Cu Phonon Dispersion with TBMD

Sections

1. Generate position files
2. Forces calculation with TBMD
3. Frequency bands calculation
4. Frequency DOS

We use the TBMD code to calculate phonon frequency bands for Cu. The method applied is the frozen phonon approximation [1] and the dispersion curves are calculated along high-symmetry directions for fcc Cu. The TBMD code calculated the forces using the TB parameters at the equilibrium volume for Cu. The supercells in the calculation and phonon spectra are caclulated using Phonopy. A link to the source code and instructions for setting up Phonopy can be found here. Further details on the first principles phonon calculations in Phonopy can also be found in Ref [2].

Position files with Phonopy

Once Phonopy is properly installed, we can use it to generate the supercell positions to be used in the MD force calculation. For this, you will need the cu.in file. This is an input file for quantum Espresso (QE). Since we will be comparing the calculated phonon frequencies to experimental values [3], we won't need to run QE. More information on Quantum Espresso can be found from their page.

To start, create a directory cu_phonons and it should have the files:

            -rw-r--r-- 1 ssilayi users     926 Jun 17 11:04 cu.in 
            

The QE input file cu.in is used to generate supercell positions with Phonopy.

• Run

  $phonopy --qe -d --dim="2 2 2" -c cu.in 

  to generate 2x2x2 translations of the primitive cell in cu.in displacement files. You should now have additional files in your directory

  -rw-r--r-- 1 ssilayi users     926 Jun 17 11:04 cu.in

  -rw-r--r-- 1 ssilayi users    7081 Jun 17 11:22 phonopy_disp.yaml

  -rw-r--r-- 1 ssilayi users    2413 Jun 17 11:22 supercell-001.in

  -rw-r--r-- 1 ssilayi users    2413 Jun 17 11:22 supercell.in 

• The generated supercell-001.in file is what we are interested in because it contains the position displacements. We use the information on cell parameters and atomic positions to build the POSTBMD file.

Next »

Force Calculations

We use the created supercell positions with displacements to build the POSTBMD file. Note that in the QE input file, distances are in atomic units while the TBMD input has the distances in Angstrom. After making that conversion, we have a POSTBMD file we can use for the TBMD run. For instructions on setting up the TBMD files and other descriptions refer to these pages.

If we created a separate cu_tbmd directory for the TBMD caclulation, we should have the following files in it:

                -rw------- 1 ssilayi users     319 Jun 17 12:26 INTBMD
                -rw-r--r-- 1 ssilayi users       8 Jun 17 12:26 KPTS
                -rw------- 1 ssilayi users    2298 Jun 17 12:26 POSTBMD
                -rwxr-xr-x 1 ssilayi users 4978586 Jun 17 12:26 tbmdk
                -rw-r--r-- 1 ssilayi users    7354 Jun 17 12:26 TBPARAM
                

• The INTBMD file should have the number of ionic steps set to at least 1 to create the FORCE file. If it is set to 0, the forces have to be extracted from the OUTTBMD file once the code is run.
• The version of the TBMD code used is tbmdk which uses additional k-points other than the Gamma point.
• The KPTS file specifies the k-point mesh that the TBMD code uses.
• The TBPARAM is the parameters file.

$./tbmdk 

We need the force_convert program generated using the extract_forces.f95 code to format the FORCE output file. So we add this to the directory and run

$./force_convert 

The file of we need for the next step is the forces.qe .

Frequency Bands

1. Copy the forces.qe file into the cu_phonons directory. Run

   $phonopy --qe -f forces.qe 

   to create the FORCES_SET file.
2. Create the band.conf file. The file should have the number of displacements in each direction as well as the high symmetry k-point path and has the format

                   DIM = 2 2 2
                   BAND =  0.0 0.0 0.0  0.5 0.0 0.5  0.5 0.25 0.75 0.5 0.0 0.5  0.375 0.375 0.75 0.0 0.0 0.0  0.5 0.5 0.5 0.375 0.375 0.75 0.5 0.25 0.75  0.5 0.5 0.5 
                   BAND_LABELS = $\Gamma$ X W X K $\Gamma$ L K W L
   
                   

3. Run

   $phonopy --qe -c cu.in -p band.conf

   and this produces a plot of the phonon frequency dispersion. The plot is saved in the same directory.

4. To also save the data for generating the plot, run

   $phonopy-bandplot --gnuplot band.yaml > cu_phonons_tbmd.dat 

5. The gnuplot script bandplot.gnu can be used with the .dat file to generate the phonon dispersion plot. The frequency endpoints and high-frequency points in the gnuplot script need to match what is in the .dat file. Run as

   $gnuplot bandplot.gnu 

The final phonon frequency bands (left) compared to experimental values [3] (right)

Frequency DOS

To plot the phonon DOS, we need the mesh.conf file. This has information on the mesh sampling and the periodic translations

        DIM = 2 2 2
        MP = 21 21 21
        

$phonopy -p mesh.conf -v

The calculated phonon frequnency distribution (left) is shown next to the experimental distribution [3] (right).

References

[1] Klein, B. M., & Cohen, R. E. (1992). Anharmonicity and the inverse isotope effect in the palladium-hydrogen system. Physical Review B, 45(21), 12405.

[2] Togo, A., & Tanaka, I. (2015). First principles phonon calculations in materials science. Scripta Materialia, 108, 1-5.

[3] Nilsson, G., & Rolandson, S. (1973). Lattice dynamics of copper at 80 K. Physical Review B, 7(6), 2393.

[4] Sinha, S. K. (1966). Lattice dynamics of copper. Physical Review, 143(2), 422.