Breakdown of Burton-Prime-Slichter approach and lateral solute segregation in radially converging flows


Breakdown of Burton-Prime-Slichter approach and lateral solute segregation in radially converging flows

Priede, J.; Gerbeth, G.

A theoretical study is presented of the effect of a radially converging melt flow on the radial solute segregation in simple solidification models. We show that the classical Burton-Prim-Slichter (BPS) theory describing the effect of a diverging flow on the solute incorporation into the solidifying material breaks down for converging flows. The breakdown is caused by a divergence of the integral defining the effective boundary layer thickness which is the basic concept of the BPS theory. The divergence can formally be avoided by restricting the axial extension of the melt to a layer of finite height. This allows us to obtain radially uniform solutions for the solute distributions which, however, are valid only for weak melt flows with an axial velocity away from the solidification front comparable to the growth rate. There is a critical melt velocity for each growth rate at which the solution passes through a singularity and becomes physically inconsistent for stronger melt flows. Thus, the radially uniform solute distribution becomes incompatible with a converging flow exceeding the growth rate, and a radial segregation sets in. The solute distribution is analysed in detail for a solidification front presented by a disk of finite radius R0 subject to a converging melt flow. We obtain similarity and matched asymptotic solutions showing that the radial solute concentration depends on the radius r as ln1/3(R0/r) and ln(R0/r) close to the rim and at large distances from it, respectively. The converging flow causes a solute pile-up forming a logarithmic concentration peak at the symmetry axis which might be an undesirable feature for crystal growth processes.

  • Journal of Crystal Growth 285(2005), 261-269

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Publ.-Id: 6475