Dear Sir,
I am trying to symmetrize the stiffness tensor. The initial structure is having a P2/m space group.
But I want to symmetrize it to a 4/mmm space group.
Initial stiffness tensor is:
214.707 51.946 90.260 0.380 0.290 1.011
51.946 214.707 90.260 -0.290 -0.380 1.011
90.260 90.260 180.453 0.185 -0.185 0.424
0.380 -0.290 0.185 112.582 -0.962 0.231
0.290 -0.380 -0.185 -0.962 112.582 -0.231
1.011 1.011 0.424 0.231 -0.231 42.883
Initial lat.in file is:
9.04825 3.96150 12.50583 90.0 96.82 90.0
1 0 0
0 1 0
0 0 1
0.7158874232310556 0.0000000000000000 0.0712990946390593 Al
0.5720638064338331 0.0000000000000000 0.3523626006435088 Al
0.6458865522592859 0.5000000000000000 0.2075025089551598 Al
0.4279361935661669 0.0000000000000000 0.6476373993564910 Al
0.5000000000000000 0.5000000000000000 0.5000000000000000 Al
0.3541134477407140 0.5000000000000000 0.7924974910448402 Al
0.2841125767689440 0.0000000000000000 0.9287009053609406 Al
0.1514389063244087 0.0000000000000000 0.2131869401726773 Al
0.2210749488116841 0.5000000000000000 0.0665550486058150 Al
0.0000000000000000 0.0000000000000000 0.5000000000000000 Al
0.0763061451543364 0.5000000000000000 0.3587690520594582 Al
0.8485610936755916 0.0000000000000000 0.7868130598273225 Al
0.9236938548456636 0.5000000000000000 0.6412309479405417 Al
0.7789250511883158 0.5000000000000000 0.9334449513941849 Al
0.5000000000000000 0.5000000000000000 0.0000000000000000 Cr,Ti
0.3601240779485727 0.5000000000000000 0.2816986015814482 Ti,Cr
0.4363855804960319 0.0000000000000000 0.1309912289124432 Ti,Cr
0.2150392783436612 0.5000000000000000 0.5751925167730597 Ti,Cr
0.2896347785367829 0.0000000000000000 0.4309402142868154 Ti,Cr
0.1382935115476341 0.0000000000000000 0.7175345935123164 Ti,Cr
0.0580157603296885 0.5000000000000000 0.8552158630247091 Ti,Cr
0.9419842396703115 0.5000000000000000 0.1447841369752908 Ti,Cr
0.0000000000000000 0.0000000000000000 0.0000000000000000 Ti,Cr
0.7849607216563389 0.5000000000000000 0.4248074832269403 Ti,Cr
0.8617064884523660 0.0000000000000000 0.2824654064876836 Ti,Cr
0.6398759220514274 0.5000000000000000 0.7183013984185518 Ti,Cr
0.7103652214632171 0.0000000000000000 0.5690597857131848 Ti,Cr
0.5636144195039681 0.0000000000000000 0.8690087710875565 Ti,Cr
using the sym.in file of 4/mmm , and gencs -s -r=6, I generated the harmnonics as:
- 0.408248x^2 + 0.408248y^2 + -0.816497*z^2
- 0.396412x^4 + -1.7298x^2y^2 + 0.396412y^4 + -0.648675x^2z^2 + -0.648675y^2z^2 + 0.216225*z^4
- 1.2792x^2y^2 + -1.2792x^2z^2 + -1.2792y^2z^2 + 0.426401*z^4
- 0.154303x^6 + -0.420827x^4y^2 + -0.420827x^2y^4 + 0.154303y^6 + -1.89372x^4z^2 + 5.04993x^2y^2z^2 + -1.89372y^4z^2 + 1.05207x^2z^4 + 1.05207y^2z^4 + -0.140276z^6
- 0.556702x^4y^2 + 0.556702x^2y^4 + -0.556702x^4z^2 + -6.68043x^2y^2z^2 + -0.556702y^4z^2 + 1.67011x^2z^4 + 1.67011y^2z^4 + -0.222681z^6
Q1. How can we use the harmonics to convert the initial stiffness tensor to a 4/mmm space group?
with best regards,
Mahfooz