PRINCIPLES OF QUANTITATIVE ABSORBENCY MEASUREMENTS IN ANISOTROPIC CRYSTALS

The accurate measurement of absorbance (A=-log T; T=I/I-0) in anisotro pic materials like crystals is highly important for the determination of the concentration and orientation of the oscillator (absorber) unde r investigation. The absorbance in isotropic material is linearly depe ndent on the concentration of the absorber and on the thickness of the sample (A=epsilon . c . t). Measurement of absorbance in anisotropic media is more complicated, but it can be obtained from polarized spect ra (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 ab sorbance values to one common basis (the total absorbance A,,,), where in all absorbers are corrected as if they were aligned parallel to the E-vector of the incident light. The total absorption coefficient (a(t ot)=A(tot)/t) is calculated by (i) a(tot)=Sigma(i=1)(3)(a(max,i)+a(min ,i))/2, or by (ii) a(tot)=a(x)+a(y)+a(z). Only in special. circumstanc es will unpolarized measurements of absorbance provide data useful for quantitative studies of anisotropic material. The theoretical approac h is confirmed by measurements on calcite and topaz. The orientation o f the absorber with respect to the axes of the indicatrix ellipsoid is calculated according to A(x)/A(tot)=cos(2) (x angle absorber), and an alogously for A(y) and A(z). In this way, correct angles are obtained for all cases of symmetry. The extinction ratio of the polarizer (Pe=I -crossed/I-parallel) has considerable influence on the measured amplit ude of absorption bands, especially in cases of strong anisotropic abs orbance. However, if Pe is known, the true absorbance values can be ca lculated even with polarizers of low extinction ratio, according to Am ax=-log [(T-max,T-obs-0.5 . Pe . T-min,T-obs)/(1-0.5 . Pe)], and simil ar for A(min).