B_2型MoTa合金的嵌入原子法研究
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摘要
由于高温淬火,塑性变形,高能粒子辐照等,致使材料中产生大量点缺陷。点缺陷的存在和扩散强烈地影响了材料的物理性能和机械性能。其能量和动力学特性直接决定了材料中点缺陷的数量及分布随时间的变化,进而改变材料的微观结构。因此,对材料中的点缺陷的研究一直是固体物理学和材料科学研究的重要问题。通过原子级模拟研究其特性,可为材料设计或改性提供参考,也可检验和丰富理论模型,因而具有实际和理论的双重意义。本文应用改进分析型嵌入原子模型(MAEAM)结合分子动力学(MD)模拟计算了B2型MoTa合金的基本物理性质,包括合金平衡晶格常数,形成能,结合能,表面能和表面结构,以及点缺陷的性质。着重研究了点缺陷在该合金体内和表面的形成和迁移机制。计算了相应的形成能和迁移能,根据能量最小化原理,对体内单空位、间隙原子和双空位,以及表面单空位的择优迁移机制做了详细的讨论。得到以下结果：
(1)B2型MoTa合金的平衡晶格常数为3.235A,合金形成能为-0.151eV,这与第一性原理计算所得晶格常数,以及实验所得合金形成能很吻合,说明MAEAM能正确描述该合金的物理性质。同时,计算所得合金结合能为7.611eV,组元Mo和Ta的结合能分别为6.821eV和8.400eV,暂无可比较的其他理论计算值或实验结果；
(2) MoTa合金体内三种孤立点缺陷的形成能分别为：单空位3.233eV,3.218eV;反位置缺陷-0.062eV,0.485eV;间隙原子7.263eV,7.759eV(前者为Mo后者为Ta)。根据能量最小化原理,当偏离理想化学配比时,反位置缺陷最易于形成。在六种空位迁移机制中,破坏了系统的局部有序性的一步最近邻跳(1NNJ)需要最小的能量。空位的一步次近邻跳(1NNNJ)和第三近邻跳(1TNNJ)虽不改变晶格秩序,但需要更高的能量,因而应被诸如S[100]6NNCJ、B[100]6NNCJ和[110]6NNCJ等六步循环跳(6NNCJ)代替。另外,除了1TNNJ,Ta空位的迁移能总是要比Mo空位低,加之前者略低的形成能,Ta空位的扩散激活能也比同样迁移方式下的Mo空位要低。这说明在MoTa合金中,Ta空位的形成和迁移比Mo空位更容易一些。Mo和Ta间隙原子迁移机制,虽然需要较低的迁移能,但是由于其相对较高的形成能,致使间隙原子迁移不是MoTa合金中的主要迁移机制。
(3)在合金体内的六种双空位构型中,稳定的双空位构型依次为INN Mo-Ta, 2NN Ta-Ta和2NN Mo-Mo。而4NN Mo-Ta,3NN Ta-Ta和3NN Mo-Mo是不稳定的,且最终会分别转化为前三种稳定的双空位构型,因而得出空位聚集的结论。考虑到迁移能的最小化并比较一步跳、两步跳和多步跳的迁移能发现,六种双空位的择优迁移方式都是由一系列连续最近跳组成的多步跳。另外,在三种稳定双空位中INN Mo-Ta最易产生且最易迁移,尤其是通过四步最近邻跳；
(4)对于MoTa合金两种截止方式的(001)表面,Ta截止表面能密度比Mo截止表面能密度小,因此Ta截止面更稳定,而且两种截止面的最表层原子都向内弛豫。计算了表面前七层原子的结合能和单空位形成能,以及表面前七层单空位的层内和层间的第一和第二近邻迁移。发现表面的存在对空位的影响可深入到前6层。空位最易于在最上层形成,且表层空位最易于通过第一近邻进行向上的迁移,从而使表面的空位浓度增大,表面有序度降低。
A mass of point defects in material can be induced by high temperature quencher, plastic deformation and high energy particle irradiation. The existence and diffusion of the point defects affect the physical and mechanical properties of the material seriously. The energetic and kinetic properties of point defects determine the temporal defect-population evolution and consequent changes in the material microstructure.Therefore, researches on point defects in material have been hot issues in solid physics and material science. The study on point defects based on atomistic simulation can be taken as reference for material design and improvement, and can also be used to verify and enrich theoretical models.So, this work has important significance theoretically and practically. In the present work, the characteristic properties of B2-type MoTa alloy, including equilibrium lattice constant, formation energy, cohesive energy, surface energy and surface structure, and the properties of point defects, have been investigated by combining molecular dynamics (MD) simulation with modified analytic embedded-atom method (MAEAM).The emphases of the present work are the formation and diffusion mechanisms of the point defects in the bulk and surface of MoTa alloy. The formation and migration energies of the defects were calculated and from the energy minimization, the favorable diffusion mechanisms of the mono-vacancy, interstitial atom and di-vacancy in the bulk and the mono-vacancy in the surface were discussed detailedly. Following results are obtained:
(1)Calculated lattice constant and formation energy of 3.235 A and-0.151eV are in good agreement with the, experimental and ab initio data. The fact proved that the present model is efficacious for the MoTa alloy. The cohesion energies of the alloy, Mo and Ta components are 7.611,6.821 and 8.400eV, respectively. There is no available data to compare with.
