Phase Pattern Formation in Grain Boundaries.

In this Letter we derive conditions that predict the existence of two-phase periodic-pattern grain boundary structures that are stable against coarsening. While previous research has established that elastic effects can lead to phase pattern formation on crystal surfaces, the possibility of stable grain boundary structures composed of alternating grain boundary phases has not been previously analyzed. Our theory identifies the specific combination of grain boundary and materials properties that enable the emergence of patterned grain boundary states and shows that the dislocation content of grain boundary phase junctions, absent in surface phenomena, weakens the stability of the patterned structures. The predictions of the theory are tested using a model copper grain boundary that exhibits multiple phases and two-phase pattern formation. We discuss how, similarly to surfaces, elastic effects associated with grain boundary phase junctions have profound implications for how grain boundary phases transform.

Boosting photoconductive large-area THz emitter via optical light confinement behind a highly refractive sapphire-fiber lens.

We report on a sapphire-fiber-based lens that can be used to enhance the emitted THz power of a large-area photoconductive antenna (PCA). Using numerical simulations, we demonstrate that the lens provides a spatial redistribution of the photocarriers density in the PCA's gap. By optimizing the diameter of the sapphire-fiber, one could reach efficient confinement of the photocarriers in the vicinity of the PCA electrodes with a 10-µm gap size for a 220-µm-thick sapphire-fiber. This allows enhancing the coupling of the incident electromagnetic waves at the interface between the sapphire fiber and the semiconductor with the antenna terminals by ∼40 times for a single PCA element, as well as boosting the total efficiency of the large-area PCA-emitter up to ∼7-10 times. To validate our approach, we propose a step-by-step process that can be used for the precise and controllable placement of the sapphire-fiber on the surface of a single PCA.

Nucleation of Grain Boundary Phases.

We derive a theory that describes homogeneous nucleation of grain boundary (GB) phases. Our analysis takes account of the energy resulting from the GB phase junction, the line defect separating two different GB structures, which is necessarily a dislocation as well as an elastic line force due to the jump in GB stresses. The theory provides analytic forms for the elastic interactions and the core energy of the GB phase junction that, along with the change in GB energy, determines the nucleation barrier. We apply the resulting nucleation model to simulations of GB phase transformations in tungsten. Our theory explains why under certain conditions GBs cannot spontaneously change their structure even to a lower energy state.

Grain boundary phases in bcc metals.

We report a computational discovery of novel grain boundary structures and multiple grain boundary phases in elemental body-centered cubic (bcc) metals represented by tungsten, tantalum and molybdenum. While grain boundary structures created by the γ-surface method as a union of two perfect half crystals have been studied extensively, it is known that the method has limitations and does not always predict the correct ground states. Herein, we use a newly developed computational tool, based on evolutionary algorithms, to perform a grand-canonical search of high-angle symmetric tilt and twist boundaries, and we find new ground states and multiple phases that cannot be described using the conventional structural unit model. We use molecular dynamics (MD) simulations to demonstrate that the new structures can coexist at finite temperature in a closed system, confirming that these are examples of different grain boundary phases. The new ground state is confirmed by first-principles calculations.

Phases, phase equilibria, and phase rules in low-dimensional systems.

We present a unified approach to thermodynamic description of one, two, and three dimensional phases and phase transformations among them. The approach is based on a rigorous definition of a phase applicable to thermodynamic systems of any dimensionality. Within this approach, the same thermodynamic formalism can be applied for the description of phase transformations in bulk systems, interfaces, and line defects separating interface phases. For both lines and interfaces, we rigorously derive an adsorption equation, the phase coexistence equations, and other thermodynamic relations expressed in terms of generalized line and interface excess quantities. As a generalization of the Gibbs phase rule for bulk phases, we derive phase rules for lines and interfaces and predict the maximum number of phases than may coexist in systems of the respective dimensionality.

Effect of interface phase transformations on diffusion and segregation in high-angle grain boundaries.

Recent experimental measurements of Ag impurity diffusion in the Σ5(310) grain boundary (GB) in Cu revealed an unusual non-Arrhenius behavior suggestive of a possible structural transformation Divinski et al., [Phys. Rev. B 85, 144104 (2012)]. On the other hand, atomistic computer simulations have recently discovered phase transformations in high-angle GBs in metals Frolov et al., [Nat. Commun. 4, 1899 (2013)]. In this Letter we report on atomistic simulations of Ag diffusion and segregation in two different structural phases of the Cu Σ5(310) GB which transform to each other with temperature. The obtained excellent agreement with the experimental data validates the hypothesis that the unusual diffusion behavior seen in the experiment was caused by a phase transformation. The simulations also predict that the low-temperature GB phase exhibits a monolayer segregation pattern while the high-temperature phase features a bilayer segregation. Together, the simulations and experiment provide the first convincing evidence for the existence of structural phase transformations in high-angle metallic GBs and demonstrate the possibility of their detection by GB diffusion measurements and atomistic simulations.

