Mechanism of internal magnetic energy of Cu-rich phase precipitation in Fe84Cu15Mn1 alloy by phase field method

Jiang Xin-An; Zhao Yu-Hong; Yang Wen-Kui; Tian Xiao-Lin; Hou Hua

doi:10.7498/aps.71.20212087

Abstract

Based on the continuous phase field model, the precipitation behavior of Cu rich phase in Fe-Cu-Mn alloy under the action of internal magnetic energy is studied. The effects of internal magnetic energy on the average particle radius, volume fraction and Gibbs free energy of Cu rich phase at different temperatures and different Mn content and Cu content are investigated. The simulation results show that the lower the Mn content and the higher the Curie temperature, the greater the contribution of internal magnetic energy to free energy is, and the contribution of internal magnetic energy decreases with temperature increasing. The internal magnetic energy reduces the phase structure transition barrier and promotes the phase structure transition. The volume fraction of precipitated phase increases with Cu content increasing. Compared with the effect of internal magnetic energy on the volume fraction of precipitated phase, the effect of internal magnetic energy leads to a large volume fraction of precipitated phase. Therefore, under the action of internal magnetic energy, the Cu rich phase has larger average particle size, volume fraction and smaller coercivity. Finally, the change trend of alloy hardness is predicted.

Keywords:

Authors and contacts

School of Materials Science and Engineering, North University of China, Taiyuan 030051, China

Corresponding author: Zhao Yu-Hong, zhaoyuhong@nuc.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 52074246) and the Shanxi Graduate Innovation Project, China (Grant No. 2021Y592).

