二维原子团簇和缺陷团簇的跃迁及扩散行为研究
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摘要
本文以几种典型的BCC结构金属、合金和萤石结构氧化物UO2作为研究对象,选取能够合理描述原子间相互作用的势函数模型,对晶体中点缺陷团簇和金属表面原子团簇的跃迁和扩散行为展开了系统的研究,并得到与实验一致的结果。在Fe-Cr合金体系中,研究Cr-V原子空位对的最小能量路径,发现Cr原子的长程跃迁是通过空位辅助机制完成的。单个Cr替位原子跃迁至近邻空位位置所需能量为0.56eV,但单独依靠这一机制无法完成Cr原子的长程跃迁,除非体系中有过饱和浓度的空位分布。Cr-V原子空位团簇的迁移过程是通过自空位辅助跃迁机制,即Fe原子和Cr原子相继跃迁至最近邻空位来完成,它可以导致Cr原子的长程跃迁,其跃迁能量势垒范围为0.64-0.89eV。NEB研究结果表明在α-Fe体系中,混合型Cr-Fe哑铃状填隙原子对很容易发生跃迁,所需能量为0.17eV,低于Fe-Fe哑铃状填隙原子对跃迁所需能量。其中,Cr-Fe填隙原子对的原地旋转和Cr原子的最近邻跃迁是完成一次净跃迁过程的主要跃迁机制。对Cr空位团簇的结合能计算结果发现,团簇的结合能强烈依赖于缺陷团簇的尺寸和缺陷团簇中Cr原子的含量。
选用Yakub势函数描述U、O和Xe原子之间的相互作用,所计算的跃迁势垒与实验值符合得很好。在UO2体系中,单空位的跃迁通过空位机制完成,其中单铀空位跃迁的能量势垒高于单氧空位跃迁所需能量。完成双氧空位净跃迁所需能量势垒为0.85eV,能量势垒的计算结果表明具有双空位结构的缺陷团簇易于发生空位的解离。在引入裂变气体Xe后,缺陷团簇有了更为复杂和多样的跃迁行为。Xe填隙原子在近邻没有空位存在的情况下很难发生跃迁,当第一近邻位置引入空位后,通过空位辅助跃迁机制使Xe填隙原子的跃迁势垒减少了1.50eV。计算结果还表明,U空位捕获Xe原子后形成替位原子,由Xe替位原子和U空位组成的缺陷团簇的跃迁势垒较高,且无法发生Xe原子的长程跃迁。较之U空位对Xe原子的捕获能力,O空位对Xe原子的捕获能力则较弱,位于O空位的Xe替位原子很容易通过简单跃迁机制直接跃迁至八面体间隙位置,并且终态结构能量更稳定。对于包含两个及以上空位的缺陷团簇,能量势垒结果同样表明空位聚集现象不会发生,双氧空位只需要很低的能量势垒就可以发生空位的解离。在Xe填隙原子和双氧空位组成的缺陷团簇中,最近邻氧空位的作用使八面体间隙位置不再是Xe原子的稳定位置,Xe填隙原子可以占据相邻U原子晶格位置,而U原子被推挤至相邻八面体间隙成为填隙原子,这一过程所需能量势垒为0.16eV。
采用dimer方法寻找可能跃迁过程的最小能量路径,研究W团簇在W纳米颗粒表面的跃迁机制、可能路径及相应的势垒能量。钨团簇结合能的计算结果表明,W团簇更趋向于在颗粒表面形成二维密排结构。相比纳米颗粒尺寸的影响,菱形十二面体界面和顶角区域对团簇跃迁行为有更明显的影响。当团簇位于边界和顶角区域时,基体原子倾向参与扩散团簇的跃迁,并形成更大的团簇继续迁移,或者通过与基体原子的交换导致团簇的解离。三聚体团簇的跃迁能量势垒表明整体跃迁机制比单原子的相继跃迁更能准确描述三聚体的跃迁行为,这是因为三聚体为密排结构,打破这样一个密排结构要求更高的能量势垒。由于四聚体的高对称性,四聚体的跃迁需要克服更高的能量势垒,dimer剪切过程是四聚体跃迁的主要机制。
采用分子动力学结合描述原子间相互作用的分析型嵌入势模型,对原子团簇在BCC(110)金属表面的自扩散动力学行为进行了系统的研究。淬火分子动力学得到的团簇结合能表明,扩散团簇的稳定构型为密排小岛结构。同时,长时分子动力学模拟得到二维团簇表面扩散的相关表征量,如扩散迁移能、扩散系数及扩散前因子,其中扩散迁移能随团簇尺寸的变化呈现非单调振荡增加的趋势。与拥有非对称性的二维团簇结构相比,密排封闭团簇结构(如四聚体和七聚体)有着明显较高的扩散迁移能。并且,采用NEB方法着重分析了W四聚体、五聚体、六聚体和七聚体的速率限制步骤所需克服的能量,以及完成一次四聚体和五聚体团簇净跃迁过程的最小能量路径。扩散机制的讨论表明,较大尺寸的二维原子团簇的扩散主要通过外围原子的跃迁、二聚体滑移或组态变化等扩散机制的共同作用来完成。
本文中所使用的两种寻找最小能量路径的方法可以很好地描述原子团簇和缺陷团簇的表面扩散与体扩散过程,并且得到了一些与实验相符的结果,说明这些方法在处理跃迁和扩散问题中具有很好的普适性和实用性。
In the present work, the appropriate empirical interatomic potentials are employed to describe the interactions between atoms in typical bcc metals, alloy and UO2. And thus the migration and diffusion behaviors of defect clusters in bulk and atomic clusters on metal surfaces have been studied systematically, which are consisted with the experimental results.
In Fe-Cr alloy systems, it is found for the first time that the Cr migration in Fe is controlled by a vacancy-assistant mechanism, and the corresponding minimum energy paths of Cr-vacancy (Cr-V) clusters and Cr interstitials inα-Fe have been determined. A substitutional Cr atom can migrate to a nearest-neighbor vacancy through an energy barrier of 0.56 eV but this simple mechanism alone is unlikely to lead to the long-distance migration of Cr unless there is a supersaturated concentration