- ANDALUSITE - Al₂SiO₅

Theoretical atomic positions and lattice parameters at experimental volum from RRUFF entry #RO50258

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):	7.7931	7.8963		5.5549
Angles (°):	90.0	90.0		90.0

Symmetry (theoretical):

Space group:	58		Pnnm
Lattice parameters (Å):	7.8276	7.8980		5.5308
Angles (°):	90.0	90.0		90.0

Cell contents:

Number of atoms:	32
Number of atom types:	3
Chemical composition:	0

Atomic positions (theoretical):

Al:	0.0000	0.0000	0.2419
Al:	0.3716	0.1395	0.5000
Si:	0.2449	0.2541	0.0000
O:	0.4277	0.3626	0.5000
O:	0.4210	0.3674	0.0000
O:	0.1019	0.4013	0.0000
O:	0.2319	0.1368	0.2406
Al:	0.6284	0.8605	0.5000
Si:	0.7551	0.7459	0.0000
O:	0.5723	0.6374	0.5000
O:	0.5790	0.6326	0.0000
O:	0.8981	0.5987	0.0000
O:	0.7681	0.8632	0.2406
Al:	0.5000	0.5000	0.2581
Al:	0.1284	0.6395	0.0000
Si:	0.2551	0.7541	0.5000
O:	0.0723	0.8626	0.0000
O:	0.0790	0.8674	0.5000
O:	0.3981	0.9013	0.5000
O:	0.2681	0.6368	0.2594
Al:	0.8716	0.3605	0.0000
Si:	0.7449	0.2459	0.5000
O:	0.9277	0.1374	0.0000
O:	0.9210	0.1326	0.5000
O:	0.6019	0.0987	0.5000
O:	0.7319	0.3632	0.2594
Al:	0.0000	0.0000	0.7581
O:	0.7681	0.8632	0.7594
O:	0.2319	0.1368	0.7594
Al:	0.5000	0.5000	0.7419
O:	0.7319	0.3632	0.7406
O:	0.2681	0.6368	0.7406

