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

International Tables for Crystallography (2013). Vol. D, ch. 2.1, pp. 311-312

## Section 2.1.5. Glossary

G. Eckolda*

aInstitut für Physikalische Chemie, Universität Göttingen, Tammannstrasse 6, D-37077 Göttingen, Germany
Correspondence e-mail: geckold@gwdg.de

### 2.1.5. Glossary

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 , , reciprocal-lattice vectors A Helmholtz free energy element of the coset modified dynamical matrix elastic stiffness in Voigt notation tensor of elastic stiffnesses lattice heat capacity at constant pressure contribution of phonon state () to the heat capacity at constant volume multiplicity of irreducible representation s lattice heat capacity at constant volume lattice heat capacity at constant volume according to the Debye model lattice heat capacity at constant volume according to the Einstein model dynamical matrix submatrix of the block-diagonalized dynamical matrix corresponding to irreducible multiplier representation σ submatrix of the dynamical matrix matrix of rotation about axis i by the angle α polarization vector of atom κ corresponding to the phonon eigenvector of the dynamical matrix corresponding to the phonon identity matrix of symmetry coordinates zero-point energy lattice energy contribution of the phonon to the energy of the lattice atom transformation table degeneracy of the eigenfrequency Fourier-transformed force-constant matrix g reciprocal-lattice vector space group of the wavevector q point group of the wavevector q augmented point group of the wavevector q order of group G density of phonon states density of phonon states according to the Debye model density of phonon states according to the Einstein model H Hamiltonian Planck constant (1.0546 × 10−34 J s) I inversion k Boltzmann constant (1.381 × 10−23 J K−1) anti-unitary operator M mass tensor mirror plane perpendicular to axis i mass of atom κ Bose factor corresponding to the phonon state () N number of atoms within the primitive cell number of primitive cells p pressure momentum of atom occupation probability of quantum state n projection operator q phonon wavevector qBZ wavevector on the Brillouin-zone boundary normal coordinate corresponding to the phonon vector to the origin of the lth primitive cell time-dependent position vector of atom equilibrium position of atom with respect to the origin of the primitive cell equilibrium position of atom within the lth primitive cell R element of the point group of the wavevector element of symmetry operation (Seitz notation) matrix of rotation space-group element that inverts the wavevector t time T temperature matrix operator associated with a symmetry operation r of the point group of the wavevector q polarization vector for elastic waves displacement vector of atom V potential energy V volume matrix of force constants acting between atoms and sound velocity fractional translation associated with symmetry operation lattice translation Z partition function tensor of thermal expansion β coefficient of volume expansion γ mean Grüneisen parameter averaged-mode Grüneisen parameter generalized-mode Grüneisen parameters propagation tensor transformation matrix Kronecker delta Dirac delta function block-diagonal matrix of irreducible representations strain tensor χ character of a representation multiplier associated with two symmetry operations and of the point group of the wavevector q potential energy isothermal compressibility Debye temperature Einstein temperature density stress tensor irreducible representation conjugated representation vector representation tensor representation Debye frequency Einstein frequency frequency of phonon arbitrary vector * denotes the complex-conjugate quantity + denotes the Hermitian conjugate matrix T denotes the transposed matrix

### References

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