of vacancies in the system. The Cr-vacancy clusters can lead to long-distance migration of a Cr atom that is accomplished by Fe and Cr atoms successively jumping to nearest-neighbor vacancy positions, defined as a self-vacancy-assisted migration mechanism, with the migration energies ranging from 0.64 to 0.89 eV. In addition, using the NEB method, a mixed Cr-Fe dumbbell interstitial can easily migrate through Fe lattices, with the migration energy barrier of 0.17, which is lower than that of the Fe-Fe interstitial. The on-site rotation of the Cr-Fe interstitial and Cr atom hopping from one site to another are believed to comprise the dominant migration mechanism. The calculated binding energies of Cr-V clusters are strongly depend on the size of clusters and the concentration of Cr atoms in clusters.
The Xe-Xe, Xe-O and Xe-U interatomic potential were described using a potential model by Yakub. The calculated energy barriers in Xe-U-O systems show that the potential of Yakub gives a better description of the migration properties. A single vacancy can migrate through the vacancy mechanism. Moreover, the energy barrier of a U-vacancy is higher than that for an O-vacancy. The net migration of an O-divacancy needs to overcome an energy barrier of 0.85eV, while the dissociation energy of the divacancy is only 0.05eV, which suggests that the O-divacancy tends to dissociate. The migration behaviors of defect clusters become more complex and various by introducing fission gases, xenon. In the case of the interstitial Xe atom migration without vacancies at nearest neighboring sites, the energy barrier is very high after introducing an O-vacancy at the nearest neighboring site, the migration barrier of interstitial Xe atom is lowered by 1.50eV via vacancy-assisted migration mechanism. The Xe atom is easy to be trapped at the U-vacancy, becoming a substitutional atom. The relatively large energy implies that, if a Xe is trapped at a U-vacancy, it can hardly lead to a long distance migration. On the other hand, the energy of a Xe trapped at the O-vacancy is lower. As a result, the substitutional Xe atom at the O-vacancy is expected to move to the octahedral interstitial site via the direct migration mechanism. The octahedral interstitial site was found to be the most stable configuration for Xe. For a defect cluster including two or more vacancies, vacancy aggregation did not happen and divacancy is more likely to dissociate. Particularly, for a defect cluster including an interstitial Xe atom and the O-divacancy, the octahedral interstitial site is unstable for Xe due to the existence of the O-divacancy. The energy barrier for the interstitial Xe to form a substitutional Xe atom and an interstitutional U atom was calculated to be 0.16eV.
