Effect of Al Concentration on the Microstructural Evolution of Fe-Cr-Al Systems: A Phase-Field Approach

Abstract

In this study, the microstructural evolution of an Fe-Cr-Al system was simulated in two-dimensional (2D) and three-dimensional (3D) systems using the phase-field method. We investigated the effect of Al concentration on the microstructural evolution of the systems, with a focus on the nucleation and growth of the Cr-rich α′ phase. In addition, we quantitatively analyzed the mechanism of the effect of Al concentration on the microstructural characteristics of the 2D and 3D systems, such as the number of precipitates, average precipitate area (volume), and α′ phase fraction. In particular, we analyzed the effect of Al concentration and the dimensions of the system cell on the formation of the interconnected structure at high Cr concentrations, such as 35 Crat% and 40 Crat%. To enhance the performance of the simulations, we applied a semi-implicit Fourier spectral method for the ternary system and a parallel graphics processing unit computing technique. The results revealed that the initiation of phase separation in the 2D and 3D simulations was enhanced with an increase in the average Al concentration in the system. In addition, with an increase in the average Al concentration in both systems, the α′ phase fraction increased, while the change in the phase fraction decreased.

Phase field modeling microstructural evolution of Fe-Cr-Al systems at thermal treatment

“…These results are related well to previous studies [see for example, Ref. (Lee et al, 2020)]. With the temperature decrease from 710 K down to 690 K (cf.…”

“…At the coarsening stage the mean precipitate size (radius) ⟨R p ⟩ increases according to the power-law ⟨R p ⟩ ∝ t n with the exponent n close to the classical Lifshits-Slyozov-Wagner (LSW) value 1/3; the total amount of precipitates at this stage decreases exponentially (see power-law and exponential decay fitting shown by dash and dash-dot lines, with fitting parameter τ). Data obtained for the mean precipitate size (around 1-1.2 nm at annealing time 300 h) and precipitate number density (1.5 × 10 19 cm −3 ) for the studied alloy relate well to experimental and numerical data for class of system related to Fe-Cr-Al alloys (Messoloras et al, 1984;Chen et al, 2019;Lee et al, 2020;Yang et al, 2020). Scaling dynamics of mean precipitate size in Fe-Cr alloys was observed experimentally [see, for example, Refs.…”

“…Mobility coefficients M Cr,Cr , M Al,Al and M Cr,Al are as follows (Huang et al, 1995;Wu et al, 2001;Wu et al, 2004;Lee et al, 2020): In the Cahn-Hilliard-Cook equation Eq. 7 with a variable mobility Eq.…”

“…Among theoretically obtained results one can issue ab initio calculations of energetic parameters for atoms relocations (Kresse and Hafner, 1993;Wu et al 10.3389/fenrg.2023.1088742 Kresse and Hafner, 1994;Kresse and Furthmüller, 1996), kinetic Monte Carlo simulations of the long-term microstructural stability of Fe-Cr-Al alloys (Ejenstam et al, 2015), molecular dynamics studying the dependence of elastic, bulk and shear moduli on alloy composition (Dai et al, 2022), classical phase field modeling precipitation kinetics [see for example, Refs. (Chen et al, 2019;Lee et al, 2020)]. A correlative theoretical and experimental research strategy has been developed in Ref.…”

Thermodynamic and Kinetic Characteristics of Spinodal Decomposition in Ternary Alloys

“…Therefore, based on the diffuse interface modeling, the phase-field method has emerged (Chen, 2002) as a good alternative for microstructure simulation. The phase-field method has successfully simulated different phase transformations (Chen, 1994;Steinbach, 2009;Muramatsu et al, 2010;Ansari et al, 2021;Lee et al, 2021), such as dendritic growth, spinodal decomposition, recrystallization, and coarsening of precipitates. Most of these works were conducted in pure metals or binary alloys.…”