Stress tensor HCP TiB2 crystal

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maartendft · #1 Post by **maartendft** » Sun Sep 05, 2010 1:30 pm

Dear VASP-users,

I'm trying to compute the elastic tensor of a simple TiB2 HCP crystal using the stress-strain linear-elastic relations. The fully relaxed lattice matrix is computed as:

3.031916 0.000000 0.000000
-1.515955 2.625712 0.000000
0.00000 0.000000 3.232479

When I apply a simple 1% uniaxial compression along the first lattice vector, it becomes:

3.001596 0.000000 0.000000
-1.515955 2.625712 0.000000
0.00000 0.000000 3.232479

Now the problem:
VASP computes the stresses as:

X 66.69
Y 8.07
Z 12.07
XY 17.09
YZ 0.00
ZX 0.00

X, Y and Z seem fine. The components C11, C12 and C13 can also be computed accurately in this way. However, the nonzero XY causes the elastic constant C14 to be nonzero and even quite high, over 100 GPa, ruling out a numerical error.

This is inconsistent with the elastic tensor representation for HCP crystals, where components such as C14, C15 and C16 should be zero.

Any suggestions or ideas where it goes wrong? Thanks a lot!

wdv · #2 Post by **wdv** » Mon Sep 06, 2010 8:19 am

since a and b of TiB2 are not normal to each other, b should also be changed to get uniaxial compression.

btw, to compute the elastic tensor, their is a simple method described in "Computer Physics Communications 181 (2010) 671â€“675"

maartendft · #3 Post by **maartendft** » Mon Sep 06, 2010 12:21 pm

Thanks for your reply!

Imagine I choose to only stretch the a-axis, i.e. I would only apply epsilon_{11} and no shear strains like epsilon_{12}, epsilon_{13} or epsilon_{23}.

In that case, VASP comes up with a high XY-stress. Referring to the 6*6 elastic tensor, this means that either of the three C14, C15 or C16 (depending on how you order them in the matrix) must be nonzero!

This is exactly the problem, since C14, C15 and C16 should be zero for HCP crystals. I'm wondering if I am doing something wrong conceptually or that VASP gives an inaccurate value for the shear stresses when uniaxial tension is applied.

Thanks a lot in advance.

forsdan · #4 Post by **forsdan** » Mon Sep 06, 2010 3:45 pm

I'll have to agree with wdv. To compress only the a-axis will not give a uniaxial strain along x. If you map out the displacement field at each atom you will see that you introduce a epsilon_{12} component as well as epsilon_{11}. Compress the x-component of b as well and your issue will most likely go away.

Cheers,
/Dan