Influence of non-glide stresses on the peierls energy of screw dislocations
Influence of non-glide stresses on the peierls energy of screw dislocations
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非滑移应力对螺旋位错佩尔斯能的影响
DOI：
10.1299/transjsme.2014cm0018
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
K. Ushioda
中科院分区：
文献类型：
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作者：
K. Kinoshita;T. Shimokawa;T. Kinari;H. Sawada;K. Kawakami;K. Ushioda
我们利用微推弹性带方法研究了非滑移应力对螺旋位错 Peierls 能量的影响。可以清楚地观察到所施加的非滑动应力场对螺旋位错 Peierls 能量的影响。此外，我们发现在特定的施加应力场下，Peierls 能量的应力场依赖性会随着螺旋位错的移动方向而改变。引入可以测量螺旋位错核周围原子弹性变形的几何参数来解释 Peierls 能量的应力场依赖性。最后，通过将沉淀物周围的应力场的解析解与我们的原子模拟获得的几何参数相结合，讨论了具有失配应变的沉淀物周围的螺旋位错的交叉滑移。 * 兵库县尼崎市扶桑町 1-8 先进技术研究中心基础冶金研究室 工程博士660-0891 新日铁住友金属技术报告第 114 期 2017 年 3 月 62 ic 模拟，开源 LAMMPS 5) 被使用，并且使用微推弹性带 (NEB) 方法 6) 获得 Peierls 能量的应力场依赖性。本文第二章描述了分析模型和原子间势能。第三章描述了非滑移应力对螺旋位错Peierls能的影响，并在不同周期边界条件和原子间势能下研究了所得结果的有效性。第四章通过关注位错核附近原子结构的变化来思考非滑移应力改变Peierls能的原因。此外，还考虑了共格析出物周围的应力场如何影响螺型位错的交叉滑移。最后，第五章给出了本文的结论。 2 分析模型和分析条件 2.1 分析模型 本研究中的分析目标是α-Fe。 x、y和z方向上的晶体取向分别为[112_]、[111]和[11_0]。这里，α-Fe的晶格常数为a0。三个向量定义为 v[112] = a0 [112 _ ] / 3、v[111] = a0 [111] / 2 和 v[110] = a0 [11 _ 0]。使用这些向量，具有两个不同周期性边界条件的分析区域 ei 如下所示。第一个模型 ei s 为： e1 s = 14 v[112], e2 s = 16 v[111], e3 s = 24 v[110] + v[111] (1) 在本研究中，这称为平方模型。第二个模型 ei p 为： e1 p = 14 v[112], e2 p = 16 v[111], e3 p = 24 v[110] + 7 v[112] + v[111] (2) 这称为平行四边形模型。图1（a）（b）显示了每个模型的分析区域，表明这两个分析模型之间的差异在于z方向的周期性边界条件。对于每个模型，x 方向上距离为 5 nm 的螺旋位错对放置在中心。图1(a)(b)显示了包含螺旋位错对的每个模型的τyz应力场。在本研究中，左侧的螺型位错被称为S1，右侧的螺型位错被称为S2。由于S1的螺型位错的伯格斯矢量为bS1 = 1/2 [111]，因此S2的螺型位错的伯格斯矢量为bS2 = -bS1。如后所述，由于本研究主要关注易核螺型位错的运动，因此在应用周期性边界条件的分析模型中，需要注意的是，相邻螺型位错之间的 x 方向距离（S1 和 S2 之间的距离以及 S2 和 S1' 之间的距离）并不严格相等。 （距离差小于 a0。）每个模型在 z 方向上使用不同的周期性边界条件。如图1（a）所示，在正方形模型中，具有相同Burgers矢量的位错在z方向上周期性排列。相反，如图1（b）所示，在平行四边形模型中，在z方向上具有不同Burgers矢量的螺旋位错是周期性排列的。相邻位错之间的相互作用是不同的，从图1（a）（b）中可以证实分析区存在不同的应力场。这里，对于两个模型，e3 在 y 方向上倾斜 1/2 v[111]。这相当于将螺旋位错对放入计算单元中所产生的塑性应变。考虑到这个 1/2 v[111]，系统中的平均应力 τyz 可以为零。利用上述分析模型，考虑了非滑移应力对螺型位错Peierls能的影响。此外，通过比较两种分析模型的结果，考虑了螺位错周期结构差异的影响。 bcc金属的螺位错核根据其原子几何形状具有能量稳定的易核和不稳定的硬核。图1(c)显示了bcc结构的{111}平面。这里，圆圈表示原子，色差表示[111]方向的深度差。从该图可以确认{111}面具有三层周期结构。在易核中，如果将螺旋位错的位移叠加到bcc结构上，则位错核的每个原子构型都保持与完美晶体相同的三层结构。 （图1（c）中绘制方块表示的位置对应于易核。）然而，在硬核中，位错核的原子构型存在于同一{111}平面上。 （换句话说，位错核的原子构型具有相同的颜色。）因此，硬核的相邻原子之间的距离比易核的相邻原子之间的距离更短，位错的能量变得更高。7）在本研究中，考虑了存在于易核中的螺旋位错到另一个相邻的易核的转移现象。 2.2 原子间势 使用两个原子间势来表示 α-Fe 作为原子间相互作用。一种是 Chamati 等人提出的嵌入式原子方法 (EAM) 8)。另一个是 Mendelev 等人提出的 EAM 潜力。9) Mendelev 等人。研究了五种类型的电势，其中最能描述 BCC 铁缺陷结构的电势被用作另一种电势。通过比较非滑移应力对这两个原子间势得到的螺旋位错 Peierls 能的影响，得到结果的有效性 1 2
We investigate the influence of non-glide stresses on the Peierls energy of screw dislocation by using Nudged-Elastic-Band method. The influence of the applied non-glide stress fields on the Peierls energy of a screw dislocation is clearly observed. Moreover, we find that the stress field dependence of the Peierls energy is changed by the moving direction of the screw dislocation under a specific applied stress field. Geometrical parameters, which can measure the atomic elastic deformation around the screw