FullText HTML : translate this paragraph

References

[1]	Que Z, Heczko M, Kuběna I, Seifert H P, Spaetig P 2020 Mater. Charact. 165 110405 Google Scholar
[2]	Deschamps A, Militzer M, Poole W 2001 ISIJ. INT. 41 196 Google Scholar
[3]	Bousquet A, Marie S, Bompard P 2012 Comp. Mater. Sci. 64 17 Google Scholar
[4]	林民东, 朱娟娟, 王伟, 周邦新, 刘文庆, 徐刚 2010 物理学报 59 1163 Google Scholar Ling M D, Zhu J J, Wang W, Zhou B X, Liu W Q, Xu G, 2010 Acta Phys. Sin. 59 1163 Google Scholar
[5]	Miodownik A 1982 J. Phase. Equil. 2 406 Google Scholar
[6]	Zhao Y, Zhang B, Hou H, Chen W, Wang M 2018 J. Mater. Sci. Technol. 35 1044 Google Scholar
[7]	祁科武, 赵宇宏, 田晓林, 彭敦维, 孙远洋, 侯华 2020 物理学报 69 140504 Google Scholar Qi K W, ZhaoY H, Tian X L, Peng D W, Sun Y Y, Hou H 2020 Acta Phys. Sin. 69 140504 Google Scholar
[8]	Cui S, Mamivand M, Morgan D 2020 Mater. Des. 191 108574 Google Scholar
[9]	Sun Y Y, Zhao Y H, Zhao B J, Yang W K, Tian X L, H Hua 2019 J. Mater. Sci. 54 11263 Google Scholar
[10]	Gorbatov O, Razumov I, Gornostyrev Y, Razumovskiy V I, Korzhavyi P, Ruban A 2013 Phys. Rev. B 88 174113 Google Scholar
[11]	Korzhavyi P A, Ruban A V, Gorbatov O I, Gornostyrev 2015 Scr. Mater. 102 11 Google Scholar
[12]	Inden G 1981 Physica B+C 103 82 Google Scholar
[13]	Koyama T 2008 Sci. Technol. Adv. Mat. 9 013006 Google Scholar
[14]	Xin T, Zhao Y, Mahjoub R, Jiang J, Yadav A, Nomoto K, Niu R, Tang S, Ji F, Quadir M, Miskovic D, Daniels J, Xu W, Liao X, Chen L Q, Hagihara K, Li X, Ringer S, Ferry M 2021 Sci. Adv. 7 3039 Google Scholar
[15]	Chen L Q, Zhao Y 2022 Prog. Mater. Sci. 124 100868 Google Scholar
[16]	Chen W, Zhao Y, Yang S, Zhang D, Hou H 2021 Adv. Compos. Hybrid Mater. 4 371 Google Scholar
[17]	Zhu N Y, Sun C, Li Y L, Lingyun Q, Hu S, Cai Y, Feng Y H 2021 Comput. Mater. Sci. 200 110858 Google Scholar
[18]	赵宇宏, 景舰辉, 陈利文, 徐芳泓, 侯华 2021 金属学报 57 19 Google Scholar Zhao Y H, Jing J H, Chen L W, Xu F H, Hou H 2021 Acta Metall. Sin. 57 19 Google Scholar
[19]	Zhang J, Wang H, Kuang W, Zhang Y, Li S, Zhao Y, Herlach D M 2018 Acta Mater. 148 86 Google Scholar
[20]	Kuang W, Wang H, Li X, Zhang J, Zhou Q, Zhao Y 2018 Acta Mater. 159 16 Google Scholar
[21]	Wang X, Qiang W 2016 J. Nucl. Mater. 482 135 Google Scholar
[22]	Cahn J, Hilliard J 1958 J. Chem. Phys. 28 258 Google Scholar
[23]	Allen S, Cahn J W 1992 Acta Metall. 20 423 Google Scholar
[24]	Kitashima T, Harada H 2009 Acta Mater. 57 2020 Google Scholar
[25]	Tsukada Y, Koyama T, Murata Y, Miura N, Kondo Y 2014 Comput. Mater. Sci. 83 371 Google Scholar
[26]	Segawa M, Yamanaka A, Nomoto S 2017 Comput. Mater. Sci. 136 67 Google Scholar
[27]	Wrobel J S, Nguyen-Manh D, Lavrentiev M Y, Muzyk M, Dudarev S L 2015 Phys. Rev. B 91 024108 Google Scholar
[28]	Liu D, Zhang L, Du Y, Jin Z 2015 J. Alloys. Compd. 634 148 Google Scholar
[29]	Deng S, Chen W, Zhong J, Zhang L, Du Y, Chen L 2017 Calphad 56 230 Google Scholar
[30]	Biner B, Rao W, Zhang Y 2016 J. Nucl. Mater. 468 9 Google Scholar
[31]	Hu Y, Wang G, Ji Y, Wang L, Rong Y, Chen L Q 2019 Mat. Sci. Eng. A-Struct. 746 105 Google Scholar
[32]	杨一波, 赵宇宏, 田晓林, 侯华 2020 物理学报 69 140201 Google Scholar Yang Y B, Zhao Y H, Tian X L, Hou H 2020 Acta Phys. Sin. 69 140201 Google Scholar