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	B2g	94	94	94	94	7.753e+37 0.4	1.066e+38 0.5	1.841e+38 0.9
5	B3g	110	110	110	110
6	B3g	122	122	122	122	2.252e+36 0.0	3.096e+36 0.0	5.347e+36 0.0
7	B2u	156	156	157	156
8	B3u	157	166	165	157
9	B1u	166	182	166	166
10	B2g	184	184	184	184	2.704e+37 0.1	3.719e+37 0.2	6.423e+37 0.3
11	B3g	197	197	197	197	6.245e+37 0.3	8.586e+37 0.4	1.483e+38 0.7
12	Au	207	207	207	207
13	Au	214	214	214	214
14	B2u	226	226	226	226
15	A1g	234	234	234	234	1.951e+38 1.0	1.425e+38 0.7	3.377e+38 1.7
16	B2g	240	240	240	240	9.983e+36 0.1	1.373e+37 0.1	2.371e+37 0.1
17	B3u	241	241	241	241
18	B3u	264	273	264	264
19	B1g	273	276	273	273	1.111e+38 0.6	1.528e+38 0.8	2.639e+38 1.3
20	B1u	276	282	276	276
21	A1g	282	283	282	282	1.377e+40 69.3	8.558e+37 0.4	1.385e+40 69.7
22	Au	283	292	283	283
23	B2g	292	293	292	292	1.184e+37 0.1	1.628e+37 0.1	2.812e+37 0.1
24	B2u	293	294	294	293
25	B1g	294	300	301	294	8.563e+37 0.4	1.177e+38 0.6	2.034e+38 1.0
26	A1g	306	306	306	306	3.676e+39 18.5	6.622e+37 0.3	3.742e+39 18.8
27	B3g	318	318	318	318	2.645e+38 1.3	3.637e+38 1.8	6.282e+38 3.2
28	B1g	320	320	320	320	4.969e+38 2.5	6.833e+38 3.4	1.180e+39 5.9
29	B2u	332	332	338	332
30	B3u	338	339	339	338
31	Au	339	340	342	339
32	B1u	342	342	344	343
33	A1g	344	344	344	344	5.266e+39 26.5	1.223e+38 0.6	5.388e+39 27.1
34	B1g	347	347	347	347
35	B3g	358	358	358	358	1.890e+37 0.1	2.599e+37 0.1	4.489e+37 0.2
36	A1g	364	364	364	364	1.724e+38 0.9	5.436e+37 0.3	2.267e+38 1.1
37	B3u	367	373	367	367
38	B2g	380	380	380	380	1.423e+38 0.7	1.957e+38 1.0	3.379e+38 1.7
39	B1g	383	383	383	383	1.226e+37 0.1	1.686e+37 0.1	2.913e+37 0.1
40	B2u	390	390	390	390
41	B2g	391	391	391	391	1.714e+37 0.1	2.357e+37 0.1	4.071e+37 0.2
42	B3g	396	396	396	396	8.182e+38 4.1	1.125e+39 5.7	1.943e+39 9.8
43	B2u	402	402	417	402
44	B3u	417	434	434	417
45	Au	434	439	439	434
46	A1g	439	442	442	439	4.668e+38 2.3	3.489e+38 1.8	8.157e+38 4.1
47	B1u	442	457	455	449
48	B2g	457	461	457	457	3.879e+38 2.0	5.334e+38 2.7	9.213e+38 4.6
49	B1g	461	469	461	461	4.803e+37 0.2	6.604e+37 0.3	1.141e+38 0.6
50	B3g	469	489	469	469	8.716e+37 0.4	1.199e+38 0.6	2.070e+38 1.0
51	B3u	494	500	494	494
52	B2u	500	521	506	500
53	A1g	522	522	522	522	1.879e+39 9.5	8.964e+37 0.5	1.968e+39 9.9
54	B3u	525	526	525	525
55	Au	526	528	526	526
56	B1g	528	533	528	528	2.262e+38 1.1	3.110e+38 1.6	5.371e+38 2.7
57	B2u	534	534	534	534
58	A1g	549	549	549	549	2.786e+38 1.4	1.243e+38 0.6	4.028e+38 2.0
59	B1u	550	550	550	561
60	Au	561	561	561	572
61	B1g	572	572	572	573	1.329e+38 0.7	1.827e+38 0.9	3.156e+38 1.6
62	B3u	573	573	573	573
63	B3g	573	573	573	574	5.448e+37 0.3	7.491e+37 0.4	1.294e+38 0.7
64	B1u	574	574	574	586
65	B2g	586	586	586	597
66	B2u	597	597	601	601
67	A1g	601	601	619	619	7.742e+37 0.4	4.956e+37 0.2	1.270e+38 0.6
68	B2g	619	619	625	625	2.517e+37 0.1	3.461e+37 0.2	5.978e+37 0.3
69	B1g	625	625	627	630	2.100e+37 0.1	2.888e+37 0.1	4.988e+37 0.3
70	B2u	630	630	637	634
71	B1u	637	637	639	639
72	B3g	639	639	667	667	3.137e+38 1.6	4.313e+38 2.2	7.450e+38 3.8
73	Au	667	667	689	679
74	A1g	689	689	690	689	1.058e+39 5.3	7.007e+37 0.4	1.128e+39 5.7
75	B1g	690	690	696	690	2.172e+38 1.1	2.987e+38 1.5	5.159e+38 2.6
76	B3u	696	714	716	696
77	B3u	736	742	736	736
78	B2u	760	760	761	760
79	A1g	792	792	792	792	1.781e+38 0.9	1.298e+38 0.7	3.079e+38 1.5
80	B1g	794	794	794	794	1.282e+37 0.1	1.763e+37 0.1	3.046e+37 0.2
81	B3u	816	830	816	816
82	B2u	830	882	831	830
83	A1g	882	882	882	882	1.981e+40 99.8	4.932e+37 0.2	1.986e+40 100.0
84	B2u	883	883	883	883
85	B3u	889	898	889	889
86	B1u	898	899	898	899
87	B3g	899	908	899	908	2.203e+39 11.1	3.029e+39 15.2	5.231e+39 26.3
88	Au	908	908	908	908
89	B2g	908	910	908	910	1.641e+38 0.8	2.257e+38 1.1	3.898e+38 2.0
90	B1g	910	912	910	912	3.087e+38 1.6	4.245e+38 2.1	7.333e+38 3.7
91	A1g	912	925	912	929	2.205e+39 11.1	9.370e+38 4.7	3.142e+39 15.8
92	B2u	929	929	938	938
93	B3u	938	980	980	980
94	B1g	980	981	1033	1033	1.475e+39 7.4	2.028e+39 10.2	3.502e+39 17.6
95	A1g	1033	1033	1047	1033	3.844e+39 19.4	2.932e+38 1.5	4.138e+39 20.8
96	B1g	1077	1077	1077	1077	7.011e+38 3.5	9.641e+38 4.9	1.665e+39 8.4

No.

Char.

ω TO

ω LOx

ω LOy

ω LOz

I ∥

I ⊥