-    POTASSIUM CARBONATE     -    K2CO3

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:  12  C2/m 
Lattice parameters (Å):  4.7123  2.7713  3.1989 
Angles (°):  90  101.32  90 

Symmetry (theoretical): 

Space group:  12  C2/m 
Lattice parameters (Å):  5.3119  5.3119  6.1685 
Angles (°):  7.79946214E+01  1.02005379E+02  1.17440928E+02 

Cell contents: 

Number of atoms:  12 
Number of atom types:  3 
Chemical composition:  0 

Atomic positions (theoretical):

K:  0.0000  0.0000  0.0000 
K:  0.0000  0.0000  0.5000 
K:  0.6661  0.3339  0.7272 
C:  0.6650  0.3350  0.2521 
O:  0.4082  0.1922  0.2991 
O:  0.7784  0.2216  0.1635 
K:  0.3339  0.6661  0.2728 
C:  0.3350  0.6650  0.7479 
O:  0.1922  0.4082  0.7009 
O:  0.2216  0.7784  0.8365 
O:  0.5918  0.8078  0.7009 
O:  0.8078  0.5918  0.2991 
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
Au
90
90
92
90
5
Bg
93
93
93
93
7.092e+37
0.1
8.033e+37
0.1
1.513e+38
0.3
6
Au
96
96
114
96
7
Ag
131
131
131
131
2.079e+38
0.4
1.144e+38
0.2
3.222e+38
0.6
8
Bu
133
133
133
141
9
Ag
145
145
145
145
7.318e+38
1.3
8.065e+38
1.4
1.538e+39
2.7
10
Bu
146
146
146
157
11
Bg
157
157
157
157
6.407e+38
1.1
7.728e+38
1.4
1.414e+39
2.5
12
Au
171
171
179
171
13
Bu
181
185
181
181
14
Bg
196
196
196
196
2.658e+39
4.7
2.999e+39
5.3
5.657e+39
9.9
15
Ag
220
220
220
220
7.732e+38
1.4
7.062e+38
1.2
1.479e+39
2.6
16
Bg
226
226
226
226
6.694e+39
11.7
8.028e+39
14.1
1.472e+40
25.8
17
Bu
229
238
229
229
18
Ag
239
239
239
239
2.497e+39
4.4
2.337e+39
4.1
4.834e+39
8.5
19
Bu
251
255
251
255
20
Ag
255
259
255
257
4.487e+39
7.9
4.573e+39
8.0
9.059e+39
15.9
21
Au
259
262
259
259
22
Au
277
277
278
277
23
Bu
278
278
290
285
24
Bu
290
329
321
334
25
Bg
692
692
692
692
1.415e+39
2.5
2.372e+39
4.2
3.786e+39
6.6
26
Au
693
693
694
693
27
Bu
706
706
706
706
28
Bu
706
707
706
707
1.397e+39
2.4
1.136e+39
2.0
2.533e+39
4.4
29
Bu
866
867
866
872
30
Ag
872
872
872
873
1.419e+38
0.2
1.377e+38
0.2
2.795e+38
0.5
31
Ag
1101
1101
1101
1101
5.435e+40
95.2
2.737e+39
4.8
5.709e+40
100.0
32
Bu
1102
1102
1102
1102
33
Au
1444
1444
1446
1444
34
Bg
1446
1446
1449
1446
2.083e+39
3.6
3.496e+39
6.1
5.579e+39
9.8
35
Bu
1449
1468
1468
1468
36
Ag
1468
1543
1551
1477
1.564e+39
2.7
1.569e+39
2.7
3.133e+39
5.5
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.