[33]	Koyama T, Onodera H 2004 Met. Mater. Int. 10 321 Google Scholar
[34]	Koyama T, Onodera H 2005 Mater. Trans. 46 1187 Google Scholar
[35]	Koyama T 2005 Defect. Diffus. Forum. 593 237 Google Scholar
[36]	Saunders N, Miodownik A 1992 Pergamon
[37]	Dinsdale A T 1991 Calphad 15 317 Google Scholar
[38]	Liu K, Hu L J, Zhang Q F, Xie Y P, Gao C, Dong H Y, Liang W Y 2017 Chin. Phys. B 26 83601 Google Scholar
[39]	赵宝军, 赵宇宏, 孙远洋, 杨文奎, 侯华 2019 金属学报 55 8 Google Scholar Zhao B J, Zhao Y H, Sun Y Y, Yang W K, Hou H 2019 Acta Metall. Sin. 55 8 Google Scholar
[40]	Tian X L, Zhao Y H, Peng D W, Guo Q W, Guo Z, Hou H 2021 T. Nonferr. Metal. Soc. 31 1175 Google Scholar
[41]	Xiong S, Qi W, Huang B, Yang W, Li Y J 2010 Mater. Chem. Phys. 120 446 Google Scholar
[42]	Zhu J, Tianlong Z, Yang Y, Liu C T 2019 Acta Mater. 166 560 Google Scholar
[43]	Waseda A, Kimura K, Ino H 1994 Mat. Sci. Eng. A-struct. 181 762 Google Scholar
[44]	Wang L, Darvishi Kamachali R 2021 Acta Mater. 207 116668 Google Scholar
[45]	Sun Y, Zhao Y, Zhao B, Guo Z, Tian X, Yang W, Hou H 2020 Calphad 69 101759 Google Scholar
[46]	Gorbatov O, Okatov S, Gornostyrev Y, Korzhavyi P, Ruban A 2013 Phys. Met. Metallogr+. 114 642 Google Scholar
[47]	Deschamps A, Militzer M, Poole W 2003 ISIJ. INT. 43 1826 Google Scholar
[48]	Osamura K, Okuda H, Shojiro O, Takashima M, Asano K, Furusaka M, Kishida K, Kurosawa F 1994 ISIJ. INT. 34 359 Google Scholar
[49]	Guo H, Enomoto M, Shang C J 2018 Comp. Mater. Sci. 141 101 Google Scholar
[50]	Shu S, Wells P B, Almirall N, Odette G R, Morgan D D 2018 Acta Mater. 157 298 Google Scholar
[51]	田晓林, 赵宇宏, 田晋忠, 侯华 2018 物理学报 67 230201 Google Scholar Tian X L, Zhao Y H, Tian J Z, Hou H 2018 Acta Phys. Sin. 67 230201 Google Scholar
[52]	Shu S, Wirth B, Wells P, Morgan D, Odette G R 2018 Acta Mater. 146 237 Google Scholar
[53]	Isheim D, Gagliano M, Fine M, Seidman D 2006 Acta Mater. 54 841 Google Scholar
[54]	Xie Y P, Zhao S J 2012 Comp. Mater. Sci. 63 329 Google Scholar
[55]	Zheng Z, Lei L, Zhou Q, Wang W H, Zeng D C, Qiu Z, Hong Y 2019 J. Magn. Magn. Mater. 484 105 Google Scholar
[56]	Xie Y P, Zhao S J 2011 Comp. Mater. Sci. 50 2586 Google Scholar
[57]	Ngayam-Happy R, Becquart C S, Domain C, Malerba L 2012 J. Nucl. Mater. 426 198 Google Scholar
[58]	Vincent E, Becquart C S, Domain C 2006 J. Nucl. Mater. 359 227 Google Scholar
[59]	Wang X, Qiang W, Shu G, Qiao J, Wu Y 2021 J. Magn. Magn. Mater. 527 167698 Google Scholar
[60]	Vandenbossche L P, Konstantinović M J, Almazouzi A, Dupré L R 2007 J. Phys. D 40 4114 Google Scholar
[61]	Kamada Y, Park D G, Takahashi S, Kikuchi H, Kobayashi S, Ara K, Hong J H, Park I G 2007 IEEE. T. Magn. 43 2701 Google Scholar
[62]	Lo C 2012 AIP Conf. Proc. 1430 1351 Google Scholar
[63]	Takahashi S, Kubota A, Kobayashi S, Kamada Y, Kikuchi H, Ara K 2007 J. Mater. Process. Technol. 181 199 Google Scholar
[64]	高阳 2008 先进材料测试仪器基础教程(上册) (北京: 清华大学出版社) Gao Y 2008 The Fundamental of Advanced Measuring Instruments for Materials (Vol. 1) (Beijing: Tsinghua University Press) (in Chinese)
[65]	Cui S, Jung I H 2017 Calphad 56 241 Google Scholar
[66]	Miettinen J 2001 Calphad 25 43 Google Scholar

