wiki:Al2O3

Al2O3 Corundum

Al2O3 Corundum structure, 60-atom orthorhombic supercell.
Ground state calculation and unit cell optimization using the PBE exchange-correlation functional.

The orthorhombic cell has dimensions (sqrt(3)aH , aH , cH) where aH and cH are the hexagonal lattice parameters. A (2x4x1) k-point grid is used.

Pseudopotentials

Ground state calculation

al2o3_60_oncv.i
Initial orthorhombic unit cell definition and atomic positions (attachment:al2o3_60_oncv.i)
# Al2O3 Corundum 60-atom orthorhombic cell
set ref_cell 17 0 0  0 11 0  0 0 26
set cell 15.5734 0 0 0 8.99132 0 0 0 24.5494
species aluminum Al_ONCV_PBE-1.0.xml
species oxygen O_ONCV_PBE-1.0.xml 
atom Al1_000 aluminum -3.89336 -2.24783 8.64828
atom Al1_100 aluminum 3.89336 2.24783 8.64828
atom Al2_000 aluminum -3.89336 -2.24783 3.62644
atom Al2_100 aluminum 3.89336 2.24783 3.62644
atom Al3_000 aluminum -3.89336 -2.24783 -8.64828
atom Al3_100 aluminum 3.89336 2.24783 -8.64828
atom Al4_000 aluminum -3.89336 -2.24783 -3.6264
atom Al4_100 aluminum 3.89336 2.24783 -3.6264
atom Al5_000 aluminum -1.29779 2.24783 -7.718
atom Al5_100 aluminum 6.48893 -2.24783 -7.718
atom Al6_000 aluminum -1.29779 2.24783 11.8096
atom Al6_100 aluminum 6.48893 -2.24783 11.8096
atom Al7_000 aluminum -1.29779 2.24783 -0.46513
atom Al7_100 aluminum 6.48893 -2.24783 -0.46513
atom Al8_000 aluminum -1.29779 2.24783 4.5567
atom Al8_100 aluminum 6.48893 -2.24783 4.5567
atom Al9_000 aluminum -6.48893 2.24783 0.4652
atom Al9_100 aluminum 1.29779 -2.24783 0.4652
atom Al10_000 aluminum -6.48893 2.24783 -4.5567
atom Al10_100 aluminum 1.29779 -2.24783 -4.5567
atom Al11_000 aluminum -6.48893 2.24783 7.71802
atom Al11_100 aluminum 1.29779 -2.24783 7.71802
atom Al12_000 aluminum -6.48893 2.24783 12.7399
atom Al12_100 aluminum 1.29779 -2.24783 12.7399
atom O1_000 oxygen -1.50751 -0.87036 6.13736
atom O1_100 oxygen 6.27921 3.6253 6.13736
atom O2_000 oxygen -6.27921 -0.87036 6.13736
atom O2_100 oxygen 1.50751 3.6253 6.13736
atom O3_000 oxygen -3.89336 3.98855 6.13736
atom O3_100 oxygen 3.89336 -0.50711 6.13736
atom O4_000 oxygen -6.27921 -3.6253 -6.1373
atom O4_100 oxygen 1.50751 0.87036 -6.1373
atom O5_000 oxygen -1.50751 -3.6253 -6.1373
atom O5_100 oxygen 6.27921 0.87036 -6.1373
atom O6_000 oxygen -3.89336 0.50711 -6.1373
atom O6_100 oxygen 3.89336 -3.98855 -6.1373
atom O7_000 oxygen 1.08806 3.6253 -10.2289
atom O7_100 oxygen -6.69863 -0.87036 -10.2289
atom O8_000 oxygen -3.68363 3.6253 -10.2289
atom O8_100 oxygen 4.10308 -0.87036 -10.2289
atom O9_000 oxygen -1.29779 -0.50711 -10.2289
atom O9_100 oxygen 6.48893 3.98855 -10.2289
atom O10_000 oxygen -3.68363 0.87036 2.0458
atom O10_100 oxygen 4.10308 -3.6253 2.0458
atom O11_000 oxygen 1.08806 0.87036 2.0458
atom O11_100 oxygen -6.69863 -3.6253 2.0458
atom O12_000 oxygen -1.29779 -3.98855 2.0458
atom O12_100 oxygen 6.48893 0.50711 2.0458
atom O13_000 oxygen -4.10308 3.6253 -2.0457
atom O13_100 oxygen 3.68363 -0.87036 -2.0457
atom O14_000 oxygen 6.69863 3.6253 -2.0457
atom O14_100 oxygen -1.08806 -0.87036 -2.0457
atom O15_000 oxygen -6.48893 -0.50711 -2.0457
atom O15_100 oxygen 1.29779 3.98855 -2.0457
atom O16_000 oxygen 6.69863 0.87036 10.229
atom O16_100 oxygen -1.08806 -3.6253 10.229
atom O17_000 oxygen -4.10308 0.87036 10.229
atom O17_100 oxygen 3.68363 -3.6253 10.229
atom O18_000 oxygen -6.48893 -3.98855 10.229
atom O18_100 oxygen 1.29779 0.50711 10.229
gs.i
Qbox input file for the ground state calculation (attachment:gs.i)
set nrowmax 72
al2o3_60_oncv.sys
kp241.i
set xc PBE
set ecut 65
set ecuts 60
set stress ON
set wf_dyn JD
randomize_wf
set scf_tol 1.e-8
run -atomic_density 0 30 5
save gs.xml
kp241.i
k-point set (2x4x1) (attachment:kp241.i)
# kpgen-1.1
# nx,ny,nz: 2 4 1
# sx,sy,sz: 0 0 0
# a0: 1 0 0
# a1: 0 1 0
# a2: 0 0 1
# b0/(2pi): 1 0 0
# b1/(2pi): 0 1 0
# b2/(2pi): 0 0 1
# 4 k-points
 kpoint delete 0 0 0
 kpoint add  0.2500000000 -0.3750000000  0.0000000000   2.50000000000000e-01
 kpoint add  0.2500000000 -0.1250000000  0.0000000000   2.50000000000000e-01
 kpoint add  0.2500000000  0.1250000000  0.0000000000   2.50000000000000e-01
 kpoint add  0.2500000000  0.3750000000  0.0000000000   2.50000000000000e-01
gs.r
Qbox output file for the ground state calculation (attachment:gs.r)
Ground state energy (hartree):
<etotal>   -2239.70535354 </etotal> 
Stress tensor (GPa):
<sigma_xx>   6.50679227 </sigma_xx> 
<sigma_yy>   6.65762281 </sigma_yy> 
<sigma_zz>   5.92091018 </sigma_zz> 
<sigma_xy>  -0.00000107 </sigma_xy> 
<sigma_yz>   0.00000430 </sigma_yz> 
<sigma_xz>  -0.00091384 </sigma_xz> 

