Knowledge Bank

In a manner analogous to the description of the refractive indices of an anisotropic material by means of an indicatrix,surface, the relation between the absorptivity of an anisotropic material and the direction of electric vector vibration of a wave may be represented by an ""absorptivitrix surface."" This surface has been mentioned in other terms by many other authors, but not quantitatively emphasized. Visible dichroism has usually been designated by a qualitative dichroic formula, for the quantitative instruments commonly have not been available to optical crystallographers, and most of the crystals dealt with have not been colored. In the infrared region, on the other hand, most crystals have absorption bands and are dichroic, and quantitative instruments are used of necessity. The symmetry relations of this surface to the crystallographic axes for the seven crystal systems are discussed. For crystals of low symmetry, the absorptivitrix will change size, shape, and orientation with change of wavelength; it is emphasized that two polarization spectra of a single crystal face with the polarizer orientation different by $90\circ$ cannot in general give maximum dichroic ratios for the different absorption bands. The description of the absorption properties of a crystal will require up to seven columns: $\sigma$, $a\alpha$, $a\beta$, $a\gamma$, $\varphi aa\alpha$, $\varphi aa\beta$, and $\varphi aa\gamma$. And the description of the refractive index properties of the crystal, which in the general case must be known in order to determine the directions of refraction and hence the path lengths within the crystal, may require seven colums as well: $\sigma$, $n\alpha$, $n\beta$, $n\gamma$, $\theta an\alpha$, $\theta bn\beta$, and $\theta cn\gamma$. Additional descriptions of the shapes of the absorptivitrix and the indicatrix may be required in the wavelength regions of absorption bands at which anomalous dispersion effects are ""large."" The relation of the absorptivitrix to the orlentation of chemical bonds and problems in the experimental determination of the absorptivitrix are mentioned.