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

International Tables for Crystallography (2013). Vol. D, ch. 1.6, p. 157

Section 1.6.3.3. The dielectric impermeability tensor

A. M. Glazera* and K. G. Coxb

aDepartment of Physics, University of Oxford, Parks Roads, Oxford OX1 3PU, England, and bDepartment of Earth Sciences, University of Oxford, Parks Roads, Oxford OX1 3PR, England
Correspondence e-mail:  glazer@physics.ox.ac.uk

1.6.3.3. The dielectric impermeability tensor

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It has been seen how the refractive indices can be described in a crystal in terms of an ellipsoid, known as the indicatrix. Thus for orthogonal axes chosen to coincide with the ellipsoid axes, one can write [ {x_1^2 \over n_1^2} + {x_2^2 \over n_2^2} + {x_3^2 \over n_3^2} = 1, \eqno(1.6.3.22)]where [n_1 = (\varepsilon_{11})^{1/2}], [n_2 =(\varepsilon_{22})^{1/2}] and [n_3 = (\varepsilon_{33})^{1/2}]. One can write this equation alternatively as [\eta_{11}x_1^2 + \eta_{22}x_2^2 + \eta_{33}x_3^2 = 1, \eqno (1.6.3.23)]where the [\eta_{ii} = 1/\varepsilon_{ii}] are the relative dielectric impermeabilities. For the indicatrix in any general orientation with respect to the coordinate axes[\eta_{11}x_1^2 + \eta_{22}x_2^2 + \eta_{33}x_3^2 + 2 \eta_{12}x_1x_2 + 2 \eta_{23}x_2x_3 + 2 \eta_{31}x_3x_1= 1. \eqno (1.6.3.24)]Thus the dielectric impermeability tensor is described by a second-rank tensor, related inversely to the dielectric tensor.








































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