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Posted: **Sat Aug 17, 2024 5:02 pm**

Dear Sir;

Are the elastic constants, Cij for hexagonal crystals arranged, in a matrix form, like those of tetragonal crystals?

Thank you very much for effort time

Sherif Yehia

Posted: **Mon Aug 19, 2024 8:32 am**

The elastic constants are written into a 6x6 matrix.
A sample output for graphite (just look at the form not the numbers since very bad parameters were used) looks like the following:
TOTAL ELASTIC MODULI (kBar)
Direction XX YY ZZ XY YZ ZX
--------------------------------------------------------------------------------
XX 12303.4048 1645.1598 47.3132 0.0000 -0.0000 0.0000
YY 1645.1598 12303.4048 47.3132 0.0000 0.0000 0.0000
ZZ 47.3132 47.3132 2557.5961 0.0000 0.0000 -0.0000
XY 0.0000 0.0000 0.0000 5329.1225 0.0000 -0.0000
YZ -0.0000 0.0000 0.0000 0.0000 1074.0250 0.0000
ZX 0.0000 0.0000 -0.0000 0.0000 0.0000 1074.0250
--------------------------------------------------------------------------------

A description how to perform elastic calculations is given here
wiki/index.php/Phonons_from_finite_differences#Output

Posted: **Mon Aug 26, 2024 7:59 pm**

I have a question regarding the arrangement of elastic constants (C_{ij}) for hexagonal and tetragonal crystals. I understand that the elastic constants are written into a 6x6 matrix. Here is a sample output for graphite (hexagonal crystal):
TOTAL ELASTIC MODULI (kBar)
Direction XX YY ZZ XY YZ ZX
-----------------------------------------------------------
XX 12303.4048 1645.1598 47.3132 0.0000 -0.0000 0.0000
YY 1645.1598 12303.4048 47.3132 0.0000 0.0000 0.0000
ZZ 47.3132 47.3132 2557.5961 0.0000 0.0000 -0.0000
XY 0.0000 0.0000 0.0000 5329.1225 0.0000 -0.0000
YZ -0.0000 0.0000 0.0000 0.0000 1074.0250 0.0000
ZX 0.0000 0.0000 -0.0000 0.0000 0.0000 1074.0250
-----------------------------------------------------------
I need to know if the (C_{ij}) matrix for tetragonal crystals is arranged in the same manner as for hexagonal crystals. Specifically, what will be the shape of the tetragonal matrix? Are the (C_{ij}) arranged similarly for both hexagonal and tetragonal structures? Please see the following link to see the (C_{ij})

https://1drv.ms/w/c/705142a2aaa1f1ee/EX ... A?e=iGqjCm
Thank you for your effort and time
Best regards,
Sherif

Posted: **Tue Aug 27, 2024 8:22 am**

Tetragonal cells can have more off diagonal elements not equal to zero, but it depends on the space group.

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