Probabilistic theory of screening of particles growth

by

Probabilistic theory of screening of particles growth

Andriy Burbelko

AGH University of Science and Technology, al. Adama Mickiewicza 30, 30-059 Kraków.

DOI:

https://doi.org/10.7494/cmms.2002.4.0028

Abstract:

The study of grains growth during a phase and structural transformations has essential importance for materials science and engineering. The existing Kolmogorov theory covers growth of grains on the assumptions of the geometric similarity of particles, their convex shape and uniform geometric distribution in space. The statistical theory is presented in the work, allowing to analyze the transformations kinetics in the case that the grains have arbitrary shapes and the arbitrary distribution of the linear growth rate on their surfaces. The case study of modeling of the growth of grains with disk and rod morphology is demonstrated

Cite as:

Burbelko, A. (2002). Probabilistic theory of screening of particles growth. Computer Methods in Materials Science, 2(4), 106 – 120. https://doi.org/10.7494/cmms.2002.4.0028

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References:

Andrienko, Y.A., Brilliantov, N.V., Krapivsky, P.L. (1992). Nucleation and growth in systems with many stable phases. Physical Review A, 45, 2263-2269.

Avrami, M. (1939). Kinetics of Phase Change. I. General Theory. Journal of Chem. Phys., 7, 1103-1112.

Avrami, M. (1940). Kinetics of Phase Change. II. Transformation ~Time Relations for Random Distribution of Nuclei. Journal of Chem. Phys., 8, 212-224.

Avrami, M. (1941). Kinetics of Phase Change. III. Granulation, Phase Change, and Microstructure. Journal of Chem. Phys., 9, 177-184.

Birnie III, D.P., Weinberg, M.C. (1996a). Shielding effects in 1-D transformation kinetics. Physica A, 223, 337-347.

Birnie III, D.P., Weinberg, M.C. (1996b). Transformation kinetics in 1-D processes with continuous nucleation: comparison of shielding and phantom effects. Physica A, 230, 484-498.

Birnie III, D.P., Weinberg, M.C. (2000). Development of anisotropic particle morphology in an isotropically transforming matrix. Physica A, 285, 279-294.

Fras, E. (1992). Krystalizacja metali i stopów. Warszawa, PWN.

Humphreys, Hatherly. (1996). Recrystallization and Related Annealing Phenomena. Oxford, Pergamon.

Johnson ,W.A., Mehl, R.F. (1939). Reaction Kinetics in Processes of Nucleation and Growth. Transaction Metallurgical Society AIME, 135, 416-442.

Kasuya, T., Ichikawa ,K., Fuji, M., Bhadeshia, H.K.D.H. (1999). Real and Extended Volume in Simultaneous Transformations. Materials Science and Technology, 15, 471-473.

Kędzierski, Z. (2003). Przemiany fazowe w układach skondensowanych. Wyd. AGH, Kraków.

Longa, W. (1989). Zagadnienie modelowania funkcji źródła ciepła krystalizacji. Zeszyty naukowe AGH. Metalurgia i Odlewnictwo. Z. 125, 103-113.

Lusk, M., Jou, H.J. (1997). On the rule of additivity in phase transformation kinetics. Metallurgical and Materials Transactions A, 28, 287-291.

Pusztai, T., Granasy, L. (1998). Monte Carlo simulation of firstorder phase transformations with mutual blocking of anisotropically growing particles up to all relevant orders. Physical Review B, 57, 14110-14118.

Ramos, R.A., Rikvold, P.A., Novotny, M.A. (1999). Test of the Kolmogorov-Johnson-Mehl-Avrami picture of metastable decay in a model with microscopic dynamics. Physical Review B, 59, 9053-9069.

Shepilov, M.P., Baik, D.S. (1994). Computer simulation of crystallization kinetics for the model with simultaneous nucleation of randomly-oriented ellipsoidal crystals. Journal of Non-Crystalline Solids, 171, 141-156.

Weinberg, M.C., Birnie, D.P. (1996a). Avrami exponents for transformations producing anisotropic particles. Journal of Non- Crystalline Solids, 202, 290-296.

Weinberg M.C., Birnie III D.P. (1996b). Transformation kinetics in one-dimensional processes with continuous nucleation: The effect of shielding. Journal of Chemical Physics, 105, 5138-5144.

Weinberg M.C., Birnie III, D.P., Farias, V.F. (2002). Simulation of anisotropic particle shape development during 2D transformation. Journal of Physical Chemistry B, 106, 8318-8325.

Weinberg, M.C., Birnie III, D.P., Shneidman, V.A. (1997). Crystallization kinetics and the JMAK equation. Journal of Non- Crystalline Solids, 219, 89-99.

Benenpknii, B.3. (1980). TeoMeTpHKO-BCDOSTHOTHBIC MOJLCJIH KDHCTAJUIM3AUMH. PCHOMCHOJIOTHYCCKHŃ MOAXOL. MockBa, Hayka.

Konmoropos, A.H. (1937). K crarucrnueckoii Teopuu kpucramm3anu MeTanmnoB. H3eecmun Axademuu Hayk CCCP. Cepua mamemamuueckax, No 3, 355-359.