金属中氦行为的计算机理论模拟
摘要
由于氦不溶于材料基体,随着基体中产生氦量的增加或通过适当的氦原子迁移,基体中的氦原子将会在空位、位错和晶界处聚集、沉淀,形成氦-空位(He-V)团,乃至形成纳米尺度的析出相—氦泡。材料中形成的氦泡会导致反应堆材料出现空洞肿胀,使材料发生脆化或表面出现泡状,变得粗糙,从而使得材料的宏观性能下降。因此,氦在材料中的产生和演变受到了很大关注。
本文采用分子动力学方法,利用MOLDY程序,系统研究了α-Fe中氦的微观行为;并采用基于密度泛函理论的从头算法,利用VASP程序,研究了过渡金属中单个氦的稳定位置和fcc Al中氦的稳定、迁移和成团情况。
1、采用分子动力学方法模拟研究了在100K和600K下α-Fe中有1at.%He—5at.%He的级联现象;采用两套作用势对比模拟研究了100K的α-铁中有1at.%He—5at.%He的级联现象,发现氦导致Fe的级联中缺陷的形成和分布情况与纯Fe明显不同:
氦使得级联中产生的点缺陷Frenkel缺陷对数目发生了明显变化。辐照温度对Frenkel缺陷对数目的影响很小,但是随着氦浓度和级联能增加,点缺陷增多。特别是氦使得级联中形成了更多较大的空位团,即氦-空位团,而纯铁的级联中只有少量小空位团,也就是说位移级联过程可以直接导致He泡成核。级联中形成氦-空位团的情况与多种因素有关。随着级联能的增加,氦-空位团的数目和尺寸一般都呈现增加趋势;随着氦浓度的增加,氦-空位团的数目和尺寸一般也呈现增加趋势;随着辐照温度的增加,级联中形成的氦-空位团数量增大,但平均尺寸基本不变。
虽然不同相互作用势对级联中氦-空位团的形成没有本质上的改变,但是形成的氦-空位团在数量和尺寸上都有较大差异。对模拟结果影响的强弱顺序为:Fe-Fe相互作用＞Fe-He相互作用＞He-He相互作用。
2、采用分子动力学方法模拟研究了位移级联与氦.空位团的相互作用。氦-空位团中初始空位数目选为10与20个,初始氦与空位个数之比(He/V)从0.2增加到3,级联能从2keV增加到10keV。模拟结果发现:
在单次级联作用下,氦-空位团的稳定性主要依赖于He/V比例的初始值和级联能的大小。当初始He/V＞1时,氦-空位团的尺寸随着级联能的增加而增加,而He/V比例随着级联能增加而降低;但是对于初始He/V＜1的氦-空位团,团的尺寸随着级联能的增加而降低,而He/V比例随着级联能增加而增加;初始He/V=1的氦-空位团很稳定。模拟还发现在单次级联作用下,在He/V比例相同的前提下,较大的氦-空位团比较小的氦-空位团更稳定。
在各向同性的5keV级联交迭作用下,氦.空位团的稳定情况与初始He/V比例有关。第一次级联碰撞决定了氦团中的空位数目,随后的级联作用对团的稳定性影响明显。利用氦-空位团内压强、氦原子的迁移、级联产生的空位数目和团中初始He/V比例对模拟结果进行了讨论。
3、采用分子静力学方法,通过计算小氦-空位团He_nV_m(n=1,2,3,4,m=1,2,3,4)在α-Fe的a/2<111>{110}刃型位错中的结合能,研究了小氦-空位团与刃型位错的相互作用。发现氦-空位团和刃型位错之间的相互作用与团中氦和空位个数之比密切相关。当He/V≥1时,在垂直于滑移面的方向上,氦-空位团被捕陷在刃型位错的扩张方,然而当He/V＜1时,氦-空位团被捕陷在位错芯的扩张和压缩方0.5nm范围内。在滑移面上,He_nV_m(n≥m)和He_nV_m(n＜m)团与位错的相互作用相似—被束缚在离位错芯1.3nm范围内,只是He_nV_m(n≥m)团与位错的作用比He_nV_m(n＜m)团与位错的作用更强。氦-空位团在滑移面上和位错的结合能与He/V比例密切相关,与团的大小有微弱关系。
4、采用基于密度泛函理论的从头算法,利用VASP程序研究了过渡金属中单个氦的稳定性。计算结果显示除了Nb这族元素外,氦在替换位置最稳定。间隙氦的稳定位置则与金属结构有关系。对于bcc结构金属,四面体间隙氦比八面体间隙氦更稳定;而对于fcc结构金属,间隙氦的稳定位置没有规律可循。单个氦原子在金属中的稳定位置与晶体是否有磁性没有直接关系。
本文还利用VASP程序研究了fcc Al中氦的稳定、迁移和小氦-空位团的稳定性。铝中八面体间隙氦比四面体间隙氦稍稳定,而间隙氦在fcc Al中的迁移路径是从八面体间隙位置出发,通过四面体间隙位置,再到达邻近的八面体间隙位置,其迁移能为0.10eV。fcc Al中双空位和三空位团不稳定,而氦的引入增加了空位团的稳定性。氦(或空位)与氦-空位团的结合能主要与团中He/V比例有关,与团的尺寸有微弱关系。
Because of the extremely low solubility of helium in metals,helium atoms generated mostly by(n,α) reactions of neutrons with matrix nuclei during neutron irradiation tend to be trapped at defects that create excess volume within the crystal such as vacancies,dislocations and grain boundaries.It has been observed that helium easily precipitates into clusters or bubbles.The formation of helium bubbles in materials can lead to void swelling and produces high temperature intergranular embrittlement, surface roughening and blistering.These effects would significantly degrade the mechanical properties of materials,therefore,the production and evolution of He atoms in metals are studied with particular concern.
In this paper,a systematic investigation of the atomitic behavior of helium inα-Fe has been carried out by molecular dynamics(MD) methods and MOLDY code. Furthermore,ab initio calculations based on density functional theory have been performed to study the relative stability of single He defect in bcc and fcc metals and the dissolution and migration of helium,and the stability of small helium-vacancy clusters in aluminum.
