Michael Widom

Electronic structure and properties of isoreticular metal-organic frameworks: The case of M-IRMOF1 (M=Zn, Cd, Be, Mg, and Ca)

We investigate the possibility of tailoring the electronic properties of isoreticular metal-organic materials by replacing the metal atom in the metal-organic cluster and by doping. The electronic structure of M-IRMOF1, where IRMOF1 stands for isoreticular metal-organic framework 1 and M = Be, Mg, Ca, Zn, and Cd, was examined using density-functional theory. The results show that these materials have similar band gaps (ca. 3.5 eV) and a conduction band that is split into two bands, the lower of which has a width that varies with metal substitution. This variation prompted us to investigate whether doping with Al or Li could be used to tailor the electronic properties of the Zn-IRMOF1 and Be-IRMOF1 materials. It is shown that replacing one metal atom with Al can effectively be used to create IRMOFs with different metallic properties. On the other hand, adding Li produces structural changes that render this approach less suitable.

Signature of nearly icosahedral structures in liquid and supercooled liquid copper

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.

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

First-principles molecular dynamics simulations reveal a liquid-liquid phase transition in supercooled elemental silicon. Two phases coexist below Tc approximately 1232 K and above pc approximately -12 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 Tc.

Total-energy-based prediction of a quasicrystal structure

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 t, the golden mean.

Symmetry, Landau theory and polytope models of glass

Abstract Order in supercooled liquids and metallic glasses is related to a regular icosahedral “crystal” consisting of 120 particles inscribed on the surface of a sphere in four dimensions. Hyperspherical harmonics and the discrete symmetry group of this four-dimensional platonic solid can be used to construct an order parameter for glasses in three-dimensional flat space. A uniformly frustrated Landau expansion in this order parameter suggests a ground state with a regular array of wedge disclination lines. Homotopy theory is used to classify all topologically stable defects. A generalization of Blochs theorem for electronic states in flat space solids allows explicit diagonalization of tight binding models defined on the curved-space icosahedral crystal.

Symmetry-broken crystal structure of elemental boron at low temperature

The crystal structure of boron is unique among chemical elements, highly complex, and imperfectly known. Experimentalists report the �-rhombohedral (black) form is stable over all temperatures from absolute zero to melting. However, early calcu- lations found its energy to be greater than the energy of the �-rhombohedral (red) form, implyingcannot be stable at low temperatures. Furthermore, � 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 temper- atures 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.

Radial fingering in a Hele-Shaw cell: a weakly nonlinear analysis

Abstract The Saffman-Taylor viscous fingering instability occurs when a less viscous fluid displaces a more viscous one between narrowly spaced parallel plates in a Hele-Shaw cell. Experiments in radial flow geometry form fan-like patterns, in which fingers of different lengths compete, spread and split. Our weakly nonlinear analysis of the instability predicts these phenomena, which are beyond the scope of linear stability theory. Finger competition arises through enhanced growth of sub-harmonic perturbations, while spreading and splitting occur through the growth of harmonic modes. Nonlinear mode-coupling enhances the growth of these specific perturbations with appropriate relative phases, as we demonstrate through a symmetry analysis of the mode coupling equations. We contrast mode coupling in radial flow with rectangular flow geometry.

Strange Objects in the Complex Plane

Julia sets are examined as examples of strange objects which arise in the study of long time properties of simple dynamical systems. Technically they are the closure of the set of unstable cycles of analytic maps. Physically, they are sets of points which lead to chaotic behavior. The mapf(z)=z2+p is analyzed for smallp where the Julia set is a closed curve, and for largep where the Julia set is completely disconnected. In both cases the Hausdorff dimension is calculated in perturbation theory and numerically. An expression for the rate at which points escape from the neighborhood of the Julia set is derived and tested in a numerical simulation of the escape.

Mechanical properties, glass transition temperature, and bond enthalpy trends of high metalloid Fe-based bulk metallic glasses

Mechanical properties and glass transition temperatures (Tg) of Fe–Cr–Mo–P–C–B bulk metallic glasses containing up to 27at.% metalloids have been studied. The shear modulus (G) is found to decrease with increasing metalloid content and a maximum plastic strain of ∼3% is obtained, despite the increase in the number of strong metal-metalloid bonds. Also, Tg increases with the decrease in G, in contrast to usual behavior. By employing first-principles calculations, the results are discussed in light of atomic bonding and connectivity in the amorphous network. The findings are relevant to understanding ductility and glass transition of metallic glasses.

Low-energy Electron Reflectivity from Graphene

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