Predictions of nucleation theory applied to ehrenfest thermodynamic transitions: II. The effects of pressure and stress

This paper is a sequel to an earlier one on the applicability of classical nucleation theory to second-order transitions in the Ehrenfest sense (1). In each case the approach was to obtain the critical size r_c and energy barrier ΔG_c for the growth of a nucleus of β-phase in an α-phase matrix by a Maclaurin series expansion of the free-energy-density g = (G_β ? G_α)/v_β as a function of θ (in BC-I) and of ΔP and Δσ in this paper where θ = (T ? T_t) is the degree of undercooling and ΔP and Δσ are analogous terms for the hydrostatic pressure shift and tensile stress shift away from the equilibrium transition. The expansion coefficients were determined by the use of thermodynamic relationships. For second-order transitions, r_c = 4γv_β T_t/ΔC_pθ², r_c = 4γ/Δβ(Δp)², and r_c = 4γ/Y_αY_β(Δσ)², respectively, for the three cases. The terms ΔC_p, Δβ, and ΔY denote the differences in heat capacity, compressibility, and Young's modulus, e.g., ΔY = Y_β ? Y_α. The interfacial energy γ_αβ is denoted by γ. The activation energy barriers for the cases developed in this paper were ΔG_c = (16π/3)γ³/(Δβ)² (Δp)⁴ and ΔG_c = (64π/3)γ³Y_α²Y_β²/(ΔY)²(Δσ)⁴. More complicated expressions are given in the paper for the r_c and ΔG_c for first-order transitions. In the long run, these expressions may prove more useful than the ones for second-order because of the modifications expressions for the kinetics of transformations.