搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

Fe-Cr合金辐照空洞微结构演化的相场法模拟

杨辉 冯泽华 王贺然 张云鹏 陈铮 信天缘 宋小蓉 吴璐 张静

引用本文:
Citation:

Fe-Cr合金辐照空洞微结构演化的相场法模拟

杨辉, 冯泽华, 王贺然, 张云鹏, 陈铮, 信天缘, 宋小蓉, 吴璐, 张静

Phase-field modeling of irradiated void microstructure evolution of Fe-Cr alloy

Yang Hui, Feng Ze-Hua, Wang He-Ran, Zhang Yun-Peng, Chen Zheng, Xin Tian-Yuan, Song Xiao-Rong, Wu Lu, Zhang Jing
PDF
HTML
导出引用
  • Fe-Cr合金作为包壳材料在高温高辐照强度等极端环境下服役, 产生空位和间隙原子等辐照缺陷, 辐照缺陷簇聚诱发空洞、位错环等缺陷团簇, 引起辐照肿胀、晶格畸变, 导致辐照硬化或软化致使材料失效. 理解辐照缺陷簇聚和长大过程的组织演化, 能更有效调控组织获得稳定服役性能. 本文采用相场法研究Fe-Cr合金中空洞的演化, 模型考虑了温度效应对点缺陷的影响以及空位和间隙的产生和复合. 选择400—800 K温度区间、0—16 dpa辐照剂量范围的Fe-Cr体系为对象, 研究在不同服役温度和辐照剂量下的空位扩散、复合和簇聚形成空洞的过程. 在400—800 K温度区间, 随着温度的升高, Fe-Cr合金空洞团簇形核率呈现出先升高后下降的趋势. 考虑空位与间隙的重新组合受温度的影响可以很好地解释空洞率随温度变化时出现先升高后降低的现象. 由于温度的变化将影响Fe-Cr合金中原子离位阀能, 从而影响产生空位和间隙原子. 同一温度下, 空洞半径和空洞的体积分数随辐照剂量的增大而增大. 辐照剂量的增大, 级联碰撞反应加强, 空位与间隙原子大量产生, 高温下空位迅速的扩散聚集在Fe-Cr合金中将形成更多数量以及更大尺寸的空洞.
    As cladding materials, Fe-Cr alloys are used in the extreme environments of high temperature, high pressure, and energetic particle radiation, thus generating irradiation defects such as vacancies and interstitials. The clustering of irradiation defects leads the voids or dislocation loops to form, resulting in irradiation swelling and lattice distortion, and further radiation hardening or softening, finally, material failure. It is beneficial to tailor desired microstructures and obtain stable service performances by understanding defects cluster and voids formation process. In this paper, the phase-field method is employed to study the evolution of voids of Fe-Cr alloy. In the model the temperature effects on point defects and generation/recombination of vacancies and interstitials are taken into consideration. The 400–800 K temperature range and 0–16 dpa radiation dose range are selected, in which the voids’ formation process including generation and recombination, as well as vacancy clustering caused by vacancy diffusion, is studied for Fe-Cr alloy. The nucleation rate of the void cluster shows a trend of first increasing and then decreasing with temperature increasing from 400 to 800 K. This phenomenon is related to complex interactions among defects concentration, atomic diffusion, recombination, nucleation, and growth conditions. At a given temperature, the average radius and the volume fraction of the voids grow bigger as the radiation dose increases. With the increase of irradiation dose, the cascade collision reaction is strengthened, and the number of Frenkel defect pairs is also increases. A large number of vacancies and interstitial atoms are generated, and the rapid diffusion and accumulation of vacancies in the Fe-Cr alloy at high temperature form a larger number and larger size of voids. The incubation period of vacancy clusters and voids are quite different due to the influence of irradiation temperature and dose. The higher the irradiation dose, the shorter the incubation period is. The relationship between the incubation period and temperature is more complicated. When the temperature is relatively low, the incubation period is shortened as the temperature increases, and as the temperature continues to increase to a higher temperature, the incubation period is extended. This relates to the increase in the concentration of vacancies, the recombination of vacancies and interstitials, and the increase of the critical nucleus radius for the growth of voids when the temperature increases.
      通信作者: 张静, Jingzhang@nwpu.edu.cn
    • 基金项目: 国家自然科学基金 (批准号: 51704243, 51674205, 51601185)、国防基础科研计划 (批准号: JCKY2017201C016)、中国博士后科学基金 (批准号: 2015M582575)和国家重点研发计划 (批准号: 2016YFB07001)资助的课题
      Corresponding author: Zhang Jing, Jingzhang@nwpu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51704243, 51674205, 51601185), the National Defense Basic Scientific Research Program of China (Grant No. JCKY2017201C016), the China Postdoctoral Science Foundation (Grant No. 2015M582575), and the National Basic Research Program of China (Grant No. 2016YFB07001)
    [1]

