lattice periodicity length
The length of periodicity of the lattice is the minimum distance at which the lattice repeats itself. For example, the lattice constant in cubic crystal systems is the lattice periodicity length along the directions.
Once the crystallographic orientations are set, e.g., the axis in the first grain has an orientation of , the lattice will repeat itself at every distance along the direction. In the simple cubic system, this distance is likely the smallest lattice periodicity length. But in the face-centered cubic (FCC) and body-centered cubic (BCC) systems, this may not be the case. For example, in FCC, when , , yet the smallest lattice periodicity length . Another example is in BCC, when , , yet .
Since each grain has its own crystallographic orientations, each grain has its own . The length vector along each direction that is the largest in magnitude among all grains is the lattice periodicity length for the simulation cell, . The largest component in the vector is the maximum lattice periodicity length for the simulation cell, .
and are the length units in four commands: fix, grain_dir, group, and modify. A question arises regarding how the lengths in these four commands are usually determined. For example, to build a stationary edge dislocation, one needs to determine the position of the dislocation, i.e., using the
modify_centroid_z variables in the modify command. In the input file, there is one line
modify modify_1 dislocation 1 3 13. 39. 17.333 90. 0.33
plane_axis = 3 means that the slip plane is normal to the z direction. As a result, the
modify_centroid_z decides the z-coordinate of the intersection between the slip plane and the z axis. Since there is only one dislocation, one usually wants to let the slip plane be within the mid-z plane, but how is the value of
modify_centroid_z, which equals 17.333 here, determined?
In the log file, there are four lines:
The boundaries of grain 1 prior to modification are (Angstrom) x from -0.413351394094665 to 128.552283563439630 length is 128.965634957534292 y from -0.715945615951370 to 222.659086560878961 length is 223.375032176830331 z from -29.228357377724798 to 213.951576004945480 length is 243.179933382670271
where the last number
243.179933382670271 is the edge length of the simulation cell along the z direction, prior to modification. Note that it is important to use the edge lengths of the grain
prior to modification instead of those under
The box boundaries/lengths are (Angstrom) because the former are used to build dislocations in the code. Another two lines in the log file are
The lattice_space_max are x 4.960216729135929 y 2.863782463805506 z 7.014805770653949
where the last number
7.014805770653949 is the maximum lattice periodicity length for the simulation cell along the z direction, , which is indeed the length unit of
modify_centroid_z. Thus, if one wants to let the slip plane be within the mid-z plane, the value of
243.179933382670271 / 7.014805770653949 / 2 = 17.333