Cited By

图 1 不同温度下GFE随Cu浓度变化情况　(a) 不考虑IME作用; (b) 考虑IME作用

Figure 1. Gibbs free energy versus Cu concentration at different temperatures: (a) The effect of internal magnetic energy is not considered; (b) the effect of internal magnetic energy is considered.

DownLoad: Full-Size Img PowerPoint

图 2 (a)—(e) 823 K时无IME作用下的演化过程　(a) $ {t}^{\mathrm{*}} $= 7500, (b) $ {t}^{\mathrm{*}} $= 8500, (c) $ {t}^{\mathrm{*}} $= 9000, (d) $ {t}^{\mathrm{*}} $= 9500, (e) $ {t}^{\mathrm{*}} $= 11000; (f)—(j) 有IME作用下的演化过程 (f) $ {t}^{\mathrm{*}} $= 7500, (g) $ {t}^{\mathrm{*}} $= 8500, (h) $ {t}^{\mathrm{*}} $= 9000, (i) $ {t}^{\mathrm{*}} $= 9500, (j) $ {t}^{\mathrm{*}} $= 11000; (k) 有IME与无IME作用下的平均颗粒半径变化

Figure 2. (a)–(e) The evolution process without internal magnetism at 823 K: (a) $ {t}^{\mathrm{*}} $= 7500, (b) $ {t}^{\mathrm{*}} $= 8500, (c) $ {t}^{\mathrm{*}} $= 9000, (d) $ {t}^{\mathrm{*}} $= 9500, (e) $ {t}^{\mathrm{*}} $= 11000; (f)–(j) the evolution process with internal magnetism: (f) $ {t}^{\mathrm{*}} $= 7500, (g) $ {t}^{\mathrm{*}} $= 8500, (h) $ {t}^{\mathrm{*}} $= 9000, (i) $ {t}^{\mathrm{*}} $= 9500, (j) $ {t}^{\mathrm{*}} $= 11000; (k) the change of average particle radius with and without internal magnetism.

DownLoad: Full-Size Img PowerPoint

图 3 温度为823 K时IME作用下Mn与Cu沉淀析出的成分曲线(原子含量)　(a) 早期(t^* = 2500)时Cu与Mn的成分曲线; (b) 不同时间步数Cu的成分曲线; (c) 不同时间步数Mn的成分曲线; (d) Mn环在不同时间步数的演化过程

Figure 3. The composition curve of precipitation of Mn and Cu under the action of magnetic energy in 823 K (atomic percent): (a) The composition curve of Cu and Mn in early (t^* = 2500); (b) composition curve of Cu with different time steps; (c) composition curve with different time step size of Mn; (d) evolution process of Mn ring with different time steps.

DownLoad: Full-Size Img PowerPoint

图 4 Cu原子和Mn原子相互作用和局部元素分布示意图　(a)—(c) Cu, Mn原子相互作用示意图; (d) Fe, Cu, Mn局部元素分布示意图

Figure 4. Schematic diagram of Cu atom and Mn atom interaction and local element distribution: (a)–(c) Schematic diagrams of Cu and Mn atom interaction; (d) schematic diagram of local element distribution of Fe, Cu and Mn.

DownLoad: Full-Size Img PowerPoint

图 5 温度为823 K　(a) Mn含量与居里温度的关系; (b) 温度与IME的关系; (c) 不同Mn含量下吉布斯自由能

Figure 5. At 823 K (a) Relationship between Mn content and Curie temperature; (b) relationship between temperature and internal magnetic energy; (c) Gibbs free energy with different Mn content.

DownLoad: Full-Size Img PowerPoint

图 6 在有无IME作用下体积分数随Cu含量的变化

Figure 6. Variation of volume fraction with Cu content with or without internal magnetic energy.

DownLoad: Full-Size Img PowerPoint

图 7 矫顽力($ {H}_{\mathrm{c}} $)与颗粒半径以及硬度的关系示意图　(a) $ {H}_{\mathrm{c}} $与平均颗粒半径的关系示意图; (b) $ {H}_{\mathrm{c}} $与硬度关系示意图

Figure 7. The relationship between coercivity ($ {H}_{\mathrm{c}} $) and particle radius and hardness: (a) Schematic diagram of relationship between $ {H}_{\mathrm{c}} $ and average particle radius; (b) schematic diagram of relationship between $ {H}_{\mathrm{c}} $ and hardness.

