Confusion in ELASTCON output:

R.Zosiamliana

When calculating the elastic constants (Cij) for bulk materials, the output values are provided in units of GPa. However, when generating a [0 0 1] surface slab (2D) from the corresponding bulk material using the SLABCUT keyword, the output elastic constant (Cij) values are given in Hartree (Ha).

Could anyone please clarify whether these values are expressed in Ha/Bohr² or Ha/Å², considering that the conventional SI unit for surface (Cij) in 2D materials is N/m?

here is my output comparison between bulk and 2D surface

For Bulk
SYMMETRIZED ELASTIC CONSTANTS FOR CUBIC CASE, IN GPa

| 121.241 47.439 47.439 0.000 0.000 0.000 |
| 121.241 47.439 0.000 0.000 0.000 |
| 121.241 0.000 0.000 0.000 |
| 71.165 0.000 0.000 |
| 71.165 0.000 |
| 71.165 |
For 2D-surface
SYMMETRIZED ELASTIC CONSTANTS FOR TRICLINIC CASE, IN HARTREE

| 2.059 0.349 0.000 |
| 2.059 0.000 |
| 1.099 |

aerba

Hi,

Elastic constants of a 3D lattice in CRYSTAL are defined and computed as:

$$
C_{ij}^\textup{3D} = \frac{1}{V} \left( \frac{\partial^2 E}{\partial \eta_i \partial \eta_j}\right)
$$

where the strain $ \eta $ is dimensionless and thus the elastic constants have units of $ \textup{energy/length}^3 $, which corresponds to force/surface (i.e. a pressure).

For 1D and 2D periodic lattices, as the volume $V$ is not defined, one may divide by the length $l $ and area $ A$ of the lattice cell instead:

$$
C_{ij}^\textup{1D} = \frac{1}{l} \left( \frac{\partial^2 E}{\partial \eta_i \partial \eta_j}\right) \qquad \textup{and} \qquad C_{ij}^\textup{2D} = \frac{1}{A} \left( \frac{\partial^2 E}{\partial \eta_i \partial \eta_j}\right)
$$

However, in CRYSTAL for 1D and 2D lattices we do not divide by $l $ or $ A$ , and just define and compute the elastic constants as:

$$
C_{ij}^\textup{1D and 2D} = \left( \frac{\partial^2 E}{\partial \eta_i \partial \eta_j}\right)
$$

with units of energy. So, starting from the constants printed in the CRYSTAL output all you have to do is divide by the area of the 2D cell if you need them expressed in $ \textup{energy/length}^2 $.

R.Zosiamliana

Thank you sir for your kind reply...