    Klueh R L, Nelson A T 2007 J. Nucl. Mater. 371 37Google Scholar

    [2]

    Buongiorno J, Swindeman R, Corwin W, Rowchitte A, McDonald P, Was G, Mansur L, Wikon D, Nanstad R, Wright I 2003 Supercritical Water Reactor (SCWR) : Survey of Materials Experience and R&D Needs to Assess Viability, Idaho National EngineeringLaboratory Report INEEL/EXT-03-00693 (Rev. 1) Idaho September 2003

    [3]

    Sass S L, Eyre B L 1973 Philos. Mag. 27 1447Google Scholar

    [4]

    Une K, Nogita K, Kashibe S, Imamura M 1992 J. Nucl. Mater. 188 65Google Scholar

    [5]

    Nogita K, Une K 1993 J. Nucl. Mater. 91 301

    [6]

    Zacharie I, Lansiart S, Combette P, Trotabas M, Coster M, Groos M 1998 J. Nucl. Mater. 255 92Google Scholar

    [7]

    Katsuyama K, Nagamine T, Matsumoto S, Ito M 2002 J. Nucl. Sci. Technol. 39 804Google Scholar

    [8]

    张娜, 刘波, 林黎蔚 2020 物理学报 69 016101Google Scholar

    Zhang N, Liu B, Lin L W 2020 Acta Phys. Sin. 69 016101Google Scholar

    [9]

    高云亮, 朱芫江, 李进平 2017 物理学报 66 057104Google Scholar

    Gao Y L, Zhu Y J, Li J P 2017 Acta Phys. Sin. 66 057104Google Scholar

    [10]

    Lindhard J, Nielsen V, Scharff M, Thomsen P V 1963 Mat. Fys. Medd. Dan. Vid. Selsk. 33 706

    [11]

    郁金南 2007 核材料科学与工程——材料辐照效应 (北京: 化学工业出版社) 第198—203页

    Yu J N 2007 Nuclear Materials Science and Engineering Radiation Effects of Materials (Beijing: Chemical Industry Press) pp198–203 (in Chinese)

    [12]

    Becker C H 1972 US Patent 3 657 707 [1972-4-18]

    [13]

    黄鹤飞, 李健健, 刘仁多, 陈怀灿, 闫隆 2014 金属学报 50 1189Google Scholar

    Huang H F, Li J J, Liu R D, Chen H C, Yan L 2014 J. Acta Metall. Sin. 50 1189Google Scholar

    [14]

    丁兆楠, 杨义涛, 宋银, 张丽卿, 缑洁, 张崇宏, 罗广南 2017 物理学报 66 112501Google Scholar

    Ding Z N, Yang Y T, Song Y, Zhang L Q, Gou J, Zhang C H, Luo G N 2017 Acta Phys. Sin. 66 112501Google Scholar

    [15]

    Lambrecht M, Malerba L 2011 Acta Mater. 59 6547Google Scholar

    [16]

