-    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 Teter "extended norm-conserving" 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):  5.0794  5.1726  5.2381 
Angles (°):  90.0  99.5  90.0 

Cell contents: 

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

Atomic positions (theoretical):

Zr:  0.2777  0.0426  0.2093 
O:  0.0723  0.3407  0.3380 
O:  0.4478  0.7581  0.4813 
Zr:  0.7223  0.5426  0.2907 
O:  0.9277  0.8407  0.1620 
O:  0.5522  0.2581  0.0187 
Zr:  0.7223  0.9574  0.7907 
O:  0.9277  0.6593  0.6620 
O:  0.5522  0.2419  0.5187 
Zr:  0.2777  0.4574  0.7093 
O:  0.0723  0.1593  0.8380 
O:  0.4478  0.7419  0.9813 
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
Ag
115
115
115
115
5.789e+40
16.5
1.013e+40
2.9
6.802e+40
19.4
5
Bg
176
176
176
176
1.730e+40
4.9
2.003e+40
5.7
3.733e+40
10.7
6
Ag
182
182
182
182
3.645e+40
10.4
2.429e+40
6.9
6.074e+40
17.4
7
Au
183
183
183
183
8
Ag
192
192
192
192
4.134e+40
11.8
3.722e+40
10.6
7.856e+40
22.4
9
Bg
225
225
225
225
1.703e+40
4.9
2.768e+40
7.9
4.471e+40
12.8
10
Bu
230
241
230
235
11
Au
241
245
241
241
12
Au
260
260
279
260
13
Bu
312
313
312
312
14
Bg
320
320
320
320
2.873e+39
0.8
3.763e+39
1.1
6.636e+39
1.9
15
Bu
321
325
321
325
16
Ag
325
333
325
325
1.123e+41
32.1
3.602e+39
1.0
1.159e+41
33.1
17
Bg
333
354
333
333
4.172e+40
11.9
6.307e+40
18.0
1.048e+41
29.9
18
Ag
354
359
354
354
3.456e+40
9.9
1.813e+40
5.2
5.268e+40
15.1
19
Au
359
363
364
359
20
Bu
364
386
374
386
21
Ag
386
391
386
391
3.037e+40
8.7
2.030e+40
5.8
5.067e+40
14.5
22
Bg
391
404
391
395
7.268e+40
20.8
1.154e+41
33.0
1.881e+41
53.8
23
Au
404
416
421
404
24
Bu
421
438
459
472
25
Ag
472
472
472
479
2.292e+41
65.5
1.208e+41
34.5
3.499e+41
100.0
26
Au
479
479
491
491
27
Bg
491
491
494
491
2.392e+40
6.8
2.551e+40
7.3
4.943e+40
14.1
28
Bu
494
540
540
540
29
Bg
540
553
553
553
3.016e+40
8.6
4.489e+40
12.8
7.505e+40
21.4
30
Ag
553
583
554
583
5.470e+40
15.6
5.817e+40
16.6
1.129e+41
32.3
31
Au
583
611
611
611
32
Bg
611
619
638
638
9.251e+40
26.4
9.961e+40
28.5
1.921e+41
54.9
33
Ag
638
638
643
643
1.208e+41
34.5
1.261e+41
36.0
2.469e+41
70.6
34
Au
643
643
722
671
35
Bu
722
754
754
726
36
Bg
754
815
764
754
1.403e+40
4.0
1.493e+40
4.3
2.896e+40
8.3
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.