M. Widom - Academia.edu (original) (raw)

Papers by M. Widom

Physical Review Letters, 2009

First-principles molecular dynamics simulations reveal a liquid-liquid phase transition in superc... more First-principles molecular dynamics simulations reveal a liquid-liquid phase transition in supercooled elemental silicon. Two phases coexist below T c % 1232 K and above p c % À12 kB. The low-density phase is nearly tetracoordinated, 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 .

Physical Review B, 2008

We investigate short range order in liquid and supercooled liquid Fe and Fe-based metallic glass ... more We investigate short range 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 ͓P. Ganesh and M. Widom, Phys. Rev. B 74, 134205 ͑2006͔͒ 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 FeZrB͒ we find that introducing small concentrations of small B atoms and large Zr atoms controls the frustration of local icosahedral order.

Philosophical Magazine, 2008

Physical Review Letters, 1987

Journal of Statistical Physics, 2001

We examine the thermodynamic limit of fluids of hard core particles that are polydisperse in size... more We examine the thermodynamic limit of fluids of hard core particles that are polydisperse in size and shape. In addition, particles may interact magnetically. Free energy of such systems is a random variable because it depends on the choice of particles. We prove that the thermodynamic limit exists with probability 1, and is independent of the choice of particles. Our proof applies to polydisperse hard-sphere fluids, colloids and ferrofluids. The existence of a thermodynamic limit implies system shape and size independence of thermodynamic properties of a system.

Physical Review B, 2002

Quasicrystals are metal alloys whose noncrystallographic symmetries challenge traditional methods... more Quasicrystals are metal alloys whose noncrystallographic symmetries challenge traditional methods of structure determination. We employ quantum-based total-energy calculations to predict the structure of a decagonal quasicrystal from first-principles considerations. Our Monte Carlo simulations take as input the knowledge that a decagonal phase occurs in Al-Ni-Co near a given composition and use a limited amount of experimental structural data. The resulting structure obeys a nearly deterministic decoration of tiles on a hierarchy of length scales related by powers of , the golden mean.

Ultramicroscopy, 2013

A computational method is developed whereby the reflectivity of low-energy electrons from a surfa... more 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 1  n zeroes in the reflectivity. Two additional imagepotential 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.

Physical Review B, 2008

The characteristics of atom packing in multicomponent metallic alloys with distinct short-and med... more The characteristics of atom packing in multicomponent metallic alloys with distinct short-and mediumrange order ͑SMRO͒ are notoriously difficult to provide as the local structure is made up of multiple overlapping pair correlations. In the case of binary glasses, several cluster models have been proposed that can describe the SMRO well going beyond models of dense random packing of hard spheres. By combining the pair density function analysis of neutron-diffraction data and modeling using ab initio computational techniques, the tendency for local atomic clustering is investigated and properties of multicomponent bulk Fe 78−x-y TM x RE y ͑C 22−z B z ͒ amorphous alloys ͓transition metal ͑TM͒ and rare earth ͑RE͔͒ are studied going beyond simple binary systems. The results are relevant to most bulk metallic glass forming alloys with more than one kind of solute ion.

Physical Review B, 2006

A growing body of experiments display indirect evidence of icosahedral structures in supercooled ... more A growing body of experiments display indirect evidence of icosahedral structures in supercooled liquid metals. Computer simulations provide more direct evidence but generally rely on approximate interatomic potentials of unproven accuracy. We use first-principles molecular dynamics simulations to generate realistic atomic configurations, providing structural detail not directly available from experiment, based on interatomic forces that are more reliable than conventional simulations. We analyze liquid copper, for which recent experimental results are available for comparison, to quantify the degree of local icosahedral and polytetrahedral order.

Physical Review B, 2008

The crystal structure of boron is unique among chemical elements, highly complex, and imperfectly... more The crystal structure of boron is unique among chemical elements, highly complex, and imperfectly known. Experimentalists report that the ␤-rhombohedral ͑black͒ 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 ␣-rhombohedral ͑red͒ form, implying that the ␤ phase cannot be stable at low temperatures. Furthermore, the ␤ form 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 ␤-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 ␤-rhombohedral structure through a phase transition at moderate temperature.

Physical Review B, 2012

By fitting to a database of ab-initio forces and energies, we can extract pair potentials for all... more 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. Furthermore, such potentials are combined with a method of discovering complex zero-temperature structures with hundreds of atoms per cell, given only the composition and the constraint of known lattice parameters, using molecular-dynamics quenches. We apply this approach to structure prediction in the Al-Cu-Sc quasicrystal-related system.

