Difference between revisions of "Anomalous dispersion"
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| − | < | + | <font color="blue">Dispersion anomale</Font> (''Fr''). <font color="red">Anomale Dispersion</font> (''Ge''). <font color="black">Dispersione anomala</font> (''It''). <font color="purple">異常分散</font> (''Ja''). <font color="green">Dispersion anómala</font> (''Sp''). |
== Definition == | == Definition == | ||
| − | The 'anomalous' dispersion corrections, which | + | The 'anomalous' dispersion corrections, which are not in fact anomalous, take into account the effect of absorption in the scattering of phonons by electrons. In the classic picture the electron is 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 |
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| − | 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 ([[resonant scattering]]). Numerical calculations usually follow the Hartree-Fock approximations. For details on the non-relativistic and | + | 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 ([[resonant scattering]]). Numerical calculations usually follow the Hartree-Fock approximations. For details on the non-relativistic and relativistic approaches, see Chapter 4.2.6 of ''International Tables for Crystallography, Volume C''. |
== History == | == History == | ||
| − | The dispersion of X-rays was theoretically predicted by Waller | + | The dispersion of X-rays was theoretically predicted by Waller [Waller, I. (1928). ''Z. Phys.'' '''51''', 213-231. |
| − | + | ''Über eine verallgemeinerte Streuungsformel''] and first calculated by Hönl [Hönl, H. (1933). ''Z. Phys.'' '''84''', 1-16. ''Zur Dispersionstheorie der Röntgenstrahlen''; Hönl, H. (1933). ''Ann. Phys.'' (Leipzig), '''18''', 625-657. ''Atomfactor für Röntgenstrahlen als Problem der Dispersionstheorie (K-Schale)'']. | |
| − | |||
== See also == | == See also == | ||
| − | [[ | + | *[[Anomalous scattering]] |
| − | [[ | + | *[[Multiwavelength anomalous diffraction (MAD)]] |
| − | + | *[[Resonant scattering]] | |
| − | + | *Chapter 4.2.6 of ''International Tables for Crystallography, Volume C'' | |
| − | |||
| − | [[Category:X-rays]] | + | [[Category:X-rays]] |
Latest revision as of 13:46, 26 March 2019
Dispersion anomale (Fr). Anomale Dispersion (Ge). Dispersione anomala (It). 異常分散 (Ja). Dispersion anómala (Sp).
Definition
The 'anomalous' dispersion corrections, which are not in fact anomalous, take into account the effect of absorption in the scattering of phonons by electrons. In the classic picture the electron is 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 (resonant scattering). Numerical calculations usually follow the Hartree-Fock approximations. For details on the non-relativistic and relativistic approaches, see Chapter 4.2.6 of International Tables for Crystallography, Volume C.
History
The dispersion of X-rays was theoretically predicted by Waller [Waller, I. (1928). Z. Phys. 51, 213-231. Über eine verallgemeinerte Streuungsformel] and first calculated by Hönl [Hönl, H. (1933). Z. Phys. 84, 1-16. Zur Dispersionstheorie der Röntgenstrahlen; Hönl, H. (1933). Ann. Phys. (Leipzig), 18, 625-657. Atomfactor für Röntgenstrahlen als Problem der Dispersionstheorie (K-Schale)].
See also
- Anomalous scattering
- Multiwavelength anomalous diffraction (MAD)
- Resonant scattering
- Chapter 4.2.6 of International Tables for Crystallography, Volume C