Variation of interface compositions during diffusion controlled precipitate growth in ternary systems

Abstract

Isothermal diffusion controlled phase growth in ternary systems has been modeled using the Crank-Nicolson finite difference equations. Local equilibrium at phase boundaries and one dimensional growth are assumed. The model includes a method of determining phase growth velocity and interface compositions consistent with the diffusion rates of both elements. It also considers the effects of finite or overlapping diffusion fields (impingement). The growth of phosphide, (FeNi)₃P, in α ferrite in the Fe−Ni−P system was chosen for the simulation. Interface compositions are predicted to change with time, controlled by the necessity to balance the two solute (Ni and P) fluxes which cause the precipitate to grow. Diffusion controls the growth process although during initial growth interface structure may be important. The ratio of the major ternary coefficientsD ^Fe_PP /D ^Fe_NiNi controls the amount of shift of the precipitate interface composition from the tie line through the bulk composition. During the major period of growth the Ni interface compositions in phosphide and α remain constant and a square root of time,t ^1/2, dependence for growth is predicted. The practical, effect of impingement is to decrease phase growth and to allow the interface compositions to shift towards the tie line through the bulk composition.