Simulation of Paraequilibrium Growth in Multicomponent Systems

A methodology to simulate paraequilibrium (PE) growth in multicomponent systems using the DICTRA (Diffusion-Controlled Transformation) software is presented. For any given multicomponent system containing substitutional and interstitial elements, the basic approach is to define a hypothetical element Z, whose thermodynamic and mobility parameters are expressed in terms of the weighted average (with respect to site fraction) of the thermodynamic parameters and mobilities of the substitutional alloying elements. This procedure facilitates the calculation of PE phase diagrams and the PE growth simulations directly in the Thermo-Calc and DICTRA software, respectively. The results of two distinct case studies in multicomponent alloys are presented. In the first example, we simulate the isothermal growth of PE cementite in an Fe-C-Co-Cr-Mo-Ni secondary hardening steel during tempering. This is of practical importance in modeling the carbide precipitation kinetics during secondary hardening. In the second example, we have presented the results of PE ferrite growth during continuous cooling from an intercritical temperature in an Fe-Al-C-Mn-Si low-alloy steel. This is of importance to the design of triple-phase steels containing an austenite that has optimum stability, to facilitate stress-induced transformation under dynamic loading. The results of both simulations are in good accord with experimental results. The model calculations do not consider any resistive or dissipative forces, such as the interfacial energy, strain energy, or solute drag, and, as a result, the interface velocities represent an upper limit under the available chemical driving force.