DownLoad: Full-Size Img PowerPoint

[1]	Que Z, Heczko M, Kuběna I, Seifert H P, Spaetig P 2020 Mater. Charact. 165 110405 Google Scholar
[2]	Deschamps A, Militzer M, Poole W 2001 ISIJ. INT. 41 196 Google Scholar
[3]	Bousquet A, Marie S, Bompard P 2012 Comp. Mater. Sci. 64 17 Google Scholar
[4]	林民东, 朱娟娟, 王伟, 周邦新, 刘文庆, 徐刚 2010 物理学报 59 1163 Google Scholar Ling M D, Zhu J J, Wang W, Zhou B X, Liu W Q, Xu G, 2010 Acta Phys. Sin. 59 1163 Google Scholar
[5]	Miodownik A 1982 J. Phase. Equil. 2 406 Google Scholar
[6]	Zhao Y, Zhang B, Hou H, Chen W, Wang M 2018 J. Mater. Sci. Technol. 35 1044 Google Scholar
[7]	祁科武, 赵宇宏, 田晓林, 彭敦维, 孙远洋, 侯华 2020 物理学报 69 140504 Google Scholar Qi K W, ZhaoY H, Tian X L, Peng D W, Sun Y Y, Hou H 2020 Acta Phys. Sin. 69 140504 Google Scholar
[8]	Cui S, Mamivand M, Morgan D 2020 Mater. Des. 191 108574 Google Scholar
[9]	Sun Y Y, Zhao Y H, Zhao B J, Yang W K, Tian X L, H Hua 2019 J. Mater. Sci. 54 11263 Google Scholar
[10]	Gorbatov O, Razumov I, Gornostyrev Y, Razumovskiy V I, Korzhavyi P, Ruban A 2013 Phys. Rev. B 88 174113 Google Scholar
[11]	Korzhavyi P A, Ruban A V, Gorbatov O I, Gornostyrev 2015 Scr. Mater. 102 11 Google Scholar
[12]	Inden G 1981 Physica B+C 103 82 Google Scholar
[13]	Koyama T 2008 Sci. Technol. Adv. Mat. 9 013006 Google Scholar
[14]	Xin T, Zhao Y, Mahjoub R, Jiang J, Yadav A, Nomoto K, Niu R, Tang S, Ji F, Quadir M, Miskovic D, Daniels J, Xu W, Liao X, Chen L Q, Hagihara K, Li X, Ringer S, Ferry M 2021 Sci. Adv. 7 3039 Google Scholar
[15]	Chen L Q, Zhao Y 2022 Prog. Mater. Sci. 124 100868 Google Scholar
[16]	Chen W, Zhao Y, Yang S, Zhang D, Hou H 2021 Adv. Compos. Hybrid Mater. 4 371 Google Scholar
[17]	Zhu N Y, Sun C, Li Y L, Lingyun Q, Hu S, Cai Y, Feng Y H 2021 Comput. Mater. Sci. 200 110858 Google Scholar
[18]	赵宇宏, 景舰辉, 陈利文, 徐芳泓, 侯华 2021 金属学报 57 19 Google Scholar Zhao Y H, Jing J H, Chen L W, Xu F H, Hou H 2021 Acta Metall. Sin. 57 19 Google Scholar
[19]	Zhang J, Wang H, Kuang W, Zhang Y, Li S, Zhao Y, Herlach D M 2018 Acta Mater. 148 86 Google Scholar
[20]	Kuang W, Wang H, Li X, Zhang J, Zhou Q, Zhao Y 2018 Acta Mater. 159 16 Google Scholar
[21]	Wang X, Qiang W 2016 J. Nucl. Mater. 482 135 Google Scholar
[22]	Cahn J, Hilliard J 1958 J. Chem. Phys. 28 258 Google Scholar
[23]	Allen S, Cahn J W 1992 Acta Metall. 20 423 Google Scholar
[24]	Kitashima T, Harada H 2009 Acta Mater. 57 2020 Google Scholar
[25]	Tsukada Y, Koyama T, Murata Y, Miura N, Kondo Y 2014 Comput. Mater. Sci. 83 371 Google Scholar
[26]	Segawa M, Yamanaka A, Nomoto S 2017 Comput. Mater. Sci. 136 67 Google Scholar
[27]	Wrobel J S, Nguyen-Manh D, Lavrentiev M Y, Muzyk M, Dudarev S L 2015 Phys. Rev. B 91 024108 Google Scholar
[28]	Liu D, Zhang L, Du Y, Jin Z 2015 J. Alloys. Compd. 634 148 Google Scholar
[29]	Deng S, Chen W, Zhong J, Zhang L, Du Y, Chen L 2017 Calphad 56 230 Google Scholar
[30]	Biner B, Rao W, Zhang Y 2016 J. Nucl. Mater. 468 9 Google Scholar
[31]	Hu Y, Wang G, Ji Y, Wang L, Rong Y, Chen L Q 2019 Mat. Sci. Eng. A-Struct. 746 105 Google Scholar
[32]	杨一波, 赵宇宏, 田晓林, 侯华 2020 物理学报 69 140201 Google Scholar Yang Y B, Zhao Y H, Tian X L, Hou H 2020 Acta Phys. Sin. 69 140201 Google Scholar
