Microscopic treatment of solute trapping and drag.

The long wavelength limit of a recent microscopic phase-field crystal (PFC) theory of a binary alloy mixture is used to derive an analytical approximation for the segregation coefficient as a function of the interface velocity, and relate it to the two-point correlation function of the liquid and the thermodynamic properties of solid and liquid phases. Our results offer the first analytical derivation of solute segregation from a microscopic model, and support recent molecular dynamics and numerical PFC simulations. Our results also provide an independent framework, motivated from classical density functional theory, from which to elucidate the fundamental nature of solute drag, which is still highly contested in the literature.

Diffusion-controlled growth rate of stepped interfaces.

For many materials, the structure of crystalline surfaces or solid-solid interphase boundaries is characterized by an array of mobile steps separated by immobile terraces. Despite the prevalence of step-terraced interfaces a theoretical description of the growth rate has not been completely solved. In this work the boundary element method (BEM) has been utilized to numerically compute the concentration profile in a fluid phase in contact with an infinite array of equally spaced surface steps and, under the assumption that step motion is controlled by diffusion through the fluid phase, the growth rate is computed. It is also assumed that a boundary layer exists between the growing surface and a point in the liquid where complete convective mixing occurs. The BEM results are presented for varying step spacing, supersaturation, and boundary layer width. BEM calculations were also used to study the phenomenon of step bunching during crystal growth, and it is found that, in the absence of elastic strain energy, a sufficiently large perturbation in the position of a step from its regular spacing will lead to a step bunching instability. Finally, an approximate analytic solution using a matched asymptotic expansion technique is presented for the case of a stagnant liquid or equivalently a solid-solid stepped interface.

Disorder trapping during crystallization of the B2-ordered NiAl compound.

Using molecular dynamics simulations, disorder trapping associated with solidification is studied for the (100), (110), and (111) growth directions in the B2 NiAl ordered alloy compound. At the high interface velocities studied we observe pronounced disorder and defect trapping, i.e., the formation of antisite defects and vacancies in the crystal at higher than equilibrium concentrations upon rapid solidification. The vacancies are located primarily on the Ni sublattice and the majority of antisite defects are Ni atoms on the Al sublattice, while the concentration of Al on the Ni sublattice is negligibly small. The defect concentration is found to increase in an approximately linear relationship with increasing the interface velocity. Further there is no significant anisotropy in the defect concentrations for different interface orientations. Our results suggest that the currently available models of disorder trapping should be extended to include both antisite defects and vacancies.

Structural disjoining potential for grain-boundary premelting and grain coalescence from molecular-dynamics simulations.

We describe a molecular-dynamics framework for the direct calculation of the short-ranged structural forces underlying grain-boundary premelting and grain coalescence in solidification. The method is applied in a comparative study of (i) a Sigma9115120 degrees twist and (ii) a Sigma9110{411} symmetric tilt boundary in a classical embedded-atom model of elemental Ni. Although both boundaries feature highly disordered structures near the melting point, the nature of the temperature dependence of the width of the disordered regions in these boundaries is qualitatively different. The former boundary displays behavior consistent with a logarithmically diverging premelted layer thickness as the melting temperature is approached from below, while the latter displays behavior featuring a finite grain-boundary width at the melting point. It is demonstrated that both types of behavior can be quantitatively described within a sharp-interface thermodynamic formalism involving a width-dependent interfacial free energy, referred to as the disjoining potential. The disjoining potential for boundary (i) is calculated to display a monotonic exponential dependence on width, while that of boundary (ii) features a weak attractive minimum. The results of this work are discussed in relation to recent simulation and theoretical studies of the thermodynamic forces underlying grain-boundary premelting.

Method for computing short-range forces between solid-liquid interfaces driving grain boundary premelting.

We present a molecular dynamics based method for accurately computing short-range structural forces resulting from the overlap of spatially diffuse solid-liquid interfaces at wetted grain boundaries close to the melting point. The method is based on monitoring the fluctuations of the liquid layer width at different temperatures to extract the excess interfacial free energy as a function of this width. The method is illustrated for a high-energy Sigma9 twist boundary in pure Ni. The short-range repulsion driving premelting is found to be dominant in comparison to long-range dispersion and entropic forces and consistent with previous experimental findings that nanometer-scale layer widths may be observed only very close to the melting point.

Size-dependent nucleation kinetics at nonplanar nanowire growth interfaces.

In nanowire growth, kinetic processes at the growth interface can play an important role in governing wire compositions, morphologies, and growth rates. Molecular-dynamics simulations have been undertaken to probe such processes in a system featuring a solid-liquid interface shape characterized by a facet bounded by rough orientations. Simulated growth rates display a dependence on nanowire diameter consistent with a size-dependent barrier for facet nucleation. A theory for the interface mobility is developed, establishing a source for size-dependent growth rates that is an intrinsic feature of systems possessing growth interfaces with faceted and rough orientations.

Crystal-melt interface stresses: atomistic simulation calculations for a Lennard-Jones binary alloy, Stillinger-Weber Si, and embedded atom method Ni.

