I have a couple of concerns about the elasticity section in the
new version:
Discrepancy in data between the legacy & new versions:
When I was working on the elastic properties of NiF2 (mp-559798), I’ve
realized that two different sets of values between the versions [mp-559798: NiF2 (Tetragonal, P4_2/mnm, 136) vs. mp-559798: NiF2 (tetragonal, P4_2/mnm, 136) ]
Values listed: New Version (Legacy Version)
Bulk Modulus, Voigt : 109 GPa (129)
Bulk Modulus, Reuss : 107 GPa (127)
Bulk Modulus, Voigt-Reuss-Hill : 108 GPa (128)
Shear Modulus, Voigt : 50 GPa (45)
Shear Modulus, Reuss : 41 GPa (35)
Shear Modulus, Voigt-Reuss-Hill : 45 GPa (40)
Poisson’s Ratio : 0.32 (0.36)
Universal Anisotropy : 1.13 (1.39)
Using the ELATE link, one can also see that, it fetches the data listed
in the legacy version.
The difference in the values is clearly stemming from the different
Stifness Tensor (& related Compliance Tensor) values.
A remark on the headings and units:
As one can also verify from the table of the reference work,
compliance tensor components (s_{ij}) and the elastic (stifness) tensor
components (C_{ij}) are related to each other by reciprocality, i.e.,
s_{ij} = C^{-1}_{ij}.
This enforces the respective units to be reciprocal as well (GPa for
compliance; 1/GPa for elastic tensor components (in the new version,
both tensors’ units are defined as GPa). However, in addition to this,
if one builds and inverts the elastic tensor, e.g.:
import numpy as np
# Stiffness Tensor / Elastic Tensor (C) [GPa]
C = np.zeros((6,6))
d = np.diag([81,92,0,0,0],1)
C += d
C[0,2] = 81
C = C + C.T
d = np.diag([201,136,136,90,43,43])
C += d
print(C)
# C
# [201., 81., 81., 0., 0., 0.],
# [ 81., 136., 92., 0., 0., 0.],
# [ 81., 92., 136., 0., 0., 0.],
# [ 0., 0., 0., 90., 0., 0.],
# [ 0., 0., 0., 0., 43., 0.],
# [ 0., 0., 0., 0., 0., 43.]
# Compliance Tensor (S) derived from Elastic Tensor
S = np.linalg.inv(C)
with np.printoptions(precision=5):
print(S)
# [ 0.00697 -0.00248 -0.00248 0. 0. 0. ]
# [-0.00248 0.01444 -0.00829 0. 0. 0. ]
# [-0.00248 -0.00829 0.01444 0. 0. 0. ]
# [ 0. -0. -0. 0.01111 -0. -0. ]
# [ 0. 0. 0. 0. 0.02326 0. ]
# [ 0. 0. 0. 0. 0. 0.02326]
# (The units are [GPa]^{-1})
# For a more convenient view, we multiply (and divide) by 1000:
with np.printoptions(precision=5):
print(S*1000)
# [ 6.9712 -2.47661 -2.47661 0. 0. 0. ]
# [-2.47661 14.43647 -8.29081 0. 0. 0. ]
# [-2.47661 -8.29081 14.43647 0. 0. 0. ]
# [ 0. -0. -0. 11.11111 -0. -0. ]
# [ 0. 0. 0. 0. 23.25581 0. ]
# [ 0. 0. 0. 0. 0. 23.25581]
which are the values displayed on the material’s page alas, the units
are now not GPa, not 1/GPa but: 1/TPa (it is being correctly displayed
in the legacy version, btw).
An innocent request:
Due to the unfortunate symbol and first letter mismatch (‘C’ for
"S"tifness tensor; ‘s’ for "C"ompliance tensor), I kindly ask you to
include the symbol next to the property name just like it was in the
legacy version (explicitly writing the stifness tensor as “elastic
stiffness tensor” can also prove to be useful as some sources use
“elastic tensor”, some “stiffness” and some both. 8)
With my best regards,
Emre S. Tasci