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Tensorial properties of local crystal susceptibilities
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)
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
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
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
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
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
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
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 ...
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)
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
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
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
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
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
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
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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