(2) The calculated formation energies of Mo and Ta mono-vacancy are 3.233 and 3.218eV,anti-site defect are-0.062 and 0.485eV,and interstitial atom are 7.263 and 7.759eV, respectively. The principle of energy minimization shows that the point defect is the anti-site defect in the nonstoichiometric case. In six migration mechanisms of Mo and Ta mono-vacancies,1NNJ (e.g."INN" means "first nearest neighbour jump" etc) is the most favorable due to its lowest activation and migration energies, but it will result in an anti-site so that a disorder in the order alloy. One 1NNNJ and onel TNNJ can maintain the ordered property of the alloy but require higher activation and migration energies, so the 1NNNJ and 1TNNJ should be replaced by S[100]6NNCJ or B[100]6NNCJ (straight or bent[100] direction six nearest neighbor cyclic jumps) and [110]6NNCJ, respectively. Although the migrations of Mo and Ta interstitial atoms need much lower energy than Mo and Ta mono-vacancies, they are not main migration mechanisms due to difficult to form in the alloy.
(3)For six type di-vacancies in the bulk of MoTa, the stability of the di-vacancy configurations decreases in the direction INN Mo-Ta,2NN Ta-Ta and 2NN Mo-Mo, whereas the 4NN Mo-Ta,3NN Ta-Ta and 3NN Mo-Mo configurations are unstable and tend to congregate to the former three stable configurations. Taking into account the minimization of the migration or activation energies, for all six types of the di-vacancy configurations, the multi-jumps involving a series of INN-jumps are energetically more favorable than either one-jump or two-jump diffusion mechanisms.Furthermore, in the three stable configurations of the INN Mo-Ta di-vacancy is not only easy to form, but also easy to migrate especially by the four-jump mechanism.
(4) The surface energies and the surface relaxations of Mo and Ta termination (001) surfaces have been calculated. The results show that the Ta termination is more stable and the most surface layer relaxes inward for both terminations.The calculated formation energy of the mono-vacancy in the uppermost seven layers shows that the effect of the surface on the vacancy is only down to the sixth layer. It is easier for the vacancy to form in the first layer. Comparing the migration energy of the vacancy migrating in the intra-and inter-layer via INN and 2NN jump, we find that the vacancies in the surface layers is preferred to migrate to the up-layer via INN jump. Thus increase the concentration of vacancy and consequently changes the surface smoothness.
(1)B2型MoTa合金的平衡晶格常数为3.235A,合金形成能为-0.151eV,这与第一性原理计算所得晶格常数,以及实验所得合金形成能很吻合,说明MAEAM能正确描述该合金的物理性质。同时,计算所得合金结合能为7.611eV,组元Mo和Ta的结合能分别为6.821eV和8.400eV,暂无可比较的其他理论计算值或实验结果；
(2) MoTa合金体内三种孤立点缺陷的形成能分别为：单空位3.233eV,3.218eV;反位置缺陷-0.062eV,0.485eV;间隙原子7.263eV,7.759eV(前者为Mo后者为Ta)。根据能量最小化原理,当偏离理想化学配比时,反位置缺陷最易于形成。在六种空位迁移机制中,破坏了系统的局部有序性的一步最近邻跳(1NNJ)需要最小的能量。空位的一步次近邻跳(1NNNJ)和第三近邻跳(1TNNJ)虽不改变晶格秩序,但需要更高的能量,因而应被诸如S[100]6NNCJ、B[100]6NNCJ和[110]6NNCJ等六步循环跳(6NNCJ)代替。另外,除了1TNNJ,Ta空位的迁移能总是要比Mo空位低,加之前者略低的形成能,Ta空位的扩散激活能也比同样迁移方式下的Mo空位要低。这说明在MoTa合金中,Ta空位的形成和迁移比Mo空位更容易一些。Mo和Ta间隙原子迁移机制,虽然需要较低的迁移能,但是由于其相对较高的形成能,致使间隙原子迁移不是MoTa合金中的主要迁移机制。
(3)在合金体内的六种双空位构型中,稳定的双空位构型依次为INN Mo-Ta, 2NN Ta-Ta和2NN Mo-Mo。而4NN Mo-Ta,3NN Ta-Ta和3NN Mo-Mo是不稳定的,且最终会分别转化为前三种稳定的双空位构型,因而得出空位聚集的结论。考虑到迁移能的最小化并比较一步跳、两步跳和多步跳的迁移能发现,六种双空位的择优迁移方式都是由一系列连续最近跳组成的多步跳。另外,在三种稳定双空位中INN Mo-Ta最易产生且最易迁移,尤其是通过四步最近邻跳；
(4)对于MoTa合金两种截止方式的(001)表面,Ta截止表面能密度比Mo截止表面能密度小,因此Ta截止面更稳定,而且两种截止面的最表层原子都向内弛豫。计算了表面前七层原子的结合能和单空位形成能,以及表面前七层单空位的层内和层间的第一和第二近邻迁移。发现表面的存在对空位的影响可深入到前6层。空位最易于在最上层形成,且表层空位最易于通过第一近邻进行向上的迁移,从而使表面的空位浓度增大,表面有序度降低。
