-    SPHAEROBISMOITE     -    Bi2O3

Theoretical atomic positions and lattice parameters at experimental volum from 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:  114  P-42_1c 
Lattice parameters (Å):  4.0953  4.0953  2.9824 
Angles (°):  90.0  90.0  90.0 

Symmetry (theoretical): 

Space group:  114  P-42_1c 
Lattice parameters (Å):  7.7936  7.7936  5.5574 
Angles (°):  90.0  90.0  90.0 

Cell contents: 

Number of atoms:  20 
Number of atom types: 
Chemical composition: 

Atomic positions (theoretical):

Bi:  0.0322  0.2639  0.2546 
O:  0.2878  0.3261  0.0632 
O:  0.0000  0.5000  0.4197 
Bi:  0.7361  0.0322  0.7454 
O:  0.6739  0.2878  0.9368 
O:  0.5000  0.0000  0.5803 
Bi:  0.4678  0.7639  0.2454 
O:  0.2122  0.8261  0.4368 
O:  0.5000  0.0000  0.0803 
Bi:  0.9678  0.7361  0.2546 
O:  0.7122  0.6739  0.0632 
Bi:  0.2361  0.4678  0.7546 
O:  0.1739  0.2122  0.5632 
O:  0.0000  0.5000  0.9197 
Bi:  0.7639  0.5322  0.7546 
O:  0.8261  0.7878  0.5632 
Bi:  0.2639  0.9678  0.7454 
O:  0.3261  0.7122  0.9368 
Bi:  0.5322  0.2361  0.2454 
O:  0.7878  0.1739  0.4368 
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
B1
33
33
33
33
8.229e+38
0.1
6.172e+38
0.0
1.440e+39
0.1
5
E
44
44
44
44
3.507e+39
0.2
4.823e+39
0.3
8.330e+39
0.6
6
E
44
44
44
44
3.507e+39
0.2
4.823e+39
0.3
8.330e+39
0.6
7
A1
60
60
60
60
4.525e+40
3.1
3.255e+40
2.2
7.780e+40
5.4
8
E
62
62
62
62
2.135e+39
0.1
2.935e+39
0.2
5.070e+39
0.3
9
E
62
68
68
62
2.135e+39
0.1
2.935e+39
0.2
5.070e+39
0.3
10
E
68
68
68
68
1.317e+40
0.9
1.811e+40
1.2
3.128e+40
2.2
11
E
68
73
73
68
1.317e+40
0.9
1.811e+40
1.2
3.128e+40
2.2
12
A2
73
74
74
73
13
A1
74
81
81
74
3.603e+41
24.8
1.770e+40
1.2
3.780e+41
26.1
14
B1
85
85
85
85
7.492e+39
0.5
5.619e+39
0.4
1.311e+40
0.9
15
E
86
86
86
86
1.054e+40
0.7
1.449e+40
1.0
2.502e+40
1.7
16
E
86
86
86
86
1.054e+40
0.7
1.449e+40
1.0
2.502e+40
1.7
17
E
105
105
105
105
1.176e+39
0.1
1.617e+39
0.1
2.793e+39
0.2
18
E
105
110
110
105
1.176e+39
0.1
1.617e+39
0.1
2.793e+39
0.2
19
A2
116
116
116
116
20
B2
118
118
118
123
1.255e+39
0.1
1.726e+39
0.1
2.981e+39
0.2
21
B1
124
124
124
124
2.650e+40
1.8
1.988e+40
1.4
4.638e+40
3.2
22
A1
124
124
124
124
1.429e+41
9.9
3.056e+40
2.1
1.735e+41
12.0
23
B2
144
144
144
153
2.444e+39
0.2
3.360e+39
0.2
5.804e+39
0.4
24
E
163
163
163
163
1.260e+39
0.1
1.732e+39
0.1
2.992e+39
0.2
25
E
163
164
164
163
1.260e+39
0.1
1.732e+39
0.1
2.992e+39
0.2
26
A1
164
164
164
164
1.133e+41
7.8
1.760e+38
0.0
1.135e+41
7.8
27
A2
164
167
167
164
28
E
181
181
181
181
6.767e+39
0.5
9.305e+39
0.6
1.607e+40
1.1
29
E
181
191
191
181
6.768e+39
0.5
9.305e+39
0.6
1.607e+40
1.1
30
B1
191
191
191
191
4.869e+39
0.3
3.652e+39
0.3
8.521e+39
0.6
31
A2
191
191
191
191
3.557e+39
0.2
2.668e+39
0.2
6.224e+39
0.4
32
B2
191
191
191
198
6.549e+39
0.5
9.005e+39
0.6
1.555e+40
1.1
33
E
231
231
231
231
3.346e+40
2.3
4.601e+40
3.2
7.947e+40
5.5
34
E
231
242
242
231
3.346e+40
2.3
4.601e+40
3.2
7.947e+40
5.5
35
E
244
244
244
244
8.731e+39
0.6
1.201e+40
0.8
2.074e+40
1.4
36
E
244
250
250
244
8.731e+39
0.6
1.201e+40
0.8
2.074e+40
1.4
37
B1
258
258
258
258
5.727e+39
0.4
4.295e+39
0.3
1.002e+40
0.7
38
E
265
265
265
265
2.765e+38
0.0
3.802e+38
0.0
6.567e+38
0.0
39
E
265
275
275
265
2.765e+38
0.0
3.802e+38
0.0
6.567e+38
0.0
40
A1
275
314
314
275
5.513e+41
38.0
2.131e+36
0.0
5.513e+41
38.0
41
B2
314
316
316
316
5.722e+39
0.4
7.868e+39
0.5
1.359e+40
0.9
42
A1
316
337
337
332
1.426e+42
98.3
2.528e+40
1.7
1.451e+42
100.0
43
B2
344
344
344
374
3.578e+40
2.5
4.920e+40
3.4
8.498e+40
5.9
44
E
374
374
374
374
2.792e+40
1.9
3.839e+40
2.6
6.631e+40
4.6
45
E
374
388
388
388
2.792e+40
1.9
3.839e+40
2.6
6.631e+40
4.6
46
A2
388
404
404
436
47
B1
456
456
456
456
9.476e+38
0.1
7.107e+38
0.0
1.658e+39
0.1
48
E
468
468
468
468
2.969e+40
2.0
4.083e+40
2.8
7.052e+40
4.9
49
E
468
484
484
468
2.969e+40
2.0
4.083e+40
2.8
7.052e+40
4.9
50
A2
484
486
486
484
51
A1
486
489
489
486
5.469e+41
37.7
2.014e+40
1.4
5.671e+41
39.1
52
A2
498
498
498
498
53
E
510
510
510
510
4.146e+39
0.3
5.700e+39
0.4
9.846e+39
0.7
54
E
510
546
546
510
4.146e+39
0.3
5.700e+39
0.4
9.846e+39
0.7
55
B2
548
548
548
555
5.300e+40
3.7
7.288e+40
5.0
1.259e+41
8.7
56
B1
555
555
555
603
1.084e+40
0.7
8.132e+39
0.6
1.898e+40
1.3
57
E
603
603
603
603
1.288e+39
0.1
1.770e+39
0.1
3.058e+39
0.2
58
E
603
617
617
613
1.288e+39
0.1
1.770e+39
0.1
3.058e+39
0.2
59
E
624
624
624
624
3.104e+39
0.2
4.268e+39
0.3
7.373e+39
0.5
60
E
624
636
636
624
3.104e+39
0.2
4.268e+39
0.3
7.373e+39
0.5
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.