Monte-Carlo simulation of mass density field coupled dynamics for microstructural evolution of Fe-Cr binary alloys

Shi Fang-Jie; Li Nan; Guo Jun-Ming; Chen Bai-Yi; Li Sa-Teng; Liu Hao-Liang; Guo Jian-Ye; Li Qian-Wu; Li Ye-Fei; Xiao Bing

doi:10.7498/aps.72.20230291

Abstract

The phase transformation kinetics and micro-structure evolutions of four different Fe-Cr binary alloys, i.e. Fe-Cr (12.8%), Fe-Cr (20.0%), Fe-Cr (30.0%) and Fe-Cr (40.0%) at 673 K, are investigated by using the kinetic Monte-Carlo simulation combined with spatial coarse-grained mass density field description. For all studied Fe-Cr alloys, it is found that the number density of Cr-rich precipitate undergoes a rather rapid increasing at the nucleation stage and then gradually decreases with the simulation time increasing in the coarsening stage during aging. Increasing the Cr concentration in Fe-Cr alloy can significantly reduce the duration of nucleation and the time interval between nucleation and coarsening. From the coarse-grained mass density field models of Cr-rich precipitates at different aging stages for the four Fe-Cr alloys, we discover that the Cr-rich phase shows the isolated spherical particle-like morphology for the aged Fe-Cr (12.8%) alloy, revealing the nucleation and growth (NG) mechanism. Meanwhile, the Cr-rich precipitates possess a characteristic three-dimensional interconnected microstructure, a signature of spinodal decomposition mechanism. Otherwise, the Cr-rich phase morphology in Fe-Cr (20.0%) exhibits the characteristics of both NG mechanism and SD mechanism. It is also found that the short-range order parameter of Cr atoms in Fe-Cr alloy is indeed very sensitive to the change of atomic structure at the early stage of aging or nucleation stage, which, however, is almost independent of the changing of morphology of Cr-precipitates in the later coarsening process. Finally, the phase transformation kinetics of Cr-rich precipitates during aging are analyzed by calculating the phase volume fraction, average diameter and number density, concluding that the Cr-rich phase growth kinetics in Fe-Cr (20.0%) alloy can be described by the well-known Lifshitz-Slyozov-Wagner law in the coarsening stage. However, the coarsening kinetics of Fe-Cr (12.8%), Fe-Cr (30.0%) and Fe-Cr (40.0%) alloys are not caused by the LSW mechanism.

Keywords:

Authors and contacts

1.
Suzhou Nuclear Power Research Institute, Suzhou 215004, China
2.
State Key Lab of Power Equipment and Insulation, School of Electrical Engineering, Xi’an Jiaotong University, Xi’an 710049, China
3.
State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an 710049, China

Corresponding author: Li Nan, ln906061119@stu.xjtu.edu.cn ; Li Ye-Fei, liyefei@xjtu.edu.cn ; Xiao Bing, bingxiao84@xjtu.edu.cn

Funds: Project supported by the National Key Research and Development Program of China (Grant No. 2020YFB1901500).

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References

[1]	Terentyev D A, Bonny G, Malerba L 2008 Acta Mater. 56 3229 Google Scholar
[2]	Zhou J, Odqvist J, Höglund L, Thuvander M, Barkar T, Hedström P 2014 Scr. Mater. 75 62 Google Scholar
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[5]	Yan Z, Li Y, Zhou X, Zhang Y, Hu R 2017 J. Alloys Compd. 725 1035 Google Scholar
[6]	Eich S M, Beinke D, Schmitz G 2015 Comput. Mater. Sci. 104 185 Google Scholar
[7]	Martínez E, Senninger O, Fu C, Soisson F 2012 Phys. Rev. B Condens. Matter Mater. Phys. 86 224109 Google Scholar
[8]	Pareige C, Roussel M, Novy S, Kuksenko V, Olsson P, Domain C, Pareige P 2011 Acta Mater. 59 2404 Google Scholar
[9]	Guo W, Garfinkel D A, Tucker J D, Haley D, Young G A, Poplawsky J D 2016 Nanotechnology 27 254004 Google Scholar
[10]	Xu X, Odqvist J, Colliander M H, Thuvander M, Steuwer A, Westraadt J E, King S, Hedstrom P 2016 Metall. Mater. Trans. A 47 5942 Google Scholar
[11]	Bonny G, Terentyev D, Malerba L 2008 Comput. Mater. Sci. 42 107 Google Scholar
[12]	Erhart P, Caro A, Serrano De Caro M, Sadigh B 2008 Phys. Rev. B Condens. Matter Mater. Phys. 77 134206 Google Scholar
[13]	Nguyen-Manh D, Lavrentiev M Y, Dudarev S L 2008 C. R. Phys. 9 379 Google Scholar
[14]	Zhou J, Odqvist J, Ruban A, Thuvander M, Xiong W, Ågren J, Olson G B, Hedström P 2017 J. Mater. Sci. 52 326 Google Scholar
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[16]	Olsson P, Wallenius J, Domain C, Nordlund K, Malerba L 2005 Phys. Rev. B Condens. Matter. 72 214119
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Cited By

