Phase Field Simulation of Grain Growth Kinetics with Solute Drag in Fe-Mo-Nb Alloy

The addition of trace Mo and Nb elements to the Fe-Cr-Al ferrite alloy of the accident tolerant fuel (ATF) cladding can play a role in solid solution strengthening and precipitation. The precipitated Laves phase distributes at the grain boundary and subgrain boundary, which can fix the grain boundary and hinder grain growth, improving the thermal stability of the alloy. According to another view, the pinning effect of the Laves phase is smaller than the solute drag effect (SDE) and does not contribute significantly. The phase field method was used to quantitatively simulate the hindrance of Mo and Nb solute elements to grain boundary migration in order to study SDE on grain boundary migration during grain growth. To model the effect of the solute elements on grain boundary migration, a polycrystalline phase field model and a solute drag additional term were introduced to the existing phase field model, and the specific expressions of these models were derived for simulation. The simulation results show that the phase field method can observe the unsteady solute separation process, in comparison to the classical steady-state SDE model. In addition, the distribution of solute at grain boundaries with different migration rates and the corresponding SDE dissipation energy at those rates are also obtained, and the action range of Nb and Mo element SDE is determined. The degree of solute segregation at the grain boundary is negatively related to the grain boundary migration rate. When the grain boundary migration rate is greater than 1×10-5 m/s, the segregation of Mo and Nb at the grain boundary tends to zero. The relationship between SDE dissipation energy and interface migration rate is parabolic, with a peak value of 69.7 J/mol at a rate of 1.124×10-6 m/s. When the interface migration rate is less than 1.124×10-6 m/s, the concentration distribution deviates from the equilibrium state and the dominant SDE dissipation energy increases. When the interface migration rate is greater than 1.124×10-6 m/s, the solute separates and the degree of segregation decreases, while the dominant SDE dissipation energy decreases. During the early stage of grain growth, the solute at the grain boundary is not in a saturated state and the interface migration rate is too high, resulting in no obvious SDE. At the same time, the high interface migration rate causes solute retention. The results of the study show that the model is suitable for simulating the SDE in the polycrystalline growth process, and can provide valuable information for a deeper understanding of the solute dragging process of Mo and Nb in materials and for material design and performance prediction.