# Example 4: Bulk moduli with CASTEP and run3¶

In this tutorial we will calculate the bulk moduli of diamond, silicon and lithium, using CASTEP and run3.

The general process for calculating the bulk modulus is as follows:

1. Relax a structure to its equilibrium volume $$V_0$$ (ideally relaxing the positions too).

2. Run total energy calculations at a series of perturbed volumes $$\alpha V_0$$ for $$\alpha \in [0.95, 1.05]$$.

3. Fit a particular form of equation of state to the resulting $$E(V)$$ curve and extract the bulk modulus.

Note: there is a supported set of scripts for calculating all the elastic constants in CASTEP, which can be found on GitHub with an additional tutorial on the CASTEP website.

As with the other tutorials, run3 expects to find a series of structures as .res files and single $seed.cell and $seed.param files. The files for this example can be found in examples/run3_elastic. The .cell file in this tutorial is basically identical to that in the geometry optimisation tutorial, but the .param file this time contains the line task: bulk_modulus. This is not a valid CASTEP task (as of 2019), but instead run3 will capture this task and use it to spawn a series of single point jobs.:

$cat bulk_mod.cell kpoints_mp_spacing: 0.05 snap_to_symmetry symmetry_tol: 0.01 symmetry_generate %block species_pot QC5 %endblock species_pot$ cat bulk_mod.param
cut_off_energy: 300 eV
write_bib: false
write_checkpoint: none
geom_max_iter: 100
xc_functional: LDA


Once the files are in place, calling run3 as run3 bulk_mod will begin to relax the first structure before deforming it. You can track the calculations progress in the log files found in logs/.

After the calculations have completed, your completed folder should look something like this:

\$ ls completed
C-OQMD_675640-CollCode28857.bands             Li-OQMD_30676-CollCode642106_bulk_mod.castep
C-OQMD_675640-CollCode28857.castep            Li-OQMD_30676-CollCode642106_bulk_mod.cell
C-OQMD_675640-CollCode28857.cell              Li-OQMD_30676-CollCode642106_bulk_mod.cst_esp
C-OQMD_675640-CollCode28857.cst_esp           Li-OQMD_30676-CollCode642106_bulk_mod.param
C-OQMD_675640-CollCode28857.geom              Li-OQMD_30676-CollCode642106_bulk_mod.png
C-OQMD_675640-CollCode28857.param             Li-OQMD_30676-CollCode642106_bulk_mod.res
C-OQMD_675640-CollCode28857.res               Li-OQMD_30676-CollCode642106_bulk_mod.results
C-OQMD_675640-CollCode28857_bulk_mod.bands    Si-OQMD_5714-CollCode29287.bands
C-OQMD_675640-CollCode28857_bulk_mod.castep   Si-OQMD_5714-CollCode29287.castep
C-OQMD_675640-CollCode28857_bulk_mod.cell     Si-OQMD_5714-CollCode29287.cell
C-OQMD_675640-CollCode28857_bulk_mod.cst_esp  Si-OQMD_5714-CollCode29287.cst_esp
C-OQMD_675640-CollCode28857_bulk_mod.param    Si-OQMD_5714-CollCode29287.geom
C-OQMD_675640-CollCode28857_bulk_mod.png      Si-OQMD_5714-CollCode29287.param
C-OQMD_675640-CollCode28857_bulk_mod.res      Si-OQMD_5714-CollCode29287.res
C-OQMD_675640-CollCode28857_bulk_mod.results  Si-OQMD_5714-CollCode29287_bulk_mod.bands
Li-OQMD_30676-CollCode642106.bands            Si-OQMD_5714-CollCode29287_bulk_mod.castep
Li-OQMD_30676-CollCode642106.castep           Si-OQMD_5714-CollCode29287_bulk_mod.cell
Li-OQMD_30676-CollCode642106.cell             Si-OQMD_5714-CollCode29287_bulk_mod.cst_esp
Li-OQMD_30676-CollCode642106.cst_esp          Si-OQMD_5714-CollCode29287_bulk_mod.param
Li-OQMD_30676-CollCode642106.geom             Si-OQMD_5714-CollCode29287_bulk_mod.png
Li-OQMD_30676-CollCode642106.param            Si-OQMD_5714-CollCode29287_bulk_mod.res
Li-OQMD_30676-CollCode642106.res              Si-OQMD_5714-CollCode29287_bulk_mod.results
Li-OQMD_30676-CollCode642106_bulk_mod.bands


You can see the results of the bulk modulus fits for each structure in completed/*_bulk_mod.results, along with plots of the fits saved as pngs.

Compare these LDA values from the three different fits to the experimental values from Wikipedia:

Material

Expt. Bulk modulus (GPa)

Predicted Bulk Modulus (GPa)

Lithium

11

17.6, 17.7, 17.8

Silicon

98

97.5, 98.0, 97.4

Diamond

442

503, 496, 496