1_Crystal

Design a crystal from scratch

In this tutorial we will create and optimize a crystal structure for a known material, wurtzite GaAs, making use of modern databases. This is a cell with hexagonal symmetry, as distinct from the diamond-like zinc blende phase.

1. Look up online the space group for the wurtzite crystal. According to Wikipedia https://en.wikipedia.org/wiki/Wurtzite_crystal_structure it is No. 186 or P6_3mc.
2. The easiest way to create an initial structure is by searching a materials database such as https://materialsproject.org (https://next-gen.materialsproject.org). After registering, search the database for GaAs, and find the entry that corresponds to this space group: it should have the index mp-8883. You might be able to find the link directly by searching e.g. "https://materialsproject.org GaAs wurtzite". The direct link is in fact: https://next-gen.materialsproject.org/materials/mp-8883?formula=GaAs
3. Browse the page and confirm this is what you are looking for. Download the geometry in the CIF format, e.g. in the conventional cell.

4. METHOD 1: At this point you can construct the PWscf input using the data in the CIF file:

   ibrav=4
   A=4.05346620
   C=6.67955800
   ATOMIC_POSITIONS {crystal} 
   Ga 0.66666667  0.33333333  0.49998900  
   Ga 0.33333333  0.66666667  0.99998900  
   As 0.66666667  0.33333333  0.87401100  
   As 0.33333333  0.66666667  0.37401100  
   

   Modify a pre-existing file, e.g.

   % ../../0_Si_bulk/3_charge/si.scf.in gaas.in
   

   making sure to modify the number of atoms, types, symmetry, etc. When you are ready, check it with xcrysden:

   % xcrysden --pwi gaas.in
   

5. Choose appropriate pseudopotentials from the quantum-ESPRESSO site. For simplicity, let's use the pseudo-DOJO again, LDA flavour. How many filled states do we expect?

   % grep z_valence *.upf
   As.upf:z_valence="   15.00"
   Ga.upf:z_valence="   13.00"
   

6. METHOD 2: Alternatively you can take the lazy option of using an input file generator at https://www.materialscloud.org/work/tools/qeinputgenerator or use some conversion tools like cif2cell https://sourceforge.net/projects/cif2cell/

7. Carry out a test calculation using a reasonable guess for the cutoff and k-point set, setting the number of bands in order to report the gap at the Gamma point. Use a small smearing. Is the gap large or small?

   Indeed, the small gap in GaAs with LDA/GGA makes calculations quite difficult to carry out. One must take much care with k-point sampling and convergence tests in general, as well as in choice of pseudopotentials.

8. Compute the band structure of wurtzite GaAs along a suitable path. Use either the Xcrysden k-path tool or the materials cloud seekpath tool: https://www.materialscloud.org/work/tools/seekpath

9. Carry out convergence tests on cutoff and k-points.

10. ADVANCED: Optimize the two lattice constants (a,c) of WZ GaAs using (1) vc-relax and (2) using a shell script.

11. ADVANCED: Repeat the exercise for zinc-blende (ZB) GaAs.

12. ADVANCED: Using fully relativistic pseudopotentials, compute the spin-orbit split-off energy for ZB GaAs.

Various material science databases:

• https://materialsproject.org
• http://oqmd.org/
• https://www.materialscloud.org/
• https://nomad-lab.eu/
• http://aflowlib.org/
• https://jarvis.nist.gov/
• https://materials.nrel.gov/
• http://www.2dmatpedia.org/
• https://omdb.mathub.io/ See https://www.nature.com/articles/s43588-020-00016-5 for a nice discussion of their use.