- POTASSIUM CARBONATE - K₂CO₃

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:	12		C2/m
Lattice parameters (Å):	8.9050	5.2370		6.0450
Angles (°):	90	101.32		90

Symmetry (theoretical):

Space group:	12		C2/m
Lattice parameters (Å):	5.1544	5.1544		6.0636
Angles (°):	75.99	104.00		116.96

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	0.7219
H:	0.6628	0.3372	0.2504
O:	0.4060	0.1905	0.3038
O:	0.7730	0.2270	0.1518
K:	0.3339	0.6661	0.2781
H:	0.3372	0.6628	0.7496
O:	0.1905	0.4060	0.6962
O:	0.2270	0.7730	0.8482
O:	0.5940	0.8095	0.6962
O:	0.8095	0.5940	0.3038

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:

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	69	69	87	69
5	Au	87	87	103	87
6	Bg	103	103	104	103	6.303e+38 1.0	7.175e+38 1.1	1.348e+39 2.1
7	Bu	144	144	144	148
8	Ag	151	151	151	151	3.788e+38 0.6	2.102e+38 0.3	5.889e+38 0.9
9	Ag	171	171	171	171	5.661e+38 0.9	6.282e+38 1.0	1.194e+39 1.9
10	Bg	174	174	174	174	8.500e+38 1.3	1.014e+39 1.6	1.864e+39 2.9
11	Bu	192	192	192	198
12	Bu	206	207	206	206
13	Au	212	212	216	212
14	Bg	246	246	246	246	2.672e+39 4.2	2.960e+39 4.7	5.633e+39 8.9
15	Bu	254	262	254	254
16	Ag	273	273	273	273	2.756e+38 0.4	1.347e+38 0.2	4.103e+38 0.6
17	Bg	277	277	277	277	4.738e+39 7.5	4.929e+39 7.8	9.667e+39 15.2
18	Bg	277	277	277	277	3.389e+39 5.3	3.702e+39 5.8	7.091e+39 11.2
19	Bu	292	299	292	297
20	Au	299	310	306	299
21	Ag	318	318	318	318	3.570e+39 5.6	3.218e+39 5.1	6.788e+39 10.7
22	Au	332	332	341	332
23	Bu	341	345	346	345
24	Bu	346	373	364	387
25	Bg	703	703	703	703	2.211e+39 3.5	3.711e+39 5.8	5.922e+39 9.3
26	Au	708	708	708	708
27	Ag	728	728	728	728	1.993e+39 3.1	1.637e+39 2.6	3.630e+39 5.7
28	Bu	729	730	729	730
29	Bu	868	869	868	876
30	Ag	876	876	876	876	5.233e+38 0.8	3.644e+38 0.6	8.877e+38 1.4
31	Ag	1130	1130	1130	1130	6.028e+40 95.0	3.178e+39 5.0	6.345e+40 100.0
32	Bu	1132	1132	1132	1132
33	Au	1477	1477	1484	1477
34	Bg	1484	1484	1485	1484	1.890e+39 3.0	3.185e+39 5.0	5.074e+39 8.0
35	Bu	1485	1508	1508	1508
36	Ag	1508	1576	1587	1520	1.344e+39 2.1	1.290e+39 2.0	2.634e+39 4.2

No.

Char.

ω TO

ω LOx

ω LOy

ω LOz

I ∥

I ⊥