/
v0.3_changes_details
12 lines (10 loc) · 1.12 KB
/
v0.3_changes_details
1
2
3
4
5
6
7
8
9
10
11
12
Detailed overview of changes from version 0.2.1 to 0.3
Combinatorial and Configurational Complexity:
I_comb is now calculated by subtracting the mixing complexity instead of addition. By this the complexity may become negative, enabling a positive mixing entropy.
See Krivovichev 2022 (10.1180/mgm.2022.23) for more details. I_conf computation is changed accordingly.
Entropy Calculation:
The computation of S_comb, S_coor, S_conf was removed as the error for crystal structures with average-sized unit cells was too large.
This error originates in the Stirling approximation which is used in deriving the entropy formula S = S_max - ln(2) * R * I that uses the complexity value.
The error of this formula is less than 1% only if the multiplicity of every crystallographic orbit is equal or higher to 90. Direct calculation of S
using the crystallographic orbits in the Boltzmann equation yields the configurational entropy S_cfg. Partial occupancies are included by determination of S_mix using
S_mix = R * ln(2) * I_comb_mix * PositionsPerReducedUnitCell. Addition of S_cfg and S_mix gives the entropy of the crystal per reduced unit cell.