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金属学报  2022, Vol. 58 Issue (7): 943-955    DOI: 10.11900/0412.1961.2020.00531
  研究论文 本期目录 | 过刊浏览 |
辐照条件下Fe-Cu合金中富Cu析出相的临界形核尺寸和最小能量路径的弦方法计算
刘续希1, 柳文波1(), 李博岩2, 贺新福3, 杨朝曦1, 恽迪1
1.西安交通大学 核科学与技术学院 西安 710049
2.清华大学 材料学院 北京 100084
3.中国原子能科学研究院 北京 102413
Calculation of Critical Nucleus Size and Minimum Energy Path of Cu-Riched Precipitates During Radiation in Fe-Cu Alloy Using String Method
LIU Xuxi1, LIU Wenbo1(), LI Boyan2, HE Xinfu3, YANG Zhaoxi1, YUN Di1
1.School of Nuclear Science and Technology, Xi'an Jiaotong University, Xi'an 710049, China
2.School of Materials Science and Engineering, Tsinghua University, Beijing 100084, China
3.China Institute of Atomic Energy, Beijing 102413, China
引用本文:

刘续希, 柳文波, 李博岩, 贺新福, 杨朝曦, 恽迪. 辐照条件下Fe-Cu合金中富Cu析出相的临界形核尺寸和最小能量路径的弦方法计算[J]. 金属学报, 2022, 58(7): 943-955.
Xuxi LIU, Wenbo LIU, Boyan LI, Xinfu HE, Zhaoxi YANG, Di YUN. Calculation of Critical Nucleus Size and Minimum Energy Path of Cu-Riched Precipitates During Radiation in Fe-Cu Alloy Using String Method[J]. Acta Metall Sin, 2022, 58(7): 943-955.

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摘要: 

基于约束弦方法和相场理论,对辐照条件下Fe-Cu合金中富Cu析出相的临界形核尺寸和最小能量路径进行了计算,得到了不同温度和不同Cu含量的富Cu团簇的最小能量路径、临界形核半径、空位浓度场分布等参数。计算结果表明:温度和Cu含量对Fe-Cu二元合金中富Cu相的析出过程的能量路径和临界形核团簇尺寸有很大影响。温度是影响形核能量路径方向的主要因素,Cu含量是影响团簇生长速率的主要因素。温度越高,Cu含量越高,形核达到临界形核尺寸所需要的时间越短,所需要翻越的能量势垒越低。Cu元素浓度场的分布对辐照空位浓度的分布有很大的影响。在富Cu团簇中的空位浓度比Fe-Cu基体中更低,而且Cu浓度越高,空位的浓度越低。上述计算结果与实验结果基本一致。

关键词 Fe-Cu合金相场方法约束条件弦方法辐照加速析出临界形核尺寸    
Abstract

As a pressure containment shell that supports all components in the nuclear reactor, reactor pressure vessel (RPV) is an irreplaceable core component during the whole life of nuclear power plant. Cu-riched particles precipitated in the early stage of radiation have significant effects on the mechanical property (such as radiation hardening and embrittlement) changes during the application of RPV steel. However, the Cu-riched precipitate with extremely small size (smaller than 2 nm) cannot be detected by the conventional experimental method, such as scanning electron microscope and transmission electron microscope. Hence, it is essential to calculate the critical nucleus size of Cu-riched precipitate under radiation in RPV steel. In this study, based on the constrained string method and phase-field theory, the critical nucleus size and minimum energy path of Cu-riched precipitate in Fe-Cu alloy under irradiation were calculated, and the minimum energy path, critical nucleus radius, and vacancy concentration distribution were also studied. The calculated results showed that both temperature and Cu concentration have a great influence on the energy path and critical nucleus cluster size of Cu-riched particles in Fe-Cu binary alloy. Temperature is the main factor influencing the energy path direction of the nucleus, while Cu concentration is the main factor influencing the growth rate of the nucleus radius. With the increase of temperature, the Cu concentration in the nucleus increases, while the time needed for the Cu-riched particles to reach its critical nucleus size decreases, and the energy barrier needed to be crossed also decreases. The distribution of Cu concentration also has a great influence on the distribution of vacancy during radiation. The vacancy concentration in the Cu-riched cluster is lower than that in the Fe-Cu matrix. The vacancy concentration decreased as the Cu concentration increased. The calculated results are consistent with the experimental results.

