Another thing that can be measured, is the response of the system, in terms of total energy variation, with respect to a strain.
By applying small strains to the equilibrium unit cell and carefully choosing the strain matrix (see presentation), we can use the response to determine the elastic constants of the system.
In the case of NaCl with rock-salt structure, the symmetries of the system make it so that only 3 independent elastic constant are present: C_11, C_12 and C_44.
Please take note of a few differences from the previous exercises:
- In this case to properly apply the strain, we are using a supercell consisting of 8 atoms instead of the primitive one consisting of 2
- Since the supercell is bigger then the primitive one, the number of k-point required to achieve convergence will be in principle lower. While the convergence parameters should always be re-evaluated, for the purpose of this exercise you can assume that a 2x2x2 grid is enough.
- The calculation type has been changed from
scftorelax. This is required as after applying the strain in the unit cell, the atoms might not be in their equilibrium position. The relax calculation will perform a series ofscfcalculation, calculating the forces acting on the atoms and moving them accordingly between each iteration, until these forces are below a certain threshold (defined by default in QE, but can be specified by the used)
- Copy the provided input files into this folder
cp ../files/NaCl.scf.in . - Copy or link the pseudopotential files for Na and Cl inside a folder named
pseudoin the same path of the input file
cp -r ../files/pseudo/ . - Modify the input file to use the converged parameters you obtained in the previous section.
As stated in the introduction, the convergence requirement on the kpoints will be lower since we are using a supercell.
Also we suggest using a slightly reduced cutoff and/or increase the number of virtual cores assigned to the virtual machine see handouts section 1.7, in order to be able to run this exercise in a reasonable time. - Run the code pw.x from terminal using the command
pw.x < Na.supercell.relax.in > Na.supercell.relax.out - Collect the total energy from the output file (It can be found close to the end, with a line starting with an exclamation mark)
NOTE: while the values of the total energy are still identifiable by an exclamation mark in the output, there will be several occurrences, one for each 'scf' iteration in the 'relax' cycle. Take care to record the last of this values which corresponds to the relaxed structure. - Modify the lattice cell vectors (rows under the input file card
CELL_PARAMETERS {alat}) by applying the strain configuration described in the presentation meant to calculateC_11 - C_12 - Repeat step 4 through 6 by applying different values of strain, from -2% to +2% in steps of 1% or 0.5%
- Fit the obtained data in order to extract the value of
C_11 - C_12 - Use the value of the Bulk modulus calculated in exercise 6 together with the value of
C_11 - C_12obtained here to derive C_11 and C_12 - Repeat step 4 through 8 with the other strain configuration provided to calculate C_44