Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-09T05:56:24.214Z Has data issue: false hasContentIssue false
  • English
  • Français

Calculation of diffuse scattering near Bragg reflections from coherent precipitates

Published online by Cambridge University Press:  31 January 2011

S. Iida ,
B. C. Larson  and
J. Z. Tischler
S. Iida*
Affiliation:
Solid State Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6024
B. C. Larson
Affiliation:
Solid State Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6024
J. Z. Tischler
Affiliation:
Solid State Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6024
*
a)Permanent address: Physics Department, Toyama University, Toyama, Japan.
Get access

Abstract

Numerical calculations of the diffuse scattering near Bragg reflections from coherent solute precipitates in a dilute alloy have been made. Results are presented for spherical precipitates in an elastically isotropic continous medium where the calculations have been reduced to a one-dimensional numerical integral. The scattering is separated into direct scattering from the precipitates, the Huang scattering from the lattice distortions, and the higher-order distortion scattering; calculations are presented for 50 Å radius precipitates with an internal strain of – 1.5%, and the sensitivity of the scattering to changes of the size and the internal strain of the precipitates is demonstrated. The possibility of using such scattering for the determination of the concentration, size distribution, and internal strain of solute precipitates is discussed.

Type
Articles
Information
Journal of Materials Research , Volume 3 , Issue 2 , April 1988 , pp. 267 - 273
Copyright
Copyright © Materials Research Society 1988

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Dederichs, P. H., Phys. Rev. B 4, 1041 (1971).CrossRefGoogle Scholar
2Trinkaus, H., Phys. Status Solidi B 51, 307 (1972).CrossRefGoogle Scholar
3Dederichs, P. H., J. Phys. F 3, 471 (1973).CrossRefGoogle Scholar
4Ehrhart, P., Trinkaus, H., and Larson, B. C., Phys. Rev. B 25, 834 (1982).CrossRefGoogle Scholar
5Larson, B. C. and Schmatz, W., Phys. Status Solidi B 99, 267 (1980).CrossRefGoogle Scholar
6Krivoglaz, M. A., Theory of X-ray and Thermal Neutron Scattering by Real Crystals (Plenum, New York, 1969).Google Scholar
7Krivoglaz, M. A., Phys. Met. Metallogr. 9, 1 (1960).Google Scholar
8Krivoglaz, M. A. and Ryaboshapka, K. P., Phys Met. Mettalogr. 16, 641 (1963).Google Scholar
9Krivoglaz, M. A. and Hao, T Yu, Phys. Met, Metallogr. 27, 1 (1969).Google Scholar
10Barabash, R. I. and Krivoglaz, M. A., Phys. Met. Metallogr. 51 (5), 1 (1981); Phys. Met. Metallogr. 45 (1), 1 (1978).Google Scholar
11Dobromyslov, A. V., Phys. Met. Metallogr. 50 (6), 118 (1980); A. V. Dobromyslov, Phys. Met. Metallogr. 42,91 (1976); N. N. Ganz-huila, L. Ye Kozlova, and V. V. Kokorin, Phys. Met. Metallogr. 52 (1), 89 (1981).Google Scholar
12Larson, B. C. and Schmatz, W., Phys. Rev. B 10, 2307 (1974).CrossRefGoogle Scholar
13Trinkaus, H., Z. Angew. Phys. 31, 229 (1971).Google Scholar
14Dederichs, P. H., Phys. Rev. B 1, 1306 (1970).CrossRefGoogle Scholar
15Holy, V., Acta Crystallogr. A 40, 675 (1984).CrossRefGoogle Scholar
16The remaining integral over rin Eq. (7) can be performed in r<, but the integral was performed numerically from 0 to ∞ in this study.Google Scholar
17Results of calculations by the authors to be published.Google Scholar