Elastic constants

Posted on : December 16, 2021 (Thu) 18:01:21

by Ivan Lobzenko

Dear AkaiKKR users and developers!

I've started using AkaiKKR only recently and ran into a problem with the calculation of elastic constants. Originally I was dealing with an multi-element alloy, but to check my understanding of AkaiKKR I turned to a test example, which is single Mo BCC crystal.

Let me explain a little bit what I am doing.

The routine is simple, I am calculating energies of structures under different transformations and then getting coefficients from fitting of the energy curve with a polynomial (mostly of the order 2). To check results I do it in AkaiKKR and in VASP for the very same structures.

So, in both VASP and AkaiKKR I got more or less same results for bulk modulus and the elastic coefficients C11 and C12, but the shear modulus differs unreasonably. It is actually three times larger in AkaiKKR than in VASP:

VASP Mo B0 = 263.81 [GPa]
VASP Mo c11 = 471.67 [GPa]
VASP Mo c12 = 166.81 [GPa]
VASP Mo c44 = 88.27 [GPa]

AkaiKKR Mo B0 = 227.96 [GPa]
AkaiKKR Mo c11 = 441.57 [GPa]
AkaiKKR Mo c12 = 121.15 [GPa]
AkaiKKR Mo c44 = 458.89 [GPa] <--- ????

I checked a lot of various parts of the process, but cannot find the source of that misfit.

Here is one of my input files.
It is BCC under a monoclinic transformation with 10% value of transformation parameter (d).
The matrix for the transformation is Tm = [[1,d,0], [d,1,0], [0,0,1/(1-d^2)]]
===========================================================
c--------------------Mo--------------------------------------
go data/Mo
c------------------------------------------------------------
c brvtyp a c/a b/a alpha beta gamma
trc 6.02764, 1.0051, 1.0000, 90.0000, 90.0000, 78.5788,
c------------------------------------------------------------
c edelt ewidth reltyp sdftyp magtyp record
0.0010 0.80000 nrl pbe nmag 2nd
c------------------------------------------------------------
c outtyp bzqlty maxitr pmix
update 8 1000 0.0400
c------------------------------------------------------------
c ntyp
1
c------------------------------------------------------------
c type ncmp rmt field mxl anclr conc
Mo 1 1 0.0000 4
42 100
c------------------------------------------------------------
c natm
2
c------------------------------------------------------------
c atmicx atmtyp
0a 0b 0c Mo
1/2a 1/2b 1/2c Mo
c------------------------------------------------------------
===========================================================

If anyone can suggest what might be wrong, please share ideas!