Enumeration of octagonal tilings

<p>Random tilings are interesting as idealizations of atomistic models of quasicrystals and for their connection to problems in combinatorics and algorithms. Of particular interest is the tiling entropy density, which measures the relation of the number of distinct tilings to the number of constituent tiles. Tilings by squares and 45° rhombi receive special attention as presumably the simplest model that has not yet been solved exactly in the thermodynamic limit. However, an exact enumeration formula can be evaluated for tilings in finite regions with fixed boundaries. We implement this algorithm in an efficient manner, enabling the investigation of larger regions of parameter space than previously were possible. Our new results appear to yield monotone increasing and decreasing lower and upper bounds on the fixed boundary entropy density that converge towardS_∞=0.36021(3).</p

First-principles study of bismuth films at transition-metal grain boundaries

Recent experiments suggest that Bi impurities segregate to form bilayer films on Ni and Cu grain boundaries (GBs) but do not segregate in Fe. To explain these phenomena, we study the total energies of Bi films on transition-metal (TM) Σ3(111) and Σ5(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, as well as evaluating the contribution of interfacial phonons at high temperature.</p

First-principles study of bismuth films on the Ni(111) surface

<p>A recent experiment suggested that bismuth forms hexagonal films on the Ni(111) surface, of heights three, five, and seven layers. A quantum size effect based on free electrons was proposed in explanation. To test this idea, we calculate the total energies of Bi on the Ni(111) surface using density functional theory. We find that hexagonal film stabilities disagree with the observed odd layer preferences, and the structures are mechanically destabilized by adding capping atoms which pucker the hexagonal layers. Furthermore, we find that rhombohedral films based on the bulk Bi structure are energetically more favorable than the proposed hexagonal films. These structures also favor odd numbers of layers, but owing to covalent chemical bonding rather than confinement of free electrons. Specifically, a strongly bound adsorbed surface monolayer forms, followed by bulk-like rhombohedral bilayers.</p

Prediction of orientational phase transition in boron carbide

<p>The assessed binary phase diagram of boron–carbon exhibits a single intrinsically disordered alloy phase designated “B₄C” 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 <em>T</em> = 0 K: one of composition B₄C with monoclinic symmetry; the other of composition B₁₃C₂ with rhombohedral symmetry. Using statistical mechanics to extend to finite temperatures, we demonstrate that the monoclinic phase reverts to the observed disordered nonstoichiometric rhombohedral phase above <em>T</em> = 600 K, along with a slight reduction on carbon content.</p

Folding Kinetics of Riboswitch Transcriptional Terminators and Sequesterers

<p>To function as gene regulatory elements in response to environmental signals, riboswitches must adopt specific secondary structures on appropriate time scales. We employ kinetic Monte Carlo simulation to model the time-dependent folding during transcription of thiamine pyrophosphate (TPP) riboswitch expression platforms. According to our simulations, riboswitch transcriptional terminators, which must adopt a specific hairpin configuration by the time they have been transcribed, fold with higher efficiency than Shine-Dalgarno sequesterers, whose proper structure is required only at the time of ribosomal binding. Our findings suggest both that riboswitch transcriptional terminator sequences have been naturally selected for high folding efficiency, and that sequesterers can maintain their function even in the presence of significant misfolding.</p

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

<p>A computational method is developed whereby the reflectivity of low-energy electrons from a surface can be obtained from a first-principles solution of the electronic structure of the system. The method is applied to multilayer graphene. Two bands of reflectivity minima are found, one at 0 – 8 eV and the other at 14 – 22 eV above the vacuum level. For a free-standing slab with n layers of graphene, each band contains n 1 zeroes in the reflectivity. Two additional 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.</p

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

<p>In this article, we show that an effective Hamiltonian fit with first-principles calculations predicts that an order/disorder transition occurs in the high-entropy alloy Mo-Nb-Ta-W. Using the Alloy Theoretic Automated Toolkit, we find <em>T</em> = 0 K 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 Mo-Nb-Ta-W. Our previously published hybrid Monte Carlo (MC)/molecular dynamics (MD) results for the Mo-Nb-Ta-W 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. A comparison of the free energy model and our MC/MD results suggests the existence of additional low-temperature phase transitions in the system likely ending with phase segregation into binary phases.</p

Prediction of stable insulating intermetallic compounds

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

First Principles Modeling of the Temperature Dependent Ternary Phase Diagram for the Cu-Pd-S System

<p>As an aid to the development of hydrogen separation membranes, we predict the temperature dependent phase diagrams using first principles calculations combined with thermodynamic principles. Our method models the phase diagram without empirical fitting parameters. By applying thermodynamic principles and solid solution models, temperature-dependent features of the Cu–Pd–S system can be explained, specifically solubility ranges for substitutions in select crystalline phases. Electronic densities of states calculations explain the relative favorability of certain chemical substitutions. In addition, we calculate sulfidization thresholds for the Pd–S₂ system and activities for the Cu–Pd binary in temperature regimes where the phase diagram contains multiple solid phases.</p

Generalized Potentials for a Mean-field Density Functional Theory of a Three-Phase Contact Line

<p>We investigate generalized potentials for a mean-field density functional theory of a three-phase contact line. Compared to the symmetrical potential introduced in our previous article [<a href="http://dx.doi.org/10.1103/PhysRevE.85.011120">Phys. Rev. E 85, 011120 (2012)</a>], the three minima of these potentials form a small triangle located arbitrarily within the Gibbs triangle, which is more realistic for ternary fluid systems. We multiply linear functions that vanish at edges and vertices of the small triangle, yielding potentials in the form of quartic polynomials. We find that a subset of such potentials has simple analytic far-field solutions and is a linear transformation of our original potential. By scaling, we can relate their solutions to those of our original potential. For special cases, the lengths of the sides of the small triangle are proportional to the corresponding interfacial tensions. For the case of equal interfacial tensions, we calculate a line tension that is proportional to the area of the small triangle.</p