By Robert E. Newnham
Utilizing examples from engineering and different disciplines, Newnham (solid kingdom technological know-how, Pennsylvania kingdom U.) describes the physics and chemistry of crystals for technological know-how and engineering scholars on the undergraduate point. He specializes in tensors, matrices, symmetry and the relationships among constitution and estate, together with transformation, thermodynamic relationships, pyroelectricity, pressure and pressure, elasticity, magnetic and nonlinear phenomena, ferrole crystals, electrical resistance, acoustic waves, optics (including nonlinear optics), dispersion and absorption and chemical anisotropy
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Extra resources for Properties of Materials: Anisotropy, Symmetry, Structure
Debye temperatures for a number of semiconductor crystals with the zincblende structure are shown in Fig. 2. Note the decrease in θD with increasing lattice parameter. Short strong bonds give large Debye temperatures. 09 a. Compare these values with the Dulong and Petit prediction and explain the structure–property relationships. b. 7 × 10−11 m2 /N). 2 Lattice vibrations Since lattice vibrations control many of the thermal properties of solid it is important to have a visual picture of these atomic motions.
It greatly simpliﬁes the description of physical properties by eliminating some coefﬁcients and equalizing others. To illustrate, consider two of the standard single crystal materials available to scientists and engineers: quartz (SiO2 ) and corundum (Al2 O3 ). Both belong to the trigonal crystal system but have different point group symmetries. Quartz ¯ is in point group 32 while corundum is somewhat higher in 3m. Symmetry arguments based on Neumann’s Principle tell us that neither crystal is pyroelectric since ﬁrst rank polar tensors disappear for both point groups.
The argument just applied to  directions in NaCl, holds for other direc¯ tions as well. In NaCl, the  and  directions are symmetry-related twofold axes, and therefore the properties will be the same when measurements ¯ are carried out in a similar way along  and . What about the properties along  and ? Will they sometimes be the same? For scalar properties the answer is, of course, yes. For higher rank tensor properties, it will depend upon the point group symmetry and the tensor rank.