The dimer method presented here for effective finding the minimum energy path has been employed to investigate the migration mechanisms of W clusters on W nanoparticles, and to determine the corresponding migration energies for the possible migration paths of these clusters. The tungsten clusters containing up to four adatoms are found to prefer 2D-compact structures with relatively low binding energies. The effect of interface and vertex regions on the migration behavior of the clusters is significantly strong, as compared to that of nanoparticle size. The migration mechanisms are quite different when the clusters are located at the center of the nanoparticle and near the interface or vertex areas. Near the interfaces and vertex areas, the substrate atoms tend to participate in the migration processes of the clusters, and can join the adatoms to form a larger cluster or lead to the dissociation of a cluster via the exchange mechanism, which results in the adatom crossing the facets. The calculated energy barriers for the trimers suggest that the concerted migration is more probable than the successive jumping of a single adatom in the clusters. One atom of the trimer jumps to the next nearest neighbor position, leading to a non-compact triangular trimer with a higher energy barrier. In addition, it is of interest to note that the dimer shearing is a dominate migration mechanism for the tetramer, but needs to overcome a relatively higher migration energy than other clusters.
The dynamic self-diffusion behaviors of clusters on a bcc (110) surface have been investigated using molecular dynamics simulations based on a modified analytic embedded-atom method. The stable configurations of clusters are predicted to be close-packed islands configurations for Fe and W cluster size up to nine atoms or even larger by the quenched MD simulation. The characterizations of diffusion behavior, such as the migration energy, the diffusion coefficient and the diffusion prefactor, can be obtained by the MD simulation for a long enough time. The migration energies show an interesting and oscillating behavior with increasing cluster size. As compared to the structures with extra atoms at the periphery, the compact geometric configurations of clusters (four- and seven-atom clusters) have an obviously higher migration energy. Moreover, the NEB method is employed to obtain the energies of the rate-limiting steps in the migration processes of W4, W5, W6 and W7, and also determine the minimum energy paths of the net migration process for tetramer and pentamer, respectively. The diffusion mechanism of 2D small clusters containing more than two atoms is achieved by the migration of extra atoms at the periphery, the dimer-shearing mechanism and the changes of the cluster shape.
Surface diffusion of atomic clusters and lattice diffusion of defect clusters could be achieved with the dimer method and NEB method for finding a minimum energy path. In principle the methods could be used to establish the understanding of migration and diffusion behaviors in the atomic scale effectively.