Unit cell optimization

relax.i
Qbox input file for the unit cell optimization (attachment:relax.i)
set nrowmax 72
load gs.xml
set xc PBE
set ecuts 60
set stress ON
set wf_dyn JD
set cell_dyn CG
set cell_lock S
set scf_tol 1.e-8
run 10 20 5
save relax.xml
relax.r
Qbox output file for the unit cell optimization (attachment:relax.r)
Final ground state energy (hartree):
<etotal> -2239.71482615 </etotal>
Final stress tensor (GPa):
<sigma_xx>   0.03039663 </sigma_xx> 
<sigma_yy>   0.02755605 </sigma_yy> 
<sigma_zz>   0.00744353 </sigma_zz> 
<sigma_xy>   0.00000001 </sigma_xy> 
<sigma_yz>   0.00000048 </sigma_yz> 
<sigma_xz>  -0.00546917 </sigma_xz> 
Final unit cell dimensions (Bohr):
<unit_cell_a_norm> 15.702675 </unit_cell_a_norm>
<unit_cell_b_norm> 9.071230  </unit_cell_b_norm>
<unit_cell_c_norm> 24.757632 </unit_cell_c_norm>
<unit_cell_alpha>  90.000    </unit_cell_alpha>
<unit_cell_beta>   90.000    </unit_cell_beta>
<unit_cell_gamma>  90.000    </unit_cell_gamma>
<unit_cell_volume> 3526.541  </unit_cell_volume>

The final unit cell dimensions correspond to hexagonal lattice parameters aH=4.800 Å or aH=4.797 Å (depending on whether aH is derived from the a or b orthorhombic cell dimension) and cH=13.101 Å

The evolution of the stress tensor during the unit cell optimization can be plotted using the sigma.plt script provided in the util directory: (attachment:al2o3_sigma.png) Evolution of the stress tensor during unit cell optimization

Last modified at 2017-02-08T02:19:46Z Last modified on 2017-02-08T02:19:46Z

Attachments (7)

Download all attachments as: .zip