Atomic Simulations of Twist Grain Boundary Structures and Deofrmation Behaviors in Aluminum Page: 2
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Al P Advances 7, 015040 (2017)
II. COMPUTATIONAL MODELS AND METHODS
A large-scale atomic molecular massively parallel simulator (LAMMPS)2 developed by Sandia
National Labs and Temple University was used to simulate the symmetric twist GBs. The forces
between atoms were calculated by the embedded atom (EAM) potential for aluminum, as described
in detail elsewhere by Mishin et al.22 This potential has been used to investigate the tension behavior
for the nanowire with a tilt GB and accurately described Young's modulus of aluminum. All the
models were visualized by AtomEye visualization software23 in this work.
Figure 1(a) shows a schematic of a twist GB model. This computational cell was also used to
investigate tilt GB.24 The system consists of the upper simulation cell, Grain 1, and lower simulation
cell, Grain 2. A twist GB with a specific misorientation or a specific CSL E value can be built by
twisting upper and lower cells. Table I lists 12 examples of twist GBs that is obtained by rotating
Grain 1 by +6/2 and rotating Grain 2 by -6/2 along rotation axis <001>. <hkl>1/<hkl>2 represents
X direction of Grain 1 and Grain 2 after rotation, respectively. Sigma value denotes that if two
crystal lattices are allowed to overlap, 1/E percent points are coincident. The sigma value is coupled
with a specific misorientation angle 0 about a specific rotation axis. Since atoms near the twist GB
are too close to each other and disturb the whole system, these atoms are deleted by defining a
critical distance.25 To allow the crystal lattices to translate during energy minimization, 3D periodic
boundaries are set in the simulation. Therefore, two twist GBs are formed: one periodic twist GB
(TGB1) at the upper and lower boundaries of the cell; and the other twist GB (TGB2) in the middle
of the cell. The normal direction of the boundary plane is represented by n, which is the rotation
axis. Figure 1(b) shows a twist GB cell that is visualized by AtomEye. In this paper, 57 twist GBs
along <001> rotation axis, 40 twist GBs along <101> rotation axis, and 29 twist GBs along <111>
rotation axis were studied.
Since two twist GBs in the system might interact with each other, the size of the system must be
large enough to minimize the interaction. According to convergence studies, the distance between the
twist GBs (lattice constant ao = 4.05 Angstroms) is set to be over 8nm, while the minimum distance
in the X and Y directions is larger than 7nm. The periodic distances along X-, Y- and Z-axes are
related to the rotation axis and misorientation angle by
L/2=nao h2 + k2 + l2 >8nm, and
B,W =mao0h2 + k2 + 12>7nm
where L, B and W are box sizes of Z, Y and X directions, as shown in Figure 1(a), h, k and 1 are the
orientation indices of grain orientation, and n and m are integers to satisfy the size requirement. The
energy related to the grain boundary was calculated by the following equation:26
EGTB + N - EFCC
EGTB _ CSL Perfect (1)
2A
Z() TGB1
Grain
TGB2V
Grain2
X TGB1
B
(a) (b)
FIG. 1. (a) Schematic of a 3D periodic computational cell, and (b) Twist GB model visualized by AtomEye.015040-2 Yin et al.
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Yin, Qing; Wang, Zhiqiang; Mishra, Rajiv & Xia, Zhenhai. Atomic Simulations of Twist Grain Boundary Structures and Deofrmation Behaviors in Aluminum, article, January 30, 2017; Melville, New York. (https://digital.library.unt.edu/ark:/67531/metadc991021/m1/2/: accessed May 9, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT College of Engineering.