    Reese E R, Almirall N, Yamamoto T 2018 Scr. Mater. 146 213Google Scholar

    [17]

    Liu Y L, Zhang Y, Zhou H B 2009 Phys. Rev. B 79 172103Google Scholar

    [18]

    Zhou H B, Liu Y L, Jin S 2010 Nucl. Fusi. 50 115010Google Scholar

    [19]

    Alkhamees A, Liu Y L, Zhou H B 2009 J. Nucl. Mater. 393 508Google Scholar

    [20]

    梁晋洁, 高宁, 李玉红 2020 物理学报 69 116102Google Scholar

    Liang J J, Gao N, Li Y H 2020 Acta Phys. Sin. 69 116102Google Scholar

    [21]

    朱琪, 王升涛, 赵福祺, 潘昊 2020 物理学报 69 036201Google Scholar

    Zhu Q, Wang S T, Zhao F Q, Pan H 2020 Acta Phys. Sin. 69 036201Google Scholar

    [22]

    梁晋洁, 高宁, 李玉红 2020 物理学报 69 036101Google Scholar

    Liang J J, Gao N, Li Y H 2020 Acta Phys. Sin. 69 036101Google Scholar

    [23]

    梁林云, 吕广宏 2013 物理学报 62 182801Google Scholar

    Liang L Y, Lü G H 2013 Acta Phys. Sin. 62 182801Google Scholar

    [24]

    李然然, 张一帆, 耿殿程, 张高伟, 渡边英雄, 韩文妥, 万发荣 2019 物理学报 68 216101Google Scholar

    Li R R, Zhang Y F, Geng D C, Zhang G W, Watanabe Hideo, Han W T, Wan F R 2019 Acta Phys. Sin. 68 216101Google Scholar

    [25]

    Hu S Y, Henager C H, Heinisch H L 2009 J. Nucl. Mater. 392 292Google Scholar

    [26]

    Rokkam S, El-Azab A, Millett P 2009 Model Simul. Mater.Sci. Eng. 17 064002Google Scholar

    [27]

    Millett P C, Rokkam S, El-Azab A 2009 Model Simul. Mater. Sci. Eng. 17 064003Google Scholar

    [28]

    Zhao B J, Zhao Y H, Sun Y Y, Yang W K, Hou H 2019 Acta Metall. Sin. 55 593

    [29]

    Yan Z W, Shi S J, Li Y S, Chen J, Maqbool S 2020 Phys. Chem. Chem. Phys. 22 3611Google Scholar

    [30]

    Provatas N, Elder K 2010 Phase-field Methods in Materials Science and Engineering (Germany: Weinheim Wiley-VCH) pp2−5

    [31]

    Hu S Y, Henager C H 2010 Acta Mater. 58 3230Google Scholar

    [32]

    Li Y, Hu S, Sun X 2010 J. Nucl. Mater. 407 119Google Scholar

    [33]

    Simeone D, Ribis J, Luneville L 2018 J. Mater. Res. 33 440Google Scholar

    [34]

    Ortiz C J, Caturla M J 2007 Phys. Rev. B 75 184101Google Scholar

    [35]

    Bacon D J, Gao F, Osetsky Y N 2000 J. Nucl. Mater. 276 1Google Scholar

    [36]

    Souidi A, Becquart C S, Domain C 2006 J. Nucl. Mater. 355 89Google Scholar

    [37]

    Boisse J, Domain C, Becquart C S 2014 J. Nucl. Mater. 455 10Google Scholar

    [38]

    徐恒均 2009 材料科学基础(第一版)(北京: 北京工业大学出版社) 第205−214页

    Xu H J 2009 Foundations of Materials Science (Vol.1) (Beijjing: Beijing University of Technology Press) pp205−214 (in Chinese)

    [39]

    Wong K L, Lee H J, Shim J H, Sadigh B, Wirth B D 2009 J. Nucl. Mater 386 227

    [40]

