International
Tables for Crystallography Volume C Mathematical, physical and chemical tables Edited by E. Prince © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. C. ch. 4.2, p. 213
Section 4.2.3.1.1. Definitions
D. C. Creaghb
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This section deals with the manner in which the photon scattering and absorption cross sections of an atom varies with the energy of the incident photon. Further information concerning these cross sections and tables of the X-ray attenuation coefficients are given in Section 4.2.4. Information concerning the anomalous-dispersion corrections is given in Section 4.2.6
.
When a highly collimated beam of monoenergetic photons passes through a medium of thickness t, it suffers a decrease in intensity according to the relation where μl is the linear attenuation coefficient. Most tabulations express μl in c.g.s. units, μl having the units cm−1.
An alternative, often more convenient, way of expressing the decrease in intensity involves the measurement of the mass per unit area mA of the specimen rather than the specimen thickness, in which case equation (4.2.3.1) takes the form
where ρ is the density of the material and (μ/ρ) is the mass absorption coefficient. The linear attenuation coefficient of a medium comprising atoms of different types is related to the mass absorption coefficients by
where
is the mass fraction of the atoms of the ith species for which the mass absorption coefficient is
. The summation extends over all the atoms comprising the medium. For a crystal having a unit-cell volume of
,
where
is the photon scattering and absorption cross section. If
is expressed in terms of barns/atom then
must be expressed in terms of Å3 and μl is in cm−1. (1 barn = 10−28 m2.)
The mass attenuation coefficient μ/ρ is related to the total photon–atom scattering cross section σ according to where
Avogadro's number = 6.0221367 (36) × 1023 atoms/gram atom (Cohen & Taylor, 1987
) and M = atomic weight relative to M(12C) = 12.0000.
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