Physica A: Statistical Mechanics and its Applications, 1997

Materials Science and Engineering: A, 2000

Two-dimensional random tilings of rhombi can be seen as projections of two-dimensional membranes ... more Two-dimensional random tilings of rhombi can be seen as projections of two-dimensional membranes embedded in hypercubic lattices of higher dimensional spaces. Here, we consider tilings projected from a D-dimensional space. We study the limiting case, when the quantity D, and therefore the number of different species of tiles, become large. We had previously demonstrated [1] that, in this limit, the thermodynamic properties of the tiling become independent of the boundary conditions. The exact value of the limiting entropy and finite D corrections remain open questions. Here, we develop a meanfield theory, which uses an iterative description of the tilings based on an analogy with avoiding oriented walks on a random tiling. We compare the quantities so-obtained with numerical calculations. We also discuss the role of spatial correlations.

Journal of Physics: Condensed Matter, 2008

Accurate simulation of multicomponent alloys demands a first-principles approach because empirica... more Accurate simulation of multicomponent alloys demands a first-principles approach because empirical potentials become increasingly inaccurate and difficult to develop with each additional constituent element. In contrast, the computational difficulty of simulating an alloy from first principles remains essentially independent of the number of elements. However, equilibration times increase with the number of elements, regardless of the choice of interaction, owing to the need for longer-range diffusion to adequately sample configuration space. The difficulty is exacerbated at low temperatures because of the rapid decline of diffusion constants. Here we discuss the application of replica exchange molecular dynamics to aid equilibration of supercooled alloys, and we also mention the possibility of Hamiltonian exchange molecular dynamics to accelerate equilibration at high temperatures.

Journal of Non-Crystalline Solids, 2004

We incorporate realistic pair potential energies directly into a non-linear least-square fit of d... more We incorporate realistic pair potential energies directly into a non-linear least-square fit of diffraction data to quantitatively compare structure models with experiment for the Ni-rich d(AlNiCo) quasicrystal. The initial structure models are derived from a few a priori assumptions (gross features of the Patterson function) and the pair potentials. In place of the common hyperspace approach to the structure refinement of quasicrystals, we use a real-space tile decoration scheme, which does not rely on strict quasiperiodicity, and makes it easy to enforce sensible local arrangements of the atoms. Inclusion of the energies provides information complementary to the diffraction data and protects the fit procedure from converging on spurious solutions. The method pinpoints sites which are likely to break the symmetry of their local environment.

Journal of Magnetism and Magnetic Materials, 1993

Using the dipolar hard-sphere fluid as a model, we study the spontaneous magnetization of ferrofl... more Using the dipolar hard-sphere fluid as a model, we study the spontaneous magnetization of ferrofluids. Mean field theory suggests magnetic order will occur in a strongly coupled ferrofluid. At fixed low density, the system phase separates at low temperature into a dilute nonmagnetic gas and a dense, magnetically ordered liquid. We focus our study on the effect of positional randomness, which is not included in conventional mean field studies. Our results show that a positionally unstructured ferrofluid exhibits magnetic order at low temperatures, provided its density is high enough. Freezing the solvent inhibits phase separation. In this case, positional randomness prevents magnetic order in a dilute frozen ferrofluid.

The assessed binary phase diagram of boron-carbon exhibits a single alloy phase designated "B 4 C... more The assessed binary phase diagram of boron-carbon exhibits a single alloy phase designated "B 4 C" with rhombohedral symmetry occupying a broad composition range that falls just short of the nominal carbon content of 20%. As this composition range is nearly temperature independent, the phase diagram suggests a violation of the third law of thermodynamics, which typically requires compounds to achieve a definite stoichiometry at low temperatures. By means of first principles total energy calculations we predict the existence of two stoichiometric phases at T=0K: one of composition B 4 C with monoclinic symmetry; the other of composition B 13 C 2 with rhombohedral symmetry. Using statistical mechanics to extend to finite temperatures, we demonstrate that the monoclinic phase reverts to the rhombohedral phase above T=600K, along with a slight reduction on carbon content.

Cadmium-based quasicrystals (Cd-Ca and Cd-Yb) were the first binary alloys discovered to form the... more Cadmium-based quasicrystals (Cd-Ca and Cd-Yb) were the first binary alloys discovered to form thermodynamically stable quasicrystals. As binary alloys, and with a strong size difference between atomic species, they are ideal systems for structural and thermodynamic analysis. Observed quasicrystal approximants with crystallographically determined structures can be interpreted as decorations of Henley's canonical cells. We use first-principles total energy calculations to resolve details of the most favourable decorations.