图 1 673 K下kMC模拟1.28×10⁵个原子超晶胞计算得到的二元合金富Cr相平均粒径、不同粒径分布范围对应颗粒数密度, 以及总颗粒数密度随模拟总步长演变趋势曲线　(a) Fe-Cr (12.8%); (b) Fe-Cr (20.0%); (c) Fe-Cr (30.0%); (d) Fe-Cr (40.0%)

Figure 1. Predicted average diameter and number density of precipitates of Fe-Cr alloys obtained by kMC simulations using a supercell model containing 1.28×10⁵ atoms, and the total number of density precipitates versus the kMC duration: (a) Fe-Cr (12.8%); (b) Fe-Cr (20.0%); (c) Fe-Cr (30.0%); (a) Fe-Cr (40.0%).

DownLoad: Full-Size Img PowerPoint

图 2 673 K下Fe-Cr合金kMC模拟演化总步长为2×10¹⁰步时其微观组织形貌　(a) Fe-Cr (12.8%); (b) Fe-Cr (20.0%); (c) Fe-Cr (30.0%); (d) Fe-Cr (40.0%). 图中Fe和Cr原子分别用黄色及蓝色表示

Figure 2. Atomic structures are simulated by kMC in Fe-Cr alloys at 2×10¹⁰ steps at 673 K: (a) Fe-Cr (12.8%); (b) Fe-Cr (20.0%); (c) Fe-Cr (30.0%); (d) Fe-Cr (40.0%). Blue balls refer to Cr atoms and other yellow balls are Fe atoms.

DownLoad: Full-Size Img PowerPoint

图 3 质量密度场空间粗粒化参数C_th数值测试及其对Fe-Cr (12.8%)合金中富Cr相微观形貌分析结果的影响　(a), (b) kMC粒子模拟结果; (c), (d) C_th = 0.2C_max; (e), (f) C_th = 0.4C_max; (g), (h) C_th = 0.6C_max

Figure 3. Testing the effect of threshold C_th values for extracting the Cr-rich precipitates on the phase morphologies in Fe-Cr (12.8%) alloy using the spatial coarse-graining method: (a), (b) Atomic obtained from kMC simulation results; (c), (d) C_th = 0.2C_max; (e), (f) C_th = 0.4C_max; (g), (h) C_th = 0.6C_max.

DownLoad: Full-Size Img PowerPoint

图 4 临界C_th取值不同时, Fe-Cr (12.8%)合金粗粒化计算结果与kMC模拟结果的比较　(a)富Cr相总粒子数密度和平均粒径; (b)相体积分数

Figure 4. Comparison of Cr rich phase calculated from coarsening of Fe-Cr (12.8%) alloy with kMC simulation results at different critical C_th values: (a) Total particle density, average particle size; (b) phase volume fraction.

