**Eugen
Libowitzky and George R. Rossman**

Division
of Geological and
Planetary
Sciences, California Institute of Technology

Pasadena, CA 91125-2500 U.S.A.

The
accurate measurement of
absorbance *(A = -log T; T = I/I*_{O}*) *in
anisotropic materials like crystals is highly important for
the determination of the concentration and orientation of the
oscillator (absorber) under investigation.

The
absorbance in isotropic
material is linearly dependent on
the concentration of the absorber and on the thickness of the
sample *(A = e
· c · t). *Measurement of absorbance
in anisotropic media is more complicated, but it can be obtained
from polarized spectra (i) on three random, but orthogonal
sections of a crystal, or (ii) preferably on two orthogonal
sections oriented parallel to each of two axes of the indicatrix
ellipsoid. To compare among different crystal classes (including
cubic symmetry) it is useful to convert measured absorbance
values to one common basis (the total absorbance *A*_{tot}*),
*wherein all absorbers are corrected as if they were aligned
parallel to the E-vector
of the incident light. The total
absorption coefficient *(**a*_{tot}*
= **A*_{tot}*/t)
*is
calculated by

_{
}

Only in special circumstances will unpolarized measurements of absorbance provide data useful for quantitative studies of anisotropic material.

The orientation of the absorber with respect to the axes of the indicatrix ellipsoid is calculated according to

and analogously for *Ay *and
*Az.
*In this way, correct angles are obtained for all cases of
symmetry.

The extinction ratio of the polarizer Only in special circumstances will unpolarized measurements of absorbance provide data useful for quantitative studies of anisotropic material.

The orientation of the absorber with respect to the axes of the indicatrix ellipsoid is calculated according to

and similar for

The theoretical approach is confirmed by measurements on calcite and topaz.

Physics and Chemistry of Minerals 23, 319-327