选用Yakub势函数描述U、O和Xe原子之间的相互作用,所计算的跃迁势垒与实验值符合得很好。在UO2体系中,单空位的跃迁通过空位机制完成,其中单铀空位跃迁的能量势垒高于单氧空位跃迁所需能量。完成双氧空位净跃迁所需能量势垒为0.85eV,能量势垒的计算结果表明具有双空位结构的缺陷团簇易于发生空位的解离。在引入裂变气体Xe后,缺陷团簇有了更为复杂和多样的跃迁行为。Xe填隙原子在近邻没有空位存在的情况下很难发生跃迁,当第一近邻位置引入空位后,通过空位辅助跃迁机制使Xe填隙原子的跃迁势垒减少了1.50eV。计算结果还表明,U空位捕获Xe原子后形成替位原子,由Xe替位原子和U空位组成的缺陷团簇的跃迁势垒较高,且无法发生Xe原子的长程跃迁。较之U空位对Xe原子的捕获能力,O空位对Xe原子的捕获能力则较弱,位于O空位的Xe替位原子很容易通过简单跃迁机制直接跃迁至八面体间隙位置,并且终态结构能量更稳定。对于包含两个及以上空位的缺陷团簇,能量势垒结果同样表明空位聚集现象不会发生,双氧空位只需要很低的能量势垒就可以发生空位的解离。在Xe填隙原子和双氧空位组成的缺陷团簇中,最近邻氧空位的作用使八面体间隙位置不再是Xe原子的稳定位置,Xe填隙原子可以占据相邻U原子晶格位置,而U原子被推挤至相邻八面体间隙成为填隙原子,这一过程所需能量势垒为0.16eV。
采用dimer方法寻找可能跃迁过程的最小能量路径,研究W团簇在W纳米颗粒表面的跃迁机制、可能路径及相应的势垒能量。钨团簇结合能的计算结果表明,W团簇更趋向于在颗粒表面形成二维密排结构。相比纳米颗粒尺寸的影响,菱形十二面体界面和顶角区域对团簇跃迁行为有更明显的影响。当团簇位于边界和顶角区域时,基体原子倾向参与扩散团簇的跃迁,并形成更大的团簇继续迁移,或者通过与基体原子的交换导致团簇的解离。三聚体团簇的跃迁能量势垒表明整体跃迁机制比单原子的相继跃迁更能准确描述三聚体的跃迁行为,这是因为三聚体为密排结构,打破这样一个密排结构要求更高的能量势垒。由于四聚体的高对称性,四聚体的跃迁需要克服更高的能量势垒,dimer剪切过程是四聚体跃迁的主要机制。
采用分子动力学结合描述原子间相互作用的分析型嵌入势模型,对原子团簇在BCC(110)金属表面的自扩散动力学行为进行了系统的研究。淬火分子动力学得到的团簇结合能表明,扩散团簇的稳定构型为密排小岛结构。同时,长时分子动力学模拟得到二维团簇表面扩散的相关表征量,如扩散迁移能、扩散系数及扩散前因子,其中扩散迁移能随团簇尺寸的变化呈现非单调振荡增加的趋势。与拥有非对称性的二维团簇结构相比,密排封闭团簇结构(如四聚体和七聚体)有着明显较高的扩散迁移能。并且,采用NEB方法着重分析了W四聚体、五聚体、六聚体和七聚体的速率限制步骤所需克服的能量,以及完成一次四聚体和五聚体团簇净跃迁过程的最小能量路径。扩散机制的讨论表明,较大尺寸的二维原子团簇的扩散主要通过外围原子的跃迁、二聚体滑移或组态变化等扩散机制的共同作用来完成。
本文中所使用的两种寻找最小能量路径的方法可以很好地描述原子团簇和缺陷团簇的表面扩散与体扩散过程,并且得到了一些与实验相符的结果,说明这些方法在处理跃迁和扩散问题中具有很好的普适性和实用性。
In the present work, the appropriate empirical interatomic potentials are employed to describe the interactions between atoms in typical bcc metals, alloy and UO2. And thus the migration and diffusion behaviors of defect clusters in bulk and atomic clusters on metal surfaces have been studied systematically, which are consisted with the experimental results.
In Fe-Cr alloy systems, it is found for the first time that the Cr migration in Fe is controlled by a vacancy-assistant mechanism, and the corresponding minimum energy paths of Cr-vacancy (Cr-V) clusters and Cr interstitials inα-Fe have been determined. A substitutional Cr atom can migrate to a nearest-neighbor vacancy through an energy barrier of 0.56 eV but this simple mechanism alone is unlikely to lead to the long-distance migration of Cr unless there is a supersaturated concentration of vacancies in the system. The Cr-vacancy clusters can lead to long-distance migration of a Cr atom that is accomplished by Fe and Cr atoms successively jumping to nearest-neighbor vacancy positions, defined as a self-vacancy-assisted migration mechanism, with the migration energies ranging from 0.64 to 0.89 eV. In addition, using the NEB method, a mixed Cr-Fe dumbbell interstitial can easily migrate through Fe lattices, with the migration energy barrier of 0.17, which is lower than that of the Fe-Fe interstitial. The on-site rotation of the Cr-Fe interstitial and Cr atom hopping from one site to another are believed to comprise the dominant migration mechanism. The calculated binding energies of Cr-V clusters are strongly depend on the size of clusters and the concentration of Cr atoms in clusters.