Physical Review Letters, 2009

First-principles molecular dynamics simulations reveal a liquid-liquid phase transition in superc... more First-principles molecular dynamics simulations reveal a liquid-liquid phase transition in supercooled elemental silicon. Two phases coexist below T c % 1232 K and above p c % À12 kB. The low-density phase is nearly tetracoordinated, 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 .

Physical Review B, 2008

We investigate short range order in liquid and supercooled liquid Fe and Fe-based metallic glass ... more We investigate short range 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 ͓P. Ganesh and M. Widom, Phys. Rev. B 74, 134205 ͑2006͔͒ 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 FeZrB͒ we find that introducing small concentrations of small B atoms and large Zr atoms controls the frustration of local icosahedral order.

Philosophical Magazine, 2008

Physical Review Letters, 1987

Journal of Statistical Physics, 2001

We examine the thermodynamic limit of fluids of hard core particles that are polydisperse in size... more We examine the thermodynamic limit of fluids of hard core particles that are polydisperse in size and shape. In addition, particles may interact magnetically. Free energy of such systems is a random variable because it depends on the choice of particles. We prove that the thermodynamic limit exists with probability 1, and is independent of the choice of particles. Our proof applies to polydisperse hard-sphere fluids, colloids and ferrofluids. The existence of a thermodynamic limit implies system shape and size independence of thermodynamic properties of a system.

Physical Review B, 2002

Quasicrystals are metal alloys whose noncrystallographic symmetries challenge traditional methods... more Quasicrystals are metal alloys whose noncrystallographic symmetries challenge traditional methods of structure determination. We employ quantum-based total-energy calculations to predict the structure of a decagonal quasicrystal from first-principles considerations. Our Monte Carlo simulations take as input the knowledge that a decagonal phase occurs in Al-Ni-Co near a given composition and use a limited amount of experimental structural data. The resulting structure obeys a nearly deterministic decoration of tiles on a hierarchy of length scales related by powers of , the golden mean.

Ultramicroscopy, 2013

A computational method is developed whereby the reflectivity of low-energy electrons from a surfa... more 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 1  n zeroes in the reflectivity. Two additional imagepotential 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.

Physical Review B, 2008

The characteristics of atom packing in multicomponent metallic alloys with distinct short-and med... more The characteristics of atom packing in multicomponent metallic alloys with distinct short-and mediumrange order ͑SMRO͒ are notoriously difficult to provide as the local structure is made up of multiple overlapping pair correlations. In the case of binary glasses, several cluster models have been proposed that can describe the SMRO well going beyond models of dense random packing of hard spheres. By combining the pair density function analysis of neutron-diffraction data and modeling using ab initio computational techniques, the tendency for local atomic clustering is investigated and properties of multicomponent bulk Fe 78−x-y TM x RE y ͑C 22−z B z ͒ amorphous alloys ͓transition metal ͑TM͒ and rare earth ͑RE͔͒ are studied going beyond simple binary systems. The results are relevant to most bulk metallic glass forming alloys with more than one kind of solute ion.

Physical Review B, 2006

A growing body of experiments display indirect evidence of icosahedral structures in supercooled ... more A growing body of experiments display indirect evidence of icosahedral structures in supercooled liquid metals. Computer simulations provide more direct evidence but generally rely on approximate interatomic potentials of unproven accuracy. We use first-principles molecular dynamics simulations to generate realistic atomic configurations, providing structural detail not directly available from experiment, based on interatomic forces that are more reliable than conventional simulations. We analyze liquid copper, for which recent experimental results are available for comparison, to quantify the degree of local icosahedral and polytetrahedral order.

Physical Review B, 2008

The crystal structure of boron is unique among chemical elements, highly complex, and imperfectly... more The crystal structure of boron is unique among chemical elements, highly complex, and imperfectly known. Experimentalists report that the ␤-rhombohedral ͑black͒ 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 ␣-rhombohedral ͑red͒ form, implying that the ␤ phase cannot be stable at low temperatures. Furthermore, the ␤ form 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 ␤-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 ␤-rhombohedral structure through a phase transition at moderate temperature.

Physical Review B, 2012

By fitting to a database of ab-initio forces and energies, we can extract pair potentials for all... more 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. Furthermore, such potentials are combined with a method of discovering complex zero-temperature structures with hundreds of atoms per cell, given only the composition and the constraint of known lattice parameters, using molecular-dynamics quenches. We apply this approach to structure prediction in the Al-Cu-Sc quasicrystal-related system.

