International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

© International Union of Crystallography 2006
International Tables for Crystallography (2006). Vol. C. ch. 5.2, p. 492

Section 5.2.2.2. Refraction

W. Parrish,a‡ A. J. C. Wilsonb‡ and J. I. Langfordc

a IBM Almaden Research Center, San Jose, CA, USA,bSt John's College, Cambridge CB2 1TP, England, and cSchool of Physics & Astronomy, University of Birmingham, Birmingham B15 2TT, England

5.2.2.2. Refraction

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X-rays, unless incident normally, are refracted away from the normal on entering matter, and while inside matter they have a longer wavelength than in vacuo. Both effects are small, but the former leads to a measurable error for solid specimens (that is, specimens without voids or binder) with flat surfaces (single crystals or polished metal blocks). This effect becomes prominent at grazing incidence, and may lead to total external reflection. For the usual powder compacts (Section 2.3.4[link] ), refraction leads to a broadening rather than a displacement (Wilson, 1940[link], 1962[link]; Wilkens, 1960[link]; Hart, Parrish, Bellotto & Lim, 1988[link]; Greenberg, 1989[link]). The greater wavelength within the powder grain leads to a pseudo-aberration; the actual wavelength ought to be used in (5.2.1.1)[link], and if the in vacuo wavelength is used instead the lattice spacing obtained will be too small by a fraction equal to the amount by which the refractive index differs from unity. The difference is typically in the fourth decimal place in the lattice parameter expressed in Å. The need for any refraction correction for very fine powders has been questioned.

References

First citation Greenberg, B. (1989). Bragg's law with refraction. Acta Cryst. A45, 238–241.Google Scholar
 First citation Hart, M., Parrish, W., Bellotto, M. & Lim, G. S. (1988). The refractive-index correction in powder diffraction. Acta Cryst. A44, 193–197.Google Scholar
 First citation Wilkens, M. (1960). Zur Brechungskorrektur bei Gitterkonstantmessungen an Pulverpräparaten. Acta Cryst. 13, 826–828.Google Scholar
 First citation Wilson, A. J. C. (1940). On the correction of lattice spacings for refraction. Proc. Cambridge Philos. Soc. 36, 485–489.Google Scholar
 First citation Wilson, A. J. C. (1962). Refraction broadening in powder diffractometer. Proc. Phys. Soc. London, 80, 303–305.Google Scholar








































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