-    BADDELEYITE     -    ZrO2

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. Computed using Troullier-Martisn (fhi) pseudopotentials 

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:  14  P2_1/c 
Lattice parameters (Å):  5.1450  5.2075  5.3107 
Angles (°):  90.0  99.2  90.0 

Symmetry (theoretical): 

Space group:  14  P2_1/c 
Lattice parameters (Å):  5.0490  5.1404  5.1411 
Angles (°):  90.0  99.9  90.0 

Cell contents: 

Number of atoms:  12 
Number of atom types:  2 
Chemical composition:  0 

Atomic positions (theoretical):

Zr:  0.2795  0.0422  0.2043 
O:  0.0780  0.3507  0.3278 
O:  0.4458  0.7598  0.4873 
Zr:  0.7205  0.5422  0.2957 
O:  0.9220  0.8507  0.1722 
O:  0.5542  0.2598  0.0127 
Zr:  0.7205  0.9578  0.7957 
O:  0.9220  0.6493  0.6722 
O:  0.5542  0.2402  0.5127 
Zr:  0.2795  0.4578  0.7043 
O:  0.0780  0.1493  0.8278 
O:  0.4458  0.7402  0.9873 
Atom type  X  Y  Z 

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.

Choose the polarization of the lasers.

I ∥ 
I ⊥ 
I Total 
Horizontal:
Xmin:
Xmax:
Vertical:
Ymin:
Ymax:
 

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
Ag
148
148
148
148
3.135e+40
10.8
6.689e+39
2.3
3.804e+40
13.2
5
Bg
201
201
201
201
8.575e+39
3.0
9.750e+39
3.4
1.832e+40
6.3
6
Au
202
202
203
202
7
Ag
206
206
206
206
1.867e+40
6.5
1.963e+40
6.8
3.831e+40
13.3
8
Ag
209
209
209
209
3.183e+39
1.1
2.864e+39
1.0
6.047e+39
2.1
9
Bg
243
243
243
243
8.041e+39
2.8
1.311e+40
4.5
2.115e+40
7.3
10
Au
248
248
252
248
11
Bu
271
291
271
279
12
Au
297
297
314
297
13
Bg
343
343
343
343
7.850e+39
2.7
1.034e+40
3.6
1.819e+40
6.3
14
Bg
355
355
355
355
1.038e+40
3.6
1.587e+40
5.5
2.626e+40
9.1
15
Ag
366
366
366
366
1.027e+41
35.5
2.209e+39
0.8
1.049e+41
36.3
16
Bu
374
374
374
374
17
Bu
386
393
386
389
18
Ag
393
396
393
393
9.737e+39
3.4
8.016e+39
2.8
1.775e+40
6.1
19
Bu
425
436
425
436
20
Au
436
449
446
438
21
Bg
449
450
449
449
5.435e+40
18.8
8.784e+40
30.4
1.422e+41
49.2
22
Ag
450
477
450
450
2.373e+40
8.2
1.600e+40
5.5
3.973e+40
13.7
23
Au
477
484
485
477
24
Bu
485
515
525
542
25
Ag
542
542
542
565
2.028e+41
70.1
8.630e+40
29.9
2.891e+41
100.0
26
Bg
566
566
566
566
3.131e+40
10.8
3.557e+40
12.3
6.687e+40
23.1
27
Bu
570
573
570
573
28
Au
573
606
606
606
29
Bg
606
633
630
633
4.164e+39
1.4
6.168e+39
2.1
1.033e+40
3.6
30
Ag
633
662
633
677
3.413e+40
11.8
3.479e+40
12.0
6.892e+40
23.8
31
Au
677
677
697
697
32
Bg
697
697
706
706
3.378e+40
11.7
3.670e+40
12.7
7.048e+40
24.4
33
Au
706
706
741
727
34
Ag
741
741
799
741
6.106e+40
21.1
5.222e+40
18.1
1.133e+41
39.2
35
Bu
799
832
832
804
36
Bg
832
890
837
832
1.281e+40
4.4
1.363e+40
4.7
2.644e+40
9.1
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.