Step free energies at faceted solid-liquid interfaces from equilibrium molecular dynamics simulations.

In this work a method is proposed for computing step free energies for faceted solid-liquid interfaces based on atomistic simulations. The method is demonstrated in an application to (111) interfaces in elemental Si, modeled with the classical Stillinger-Weber potential. The approach makes use of an adiabatic trapping procedure, and involves simulations of systems with coexisting solid and liquid phases separated by faceted interfaces containing islands with different sizes, for which the corresponding equilibrium temperatures are computed. We demonstrate that the calculated coexistence temperature is strongly affected by the geometry of the interface. We find that island radius is inversely proportional to superheating, allowing us to compute the step free energy by fitting simulation data within the formalism of classical nucleation theory. The step free energy value is computed to be γ(st) = 0.103 ± 0.005 × 10(-10) J/m. The approach outlined in this work paves the way to the calculation of step free energies relevant to the solidification of faceted crystals from liquid mixtures, as encountered in nanowire growth by the vapor-liquid-solid mechanism and in alloy casting. The present work also shows that at low undercoolings the Stillinger-Weber interatomic potential for Si tends to crystallize in the wurtzite, rather than the diamond-cubic structure.

Liquid nucleation at superheated grain boundaries.

Grain boundaries with relatively low energies can be superheated above the melting temperature and eventually melt by heterogeneous nucleation of liquid droplets. We propose a thermodynamic model of this process based on the sharp-interface approximation with a disjoining potential. The distinct feature of the model is its ability to predict the shape and size of the critical nucleus by using a variational approach. The model reduces to the classical nucleation theory in the limit of large nuclei but is more general and remains valid for small nuclei. Contrary to the classical nucleation theory, the model predicts the existence of a critical temperature of superheating and offers a simple formula for its calculation. The model is tested against molecular dynamic simulations in which liquid nuclei at a superheated boundary were obtained by an adiabatic trapping procedure. The simulation results demonstrate a reassuring consistency with the model.

Stable nanocolloidal structures in metallic systems.

Molecular dynamics simulations with a semiempirical interatomic potential predict the existence of a thermodynamically stable colloidal structure with nanometer-size Ta particles suspended in liquid Cu. The thermodynamic stability of this structure against coarsening, coalescence or transformation to a homogeneous solution is explained by a negative and strongly curvature-dependent tension of the Cu/Ta interfaces. Simulations with this potential provide a simple computational model for studies of generic thermodynamic properties of nanodisperse systems with a negative interface free energy.

Solid-liquid interface free energy in binary systems: theory and atomistic calculations for the (110) Cu-Ag interface.

We analyze thermodynamics of solid-liquid interfaces in binary systems when the solid is in a nonhydrostatic state of stress. The difficulty lies in the fact that chemical potential of at least one of the chemical components in a nonhydrostatic solid is an undefined quantity. We show, nevertheless, that the interface free energy gamma can be defined as excess of an appropriate thermodynamic potential that depends on the chemical potentials in the liquid phase. We derive different forms of the adsorption equation for solid-liquid interfaces, with differential coefficients representing excesses of extensive properties. This leads, in particular, to the formulation of interface stress tau(ij) as an appropriate excess over nonhydrostatic bulk stresses. The interface stress is not unique unless the solid is in a hydrostatic state of stress. We also derive Gibbs-Helmholtz type equations that can be applied for thermodynamic integration of gamma. All thermodynamic relations derived here are presented in forms suitable for atomistic simulations. In particular, the excess quantities can be computed without constructing interface profiles. As an application, we perform semigrand canonical Monte Carlo simulations of the (110) solid-liquid interface in the Cu-Ag system. We show that gamma computed by thermodynamic integration along a coexistence path decreases with increasing composition difference between the phases. At the same time, tau(ij) remains negative (i.e., the interface is in a state of compression), drastically increases in magnitude, and becomes highly anisotropic. Some of the interface excess properties are computed by different methods and demonstrate accurate agreement with each other, confirming the correctness of our analysis.