Phase field simulations of FCC to BCC phase transformation in (Al)CrFeNi medium entropy alloys

Abstract

Microstructure simulations for quaternary alloys are still a challenge, although it is of high importance for alloy development. This work presents a Phase field (PF) approach capable of resolving phase transformation in a multicomponent system with a simple and effective way to include the thermodynamic and kinetic information for such a complex system. The microstructure evolution during diffusional transformation between FCC and BCC phase at 700 °C for AlCrFeNi alloys was simulated, accounting for composition dependence and off-diagonal terms in the diffusion tensor. The reliability of the presented PF method is validated by comparing the 1-D simulation results with simulations by Diffusion Module (DICTRA) of Thermo-Calc Software. Additionally, 2-D PF simulations of precipitate growth and Ostwald ripening are performed for different alloy systems, and the coarsening behavior is compared. Results showed that thermodynamic and kinetic information is accurately described in the applied PF method. The simulation results show that the diffusion behavior is influenced evidently by variations in the amounts of the different elements in the system. These findings demonstrate the necessity of applying accurate thermodynamic and kinetic models to fully understand the complex interdiffusion behavior in high and medium entropy alloys.

A phase-field approach to study BCC precipitate evolution in FCC AlxCrFeNi medium entropy alloy including elastic effects

“…Their values were calculated using Thermo-Calc software with MOBHEA2 database and assuming the equilibrium composition of each phase. It was verified that the atomic mobilities are indeed almost constant over the considered concentration region and that the composition dependence of the diffusion in this quaternary alloys is well represented [7,8].…”

“…The next two terms represent the bulk chemical contribution with and , the free energy densities as a function of composition, as Gibbs energy functions of the FCC and BCC phase and a reference molar volume (difference in molar volumes of the different phases are considered through the eigenstrains in the elastic contribution). The Gibbs energy functions are obtained fitting higher order polynomial functions through a large set of Gibbs energy data calculated for the composition domain of interest using Thermo-Calc using the TCHEA2 database, as discussed in detail in previous papers [7,8].…”

“…The aim of this paper is to present initial results using a phase-field approach investigating microstructure evolution in the presence of elastic effects due to lattice misfit including CALPHAD data on the composition dependence of the thermodynamic and diffusion mobilities. Zuo et al [7,8] recently introduced a phase-field model for multicomponent precipitate growth and coarsening taking into account in a highly efficient way the CALPHAD Gibbs energy and diffusion mobility data for the quaternary alloy. In the current paper, elastic effects are added to this model description and initial simulations considering a single BCC precipitate in an FCC matrix are presented showing the effects of the elastic mismatch on precipitate shape, precipitate volume fraction and composition in the matrix as a function of time.…”

Phase-field study of elastic effects on precipitate evolution in (Al)0.05CrFeNi

“…The elastic properties are calculated through DFT calculations for the AlCrFeNi alloy. The PF model is based on our previous model [51,52], taking into account CALPHAD Gibbs energies and diffusion mobility data for the quaternary alloy in a highly efficient way. Elastic stress is added to this model using the micro-elasticity approach of Khachaturyan [34].…”

Phase-field-method-studied mechanism of Cu-rich phase precipitation in Al_<i>x</i>CuMnNiFe high-entropy alloy