Molecular-dynamics and Monte Carlo simulations have been used to compute the crystal-melt interface stress (f) in a model Lennard-Jones (LJ) binary alloy system, as well as for elemental Si and Ni modeled by many-body Stillinger-Weber and embedded-atom-method (EAM) potentials, respectively. For the LJ alloys the interface stress in the (100) orientation was found to be negative and the f vs composition behavior exhibits a slight negative deviation from linearity. For Stillinger-Weber Si, a positive interface stress was found for both (100) and (111) interfaces: f{100}=(380+/-30)mJ/m{2} and f{111}=(300+/-10)mJ/m{2}. The Si (100) and (111) interface stresses are roughly 80 and 65% of the value of the interfacial free energy (gamma) , respectively. In EAM Ni we obtained f{100}=(22+/-74)mJ/m{2}, which is an order of magnitude lower than gamma. A qualitative explanation for the trends in f is discussed.

Atomistic underpinnings for orientation selection in alloy dendritic growth.

In dendritic solidification, growth morphologies often display a pronounced sensitivity to small changes in composition. To gain insight into the origins of this phenomenon, we undertake an atomistic calculation of the magnitude and anisotropy of the crystal-melt interfacial free energy in a model alloy system featuring no atomic size mismatch and relatively ideal solution thermodynamics. By comparing the results of these calculations with predictions from recent phase-field calculations, we demonstrate that alloying gives rise to changes in free-energy anisotropies that are substantial on the scale required to induce changes in growth orientations.

Equilibrium adsorption at crystal-melt interfaces in Lennard-Jones alloys.

Although the properties of crystal-melt interfaces have been extensively studied in pure materials, effects of alloying on the interfacial free energy remain relatively poorly understood. In this work we make use of Monte Carlo computer simulations for model binary Lennard-Jones alloys to explore the effects which variations in atomic-size mismatch and the chemical contributions to mixing energies have upon density and composition profiles, as well as the resulting magnitudes of equilibrium adsorption coefficients in concentrated alloys. We study four different model systems covering a range of chemical and size mismatch, finding relatively small adsorption values which are nevertheless statistically different from zero.

Effect of stress on melting and freezing in nanopores.

A thermodynamic treatment of the freezing of fluids confined to nanosized closed pores is presented. The model includes the effects of pressure in the liquid, the volume change on solidification, and the strain energy in both the solidifying material and the wall material. When applied to the system of Pb droplets in Al, the model predicts an elevation of the melting point, in agreement with experiment.

Elastic relaxations in ultrathin epitaxial alloy films.

Elastic interactions responsible for the stability of nanometer-scale patterns in ultrathin, bulk-immiscible-alloy films are analyzed within the context of a hybrid atomistic-continuum model. Two apparently different descriptions of alloy film behavior, a continuum elasticity theory describing a deformable substrate and a rigid substrate atomistic scheme, emerge naturally as limiting cases on long and short length scales, respectively. Quantitative first-principles calculations explain the origin of recently observed nanoscale patterns in Co-Ag/Ru(0001), and reveal a surprising failure of the continuum model.

Method for computing the anisotropy of the solid-liquid interfacial free energy.

We present a method to compute accurately the weak anisotropy of the solid-liquid interfacial free energy, a parameter which influences dendritic evolution in materials with atomically rough interfaces. The method is based on monitoring interfacial fluctuations during molecular dynamics simulation and extracting the interfacial stiffness which is an order of magnitude more anisotropic than the interfacial free energy. We present results for pure Ni with interatomic potentials derived from the embedded atom method.

Role of stress in thin film alloy thermodynamics: competition between alloying and dislocation formation.

Using scanning tunneling microscopy (STM) and first-principles local-spin-density-approximation calculations to study submonolayer films of Co (1-c)Ag (c)/Ru(0001) alloys, we have discovered a novel phase-separation mechanism. When the Ag concentration c exceeds 0.4, the surface phase separates between a dislocated, pure Ag phase and a pseudomorphically strained Co(0.6)Ag (0.4) surface alloy. We attribute the phase separation to the competition between two stress relief mechanisms: surface alloying and dislocation formation. The agreement between STM measurements and our calculated phase diagram supports this interpretation.

Test of the universal scaling law for the diffusion coefficient in liquid metals.

The recently proposed scaling law relating the diffusion coefficient and the excess entropy of a liquid [M. Dzugutov, Nature (London) 381, 137 (1996)] is tested for several metals using molecular dynamics simulations. Interatomic potentials derived from the embedded atom method are used to study Ag, Au, Cu, Ni, Pd, Pt, Ni(3)Al, and AuPt and the angular dependent Stillinger-Weber form is used to investigate Si.

Boundary element modeling of electrokinetically driven fluid flow in two-dimensional microchannels.

In recent years there has been considerable interest in fabricating electrophoretic separation systems on microchips. In this study the boundary element method is used to numerically model both the electrical charge density and the electrokinetically driven fluid flow velocity field in two-dimensional microchannels containing an arbitrary configuration of circular flow obstacles. An estimate of both the average velocity and the resolution has been determined for various obstacle configurations, obstacle sizes, area fractions, surface line lengths per unit area and for different values of the thickness of the electrical double layer. Based on the results, an optimal microchannel design is suggested. In addition, the recently observed phenomenon of recirculated flow in an open region of an otherwise packed electrochromatography column has been confirmed with the numerical model.