- Magnesium Sulfate-beta - MgSO₄

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		Pbnm
Lattice parameters (Å):	4.7343	8.5817		6.6726
Angles (°):	90	90		90

Symmetry (theoretical):

Space group:	62		Pbnm
Lattice parameters (Å):	4.6788	8.4992		6.5056
Angles (°):	90	90		90

Cell contents:

Number of atoms:	24
Number of atom types:	3
Chemical composition:	0

Atomic positions (theoretical):

Mg:	0.0000	0.0000	0.0000
S:	0.4783	0.1788	0.2500
O:	0.7792	0.1246	0.2500
O:	0.4609	0.3541	0.2500
O:	0.3386	0.1242	0.0638
Mg:	0.5000	0.5000	0.0000
S:	0.9783	0.3212	0.7500
O:	0.2792	0.3754	0.7500
O:	0.9609	0.1459	0.7500
O:	0.8386	0.3758	0.9362
Mg:	0.0000	0.0000	0.5000
S:	0.5217	0.8212	0.7500
O:	0.2208	0.8754	0.7500
O:	0.5391	0.6459	0.7500
O:	0.6614	0.8758	0.5638
Mg:	0.5000	0.5000	0.5000
S:	0.0217	0.6788	0.2500
O:	0.7208	0.6246	0.2500
O:	0.0391	0.8541	0.2500
O:	0.1614	0.6242	0.4362
O:	0.6614	0.8758	0.9362
O:	0.1614	0.6242	0.0638
O:	0.3386	0.1242	0.4362
O:	0.8386	0.3758	0.5638

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	B2u	86	86	86	86
5	Au	115	115	115	115
6	B2g	119	119	119	119	7.975e+36 0.0	1.097e+37 0.0	1.894e+37 0.0
7	B1u	127	127	127	143
8	Au	143	143	143	147
9	B3u	147	148	147	149
10	B3g	154	154	154	154	3.471e+38 0.3	4.772e+38 0.4	8.243e+38 0.6
11	Au	160	160	160	160
12	A1g	165	165	165	165	7.257e+37 0.1	2.419e+37 0.0	9.676e+37 0.1
13	Au	176	176	176	176
14	B1u	178	178	178	178
15	B1g	178	178	178	191	2.163e+36 0.0	2.973e+36 0.0	5.136e+36 0.0
16	B2u	199	199	204	199
17	B1u	204	204	209	209
18	B1g	209	209	216	214	3.176e+38 0.2	4.366e+38 0.3	7.542e+38 0.6
19	B3u	216	216	218	216
20	A1g	218	218	233	218	6.309e+39 4.7	6.228e+38 0.5	6.932e+39 5.1
21	B3g	241	241	241	241	8.312e+38 0.6	1.143e+39 0.8	1.974e+39 1.5
22	A1g	243	243	243	243	2.938e+38 0.2	4.821e+37 0.0	3.420e+38 0.3
23	B2u	250	250	254	250
24	B3u	254	259	259	254
25	B1g	259	260	260	259	2.261e+38 0.2	3.109e+38 0.2	5.370e+38 0.4
26	B2g	260	269	269	260	4.524e+38 0.3	6.221e+38 0.5	1.075e+39 0.8
27	B2g	269	297	270	269	4.464e+37 0.0	6.138e+37 0.0	1.060e+38 0.1
28	Au	297	304	297	297
29	B1u	304	307	304	307
30	B3g	307	325	307	321	8.199e+38 0.6	1.127e+39 0.8	1.947e+39 1.4
31	B3u	341	342	341	341
32	B2u	371	371	404	371
33	B2u	404	404	417	404
34	Au	417	417	420	417
35	B3u	420	428	424	420
36	B1u	429	429	429	437
37	A1g	437	437	437	458	1.477e+40 11.0	1.396e+39 1.0	1.616e+40 12.0
38	B1g	461	461	461	461	6.470e+39 4.8	8.896e+39 6.6	1.537e+40 11.4
39	B3g	493	493	493	493	4.135e+39 3.1	5.686e+39 4.2	9.820e+39 7.3
40	B1u	495	495	495	503
41	B2g	503	503	503	503	4.677e+39 3.5	6.431e+39 4.8	1.111e+40 8.2
42	B2u	504	504	506	504
43	Au	506	506	506	506
44	B3u	506	524	527	506
45	B1g	582	582	582	582	1.113e+39 0.8	1.531e+39 1.1	2.644e+39 2.0
46	A1g	586	586	586	586	1.100e+40 8.2	5.921e+39 4.4	1.692e+40 12.6
47	B3u	589	591	589	589
48	B2u	591	598	594	591
49	A1g	598	609	598	598	9.894e+39 7.3	5.948e+39 4.4	1.584e+40 11.8
50	B2u	609	611	611	609
51	B1g	611	612	612	611	8.921e+38 0.7	1.227e+39 0.9	2.119e+39 1.6
52	B3u	624	624	624	624
53	B2g	668	668	668	668	1.749e+39 1.3	2.405e+39 1.8	4.155e+39 3.1
54	B1u	686	686	686	688
55	B3g	688	688	688	707	1.226e+39 0.9	1.686e+39 1.3	2.912e+39 2.2
56	Au	707	707	707	718
57	B1g	995	995	995	995	1.192e+39 0.9	1.639e+39 1.2	2.831e+39 2.1
58	B3u	998	1006	998	998
59	A1g	1006	1006	1006	1006	1.333e+41 98.9	1.472e+39 1.1	1.348e+41 100.0
60	B2u	1008	1008	1013	1008
61	A1g	1036	1036	1036	1036	1.649e+40 12.2	4.831e+39 3.6	2.133e+40 15.8
62	B2u	1058	1058	1098	1058
63	B3u	1098	1107	1116	1098
64	B1g	1116	1116	1123	1116	1.622e+39 1.2	2.230e+39 1.7	3.852e+39 2.9
65	A1g	1128	1128	1128	1128	3.703e+40 27.5	2.809e+39 2.1	3.984e+40 29.6
66	B3u	1138	1168	1138	1138
67	B2u	1168	1196	1196	1168
68	B1u	1196	1213	1213	1213
69	B1g	1213	1223	1223	1223	1.286e+37 0.0	1.768e+37 0.0	3.054e+37 0.0
70	Au	1223	1225	1223	1225
71	B2g	1225	1243	1225	1260	5.865e+39 4.4	8.065e+39 6.0	1.393e+40 10.3
72	B3g	1260	1260	1260	1293	1.397e+39 1.0	1.921e+39 1.4	3.317e+39 2.5

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.

Normalized

Raw

Options for intensity.

Nx:
Ny:
Nz:

- Magnesium Sulfate-beta - MgSO4