Physica A: Statistical Mechanics and its Applications, 1997

Materials Science and Engineering: A, 2000

Two-dimensional random tilings of rhombi can be seen as projections of two-dimensional membranes ... more Two-dimensional random tilings of rhombi can be seen as projections of two-dimensional membranes embedded in hypercubic lattices of higher dimensional spaces. Here, we consider tilings projected from a D-dimensional space. We study the limiting case, when the quantity D, and therefore the number of different species of tiles, become large. We had previously demonstrated [1] that, in this limit, the thermodynamic properties of the tiling become independent of the boundary conditions. The exact value of the limiting entropy and finite D corrections remain open questions. Here, we develop a meanfield theory, which uses an iterative description of the tilings based on an analogy with avoiding oriented walks on a random tiling. We compare the quantities so-obtained with numerical calculations. We also discuss the role of spatial correlations.

Journal of Physics: Condensed Matter, 2008

Accurate simulation of multicomponent alloys demands a first-principles approach because empirica... more Accurate simulation of multicomponent alloys demands a first-principles approach because empirical potentials become increasingly inaccurate and difficult to develop with each additional constituent element. In contrast, the computational difficulty of simulating an alloy from first principles remains essentially independent of the number of elements. However, equilibration times increase with the number of elements, regardless of the choice of interaction, owing to the need for longer-range diffusion to adequately sample configuration space. The difficulty is exacerbated at low temperatures because of the rapid decline of diffusion constants. Here we discuss the application of replica exchange molecular dynamics to aid equilibration of supercooled alloys, and we also mention the possibility of Hamiltonian exchange molecular dynamics to accelerate equilibration at high temperatures.

Journal of Non-Crystalline Solids, 2004

We incorporate realistic pair potential energies directly into a non-linear least-square fit of d... more We incorporate realistic pair potential energies directly into a non-linear least-square fit of diffraction data to quantitatively compare structure models with experiment for the Ni-rich d(AlNiCo) quasicrystal. The initial structure models are derived from a few a priori assumptions (gross features of the Patterson function) and the pair potentials. In place of the common hyperspace approach to the structure refinement of quasicrystals, we use a real-space tile decoration scheme, which does not rely on strict quasiperiodicity, and makes it easy to enforce sensible local arrangements of the atoms. Inclusion of the energies provides information complementary to the diffraction data and protects the fit procedure from converging on spurious solutions. The method pinpoints sites which are likely to break the symmetry of their local environment.

Journal of Magnetism and Magnetic Materials, 1993

Using the dipolar hard-sphere fluid as a model, we study the spontaneous magnetization of ferrofl... more Using the dipolar hard-sphere fluid as a model, we study the spontaneous magnetization of ferrofluids. Mean field theory suggests magnetic order will occur in a strongly coupled ferrofluid. At fixed low density, the system phase separates at low temperature into a dilute nonmagnetic gas and a dense, magnetically ordered liquid. We focus our study on the effect of positional randomness, which is not included in conventional mean field studies. Our results show that a positionally unstructured ferrofluid exhibits magnetic order at low temperatures, provided its density is high enough. Freezing the solvent inhibits phase separation. In this case, positional randomness prevents magnetic order in a dilute frozen ferrofluid.

The assessed binary phase diagram of boron-carbon exhibits a single alloy phase designated "B 4 C... more The assessed binary phase diagram of boron-carbon exhibits a single alloy phase designated "B 4 C" with rhombohedral symmetry occupying a broad composition range that falls just short of the nominal carbon content of 20%. As this composition range is nearly temperature independent, the phase diagram suggests a violation of the third law of thermodynamics, which typically requires compounds to achieve a definite stoichiometry at low temperatures. By means of first principles total energy calculations we predict the existence of two stoichiometric phases at T=0K: one of composition B 4 C with monoclinic symmetry; the other of composition B 13 C 2 with rhombohedral symmetry. Using statistical mechanics to extend to finite temperatures, we demonstrate that the monoclinic phase reverts to the rhombohedral phase above T=600K, along with a slight reduction on carbon content.

Cadmium-based quasicrystals (Cd-Ca and Cd-Yb) were the first binary alloys discovered to form the... more Cadmium-based quasicrystals (Cd-Ca and Cd-Yb) were the first binary alloys discovered to form thermodynamically stable quasicrystals. As binary alloys, and with a strong size difference between atomic species, they are ideal systems for structural and thermodynamic analysis. Observed quasicrystal approximants with crystallographically determined structures can be interpreted as decorations of Henley's canonical cells. We use first-principles total energy calculations to resolve details of the most favourable decorations.