Difference between revisions of "Anomalous dispersion"
From Online Dictionary of Crystallography
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| − | = | + | <Font color='blue'>Dispersion anormale </Font>(''Fr''). <Font color='red'>Anomale Dispersion </Font>(''Ge''). <Font color='green'>Dispersion anómala </Font>(''Sp''). |
| − | == | + | == Definition == |
| − | + | The 'anomalous' dispersion corrections, which have nothing anomalous, come in to into account the effect of absorption in the scattering of phonons by electrons. In the classic picture the electron is then approximated by a damped harmonic oscillator. The scattering factor of the electron is then complex and the atomic scattering factor, or atomic form factor is given by: | |
| − | + | <center> | |
| + | ''f'' + ''f' '' + i ''f"'' | ||
| + | </center> | ||
| + | |||
| + | where ''f' '' and ''f" '' are the real and imaginary parts of the anomalous dispersion correction. Their importance increases as one gets closer to an absorption edge. Numerical calculations usually follow the Hartree-Fock approximations. For details on the non-relativistic and relativostic approaches, see Section 4.2.6 of ''International Tables of Crystallography, Volume C''. | ||
== History == | == History == | ||
Revision as of 07:55, 24 February 2006
Dispersion anormale (Fr). Anomale Dispersion (Ge). Dispersion anómala (Sp).
Definition
The 'anomalous' dispersion corrections, which have nothing anomalous, come in to into account the effect of absorption in the scattering of phonons by electrons. In the classic picture the electron is then approximated by a damped harmonic oscillator. The scattering factor of the electron is then complex and the atomic scattering factor, or atomic form factor is given by:
f + f' + i f"
where f' and f" are the real and imaginary parts of the anomalous dispersion correction. Their importance increases as one gets closer to an absorption edge. Numerical calculations usually follow the Hartree-Fock approximations. For details on the non-relativistic and relativostic approaches, see Section 4.2.6 of International Tables of Crystallography, Volume C.
History
The dispersion of X-rays was theoretically predicted by Waller (Waller, I., 1928, Über eine verallgemeinerte Streuungsformel. Z. Phys. 51, 213-231.) and first calculated by Hönl (Hönl, H., 1933, Zur Dispersionstheorie der Röntgenstrahlen. Z. Phys. 84, 1-16; Hönl, H., 1933, Atomfactor für Röntgenstrahlen als Problem der Dispersionstheorie (K-Schale). Ann. Phys. (Leipzig), 18, 625-657.
See also
anomalous scattering
multiwavelength anomalous diffraction (MAD)
Section 4.2.6 of International Tables of Crystallography, Volume C