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Direct Determination of the Reciprocal Lattice Spacing and the Radial Interference Distribution by the Fourier Method

Published online by Cambridge University Press:  06 March 2019

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Abstract

A procedure for extracting the interference distribution from the X-ray diffraction line using measured instrumental and wavelength distributions has been applied to the study of residual stress in copper following extension.

In the direct unfolding method the principal instrumental distributions due to the source and to specimen absorption are unfolded by the Fourier method. The remaining instrumental aberrations are extracted using the centroid displacements. The resultant scattering distribution is transformed by the relations of Mitchell and de Wolff and the spectral distribution unfolded. Conditions limiting the Fourier coefficients are applied to preserve stability. Measurements have been carried out with a diffractometer equipped with a diffracted beam monochromator.

The 420 and 331 interference distributions in copper following 10% extension have been compared with those of stress - free material. The distributions are symmetric both in the annealed specimen and after extension. In extension the distributions are displaced by an amount equivalent to a surface compressive stress of 6 kg/mm2, The symmetry of the interference distributions indicates that the displacement is due to a macrostress distribution.

Type
Research Article
Information
Advances in X-Ray Analysis , Volume 12: Seventeenth Annual Conference on Applications of X-ray Analysis, August 21-23, 1968 , 1968 , pp. 354 - 371
Copyright
Copyright © International Centre for Diffraction Data 1968

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References

1. Stokes, A. R., “A Numerical Fourier Analysis Method for the Correction of Widths and Shapes, of Lines on X-ray Powder Photographs”. Proc. Phys. Soc. Lond, 61, 382–391, 1948.Google Scholar
2. Bollenrath, F., Osswald, E., Moller, H., Neerfeld, H.. “Der Unterschied Zwischen Mec-hanisch und Rontgenographisch Ermittelten Elastizitats Konstanten”, Arch. Eisenhuttenw. 15 p. 183–194, 1941.Google Scholar
3. Macherauch, E., “Lattice Strain Measurements on Deformed FCC Metals”, Advances in X-Ray Analysis Vol. 9 Plenum Press, New York, 1965, p. 103–114.Google Scholar
4. Seitz, F.. “Physics of Metals”. McGraw Hill, New York, 1963.Google Scholar
5. Greenough, G. B., “Quantitative X-Ray Diffraction Observations on Strained Metal Aggregates”, Progress in Metal Physics, Vol. 3, Pergamon Press, London 1952, p. 176-219.Google Scholar
6. Jaoul, B., “Etude de la Plasticite et Application aux Metaux”. Dunod, Paris, 1967.Google Scholar
7. Mitchell, C. M. and de Wolff, P. M.. “Elimination of the Dispersion Effect in the Analyses of Diffraction Line Profiles”. Acta Cryst, 22: 325–328, 1967.Google Scholar
8. Mitchell, C. M.. “Instability in the Stokes Method of Resolving X-Ray Diffraction Lines”. Acta Cryst. 16 Supplement p. A156, 1963. I. U. Cr Symposium, Rome, Italy.Google Scholar
9. Rollett, J. S. and Higgs, L. A.. “Correction of Spectroscopic Line Profiles for Instrumental Broadening by the Fourier Method”, Proc. Phys. Soc. 79, 87–93, 1962.Google Scholar
10. Mitchell, C. M.. “Instability in Unfolding using the Fourier Method in the Analysis of Diffraction Line Profiles”. American Crystallographic Association Meeting, U. of Minnesota, August 1967, Abstract Q9.Google Scholar
11. Wilson, A. J. C.. “Mathematical Theory of X-Ray Powder Diffractometry”. Philips Technical Library, Netherlands, 1963.Google Scholar