    Norris, D I R 1972 Radiation Effects 14 1Google Scholar

    [41]

    Getto E, Jiao Z, Monterrosa A M 2015 J. Nucl.Mater. 462 458Google Scholar

    [42]

    Toloczko M B, Garner F A, Voyevodin V N 2014 J. Nucl.Mater. 453 323Google Scholar

    [43]

    Brailsford A D, Bullough R, Hayns M R 1978 J. Nucl. Mater. 60 246

  • 图 1  不同辐照温度和剂量下Fe-Cr合金中空洞形貌的变化

    Fig. 1.  Morphology evolution of voids of Fe-Cr alloys at different irradiation temperature and dose.

    图 2  Fe-Cr合金空位及间隙原子扩散速度与温度的关系

    Fig. 2.  The relationship between the diffusion rate of Fe-Cr alloy vacancies, the interstitial atoms and temperature.

    图 3  Fe-Cr合金中空位浓度、空位-间隙重组率与温度的关系

    Fig. 3.  Relationship between vacancy concentration, vacancy-interstitial recombination rate, and temperature in Fe-Cr alloy.

    图 4  Fe-Cr合金在700 K温度下0—16 dpa辐照剂量下空洞的平均半径演化

    Fig. 4.  The average radius of the voids of Fe-Cr alloy suffer different irradiation doses at 700 K.

    图 5  Fe-Cr合金在700 K时0—16 dpa不同辐照剂量下空洞的数量演化

    Fig. 5.  Void numbers of Fe-Cr alloy suffers different irradiation doses at 700 K.

    图 6  Fe-Cr合金在700 K时空洞数量与辐照剂量的关系

    Fig. 6.  Relationship between the number of voids and irradiation dose in Fe-Cr alloy at 700 K.

    图 7  Fe-Cr合金在700 K时空洞形貌随时间和辐照剂量的时间演化

    Fig. 7.  Temporal evolution of void in the Fe-Cr alloy at 700 K as functions of time and irradiation dose.

    图 8  Fe-Cr合金在辐照剂量为8 dpa时空洞数量与温度的关系

    Fig. 8.  Relationship between the number of voids and temperature in Fe-Cr alloy irradiated at 8 dpa.

    图 9  Fe-Cr合金在辐照剂量为8 dpa时400—800 K温度下的空洞数量

    Fig. 9.  Comparison of the number of voids in Fe-Cr alloy at different irradiation temperatures of 8 dpa.

    图 10  Fe-Cr合金在辐照剂量为8 dpa时400—800 K温度下的空洞体积分数

    Fig. 10.  Comparison of the results of void volume fractions of Fe-Cr alloy at different irradiation temperatures at 8 dpa.

    表 1  本文模拟使用的物性和模拟参数[33]

    Table 1.  Physical properties and simulation parameters used in this paper[33].

    kB/(eV·K–1)ab0b1b2b3b4MvMiLkcvkci
    8.61733 × 10–58.00.022.850.4–105.452.21.01.01.01.01.0
    下载: 导出CSV
  • [1]

    Klueh R L, Nelson A T 2007 J. Nucl. Mater. 371 37Google Scholar

    [2]

    Buongiorno J, Swindeman R, Corwin W, Rowchitte A, McDonald P, Was G, Mansur L, Wikon D, Nanstad R, Wright I 2003 Supercritical Water Reactor (SCWR) : Survey of Materials Experience and R&D Needs to Assess Viability, Idaho National EngineeringLaboratory Report INEEL/EXT-03-00693 (Rev. 1) Idaho September 2003

    [3]

    Sass S L, Eyre B L 1973 Philos. Mag. 27 1447Google Scholar

    [4]

    Une K, Nogita K, Kashibe S, Imamura M 1992 J. Nucl. Mater. 188 65Google Scholar

    [5]

    Nogita K, Une K 1993 J. Nucl. Mater. 91 301

    [6]

