Journal of Materials Research

Articles

Aperiodic stepwise growth model for the velocity and orientation dependence of solute trapping

L. M. Goldmana1 and M. J. Aziza2 p1

a1 Division of Applied Sciences, Harvard University, Cambridge, Massachusetts 02138

a2 Solid State Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831

Abstract

An atomistic model for the dependence on interface orientation and velocity v of the solute partition coefficient k during rapid solidification is developed in detail. Starting with a simple stepwise growth model, the simple continuous growth model result is obtained for k(v) when the growth steps are assumed to pass at random intervals rather than periodically. The model is applied to rapid solidification of silicon. Crystal growth at all orientations is assumed to occur by the rapid lateral passage of (111) steps at speeds determined by the interface velocity and orientation. Solute escape is parametrized by a diffusion coefficient at the edge of the moving step and a diffusion coefficient at the terrace, far from the step edge. The model results in an excellent fit to data for the velocity and orientation dependence of k of Bi in Si.

(Received January 30 1987)

(Accepted April 08 1987)

Correspondence:

p1 Permanent address: Division of Applied Sciences, Harvard University, Cambridge, Massachusetts 02138.

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