Elastic constants of bcc shape-memory binary alloys: Effect of the configurational ordering

The relationship between the elastic shear modulus C’=1/2($C_{11}$-$C_{12}$) and the atomic order state in a shape-memory binary alloy $A_x$ $B_{1\mathrm{-}x}$ above its martensitic transition temperature is analyzed. We first present a simple method to evaluate the elastic constants in binary alloys, assuming the atoms interact via a two-body Morse potential. For CuZn and AgZn alloys, the potential parameters corresponding to the different A-A, B-B, and A-B pairs are determined from experimental data of the elastic constant C’ for different alloy compositions. We next calculate C’ at 0 K as a function of the ordering state. To do this, we use atomic configurations obtained with a Monte Carlo simulation of the Ising model for a bcc binary alloy, at each temperature $T_i$. We obtain a linear relationship between C’ and the short-range-order parameter η. We also show that the deviations from the linear behavior observed when C’ is represented against the square of the long-rang-order parameter 〈S〉 come mainly from the critical behavior of the system near the order-disorder temperature $T_c$.