Comparative analysis of the size distributions of linear, planar, and spatial Poisson Voronoi cells

Materials Characterization

Volumn 36, Issue 2, 1996, Pages 53-63

  Marthinsen, Knut ^a  

^a SINTEF   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; CRYSTAL MICROSTRUCTURE; GRAIN GROWTH; GRAIN SIZE AND SHAPE; SPATIAL VARIABLES MEASUREMENT; THREE DIMENSIONAL;

CELL SIZE DISTRIBUTIONS; GAMMA DISTRIBUTION FUNCTIONS; LOGARITHMIC SCALE; POISSON VORONOI CELL STRUCTURES;

PARTICLE SIZE ANALYSIS;

EID: 0030080282     PISSN: 10445803     EISSN: None     Source Type: Journal    
DOI: 10.1016/1044-5803(95)00253-7     Document Type: Article

References (21)

1. G. Abruzzeese and P. Brozzo, eds., Grain Growth in Polycrystalline Materials, Trans. Tech. Publications, Zurich (1992).
2. T. O. Sætre, O. Hunderi, and E. Nes, Computer simulation of primary recrystallization microstructures: the effects of nucleation and growth kinetics, Acta. Metall. 34:981-987 (1986).
3. K. Marthinsen, O. Lohne, and E. Nes, The development of recrystallization microstructures studied experimentally; and by computer simulation, Acta Metall. 37:135-145 (1989).
4. K. Marthinsen, O. Hunderi, and N. Ryum, The influence of spatial grain size correlation and topography on normal grain growth in two dimensions. Acta Metall. (in press, 1996).
5. E. N. Gilbert, Random subdivisions of space into crystals, Ann. Math. Stat. 33:958-972 (1962).
6. T. Kiang, Random fragmentation in two and three dimensions, Z. Astrophys. 64:433-439 (1966).
7. A. L. Hinde and R. E. Miles, Monte-Carlo estimates of the distributions of random polygons of the Voronoi tesselation with respect to a Poisson process. J. Stat. Comput. Simul. 10:205-223 (1980).
8. K. W. Mahin, K. Hanson, and J. W. Morris, Jr., Comparative analysis of the cellular and Johnson-Mehl microstructures through computer simulation, Acta Metall. 28:443-453 (1980).
9. R. E. Miles, Sectional Voronoi tesselations, Rev. Mater. Argent. 29:310-327 (1984).
10. D. Weaire, J. P. Kermode, and J. Weichert, On the distribution of cell areas in a Voronoi network, Philos. Mag. Lett. B 53:L101-L105 (1986).
11. P. N. Andrade and M. A. Fortes, Distributions of cell volumes in a Voronoi partition. Philos. Mag. B 58:671-674 (1988).
12. M. F. Vaz and M. A. Fortes, Grain size distribution: the lognormal and the gamma function, Scripta Metall. 22:35-45 (1988).
13. d, adv. Appl. Probl. 21:37-73 (1989).
14. U. Lorz, Cell-area distributions of planar sections of spatial Voronoi mosaic, Mater. Char. 25:297-309 (1990).
15. S. Kumar, S. K. Kurtz, J. R. Banavar, and M. G. Sharma, Properties of a three-dimensional Poisson Voronoi tesselation: a Monte Carlo study. J. Stat. Phys. 67:523-551 (1992).
16. S. Kumar and S. K. Kurtz, Properties of two-dimensional Poisson-Voronoi tesselation: a Monte Carlo study, Mater. Char. 31:55-68 (1993).
17. L. Muche and D. Stoyan, Contact and chord length distributions of the Poisson Voronoi tesselations. J. Appl. Probl. 29:467-471 (1992).
18. A. Thorvaldsen, Simulation of 3D Voronoi polygons, Mater. Sci. Forum 94-96:307-312 (1992).
19. A. Okabe, B. Boots, and K. Sugihara, Spatial Tesselations: Concepts and Applications of Voronoi Diagrams. John Wiley and Sons, New York (1992).
20. G. E. W. Schulze, Modellbetrachtung zur primaren Rekristallisation in einer Dimension, Z. Metallkde 69:605-610 (1978).
21. T. Furu, K. Marthinsen, and E. Nes, Modeling of recrystallization, Mater. Sci. Technol. 6:1093-1102 (1990).