By Alexander Shtukenberg, Yurii Punin, Bart Kahr
Optically Anomalous Crystals starts off with an historic advent masking the contributions of Brewster, Biot, Mallard, Brauns, Tamman, and lots of different uncommon crystallographers. From this follows an instructional in crystal optics. extra chapters speak about the 2 major mechanisms of optical dissymmetry: 1. the piezo-optic impression, and a pair of. the kinetic ordering of atoms. The textual content then tackles advanced, inhomogeneous crystals, and the complicated optical houses because of the superposition of anomalies having a variety of etiologies. The e-book treats the literature comprehensively, yet makes use of illustrations from the authors laboratories because the topics of distinctive analyses. this is often a useful textual content for crystallographers, mineralogists, and petrologists drawn to the expansion of minerals and artificial crystals, and their optical homes. it's also perfect to scholars of optical mineralogy, expert scientists and engineers in addition to historians of technology.
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Extra info for Optically Anomalous Crystals
8 shows the rhythmic zoning observed in quartz related to periodic changes in content of Al and OH (Frondel, 1985). This is the result of the cyclic interplay between diffusion and growth rate. 2. Macroscopic Deformations of Crystals Distortions of the indicatrix due to macroscopic deformations are not considered genuine optical anomalies. If we put a crystal in a thumb screw, it is obvious that distortions in the optical indicatrix are a consequence of the stresses imposed upon it externally. On the other hand, internal stress resulting in strain from isomorphous impurities or dislocations, may have non-obvious etiologies and associated anomalies do indeed fall within the bounds of our discussion.
Under elastic stress, the mutual displacement of atoms leads to distortions of bond lengths, valence angles, and attendant electronic structure. Lattice constants change, too. As a result, the absolute values of anisotropic polarizabilities change, affecting the impermittivity tensor and the optical indicatrix. 1) ij = i j k l=1 2 3 ijkl kl where ijkl is the fourth rank piezooptic tensor. 2) where = ij = kl = ij ↔ kl ↔ ij ↔ ijkl ij ↔ ijkl 2 =1 2 6 =1 2 =1 2 =1 2 6 6 kl ↔ 6 kl ↔ =1 2 3 =4 5 6 The relationship between indices is written using the following convention: 11 1 22 2 33 3 23 32 4 13 31 5 12 21 6 −1 Piezooptic coefficients have the units of area/force m2 N with typical values of −1 −1 10−12 m2 N 10−11 cm2 dyn .
The causes of such stresses include the following: 1. Lattice mismatch between the crystalline host and an inclusion that precipitates from a solid solution. 48 Chapter 2 2. Post-growth changes of temperature and pressure leading to local differences in thermal expansion coefficients or compressibilities. 3. Accumulation of stress from other sources at the inclusion. 4. Crystallization pressure acting during inclusion formation. 2), then = amatrix − ainclusion a. As shown above, the anomalous birefringence is proportional to the maximal shear stress 2 max = rr − , where are the principal stresses in the plane under consideration (the polar rr and coordinate frame has been chosen for convenience).