1.Displacement cascades are simulated by MD methods inα-Fe containing a concentration of substitutional He atoms varying from 1 to 5 at.%at irradiation temperatures of 100 K and 600 K.Furthermore,the effects of using different interatomic potentials in MD simulations of the formation of He-vacancy clusters within displacement cascades inα-Fe are investigated using two sets of potentials.
The results are compared with those performed in pureα-Fe.There are distinct differences in the number and size of point defects and defect clusters within displacement cascades with and without substitutional helium atoms.We find that the effect of the irradiation temperature on Frenkel pairs(N_F) is small as the temperature increases from 100 K to 600 K and the total number of point defects increases with increasing He concentrations and primary knock-on atom(PKA) energies.Particularly, large numbers of helium-vacancy(He-V) dusters are generated directly in displacement cascades,and the sizes of these clusters are much larger than those observed for clusters in pureα-Fe,i.e.in the presence of substitutional He atoms large vacancy clusters can be nucleated directly in displacement cascades.Furthermore,the number and size of He-V clusters generally increase with increasing helium concentration and PKA energy. The number density of He-V clusters almost increases with increasing temperature, while the mean size of He-V clusters remains almost constant for the same He concentration and PKA energy.
Although the effects of interatomic potentials on the nucleation of He-vacancy clusters induced by cascades are relatively small,the number and size of He-vacancy clusters produced are significantly different for the different potentials employed in this study.From these studies,it is dear that Fe-Fe potential has significant effects on the formation of He-V clusters within cascades,followed by Fe-He potential,but He-He potential has little influences on cascade-induced cluster formation.
2.The interactions of displacement cascades with helium-vacancy clusters are investigated using molecular dynamics simulations.Initial He-V clusters consist of 10 and 20 vacancies with the He-to-vacancy(He/V) ratios ranging from 0.2 to 3 and the PKA energy,Ep,varying from 2 keV to 10 keV.The effects of a single displacement cascade on the stability of a He-V cluster depend on the He/V ratio and the PKA energy. When the initial He/V ratio is larger than 1,the size of He-V clusters increases,and the He/V ratio decreases with the PKA energy increasing,but when the initial He/V ratio is less than 1,the size of He-V clusters decreases,and the He/V ratio increases with the PKA energy increasing.The clusters with the He/V ratio of 1 are relatively stable, which is independent of the PKA energy.One of the striking results is that large He-vacancy clusters are more stable than small clusters for the same He/V ratio under mono-irradiation condition.
