-    PEROVSKITE     -    CaTiO3

Experimental structure. Atomic position and lattice parameters 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:  62  Pnma 
Lattice parameters (Å):  5.4043  5.4224  7.6510 
Angles (°):  90.0  90.0  90.0 

Symmetry (theoretical): 

Space group:  62  Pnma 
Lattice parameters (Å):  5.4043  5.4224  7.6510 
Angles (°):  90.0  90.0  90.0 

Cell contents: 

Number of atoms:  20 
Number of atom types:  3 
Chemical composition:  0 

Atomic positions (theoretical):

Ca:  0.9916  0.0123  0.2500 
Ti:  0.5000  0.0000  0.0000 
O:  0.0586  0.4687  0.2500 
O:  0.7130  0.2880  0.0371 
Ca:  0.4916  0.4877  0.7500 
Ti:  0.0000  0.5000  0.0000 
O:  0.5586  0.0313  0.7500 
O:  0.2130  0.2120  0.9629 
Ca:  0.0084  0.9877  0.7500 
Ti:  0.5000  0.0000  0.5000 
O:  0.9414  0.5313  0.7500 
O:  0.2870  0.7120  0.5371 
Ca:  0.5084  0.5123  0.2500 
Ti:  0.0000  0.5000  0.5000 
O:  0.4414  0.9687  0.2500 
O:  0.7870  0.7880  0.4629 
O:  0.2870  0.7120  0.9629 
O:  0.7870  0.7880  0.0371 
O:  0.7130  0.2880  0.4629 
O:  0.2130  0.2120  0.5371 
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
A1g
80
80
80
80
2.004e+40
13.8
1.493e+40
10.3
3.497e+40
24.1
5
A1g
110
110
110
110
3.616e+39
2.5
2.406e+39
1.7
6.022e+39
4.2
6
Au
114
114
114
114
7
B3u
132
139
132
132
8
B1g
139
139
139
139
2.713e+39
1.9
3.731e+39
2.6
6.444e+39
4.4
9
B1u
139
141
139
155
10
B3g
157
157
157
157
1.062e+36
0.0
1.460e+36
0.0
2.521e+36
0.0
11
B2u
169
169
174
169
12
Au
174
174
185
174
13
B1g
199
199
199
199
1.049e+40
7.2
1.442e+40
9.9
2.491e+40
17.2
14
Au
200
200
200
200
15
B2u
217
217
218
217
16
B2g
223
223
223
223
1.336e+39
0.9
1.838e+39
1.3
3.174e+39
2.2
17
B1u
224
224
224
232
18
B3u
232
233
232
232
19
B1u
233
237
233
237
20
B3g
237
245
237
255
1.960e+39
1.4
2.695e+39
1.9
4.655e+39
3.2
21
Au
255
255
255
256
22
B1g
256
256
256
265
8.985e+39
6.2
1.236e+40
8.5
2.134e+40
14.7
23
B2u
265
265
275
277
24
B3u
277
281
277
299
25
B2u
299
299
302
302
26
A1g
302
302
316
316
2.008e+40
13.8
3.889e+39
2.7
2.396e+40
16.5
27
A1g
316
316
324
324
2.485e+40
17.1
3.048e+39
2.1
2.789e+40
19.2
28
B3u
324
352
340
342
29
B2g
370
370
370
370
2.055e+38
0.1
2.826e+38
0.2
4.881e+38
0.3
30
Au
381
381
381
381
31
B2u
381
381
388
381
32
B1u
388
388
395
395
33
A1g
395
395
412
412
1.170e+40
8.1
8.636e+39
6.0
2.034e+40
14.0
34
B3u
412
427
427
427
35
B1g
427
431
434
434
2.847e+39
2.0
3.914e+39
2.7
6.761e+39
4.7
36
B3u
434
434
445
445
37
B3g
445
445
456
456
1.384e+39
1.0
1.903e+39
1.3
3.288e+39
2.3
38
B3u
456
460
459
460
39
B2u
460
500
500
473
40
B1g
500
506
506
500
2.960e+39
2.0
4.070e+39
2.8
7.031e+39
4.8
41
B1u
506
514
514
514
42
B2g
514
532
521
532
1.950e+40
13.4
2.681e+40
18.5
4.631e+40
31.9
43
Au
532
535
532
535
44
A1g
535
547
535
547
9.683e+40
66.8
4.820e+40
33.2
1.450e+41
100.0
45
B2u
547
550
549
550
46
B1g
550
550
550
556
2.807e+40
19.4
3.860e+40
26.6
6.667e+40
46.0
47
Au
564
564
564
564
48
B3u
573
581
573
573
49
B2g
581
583
581
581
2.189e+40
15.1
3.010e+40
20.8
5.200e+40
35.9
50
B2u
604
604
614
604
51
B1u
615
615
615
662
52
B3g
662
662
662
682
1.222e+40
8.4
1.680e+40
11.6
2.902e+40
20.0
53
A1g
682
682
682
688
8.785e+40
60.6
1.670e+40
11.5
1.046e+41
72.1
54
Au
688
688
688
705
55
B3u
705
719
705
710
56
B1u
719
727
719
727
57
B2u
727
784
784
784
58
B3g
784
923
923
838
1.392e+40
9.6
1.915e+40
13.2
3.307e+40
22.8
59
B1g
923
927
927
923
2.851e+38
0.2
3.920e+38
0.3
6.771e+38
0.5
60
B2g
927
940
958
927
8.608e+38
0.6
1.184e+39
0.8
2.044e+39
1.4
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.