A mass of point defects in material can be induced by high temperature quencher, plastic deformation and high energy particle irradiation. The existence and diffusion of the point defects affect the physical and mechanical properties of the material seriously. The energetic and kinetic properties of point defects determine the temporal defect-population evolution and consequent changes in the material microstructure.Therefore, researches on point defects in material have been hot issues in solid physics and material science. The study on point defects based on atomistic simulation can be taken as reference for material design and improvement, and can also be used to verify and enrich theoretical models.So, this work has important significance theoretically and practically. In the present work, the characteristic properties of B2-type MoTa alloy, including equilibrium lattice constant, formation energy, cohesive energy, surface energy and surface structure, and the properties of point defects, have been investigated by combining molecular dynamics (MD) simulation with modified analytic embedded-atom method (MAEAM).The emphases of the present work are the formation and diffusion mechanisms of the point defects in the bulk and surface of MoTa alloy. The formation and migration energies of the defects were calculated and from the energy minimization, the favorable diffusion mechanisms of the mono-vacancy, interstitial atom and di-vacancy in the bulk and the mono-vacancy in the surface were discussed detailedly. Following results are obtained:
(1)Calculated lattice constant and formation energy of 3.235 A and-0.151eV are in good agreement with the, experimental and ab initio data. The fact proved that the present model is efficacious for the MoTa alloy. The cohesion energies of the alloy, Mo and Ta components are 7.611,6.821 and 8.400eV, respectively. There is no available data to compare with.
(2) The calculated formation energies of Mo and Ta mono-vacancy are 3.233 and 3.218eV,anti-site defect are-0.062 and 0.485eV,and interstitial atom are 7.263 and 7.759eV, respectively. The principle of energy minimization shows that the point defect is the anti-site defect in the nonstoichiometric case. In six migration mechanisms of Mo and Ta mono-vacancies,1NNJ (e.g."INN" means "first nearest neighbour jump" etc) is the most favorable due to its lowest activation and migration energies, but it will result in an anti-site so that a disorder in the order alloy. One 1NNNJ and onel TNNJ can maintain the ordered property of the alloy but require higher activation and migration energies, so the 1NNNJ and 1TNNJ should be replaced by S[100]6NNCJ or B[100]6NNCJ (straight or bent[100] direction six nearest neighbor cyclic jumps) and [110]6NNCJ, respectively. Although the migrations of Mo and Ta interstitial atoms need much lower energy than Mo and Ta mono-vacancies, they are not main migration mechanisms due to difficult to form in the alloy.
(3)For six type di-vacancies in the bulk of MoTa, the stability of the di-vacancy configurations decreases in the direction INN Mo-Ta,2NN Ta-Ta and 2NN Mo-Mo, whereas the 4NN Mo-Ta,3NN Ta-Ta and 3NN Mo-Mo configurations are unstable and tend to congregate to the former three stable configurations. Taking into account the minimization of the migration or activation energies, for all six types of the di-vacancy configurations, the multi-jumps involving a series of INN-jumps are energetically more favorable than either one-jump or two-jump diffusion mechanisms.Furthermore, in the three stable configurations of the INN Mo-Ta di-vacancy is not only easy to form, but also easy to migrate especially by the four-jump mechanism.
(4) The surface energies and the surface relaxations of Mo and Ta termination (001) surfaces have been calculated. The results show that the Ta termination is more stable and the most surface layer relaxes inward for both terminations.The calculated formation energy of the mono-vacancy in the uppermost seven layers shows that the effect of the surface on the vacancy is only down to the sixth layer. It is easier for the vacancy to form in the first layer. Comparing the migration energy of the vacancy migrating in the intra-and inter-layer via INN and 2NN jump, we find that the vacancies in the surface layers is preferred to migrate to the up-layer via INN jump. Thus increase the concentration of vacancy and consequently changes the surface smoothness.
引文
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