Atomic form factor

In physics, the atomic form factor, or atomic scattering factor, is a measure of the scattering intensity of a wave by an isolated atom. The atomic form factor depends on the type of scattering, typically X-ray, electron or neutron. For crystals, atomic form factors are used to calculate the structure factor of a unit cell.

X-ray form factor

X-rays are scattered by the electron cloud of the atom and hence the scattering power of x-rays increases with the atomic number of the atoms in a sample. As a result, x-rays are not very sensitive to light atoms, such as hydrogen and helium, and there is very little contrast between elements adjacent to each other in the periodic table. The x-ray form factor is defined as the Fourier transform of the electron charge density.

Electron form factor

Electron form factors can be defined as the Fourier transform of the potential distribution of the atom. [cite book |last=Cowley |first=John M. |authorlink=John M. Cowley |title=Diffraction Physics |year=1981 |publisher=North-Holland Physics Publishing |isbn=0-444-86121-1 |pages=p. 78 ] The electron form factors are normally calculated from X-ray form factors using the Mott-Bethe formula. [cite book |last=De Graef |first=Marc |title=Introduction to Conventional Transmission Electron Microscopy |year=2003 |publisher=Cambridge University Press |isbn=0-521-62995-0 |pages=p. 113 ] This formula takes into account both elastic electron-cloud scattering and elastic nuclear scattering.

Neutron form factor

Neutrons are scattered by the nucleus of the atom but due to their finite magnetic moment they will also interact with the electron clouds of magnetic ions. Neutron form factors are usually described by the neutron scattering length, "b". The neutron scattering length may only be determined experimentally since the theory of nuclear forces is not adequate to calculate or predict "b" from other properties of the nucleus. [Squires, "Introduction to the theory of thermal neutron scattering", Dover Publications (1996) ISBN 048669447X] Neutron scattering lengths vary erractically between neighbouring elements in the periodic table and even between isotopes of the same element. Hence isotopic substitution in neutron diffraction may be used to distinguish between individual atomic sites in a sample. Since the measured intensity of the diffraction patterns are related to the magnitude of the neutron scattering lengths, differences between subsequent diffraction patterns of compositionally identical samples containing different isoptopes may be taken to yield the individual atomic contributions.

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