DownLoad: Full-Size Img PowerPoint

图 5 富Cr相在Fe-Cr (12.8%)合金中kMC模拟1.28×10⁵个原子晶胞　(a)—(d)不同时效阶段原子尺度晶体结构; (e)—(h)对应质量密度场空间粗粒化形貌分析三维空间分布图; (i)—(l)典型二维截面图

Figure 5. Cr-rich phase is simulated by kMC in Fe-Cr (12.8%) alloy with 1.28×10⁵ atoms: (a)–(d) Atomic structures obtained from kMC at different kMC steps; (e)–(h) 3D phase morphologies of Cr-rich precipitates in ferrite matrix; (i)–(l) phase morphologies illustrated on 2D slices.

DownLoad: Full-Size Img PowerPoint

图 6 富Cr相在Fe-Cr (20.0%)合金中kMC模拟1.28×10⁵个原子晶胞　(a)—(d)在不同时效阶段原子尺度晶体结构; (e)—(h)对应质量密度场空间粗粒化形貌分析三维空间分布图; (i)—(l)典型二维截面图

Figure 6. Cr-rich phase is simulated by kMC in Fe-Cr (20.0%) alloy with 1.28×10⁵ atoms: (a)–(d) Atomic structures obtained from kMC at different kMC steps; (e)–(h) 3D phase morphologies of Cr-rich precipitates in ferrite matrix; (i)–(l) phase morphologies illustrated on 2D slices.

DownLoad: Full-Size Img PowerPoint

图 7 富Cr相在Fe-Cr (20.0%)合金中kMC模拟1.28×10⁵个原子晶胞　(a)—(d) 在不同时效阶段原子尺度晶体结构; (e)—(h) 对应质量密度场空间粗粒化形貌分析三维空间分布图; (i)—(l)典型二维截面图

Figure 7. Cr-rich phase is simulated by kMC in Fe-Cr (20.0%) alloy with 1.28×10⁵ atoms: (a)–(d) Atomic structures obtained from kMC at different kMC steps; (e)–(h) 3D phase morphologies of Cr-rich precipitates in ferrite matrix; (i)–(l) phase morphologies illustrated on 2D slices.

DownLoad: Full-Size Img PowerPoint

图 8 富Cr相在Fe-Cr (40.0%)合金中kMC模拟1.28×10⁵个原子晶胞　(a)—(d)不同时效阶段原子尺度晶体结构; (e)—(h) 质量密度场空间粗粒化形貌分析三维空间分布图; (i)—(l)典型二维截面图

Figure 8. Cr-rich phase is simulated by kMC in Fe-Cr (40.0%) alloy with 1.28×10⁵ atoms: (a)–(d) Atomic structures obtained from kMC at different kMC steps; (e)–(h) 3D phase morphologies of Cr-rich precipitates in ferrite matrix; (i)–(l) phase morphologies illustrated on 2D slices.

DownLoad: Full-Size Img PowerPoint

图 9 4种Fe-Cr二元合金原子SRO与富Cr相粒子数密度随着kMC模拟总步长增加的变化

Figure 9. Variations of SRO and Cr-rich precipitates versus total number of kMC steps for four different Fe-Cr binary alloys.

DownLoad: Full-Size Img PowerPoint

图 10 基于质量密度场空间粗粒化模型计算的Fe-Cr合金Cr原子含量空间分布ACF在kMC不同时效阶段曲线　(a) Fe-Cr (12.8%); (b) Fe-Cr (20.0%); (c) Fe-Cr (30.0%); (d) Fe-Cr (40.0%)

Figure 10. Obtained Cr atomic concentration ACF profiles at different aging stages in kMC simulations for four Fe-Cr alloys: (a) Fe-Cr (12.8%); (b) Fe-Cr (20.0%); (c) Fe-Cr (30.0%); (d) Fe-Cr (40.0%).

DownLoad: Full-Size Img PowerPoint

图 11 基于空间粗粒化模型分析Fe-Cr合金时效富Cr相形成动力学参数随kMC总步长及时效时间变化曲线　(a)富Cr相体积分数; (b)平均粒径; (c)富Cr相颗粒数密度

Figure 11. Variations of phase transformation kinetic parameters versus the total kMC simulation steps and physical aging time for the formation of Cr-rich precipitates in four different Fe-Cr binary alloys based on spatial coarse-grained mass density field description: (a) Volume fraction of Cr-rich phase; (b) average diameter of precipitates; (c) number of density of Cr-rich precipitates.

