Second-, third-, and fourth-order elastic constants of mixed alkali-halide crystals

Analysis of Combination Rules for Elastic Constants of Mixed Ionic Crystals

“…A numerical analysis based on different sets reveals that the results are so close to each other that either the difference is insignificant or it is of the order of experimental uncertainty (around 1%). I n Tables 1 and 2 we T a b l e 1 Elastic constants (in 1010 Pa) of mixed KCll-,Er, crystals calculated using different sets of combination rules based on (a) Shanker and Jain model [5]; (b) Singh et al model [6]; (c) Giri (Al-,B,) is the bulk modulus of the mixed system, K(A) and K(B) are the bulk moduli of the two end members A and B, respectively, and V(A) and B(B) denote the molar volumes of A and B, respectively. Equation (11) has been found to produce good agreement with experimental elastic data for mixed ionic crystals [8,9,20,211.…”

Higher‐Order Elastic Constants and Thermoelastic Properties of Ionic Solids

“…An important application of the model developed by Shanker et al [53] has been made to study the higher-order elastic constants of mixed crystals of alkali halides [63] and AgC1-AgBr solid solutions [56]. It has also been demonstrated [63] that the knowledge of TOEC and POEC is useful in predicting the conductivity and thermal expansion coefficient of mixed crystals.…”

“…It has also been demonstrated [63] that the knowledge of TOEC and POEC is useful in predicting the conductivity and thermal expansion coefficient of mixed crystals.…”

Temperature Dependence of Fourth‐Order Elastic Constants of Alkali Halide Crystals

“…In the present paper, we extend this method to calculate the temperature dependence of fourth-order elastic constants (FOEC) for alkali halides. Since the contributions from third-and fourth-order coupling parameters to many anharmonic properties are of the same order of magnitude, the knowledge of FOEC is equally important as that of TOEC [15]. In Section 2, we present the method of analysis.…”

“…0891~ ( a 3 g ) + 13.3833~ (a2;) -157.62868 ( a ; ) j ,(15) 0 0 C,,,, = -15.4693T/?BT + -7.7347(B1 + B,) + Rl + 9.04598 (az g)o + 31.09608 ( a g)j, (18) C,,,, = 7.0808T#?BT + -1.5404(B1 + B,) + Rl f 1.04458 (19) -1.5404(B1 + B,) + Rl -16.64288+ 9.60878 ( a : ) j ,(20)C,,,, = -16.1604T/?BT + 8.0802(B1 + B,) + Rl + 2.08918 (21) c 1 1 4 4 = -16.1605Tj3BT + -8.0802(B1 + B,) + R, ,,,, = -16.1604T/?BT + -8.0802(B1 + B,) + R, Rl -5.5476~ a 2 -( 2) 0 + + 1 . 2 0 2 9~( a z ) j (25) and the equilibrium condition at P = 0 is e2 8a4 TPB, = -[0.3392~(~ + 16/(r)), + Bl + B2] , where D 1 -6C1 + 15A1 -15B1 54 D, -6C2 + 15A2 -15B2 54 D2 -6C2 + 15A2 -…”