ANALYSIS OF MOVING BOUNDARY PRO- BLEM OF GROWTH OF BISMUTH GERMANATE CRYSTAL BY HEAT EXCHANGER METHOD

Wang JH; Kim DH; Chung DS

Korean Journal of Chemical Engineering, Vol.13, No.5, 503-509, September, 1996

Transient two-dimensional model of the growth of BGO crystal by heat exchanger method has been developed. A finite element method with nonorthogonal mapping technique for the solution of the moving boundary problem is developed where the melt/solid interface shape changes from hemispherical to planar. The moving boundary problems for the melt/solid interface location and the temperature field were solved by two mapping rule method which enables the computation of interface shape changing from hemispherical to planar. The maxi- mum deflection of interface is shown when the melt/solid interface meets the corner of crucible. As the excess heating temperature and the heat exchanger temperature were increased, more growth time for whole process is required but the quality of BGO crystal may be improved. The ratio of the height to the radius of crucible hardly affects the deflection of BGO melt/solid interface when it is greater than 1.5. As the cooling zone radius is decreased, maximum deflection is decreased. The heat transfer between the crucible and the heating element should be suppressed to maximize planarity of the interface shape.

Keywords:Heat Exchanger Method;Bismuth Germanate;Finite Element Method;Moving Boundary Problem;Nonorthogonal Mapping

[References]

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Berkowski M, Iliev K, Nikolov V, Peshev P, Piekarczyk W, J. Cryst. Growth, 108, 225 (1991)
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Ettouney HM, Brown RA, Comput. Phys., 49, 118 (1983)
Fan S, Shan G, Li J, Wang W, Crystal Properties Preparation, 36-38, 42 (1991)
Finlayson BA, "Nonlinear Analysis in Chemical Engineering," McGraw-Hill, New York (1980)
Gallagher RH, Oden JT, Zienkiewicz OC, Kawai T, Kawahara M, "Finite Elements in Fluids," John Wiley & Sons, New York, 5 (1984)
Gelinas RJ, Doss SK, Miller K, J. Comput. Phys., 40, 202 (1981)
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Kaldis E, "Crystal Growth of Electronic Materials," Elsevier Science Publishers B.V. (1985)
Kawano K, Yoshida T, Nakata R, Yamada N, Sumita M, Jpn. J. Appl. Phys., 32, 1736 (1993)
Lynch DR, Gray WG, J. Comput. Phys., 36, 135 (1980)
Quon DHH, Chehab S, Aota J, Kuriakose AK, Wang SSB, Saghir MZ, Chen HL, J. Cryst. Growth, 134, 266 (1993)
Saito H, Scriven LE, J. Comput. Phys., 42, 53 (1981)
Schmid F, Khattak CP, Felt DM, Am. Ceram. Soc. Bull., 73, 39 (1994)
Shigematsu K, Anzai Y, Omote K, Kimura S, J. Cryst. Growth, 137, 509 (1994)
Takagi K, Fukazawa T, J. Cryst. Growth, 76, 328 (1986)
Ungar LH, Ramprasad N, Brown RA, J. Sci. Comput., 3, 77 (1988)
Weber MJ, Monchamp RR, J. Appl. Phys., 44, 5495 (1973)

[Referenced By]

[1] Aris R, "Vectors, Tensors and the Basic Equations of Fluid Mechanics," Prentice-Hall, Englewood Cliffs (1962)

[2] Berkowski M, Iliev K, Nikolov V, Peshev P, Piekarczyk W, J. Cryst. Growth, 108, 225 (1991)

[3] Bird RB, Stewart WE, Lightfoot EN, "Transport Phenomena," John Wiley & Sons, New York (1960)

[4] Ettouney HM, Brown RA, Comput. Phys., 49, 118 (1983)

[5] Fan S, Shan G, Li J, Wang W, Crystal Properties Preparation, 36-38, 42 (1991)

[6] Finlayson BA, "Nonlinear Analysis in Chemical Engineering," McGraw-Hill, New York (1980)

[7] Gallagher RH, Oden JT, Zienkiewicz OC, Kawai T, Kawahara M, "Finite Elements in Fluids," John Wiley & Sons, New York, 5 (1984)

[8] Gelinas RJ, Doss SK, Miller K, J. Comput. Phys., 40, 202 (1981)

[9] Hood P, Int. J. Numer. Methods Eng., 10, 379 (1976)

[10] Kaldis E, "Crystal Growth of Electronic Materials," Elsevier Science Publishers B.V. (1985)

[11] Kawano K, Yoshida T, Nakata R, Yamada N, Sumita M, Jpn. J. Appl. Phys., 32, 1736 (1993)

[12] Lynch DR, Gray WG, J. Comput. Phys., 36, 135 (1980)

[13] Quon DHH, Chehab S, Aota J, Kuriakose AK, Wang SSB, Saghir MZ, Chen HL, J. Cryst. Growth, 134, 266 (1993)

[14] Saito H, Scriven LE, J. Comput. Phys., 42, 53 (1981)

[15] Schmid F, Khattak CP, Felt DM, Am. Ceram. Soc. Bull., 73, 39 (1994)

[16] Shigematsu K, Anzai Y, Omote K, Kimura S, J. Cryst. Growth, 137, 509 (1994)

[17] Takagi K, Fukazawa T, J. Cryst. Growth, 76, 328 (1986)

[18] Ungar LH, Ramprasad N, Brown RA, J. Sci. Comput., 3, 77 (1988)

[19] Weber MJ, Monchamp RR, J. Appl. Phys., 44, 5495 (1973)