Stereology of grain boundary precipitates

Vratislav Horálek

Aplikace matematiky (1989)

  • Volume: 34, Issue: 4, page 303-317
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Horálek, Vratislav. "Stereology of grain boundary precipitates." Aplikace matematiky 34.4 (1989): 303-317. <http://eudml.org/doc/15585>.

@article{Horálek1989,
abstract = {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.},
author = {Horálek, Vratislav},
journal = {Aplikace matematiky},
keywords = {random tesselation; stereology; lens-shaped discs; stereological model; parameter estimations; random tesselation; stereology; lens-shaped discs; stereological model},
language = {eng},
number = {4},
pages = {303-317},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Stereology of grain boundary precipitates},
url = {http://eudml.org/doc/15585},
volume = {34},
year = {1989},
}

TY - JOUR
AU - Horálek, Vratislav
TI - Stereology of grain boundary precipitates
JO - Aplikace matematiky
PY - 1989
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 34
IS - 4
SP - 303
EP - 317
AB - 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.
LA - eng
KW - random tesselation; stereology; lens-shaped discs; stereological model; parameter estimations; random tesselation; stereology; lens-shaped discs; stereological model
UR - http://eudml.org/doc/15585
ER -

References

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  2. R. Coleman, Line section sampling of Wicksell's corpuscles, Acta Stereologica, 6 (1987), 33-36. (1987) Zbl0619.60017
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  4. A. M. Gokhale A. K. Jena, 10.1016/0026-0800(80)90028-2, Metallography 13 (1980), 307-17. (1980) DOI10.1016/0026-0800(80)90028-2
  5. V. Horálek, Statistical Models of Some Testing and Inspection Procedures of Products, Materials and Raw Materials, (in Czech). Thesis, Charles University Praha, 1961. (1961) 
  6. A. J. Jakeman R. S. Anderssen, Abel type integral equation in stereology. I. General discussion, J. Microscopy, 105 (1975), 121-33. (1975) 
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  9. R. E. Miles, The random division of space, Suppl. Adv. Appl. Prob., 1972, 243-66. (1972) Zbl0258.60015
  10. J. Møller, Random tessellation in R d , Memoirs No. 9, Department of Theoretical Statistics, University of Aarhus, Denmark, 1986. (1986) 
  11. S. A. Saltykov, Stereometric Metallography, 2nd. Ed., Metallurgizdat, Moscow, 1958. (1958) 
  12. C. S. Smith L. Guttman, Measurement of internal boundaries in three-dimensional structure by random sectioning, Trans: AIME 197 (1953), 81 - 87. (197) 
  13. D. Stoyan W. S. Kendall J. Mecke, Stochastic Geometry and Its Applications, Akademie Verlag, Berlin, 1987. (1987) MR0879119
  14. E. E. Underwood, Quantitative Stereology, Addison-Wesley, Reading, Mass., 1970. (1970) 
  15. S. D. Wicksell, The corpuscle problem. A mathematical study of a biometric problem, Biometrika, 17 (1925), 84-99. (1925) 

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