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Results for DC.creator="A." AND DC.creator="Kirfel" in section 1.11.6 of volume D |
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 ...
Tensor atomic factors (magnetic case)
International Tables for Crystallography (2013). Vol. D, Section 1.11.6.5, pp. 278-279 [ doi:10.1107/97809553602060000910 ]
... possess different densities of states with opposite spin directions. During a multipole transition from the ground state to an excited state ... with time reversal because if and/or (Zeeman splitting in a magnetic field). That the antisymmetric parts of the tensors ... it is parity-even and time-odd, being associated with a magnetic moment (1.11.6.41). This part of the tensor ...
Tensor structure factors
International Tables for Crystallography (2013). Vol. D, Section 1.11.6.4, p. 278 [ doi:10.1107/97809553602060000910 ]
... elements), the index u denotes the crystallographically equivalent positions; is a site-occupancy factor, and is the Debye-Waller temperature factor. ... reflections are different for tensor structure factors of different ranks, a circumstance that may be used for experimental separation of different ...
Resonant atomic factors: multipole expansion
International Tables for Crystallography (2013). Vol. D, Section 1.11.6, pp. 275-280 [ doi:10.1107/97809553602060000910 ]
... the resonant part of the atomic factor (1.11.4.3) aswhere , is a dimensionless tensor corresponding to the dipole-dipole contribution, is the ... contribution to the resonant atomic factor can be represented as a sum of an isotropic, a symmetric and an antisymmetric part, written as (Blume, 1994) ...
Tensor atomic factors (non-magnetic case)
International Tables for Crystallography (2013). Vol. D, Section 1.11.6.2, pp. 276-277 [ doi:10.1107/97809553602060000910 ]
... third-rank tensor describing the dipole-quadrupole term, and denotes a symmetric quadrupole-quadrupole contribution. From the physical point of view ... wavevectors and . Equation (1.11.6.16) is also frequently considered as a phenomenological expression of the tensor atomic factor where each tensor ... instance, the tensor is symmetric, the rank-3 tensor has a symmetric and a antisymmetric part, and the rank-4 ...
Tensor atomic factors: internal symmetry
International Tables for Crystallography (2013). Vol. D, Section 1.11.6.1, pp. 275-276 [ doi:10.1107/97809553602060000910 ]
... contribution to the resonant atomic factor can be represented as a sum of an isotropic, a symmetric and an antisymmetric part, written as (Blume, 1994)where ... of the time-reversed state . If, for example, has a magnetic quantum number m, then has a magnetic quantum ...
Hidden internal symmetry of the dipole-quadrupole tensors in resonant atomic factors
International Tables for Crystallography (2013). Vol. D, Section 1.11.6.3, pp. 277-278 [ doi:10.1107/97809553602060000910 ]
... versa). Indeed, both of them can be described by a symmetric third-rank tensor resulting from the second-order Born ... symmetry, and have the same number of independent elements (with a maximum 18 for site symmetry 1). Thus, one can ... which the antisymmetric part of the dipole-quadrupole term is a linear function of the symmetric one [however, not vice ...
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 ...
Tensor atomic factors (magnetic case)
International Tables for Crystallography (2013). Vol. D, Section 1.11.6.5, pp. 278-279 [ doi:10.1107/97809553602060000910 ]
... possess different densities of states with opposite spin directions. During a multipole transition from the ground state to an excited state ... with time reversal because if and/or (Zeeman splitting in a magnetic field). That the antisymmetric parts of the tensors ... it is parity-even and time-odd, being associated with a magnetic moment (1.11.6.41). This part of the tensor ...
Tensor structure factors
International Tables for Crystallography (2013). Vol. D, Section 1.11.6.4, p. 278 [ doi:10.1107/97809553602060000910 ]
... elements), the index u denotes the crystallographically equivalent positions; is a site-occupancy factor, and is the Debye-Waller temperature factor. ... reflections are different for tensor structure factors of different ranks, a circumstance that may be used for experimental separation of different ...
Resonant atomic factors: multipole expansion
International Tables for Crystallography (2013). Vol. D, Section 1.11.6, pp. 275-280 [ doi:10.1107/97809553602060000910 ]
... the resonant part of the atomic factor (1.11.4.3) aswhere , is a dimensionless tensor corresponding to the dipole-dipole contribution, is the ... contribution to the resonant atomic factor can be represented as a sum of an isotropic, a symmetric and an antisymmetric part, written as (Blume, 1994) ...
Tensor atomic factors (non-magnetic case)
International Tables for Crystallography (2013). Vol. D, Section 1.11.6.2, pp. 276-277 [ doi:10.1107/97809553602060000910 ]
... third-rank tensor describing the dipole-quadrupole term, and denotes a symmetric quadrupole-quadrupole contribution. From the physical point of view ... wavevectors and . Equation (1.11.6.16) is also frequently considered as a phenomenological expression of the tensor atomic factor where each tensor ... instance, the tensor is symmetric, the rank-3 tensor has a symmetric and a antisymmetric part, and the rank-4 ...
Tensor atomic factors: internal symmetry
International Tables for Crystallography (2013). Vol. D, Section 1.11.6.1, pp. 275-276 [ doi:10.1107/97809553602060000910 ]
... contribution to the resonant atomic factor can be represented as a sum of an isotropic, a symmetric and an antisymmetric part, written as (Blume, 1994)where ... of the time-reversed state . If, for example, has a magnetic quantum number m, then has a magnetic quantum ...
Hidden internal symmetry of the dipole-quadrupole tensors in resonant atomic factors
International Tables for Crystallography (2013). Vol. D, Section 1.11.6.3, pp. 277-278 [ doi:10.1107/97809553602060000910 ]
... versa). Indeed, both of them can be described by a symmetric third-rank tensor resulting from the second-order Born ... symmetry, and have the same number of independent elements (with a maximum 18 for site symmetry 1). Thus, one can ... which the antisymmetric part of the dipole-quadrupole term is a linear function of the symmetric one [however, not vice ...
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