Powder diffraction

Jagodzinski, H.; Frey, F.

doi:10.1107/97809553602060000564

International
Tables for
Crystallography
Volume B
Reciprocal space
Edited by U. Shmueli

pdf | chapter contents | chapter index | related articles

International Tables for Crystallography (2006). Vol. B. ch. 4.2, p. 435 | 1 | 2 |

Section 4.2.4.4.6. Powder diffraction

H. Jagodzinski^a and F. Frey^b

^aInstitut für Kristallographie und Mineralogie, Universität, Theresienstrasse 41, D-8000 München 2, Germany, and ^bInstitut für Kristallographie und Mineralogie, Universität, Theresienstrasse 41, D-8000 München 2, Germany

4.2.4.4.6. Powder diffraction

| top | pdf |

Evaluation of diffuse-scattering data from powder diffraction follows the same theoretical formulae developed for the determination of the radial distribution function for glasses and liquids (Debye & Menke, 1931; Warren & Gingrich, 1934). The final formula for random distributions may be given as (Fender, 1973) $[{I_{d}^{p} = \{\langle |F ({\bf H})|^{2}\rangle - |\langle F ({\bf H})\rangle |^{2}\} \textstyle\sum\limits_{i} s_{i} \sin (2 \pi Hr_{i}) / (2 \pi Hr_{i}).} \eqno(4.2.4.82)]$ $[s_{i}]$ represents the number of atoms at distance $[r_{i}]$ from the origin. An equivalent expression for a substitutional binary alloy is $[{I_{d}^{p} = \alpha (1 - \alpha) \{|\;f_{2} ({\bf H}) - f_{2} ({\bf H})|^{2}\} \textstyle\sum\limits_{i} s_{i} \sin (2 \pi Hr_{i}) / (2 \pi Hr_{i}).} \eqno(4.2.4.83)]$

References

Debye, B. & Menke, H. (1931). Untersuchung der molekularen Ordnung in Flüssigkeiten mit Röntgenstrahlung. Ergeb. Tech. Roentgenkd. II, 1–22.Google Scholar

Fender, B. E. F. (1973). Diffuse scattering and the study of defect solids. In Chemical applications of thermal neutron scattering, ch. 11, edited by B. T. M. Willis. Oxford University Press.Google Scholar

Warren, B. E. & Gingrich, N. S. (1934). Fourier integral analysis of X-ray powder patterns. Phys. Rev. 46, 368–372.Google Scholar

International Tables for Crystallography (2006). Vol. B. ch. 4.2, p. 435