Band unfolding for phonons (http://yuzie007.github.io/upho/)

• numpy
• h5py
• phonopy>=2.7.0

pip install git+https://github.com/yuzie007/upho.git@v0.6.6

Here we consider the hypothetical case when Cu₃Au with the L1₂ structure is regarded as a random configuration of the A1 (fcc) structure. You can find the input files in the examples directory.

1. Create FORCE_SETS file for the structure (maybe including disordered chemical configuration) you want to investigate using phonopy in a usual way. Be careful that the number of the structures with atomic displacements to get FORCE_SETS can be huge (>100) for a disordered configuration.

2. Create FORCE_CONSTANTS file from FORCE_SETS file using phonopy as

   phonopy writefc.conf
   

   where writefc.conf is a text file like

   FORCE_CONSTANTS = WRITE
   DIM = 2 2 2
   

   DIM must be the same as that what you used to get FORCE_SETS.

3. Prepare two VASP-POSCAR-type files, POSCAR and POSCAR_ideal. POSCAR includes the original chemical configuration, which may be disordered.

   Cu Au
      1.00000000000000
        3.7530000000000001    0.0000000000000000    0.0000000000000000
        0.0000000000000000    3.7530000000000001    0.0000000000000000
        0.0000000000000000    0.0000000000000000    3.7530000000000001
      Cu   Au
        3     1
   Direct
     0.0000000000000000  0.5000000000000000  0.5000000000000000
     0.5000000000000000  0.0000000000000000  0.5000000000000000
     0.5000000000000000  0.5000000000000000  0.0000000000000000
     0.0000000000000000  0.0000000000000000  0.0000000000000000
   

   Note that although FORCE_CONSTANTS may be obtained using relaxed atomic positions, here the positions must be the ideal ones.

   POSCAR_ideal is the ideal configuration, from which the crystallographic symmetry is extracted.

   X
       1.00000000000000
           3.7530000000000001    0.0000000000000000    0.0000000000000000
           0.0000000000000000    3.7530000000000001    0.0000000000000000
           0.0000000000000000    0.0000000000000000    3.7530000000000001
       X
           4
   Direct
       0.0000000000000000  0.5000000000000000  0.5000000000000000
       0.5000000000000000  0.0000000000000000  0.5000000000000000
       0.5000000000000000  0.5000000000000000  0.0000000000000000
       0.0000000000000000  0.0000000000000000  0.0000000000000000
   

   In this file I recommend to use dummy symbols like 'X' to avoid confusion.

4. Prepare band.conf file including something like

   DIM =  2 2 2
   PRIMITIVE_AXIS =  0 1/2 1/2  1/2 0 1/2  1/2 1/2 0
   BAND =   0 0 0  0 1/2 1/2, 1 1/2 1/2  0 0 0  1/2 1/2 1/2
   BAND_POINTS = 101
   BAND_LABELS =  \Gamma X \Gamma L
   FORCE_CONSTANTS = READ
   

   The style is very similar to that of phonopy conf files, but be careful about the following tags.

   • DIM describes the expansion from the original POSCAR to the POSCARs with atomic displacements used to get FORCE_SETS. Therefore, this should be the same as the phonopy option when creating the structures with atomic displacements (1).

   • PRIMITIVE_AXIS is the conversion matrix from POSCAR_ideal to the primitive cell you expect.

   Since v0.6.2: We can also use BAND = AUTO like

   DIM =  2 2 2
   PRIMITIVE_AXIS =  0 1/2 1/2  1/2 0 1/2  1/2 1/2 0
   BAND = AUTO
   BAND_POINTS = 101
   FORCE_CONSTANTS = READ
   

   Internally, this uses SeeK-path via phonopy.

5. Run

   upho_weights band.conf
   

   You hopefully get band.hdf5 file. Note that this file can be in the order of GB.

6. Run

   upho_sf --fpitch 0.01 -s 0.05 --function lorentzian --format text
   

   You hopefully get sf_E1.dat, sf_E2.dat, and sf_SR.dat files. In these files:

   • 1st column: distance in the reciprocal space
   • 2nd column: frequencies
   • 3rd column: values of spectral functions

   Further

   • sf_E1.dat has the element-pair-resolved spectral functions.
   • sf_E2.dat has the element-resolved spectral functions.
   • sf_SR.dat has the spectral functions decomposed by the small representations.

7. Plot the spectral functions. You can refer to plot.py in the example directory. Hopefully you get the figure like below:

   

Atomic masses whose sites are equivalent in the underlying structure are averaged.

FC elements which are equivalent under the symmetry operations for the underlying structure are averaged.

Filename for the data of weights.

Output file format.

Function used for the smearing.

Parameter for the smearing function (THz). For Gaussian, this is the standard deviation. For Lorentzian, this is the HWHM (gamma).

Maximum frequency (THz).

Minimum frequency (THz).

Frequency pitch (THz).

Use squared frequencies instead of raw frequencies.

(Projective) representations of little cogroup may be treated in a wrong way when we consider wave vectors on the BZ boundary and translational parts of symmetry operations are not equal to zero.

Yuji Ikeda (yuji.ikeda.ac.jp@gmail.com, Universität Stuttgart, Germany)

When using this code, please cite the following article.

*Mode decomposition based on crystallographic symmetry in the band-unfolding method*,
Yuji Ikeda, Abel Carreras, Atsuto Seko, Atsushi Togo, and Isao Tanaka,
Phys. Rev. B **95**, 024305 (2017).
http://journals.aps.org/prb/abstract/10.1103/PhysRevB.95.024305

For high entropy alloy works, you can also consider

*Phonon Broadening in High Entropy Alloys*,
Fritz Körmann, Yuji Ikeda, Blazej Grabowski, and Marcel H. F. Sluiter,
Npj Comput. Mater. **3**, 1 (2017).
https://www.nature.com/articles/s41524-017-0037-8