    Zacharie I, Lansiart S, Combette P, Trotabas M, Coster M, Groos M 1998 J. Nucl. Mater. 255 92Google Scholar

    [7]

    Katsuyama K, Nagamine T, Matsumoto S, Ito M 2002 J. Nucl. Sci. Technol. 39 804Google Scholar

    [8]

    张娜, 刘波, 林黎蔚 2020 物理学报 69 016101Google Scholar

    Zhang N, Liu B, Lin L W 2020 Acta Phys. Sin. 69 016101Google Scholar

    [9]

    高云亮, 朱芫江, 李进平 2017 物理学报 66 057104Google Scholar

    Gao Y L, Zhu Y J, Li J P 2017 Acta Phys. Sin. 66 057104Google Scholar

    [10]

    Lindhard J, Nielsen V, Scharff M, Thomsen P V 1963 Mat. Fys. Medd. Dan. Vid. Selsk. 33 706

    [11]

    郁金南 2007 核材料科学与工程——材料辐照效应 (北京: 化学工业出版社) 第198—203页

    Yu J N 2007 Nuclear Materials Science and Engineering Radiation Effects of Materials (Beijing: Chemical Industry Press) pp198–203 (in Chinese)

    [12]

    Becker C H 1972 US Patent 3 657 707 [1972-4-18]

    [13]

    黄鹤飞, 李健健, 刘仁多, 陈怀灿, 闫隆 2014 金属学报 50 1189Google Scholar

    Huang H F, Li J J, Liu R D, Chen H C, Yan L 2014 J. Acta Metall. Sin. 50 1189Google Scholar

    [14]

    丁兆楠, 杨义涛, 宋银, 张丽卿, 缑洁, 张崇宏, 罗广南 2017 物理学报 66 112501Google Scholar

    Ding Z N, Yang Y T, Song Y, Zhang L Q, Gou J, Zhang C H, Luo G N 2017 Acta Phys. Sin. 66 112501Google Scholar

    [15]

    Lambrecht M, Malerba L 2011 Acta Mater. 59 6547Google Scholar

    [16]

    Reese E R, Almirall N, Yamamoto T 2018 Scr. Mater. 146 213Google Scholar

    [17]

    Liu Y L, Zhang Y, Zhou H B 2009 Phys. Rev. B 79 172103Google Scholar

    [18]

    Zhou H B, Liu Y L, Jin S 2010 Nucl. Fusi. 50 115010Google Scholar

    [19]

    Alkhamees A, Liu Y L, Zhou H B 2009 J. Nucl. Mater. 393 508Google Scholar

    [20]

    梁晋洁, 高宁, 李玉红 2020 物理学报 69 116102Google Scholar

    Liang J J, Gao N, Li Y H 2020 Acta Phys. Sin. 69 116102Google Scholar

    [21]

    朱琪, 王升涛, 赵福祺, 潘昊 2020 物理学报 69 036201Google Scholar

    Zhu Q, Wang S T, Zhao F Q, Pan H 2020 Acta Phys. Sin. 69 036201Google Scholar

    [22]

    梁晋洁, 高宁, 李玉红 2020 物理学报 69 036101Google Scholar

    Liang J J, Gao N, Li Y H 2020 Acta Phys. Sin. 69 036101Google Scholar

    [23]

    梁林云, 吕广宏 2013 物理学报 62 182801Google Scholar

    Liang L Y, Lü G H 2013 Acta Phys. Sin. 62 182801Google Scholar

    [24]

    李然然, 张一帆, 耿殿程, 张高伟, 渡边英雄, 韩文妥, 万发荣 2019 物理学报 68 216101Google Scholar

    Li R R, Zhang Y F, Geng D C, Zhang G W, Watanabe Hideo, Han W T, Wan F R 2019 Acta Phys. Sin. 68 216101Google Scholar

    [25]

