-    CORUNDUM     -    Al2O3

The crystal structure is fully relaxed (both unit cell parameters and atomic positions under symmetry constraints) starting from an experimental structure similar to the one reported in AMCSD 

Crystal Structure 


Because of the translational symmetry all the calculations are performed in the primitive unit cell and not in the conventional unit cell. The following information regarding the structure is given with respect to this primitive unit cell, which sometimes can take an unintuitive shape.

Symmetry (experimental): 

Space group:  167  R-3c 
Lattice parameters (Å):  2.5190  2.5190  6.8758 
Angles (°):  90.0  90.0  120.0 

Symmetry (theoretical): 

Space group:  167  R-3c 
Lattice parameters (Å):  5.0460  5.0460  5.0460 
Angles (°):  55.3  55.3  55.3 

Cell contents: 

Number of atoms:  10 
Number of atom types: 
Chemical composition: 

Atomic positions (theoretical):

Al:  0.3520  0.3520  0.3520 
Al:  0.8520  0.8520  0.8520 
Al:  0.6480  0.6480  0.6480 
Al:  0.1480  0.1480  0.1480 
O:  0.5563  0.9437  0.2500 
O:  0.2500  0.5563  0.9437 
O:  0.9437  0.2500  0.5563 
O:  0.4437  0.0563  0.7500 
O:  0.7500  0.4437  0.0563 
O:  0.0563  0.7500  0.4437 
Atom type 

We have listed here the reduced coordinates of all the atoms in the primitive unit cell.
It is enough to know only the position of the atoms from the assymetrical unit cell and then use the symmetry to build the whole crystal structure.

Visualization of the crystal structure: 

Size:

  
Nx:  Ny:  Nz:    
You can define the size of the supercell to be displayed in the jmol panel as integer translations along the three crys­tallo­gra­phic axis.
Please note that the structure is represented using the pri­mi­tive cell, and not the conventional one.
     

Powder Raman 

Powder Raman spectrum

The intensity of the Raman peaks is computed within the density-functional perturbation theory. The intensity depends on the temperature (for now fixed at 300K), frequency of the input laser (for now fixed at 21834 cm-1, frequency of the phonon mode and the Raman tensor. The Raman tensor represents the derivative of the dielectric tensor during the atomic displacement that corresponds to the phonon vibration. The Raman tensor is related to the polarizability of a specific phonon mode.

Horizontal:
Xmin:
Xmax:
Vertical:
Ymin:
Ymax:
 
Choose the polarization of the lasers.
I ∥ 
I ⊥ 
I Total 

Data about the phonon modes

Frequency of the transverse (TO) and longitudinal (LO) phonon modes in the zone-center. The longitudinal modes are computed along the three cartesian directions. You can visualize the atomic displacement pattern corresponding to each phonon by clicking on the appropriate cell in the table below.

1
ac
0
0
0
0
2
ac
0
0
0
0
3
ac
0
0
0
0
4
A2g
305
305
305
305
5
Eg
377
377
377
377
5.579e+38
9.5
9.079e+38
15.5
1.466e+39
25.0
6
Eg
377
377
377
377
5.579e+38
9.5
6.263e+38
10.7
1.184e+39
20.2
7
Eu
384
384
384
384
8
Eu
384
387
387
384
9
A2u
395
395
395
418
10
A1g
418
418
418
432
5.722e+39
97.7
1.365e+38
2.3
5.858e+39
100.0
11
Eg
432
432
432
432
2.854e+38
4.9
4.295e+38
7.3
7.149e+38
12.2
12
Eg
432
432
432
439
2.854e+38
4.9
3.870e+38
6.6
6.723e+38
11.5
13
Eu
439
439
439
439
14
Eu
439
446
446
446
15
Eg
446
446
446
446
1.228e+38
2.1
1.594e+38
2.7
2.822e+38
4.8
16
Eg
446
481
481
504
1.228e+38
2.1
1.709e+38
2.9
2.937e+38
5.0
17
A2g
535
535
535
535
18
Eu
570
570
570
570
19
Eu
570
575
575
570
20
Eg
575
575
575
575
1.480e+38
2.5
1.969e+38
3.4
3.449e+38
5.9
21
Eg
575
580
580
575
1.480e+38
2.5
1.176e+38
2.0
2.655e+38
4.5
22
A2u
580
599
599
599
23
A1u
599
630
630
634
24
Eu
634
634
634
634
25
Eu
634
644
644
644
26
A1g
644
696
696
696
8.933e+38
15.2
5.679e+38
9.7
1.461e+39
24.9
27
A1u
696
753
753
753
28
Eg
753
753
753
753
7.762e+38
13.2
7.489e+38
12.8
1.525e+39
26.0
29
Eg
753
754
754
754
7.762e+38
13.2
8.200e+38
14.0
1.596e+39
27.2
30
A2g
754
901
901
872
No.  Char.  ω TO  ω LOx  ω LOy  ω LOz  I ∥  I ⊥  I Total 
You can define the size of the supercell for the visualization of the vibration.
Nx: 
Ny: 
Nz: 
Normalized
Raw
Options for intensity.