D endritic alloy microstructures are formed during a wide range of solidification processes from casting to welding. These microstructures result from a morphological instability of the solid-liquid interface that produces dendrites, which are highly hierarchical branched patterns with primary-, secondary-and higher-order branches. As alloy impurities segregate in the interdendritic liquid during solidification, the spatially inhomogeneous distribution of impurities in the completely solidified alloy is a direct footprint of the dendritic network that formed and coarsened during the solidification process. It also determines the formation and distribution of secondary phases, and thus has a profound influence on the properties of a wide range of technologically important structural materials, from light-weight aluminium alloys used in the automotive industry to nickel-based superalloys used for turbine blades. The study of dendritic growth 1,2 has also been of long-standing fundamental interest because of the ubiquity of branched structures exhibited by diverse interfacial pattern formation systems [3][4][5] .Major theoretical and computational advances over the past two decades have improved our fundamental understanding of dendrite growth, as well as new capabilities to simulate and predict dendritic microstructures on experimentally relevant length and timescales 6 and to elucidate new pattern formation mechanisms 7,8 that enlarge the scope of our understanding of these structures. The commonly accepted microscopic solvability theory of steadystate dendrite growth 9-12 , which builds on the earlier diffusive transport theory of Ivantsov 13 , has led to the understanding that crystalline anisotropy is a crucial parameter that uniquely determines the growth rate and tip radius of dendrites, which is the basic scaling length for the entire dendritic network. Predictions of this theory have been largely validated by phase-field simulations of dendritic evolution over the past few years for both small [14][15][16][17][18][19] and large 20 growth rate. Moreover, molecular dynamics (MD) simulation methods [21][22][23][24][25][26][27][28][29][30] as well as experimental techniques 31,32 have recently been developed to accurately compute anisotropic interfacial properties that control dendritic evolution.Despite this progress, dendrite growth theory remains limited to predicting the steady-state characteristics of dendrites growing along simple crystallographic directions, such as the 100 directions that correspond to the main crystal axes for materials with cubic symmetry, or the six directions in the basal plane of

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When liquids solidify, the interface between a crystal and its melt often forms branching structures (dendrites), just as frost spreads across a window. The development of a quantitative understanding of dendritic evolution continues to present a major theoretical and experimental challenge within the metallurgical community. This article looks at key parameters that describe the interface—excess free energy and mobility—and discusses how these important properties relate to our understanding of crystal growth and other interfacial phenomena such as wetting and spreading of droplets and nucleation of the solid phase from the melt. In particular, two new simulation methods have emerged for computing the interfacial free energy and its anisotropy:the cleaving technique and the capillary fluctuation method. These are presented, along with methods for extracting the kinetic coefficient and a comparison of the results to several theories of crystal growth rates.

In this paper we present molecular dynamics (MD) calculations of the interdiffusion coefficient for asymmetric mixed plasma for thermodynamic conditions relevant to astrophysical and inertial confinement fusion plasmas. Specifically, we consider mixtures of deuterium and argon at temperatures of 100-500 eV and a number density ∼10(25) ions/cm(3). The motion of 30,000-120,000 ions is simulated in which the ions interact via the Yukawa (screened Coulomb) potential. The electric field of the electrons is included in this effective interaction; the electrons are not simulated explicitly. The species diffusivity is then calculated using the Green-Kubo approach using an integral of the interdiffusion current autocorrelation function, a quantity calculated in the equilibrium MD simulations. Our MD simulation results show that a widely used expression relating the interdiffusion coefficient with the concentration-weighted sum of self-diffusion coefficients overestimates the interdiffusion coefficient. We argue that this effect due to cross-correlation terms in velocities is characteristic of asymmetric mixed plasmas. Comparison of the MD results with predictions of kinetic theories also shows a discrepancy with MD giving effectively a larger Coulomb logarithm.

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.