E_in-plane

[Dipankar Saha]

Hello,
Say X_Y is the 2D plane that I'm considering.... and, I need the E_in-plane.  From E_X and E_Y .., how can I get the E_in-plane ?

(Should I look into the compliance tensor coefficients  e.g. S11 or, S22 for the purpose??! )

Moreover, I didn't quite get  that, why do I need to go for another round of optimization (LBFGS)....when my cell is already optimized?!!
Generally, a force tolerance of 0.01-0.05 eV/ Ang. is suff. for diff.  lattice vibration and electronic structure calculations. However, for finding elastic constants.... you suggested to take a force tolerance of 0.001 ev/ Ang. !!

Thanks & Regards_
Dipankar

[zh]

What is the meaning of "E" in "E_in-plane"?


The first round of geometry optimization will  let you obtain the structure in the equilibrium state, i.e., the atomic forces on atoms are close to zero and the stress  on cell are also close to zero.

The second round of geometry optimization in the elastic constant calculations  will optimize only the atomic positions. In this case, the cell is deformed from the equilibrium state.   This will take into account the contribution of atomic relaxation to the stress on the strained cell.

[Dipankar Saha]

Thank you zh for the details ... /  'E' is meant to denote_Young’s Modulus  ....
 

[zh]

For the 3D materials, you can refer to the relationship between elastic modulus and and elastic compliances to get the Young's moduls.

If the material is cubic and isotropic, the Young’s modulus is the reciprocal  of S11.

please refer to the following paper for the estimation of Young's moduls of 2d materials:
https://www.researchgate.net/publication/233730678_In-plane_force_fields_and_elastic_properties_of_graphene

https://arxiv.org/ftp/arxiv/papers/0905/0905.1440.pdf

[Julian Schneider]

You can get the young's modulus in x- and y- direction by simply calculating the elastic constants and printing the results via nlprint. At the end, the report will give the young's moduli in x, y, and z. If your sheet is not oriented in the x-y-plane, you may need to uncheck the "Enable symmetry" check box in the elastic constants settings, to avoid averaging over X- and Y-direction. You'll get something like this (my sheet is oriented in the Y-Z-plane):

Code

+------------------------------------------------------------------------------+
| Elastic Constants in GPa                                                     |
+------------------------------------------------------------------------------+
|    -0.01       0.01       0.06       0.01      -0.00       0.00              |
|              178.44      11.83      -0.03      -0.03       0.01              |
|                         178.43      -0.03       0.00      -0.02              |
|                                     83.33       0.01       0.03              |
|                                                 0.00       0.00              |
|                                                           -0.01              |
+------------------------------------------------------------------------------+
+------------------------------------------------------------------------------+
| Elastic compliance in 1/GPa                                                  |
+------------------------------------------------------------------------------+
| -114.22226    -0.01098     0.03355     0.03203   -81.49647   -31.50235       |
|               0.00563    -0.00037    -0.00000     0.02350     0.01200        |
|                           0.00562    -0.00000     0.02595    -0.00410        |
|                                       0.01199    -0.00886     0.03186        |
|                                                 125.35569    19.71968        |
|                                                             -94.55384        |
+------------------------------------------------------------------------------+
+------------------------------------------------------------------------------+
| Material properties calculated from the elastic constants:                   |
+------------------------------------------------------------------------------+
| Moduli in units of GPa:                                                      |
+------------------------------------------------------------------------------+
|                 Reuss     Voigt     Hill                                     |
+------------------------------------------------------------------------------+
| Bulk modulus:    -0.0088   42.2957   21.1435                                 |
| Shear modulus:   -0.0412   39.6633   19.8111                                 |
+------------------------------------------------------------------------------+
|                     X         Y         Z                                    |
| Young's modulus:    -0.0088  177.5432  178.0172                              |
+------------------------------------------------------------------------------+
|                     XY        XZ         YZ                                  |
| Poisson ratios:      1.9495   -5.9729    0.0656                              |
|                     YX        ZX         ZY                                  |
|                     -0.0001    0.0003    0.0654                              |
+------------------------------------------------------------------------------+

[Dipankar Saha]

The second round of geometry optimization in the elastic constant calculations  will optimize only the atomic positions. In this case, the cell is deformed from the equilibrium state.   This will take into account the contribution of atomic relaxation to the stress on the strained cell.

Hi zh,
Can you please tell...
what did you mean by saying  " take into account the contribution of atomic relaxation to the stress on the strained cell" ?!!

How it is different from the case... where I opt for the "Optimization=None"   (I'm talking about the 2nd round of optimization) ??

Thanks and Regards_
Dipankar

[Dipankar Saha]

 Julian Schneider,

Thanks a lot Julian ... / I have sent the script... with necessary details...

Regards_
Dipankar

[Dipankar Saha]

If the material is cubic and isotropic, the Young’s modulus is the reciprocal  of S11.

please refer to the following paper for the estimation of Young's moduls of 2d materials:
https://www.researchgate.net/publication/233730678_In-plane_force_fields_and_elastic_properties_of_graphene

https://arxiv.org/ftp/arxiv/papers/0905/0905.1440.pdf

Thank you very much zh .... for those information...

Best_
Dipankar

[Petr Khomyakov]

what did you mean by saying  " take into account the contribution of atomic relaxation to the stress on the strained cell" ?!!

How it is different from the case... where I opt for the "Optimization=None"   (I'm talking about the 2nd round of optimization) ??

Applying general stress to a solid deforms the shape and volume of its unit cell. Consequently, the atoms in the deformed unit cell may or may not be at their equilibrium positions anymore, even so they were at equilibrium positions in the original unit cell before stress application. So, the atoms are to be allowed to relax to their equilibrium positions in the deformed unit cell. This is why one has to do a second geometry optimization for atoms only, keeping the shape and volume of the deformed unit cell fixed indeed.