid state entropy formulas based on configurational probability distributions are examined for Lennard-Jones fluids across a range temperatures and densities. These formulas are based on expansions of the entropy in series of $n$-body distribution functions. We focus on two special cases. One, which we term the ``perfect gas'' series, starts with the entropy of an ideal gas; the other, which we… ▽ More Liquid state entropy formulas based on configurational probability distributions are examined for Lennard-Jones fluids across a range temperatures and densities. These formulas are based on expansions of the entropy in series of $n$-body distribution functions. We focus on two special cases. One, which we term the ``perfect gas'' series, starts with the entropy of an ideal gas; the other, which we term the ``dense liquid series'' removes a many-body contribution from the ideal gas entropy and reallocates it among the subsequent $n$-body terms. We show that the perfect gas series is most accurate at low density, while the dense liquid series is most accurate at high density. We propose empirical interpolation methods that are capable of connecting the two series and giving consistent predictions in most situations. △ Less

Submitted 16 December, 2023; originally announced December 2023.

Integrated Design of Aluminum-Containing High-entropy Refractory B2 Alloys with Synergy of High Strength and Ductility

Authors: Jie Qi, Xuesong Fan, Diego Ibarra Hoyos, Michael Widom, Peter K. Liaw, Joseph Poon

Abstract: Refractory high-entropy alloys, RHEAs, are promising high-temperature structural materials. Their large compositional space poses great design challenges for phase control and high strength-ductility synergy. The present research pioneers using integrated high-throughput machine learning with Monte Carlo simulations to effectively navigate phase-selection and mechanical-properties predictions, dev… ▽ More Refractory high-entropy alloys, RHEAs, are promising high-temperature structural materials. Their large compositional space poses great design challenges for phase control and high strength-ductility synergy. The present research pioneers using integrated high-throughput machine learning with Monte Carlo simulations to effectively navigate phase-selection and mechanical-properties predictions, developing aluminum-containing RHEAs in single-phase ordered B2 alloys demonstrating both high strength and ductility. These aluminum-containing RHEAs achieve remarkable mechanical properties, including compressive yield strengths up to 1.6 GPa, fracture strains exceeding 50 percent, and significant high-temperature strength retention. They also demonstrate a tensile yield strength of 1.1 GPa with a tension ductility of 6.3 percent. Besides, we identify a valence-electron-count domain for alloy brittleness with the explanation from density-functional theory and provide crucial insights into elements' influence on atomic ordering and mechanical performance. The work sets forth a strategic blueprint for high-throughput alloy design and reveals fundamental principles that govern the mechanical properties of advanced structural alloys. △ Less

Submitted 7 December, 2023; originally announced December 2023.

Ab-initio tensile tests applied to BCC refractory alloys

Authors: Vishnu Raghuraman, Saro San, Michael C. Gao, Michael Widom

Abstract: Refractory metals exhibit high strength at high temperature, but often lack ductility. Multiprinciple element alloys such as high entropy alloys offer the potential to improve ductility while maintaining strength, but we don't know $a-priori$ what compositions will be suitable. A number of measures have been proposed to predict the ductility of metals, notably the Pugh ratio, the Rice-Thomson D-pa… ▽ More Refractory metals exhibit high strength at high temperature, but often lack ductility. Multiprinciple element alloys such as high entropy alloys offer the potential to improve ductility while maintaining strength, but we don't know $a-priori$ what compositions will be suitable. A number of measures have been proposed to predict the ductility of metals, notably the Pugh ratio, the Rice-Thomson D-parameter, among others. Here we examine direct $ab-initio$ simulation of deformation under tensile strain, and we apply this to a variety of Nb- and Mo-based binary alloys and to several quaternary alloy systems. Our results exhibit peak stresses for elastic deformation, beyond which defects such as lattice slip, stacking faults, transformation, and twinning, relieve the stress. The peak stress grows strongly with increasing valence electron count. Correlations are examined among several physical properties, including the above-mentioned ductility parameters. △ Less

Submitted 5 December, 2023; v1 submitted 29 November, 2023; originally announced November 2023.

