Atomic scattering factors

The atomic scattering factors are measures of the scattering power of individual atoms. Each element has a different atomic scattering factor, which represents how strongly x-rays interact with those atoms.

The scattering factor has two components: f₁ and f₂, which describe the dispersive and absorptive components. In other words, f₂ describes how strongly the material absorbs the radiation, while f₁ describes the non-absorptive interaction (which leads to refraction).

Elemental dependence

Because x-ray interactions occur with an atom's electron cloud, the scattering factors increase with number of electrons, and thus with atomic number (Z). However, the relationship between f and Z is not monotonic, owing to resonant (absorption) edges.

Energy dependence

The atomic scattering factors vary with x-ray wavelength. In particular, a given element will have resonant edges at certain energies, where the absorption increases markedly. The dispersive component f₁ will also vary rapidly in the vicinity of an absorption edge (c.f. Kramers-Kronig relations). In general, absorption decreases with increasing energy (i.e. high-energy x-rays can penetrate more efficiently through materials).

Examples

silicon

gold

Elemental/Energy dependence

Related forms

There are a variety of quantities related to the material's x-ray interaction strength:

• Dispersive atomic scattering factor $f_{1}$, the intrinsic interaction of the material.
• Critical angle $\theta _{c}$, the angle below which the beam undergoes total external reflection.
• Critical q $q_{c}$, the wave-vector (in reciprocal-space) corresponding to the critical angle.
• Real refractive index $\delta$, the refractive component of the refractive index.
• Real Scattering Length Density $\mathrm {Re} (\mathrm {SLD} )$, the primary (non-absorptive) component of the scattering contrast.

$f_{1}$			$f_{1}={\frac {2\pi }{n_{a}r_{e}\lambda ^{2}}}\delta$
	$\theta _{c}$
		$q_{c}$
$\delta ={\frac {n_{a}r_{e}\lambda ^{2}}{2\pi }}f_{1}$			$\delta$
				$\mathrm {Re} (\mathrm {SLD} )$

See also absorption length for a comparison of the quantities related to f₂.

See Also

• Periodic table of atomic scattering factors: Useful tool for looking up the values for any element.
• APS Python code for calculating f
• Online Dictionary of Crystallography: Atomic scattering factor