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The effect of an axial magnetic field on periodic growth rate fluctuations in Czochralski crystal growth

The effect of an axial magnetic field on periodic growth rate fluctuations in Czochralski crystal growth
The effect of an axial magnetic field on periodic growth rate fluctuations in Czochralski crystal growth
In this paper we develop a mathematical model to investigate the effect of growth rate fluctuations in magnetic Czochralski crystal growth. The pull rate is assumed constant and the growth rate fluctuates with frequency ? rad/s, the crystal rotation rate. We explore the effect of the magnetic field and the crucible rotation on fluid flow and mass transfer in the vicinity of the crystal/melt interface. Numerical results are obtained for 0?N?32 and -0.1?s?1.0, where N is the magnetic interaction parameter and s is the ratio of crucible to crystal rotation. Asymptotic results are obtained for the velocity field for large N and agreement is good for N>4. The analysis is extended to the concentration field to give asymptotic results for N??, Sc??, N/Sc2?? where Sc is the Schmidt number. Again the asymptotic results agree well with the numerical solutions. We conclude that the phase of the resulting concentration fluctuations appears to be independent of N and s. The spatially averaged effective distribution coefficient, keff and the amplitude of the concentration oscillations, Ac, are linked. As keff?1, Ac increases and so improved macrosegregation is accompanied by a deterioration in microsegregation.
0022-0248
466-480
Cartwright, R.A.
d01c44b2-1973-4016-910f-5aea98cb73fe
Wheeler, A.A.
eb831100-6e51-4674-878a-a2936ad04d73
Cartwright, R.A.
d01c44b2-1973-4016-910f-5aea98cb73fe
Wheeler, A.A.
eb831100-6e51-4674-878a-a2936ad04d73

Cartwright, R.A. and Wheeler, A.A. (1988) The effect of an axial magnetic field on periodic growth rate fluctuations in Czochralski crystal growth. Journal of Crystal Growth, 87 (4), 466-480. (doi:10.1016/0022-0248(88)90095-4).

Record type: Article

Abstract

In this paper we develop a mathematical model to investigate the effect of growth rate fluctuations in magnetic Czochralski crystal growth. The pull rate is assumed constant and the growth rate fluctuates with frequency ? rad/s, the crystal rotation rate. We explore the effect of the magnetic field and the crucible rotation on fluid flow and mass transfer in the vicinity of the crystal/melt interface. Numerical results are obtained for 0?N?32 and -0.1?s?1.0, where N is the magnetic interaction parameter and s is the ratio of crucible to crystal rotation. Asymptotic results are obtained for the velocity field for large N and agreement is good for N>4. The analysis is extended to the concentration field to give asymptotic results for N??, Sc??, N/Sc2?? where Sc is the Schmidt number. Again the asymptotic results agree well with the numerical solutions. We conclude that the phase of the resulting concentration fluctuations appears to be independent of N and s. The spatially averaged effective distribution coefficient, keff and the amplitude of the concentration oscillations, Ac, are linked. As keff?1, Ac increases and so improved macrosegregation is accompanied by a deterioration in microsegregation.

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Published date: 1988

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Local EPrints ID: 829
URI: https://eprints.soton.ac.uk/id/eprint/829
ISSN: 0022-0248
PURE UUID: 8f86126a-681d-4f96-a4a6-ffcd449f32be

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Date deposited: 05 Apr 2004
Last modified: 17 Jul 2017 17:17

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