    Hu S Y, Henager C H, Heinisch H L 2009 J. Nucl. Mater. 392 292Google Scholar

    [26]

    Rokkam S, El-Azab A, Millett P 2009 Model Simul. Mater.Sci. Eng. 17 064002Google Scholar

    [27]

    Millett P C, Rokkam S, El-Azab A 2009 Model Simul. Mater. Sci. Eng. 17 064003Google Scholar

    [28]

    Zhao B J, Zhao Y H, Sun Y Y, Yang W K, Hou H 2019 Acta Metall. Sin. 55 593

    [29]

    Yan Z W, Shi S J, Li Y S, Chen J, Maqbool S 2020 Phys. Chem. Chem. Phys. 22 3611Google Scholar

    [30]

    Provatas N, Elder K 2010 Phase-field Methods in Materials Science and Engineering (Germany: Weinheim Wiley-VCH) pp2−5

    [31]

    Hu S Y, Henager C H 2010 Acta Mater. 58 3230Google Scholar

    [32]

    Li Y, Hu S, Sun X 2010 J. Nucl. Mater. 407 119Google Scholar

    [33]

    Simeone D, Ribis J, Luneville L 2018 J. Mater. Res. 33 440Google Scholar

    [34]

    Ortiz C J, Caturla M J 2007 Phys. Rev. B 75 184101Google Scholar

    [35]

    Bacon D J, Gao F, Osetsky Y N 2000 J. Nucl. Mater. 276 1Google Scholar

    [36]

    Souidi A, Becquart C S, Domain C 2006 J. Nucl. Mater. 355 89Google Scholar

    [37]

    Boisse J, Domain C, Becquart C S 2014 J. Nucl. Mater. 455 10Google Scholar

    [38]

    徐恒均 2009 材料科学基础(第一版)(北京: 北京工业大学出版社) 第205−214页

    Xu H J 2009 Foundations of Materials Science (Vol.1) (Beijjing: Beijing University of Technology Press) pp205−214 (in Chinese)

    [39]

    Wong K L, Lee H J, Shim J H, Sadigh B, Wirth B D 2009 J. Nucl. Mater 386 227

    [40]

    Norris, D I R 1972 Radiation Effects 14 1Google Scholar

    [41]

    Getto E, Jiao Z, Monterrosa A M 2015 J. Nucl.Mater. 462 458Google Scholar

    [42]

    Toloczko M B, Garner F A, Voyevodin V N 2014 J. Nucl.Mater. 453 323Google Scholar

    [43]

