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

International Tables for Crystallography (2013). Vol. D, ch. 1.1, pp. 32-33

Section 1.1.6. Glossary

A. Authiera*

aInstitut de Minéralogie et de Physique des Milieux Condensés, 4 Place Jussieu, 75005 Paris, France
Correspondence e-mail:

1.1.6. Glossary

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[{\bf e}_i] basis vectors in direct space (covariant)
[{\bf e}^i] basis vectors in reciprocal space (contravariant)
[x^i] components of a vector in direct space (contravariant)
[x_{i}] components of a vector in reciprocal space (covariant)
[g_{ij}] components of the metric tensor
[t_{i_{1} \ldots i_{p}}^{j_1 \ldots j_q}] components of a tensor of rank n, p times covariant and q times contravariant ([n = p+q])
[A^T] transpose of matrix A
[\otimes] tensor product
[\bigwedge] outer product
[\wedge] vector product
[\partial_i] partial derivative with respect to [x_i]
[\delta_i^j] Kronecker symbol
[\varepsilon_{ijk}] permutation tensor
V volume
p pressure
[u_{i}] components of the displacement vector
[S_{ij}] components of the strain tensor
[S_{\alpha}] components of the strain Voigt matrix
[T_{ij}] components of the stress tensor
[T_{\alpha}] components of the stress Voigt matrix
[s_{ijkl}] elastic compliances
[s_{\alpha\beta}] reduced elastic compliances
[(s_{ijkl})^{\sigma}] adiabatic elastic compliances
[c_{ijkl}] elastic stiffnesses
[c_{\alpha\beta}] reduced elastic stiffnesses
ν Poisson's ratio
E Young's modulus
Θ temperature
σ entropy
[\alpha_{ij}] thermal expansion
[\lambda_{ij}] temperature-stress constant
[{\cal U}] internal energy
[{\cal G}] Gibbs free energy
[C^{E,T}] specific heat at constant stress and applied electric field
E electric field
D electric displacement
H magnetic field
B magnetic induction
[\varepsilon_o] permittivity of vacuum
[epsilon] dielectric constant
[\varepsilon_{ij}] dielectric tensor
[(\varepsilon_{ij})^{\sigma}] adiabatic dielectric tensor
[\chi_{e}] dielectric susceptibility
[\eta_{ij}] dielectric impermeability
[p_{i}] pyroelectric tensor
[d_{ijk}] piezoelectric tensor
[d_{i\alpha}] reduced piezoelectric tensor
[d_{\alpha i}] reduced inverse piezoelectric tensor
[(d_{ijk})^{\sigma}] adiabatic piezoelectric tensor
[e_{ijk}] piezoelectric tensor at constant strain
[Q_{ijkl}] electrostriction tensor
[Q_{\alpha\beta}] reduced electrostriction tensor
[\pi_{ijkl}] piezo-optic tensor
[\pi_{\alpha\beta}] reduced piezo-optic tensor
[p_{ijkl}] elasto-optic tensor
[p_{\alpha\beta}] reduced elasto-optic tensor
[R_{H\ \ ijk}] Hall constant

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