dislocation core, are introduced to explain the stress field dependence of the Peierls energy. Finally, the cross slip of a screw dislocation around a precipitate with a misfit strain is discussed by combining the analytical solution of stress fields around the precipitate with the geometrical parameters obtained by our atomic simulations. * Dr.Eng., Fundamental Metallurgy Research Lab., Advanced Technology Research Laboratories 1-8 Fuso-cho, Amagasaki, Hyogo Pref. 660-0891 NIPPON STEEL & SUMITOMO METAL TECHNICAL REPORT No. 114 MARCH 2017 62 ic simulation, open-sourced LAMMPS 5) is used and the stress field dependency of the Peierls energy is obtained by using the Nudged Elastic Band (NEB) method 6). In this paper, Chapter 2 describes the analysis model and the inter-atomic potential energy. Chapter 3 describes the influence of the non-glide stress on the Peierls energy of the screw dislocation, and the validity of the results obtained is investigated under different periodic boundary conditions and the inter-atomic potential energy. In Chapter 4, why the Peierls energy is changed by the non-glide stress is considered by focusing on the change of the atomic structure near the dislocation core. In addition, how the stress field around the coherent precipitate exerts influence on the cross-slip of the screw dislocation is considered. Lastly, the conclusion of this paper is given in Chapter 5. 2. Analysis Model and Analysis Conditions 2.1 Analysis model In this study, the analysis target is α-Fe. The crystal orientations in the directions of x, y and z are [112 _ ], [111] and [11 _ 0], respectively. Here, the lattice constant of α-Fe is a0. Three vectors are defined as v[112] = a0 [112 _ ] / 3, v[111] = a0 [111] / 2 and v[110] = a0 [11 _ 0]. Using these vectors, analysis zone ei , which has two different periodic boundary conditions is indicated as follows. First model ei s is: e1 s = 14 v[112], e2 s = 16 v[111], e3 s = 24 v[110] + v[111] (1) In this study, this is called the square model. Second model ei p is: e1 p = 14 v[112], e2 p = 16 v[111], e3 p = 24 v[110] + 7 v[112] + v[111] (2) This is called the parallelogram model. Figure 1 (a)(b) shows the analysis zone of each model, indicating that the difference between these two analysis models is the periodic boundary condition in the z direction. For each model, a screw dislocation pair with a distance of 5 nm in between in the x direction is placed at the center. Figure 1 (a)(b) shows the τyz stress field of each model including the screw dislocation pair. In this study, the screw dislocation on the left is referred to as S1 and the screw dislocation on the right is referred to as S2. Since the screw dislocation of S1 has the Burgers vector of bS1 = 1/2 [111], the screw dislocation of S2 has the Burgers vector of bS2 = −bS1. As described later, since this study focuses on the motion of easy-core screw dislocation, in this analysis model to which the periodic boundary conditions are applied, it is necessary to note that the distance in the x direction (distance between S1 and S2 and distance