Difference between revisions of "Cromer–Mann coefficients"
From Online Dictionary of Crystallography
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<math>f^0(\sin\theta/\lambda) = \sum_{i=1}^4 a_i \exp[-b_i(\sin\theta/\lambda)^2] + c</math> | <math>f^0(\sin\theta/\lambda) = \sum_{i=1}^4 a_i \exp[-b_i(\sin\theta/\lambda)^2] + c</math> | ||
| − | for <math>0 < (\sin\theta)/\lambda < 2.0\,\mathrm{ | + | for <math>0 < (\sin\theta)/\lambda < 2.0\,\mathrm{Å}^{-1}</math>. |
This expression is convenient for calculation in crystal structure software suites. | This expression is convenient for calculation in crystal structure software suites. | ||
| Line 11: | Line 11: | ||
== History == | == History == | ||
| − | Atomic scattering factors for non-hydrogen atoms were calculated from relativistic Hartree–Fock wavefunctions by Doyle, P. A. | + | Atomic scattering factors for non-hydrogen atoms were calculated from relativistic Hartree–Fock wavefunctions by Doyle, P. A. and Turner, P. S. [(1968). [https://doi.org/10.1107/S0567739468000756 ''Acta Cryst.'' A'''24''', 390–397]. ''Relativistic Hartree–Fock and electron scattering factors''] using the wavefunctions of Coulthard, M. A. [(1967). [https://doi.org/10.1088/0370-1328%2F91%2F1%2F309 ''Proc. Phys. Soc.'' '''91''', 44–49]. ''A relativistic Hartree–Fock atomic field calculation''], and in 1968 by Cromer, D. T. and Waber, J. T. using the unpublished wavefunctions of J. B. Mann [''International Tables for X-ray Crystallography'' (1974), Vol. IV, p. 71. Birmingham: Kynoch Press]. The latter are based on a more exact treatment of potential that allows for the finite size of the nucleus. Subsequent calculations [Fox, A. G., O'Keefe, M. A. and Tabbernor, M. A. (1989). [https://doi.org/10.1107/S0108767389007567 ''Acta Cryst.'' A'''45''', 786–793]. ''Relativistic Hartree–Fock X-ray and electron atomic scattering factors at high angles''] extended the useful range to 6 Å<sup>−1</sup> to accommodate the increasing numbers of applications for high-angle scattering factors. |
== See also == | == See also == | ||
| − | Intensity of diffracted intensities. | + | *Intensity of diffracted intensities. P. J. Brown, A. G. Fox, E. N. Maslen, M. A. O'Keefe and B. T. M. Willis. ''International Tables for Crystallography'' (2006). [https://doi.org/10.1107/97809553602060000600 Vol. C, ch. 6.1, pp. 554-595], especially Table 6.1.1.4. |
| − | P. J. Brown, A. G. Fox, E. N. Maslen, M. A. O'Keefe and B. T. M. Willis. ''International Tables for Crystallography'' (2006). Vol. C, ch. 6.1, pp. 554-595 | ||
[[Category:Structure determination]] | [[Category:Structure determination]] | ||
[[Category:X-rays]] | [[Category:X-rays]] | ||
Latest revision as of 15:19, 8 June 2021
Definition
The set of nine coefficients [math]a_i, b_i, c\, (i=1,\dots, 4)[/math] in a parameterization of the non-dispersive part of the atomic scattering factor for neutral atoms as a function of [math](\sin \theta)/\lambda[/math]:
[math]f^0(\sin\theta/\lambda) = \sum_{i=1}^4 a_i \exp[-b_i(\sin\theta/\lambda)^2] + c[/math]
for [math]0 \lt (\sin\theta)/\lambda \lt 2.0\,\mathrm{Å}^{-1}[/math].
This expression is convenient for calculation in crystal structure software suites.
History
Atomic scattering factors for non-hydrogen atoms were calculated from relativistic Hartree–Fock wavefunctions by Doyle, P. A. and Turner, P. S. [(1968). Acta Cryst. A24, 390–397. Relativistic Hartree–Fock and electron scattering factors] using the wavefunctions of Coulthard, M. A. [(1967). Proc. Phys. Soc. 91, 44–49. A relativistic Hartree–Fock atomic field calculation], and in 1968 by Cromer, D. T. and Waber, J. T. using the unpublished wavefunctions of J. B. Mann [International Tables for X-ray Crystallography (1974), Vol. IV, p. 71. Birmingham: Kynoch Press]. The latter are based on a more exact treatment of potential that allows for the finite size of the nucleus. Subsequent calculations [Fox, A. G., O'Keefe, M. A. and Tabbernor, M. A. (1989). Acta Cryst. A45, 786–793. Relativistic Hartree–Fock X-ray and electron atomic scattering factors at high angles] extended the useful range to 6 Å−1 to accommodate the increasing numbers of applications for high-angle scattering factors.
See also
- Intensity of diffracted intensities. P. J. Brown, A. G. Fox, E. N. Maslen, M. A. O'Keefe and B. T. M. Willis. International Tables for Crystallography (2006). Vol. C, ch. 6.1, pp. 554-595, especially Table 6.1.1.4.