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adsorbed aggregate of particles anhedral argon As-Received atoms boron capillarity Carbide chemical potential constant curve cusps diffusion coefficient diffusion path dissolve distribution function f(r^,t equation equilibrium shape experimental Figure flux of material free energy impurity layer increase interface internal phase Lifshitz and Slyozov liquid iron low index plane mean arithmetic mean particle diameter mean particle separation mean radius mean separation distance microns molar free energy molar volume NbC in liquid nearest neighbors Niobium Carbide number of particles Nv no./cm Oriani particle of radius particle separation distance particle size particles in liquid particles per unit periclase phase boundary reaction powder precipitate particles principal curvatures pyrolytic graphite radius of curvature rate controlling step sample solid-liquid solubility solution specimen sintered spherical grains spherical harmonic spherical particle stoichiometric surface step surface tension temperature dependent function unit area unit volume vapor pressure volume diffusion volume fraction dispersant volume fraction liquid zero