- SULFUR - S₁₂

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 Zeitschrift ruer Anorganische ind Allgemeine Chemie (1950) (DE) (1981) 476, p171-p178

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:	58		Pnnm
Lattice parameters (Å):	4.7250	9.1040		14.5320
Angles (°):	90	90		90

Symmetry (theoretical):

Space group:	58		Pnnm
Lattice parameters (Å):	4.3240	8.8504		14.2063
Angles (°):	90	90		90

Cell contents:

Number of atoms:	24
Number of atom types:	1
Chemical composition:	0

Atomic positions (theoretical):

S:	0.0000	0.0000	0.2693
S:	0.2576	0.1349	0.3568
S:	0.0124	0.3290	0.3833
S:	0.2447	0.2100	0.0000
S:	0.7424	0.8651	0.3568
S:	0.9876	0.6710	0.3833
S:	0.7553	0.7900	0.0000
S:	0.5000	0.5000	0.2307
S:	0.2424	0.6349	0.1432
S:	0.4876	0.8290	0.1167
S:	0.2553	0.7100	0.5000
S:	0.7576	0.3651	0.1432
S:	0.5124	0.1710	0.1167
S:	0.7447	0.2900	0.5000
S:	0.0000	0.0000	0.7307
S:	0.7424	0.8651	0.6432
S:	0.9876	0.6710	0.6167
S:	0.2576	0.1349	0.6432
S:	0.0124	0.3290	0.6167
S:	0.5000	0.5000	0.7693
S:	0.7576	0.3651	0.8568
S:	0.5124	0.1710	0.8833
S:	0.2424	0.6349	0.8568
S:	0.4876	0.8290	0.8833

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	B3u	24	24	24	24
5	B3g	30	30	30	30	7.439e+41 5.2	1.023e+42 7.1	1.767e+42 12.3
6	B2u	32	32	32	32
7	B2g	36	36	36	36	1.029e+41 0.7	1.415e+41 1.0	2.445e+41 1.7
8	B2g	38	38	38	38	6.737e+39 0.0	9.264e+39 0.1	1.600e+40 0.1
9	B3u	40	40	40	40
10	B2u	43	43	44	43
11	Ag	48	48	48	48	9.527e+41 6.6	7.144e+41 5.0	1.667e+42 11.6
12	B3g	54	54	54	54	3.286e+41 2.3	4.518e+41 3.1	7.804e+41 5.4
13	B1g	56	56	56	56	1.917e+40 0.1	2.636e+40 0.2	4.554e+40 0.3
14	B2g	62	62	62	62	2.639e+41 1.8	3.628e+41 2.5	6.267e+41 4.4
15	Ag	69	69	69	69	5.262e+38 0.0	7.215e+38 0.0	1.248e+39 0.0
16	B1g	69	69	69	69	6.086e+41 4.2	3.841e+41 2.7	9.927e+41 6.9
17	Au	73	73	73	73
18	B3g	74	74	74	74	3.367e+41 2.3	4.630e+41 3.2	7.998e+41 5.6
19	B2u	77	77	77	77
20	Au	81	81	81	81
21	B1u	83	83	83	84
22	B3u	89	89	89	89
23	B2g	100	100	100	100	3.396e+39 0.0	4.669e+39 0.0	8.064e+39 0.1
24	B3g	113	113	113	113	1.116e+40 0.1	1.535e+40 0.1	2.652e+40 0.2
25	B1g	115	115	115	115	1.500e+40 0.1	2.062e+40 0.1	3.562e+40 0.2
26	Ag	124	124	124	124	4.156e+42 28.9	8.947e+41 6.2	5.050e+42 35.1
27	B3g	147	147	147	147	2.794e+41 1.9	3.842e+41 2.7	6.636e+41 4.6
28	Au	149	149	149	149
29	B2g	157	157	157	157	1.913e+41 1.3	2.630e+41 1.8	4.543e+41 3.2
30	Ag	163	163	163	163	9.045e+41 6.3	5.221e+41 3.6	1.427e+42 9.9
31	B2u	165	165	165	165
32	B1u	166	166	166	166
33	B3u	167	167	167	167
34	B1g	170	170	170	170	1.118e+41 0.8	1.537e+41 1.1	2.655e+41 1.8
35	Au	173	173	173	173
36	B1u	177	177	177	178
37	B3g	227	227	227	227	1.570e+41 1.1	2.159e+41 1.5	3.728e+41 2.6
38	B3u	232	232	232	232
39	B2u	234	234	235	234
40	Au	235	235	235	236
41	B1u	236	236	236	237
42	B2g	238	238	238	238	1.624e+41 1.1	2.233e+41 1.6	3.858e+41 2.7
43	Ag	240	240	240	240	3.319e+41 2.3	2.423e+41 1.7	5.742e+41 4.0
44	B1g	243	243	243	243	1.619e+40 0.1	2.226e+40 0.2	3.845e+40 0.3
45	B3u	257	259	257	257
46	B2u	266	266	266	266
47	Ag	278	278	278	278	7.109e+41 4.9	4.983e+41 3.5	1.209e+42 8.4
48	B1g	280	280	280	280	2.838e+39 0.0	3.902e+39 0.0	6.740e+39 0.0
49	B3g	355	355	355	355	4.375e+40 0.3	6.015e+40 0.4	1.039e+41 0.7
50	B2g	358	358	358	358	2.581e+39 0.0	3.548e+39 0.0	6.129e+39 0.0
51	Au	374	374	374	374
52	B1u	377	377	377	377
53	B3u	377	377	377	377
54	B2u	379	379	379	379
55	B1g	412	412	412	412	4.150e+41 2.9	5.706e+41 4.0	9.856e+41 6.9
56	Ag	414	414	414	414	4.501e+42 31.3	1.845e+42 12.8	6.347e+42 44.1
57	B3g	420	420	420	420	5.160e+41 3.6	7.095e+41 4.9	1.225e+42 8.5
58	B2g	422	422	422	422	6.300e+41 4.4	8.662e+41 6.0	1.496e+42 10.4
59	B1u	440	440	440	440
60	Ag	443	443	443	443	1.428e+43 99.3	1.013e+41 0.7	1.438e+43 100.0
61	Au	444	444	444	444
62	B1g	447	447	447	447	1.520e+39 0.0	2.090e+39 0.0	3.609e+39 0.0
63	B2u	448	448	448	448
64	B3u	449	449	449	449
65	B2u	454	454	454	454
66	B3u	455	455	455	455
67	B1u	455	455	455	455
68	Au	458	458	458	458
69	B2g	458	458	458	458	7.559e+39 0.1	1.039e+40 0.1	1.795e+40 0.1
70	B3g	461	461	461	461	7.808e+40 0.5	1.074e+41 0.7	1.854e+41 1.3
71	B1g	462	462	462	462	9.051e+39 0.1	1.245e+40 0.1	2.150e+40 0.1
72	Ag	469	469	469	469	2.380e+40 0.2	1.421e+40 0.1	3.801e+40 0.3

No.

Char.

ω TO

ω LOx

ω LOy

ω LOz

I ∥

I ⊥