Three-dimensional phase field simulation of the morphology and growth kinetics of Ni₄Ti₃precipitates in a NiTi alloy

A three-dimensional phase field model is applied to study the morphology and growth kinetics of Ni4Ti3 precipitates, as well as the Ni concentration distribution feature, during the aging of a NiTi alloy. The model can reproduce well the multiple-variants morphology of Ni4Ti3 precipitates. The diameter-to-thickness ratio of lenticular Ni4Ti3 precipitates in the equilibrium shape is 4.2. Simulation results show that the Ni depletion region near the face of Ni4Ti3 precipitates is broader than that near the edge of the precipitates, and both the depletion level of Ni concentration and the length of the Ni depletion region adjacent to the precipitates increase with the aging time. The growth of the precipitate diameter and thickness can be described by the power-law fitting equation, with growth exponent m = 0.47 for the diameter and m = 0.46 for the thickness, which are in good agreement with those obtained in previous experimental and analytical studies.