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.[1] The electron form factors are normally calculated from X-ray form factors using the Mott-Bethe formula.[2] This formula takes into account both elastic electron-cloud scattering and elastic nuclear scattering.
Neutron form factor
There are two distinct scattering interactions of neutrons by nuclei. Both are used in the investigation structure and dynamics of condensed matter: they are termed nuclear (sometimes also termed chemical) and magnetic scattering.
Nuclear scattering of the free neutron by the nucleus is mediated by the strong nuclear force. The wavelength of thermal (several Angstroms) and cold neutrons (up to tens of Angstroms) typically used for such investigations is 4-5 orders of magnitude larger than the dimension of the nucleus (femtometres). The free neutrons in a beam travel in a plane wave; for those that undergo nuclear scattering from a nucleus, the nucleus acts as a secondary point source, and radiates scattered neutrons as a spherical wave. (Although a quantum phenomenon, this can be visualized in simple classical terms by the Huygens–Fresnel principle.) Therefore the physical extent of any nucleus is an infinitesimal point (delta function) with respect to the neutron wavelength. The Fourier transform of a delta function is unity; therefore, it is commonly said that neutrons "do not have a form factor."
However each isotope has a different scattering amplitude. This Fourier transform is scaled by the amplitude of the spherical wave, which has dimensions of length. Hence, the amplitude of scattering that characterizes the interaction of a neutron with a given isotope is termed the scattering length, b. Neutron scattering lengths vary erratically between neighbouring elements in the periodic table and between isotopes of the same element. They 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.[3]
Although neutral, neutrons also have a nuclear spin. They are a composite fermion and hence have an associated magnetic moment. This moment interacts with the magnetic moments arising from unpaired electrons in the outer orbitals of certain atoms. Since these orbitals are typically of a similar order of magnitude to the wavelength of the free neutrons, the resulting form factor is non-uniform, and resembles that of the X-ray form factor. However, the Fourier transform is of the outer electrons, rather than being heavily weighted by the core electrons, as is the case for X-ray scattering. Hence, in strong contrast to the case for nuclear scattering, the scattering object for magnetic scattering is far from a point source; it is more diffuse still than the effective size of the source for X-ray scattering, and the resulting Fourier transform (the magnetic form factor) decays more rapidly than even the X-ray form factor. Also, in contrast to nuclear scattering, the magnetic form factor is not isotope dependent, but is dependent on the oxidation state of the atom.
References
- ^ Cowley, John M. (1981). Diffraction Physics. North-Holland Physics Publishing. pp. p. 78. ISBN 0-444-86121-1.
{{cite book}}:|pages=has extra text (help) - ^ De Graef, Marc (2003). Introduction to Conventional Transmission Electron Microscopy. Cambridge University Press. pp. p. 113. ISBN 0-521-62995-0.
{{cite book}}:|pages=has extra text (help) - ^ Squires, Introduction to the Theory of Thermal Neutron Scattering, Dover Publications (1996) ISBN 048669447X
 | This physics-related article is a stub. You can help Wikipedia by expanding it. |