Research Institute for Ubiquitous Energy Devices, National Institute for Advanced Industrial Science and Technology, Ikeda, Osaka, Japan.
J Phys Condens Matter. 2013 Apr 3;25(13):135004. doi: 10.1088/0953-8984/25/13/135004. Epub 2013 Mar 11.
We present first-principle calculations on symmetric tilt grain boundaries (GBs) in bcc Fe. Using density functional theory (DFT), we studied the structural, electronic and magnetic properties of Σ3(111) and Σ11(332) GBs formed by rotation around the [110] axis. The optimized structures, GB energies and GB excess free volumes are consistent with previous DFT and classical simulation studies. The GB configurations can be interpreted by the structural unit model as given by Nakashima and Takeuchi (2000 ISIJ 86 357). Both the GBs are composed of similar structural units of three- and five-membered rings with different densities at the interface according to the rotation angle. The interface atoms with larger atomic volumes reveal higher magnetic moments than the bulk value, while the interface atoms with shorter bond lengths have reduced magnetic moments in each GB. The charge density and local density of states reveal that the interface bonds with short bond lengths have more covalent nature, where minority-spin electrons play a dominant role as the typical nature of ferromagnetic Fe. In order to understand the structural stability of these GBs, we calculated the local energy and local stress for each atomic region using the scheme of Shiihara et al (2010 Phys. Rev. B 81 075441). In each GB, the interface atoms with larger atomic volumes and enhanced magnetic moments reveal larger local energy increase and tensile stress. The interface atoms constituting more covalent-like bonds with reduced magnetic moments have lower local energy increase, contributing to the stabilization, while compressive stress is generated at these atoms. The relative stability between the two GBs can be understood by the local energies at the structural units. The local energy and local stress analysis is a powerful tool to investigate the structural properties of GBs based on the behavior of valence electrons.
我们对 bcc Fe 中的对称倾斜晶界（GB）进行了第一性原理计算。使用密度泛函理论（DFT），我们研究了绕[110]轴旋转形成的Σ3（111）和Σ11（332）GB 的结构、电子和磁性性质。优化的结构、GB 能量和 GB 过剩自由体积与之前的 DFT 和经典模拟研究一致。根据 Nakashima 和 Takeuchi（2000 ISIJ 86 357）提出的结构单元模型，可以解释 GB 构型。两个 GB 都由具有不同密度的三元和五元环的类似结构单元组成，具体取决于旋转角度。界面原子的原子体积越大，磁矩越高，超出体值，而键长较短的界面原子在每个 GB 中的磁矩降低。电荷密度和局域态密度表明，键长较短的界面键具有更多的共价性质，其中少数自旋电子起主导作用，为典型的铁磁 Fe。为了理解这些 GB 的结构稳定性，我们使用 Shiihara 等人的方案（2010 Phys. Rev. B 81 075441）计算了每个原子区域的局部能量和局部应力。在每个 GB 中，原子体积较大且磁矩增强的界面原子会导致局部能量增加和拉伸应力增大。具有较小磁矩且键合更类似共价的界面原子的局部能量增加较小，有助于稳定，而这些原子会产生压缩应力。通过结构单元的局部能量可以理解两种 GB 之间的相对稳定性。局部能量和局部应力分析是一种强大的工具，可以根据价电子的行为研究 GB 的结构性质。
