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 Results for DC.creator="G." AND DC.creator="Eckold" in section 2.1.3 of volume D   page 1 of 2 pages.
Symmetry of lattice vibrations
Eckold, G.  International Tables for Crystallography (2013). Vol. D, Section 2.1.3, pp. 294-311 [ doi:10.1107/97809553602060000911 ]
... of the wavevector q by an arbitrary reciprocal lattice vector g. Hence, the elements of the dynamical matrix represent periodic functions ... our considerations to the symmetry operations of the space group G(q) of the wavevector q that leave the wavevector invariant modulo some reciprocal-lattice vector g(q, S),then equation (2.1.3.13) provides an ordinary (3N- ...

Optical selection rules
Eckold, G.  International Tables for Crystallography (2013). Vol. D, Section 2.1.3.7, pp. 310-311 [ doi:10.1107/97809553602060000911 ]
Optical selection rules 2.1.3.7. Optical selection rules Inelastic neutron scattering is the unique experimental method for the determination of phonons at arbitrary wavevectors. Additional information can be obtained by optical methods, infrared absorption and Raman spectroscopy. For the detection of lattice vibrations, electromagnetic radiation of appropriate frequencies in the THz regime ...

Example
Eckold, G.  International Tables for Crystallography (2013). Vol. D, Section 2.1.3.6.1, pp. 309-310 [ doi:10.1107/97809553602060000911 ]
Example 2.1.3.6.1. Example To illustrate compatibility relations, let us once more consider the example of space group as introduced in Sections 2.1.3.1.1, 2.1.3.3.1 and 2.1.3.4.1. For wavevectors along we have and there are two irreducible representations, a symmetric one (with respect to ) with and an antisymmetric one with . Remember the ...

Compatibility relations
Eckold, G.  International Tables for Crystallography (2013). Vol. D, Section 2.1.3.6, pp. 309-310 [ doi:10.1107/97809553602060000911 ]
Compatibility relations 2.1.3.6. Compatibility relations In our last example, we recognized that the group of the wavevector consists of the same elements, irrespective of whether the [Gamma] point, the zone-boundary A point or any other wavevector along the hexagonal axis is concerned. This behaviour, however, is the exception rather than ...

Example
Eckold, G.  International Tables for Crystallography (2013). Vol. D, Section 2.1.3.5.3, pp. 308-309 [ doi:10.1107/97809553602060000911 ]
... point) are triply and doubly degenerate, respectively. An index or g/u is often used to distinguish representations that are symmetric ... extended zone scheme according to the different irreducible representations [after Eckold & Hahn (1987)]. The symbols represent experimental data and the ...

Time-reversal degeneracy
Eckold, G.  International Tables for Crystallography (2013). Vol. D, Section 2.1.3.5.2, pp. 306-308 [ doi:10.1107/97809553602060000911 ]
Time-reversal degeneracy 2.1.3.5.2. Time-reversal degeneracy In Section 2.1.3.3, we considered in some detail the symmetry of phonon eigenvectors with respect to the symmetry operations contained in the point group of the wavevector. We know, however, that those symmetry operations that invert the wavevector give rise to additional constraints for ...

Accidental degeneracy
Eckold, G.  International Tables for Crystallography (2013). Vol. D, Section 2.1.3.5.1, p. 306 [ doi:10.1107/97809553602060000911 ]
Accidental degeneracy 2.1.3.5.1. Accidental degeneracy The symmetry analysis of lattice vibrations provides a powerful tool not only for the characterization of eigenvectors but also for the presentation of experimental results. In neutron scattering experiments, for example, a series of single phonons may be detected but symmetry determines which of these phonons ...

Degeneracy of lattice vibrations
Eckold, G.  International Tables for Crystallography (2013). Vol. D, Section 2.1.3.5, pp. 306-309 [ doi:10.1107/97809553602060000911 ]
... point) are triply and doubly degenerate, respectively. An index or g/u is often used to distinguish representations that are symmetric ... extended zone scheme according to the different irreducible representations [after Eckold & Hahn (1987)]. The symbols represent experimental data and the ...

Example
Eckold, G.  International Tables for Crystallography (2013). Vol. D, Section 2.1.3.4.1, pp. 304-306 [ doi:10.1107/97809553602060000911 ]
Example 2.1.3.4.1. Example Let us try to find the symmetry coordinates corresponding to our sample structure introduced in Section 2.1.3.1.1 for . Using the irreducible representations displayed in Section 2.1.3.3.1, we write down the projection operator for representation according to equation (2.1.3.51): with the abbreviations From the results in Section 2.1.3.4 ...

Symmetry coordinates
Eckold, G.  International Tables for Crystallography (2013). Vol. D, Section 2.1.3.4, pp. 303-306 [ doi:10.1107/97809553602060000911 ]
Symmetry coordinates 2.1.3.4. Symmetry coordinates So far, we have used the 3N Cartesian coordinates of all atoms within a primitive cell in order to describe the dynamics of the crystal lattice. Within this coordinate system, the elements of the dynamical matrix can be calculated on the basis of specific models for ...

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