Temperature dependence of elastic constants of some fluorite crystals

Abstract

The temperature dependence of elastic constants of some fluorite-structure crystals (namely BaF2, PbF&, and SrC12) has been investigated by means of potential models that include the effects of three-body interactions (TBI) and lattice anharmonicity arising from thermal-phonon pressure. The agreement between the experimental and present theoretical model I {with TBI) is better than that obtained from model II {without TBI) and is comparable with those calculated from measured Brillouin-scattering frequencies [Catlow et al. , J. Phys. C 11, 3179 (1978)]. It has been found that the lattice anharmonicity is responsible for an anomalous change in elastic constants with temperature for the Auorites. I. INTRGDUCTIQNThere has been considerable interest in the study of materials showing superionic behavior. The fluorite crystals constitute the simplest superionic conductors, ' and they are the model systems for the study of a variety of solid-state phenomena.One of the most interesting features of the Quorites is the temperature dependence of their elastic constants and specific heats. ' Some of these crystals (CaF2, BaFz, SrClz, and PbF2) are well known to exhibit elastic and specific-heat anomalies at temperatures T, well below the melting temperature T This anomaly is understood to be associated with the development of extensive disorder in the anion sublattice. The,effects of such high-temperature disorders have been investigated on Raman-scattering, ' the elastic constants using Brillouin scattering, and the acoustic-phonon modes using neutron scattering. Both the Brillouinscattering and neutron-scattering studies have shown large decreases of the elastic constants C» near T, without any marked change in C&2 and C44.The anomalous temperature dependence of the elastic constants has been attributed to three main physical reasons: (i) the normal lattice anharmonicity, " (ii) the increase in concentration of interstitials near the transition temperature T"and (iii) the hopping motion of defects.In the past three have been several attempts to study the variation of the elastic constants with temperatures using different experimental probes ' ' and theoretical models s'7'2 Catlow et al. have derived the elastic constants from the Brillouin-scattering measurements assuming that the square of the scattering frequency is directly proportional to the elastic constants. They have found that the Coulomb interactions between anion vacancies and interstitials are primarily responsible for the cooperative anion disorder in the Auorites. Ghosh and Dasgupta' have considered the effects of both anharmonicity and the Frenekl disorder to explain the temperature dependence of bulk modulus. On the other hand, Kleppmann' has investigated the efFects of the change in nearest-neighbor central force constants on vacancies and interstitials and found that they alone cannot account for the experimentally observed difference in the temperature dependence of C&& (large decrease) and C&z and C~(no measurable decrease) near T, . He has shown from ...

Calculated structural, elastic and electronic properties of SrCl2

“…From the experimental side several interesting properties of alkaline-earth halides such as electronic structure and optical spectra, elastic constants, lattice dynamics and high-pressure structural phase transitions have been studied [2][3][4][5][6][7][8][9]. From the theoretical point of view the electronic structure, structural phase stability, equation of state, elastic constants, ionic conductivity, and temperature dependence of elastic parameters have been determined [10][11][12][13][14][15][16][17][18][19].…”

Cohesive and Anharmonic Properties of Some Fluorite Structure Nitrates

“…The last four terms represent the SR overlap repulsive energy contributed by first-and second-neighhour interactions. The notations involved in (1) are the same as those defined elsewhere [2,31. The present TBP model contains only two model parameters, namely b andf(r), whose values are determined from the knowledge of the shear modulus ((Cll -CI2)/2) of the SOECs expressed as [3] ( 2 )…”

“…and the equilibrium condition [2] B , + B , = -1.9395g (4) with L = e2/4r4, g = Z ( Z + Sf(. )), and g' = rof'(ro).…”

A Simple, Potential-Free Model to Calculate Elastic Constants of Solids at High Temperature

“…Nevertheless, there have been some serious weaknesses in these models. For example, in the three-body potential model [14], the short-range overlap potential parameters calculated at 300 K, have been used in the high temperature range as such, presuming to be independent of temperature. Moreover, the Van der Waal's coefficient calculated from the lattice sums was also taken as temperature independent.…”

“…The elastic constants of some minerals have been calculated starting from the room temperature to higher temperatures, but there are deviations from experimental results after Debye temperature [10][11][12]. As far as the theoretical studies are concerned, methods like the Monte-Carlo and lattice dynamical simulation using a rigid body model [13] and three-body potential model [14] have been adopted with reasonable amount of success. Nevertheless, there have been some serious weaknesses in these models.…”