The Xe-Xe, Xe-O and Xe-U interatomic potential were described using a potential model by Yakub. The calculated energy barriers in Xe-U-O systems show that the potential of Yakub gives a better description of the migration properties. A single vacancy can migrate through the vacancy mechanism. Moreover, the energy barrier of a U-vacancy is higher than that for an O-vacancy. The net migration of an O-divacancy needs to overcome an energy barrier of 0.85eV, while the dissociation energy of the divacancy is only 0.05eV, which suggests that the O-divacancy tends to dissociate. The migration behaviors of defect clusters become more complex and various by introducing fission gases, xenon. In the case of the interstitial Xe atom migration without vacancies at nearest neighboring sites, the energy barrier is very high after introducing an O-vacancy at the nearest neighboring site, the migration barrier of interstitial Xe atom is lowered by 1.50eV via vacancy-assisted migration mechanism. The Xe atom is easy to be trapped at the U-vacancy, becoming a substitutional atom. The relatively large energy implies that, if a Xe is trapped at a U-vacancy, it can hardly lead to a long distance migration. On the other hand, the energy of a Xe trapped at the O-vacancy is lower. As a result, the substitutional Xe atom at the O-vacancy is expected to move to the octahedral interstitial site via the direct migration mechanism. The octahedral interstitial site was found to be the most stable configuration for Xe. For a defect cluster including two or more vacancies, vacancy aggregation did not happen and divacancy is more likely to dissociate. Particularly, for a defect cluster including an interstitial Xe atom and the O-divacancy, the octahedral interstitial site is unstable for Xe due to the existence of the O-divacancy. The energy barrier for the interstitial Xe to form a substitutional Xe atom and an interstitutional U atom was calculated to be 0.16eV.
The dimer method presented here for effective finding the minimum energy path has been employed to investigate the migration mechanisms of W clusters on W nanoparticles, and to determine the corresponding migration energies for the possible migration paths of these clusters. The tungsten clusters containing up to four adatoms are found to prefer 2D-compact structures with relatively low binding energies. The effect of interface and vertex regions on the migration behavior of the clusters is significantly strong, as compared to that of nanoparticle size. The migration mechanisms are quite different when the clusters are located at the center of the nanoparticle and near the interface or vertex areas. Near the interfaces and vertex areas, the substrate atoms tend to participate in the migration processes of the clusters, and can join the adatoms to form a larger cluster or lead to the dissociation of a cluster via the exchange mechanism, which results in the adatom crossing the facets. The calculated energy barriers for the trimers suggest that the concerted migration is more probable than the successive jumping of a single adatom in the clusters. One atom of the trimer jumps to the next nearest neighbor position, leading to a non-compact triangular trimer with a higher energy barrier. In addition, it is of interest to note that the dimer shearing is a dominate migration mechanism for the tetramer, but needs to overcome a relatively higher migration energy than other clusters.
The dynamic self-diffusion behaviors of clusters on a bcc (110) surface have been investigated using molecular dynamics simulations based on a modified analytic embedded-atom method. The stable configurations of clusters are predicted to be close-packed islands configurations for Fe and W cluster size up to nine atoms or even larger by the quenched MD simulation. The characterizations of diffusion behavior, such as the migration energy, the diffusion coefficient and the diffusion prefactor, can be obtained by the MD simulation for a long enough time. The migration energies show an interesting and oscillating behavior with increasing cluster size. As compared to the structures with extra atoms at the periphery, the compact geometric configurations of clusters (four- and seven-atom clusters) have an obviously higher migration energy. Moreover, the NEB method is employed to obtain the energies of the rate-limiting steps in the migration processes of W4, W5, W6 and W7, and also determine the minimum energy paths of the net migration process for tetramer and pentamer, respectively. The diffusion mechanism of 2D small clusters containing more than two atoms is achieved by the migration of extra atoms at the periphery, the dimer-shearing mechanism and the changes of the cluster shape.
Surface diffusion of atomic clusters and lattice diffusion of defect clusters could be achieved with the dimer method and NEB method for finding a minimum energy path. In principle the methods could be used to establish the understanding of migration and diffusion behaviors in the atomic scale effectively.
引文
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