Stereology of grain boundary precipitates
Horálek, Vratislav
Applications of Mathematics, Tome 34 (1989), p. 303-317 / Harvested from Czech Digital Mathematics Library
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Precipitates modelled by rotary symmetrical lens-shaped discs are situated on matrix grain boundaries and the homogeneous specimen is intersected by a plate section. The stereological model presented enables one to express all basic parameters of spatial structure and moments of the corresponding probability distributions of quantitative characteristics of precipitates in terms of planar structure parameters the values of which can be estimated from measurements carried out in the plane section. The derived relationships are transformed into those valid for spherical precipitates.

Publié le : 1989-01-01
Classification:  52A22,  60D05,  92F05 
@article{104358,
     author = {Vratislav Hor\'alek},
     title = {Stereology of grain boundary precipitates},
     journal = {Applications of Mathematics},
     volume = {34},
     year = {1989},
     pages = {303-317},
     zbl = {0688.60010},
     mrnumber = {1008582},
     language = {en},
     url = {http://dml.mathdoc.fr/item/104358}
}

Horálek, Vratislav. Stereology of grain boundary precipitates. Applications of Mathematics, Tome 34 (1989) pp. 303-317. http://gdmltest.u-ga.fr/item/104358/

R. Coleman An Introduction to Mathematical Stereology, Memoirs No. 3, Department of Theoretical Statistics, University of Aarhus, Denmark, 1979. (1979) | MR 0547508 | Zbl 0442.60019

R. Coleman Line section sampling of Wicksell's corpuscles, Acta Stereologica, 6 (1987), 33-36. (1987) | Zbl 0619.60017

E. N. Gilbert Random subdivision of space into crystals, Ann. Math. Statistics, 33 (1962), 958-72. (1962) | Article | MR 0144253

A. M. Gokhale A. K. Jena Size distribution of grain-boundary precipitates, Metallography 13 (1980), 307-17. (1980) | Article

V. Horálek Statistical Models of Some Testing and Inspection Procedures of Products, Materials and Raw Materials, (in Czech). Thesis, Charles University Praha, 1961. (1961)

A. J. Jakeman R. S. Anderssen Abel type integral equation in stereology. I. General discussion, J. Microscopy, 105 (1975), 121-33. (1975)

J. W. Martin R. D. Doherty Stability of Microstructure in Metallic Systems, Cambridge University Press, London, 1975. (1975)

J. L. Meijering Interface area, edge length and number of vertices in crystal aggregates with random nucleation, Philips Res. Rep. 8 (1953), 270-90. (1953) | Zbl 0053.33401

R. E. Miles The random division of space, Suppl. Adv. Appl. Prob., 1972, 243-66. (1972) | Zbl 0258.60015

J. Møller Random tessellation in $R^d$, Memoirs No. 9, Department of Theoretical Statistics, University of Aarhus, Denmark, 1986. (1986)

S. A. Saltykov Stereometric Metallography, 2nd. Ed., Metallurgizdat, Moscow, 1958. (1958)

C. S. Smith L. Guttman Measurement of internal boundaries in three-dimensional structure by random sectioning, Trans: AIME 197 (1953), 81 - 87. (197 )

D. Stoyan W. S. Kendall J. Mecke Stochastic Geometry and Its Applications, Akademie Verlag, Berlin, 1987. (1987) | MR 0879119

E. E. Underwood Quantitative Stereology, Addison-Wesley, Reading, Mass., 1970. (1970)

S. D. Wicksell The corpuscle problem. A mathematical study of a biometric problem, Biometrika, 17 (1925), 84-99. (1925)