Temperature dependence of elastic constants for ionic solids

Diffusion in periclase by combination of analytical formulas and thermodynamic model

“…The values of a and at different temperatures in the range (1800-2500) K are listed in Tables 1 and 2. For the estimation of the constant c act , we inserted in Eq. (4) for the lower temperature T = 1820 K the corresponding values (Table 1): a (1820) = 4.399 × 10 −8 cm, (1820) = 10.641 × 10 −24 cm 3 , B (1820) = 116.1 GPa (Sarkar et al, 2009) and D (1820) = 1 × 10 −17 cm 2 s −1 (Yang and Flynn, 1994 in their Fig. 1) and we obtained c act = 0.7243.…”

“…Here, by using the values of elastic parameters obtained from analytical relations that have been recently deduced (Sarkar et al, 2009), we proceed to the estimation of the self diffusion coefficients of MgO in temperatures prevailing in the lower mantle (1800-2500) K, and for which experimental data are available (Yang and Flynn, 1994 (Murnaghan, 1944) are given by Eqs. (5) and (6), respectively, as…”

“…In a recent paper (Sarkar et al, 2009), the elastic constants and the bulk modulus for ionic solids of cubic structure such as NaCl, KCl, MgO, CaO have been evaluated at different temperatures by means of analytical formulas based on Murnaghan's equation of state (Murnaghan, 1944) and Tallon's (Tallon, 1980) models. Various equation of state for the thermal dependence of elastic properties of solids are reported in literature (Anderson, 1995) and experimental data for the variation of these properties with temperature for a large number of materials can be found in Anderson and Isaak's book (1995).…”

“…Scope of the present work is to show that a combination from one side of the elastic data for MgO at any temperature, obtained by Sarkar (2009) through analytical formulas (Tallon, 1995;Murnaghan, 1944) and from the other side of a thermodynamical model that interconnects bulk properties and defect parameters, leads to the estimation of diffusion coefficients of MgO at any temperature and especially at those dominating in the lower mantle.…”

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

“…The study of temperature dependence of elastic constants for solids has been a subject of wide interest [3], [4]. Therefore, a number of theoretical as well as experimental physicists are currently engaged in the investigations related to elastic constants of diverse materials, employing a wide variety of approaches [5][6][7][8][9][10]. 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].…”