Hello,
I’d like to do a simple test to calculate the cohesive energy of HCPMg for different directions. Using this command to create lattice
lattice custom 4 a1 1 0 0 a2 0 sqrt(3) 0 a3 0 0 sqrt(8/3) basis 0.0 0.0 0.0 basis 0.5 0.5 0.0 basis 0.5 0.83333333 0.5 basis 0.0 0.33333333 0.5 orient x 1 0 0 orient y 0 1 0 orient z 0 0 1
I get: Cohesive energy per atom=1.510114302, a= 3.202795516, and c/a=1.619608977 which seem to be right for me.
The problem rises when I want to find orguments of x, y, and z for orient command above for one of pyramidal slip systems; e.g. {1101}<1120>. Here is what I figured to do to find the directions for lammps:

I found another direction in {1101} plane which is <1102>.

I converted these two directions from [uvtw] format to [UVw] and then to cartesian coordinate system as a1=<100> and a2=<012> keeping in mind that unit vectors in cartesian coordinate system aren’t really unit from the definitions of a1, a2, and a3.

I calcuate a3=a1 cross a2=2(c/4)/sqrt(3)j+sqrt(3)/(c/a). and found the closest integer number for this as <0 7 4>

recalculated a2=a3 cross a1= <0 4 7>
Then I used the following commands:
variable facx equal sqrt((v_x1)^2+(v_x2v_ay)^2+(v_x3v_ca)^2)
variable facy equal sqrt((v_y1)^2+(v_y2v_ay)^2+(v_y3v_ca)^2)
variable facz equal sqrt((v_z1)^2+(v_z2v_ay)^2+(v_z3v_ca)^2)
variable latdisx equal “1v_latparamv_facx0.05”
variable latdisy equal “1v_latparamv_facy0.05”
variable latdisz equal “1v_latparamv_facz0.05”
lattice custom 4 a1 1 0 0 a2 0 sqrt(3) 0 a3 0 0 sqrt(8/3) basis 0.0 0.0 0.0 basis 0.5 0.5 0.0 basis 0.5 0.83333333 0.5 basis 0.0 0.33333333 0.5 orient x 1 0 0 orient y 0 4 7 orient z 0 7 4
region box block 0.05 {latdisx} 0.05 {latdisy} 0.05 ${latdisz} units box
and got Cohesive energy=1.502639033
I am pretty much sure that I don’t have the periodic simulation box. I guess the problem is that the unit vectors are not actually unite in the lattice command (a1, a2, and a3).
Is there anybody here who worked on HCP structures before and see where I went wrong?
Thanks,
Ebrahim