DownLoad: Full-Size Img PowerPoint

[1]	Terentyev D A, Bonny G, Malerba L 2008 Acta Mater. 56 3229 Google Scholar
[2]	Zhou J, Odqvist J, Höglund L, Thuvander M, Barkar T, Hedström P 2014 Scr. Mater. 75 62 Google Scholar
[3]	史佳庆, 薛飞, 彭群家, 沈耀 2020 材料研究学报 34 328 Google Scholar Shi J Q, Xue F, Peng Q J, Shen Y 2020 Chin. J. Mater. Res. 34 328 Google Scholar
[4]	Xu X, Westraadt J E, Odqvist J, Youngs T G A, King S M, Hedström P 2018 Acta Mater. 145 347 Google Scholar
[5]	Yan Z, Li Y, Zhou X, Zhang Y, Hu R 2017 J. Alloys Compd. 725 1035 Google Scholar
[6]	Eich S M, Beinke D, Schmitz G 2015 Comput. Mater. Sci. 104 185 Google Scholar
[7]	Martínez E, Senninger O, Fu C, Soisson F 2012 Phys. Rev. B Condens. Matter Mater. Phys. 86 224109 Google Scholar
[8]	Pareige C, Roussel M, Novy S, Kuksenko V, Olsson P, Domain C, Pareige P 2011 Acta Mater. 59 2404 Google Scholar
[9]	Guo W, Garfinkel D A, Tucker J D, Haley D, Young G A, Poplawsky J D 2016 Nanotechnology 27 254004 Google Scholar
[10]	Xu X, Odqvist J, Colliander M H, Thuvander M, Steuwer A, Westraadt J E, King S, Hedstrom P 2016 Metall. Mater. Trans. A 47 5942 Google Scholar
[11]	Bonny G, Terentyev D, Malerba L 2008 Comput. Mater. Sci. 42 107 Google Scholar
[12]	Erhart P, Caro A, Serrano De Caro M, Sadigh B 2008 Phys. Rev. B Condens. Matter Mater. Phys. 77 134206 Google Scholar
[13]	Nguyen-Manh D, Lavrentiev M Y, Dudarev S L 2008 C. R. Phys. 9 379 Google Scholar
[14]	Zhou J, Odqvist J, Ruban A, Thuvander M, Xiong W, Ågren J, Olson G B, Hedström P 2017 J. Mater. Sci. 52 326 Google Scholar
[15]	Mukherjee D, Forslund A, Höglund L, Ruban A, Larsson H, Odqvist J 2022 Comput. Mater. Sci. 202 110955 Google Scholar
[16]	Olsson P, Wallenius J, Domain C, Nordlund K, Malerba L 2005 Phys. Rev. B Condens. Matter. 72 214119
[17]	Ackland G J, Mendelev M I, Srolovitz D J, Han S, Barashev A V 2004 J. Phys. Condens. Matter. 16 S2629 Google Scholar
[18]	Vineyard G H 1957 J. Phys. Chem. Solids 3 121 Google Scholar
[19]	Willard A P, Chandler D 2010 J. Phys. Chem. B 114 1954 Google Scholar
[20]	Mathon M H, de Carlan Y, Geoffroy G, Averty X, Alamo A, de Novion C H 2003 J. Nucl. Mater. 312 236 Google Scholar
[21]	Miller M K, Hyde J M, Hetherington M G, Cerezo A, Smith G D W, Elliott C M 1995 Acta Metall. Mater. 43 3385 Google Scholar
[22]	Huse D A 1986 Phys. Rev. B 34 7845
[23]	Lifshitz I M, Slyozov V V 1961 J. Phys. Chem. Solids 19 35 Google Scholar
[24]	Wagner C 1961 Elektro. Chem. 65 581
[25]	Lebowitz J L, Marro J, Kalos M H 1982 Acta Metall. Mater. 30 297 Google Scholar
[26]	Novy S, Pareige P, Pareige C 2009 J. Nucl. Mater. 384 96 Google Scholar

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