Non-isothermal finite diffusion-controlled growth in ternary systems

Abstract

A mathematical model has been developed for diffusion controlled phase growth in ternary systems. Local equilibrium at phase boundaries and one dimensional diffusion controlled growth is assumed. The model includes a method of determining phase growth velocity and interface compositions consistent with the diffusion rate of both solute elements. This method also accounts for the effects of overlapping diffusion fields and nonisothermal growth. Initial conditions can be any curvilinear composition gradients and boundary conditions can be fixed or vary with time and/or temperature. The Crank-Nicolson finite difference equations are used to provide numerical stability and flexibility. Other capabilities of the model include treatment of finite systems, of nonisothermal phase growth and of off-diagonal ternary coefficients (D ₂₁ ³,D ₁₂ ³). Several sample simulations of the constant cooling of a 2.1 wt pct P, 4.1 wt pct Ni, 93.8 wt pct Fe alloy are presented. Three cooling rates are used: 5×10⁻³, 5×l0⁻⁴, and 5×l0⁻⁵ °C/s. An Fe-Ni-P alloy of this same composition was cooled in the laboratory for five days at 5×lo⁻⁴ °C/s from 900 to 685°C. Excellent agreement was found for the predicted and measured composition gradients and precipitate sizes.