Comments: 22 pages, 13 figures, accepted for publication in Physical Review Materials

First principles residual resistivity using locally self-consistent multiple scattering method

Authors: Vishnu Raghuraman, Markus Eisenbach, Michael Widom, Yang Wang

Abstract: The locally self-consistent multiple scattering (LSMS) method can perform efficient first-principles calculations of systems with large number of atoms. In this work, we combine the Kubo-Greenwood equation with LSMS, enabling us to calculate first-principles residual resistivity of large systems. This has been implemented in the open-source code lsms. We apply this method to selected pure elements… ▽ More The locally self-consistent multiple scattering (LSMS) method can perform efficient first-principles calculations of systems with large number of atoms. In this work, we combine the Kubo-Greenwood equation with LSMS, enabling us to calculate first-principles residual resistivity of large systems. This has been implemented in the open-source code lsms. We apply this method to selected pure elements and binary random alloys. The results compare well with experiment, and with values obtained from a first-principles effective medium technique (KKR-CPA). We discuss future applications of this method to complex systems where other methods are not applicable. △ Less

Submitted 20 November, 2023; originally announced November 2023.

Comments: 16 pages, 5 figures

Quasicrystal structure prediction: A review

Authors: Michael Widom, Marek Mihalkovic

Abstract: Predicting quasicrystal structures is a multifaceted problem that can involve predicting a previously unknown phase, predicting the structure of an experimentally observed phase, or predicting the thermodynamic stability of a given structure. We survey the history and current state of these prediction efforts with a focus on methods that have improved our understanding of the structure and stabili… ▽ More Predicting quasicrystal structures is a multifaceted problem that can involve predicting a previously unknown phase, predicting the structure of an experimentally observed phase, or predicting the thermodynamic stability of a given structure. We survey the history and current state of these prediction efforts with a focus on methods that have improved our understanding of the structure and stability of known metallic quasicrystal phases. Advances in the structural modeling of quasicrystals, along with first principles total energy calculation and statistical mechanical methods that enable the calculation of quasicrystal thermodynamic stability, are illustrated by means of cited examples of recent work. △ Less

Submitted 17 August, 2023; originally announced August 2023.

Formation enthalpies of Al-Mn-Pd and the structure of the $i$-AlMnPd quasicrystal

Authors: Marek Mihalkovic, Michael Widom

Abstract: This paper reports formation enthalpies of phases in the Al-Mn-Pd ternary alloy system as calculated from first principles using electronic density functional theory. We consider all crystal structures as reported in the assessed phase diagrams of the ternary and its binary alloy subsystems (Al-Mn, Al-Pd, and Mn-Pd), as well as additional reported or hypothetical structures. Icosahedral and decago… ▽ More This paper reports formation enthalpies of phases in the Al-Mn-Pd ternary alloy system as calculated from first principles using electronic density functional theory. We consider all crystal structures as reported in the assessed phase diagrams of the ternary and its binary alloy subsystems (Al-Mn, Al-Pd, and Mn-Pd), as well as additional reported or hypothetical structures. Icosahedral and decagonal quasicrystalline approximants are among the structures that we predict to be stable, or nearly so. Our results suggest the need for careful experimental reexamination of phase stability in each of the alloy systems, in tandem with further efforts to refine crystallographic and ab-initio structures. △ Less

Submitted 24 February, 2023; v1 submitted 23 February, 2023; originally announced February 2023.

