grain boundaries are a specific type of grain boundary, where the two grains are rotated around the same crystallographic axis. When the two grains are rotated by opposite angles, the tilt grain boundary is symmetric.

(a) Insert two nodes at the reduced coordinates (0.5,0.25,0) and (0.5,0.75,0). By doing so, the grain boundary is located at the center of the final cell (horizontal blue line). Note that, because of periodic boundary conditions, there will also be a grain boundary at the bottom of the box, and one at the top.

(b) Insert the seeds at the positions of the nodes. Rotate one seed by an angle +α/2 and the other one by -α/2 around Z, so that the desorientation between the two grains is α.

(c) Duplicate the seed in all directions of space, and cut each grain at the grain boundary.

Another particular type of grain boundaries are twist grain boundaries, where the two grains are rotated around the axis normal to the grain boundary, i.e. around the Y axis in the examples above. In this case, the box size along Y is an integer multiple of the lattice constant, and the sizes along X and Z change depending on the twist angle.

As an example, let us construct a pure twist grain boundary in aluminium, using the same rotation angle as in the previous section. We know that the box size along Y must be multiple of the lattice constant, so let us set it to ten times the lattice constant, 40.46 Å. Along X and Z, the box size must be a multiple of the length of the [210] lattice vector; let us use the minimum period, 9.047131 Å, in each direction. Finally the seeds must be placed in the middle of the XZ plane, i.e. at the reduced coordinates (½ ¼ ½) and (½ ¾ ½). If we incorporate all that into the parameter file, it should look like the following:

polyX.txt

box 9.047131 40.46 9.047131 node 0.5*box 0.25*box 0.5*box 0° -26.57° 0° node 0.5*box 0.75*box 0.5*box 0° 26.57° 0°

grain boundaries are a specific type of grain boundary, where the two grains are rotated around the same crystallographic axis. When the two grains are rotated by opposite angles, the tilt grain boundary is symmetric.