    Brailsford A D, Bullough R, Hayns M R 1978 J. Nucl. Mater. 60 246

  • [1] 刘钟磊, 曹津铭, 王智, 赵宇宏. 相场法探究铁电体涡旋拓扑结构与准同型相界. 物理学报, 2023, 72(3): 037702. doi: 10.7498/aps.72.20221898
    [2] 王凯乐, 杨文奎, 史新成, 侯华, 赵宇宏. 相场法研究AlxCuMnNiFe高熵合金富Cu相析出机理. 物理学报, 2023, 72(7): 076102. doi: 10.7498/aps.72.20222439
    [3] 蒋新安, 赵宇宏, 杨文奎, 田晓林, 侯华. 相场法研究Fe84Cu15Mn1合金富Cu相析出的内磁能作用机理. 物理学报, 2022, 71(8): 080201. doi: 10.7498/aps.71.20212087
    [4] 姜彦博, 柳文波, 孙志鹏, 喇永孝, 恽迪. 外加应力作用下 UO2 中空洞演化过程的相场模拟. 物理学报, 2022, 71(2): 026103. doi: 10.7498/aps.71.20211440
    [5] 郭震, 赵宇宏, 孙远洋, 赵宝军, 田晓林, 侯华. 相场法研究Fe-Cu-Mn-Al合金富Cu相析出机制. 物理学报, 2021, 70(8): 086401. doi: 10.7498/aps.70.20201843
    [6] 罗海滨, 李俊杰, 马渊, 郭春文, 王锦程. 粗化过程中颗粒界面形状演化的三维多相场法研究. 物理学报, 2014, 63(2): 026401. doi: 10.7498/aps.63.026401
    [7] 王陶, 李俊杰, 王锦程. 界面润湿性及固相体积分数对颗粒粗化动力学影响的相场法研究. 物理学报, 2013, 62(10): 106402. doi: 10.7498/aps.62.106402
    [8] 崔振国, 勾成俊, 侯氢, 毛莉, 周晓松. 低能中子在锆中产生的辐照损伤的计算机模拟研究. 物理学报, 2013, 62(15): 156105. doi: 10.7498/aps.62.156105
    [9] 王雅琴, 王锦程, 李俊杰. 定向倾斜枝晶生长规律及竞争行为的相场法研究. 物理学报, 2012, 61(11): 118103. doi: 10.7498/aps.61.118103
    [10] 王明光, 赵宇宏, 任娟娜, 穆彦青, 王伟, 杨伟明, 李爱红, 葛洪浩, 侯华. 相场法模拟NiCu合金非等温凝固枝晶生长. 物理学报, 2011, 60(4): 040507. doi: 10.7498/aps.60.040507
    [11] 龙文元, 吕冬兰, 夏春, 潘美满, 蔡启舟, 陈立亮. 强迫对流影响二元合金非等温凝固枝晶生长的相场法模拟. 物理学报, 2009, 58(11): 7802-7808. doi: 10.7498/aps.58.7802
    [12] 宗亚平, 王明涛, 郭巍. 再结晶和外力场下第二相析出的相场法模拟. 物理学报, 2009, 58(13): 161-S168. doi: 10.7498/aps.58.161
    [13] 陈玉娟, 陈长乐. 相场法模拟对流速度对上游枝晶生长的影响. 物理学报, 2008, 57(7): 4585-4589. doi: 10.7498/aps.57.4585
    [14] 肖中银, 王廷云, 罗文芸, 王子华. 高能粒子辐照二氧化硅玻璃E′色心形成机理研究. 物理学报, 2008, 57(4): 2273-2277. doi: 10.7498/aps.57.2273
    [15] 李俊杰, 王锦程, 许 泉, 杨根仓. 外来夹杂物颗粒对枝晶生长形态影响的相场法研究. 物理学报, 2007, 56(3): 1514-1519. doi: 10.7498/aps.56.1514
    [16] 肖中银, 罗文芸, 王廷云. 高纯硅低能粒子辐照E′色心形成动力学研究. 物理学报, 2007, 56(5): 2731-2735. doi: 10.7498/aps.56.2731
    [17] 路 阳, 王 帆, 朱昌盛, 王智平. 等温凝固多晶粒生长相场法模拟. 物理学报, 2006, 55(2): 780-785. doi: 10.7498/aps.55.780
    [18] 龙文元, 蔡启舟, 魏伯康, 陈立亮. 相场法模拟多元合金过冷熔体中的枝晶生长. 物理学报, 2006, 55(3): 1341-1345. doi: 10.7498/aps.55.1341
    [19] 张玉祥, 王锦程, 杨根仓, 周尧和. 相场法模拟弹性场对沉淀相变组织演化及相平衡成分的影响. 物理学报, 2006, 55(5): 2433-2438. doi: 10.7498/aps.55.2433
    [20] 杨 弘, 张清光, 陈 民. 热扰动对过冷熔体中二次枝晶生长影响的相场法模拟. 物理学报, 2005, 54(8): 3740-3744. doi: 10.7498/aps.54.3740
计量
  • 文章访问数:  4494
  • PDF下载量:  101
  • 被引次数: 0
出版历程
  • 收稿日期:  2020-09-02
  • 修回日期:  2020-09-28
  • 上网日期:  2021-02-21
  • 刊出日期:  2021-03-05

/

返回文章
返回