Universal grain size distribution, most chaotic microstructures and tessellation condition

International Journal of Engineering Science

Volumn 57, Issue , 2012, Pages 24-35

  Berdichevsky, Victor L ^a  

^a Wayne State University   (United States)

Author keywords

Grain growth; Grain size distribution; Microstructure entropy; Recrystallization; Tessellation

Indexed keywords

EXPERIMENTAL DATA; FITTING PARAMETERS; GEOMETRICAL PARAMETERS; GRAIN BOUNDARY STRUCTURE; GRAIN SIZE; GRAIN SIZE DISTRIBUTION; INFINITE CHAINS; SELF-SIMILAR; SUFFICIENT CONDITIONS; TESSELLATION;

CRYSTALLIZATION; GRAIN BOUNDARIES; GRAIN GROWTH; MICROSTRUCTURE; PROBABILITY DISTRIBUTIONS;

GRAIN SIZE AND SHAPE;

EID: 84861808860     PISSN: 00207225     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijengsci.2012.03.037     Document Type: Article

References (20)

1. M.P. Anderson, D.J. Srolovitz, G.S. Grest, and P.S. Sahni Computer simulation of grain growth - I, Kinetics Acta Metallurgica 32 1984 783 791 (Pubitemid 14591002)
2. E.F. Beckenbach, and R. Bellman Inequalities 1961 Springer-Verlag
3. R. Bellman A generalization of some integral identities due to Ingham and Siegel Duke Mathematical Journal 24 1956 571 578
4. V.L. Berdichevsky Entropy of microstructure Journal of Mechanics and Physics of Solids 56 2008 742 771 (Pubitemid 351248896)
5. V.L. Berdichevsky Variational principles of continuum mechanics 2009 Springer-Verlag Heidelberg-Berlin
6. V.L. Berdichevsky Introduction to stochastic variational problems CISM Courses and Lectures Vol. 535 2011 Heidelberg-Berlin Springer-Verlag pp. 211-248
7. L.-Q. Chen, and W. Yang Computer simulations of the domain dynamics of a quenched system with a large number of nonconserved order parameters: The grain-growth kinetics Physical Review B 50 1994 15752
8. P. Feltham Grain growth Acta Metallurgica 5 1957 97 105
9. M. Hillert On the theory of normal and anomalous grain growth Acta Metallurgica 13 1965 227 238
10. A.E. Ingham An integral which occurs in statistics Proceedings of the Cambridge Philological Society 29 1933 271 276
11. C.E. Krill, and R. Birrenger Estimating grain-size distribution in nanocrystalline materials from X-ray diffraction profile analysis Philosophical Magazine A 77 1998 621 640
12. I.M. Lifshitz, and V.V. Slyozov On the kinetics of precipitation from supersaturated solid solution Zh. Exp. Theor. Phys. 35 1958 479 492
13. C.S. Pande On stochastic theory of grain growth Acta Metallurgica 35 1987 2671 2678
14. C.S. Pande, and A.K. Rajagopal Uniqueness and self similarity of size distributions in grain growth and coarsening Acta Metallurgica 49 2001 1805 1811 (Pubitemid 32427382)
15. C.S. Pande, and G.B. McFadden Self-similar grain size disribution in three dimensions: A stochastic treatment Acta Metallurgica 58 2010 1037 1044
16. Siegel, C. L. (1934-1935). The analytical theory of quadratic forms. Mimeographed notes, Princeton.
17. D.J. Srolovitz, M.P. Andeson, P.S. Sahni, and G.S. Grest Computer simulation of grain growth - II Acta Metallurgica 32 1984 793 802
18. F. Wakai, N. Enomoto, and H. Ogawa Three dimensional microstructural evolution in ideal grain growth-general statistics Acta Metallurgica 48 2000 1297 1311 (Pubitemid 30577708)
19. H. Wang, G.Q. Liu, and X.G. Qin Grain size distribution and topology in 3D grain growth simulation with large-scale Monte-Carlo method International Journal of Minerals. Metallurgy and Materials 16 2009 37 42
20. C. Zhang, A. Suzuki, T. Ishimaru, and M. Enomoto Characterization of three-dimensional grain structure in polycrystalline iron by serial sectioning Metallurgical and Materials Transaction A 35A 2004 1927 1933