computing elastic constants
This video sketches in a qualitative way two procedures that allow you to determine by DFT the stress-strain relation for a given crystalline material.
A few typos in the slides used for this video have been corrected later, the downloadable slides have the corrected version.
If after this video you feel you want to learn more about continuum mechanics, then www.continuummechanics.org is an excellent source.
There are two tasks related to this video, one mandatory and one optional one:
Mandatory task
Use the total energy method to determine the elastic constants of fcc aluminum. One of the drawbacks of this method is that it requires quite some independent DFT calculations. Therefore, let us parallellize these over all participants: you do one small part, add it to a shared spreadsheet, and in the next feedback webinar we’ll see the collective result.
It’s important that all of us do these calculations in exactly the same conditions. This is the cif file for a (conventional) unit cell of fcc-Al (4 atoms), with the PBE-optimized lattice parameter. Use this pseudopotential, the PBE exchange-correlation functional, ecutwfc=60 Ry, ecutrho=300 Ry, and a 25x25x25 k-mesh. These are quite demanding settings, as we aim for precise calculations — expect 10-15 minutes for a static calculation (if you get for this ground state case a total energy of -158.01241434 Ry, then you’re doing it correctly).
Now choose your case (the first, second or third tab on the spreadsheet), choose your value for the strain, determine the deformed unit cell, and find the total energy. Add your value to this spreadsheet (there is one tab for each of the three cases, add your username in column B). In the spreadsheet, there is one example value for each of the cases. You might try to reproduce this one first, to make sure you are doing it right.
The spreadsheet will be editable during the week preceding the due date of this chapter. Afterwards, the spreadsheet will be visible yet not editable any longer. We’ll analyse the result of your work during the next feedback webinar.
Optional task
Calculate the elastic constants of fcc aluminum via the stress tensor method, i.e. reproduce the calculations described in the corresponding section of the exercices.
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