Interaction models and configurational entropies of binary MoTa and the MoNbTaW high entropy alloy

Authors: Andrew D. Kim, Michael Widom

Abstract: We introduce a simplified method to model the interatomic interactions of high entropy alloys based on a lookup table of cluster energies. These interactions are employed in replica exchange Monte Carlo simulations with histogram analysis to obtain thermodynamic properties across a broad temperature range. Kikuchi's Cluster Variation Method entropy formalism and high temperature series expansions… ▽ More We introduce a simplified method to model the interatomic interactions of high entropy alloys based on a lookup table of cluster energies. These interactions are employed in replica exchange Monte Carlo simulations with histogram analysis to obtain thermodynamic properties across a broad temperature range. Kikuchi's Cluster Variation Method entropy formalism and high temperature series expansions are applied to directly calculate entropy from statistics on short- and long-range chemical order, and we discuss the convergence of the entropy as clusters of differing size are included. △ Less

Submitted 5 December, 2022; originally announced December 2022.

Analysis of ab-initio total energies obtained by different DFT implementations

Authors: Vishnu Raghuraman, Yang Wang, Michael Widom

Abstract: Ab-initio crystal structure prediction depends on accurate calculation of the energies of competing structures. Many DFT codes are available that utilize different approaches to solve the Kohn-Sham equation. We evaluate the consistency of three software packages (WIEN2k, VASP and MuST) that utilize three different methods (FL-APW, plane-wave pseudopotential and the KKR-Green's Function methods) by… ▽ More Ab-initio crystal structure prediction depends on accurate calculation of the energies of competing structures. Many DFT codes are available that utilize different approaches to solve the Kohn-Sham equation. We evaluate the consistency of three software packages (WIEN2k, VASP and MuST) that utilize three different methods (FL-APW, plane-wave pseudopotential and the KKR-Green's Function methods) by comparing the relative total energies obtained for a set of BCC and FCC binary metallic alloys. We focus on the impact of choices such as muffin-tin $vs.$ full-potential, angular momentum cutoff and other important KKR parameters. Different alloy systems prove more or less sensitive to these choices, and we explain the differences through study of the angular variation of their potentials. Our results can provide guidance in the application of KKR as a total energy method for structure prediction. △ Less

Submitted 18 October, 2022; originally announced October 2022.

Comments: 18 pages, 9 figures

Vibrational entropy of crystalline solids from covariance of atomic displacements

Authors: Yang Huang, Michael Widom

Abstract: 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 $\ln{ρ_N}$. A… ▽ More 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. △ Less

Submitted 25 March, 2022; originally announced March 2022.

Nonlinear deformation and elasticity of BCC refractory metals and alloys

Authors: Vishnu Raghuraman, Michael Widom, Michael C. Gao

Abstract: 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 to… ▽ More 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. △ Less

Submitted 21 April, 2022; v1 submitted 2 February, 2022; originally announced February 2022.

Comments: 31 pages, 17 figures, 1 table, accepted to Physical Review Materials

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

Authors: Vishnu Raghuraman, Yang Wang, Michael Widom

Abstract: 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… ▽ More 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. △ Less

Submitted 26 August, 2021; originally announced August 2021.

Comments: 18 pages, 9 figures (not including Supplementary Material). The article has been submitted to Applied Physics Letters

Journal ref: Appl. Phys. Lett. 119, 121903 (2021)

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

Authors: Yang Huang, Michael Widom, Michael C. Gao

Abstract: 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… ▽ More 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. △ Less

Submitted 18 May, 2021; originally announced May 2021.

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

Authors: Francesco Maresca, Chanho Lee, Rui Feng, Yi Chou, Tamas Ungar, Michael Widom, Ke An, John Poplawsky, Yi-Chia Chou, Peter Liaw, William Curtin

Abstract: 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-resolu… ▽ More 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. △ Less

Submitted 26 August, 2020; originally announced August 2020.

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

Authors: Nathaniel Hoffman, Michael Widom

Abstract: 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 m… ▽ More 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. △ Less

Submitted 26 July, 2020; originally announced July 2020.

Comments: 13 pages, 8 figures

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

Authors: Vishnu Raghuraman, Yang Wang, Michael Widom

Abstract: 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… ▽ More 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. △ Less

Submitted 4 August, 2020; v1 submitted 16 June, 2020; originally announced June 2020.

