Wrong coefficients in `hexagonal`

[yuzie007]

Apart from #64, I would also like to report wrong coefficients in hexagonal.

Here, we have unnecessary coefficients of 2. This is inconsistent with the Elastic document itself as well as my own derivation (main.pdf).

To demonstrate this is really an issue, I have conducted a test calculation for graphite (graphite_gaussian.zip). In experiments (Ref. 11 in this):

• C11 = 1060 GPa, C12 = 180 GPa, C13 = 15 GPa, C33 = 36.5 GPa, C44 = 4 GPa, C66 = (C11-C12)/2 = 440 GPa

Fo DFT (PBE-D3(BJ)), using VASP IBRION=6, I obtain (without ionic-relaxation contribution)

• C11 = 1075 GPa, C12 = 237 GPa, C13 = -4 GPa, C33 = 36 GPa, C44 = -5 GPa, C66 = (C11-C12)/2 = 419 GPa

Using Elastic with get_elastic_tensor (which calls hexagonal) I get

• C11 = 948 GPa, C12 = 69 GPa C13 = -3 GPa, C33 = 36 GPa, C44 = -5 GPa, C66 = (C11-C12)/2 = 440 GPa

Which is substantially deviated from the IBRION=6 values for C11 and C12, because of the coefficient error in hexagonal.

If we use the one-axis approach (i.e., without hexagonal) (with solving the issue in #64), I get

• C11 = 1090 GPa, C12 = 225 GPa, C13 = -4 GPa, C33 = 36 GPa, C44 = -6 GPa, C66 = (C11-C12)/2 = 432 GPa

Which is consistent with IBRION=6.

If we will fix the coefficients in hexagonal, then get_elastic_tensor gives

• C11 = 1077 GPa, C12 = 240 GPa C13 = -3 GPa, C33 = 36 GPa, C44 = -5 GPa, C66 = (C11-C12)/2 = 419 GPa

which is consistent with IBRION=6.

[jochym]

Thanks again @yuzie007 ! I will review the change and get back to you.

[jochym]

@yuzie007: It seems you are right. Thanks. I will merge your change as a first one after update of the build tool chain - which I am doing right now.

[yuzie007]

@jochym Thank you so much also for cross-checking the coefficients. I fully agree on your suggested procedure, and it's really helpful to have new Elastic release with the fixed coefficients!