“…形成的单相固溶体结构，忽视了高熵合金相分离的过程，研究表明高熵合金混合 熵与混合焓之间的相互竞争导致其在熔炼或时效过程中表现出相分离(包括调幅 分解)并有形成有序第二相沉淀的趋势 [8,9,10] 。 Cu 元素有促进凝固前液相分离的趋势，可以在纳米尺度上析出形成纳米富 Cu 相。根据 Dabrowa 等人的研究 [10] ，添加 Cu 元素会提升 CoCrFeMoNiCu x 高熵 合金的强度，主要原因是 Cu 元素有较大正混合焓，可以与许多金属元素形成弱 键 [11] ，使其易于偏析到枝晶间区域，从而形成富 Cu 相。Xian 等人 [12] 进一步研究 了 Cu 对 CrMnFeCoNiCu x 高熵合金的影响，发现微观组织会出现贫 Cu 枝晶和富 (Cu，Mn)枝晶，均匀弥散分布的纳米富 Cu 相会阻碍位错运动，显著提高屈服 强度和硬度，因此，研究人员对高熵合金中富 Cu 相与不同元素的作用以及多尺 度相分离产生了兴趣。 多尺度分解会导致复杂的有序和无序固溶相的混合，Borkar [13] 等人通过多种 实验分析方法研究 Al 2 CuCrFeNi 2 高熵合金铸态组织的分级演化过程， 发现在凝固 过程中 Al 2 CuCrFeNi 2 高熵合金会形成 B2 e (有序 BCC 相)和𝛽 𝑒 (无序 BCC 相) 的两相混合物，随后 B2 e 相分解为 B2 f 、板条状 Cu 颗粒、球状 Cu 颗粒和少量的 二元 FeCr 的𝛽 𝑓2 ， 𝛽 𝑒 相进一步分解为 Cu/B2 s 的核/壳复合纳米颗粒，而 Cu 元素 则充当了 B2 s 的异质形核点，同样在 FCC 基 Al 0.3 CuFeCrNi 2 高熵合金的微观组织 中 [14] ，Cu 元素也充当 L1 2 (𝛾 ′ )的异质形核点，形成富 Cu 相和有序的 L1 2 (𝛾 ′ ) 析出相，可以看出 Cu 元素对有序的 B2 相有促进作用；在含有 Mn 元素的铸态 CrFeNiMn 0.5 Cu 0.5 高熵合金， Shim [15] 等人发现了其具有三种微观结构， BCC 的 FeCr 相，FCC 的富 FeCrNi 针状相以及更小的 FCC 的富 CuMnNi 针状相，三种结构的 析出相使得该合金有优异综合力学性能， 兼具抗拉强度和延展率 (1.02GPa/28%) ， 因此复杂的有序相和无序相的结合可以使得合金具有优异的综合力学性能。Al 稳定 BCC 结构，抑制 Cu 向枝晶间区的偏析，提高合金韧性 [15] 。因此，在高熵合 金体系中主要分为两种元素，FCC 相形成元素 Cu、Mn、Ni、Co 以及 BCC 相形 成元素 Al、Cr、W、V、Ti，因为 Co 元素较为昂贵，故本文参考抗腐蚀性能较 好的 FeCuMnNiCr [7] 高熵合金，利用过渡族团簇模型设计了有序无序共存的且性 价比高的 FeCuMnNiAl 高熵合金。 通过实验来揭示高熵合金微观组织演化规律已经是一种资源密集型方法，而 利用相场建模对高熵合金的微观结构的演变进行定量模拟可以显着降低实验负 担， 为合金设计提供可持续的框架 [16] 。 相场法可以用于模拟凝固过程的枝晶生长， 晶粒取向转变以及析出相的形貌演变，在处理多种类型的微观结构变化中已成为 一种强大的计算方法 [17][18][19][20][21][22][23][24][25][26][27] 。目前高熵合金的相场模型可以模拟位错运动、有序无 序转变、不同结构的相变路径以及晶格错配度调控析出相形貌 [28][29][30][31][32] ，Zeng 等人 [28] 利用相场位错动力学模型(Phase field dislocation dynamics PFDD)研究 FCC 基高 熵合金在 0℃下位错运动，推导出层错界面宽度对合金屈服强度的影响；Kadirvel 等人 [29] 利用相场法根据自由能变化设计了耐火高熵合金 AlMo 0.5 NbTa 0.5 TiZr 微观 组织相变路径(Phase transformation pathway PTP) ，结合不同参数分别模拟了有 序基体析出无序相和无序基体析出有序相两种不同的结果，为模拟不同有序无序 相奠定基础。 Zuo 等人 [30] 将 CALPHAD 数据库的热力学和动力学信息拟合成分相 关的吉布斯自由能密度数据开发了一种新的形式的相场模型，该方法成功模拟了 (Al)CrFeNi 中熵合金中 FCC 到 ...…”