Numerical analysis of solid and liquid diffusion in microsegregation of binary alloys

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Abstract
A numerical method has been devised which enables the simultaneous changes of solute distribution in the solid and the liquid in the solidifying volume between secondary dendrite arms to be described. Simplifying assumptions are made in the geometric model, but not of solid or liquid diffusivities. A previously used first order approximation and a new second order approximation of the solidification parameter averaging diffusion throughout the solidification interval are compared to the exact solution, and the proportionality constants between these parameters are determined. A simple but sufficiently accurate temperature averaging procedure makes possible the use of the first order approximation with simple correction factors in all practical cases for liquid and solid state diffusion. The values of solidification parameters for the limiting cases (negligible solid state diffusion or infinitely fast liquid diffusion) are given, and a homogenization parameter is defined which enables the degree of solute redistribution during cooling to be described quantitatively as a function of cooling rate, partition coefficient, and diffusion coefficients. The reliability of the method is demonstrated by application to Al–Cu alloys and to the segregation of carbon, sulphur, and phosphorus in iron. MST/149