Atomic form factor

In <a href="/facts/Physics/a7aH2y08">physics</a>, the atomic form factor, or atomic scattering factor, is a measure of the <a href="/facts/Scattering_amplitude/TmdeAs1o">scattering amplitude</a> of a wave by an isolated atom. The atomic form factor depends on the type of <a href="/facts/Scattering/nMou7lEH">scattering</a>, which in turn depends on the nature of the incident radiation, typically <a href="/facts/X-ray_diffraction/WtI0F5DN">X-ray</a>, <a href="/facts/Electron_diffraction/IlFzQyVu">electron</a> or <a href="/facts/Neutron_diffraction/fYXAunDW">neutron</a>. The common feature of all form factors is that they involve a <a href="/facts/Fourier_transform/XXhKJtc8">Fourier transform</a> of a spatial density distribution of the scattering object from <a href="/facts/Space/tq6LUM3C">real space</a> to <a href="/facts/Momentum_space/kxKPCeoI">momentum space</a> (also known as <a href="/facts/Reciprocal_space/jYCjcEpH">reciprocal space</a>). For an object with spatial density distribution, 
 
 
 
 ρ
 (
 
 r
 
 )
 
 
 {\displaystyle \rho (\mathbf {r} )}
 
, the form factor, 
 
 
 
 f
 (
 
 Q
 
 )
 
 
 {\displaystyle f(\mathbf {Q} )}
 
, is defined as

f
 (
 
 Q
 
 )
 =
 ∫
 ρ
 (
 
 r
 
 )
 
 e
 
 i
 
 Q
 
 ⋅
 
 r
 
 
 
 
 
 d
 
 
 3
 
 
 
 r
 
 
 
 {\displaystyle f(\mathbf {Q} )=\int \rho (\mathbf {r} )e^{i\mathbf {Q} \cdot \mathbf {r} }\mathrm {d} ^{3}\mathbf {r} }
 
,
where 
 
 
 
 ρ
 (
 
 r
 
 )
 
 
 {\displaystyle \rho (\mathbf {r} )}
 
 is the spatial density of the scatterer about its <a href="/facts/Center_of_mass/n4Lr9GAz">center of mass</a> (
 
 
 
 
 r
 
 =
 0
 
 
 {\displaystyle \mathbf {r} =0}
 
), and 
 
 
 
 
 Q
 
 
 
 {\displaystyle \mathbf {Q} }
 
 is the <a href="/facts/Momentum_transfer/Aee5CMKq">momentum transfer</a>. As a result of the nature of the Fourier transform, the broader the distribution of the scatterer 
 
 
 
 ρ
 
 
 {\displaystyle \rho }
 
 in real space 
 
 
 
 
 r
 
 
 
 {\displaystyle \mathbf {r} }
 
, the narrower the distribution of 
 
 
 
 f
 
 
 {\displaystyle f}
 
 in 
 
 
 
 
 Q
 
 
 
 {\displaystyle \mathbf {Q} }
 
; i.e., the faster the decay of the form factor.
For crystals, atomic form factors are used to calculate the <a href="/facts/Structure_factor/ulu9jjuc">structure factor</a> for a given <a href="/facts/Bragg_peak/jlGM6Mfe">Bragg peak</a> of a <a href="/facts/Crystal/e2R2mk3E">crystal</a>.

Atomic form factor open-in-new

Atomic form factor