A generalized set of strain variablesq_r^N, has been defined to develop the expression for a generalized set of second order and third-order elastic moduliC_rs^N andC_rst^N for a cubic crystal deformed to orthorhombic structure. The HessainC_rs^Nδq_rδq_s andC_rst^Nδq_rδq_sδq_t (r=1, 2……6; summation convention) are calculated in the new variables and compared withG-strength andS-strength, for both positive and negative loading environment.

The convexity of the internal energy relative to various choice of strain measure is examined considering up to third degree terms in the internal energy expression. The computational results forbcc iron is presented according to the new moduli. The stable ranges thus obtained for iron under hydrostatic compressive and tensile stresses is found to generate the classical stable range, green-stable range and stretch-stable range as the specific cases. However,bcc iron does not seem to follow any conventional stable ranges under hydrostatic compression, where the present generalized stable range is found satisfactory.

Various state-equations, derived by expanding energy as a function of volume in Taylor series and using different order Pade’s approximants, have been combined with quasi-harmonic approximation for free energy to reproduce the pressure dependence of thermodynamic properties of NaBr, NaI and AgCl crystals. We have used these state-equations to compute the reduced volume, the isothermal bulk modulus and the pressure derivative of isothermal bulk modulus for the three crystals at various pressures (up to 80 kbar) and at room temperature (T=298 K). The results obtained are reasonably good lending support to the state-equations and the technique used to extend their applicability. The significant results obtained in the present study include the unified reduced equation of state for the three crystals which generates almost a single curve for theP – V behaviour at room temperature.