Morphological stability diagram for slowly and rapidly solidifying binary systems

Abstract

A linear morphological stability of the solid-liquid interface is analyzed for a binary alloy in the limit of low and high crystal growth velocities. Using the result of this analysis, a diagram of morphologies is derived for a whole range of solidification rates with indicating critical growth velocities for the transitions planar front ⇔ cellular/dendritic structure. It is specially noted that the speed of solute diffusion in the bulk liquid limits the absolute chemical stability velocity from the high-rate transition cells/dendrites ⇒ planar front. a

Application of two-grid interpolation to enhance average gradient method for solving partial differential equations

“…In the physical science based numerical full field modelling of mesoscale phenomena, it is often necessary to solve partial differential equations describing the physical phenomena such as phase transformations [5,6,7], deformation [8,7], diffusion [5,7], fluid flow [9,10], recrystallization [11,12] etc. During processing of materials, deformation of the material is often necessary in order to obtain desired shape.…”