Ostwald ripening of spheroidal particles in multicomponent alloys

Abstract We propose a general theory of Ostwald ripening for prolate spheroidal particles in a nonideal nondilute multicomponent alloy. The diffusion problem of a growing or shrinking particle is solved using prolate spheroidal coordinates under the assumption that the spheroidal particle has a constant Wulff shape. The result shows that the diffusional growth rate increases with an increasing particle aspect ratio due to the increased surface area per volume. The anisotropic interfacial energy necessary to guarantee that the particles are always prolate spheroids with a given aspect ratio is also determined. We find that the chemical potential decreases with an increasing particle aspect ratio under a constant volume-equivalent radius. Based on the two correction factors, asymptotic analysis reveals that the temporal exponents for the coarsening laws for spheroid particles are identical to that for spherical particles. However, as the aspect ratio increases the amplitudes of the temporal power laws of the average equivalent radius, the matrix supersaturations, and the particle composition decrease, whereas the amplitude of the number of particles per volume increases. It is also shown that the particle shape anisotropy affects the amplitudes, but not the direction of the vector representing the matrix supersaturation and particle composition.