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Tensorial properties of local crystal susceptibilities
Dmitrienko, V. E., Kirfel, A. and Ovchinnikova, E. N.  International Tables for Crystallography (2013). Vol. D, ch. 1.11, pp. 269-283 [ doi:10.1107/97809553602060000910 ]
... by its energy (frequency), polarization and wavevector. The response is a polarization of the medium, finally resulting in a scattered wave with properties generally different from the initial ones. Thus, the dielectric susceptibility plays the role of a scattering amplitude, which relates the scattered wave to the ...

Tensor atomic factors (spherical tensor representation)
Dmitrienko, V. E., Kirfel, A. and Ovchinnikova, E. N.  International Tables for Crystallography (2013). Vol. D, Section 1.11.6.6, pp. 279-280 [ doi:10.1107/97809553602060000910 ]
... In order to obtain the scattering amplitude and intensity for a resonant process described by some set of spherical tensor components ... tensor that describes the atomic scattering must be contracted by a tensor of the same rank and inversion/time-reversal symmetry ... the X-ray probe, so that the result would be a scalar. There are well known relations between the components ...
     [more results from section 1.11.6 in volume D]

Non-resonant magnetic scattering
Dmitrienko, V. E., Kirfel, A. and Ovchinnikova, E. N.  International Tables for Crystallography (2013). Vol. D, Section 1.11.5, p. 275 [ doi:10.1107/97809553602060000910 ]
... term is small compared to the charge (Thomson) scattering owing (a) to small numbers of unpaired (magnetic) electrons and (b) to the factor of about 0.02 for a typical X-ray energy . This is the reason why ... different, as described by the tensors (Blume, 1994)where is a completely antisymmetric unit tensor (the Levi-Civita symbol). ...

Physical mechanisms for the anisotropy of atomic X-ray susceptibility
Dmitrienko, V. E., Kirfel, A. and Ovchinnikova, E. N.  International Tables for Crystallography (2013). Vol. D, Section 1.11.4, p. 274 [ doi:10.1107/97809553602060000910 ]
... solids. They predicted the sensitivity of X-ray diffraction to a magnetic structure of a crystal, as later observed in the pioneering works of de ... by the Pauli equation (Berestetskii et al., 1982), which is a low-energy approximation to the Dirac equation (typical X- ...

Polarization properties and azimuthal dependence
Dmitrienko, V. E., Kirfel, A. and Ovchinnikova, E. N.  International Tables for Crystallography (2013). Vol. D, Section 1.11.3, pp. 272-274 [ doi:10.1107/97809553602060000910 ]
... are two of the most informative characteristics of forbidden reflections. A third one, energy dependence, is determined by physical interactions, electronic ... reflections, one obtains for unpolarized incident radiation the intensity of a conventional reflection as given bywhere is the Bragg angle, is the scalar structure factor of reflection , and is a scale factor, which depends on the incident beam intensity, ...

Local tensorial susceptibility of cubic crystals
Dmitrienko, V. E., Kirfel, A. and Ovchinnikova, E. N.  International Tables for Crystallography (2013). Vol. D, Section 1.11.2.3, pp. 271-272 [ doi:10.1107/97809553602060000910 ]
... cubic symmetry the second-rank tensor is isotropic, so that a global anisotropy is absent (but it exists for tensors of ... are chosen here as in International Tables for Crystallography Volume A (Hahn, 2005); the first one being adopted if Volume A offers two alternative origins. The expressions (1.11.2.10) or (1.11.2.11) ...
     [more results from section 1.11.2 in volume D]

Introduction
Dmitrienko, V. E., Kirfel, A. and Ovchinnikova, E. N.  International Tables for Crystallography (2013). Vol. D, Section 1.11.1, pp. 269-270 [ doi:10.1107/97809553602060000910 ]
... by its energy (frequency), polarization and wavevector. The response is a polarization of the medium, finally resulting in a scattered wave with properties generally different from the initial ones. Thus, the dielectric susceptibility plays the role of a scattering amplitude, which relates the scattered wave to the ...

Glossary
Dmitrienko, V. E., Kirfel, A. and Ovchinnikova, E. N.  International Tables for Crystallography (2013). Vol. D, Section 1.11.7, p. 281 [ doi:10.1107/97809553602060000910 ]
... the scattering plane Bragg angle azimuthal angle of rotation about a reciprocal-lattice vector vector potential of the electromagnetic wave momentum ... of an electromagnetic wave wavelength of the radiation energy of a discrete atomic level spin of an electron scattering amplitude scattering vector Levi-Civita symbol transition frequency for states a and c energy width of the excited state probability ...

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