Anharmonic properties of rocksalt structure solids

Temperature Dependent Anharmonic Properties of Lead Chalcogenides

“…The elastic energy density for a crystal of a cubic symmetry can be expanded up to quartic terms as shown below [1]: (1) where C ijkl , C ijklmn and C ijklmnpq are the SOECs, TOECs and FOECs in tensorial form; x ij are the Lagrangian strain components, C IJ , C IJK and C IJKL are the SOECs, TOECs and FOECs in Brügger's definition [7] and Voigt notations [8]. The SOECs, TOECs and FOECs are as given below…”

“…Kailash et al [1] have recently derived general expressions for the anharmonic properties of NaCl-structure ionic solids following the well-known method of homogeneous deformation. These expressions are easily applicable [2,3] to determine the higher order elastic constants and related properties at temperature near melting point.…”

“…These expressions are easily applicable [2,3] to determine the higher order elastic constants and related properties at temperature near melting point. Nowadays, determination of anharmonic properties at high temperatures [1][2][3][4][5][6] is of common interest, therefore, we have used these expressions to evaluate the second-, third-and fourth-order elastic constants (SOECs, TOECs and FOECs), the first-order pressure derivatives (FOPDs) of SOECs and TOECs, second--order pressure derivatives (SOPDs) of SOECs and partial contractions of lead chalcogenide crystals crystallising in the NaCl-structure. Since the thermal effects contribute significantly, the temperature dependence of elastic constants is much more sensitive to the short-range interactions.…”

Elastic Constants and Pressure Derivatives of Calcium Oxide

“…The superscript " 0 " has been introduced to emphasize that the static elastic constants correspond to 0 K. By adding the vibrational elastic constants to the static elastic constants, one may get SOECs and TOECs at any temperature for fcc crystals. The general expressions for these properties have been reported in [1] [5] and therefore are not repeated in this paper.…”

“…As a matter of fact, they require computation, point by point, of the hypersurface of the total energy for applicable lattice deformations and numerical calculation of the second derivatives of the energy with respect to strain components. The electrostatic and Börn-Mayer repulsive potentials method [1] implemented in the crystal allows this type of calculation as the cyanides, chalcogenides, alkali halides, alkaline oxides and sulphides examples shown in [2]- [7]. A good agreement obtained for the temperature dependence of anharmonic properties, encouraged the author to extend this model for the study of the temperature dependence of higher order elastic constants and pressure derivatives for divalent materials.…”