During multiple 5 keV cascade events,the final size of He-V clusters only depends on the initial He/V ratios.It is of interest to notice that the number of vacancies in a He-V cluster is determined by the first cascade event,while subsequent cascade overlap has a significant effect on its stability.These results are discussed in terms of the internal pressure of He-V clusters,the mobility of He atoms,the number of vacancies produced by cascades and the He/V ratio.
3.Molecular static methods are performed to study the interaction between He-V clusters and an a/2＜111＞{110} edge dislocation inα-Fe through calculating the binding energies of He-V clusters in and near the edge dislocation with empirical potentials.The results show that the interaction depends on the He/V ratio of the clusters.For the ratio equal to or larger than 1,He-V clusters are strongly trapped on the tension side of edge dislocations and repelled from the compression side of edge dislocations,however,for the ratio less than 1,He-V clusters are trapped within about 0.5 nm from the dislocation core on both the compression and tension sides.On the slip plane,the effects of dislocations on the formation of He-V clusters is very small for the distances more than about 1.3 nm from the dislocation core.
4.The relative stability of single He defect in bee and fee metals is investigated using ab initio calculations based on density functional theory(DFT).The calculations reveal that for all metals involved,except for V and Nb,the substitutional position is the most stable.Furthermore,the tetrahedral site is energetically more favorable for the He interstitial than the octahedral site in the bee metals,but the relative stability of He defects in the fcc metals is not definitive.It is interesting to find that the magnetism of host atoms does not directly affect the relative stabilities of He interstitial sites.
Ab initio calculations based on density functional theory is also performed to study the dissolution and migration of helium,and the stability of small helium-vacancy clusters He_nV_m(n,m=0 to 4) in aluminum.The results indicate that the octahedral configuration is more stable than the tetrahedral.Interstitial helium atoms are predicted to have attractive interactions and jump between two octahedral sites via an intermediate tetrahedral site with low migration energy of 0.10 eV.The results indicate that the divacancy and trivacancy clusters are not stable,but He atoms can increase the stability of vacancy clusters.The binding energies of an interstitial He atom and an isolated vacancy to a He-V cluster mainly depend on the He/V ratio of the clusters rather than the cluster size.
本文采用分子动力学方法,利用MOLDY程序,系统研究了α-Fe中氦的微观行为;并采用基于密度泛函理论的从头算法,利用VASP程序,研究了过渡金属中单个氦的稳定位置和fcc Al中氦的稳定、迁移和成团情况。
1、采用分子动力学方法模拟研究了在100K和600K下α-Fe中有1at.%He—5at.%He的级联现象;采用两套作用势对比模拟研究了100K的α-铁中有1at.%He—5at.%He的级联现象,发现氦导致Fe的级联中缺陷的形成和分布情况与纯Fe明显不同:
