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The X-Ray Diffraction Image of a Stacking Fault

Published online by Cambridge University Press:  06 March 2019

Norio Kato ,
Katsuhisa Usami  and
Takeshi Katagawa
Norio Kato
Affiliation:
Nagoya University Nagoya, Japan
Katsuhisa Usami
Affiliation:
Nagoya University Nagoya, Japan
Takeshi Katagawa
Affiliation:
Nagoya University Nagoya, Japan
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Abstract

The spherical wave theory of X-ray Pendellosung fringes in perfect crystals (N. Kato, Acta Cryst, 14: 526, 627, 1961) is extended to the case of crystals including a single stacking fault in an arbitrary way, Kelvin's stationary phase method is used extensively. The stationary phase condition gives us the trajectories of X-ray beams in the crystal. The phase and the amplitude along each trajectory are obtained by straightforward calculation. Based on this crystal wave field, the section patterns in X-ray diffraction topographs are obtained both for the direct and the Braggreflected waves. Characteristic fringe-patterns are expected. Through the image of a fault plane in a single section pattern, the geometrical configuration inside the crystal and the magnitude of the fault vector can be determined. Traverse patterns are also discussed. The fault image based on the plane wave theory (Whelan and Hirsch, Phil. Mag. 2: 1121, 1303, 1957) is also reformulated in the most general Laue case without the use of ad hoc assumptions on the shape of the dispersion surface.

Type
Research Article
Information
Advances in X-Ray Analysis , Volume 10: Fifteenth Annual Conference on Applications of X-ray Analysis, August 10-12, 1966 , 1966 , pp. 46 - 66
Copyright
Copyright © International Centre for Diffraction Data 1966

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References

1. Whelan, M. J., Hirsch, P. B., Home, R. W., and Bollmann, W., “Dislocation and Stacking Faults in Stainless Steel,” Proc. Roy. Soc. 240: 524, 1957.Google Scholar
2. Kohra, K. and Yoshimatsu, M., “X-Ray Observations of Lattice Defects—in Particular, Stacking Faults in the Neighbourhood of a Twin Boundary,” J. Phys. Soc. Japan 17: 1041, 1962.Google Scholar
3. Lang, A. R., “Direct Observation of Individual Dislocations by X-Ray Diffraction,” J. Appl. Phys. 29: 597, 1958.Google Scholar
4. Lang, A. R., “The Projection Topograph: A New Method in X-Ray Diffraction Microradiography,” Acta Cryst. 12: 249, 1959.Google Scholar
5. Katoand, N. Lang, A. R., “A Study of Pendellosung Fringes in X-Ray Diffraction,”. Acta Cryst. 12: 787, 1959.Google Scholar
6. Kato, N., “A Theoretical Study of Pendellosung Fringes. Part I, General Considerations,” Acta Cryst. 14: 526, 1961.Google Scholar
7. Kato, N., “A Theoretical Study of Pendellosung Fringes, Part II, Detailed Discussion Based upon a Spherical Wave Theory,” Acta Cryst. 14: 627, 1961.Google Scholar
8. Kato, N., “Wave Optical Theory of Diffraction in Single Crystals,” in: G. N. Ramachandran, Crystallography and Crystal Perfection, Academic Press, London, 1963, p. 153. [A correction should be made to equation (14) of this review article (see S. Homma, Y. Ando and N. Kato, “Absolute Positions of Pendellosung Fringes in X-Ray Cases,” J. Phys. Soc. Japan 21: 1160, 1966).]Google Scholar
9. Yoshimatsu, M., “A New Type of X-Ray Pendellosung Fringe Observed in a Quartz Single Crystal,” Japanese J. Appl. Phys, 4: 619, 1965.Google Scholar
10. Homma, S., unpublished.Google Scholar
11. Whelarx, M. J. and Hirsch, P. B., “Electron Diffraction from Crystals Containing Stacking Faults (1),” Phil. Mag. 2: 1121, 1957.Google Scholar
12. Whelan, M. J. and Hirsch, P. B., “Electron Diffraction from Crystals Containing Stacking Faults (11),” Phil. Mag. 2: 1303, 1957.Google Scholar
13. von Laue, M., ‘'Die Energiestrômung bei RontgenstrahUnterferenzen in Kristallen,” Acta Cryst. 5: 619, 1952.Google Scholar
14. Kato, N., “Dynamical Theory of Electron Diffraction for a Finite Polyhedral Crystal. (I) Extension of Bethe's Theory,” J. Phys. Soc. Japan 1: 397, 1952.Google Scholar
15. Ewald, P. P., “Group Velocity and Phase Velocity in X-Ray Crystal Optics,” Acta Cryst. 11: 888, 1958.Google Scholar
16. Kato, N., “The Flow of X-Ray and Material Waves in Ideally Perfect Single Crystals,” Acta Cryst. 11: 885, 1958.Google Scholar
17. von Laue, M., “Die Flumreszenzrontgenstrahlung von Einkriscallen,” Ann. Physik. 23: 705, 1935.Google Scholar
18. Zachariasen, W. H., Theory of X-ray Diffraction in Crystals, John Wiley, New York, 1945, Section III, p. 111.Google Scholar