[33]	Koyama T, Onodera H 2004 Met. Mater. Int. 10 321 Google Scholar
[34]	Koyama T, Onodera H 2005 Mater. Trans. 46 1187 Google Scholar
[35]	Koyama T 2005 Defect. Diffus. Forum. 593 237 Google Scholar
[36]	Saunders N, Miodownik A 1992 Pergamon
[37]	Dinsdale A T 1991 Calphad 15 317 Google Scholar
[38]	Liu K, Hu L J, Zhang Q F, Xie Y P, Gao C, Dong H Y, Liang W Y 2017 Chin. Phys. B 26 83601 Google Scholar
[39]	赵宝军, 赵宇宏, 孙远洋, 杨文奎, 侯华 2019 金属学报 55 8 Google Scholar Zhao B J, Zhao Y H, Sun Y Y, Yang W K, Hou H 2019 Acta Metall. Sin. 55 8 Google Scholar
[40]	Tian X L, Zhao Y H, Peng D W, Guo Q W, Guo Z, Hou H 2021 T. Nonferr. Metal. Soc. 31 1175 Google Scholar
[41]	Xiong S, Qi W, Huang B, Yang W, Li Y J 2010 Mater. Chem. Phys. 120 446 Google Scholar
[42]	Zhu J, Tianlong Z, Yang Y, Liu C T 2019 Acta Mater. 166 560 Google Scholar
[43]	Waseda A, Kimura K, Ino H 1994 Mat. Sci. Eng. A-struct. 181 762 Google Scholar
[44]	Wang L, Darvishi Kamachali R 2021 Acta Mater. 207 116668 Google Scholar
[45]	Sun Y, Zhao Y, Zhao B, Guo Z, Tian X, Yang W, Hou H 2020 Calphad 69 101759 Google Scholar
[46]	Gorbatov O, Okatov S, Gornostyrev Y, Korzhavyi P, Ruban A 2013 Phys. Met. Metallogr+. 114 642 Google Scholar
[47]	Deschamps A, Militzer M, Poole W 2003 ISIJ. INT. 43 1826 Google Scholar
[48]	Osamura K, Okuda H, Shojiro O, Takashima M, Asano K, Furusaka M, Kishida K, Kurosawa F 1994 ISIJ. INT. 34 359 Google Scholar
[49]	Guo H, Enomoto M, Shang C J 2018 Comp. Mater. Sci. 141 101 Google Scholar
[50]	Shu S, Wells P B, Almirall N, Odette G R, Morgan D D 2018 Acta Mater. 157 298 Google Scholar
[51]	田晓林, 赵宇宏, 田晋忠, 侯华 2018 物理学报 67 230201 Google Scholar Tian X L, Zhao Y H, Tian J Z, Hou H 2018 Acta Phys. Sin. 67 230201 Google Scholar
[52]	Shu S, Wirth B, Wells P, Morgan D, Odette G R 2018 Acta Mater. 146 237 Google Scholar
[53]	Isheim D, Gagliano M, Fine M, Seidman D 2006 Acta Mater. 54 841 Google Scholar
[54]	Xie Y P, Zhao S J 2012 Comp. Mater. Sci. 63 329 Google Scholar
[55]	Zheng Z, Lei L, Zhou Q, Wang W H, Zeng D C, Qiu Z, Hong Y 2019 J. Magn. Magn. Mater. 484 105 Google Scholar
[56]	Xie Y P, Zhao S J 2011 Comp. Mater. Sci. 50 2586 Google Scholar
[57]	Ngayam-Happy R, Becquart C S, Domain C, Malerba L 2012 J. Nucl. Mater. 426 198 Google Scholar
[58]	Vincent E, Becquart C S, Domain C 2006 J. Nucl. Mater. 359 227 Google Scholar
[59]	Wang X, Qiang W, Shu G, Qiao J, Wu Y 2021 J. Magn. Magn. Mater. 527 167698 Google Scholar
[60]	Vandenbossche L P, Konstantinović M J, Almazouzi A, Dupré L R 2007 J. Phys. D 40 4114 Google Scholar
[61]	Kamada Y, Park D G, Takahashi S, Kikuchi H, Kobayashi S, Ara K, Hong J H, Park I G 2007 IEEE. T. Magn. 43 2701 Google Scholar
[62]	Lo C 2012 AIP Conf. Proc. 1430 1351 Google Scholar
[63]	Takahashi S, Kubota A, Kobayashi S, Kamada Y, Kikuchi H, Ara K 2007 J. Mater. Process. Technol. 181 199 Google Scholar
[64]	高阳 2008 先进材料测试仪器基础教程(上册) (北京: 清华大学出版社) Gao Y 2008 The Fundamental of Advanced Measuring Instruments for Materials (Vol. 1) (Beijing: Tsinghua University Press) (in Chinese)
[65]	Cui S, Jung I H 2017 Calphad 56 241 Google Scholar
[66]	Miettinen J 2001 Calphad 25 43 Google Scholar

