By D.E. Newland
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Great for engineers and pros, too uncomplicated for mathematicians.
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Additional resources for An Introduction to Random Vibrations, Spectral & Wavelet Analysis: Third Edition
Dielectric breakdown occurs before saturation. In a ferroelectric crystal, however, the polarization can become so large that nonlinear effects become dominant. This means that even in a single-domain crystalS P is in general a nonlinear function of E, and conversely, E is a nonlinear function of P [Ref. 12, p. 29]. The free energy can therefore be expanded in terms of the components of P. If the crystal has a center of symmetry above the Curie temperature, only even terms are significant in this expansion.
A direct comparison between GQQ and G QQ is only possible for qr<:1 as relevant for piezoelectricity; in this case cos(4qr /3) ~ 1 and the comparison yields Ix = Iy = 2H, = gy = i(2K + 5H) gx . 60) . 53) we obtain I 1 I ell3 I = f223 = -2" f 333 = - 1 e* K - 2H y'3 a5 K + 4H The piezoelectric constants of ZnS are usually not referred to the system (x, y, z) with zll(111) but rather to the system (x}, X2, X3) with axis parallel to the edges of the cube. The transformation between the two coordinate systems is given by m~ (an a22 a31 a32 C}.
2]. In the vicinity of the transition temperature e 00 may be neglected. 2) in this region, where C = C' /41r is called the Curie constant. 2b]. 1 A physical meaningful dielectric constant is also measured in the paraelectric state as T--+To or on single domain crystals. 3]. First there is Rochelle salt, NaK(C4H406) ·4H 20, and related isomorphous salts. Rochelle salt is a complicated crystal; for a summary of properties see Mueller and Mason . The second group of ferroelectric crystals is the KDP group, where KDP stands for KD 2P0 4.
An Introduction to Random Vibrations, Spectral & Wavelet Analysis: Third Edition by D.E. Newland