scholarly journals A Method for Determining the Solid-Liquid Interface Shape during the Czochralski Growth of Copper Crystals

1972 ◽  
Vol 13 (5) ◽  
pp. 370-371 ◽  
Author(s):  
Tetsuo Inoue ◽  
Jiro Watanabe ◽  
Mikio Yamamoto
Keyword(s):  
Liquid Interface ◽  
Czochralski Growth ◽  
Interface Shape ◽  
Solid Liquid Interface ◽  
Solid Liquid ◽  
Copper Crystals

Numerical simulation of melt growth: prediction of solid-liquid interface shape

1993 ◽  
Vol 129 (1-2) ◽  
pp. 30-36
Author(s):  
K. Oda ◽  
T. Saito ◽  
J. Nishihama ◽  
T. Ishihara ◽  
M. Sato
Keyword(s):  
Numerical Simulation ◽  
Liquid Interface ◽  
Interface Shape ◽  
Melt Growth ◽  
Growth Prediction ◽  
Solid Liquid Interface ◽  
Solid Liquid

Finite Elenent Analysis of The Effect of a Non-Planar Solid-Liquid Interface on The Lateral Solute Segregation During Unidirectional Solidification.

1981 ◽  
Vol 9 ◽  
Author(s):  
F. M. Carlson ◽  
L-Y Chin ◽  
A. L. Fripp ◽  
R. K. Crouch
Keyword(s):  
Finite Element ◽  
Concentration Field ◽  
Solute Segregation ◽  
Planar Interface ◽  
Unidirectional Solidification ◽  
Liquid Interface ◽  
Interface Shape ◽  
Element Technique ◽  
Solid Liquid Interface ◽  
Solid Liquid

ABSTRACTThe effect of solid-liquid interface shape on lateral solute segregation during steady-state unidirectional solidification of a binary mixture is calculated under the assumption of no convection in the liquid. A finite element technique is employed to compute the concentration field in the liquid and the lateral segregation in the solid with a curved boundary between the liquid and solid phases. The computational model is constructed assuming knowledge of the solid-liquid interface shape; no attempt is made to relate this shape to the thermal field. The influence of interface curvature on the lateral compositional variation is investigated over a range of system parameters including diffusivity, growth speed, distribution coefficient, and geometric factors of the system. In the limiting case of a slightly non-planar interface, numerical results from the finite element technique are in good agreement with the analytical solutions of Coriell and Sekerka obtained by using linear theory. For the general case of highly non-planar interface shapes, the linear theory fails and the concentration field in the liquid as well as the lateral solute segregation in the solid can be calculated by using the finite element method.

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