Comments: 9 pages, 7 figures; minor revisions based on reviewer comments; added a section on self-consistent CA-CPA

Journal ref: Phys. Rev. B 102, 054207 (2020)

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

Authors: Marek Mihalkovic, Michael Widom

Abstract: 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-centere… ▽ More 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. △ Less

Submitted 9 August, 2019; originally announced August 2019.

Journal ref: Phys. Rev. Research 2, 013196 (2020)

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

Authors: Jun Li, Qingxiao Wang, Guowei He, Michael Widom, Lydia Nemec, Volker Blum, Moon Kim, Patrick Rinke, Randall M. Feenstra

Abstract: 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 transmiss… ▽ More 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. △ Less

Submitted 13 August, 2019; v1 submitted 10 May, 2019; originally announced May 2019.

Comments: 19 pages with 8 figures, along with 6 pages of Supplemental Material; v2 adds refs. 56,59-62 all being prior work, along with several paragraphs in the Discussion or Summary sections of the manuscript discussing this prior work; v3 corrects several typographical errors

Journal ref: Phys. Rev. Materials 3, 084006 (2019)

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

Authors: Gheorghe Lucian Pascut, Michael Widom, Kristjan Haule, Khandker F. Quader

Abstract: 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… ▽ More 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. △ Less

Submitted 30 April, 2019; originally announced May 2019.

Comments: 17 pages, 11 figures

Journal ref: Phys. Rev. B 100, 125114 (2019)

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

Authors: Felix Lüpke, Dacen Waters, Sergio C. de la Barrera, Michael Widom, David G. Mandrus, Jiaqiang Yan, Randall M. Feenstra, Benjamin M. Hunt

Abstract: 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… ▽ More 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. △ Less

Submitted 16 July, 2019; v1 submitted 1 March, 2019; originally announced March 2019.

Band Structure Theory of the BCC to HCP Burgers Distortion

Authors: Bojun Feng, Michael Widom

Abstract: 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 te… ▽ More 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. △ Less

Submitted 17 September, 2018; originally announced September 2018.

Journal ref: Phys. Rev. B 98, 174108 (2018)

Information entropy of liquid metals

Authors: M. C. Gao, M. Widom

Abstract: 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 meth… ▽ More 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. △ Less

Submitted 20 February, 2018; v1 submitted 20 December, 2017; originally announced December 2017.

First-principles prediction of high-entropy-alloy stability

Authors: Rui Feng, Peter K. Liaw, Michael C. Gao, Michael Widom

Abstract: 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 demons… ▽ More 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. △ Less

Submitted 28 June, 2017; originally announced June 2017.

Phase Diagram of Carbon Nickel Tungsten: Superatom Model

Authors: Sanxi Yao, Qin Gao, Michael Widom, Christopher Marvel, Martin Harmer

Abstract: 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 compositi… ▽ More 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. △ Less

Submitted 18 May, 2017; originally announced May 2017.

Journal ref: Phys. Rev. Materials 1, 043402 (2017)

Elastic stability and lattice distortion of refractory high entropy alloys

Authors: Bojun Feng, Michael Widom

Abstract: 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 t… ▽ More 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. △ Less

Submitted 10 March, 2017; originally announced March 2017.

Phase Diagram of Boron Carbide With Variable Carbon Composition

Authors: Sanxi Yao, Qin Gao, Michael Widom

Abstract: 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 interacti… ▽ More 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. △ Less

Submitted 16 December, 2016; originally announced December 2016.

Journal ref: Phys. Rev. B 95, 054101 (2017)

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

Authors: P. C. Mende, Q. Gao, A. Ismach, H. Chou, M. Widom, R. Ruoff, L. Colombo, R. M. Feenstra

Abstract: 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 descripti… ▽ More 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. △ Less

Submitted 4 February, 2017; v1 submitted 15 November, 2016; originally announced November 2016.

Comments: v2, added fig 10 and Supplementary Material; total is 29 pages, 17 figures

Journal ref: Surf. Sci. 659, 31 (2017)

Frequency estimate for multicomponent crystalline compounds

Authors: M. Widom

Abstract: 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 di… ▽ More 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. △ Less

Submitted 17 November, 2016; v1 submitted 6 October, 2016; originally announced October 2016.