[1]	Liu Zhong-Lei, Cao Jin-Ming, Wang Zhi, Zhao Yu-Hong. Phase-field method explored ferroelectric vortex topology structure and morphotropic phase boundaries. Acta Physica Sinica, 2023, 72(3): 037702. doi: 10.7498/aps.72.20221898
[2]	Wang Kai-Le, Yang Wen-Kui, Shi Xin-Cheng, Hou Hua, Zhao Yu-Hong. Phase-field-method-studied mechanism of Cu-rich phase precipitation in Al_xCuMnNiFe high-entropy alloy. Acta Physica Sinica, 2023, 72(7): 076102. doi: 10.7498/aps.72.20222439
[3]	Guo Can, Kang Chen-Rui, Gao Ying, Zhang Yi-Chi, Deng Ying-Yuan, Ma Chao, Xu Chun-Jie, Liang Shu-Hua. A phase-field model for in-situ reaction process of metal-matrix composite materials. Acta Physica Sinica, 2022, 71(9): 096401. doi: 10.7498/aps.71.20211737
[4]	Yang Hui, Feng Ze-Hua, Wang He-Ran, Zhang Yun-Peng, Chen Zheng, Xin Tian-Yuan, Song Xiao-Rong, Wu Lu, Zhang Jing. Phase-field modeling of irradiated void microstructure evolution of Fe-Cr alloy. Acta Physica Sinica, 2021, 70(5): 054601. doi: 10.7498/aps.70.20201457
[5]	Guo Zhen, Zhao Yu-Hong, Sun Yuan-Yang, Zhao Bao-Jun, Tian Xiao-Lin, Hou Hua. Phase field study of effect of Al on Cu-rich precipitates in Fe-Cu-Mn-Al alloys. Acta Physica Sinica, 2021, 70(8): 086401. doi: 10.7498/aps.70.20201843
[6]	Wang Tao, Li Jun-Jie, Wang Jin-Cheng. Phase field modeling of the influence of interfacial wettability and solid volume fraction on the kinetics of coarsening. Acta Physica Sinica, 2013, 62(10): 106402. doi: 10.7498/aps.62.106402
[7]	Wang Ya-Qin, Wang Jin-Cheng, Li Jun-Jie. Phase field modeling of the growth and competition behavior of tilted dendrites in directional solidification. Acta Physica Sinica, 2012, 61(11): 118103. doi: 10.7498/aps.61.118103
[8]	Zhang Xian-Gang, Zong Ya-Ping, Wu Yan. A model for releasing of stored energy and microstructure evolution during recrystallization by phase-field simulation. Acta Physica Sinica, 2012, 61(8): 088104. doi: 10.7498/aps.61.088104
[9]	Wang Ming-Guang, Zhao Yu-Hong, Ren Juan-Na, Mu Yan-Qing, Wang Wei, Yang Wei-Ming, Li Ai-Hong, Ge Hong-Hao, Hou Hua. Phase-field simulation of Non-Isothermal dendritic growth of NiCu alloy. Acta Physica Sinica, 2011, 60(4): 040507. doi: 10.7498/aps.60.040507
[10]	Long Wen-Yuan, Lü Dong-Lan, Xia Chun, Pan Mei-Man, Cai Qi-Zhou, Chen Li-Liang. Phase-field simulation of non-isothermal solidification dendrite growth of binary alloy under the force flow. Acta Physica Sinica, 2009, 58(11): 7802-7808. doi: 10.7498/aps.58.7802
