Elastic constants¶

By applying cell deformations which correspond to the elastic constants you want to calculate, you can obtain elastic constants by calculating potential energy for each deformed structure. (Note that this script works only for cubic systems.)

Here, it is assumed that the minimum energy lattice constant is already determined via Lattice constant section.

Set the correct lattice constant in pmdini file.
Run the elasticity.py script for preparation of several pmd computations as,
```
$ python /path/to/nap/nappy/elasticity prepaer prepare pmdini
```
This will create elast_## directories which contain pmdini file, and conf.elast.yaml file that stores some options.

Then run pmd in each directories.

$ for d in elast_*; do echo $d ; cd $d; ln -s ../in.p* .; pmd > out.pmd ; cd ..; done

Finally, run the elasticity.py script again to compute elastic constants.

$ python /path/to/nap/nappy/elasticity.py analyze pmdini strs.pmd
 C_ij [GPa]:
    108.338     74.200     74.115      0.096      0.000      0.019
     74.200    108.263     74.061      0.071     -0.001      0.013
     74.115     74.061    108.275      0.039     -0.002      0.005
      0.096      0.071      0.039    108.211     -0.039      0.055
      0.000     -0.001     -0.002     -0.039    108.211      0.057
      0.019      0.013      0.005      0.055      0.057    108.211
Spacegroup number =  1  ==> Triclinic
 C_ij [GPa]:
    108.338     74.200     74.115      0.096      0.000      0.019
     74.200    108.263     74.061      0.071     -0.001      0.013
     74.115     74.061    108.275      0.039     -0.002      0.005
      0.096      0.071      0.039    108.211     -0.039      0.055
      0.000     -0.001     -0.002     -0.039    108.211      0.057
      0.019      0.013      0.005      0.055      0.057    108.211

 Bulk modulus (K)      =     85.514 GPa
 shear modulus (G)     =     53.145 GPa
 Poisson's ratio (nu) =      0.243

 Definition of elastic moduli, see https://materialsproject.org/wiki/index.php/Elasticity_calculations
   c123 = c11 +c22 +c33  =    324.876
   c231 = c12 +c13 +c23  =    222.376
   c456 = c44 +c55 +c66  =    324.633
   s123 = s11 +s22 +s33  =      0.062
   s231 = s12 +s13 +s23  =     -0.025
   s456 = s44 +s55 +s66  =      0.028
   Kv   = (c123 +2*c231)/9  =     85.514
   Kr   = 1.0 /(s123 +2*s231)  =     85.514
   Gv   = (c123 -c231 +3*c456)/15  =     71.760
   Gr   = 15.0 /(4.0*s123 -4.0*s231 +3.0*s456)  =     34.531
   K    = (Kv +Kr)/2
   G    = (Gv +Gr)/2
   nu   = (3*K -2*G)/(6*K +2*G)

 elasticity.py analyze done