Many‐body lattice theory of elastic dielectric and its application to solids with NaCl structure

Abstract

A phenomenological lattice theory of elastic dielectric based on the Lundqvist potential of ionic cohesion is developed. In this theory the lattice is considered to be initially in the deformed and polarised state. The theory yields the expressions for the second order elastic constant, third order elastic constants, dielectric constants, and its strain derivatives. The many body lattice theory (MLT) of elastic dielectric so developed is applied to calculate the strain derivatives of the high and low frequency dielectric constants of the alkali halide solids. The calculated values of these constants are better than those obtained in all earlier models and are in excellent agreement with the experimental values.Es wird eine phanomenologische Gittertheorie elastischer Dielektrika entwickelt, die auf dem Lundqvistpotential fur die Ionenkohasion beruht. In dieser Theorie wird angenommen, daI3 das Gitter anfanglich im deformierten und polarisierten Zustand ist. Die Theorie liefert die Ausdrucke fur die elastischen Konstanten zweiter Ordnung, elastischen Konstanten dritter Ordnung, dielektrischen Konstanten und ihre Spannungsableitungen. Die so entwickelte Vielkorper-Gitter-Theorie (MCT) elastischer Dielektrika wird benutzt, um die Spannungsableitungen der Hoch-und Niederfrequenz-Dielektrizitatskonstanten der Alkalihalogenide zu berechnen. Die berechneten Werte dieser Konstanten sind besser als die, die mit allen fruherenModellen erhalten wurden, und stimmen ausgezeichnet mit den experimentellen Werten uberein.

Electric-Field-Induced Piezoelectricity of Some Pure and Doped Alkali Halides

“…[15] and [16]. More detailed calculations using sophisticated interaction potentials and semi-empirical parametrization have been done in e.g.…”

“…In their application to experimental data it is neccessary to slightly modify the expressions (15) and (16) because one is faced with the following problem: Although the stress in the sample is sufficiently homogeneous and unidirectional in the region of the electrodes, the electric field shows some fringing, especially in the case of longitudinal electrodes. This nonuniformity of the field leads to a ''cross-talk" of different tensor elements, e.g.…”

“…We arrive at numerical expressions for the ratio of the piezoelectric charge to the dielectric charge analogeous to (15) and (16) but including the mixing effect described above in form of weighting factors for the coefficients g ijkl . In these calculations, the stress-induced changes of the sample shape and of the electrode dimensions are also taken into account.…”

An estimation of the quadratic electrostrictive coefficients in LiCl, LiBr, NaI, KF and RbF crystals

“…212 = 113% where superscripts I and II denote different models. The latest theoretical coefficients published by Goyal et al (1978) for LiF, NaCl, KCl, KBr and KI lead to σι m = 20%,ffn 22 = 54% anda t212 = 104%. In the theoretical treatments the temperature effects were neglected therefore their results are valid at 0 K. However, one can expect that changes in d¡j U between the low and room temperatures are not significant (Bohaty and Haussühl, 1977).…”

“…The determination of the elastooptic-electrostrictive term is necessary to discuss the nature of the quadratic electrooptic effect and interpret the theoretical results obtained, for an example, in the framework of the bond-charge model (Kucharczyk, 1987). There exist also some calculations of the électrostriction (Grindlay and Wong, 1969;Srinivasan and Srinivasan, 1972;Goyal et al, 1978). One can compare the agreement between theory and experiment by evaluating the quantity where the summation is extended over the η species under investigation.…”