| Title:
|
Stereology of grain boundary precipitates (English) |
| Author:
|
Horálek, Vratislav |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
34 |
| Issue:
|
4 |
| Year:
|
1989 |
| Pages:
|
303-317 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
random tesselation |
| Keyword:
|
stereology |
| Keyword:
|
lens-shaped discs |
| Keyword:
|
stereological model |
| Keyword:
|
parameter estimations |
| MSC:
|
52A22 |
| MSC:
|
60D05 |
| MSC:
|
92F05 |
| idZBL:
|
Zbl 0688.60010 |
| idMR:
|
MR1008582 |
| DOI:
|
10.21136/AM.1989.104358 |
| . |
| Date available:
|
2008-05-20T18:37:05Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104358 |
| . |
| Reference:
|
[1] R. Coleman: An Introduction to Mathematical Stereology.Memoirs No. 3, Department of Theoretical Statistics, University of Aarhus, Denmark, 1979. Zbl 0442.60019, MR 0547508 |
| Reference:
|
[2] R. Coleman: Line section sampling of Wicksell's corpuscles.Acta Stereologica, 6 (1987), 33-36. Zbl 0619.60017 |
| Reference:
|
[3] E. N. Gilbert: Random subdivision of space into crystals.Ann. Math. Statistics, 33 (1962), 958-72. MR 0144253, 10.1214/aoms/1177704464 |
| Reference:
|
[4] A. M. Gokhale A. K. Jena: Size distribution of grain-boundary precipitates.Metallography 13 (1980), 307-17. 10.1016/0026-0800(80)90028-2 |
| Reference:
|
[5] V. Horálek: Statistical Models of Some Testing and Inspection Procedures of Products, Materials and Raw Materials.(in Czech). Thesis, Charles University Praha, 1961. |
| Reference:
|
[6] A. J. Jakeman R. S. Anderssen: Abel type integral equation in stereology. I. General discussion.J. Microscopy, 105 (1975), 121-33. |
| Reference:
|
[7] J. W. Martin R. D. Doherty: Stability of Microstructure in Metallic Systems.Cambridge University Press, London, 1975. |
| Reference:
|
[8] J. L. Meijering: Interface area, edge length and number of vertices in crystal aggregates with random nucleation.Philips Res. Rep. 8 (1953), 270-90. Zbl 0053.33401 |
| Reference:
|
[9] R. E. Miles: The random division of space.Suppl. Adv. Appl. Prob., 1972, 243-66. Zbl 0258.60015 |
| Reference:
|
[10] J. Møller: Random tessellation in $R^d$.Memoirs No. 9, Department of Theoretical Statistics, University of Aarhus, Denmark, 1986. |
| Reference:
|
[11] S. A. Saltykov: Stereometric Metallography.2nd. Ed., Metallurgizdat, Moscow, 1958. |
| Reference:
|
[12] C. S. Smith L. Guttman: Measurement of internal boundaries in three-dimensional structure by random sectioning.Trans: AIME 197 (1953), 81 - 87. |
| Reference:
|
[13] D. Stoyan W. S. Kendall J. Mecke: Stochastic Geometry and Its Applications.Akademie Verlag, Berlin, 1987. MR 0879119 |
| Reference:
|
[14] E. E. Underwood: Quantitative Stereology.Addison-Wesley, Reading, Mass., 1970. |
| Reference:
|
[15] S. D. Wicksell: The corpuscle problem. A mathematical study of a biometric problem.Biometrika, 17 (1925), 84-99. |
| . |
