By Professor Dr. L. A. Shuvalov (auth.), Professor Dr. L. A. Shuvalov (eds.)
Modern Crystallography IV is dedicated to a scientific and up- to-date description of primary actual houses of good and liquid crystals. those comprise elastic and mechanical, dielectric and ferroelectric, magnetic and optical homes, shipping phenomena and spectroscopy. a tremendous characteristic of the therapy is its use of the crystallographic strategy, an advent to that is given within the starting bankruptcy of the ebook. the themes are handled at a degree comprehensible to scholars who've years of collage physics. Researchers and engineers engaged on sensible purposes also needs to locate the publication beneficial, as may still experts in different fields who desire to develop their wisdom of crystallography and fabrics technological know-how. The publication is written via a bunch of top scientists from the Institute of Crystallography of the USSR Academy of Sciences.
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Extra resources for Modern Crystallography IV: Physical Properties of Crystals
The ambiguity of the choice of the crystallographic axes increases the arbitrariness still further. This must be taken into consideration when comparing the results of different authors' measurements of the physical properties of particular crystals. The same circumstance obliges the researcher to ensure unambiguous setting of the crystal in experiment and describe it in clear terms when presenting the results. 5 Symmetry of Physical Properties 33 take, as the "crystallophysical" system, the principal system of the tensor of the property being measured under definite conditions (for instance, in optical measurements, the main axes of the optic indicatrix with fixed values of wavelength I\.
In a tensor related to the principal axes (or, as is customary to say, to the diagonal form) the number of independent components decreases to three. The number of the "degrees of freedom," however, generally remains equal to six, since the three independent values are now needed for determining the direction of the fixed principal coordinate axes (the principal axes of the tensor). 47) it follows at once that when vector b is directed along anyone of the principal axes of the tensor, vector a is parallel to it.
In an arbitrary direction, defined by direction cosines ej, e2, and e3, we assign b = [ejb, e2b, e3b]. Then 20 1. Fundamentals of Tensor and Symmetry Description Hence, the direction cosines of vector a are proportional to Tl ej, T2e2, and T3 e3' We now direct radius vector r parallel to b (Fig. 4). Clearly, It is known from analytic geometry that the direction cosines of a normal to surface F(x;) = 0 at a given point are proportional to 8E(Xi)/8xi calculated at this point. , will be proportional to the direction cosines of vector a.
Modern Crystallography IV: Physical Properties of Crystals by Professor Dr. L. A. Shuvalov (auth.), Professor Dr. L. A. Shuvalov (eds.)