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. 6.1, p. 590

Section 6.1.1.7. Structure factor

E. N. Maslen,e‡ A. G. Foxb and M. A. O'Keefec

6.1.1.7. Structure factor

| top | pdf |

The amplitude of coherent scattering from the contents of one unit cell in a crystalline material is the structure factor [F({\bf S})=\textstyle\int\rho({\bf r})\exp(i{\bf S}\cdot{\bf r})\,{\rm d}r,\eqno (6.1.1.92)]where the integration extends over the unit cell. If there are N atoms in the cell, this may be expressed as [F({\bf S})=\textstyle\sum\limits^N_{j=1}\,f_jT_j\exp(i{\bf S}\cdot{\bf r}_j),\eqno (6.1.1.93)]where [{\bf r}_j] is the mean position and [T_j] is the temperature factor of the jth atom. In an ideal model of the scattering process in which (6.1.1.93)[link] is exact, [f_j] is the atomic scattering factor derived from (6.1.1.7)[link]. In practice, there are wavelength-dependent changes to the amplitude and phase of the atom's scattering due to dispersion or resonance. To correct for this, each scattering factor may be written [f=f^0+f'+if'',\eqno (6.1.1.94)]where [f^0] is the kinematic scattering factor and f′ and f′′ are real and imaginary corrections for dispersion.








































to end of page
to top of page