氦使得级联中产生的点缺陷Frenkel缺陷对数目发生了明显变化。辐照温度对Frenkel缺陷对数目的影响很小,但是随着氦浓度和级联能增加,点缺陷增多。特别是氦使得级联中形成了更多较大的空位团,即氦-空位团,而纯铁的级联中只有少量小空位团,也就是说位移级联过程可以直接导致He泡成核。级联中形成氦-空位团的情况与多种因素有关。随着级联能的增加,氦-空位团的数目和尺寸一般都呈现增加趋势;随着氦浓度的增加,氦-空位团的数目和尺寸一般也呈现增加趋势;随着辐照温度的增加,级联中形成的氦-空位团数量增大,但平均尺寸基本不变。
虽然不同相互作用势对级联中氦-空位团的形成没有本质上的改变,但是形成的氦-空位团在数量和尺寸上都有较大差异。对模拟结果影响的强弱顺序为:Fe-Fe相互作用＞Fe-He相互作用＞He-He相互作用。
2、采用分子动力学方法模拟研究了位移级联与氦.空位团的相互作用。氦-空位团中初始空位数目选为10与20个,初始氦与空位个数之比(He/V)从0.2增加到3,级联能从2keV增加到10keV。模拟结果发现:
在单次级联作用下,氦-空位团的稳定性主要依赖于He/V比例的初始值和级联能的大小。当初始He/V＞1时,氦-空位团的尺寸随着级联能的增加而增加,而He/V比例随着级联能增加而降低;但是对于初始He/V＜1的氦-空位团,团的尺寸随着级联能的增加而降低,而He/V比例随着级联能增加而增加;初始He/V=1的氦-空位团很稳定。模拟还发现在单次级联作用下,在He/V比例相同的前提下,较大的氦-空位团比较小的氦-空位团更稳定。
在各向同性的5keV级联交迭作用下,氦.空位团的稳定情况与初始He/V比例有关。第一次级联碰撞决定了氦团中的空位数目,随后的级联作用对团的稳定性影响明显。利用氦-空位团内压强、氦原子的迁移、级联产生的空位数目和团中初始He/V比例对模拟结果进行了讨论。
3、采用分子静力学方法,通过计算小氦-空位团He_nV_m(n=1,2,3,4,m=1,2,3,4)在α-Fe的a/2<111>{110}刃型位错中的结合能,研究了小氦-空位团与刃型位错的相互作用。发现氦-空位团和刃型位错之间的相互作用与团中氦和空位个数之比密切相关。当He/V≥1时,在垂直于滑移面的方向上,氦-空位团被捕陷在刃型位错的扩张方,然而当He/V＜1时,氦-空位团被捕陷在位错芯的扩张和压缩方0.5nm范围内。在滑移面上,He_nV_m(n≥m)和He_nV_m(n＜m)团与位错的相互作用相似—被束缚在离位错芯1.3nm范围内,只是He_nV_m(n≥m)团与位错的作用比He_nV_m(n＜m)团与位错的作用更强。氦-空位团在滑移面上和位错的结合能与He/V比例密切相关,与团的大小有微弱关系。
4、采用基于密度泛函理论的从头算法,利用VASP程序研究了过渡金属中单个氦的稳定性。计算结果显示除了Nb这族元素外,氦在替换位置最稳定。间隙氦的稳定位置则与金属结构有关系。对于bcc结构金属,四面体间隙氦比八面体间隙氦更稳定;而对于fcc结构金属,间隙氦的稳定位置没有规律可循。单个氦原子在金属中的稳定位置与晶体是否有磁性没有直接关系。
本文还利用VASP程序研究了fcc Al中氦的稳定、迁移和小氦-空位团的稳定性。铝中八面体间隙氦比四面体间隙氦稍稳定,而间隙氦在fcc Al中的迁移路径是从八面体间隙位置出发,通过四面体间隙位置,再到达邻近的八面体间隙位置,其迁移能为0.10eV。fcc Al中双空位和三空位团不稳定,而氦的引入增加了空位团的稳定性。氦(或空位)与氦-空位团的结合能主要与团中He/V比例有关,与团的尺寸有微弱关系。
Because of the extremely low solubility of helium in metals,helium atoms generated mostly by(n,α) reactions of neutrons with matrix nuclei during neutron irradiation tend to be trapped at defects that create excess volume within the crystal such as vacancies,dislocations and grain boundaries.It has been observed that helium easily precipitates into clusters or bubbles.The formation of helium bubbles in materials can lead to void swelling and produces high temperature intergranular embrittlement, surface roughening and blistering.These effects would significantly degrade the mechanical properties of materials,therefore,the production and evolution of He atoms in metals are studied with particular concern.
In this paper,a systematic investigation of the atomitic behavior of helium inα-Fe has been carried out by molecular dynamics(MD) methods and MOLDY code. Furthermore,ab initio calculations based on density functional theory have been performed to study the relative stability of single He defect in bcc and fcc metals and the dissolution and migration of helium,and the stability of small helium-vacancy clusters in aluminum.
1.Displacement cascades are simulated by MD methods inα-Fe containing a concentration of substitutional He atoms varying from 1 to 5 at.%at irradiation temperatures of 100 K and 600 K.Furthermore,the effects of using different interatomic potentials in MD simulations of the formation of He-vacancy clusters within displacement cascades inα-Fe are investigated using two sets of potentials.