[11]	Zong Ya-Ping, Wang Ming-Tao, Guo Wei. Phase field simulation on recrystallization and secondary phase precipitation under strain field. Acta Physica Sinica, 2009, 58(13): 161-S168. doi: 10.7498/aps.58.161
[12]	Chen Yu-Juan, Chen Chang-Le. Simulation of the influence of convection velocity on upstream dendritic growth using phase-field method. Acta Physica Sinica, 2008, 57(7): 4585-4589. doi: 10.7498/aps.57.4585
[13]	Feng Li, Wang Zhi-Ping, Lu Yang, Zhu Chang-Sheng. Phase-field model of isothermal solidification of binary alloy with multiple grains. Acta Physica Sinica, 2008, 57(2): 1084-1090. doi: 10.7498/aps.57.1084
[14]	Li Jun-Jie, Wang Jin-Cheng, Xu Quan, Yang Gen-Cang. Effect of foreign particles on the dendritic growth in phase-field theory. Acta Physica Sinica, 2007, 56(3): 1514-1519. doi: 10.7498/aps.56.1514
[15]	Lu Yang, Wang Fan, Zhu Chang-Sheng, Wang Zhi-Ping. Simulation of multiple grains for isothermal solidification of binary alloy using phase-field model. Acta Physica Sinica, 2006, 55(2): 780-785. doi: 10.7498/aps.55.780
[16]	Long Wen-Yuan, Cai Qi-Zhou, Wei Bo-Kang, Chen Li-Liang. Simulation of dendritic growth of multicomponent alloys using phase-field method. Acta Physica Sinica, 2006, 55(3): 1341-1345. doi: 10.7498/aps.55.1341
[17]	Zhang Yu-Xiang, Wang Jin-Cheng, Yang Gen-Cang, Zhou Yao-He. Phase-field simulation of the influence of elastic field on microstructure evolution and equilibrium composition of precipitation. Acta Physica Sinica, 2006, 55(5): 2433-2438. doi: 10.7498/aps.55.2433
[18]	Yang Hong, Zhang Qing-Guang, Chen Min. A phase-field simulation on the influence of thermal fluctuation on secondary branch growth in undercooled melt. Acta Physica Sinica, 2005, 54(8): 3740-3744. doi: 10.7498/aps.54.3740
[19]	Li Mei-E, Yang Gen-Cang, Zhou Yao-He. Phase field modeling of directional solidification of a binary alloy at high velocities. Acta Physica Sinica, 2005, 54(1): 454-459. doi: 10.7498/aps.54.454
[20]	Long Wen-Yuan, Cai Qi-Zhou, Chen Li-Liang, Wei Bo-Kang. Phase-field modeling of isothermal solidification in binary alloy. Acta Physica Sinica, 2005, 54(1): 256-262. doi: 10.7498/aps.54.256

Catalog

Vol. 71, Issue 8 - 2022-04-20

Metrics

Abstract views: 4157
PDF Downloads: 71
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板

Mechanism of internal magnetic energy of Cu-rich phase precipitation in Fe₈₄Cu₁₅Mn₁ alloy by phase field method