# Atomic scattering factor

### From Online Dictionary of Crystallography

Facteur de diffusion atomique (*Fr*). Atomformfaktor, Formfaktor (*Ge*). Fattore di diffusione atomico (*It*). 原子散乱因子 (*Ja*). Factor de forma atómica (*Sp*).

## Definition

A measure of the scattering power of an isolated atom. Also known as the **atomic form factor**. The scattering factor depends on the scattering amplitude of an individual atom, on the Bragg angle and the type of radiation involved.

## X-ray scattering

The scattering from a crystal of an X-ray beam results from the interaction between the electric component of the incident electromagnetic radiation and the electrons in the crystal. Tightly bound electrons scatter coherently (Rayleigh scattering); free electrons scatter incoherently (Compton scattering). The scattering process from atomic electrons in a crystal lattice has both coherent and incoherent components, and is described as Thomson scattering.

The scattering amplitude from a neutral atom depends on the number of electrons (*Z* = the atomic number) and also on the Bragg angle θ – destructive interference among waves scattered from the individual electrons reduces the intensity at other than zero scattering angle. For θ = 0 the scattering amplitude is normally equal to *Z*. However, the scattering factor is modified by anomalous scattering if the incident wavelength is near an absorption edge of the scattering element.

The X-ray scattering factor is evaluated as the Fourier transform of the electron density distribution of an atom or ion, which is calculated from theoretical wavefunctions for free atoms.

## References

*Electron diffraction*: C. Colliex, J. M. Cowley, S. L. Dudarev, M. Fink, J. Gjønnes, R. Hilderbrandt, A. Howie, D. F. Lynch, L. M. Peng, G. Ren, A. W. Ross, V. H. Smith Jr, J. C. H. Spence, J. W. Steeds, J. Wang, M. J. Whelan and B. B. Zvyagin.*International Tables for Crystallography*(2006). Vol. C, ch. 4.3, pp. 259-429 doi:10.1107/97809553602060000593*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 doi:10.1107/97809553602060000600*Neutron techniques*: I. S. Anderson, P. J. Brown, J. M. Carpenter, G. Lander, R. Pynn, J. M. Rowe, O. Schärpf, V. F. Sears and B. T. M. Willis.*International Tables for Crystallography*(2006). Vol. C, ch. 4.4, pp. 430-487 doi:10.1107/97809553602060000594