(International Tables for Crystallography) Tensorial properties of local crystal susceptibilities

International
Tables for
Crystallography
Volume D
Physical properties of crystals
Edited by A. Authier

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International Tables for Crystallography (2013). Vol. D. ch. 1.11, p. 281

Section 1.11.7. Glossary

V. E. Dmitrienko,^a ^* A. Kirfel^b and E. N. Ovchinnikova^c

^aA. V. Shubnikov Institute of Crystallography, Leninsky pr. 59, Moscow 119333, Russia,^bSteinmann Institut der Universität Bonn, Poppelsdorfer Schloss, Bonn, D-53115, Germany, and ^cFaculty of Physics, M. V. Lomonosov Moscow State University, Leninskie Gory, Moscow 119991, Russia
Correspondence e-mail: dmitrien@crys.ras.ru

1.11.7. Glossary

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$[\chi({\bf r})]$	local susceptibility tensor in direct space
$[\chi({\bf H})]$	Fourier components of the local susceptibility tensor
$[{\bf H}]$	reciprocal-lattice vector
$[{\bf e}]$	polarization vector of an X-ray wave
$[\bf k]$	wavevector of an X-ray wave
$[R_{ij}^g ]$	matrix corresponding to point-group operator
$[{\boldsigma}]$	polarization vector perpendicular to the scattering plane
$[\boldpi ]$	polarization vector in the scattering plane
$[\theta]$	Bragg angle
$[\varphi]$	azimuthal angle of rotation about a reciprocal-lattice vector
$[{\bf A}({\bf r})]$	vector potential of the electromagnetic wave
$[{\bf P}({\bf r})]$	momentum of an electron
$[\omega]$	frequency of an electromagnetic wave
$[\lambda]$	wavelength of the radiation
	energy of a discrete atomic level
$[\bf s]$	spin of an electron
$[f({\bf k},{\bf e},{\bf k}^{\prime},{\bf e}^{\prime})]$	scattering amplitude
$[\bf G]$	scattering vector
$[\epsilon_{ijk}]$	Levi-Civita symbol
$[\omega_{ca}]$	transition frequency for states a and c
$[\Gamma]$	energy width of the excited state
	probability that the state $[\|a\rangle]$ of the scatterer is occupied
$[f_{jk}]$	tensor atomic factor
$[F_{jk}({\bf H})]$	structure-factor tensor of rank 2
$[I_{{\bf H}}({\bf e}^{\prime},{\bf e})]$	intensity of the reflection
	notation of the electric multipole transition. : the dipole; : the quadrupole
	notation of the magnetic multipole transition
	orbital moment of electron
$[D_{jk}]$	dipole–dipole tensor atomic factor
$[D_{jk}^+]$	symmetric part of the dipole–dipole tensor atomic factor
$[D_{jk}^-]$	antisymmetric part of the dipole–dipole tensor atomic factor
$[I_{jkl}]$	third-rank tensor describing the dipole–quadrupole resonant X-ray scattering
$[I_{jkl}^{++}]$	part of the third-rank tensor invariant under time inversion and symmetric under the permutation of j and k
$[I_{jkl}^{+-}]$	part of the third-rank tensor non-invariant under time inversion and symmetric under the permutation of j and k
$[I_{jkl}^{-+}]$	part of the third-rank tensor invariant under time inversion and antisymmetric under the permutation of j and k
$[I_{jkl}^{--}]$	part of the third-rank tensor non-invariant under time inversion and antisymmetric under the permutation of j and k
$[Q_{ijkl}]$	fourth-rank tensor describing the quadrupole–quadrupole resonant X-ray scattering
Tr	trace of matrix
$[\bf m]$	magnetic moment of an atom
Y_LM	spherical tensor
$[X^{(p)}_q]$	component of the spherical tensor depending only on the incident and scattered radiation
$[F^{(p)}_-q]$	component of the spherical tensor associated with the tensor properties of the absorbing atom

References

Di Matteo, S., Joly, Y. & Natoli, C. R. (2005). Detection of electromagnetic multipoles by X-ray spectroscopies. Phys. Rev. B, 72, 144406.Google Scholar

Paolasini, L. (2012). Magnetism in condensed matter: resonant and magnetic scattering by synchrotron radiation. In Italian School on Magnetism, Pavia 2012, pp. 1–83. Universita di Pavia.Google Scholar

International Tables for Crystallography (2013). Vol. D. ch. 1.11, p. 281