Comments: Revised version submitted to J. Stat. Phys. (2016)

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

Authors: Sergio C. de la Barrera, Yu-Chuan Lin, Sarah M. Eichfeld, Joshua A. Robinson, Qin Gao, Michael Widom, Randall M. Feenstra

Abstract: 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 mon… ▽ More 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. △ Less

Submitted 13 June, 2016; originally announced June 2016.

Comments: 15 pages, 7 figures

Journal ref: J. Vac. Sci. Technol. B 34, 04J106 (2016)

A microscopic continuum model for defect dynamics in metallic glasses

Authors: Amit Acharya, Michael Widom

Abstract: 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 predictiv… ▽ More 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. △ Less

Submitted 8 March, 2016; originally announced March 2016.

Machine Learning methods for interatomic potentials: application to boron carbide

Authors: Qin Gao, Sanxi Yao, Jeff Schneider, Michael Widom

Abstract: 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 st… ▽ More 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. △ Less

Submitted 30 December, 2015; originally announced December 2015.

Predicted phase diagram of B-C-N

Authors: Hantao Zhang, Sanxi Yao, Michael Widom

Abstract: 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 materia… ▽ More 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. △ Less

Submitted 22 December, 2015; originally announced December 2015.

Journal ref: Phys. Rev. B 93, 144107 (2016)

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

Authors: Michael Widom, Khandker Quader

Abstract: 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 t… ▽ More 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. △ Less

Submitted 31 August, 2015; originally announced August 2015.

Comments: 4 pages, 3 figures

Entropy and diffuse scattering: comparison of NbTiVZr and CrMoNbV

Authors: M. Widom

Abstract: 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… ▽ More 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. △ Less

Submitted 1 May, 2015; originally announced May 2015.

Comments: Submitted to Met Mat Trans A: TMS Symposium on High Entropy Alloys (2015)

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

Authors: Qin Gao, P. C. Mende, M. Widom, R. M. Feenstra

Abstract: 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 accorda… ▽ More 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. △ Less

Submitted 24 November, 2014; originally announced November 2014.

Comments: 21 pages, 7 figures

Journal ref: J. Vac. Sci. Technol. B 33, 02B105 (2015)

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

Authors: Sanxi Yao, W. P. Huhn, M. Widom

Abstract: 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… ▽ More 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. △ Less

Submitted 11 October, 2014; originally announced October 2014.

Journal ref: Solid State Sciences, Volume 47, September 2015, Pages 21-26

Lifshitz Transitions in 122-Pnictides Under Pressure

Authors: Khandker Quader, Michael Widom

Abstract: 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 const… ▽ More 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. △ Less

Submitted 28 January, 2014; originally announced January 2014.

Journal ref: Phys. Rev. B 90, 144512 (2014)

First Principles Study of Bismuth Films at Transition Metal Grain Boundaries

Authors: Qin Gao, Michael Widom

Abstract: 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… ▽ More 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. △ Less

Submitted 11 December, 2013; originally announced December 2013.

Comments: 10 pages, 5 figures, including supplementary material

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

Authors: William Paul Huhn, Michael Widom, Andrew M. Cheung, Gary J. Shiflet, S. Joseph Poon, John Lewandowski

Abstract: 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… ▽ More 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. △ Less

Submitted 5 August, 2014; v1 submitted 24 October, 2013; originally announced October 2013.

Comments: 11 pages, 7 figures, 6 tables

Journal ref: Phys. Rev. B, March 2014, Volume 89, pp 104103

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

Authors: William Paul Huhn, Michael Widom

Abstract: 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… ▽ More 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. △ Less

Submitted 21 June, 2013; originally announced June 2013.

Comments: 18 pages, 4 figures, 2 tables

Journal ref: JOM, December 2013, Volume 65, Issue 12, pp 1772-1779