The analysis of phase decomposition was carried out using the nonlinear and linear Cahn-Hilliard equations in a hypothetical A-B alloy system with a miscibility gap. These equations were solved by the explicit finite difference method assuming a regular solution model. The supersaturated solid solution and decomposed phases were considered to have an fcc structure. Different aging temperatures and thermodynamic interaction parameters Ω A-B were used to simulate different alloy systems. The numerical simulation results showed that the growth kinetics of phase decomposition in the alloy with 30at.% A was slower than that of 50 at.% A. Additionally, the start time and modulation wavelength of phase decomposition are strongly affected by the thermodynamic interaction parameter Ω A-B value. The numerical simulation results showed that the growth kinetics of phase decomposition with the linear equation is slower than that with the nonlinear one.
ResumenEl Método de Campo de Fases, basado en fundamentos de termodinámica, mecanismos y cinética de reacciones de precipitación en aleaciones, es útil para simular numéricamente la solidificación de aleaciones de interés industrial, su microestructura y su evolución durante ciclos térmicos. Este método resuelve la ecuación diferencial parcial de Cahn y Hilliard y ofrece como ventajas su sencillez y rapidez computacional. En este trabajo se analizó el efecto de los parámetros que intervienen en tal ecuación sobre la morfología y cinética de la separación de fases de sistemas de aleación hipotéticos A-B y A-B-C con laguna de inmiscibilidad. Los resultados obtenidos mostraron que los cambios en la movilidad atómica modifican la cinética de la separación. En contraste, la energía de deformación elástica afecta directamente la morfología de las fases, causando que la morfología pase de esferas a cubos con bordes redondeados o placas con alineación cristalográfica preferencial. Palabras ClaveSimulación numérica; Descomposición espinodal; Aleaciones hipotéticas; Ecuación Cahn-Hilliard. Numerical simulation of the spinodal decomposition in hypothetical A-B and A-B-C alloy systems AbstractThe phase field method is based on the thermodynamics, mechanism and kinetic of the precipitation reactions in alloys. This method can be used to simulate numerically the microstructural evolution in an alloy system, and constitutes a powerful tool to predict the phase transformations. The phase field method solves the nonlinear CahnHilliard partial differential equation and offers computational advantages. The effect of the parameters into this equation on the morphology and kinetics of the phase separation in binary A-B and ternary A-B-C hypothetical alloy systems with a miscibility gap was analyzed. The results showed that the atomic mobility modifies the phase separation kinetics. In contrast, elastic-strain energy is an important parameter that affects the morphology of phases causing changes from spheres to cuboids or plates with preferential crystallographic alignment.
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