A microscopic model for impurity uptake at a sharp crystal‐liquid interface during alloy solidification is presented in terms of the bulk properties of the liquid and solid phases. The results for stepwise growth and continuous growth at the same interface velocity differ quantitatively but exhibit the same qualitative features. A transition from equilibrium segregation to complete solute trapping occurs as the velocity surpasses the diffusive speed of solute in the liquid. The location of the transition varies little with equilibrium segregation coefficient, and a kinetic limit to solute trapping is found to be quite unlikely. Comparison is made with other models; critical differences are pointed out. Coupled with a growth velocity equation and with macroscopic heat‐ and solute‐diffusion equations, the model forms a complete description of one‐dimensional crystal growth. The steady‐state solution to this system is indicated for the case of a planar interface. The results are applied to describe regrowth from laser‐induced melting. Preliminary comparison with experiment is made. The steady‐state solution for thermal and impurity transport is suggested for use whenever detailed computer calculations are unavailable or are unnecessarily involved.

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Model for solute redistribution during rapid solidification

Quantitative models of trace element behavior in magmatic processes

Growth, structure, and properties of sea ice.

Fundamentals of crystallization: Kinetic effects on particle size distributions and morphology

A mathematical analysis is made of the redistribution of solute which occurs during the solidification, without convection, of a single-phase alloy. Calculations of solute distributions are carried...

a Mathematical Analysis of Solute Redistribution during Solidification

The incorporation of solute elements into single crystals of germanium grown from the melt is examined in terms of a simple model. The theory takes account of the contribution of solute transport in the melt, owing to diffusion and fluid motion, to the over‐all process of impurity incorporation during steady‐state crystallization. The analysis is extended to treat the transient inclusion of solute which results when the composition of the melt is abruptly changed.

W. P. Slichter

Papers

The Distribution of Solute in Crystals Grown from the Melt. Part I. Theoretical