between S2 and S1') between adjacent screw dislocations is not strictly equal. (The difference of the distances is smaller than a0.) Each model uses different periodic boundary conditions in the z direction. As shown in Fig. 1 (a), in the square model, the dislocations that have the same Burgers vector are periodically aligned in the z direction. In contrast, as shown in Fig. 1 (b), in the parallelogram model, the screw dislocations that have different Burgers vector in the z direction are periodically aligned. The interaction between adjacent dislocations is different, and the different stress field in the analysis zone can be confirmed from Fig. 1 (a)(b). Here, e3 is inclined in the y direction by 1/2 v[111] for both models. This is equivalent to the plastic strain generated by putting the screw dislocation pair in the calculation cell. Considering this 1/2 v[111], average stress τyz in the system can be made zero. Using the analysis model above, the influence of the non-glide stress on the Peierls energy of the screw dislocation is considered. In addition, by comparing the results obtained from two analysis models, the influence of the difference of the periodic structure of the screw dislocation is considered. The screw dislocation core of bcc metal has energetically stable easy-cores and unstable hard-cores depending on its atomic geometry. Figure 1 (c) shows the {111} plane of the bcc structure. Here, the circles indicate atoms and the color difference indicates the depth difference in the [111] direction. From this figure, it is confirmed that the {111} plane has the three-layer periodic structure. In an easy-core, if displacement of the screw dislocation is superposed onto a bcc structure, each atomic configuration of the dislocation core maintains the three-layer structure that is the same as a perfect crystal. (The positions indicated by plotting squares in Fig. 1 (c) correspond to easy-cores.) However, in a hard-core, atomic configurations of the dislocation core exist on the same {111} plane. (In other words, atomic configuration of the dislocation core has the same color.) Therefore, the distance between adjacent atoms of a hardcore is shorter than that of an easy-core and the energy of dislocation becomes higher.7) In this study, a transfer phenomenon of the screw dislocation that exists in an easy-core to another adjacent easy-core is considered. 2.2 Inter-atomic potential Two inter-atomic potentials to indicate α-Fe as the inter-atomic interaction are used. One is the embedded atomic method (EAM) 8) by Chamati, et al. and the other is the EAM potential by Mendelev, et al.9) Mendelev, et al. have studied five types of potentials, from which a potential that best describes a defect structure in bcc iron is used as the other one. By comparing the influence of non-glide stress on the Peierls energy of the screw dislocation obtained from these two inter-atomic potentials, the validity of the result obtained 1 2
影响因子：
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作者：
HONEYCUTT, JD;ANDERSEN, HC
通讯作者：
ANDERSEN, HC