I don't think I agree with you. Comments below, thanks.
In this case, It does not comes from non-convergence of data in a series of
displacement-minimization process as Axel mentioned, but from orientation of
Elastic constants always depend on orientation. Strain X then measure
stress in X gives you C11, while straining YZ then measure stress in
XY gives you C46, etc.
For bulk property such as bulk modulus, it doesn't matter.
But, elastic constants are affected by orientation of the structure.
Elastic constants are also bulk properties, which by definition are
intensive properties of the system that does not depend on the size.
Let me say z indicate (001), then x and y orientation can have arbitrary
orientations if both are perpendicular and satisfied with the right-hand
Consider following two cases:
1) orient x 1 -1 0 orient y 1 1 0 orient z 0 0 1
What you think is c11 is actually C66, which is equal to C44 for a
diamond cubic. C11 is a notation for C1111, while C66 is C1212
(meaning straining xy then measuring stress in xy). In the above
scenario, X is orientated along [1-10], which is the same as xy. So
that "c11" is actually C1212 = C66.
2) rotated 1) by 45 degrees along z direction
Does not this rotate the crystal back to its normal orientation? X is
aligned with , Y , or the opposite. So that this C11 is the
true C11, or C22. But again, C11 = C22 for a diamond cubic.
c11(cxx) would be different between 1) and 2).
Yes, they are different, but only because one is C66 and the other C11.