The results are compared with those performed in pureα-Fe.There are distinct differences in the number and size of point defects and defect clusters within displacement cascades with and without substitutional helium atoms.We find that the effect of the irradiation temperature on Frenkel pairs(N_F) is small as the temperature increases from 100 K to 600 K and the total number of point defects increases with increasing He concentrations and primary knock-on atom(PKA) energies.Particularly, large numbers of helium-vacancy(He-V) dusters are generated directly in displacement cascades,and the sizes of these clusters are much larger than those observed for clusters in pureα-Fe,i.e.in the presence of substitutional He atoms large vacancy clusters can be nucleated directly in displacement cascades.Furthermore,the number and size of He-V clusters generally increase with increasing helium concentration and PKA energy. The number density of He-V clusters almost increases with increasing temperature, while the mean size of He-V clusters remains almost constant for the same He concentration and PKA energy.
Although the effects of interatomic potentials on the nucleation of He-vacancy clusters induced by cascades are relatively small,the number and size of He-vacancy clusters produced are significantly different for the different potentials employed in this study.From these studies,it is dear that Fe-Fe potential has significant effects on the formation of He-V clusters within cascades,followed by Fe-He potential,but He-He potential has little influences on cascade-induced cluster formation.
2.The interactions of displacement cascades with helium-vacancy clusters are investigated using molecular dynamics simulations.Initial He-V clusters consist of 10 and 20 vacancies with the He-to-vacancy(He/V) ratios ranging from 0.2 to 3 and the PKA energy,Ep,varying from 2 keV to 10 keV.The effects of a single displacement cascade on the stability of a He-V cluster depend on the He/V ratio and the PKA energy. When the initial He/V ratio is larger than 1,the size of He-V clusters increases,and the He/V ratio decreases with the PKA energy increasing,but when the initial He/V ratio is less than 1,the size of He-V clusters decreases,and the He/V ratio increases with the PKA energy increasing.The clusters with the He/V ratio of 1 are relatively stable, which is independent of the PKA energy.One of the striking results is that large He-vacancy clusters are more stable than small clusters for the same He/V ratio under mono-irradiation condition.
During multiple 5 keV cascade events,the final size of He-V clusters only depends on the initial He/V ratios.It is of interest to notice that the number of vacancies in a He-V cluster is determined by the first cascade event,while subsequent cascade overlap has a significant effect on its stability.These results are discussed in terms of the internal pressure of He-V clusters,the mobility of He atoms,the number of vacancies produced by cascades and the He/V ratio.
3.Molecular static methods are performed to study the interaction between He-V clusters and an a/2＜111＞{110} edge dislocation inα-Fe through calculating the binding energies of He-V clusters in and near the edge dislocation with empirical potentials.The results show that the interaction depends on the He/V ratio of the clusters.For the ratio equal to or larger than 1,He-V clusters are strongly trapped on the tension side of edge dislocations and repelled from the compression side of edge dislocations,however,for the ratio less than 1,He-V clusters are trapped within about 0.5 nm from the dislocation core on both the compression and tension sides.On the slip plane,the effects of dislocations on the formation of He-V clusters is very small for the distances more than about 1.3 nm from the dislocation core.
4.The relative stability of single He defect in bee and fee metals is investigated using ab initio calculations based on density functional theory(DFT).The calculations reveal that for all metals involved,except for V and Nb,the substitutional position is the most stable.Furthermore,the tetrahedral site is energetically more favorable for the He interstitial than the octahedral site in the bee metals,but the relative stability of He defects in the fcc metals is not definitive.It is interesting to find that the magnetism of host atoms does not directly affect the relative stabilities of He interstitial sites.
Ab initio calculations based on density functional theory is also performed to study the dissolution and migration of helium,and the stability of small helium-vacancy clusters He_nV_m(n,m=0 to 4) in aluminum.The results indicate that the octahedral configuration is more stable than the tetrahedral.Interstitial helium atoms are predicted to have attractive interactions and jump between two octahedral sites via an intermediate tetrahedral site with low migration energy of 0.10 eV.The results indicate that the divacancy and trivacancy clusters are not stable,but He atoms can increase the stability of vacancy clusters.The binding energies of an interstitial He atom and an isolated vacancy to a He-V cluster mainly depend on the He/V ratio of the clusters rather than the cluster size.
引文
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