Key wordsFe-Cu alloy    phase-field method    constrained string method    radiation-enhanced precipitate    critical nucleus size
收稿日期: 2020-12-30     
ZTFLH:  TG142  
基金资助:国家自然科学基金项目(U1830124);国家自然科学基金项目(11705137);中国博士后科学基金项目(2019M663738);中国核工业集团有限公司领创科研项目
作者简介: 刘续希,男,2000年生,硕士生
图1  形核过程鞍点示意图
Elementα1α2α3α4βγL
Cu6242.2122.833-23.5902-0.004761-5.9197000038022.8
Fe1225.7124.134-23.5143-0.004397-5.89277358.538022.8
表1  Fe-Cu合金Gibbs自由能参数[18,28,30]
ParameterValueUnit
κCu5 × 10-15J·m2·mol-1
κV1 × 10-15J·m2·mol-1
εCu122.833
εV124.134
表2  Fe-Cu合金的界面能参数与本征应变系数[28,29]
T / KDFe / (m2·s-1)DCu / (m2·s-1)MFe / (mol·m·s·kg-1)MCu / (mol·m·s·kg-1)
5507.2 × 10-325.0 × 10-296.7 × 10-174.6 × 10-14
6504.2 × 10-278.0 × 10-253.9 × 10-127.4 × 10-10
表3  不同温度下扩散系数及迁移率的取值[29,35]
图2  650 K时Fe-0.3%Cu合金在辐照强度0.01 dpa/s下演化2步和50步后的能量路径
图3  650 K和0.01 dpa/s下Fe-0.3%Cu演化2步和50步后临界团簇的Cu元素浓度分布和团簇形貌
图4  不同温度下演化50步后Fe-0.3%Cu合金的最小能量路径
图5  不同温度下演化50步后Fe-0.3%Cu合金临界团簇的Cu元素浓度分布和团簇形貌
T / KRC / nmCC / %
5501.72245.4355
6001.76247.8542
6501.79450.2122
7001.82152.5147
表4  不同温度下演化50步后Fe-0.3%Cu合金临界团簇半径与浓度计算结果
图6  不同温度下演化50步后Fe-0.3%Cu合金临界团簇Cu元素浓度的一维分布曲线
图7  650 K下演化50步后不同Cu元素浓度Fe-Cu合金的最小能量路径
图8  650 K下演化50步后不同Cu元素元素浓度Fe-Cu合金临界团簇的Cu元素浓度分布和团簇形貌
AlloyRC / nmCC / %
Fe-0.05Cu1.19026.9862
Fe-0.1Cu1.29235.3291
Fe-0.3Cu1.76247.8542
Fe-0.5Cu2.01452.8991
表5  650 K下演化50步后不同Fe-Cu合金的临界团簇半径与平均浓度计算结果
图9  650 K下演化50步后不同Fe-Cu合金临界团簇中Cu元素浓度的一维分布曲线
图10  不同温度和不同Cu元素浓度下演化50步后团簇半径的变化曲线
图11  650 K下演化50步后不同辐照强度下Fe-0.3%Cu和Fe-0.5%Cu合金临界团簇状态的空位增量分布图
图12  650 K下演化50步后辐照强度0.01 dpa/s下Fe-0.3%Cu合金在不同时刻的空位浓度分布
t / stepRC / nmMin.CVMax.CV - Min.CVSum.CV
301.5580.001028.63 × 10-517.149
601.7630.001823.89 × 10-434.381
901.8840.002298.92 × 10-451.535
1202.0390.002801.65 × 10-369.190
表6  演化50步后不同时刻下团簇空位浓度信息计算结果
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