Information Entropy of Liquid Metals.

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

Low-energy electron reflectivity from graphene: first-principles computations and approximate models.

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

Phase stability and elastic properties of Cr-V alloys.

V is the only element in the periodic table that forms a complete solid solution with Cr and thus is particularly important in alloying strategy to ductilize Cr. This study combines first-principles density functional theory calculations and experiments to investigate the phase stability and elastic properties of Cr-V binary alloys. The cluster expansion study reveals the formation of various ordered compounds at low temperatures that were not previously known. These compounds become unstable due to the configurational entropy of bcc solid solution as the temperature is increased. The elastic constants of ordered and disordered compounds are calculated at both T = 0 K and finite temperatures. The overall trends in elastic properties are in agreement with measurements using the resonant ultrasound spectroscopy method. The calculations predict that addition of V to Cr decreases both the bulk modulus and the shear modulus, and enhances the Poisson's ratio, in agreement with experiments. Decrease in the bulk modulus is correlated to decrease in the valence electron density and increase in the lattice constant. An enhanced Poisson's ratio for bcc Cr-V alloys (compared to pure Cr) is associated with an increased density of states at the Fermi level. Furthermore, the difference charge density in the bonding region in the (110) slip plane is highest for pure Cr and decreases gradually as V is added. The present calculation also predicts a negative Cauchy pressure for pure Cr, and it becomes positive upon alloying with V. The intrinsic ductilizing effect from V may contribute, at least partially, to the experimentally observed ductilizing phenomenon in the literature.

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.

Probing hydrogen interactions with amorphous metals using first-principles calculations.

Amorphous metals are interesting candidates for use as H(2) purification membranes and occur in some applications of H(2) storage. We introduce a general strategy combining density functional theory and statistical mechanics for quantitatively predicting the properties of interstitial H in amorphous metals. We systematically investigate H solubility in amorphous Fe(3)B, comparing our results with ones for a crystalline material with the same composition. H-H interactions in the amorphous material play a crucial role in determining the net solubility. H solubility in the amorphous and crystalline materials differs by orders of magnitude under conditions relevant for practical H(2) purification membranes. Our results give atomic-level insight into the properties of H in amorphous metals that has not been previously available.

First-principles simulation of supercooled liquid alloys.

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.

Soft modes near the buckling transition of icosahedral shells.

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

First-principles prediction of a decagonal quasicrystal containing boron.

We interpret experimentally known B-Mg-Ru crystals as quasicrystal approximants whose deterministic decoration of tiles by atoms can be extended quasiperiodically. Experimentally observed disorder corresponds to phason fluctuations. First-principles total energy calculations find many distinct tilings close to stability and suggest a phase transition from a crystalline state at low temperatures to a high temperature state characterized by tile fluctuations. We predict B38Mg17Ru45 forms a metastable decagonal quasicrystal that may be thermodynamically stable at high temperatures.

Saffman-Taylor problem on a sphere.

The Saffman-Taylor problem addresses the morphological instability of an interface separating two immiscible, viscous fluids when they move in a narrow gap between two flat parallel plates (Hele-Shaw cell). In this work, we extend the classic Saffman-Taylor situation, by considering the flow between two curved, closely spaced, concentric spheres (spherical Hele-Shaw cell). We derive the mode-coupling differential equation for the interface perturbation amplitudes and study both linear and nonlinear flow regimes. The effect of the spherical cell (positive) spatial curvature on the shape of the interfacial patterns is investigated. We show that stability properties of the fluid-fluid interface are sensitive to the curvature of the surface. In particular, it is found that positive spatial curvature inhibits finger tip-splitting. Hele-Shaw flow on weakly negative, curved surfaces is briefly discussed.

Gravity-driven instability in a spherical Hele-Shaw cell.

A pair of concentric spheres separated by a small gap form a spherical Hele-Shaw cell. In this cell an interfacial instability arises when two immiscible fluids flow. We derive the equation of motion for the interface perturbation amplitudes, including both pressure and gravity drivings, using a mode coupling approach. Linear stability analysis shows that mode growth rates depend upon interface perimeter and gravitational force. Mode coupling analysis reveals the formation of fingering structures presenting a tendency toward finger tip-sharpening.

Ferromagnetic liquid thin films under applied field

Theoretical calculations, computer simulations, and experiments indicate the possible existence of a ferromagnetic liquid state, although definitive experimental evidence is lacking. Should such a state exist, demagnetization effects would force a nontrivial magnetization texture. Since liquid droplets are deformable, the droplet shape is coupled with the magnetization texture. In a thin-film geometry in zero applied field, the droplet has a circular shape and a rotating magnetization texture with a point vortex at the center. We calculate the elongation and magnetization texture of such a ferromagnetic thin-film liquid droplet confined between two parallel plates under a weak applied magnetic field. The vortex stretches into a domain wall and exchange forces break the reflection symmetry. This behavior contrasts qualitatively and quantitatively with the elongation of paramagnetic thin films.

Parallel flow in hele-shaw cells with ferrofluids

Parallel flow in a Hele-Shaw cell occurs when two immiscible liquids flow with relative velocity parallel to the interface between them. The interface is unstable due to a Kelvin-Helmholtz type of instability in which fluid flow couples with inertial effects to cause an initial small perturbation to grow. Large amplitude disturbances form stable solitons. We consider the effects of applied magnetic fields when one of the two fluids is a ferrofluid. The dispersion relation governing mode growth is modified so that the magnetic field can destabilize the interface even in the absence of inertial effects. However, the magnetic field does not affect the speed of wave propogation for a given wave number. We note that the magnetic field creates an effective interaction between the solitons.

Rayleigh-taylor instability with magnetic fluids: experiment and theory

We present experiments showing the Rayleigh-Taylor instability at the interface between a dense magnetic liquid and an immiscible less dense liquid. The liquids are confined in a Hele-Shaw cell and a magnetic field is applied perpendicular to the cell. We measure the wavelength and the growth rate at the onset of the instability as a function of the external magnetic field. The wavelength decreases as the field increases. The amplitude of the interface deformation grows exponentially with time in the early stage, and the growth rate is an increasing function of the field. These results are compared to theoretical predictions given in the framework of linear stability analysis.

Elongation of confined ferrofluid droplets under applied fields.

Ferrofluids are strongly paramagnetic liquids. We study the behavior of ferrofluid droplets confined between two parallel plates with a weak applied field parallel to the plates. The droplets elongate under the applied field to reduce their demagnetizing energy and reach an equilibrium shape where the magnetic forces balance against the surface tension. This elongation varies logarithmically with aspect ratio of droplet thickness to its original radius, in contrast to the behavior of unconfined droplets. Experimental studies of a ferrofluid-water-surfactant emulsion confirm this prediction.