- SILLIMANITE - Al₂SiO₅

Theoretical atomic positions and lattice parameters 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:	62		Pnma
Lattice parameters (Å):	7.4857	7.6750		5.7751
Angles (°):	90.0	90.0		90.0

Symmetry (theoretical):

Space group:	62		Pnma
Lattice parameters (Å):	7.4857	7.6750		5.7751
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	0.0000
Al:	0.1417	0.3452	0.2500
Si:	0.1532	0.3404	0.7500
O:	0.3602	0.4089	0.7500
O:	0.3566	0.4339	0.2500
O:	0.4767	0.0009	0.7500
O:	0.1255	0.2232	0.5145
Al:	0.5000	0.5000	0.0000
Al:	0.6417	0.1548	0.7500
Si:	0.6532	0.1596	0.2500
O:	0.8602	0.0911	0.2500
O:	0.8566	0.0661	0.7500
O:	0.9767	0.4991	0.2500
O:	0.6255	0.2768	0.4855
Al:	0.0000	0.0000	0.5000
Al:	0.8583	0.6548	0.7500
Si:	0.8468	0.6596	0.2500
O:	0.6398	0.5911	0.2500
O:	0.6434	0.5661	0.7500
O:	0.5233	0.9991	0.2500
O:	0.8745	0.7768	0.0145
Al:	0.5000	0.5000	0.5000
Al:	0.3583	0.8452	0.2500
Si:	0.3468	0.8404	0.7500
O:	0.1398	0.9089	0.7500
O:	0.1434	0.9339	0.2500
O:	0.0233	0.5009	0.7500
O:	0.3745	0.7232	0.9855
O:	0.8745	0.7768	0.4855
O:	0.3745	0.7232	0.5145
O:	0.1255	0.2232	0.9855
O:	0.6255	0.2768	0.0145

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	121	122	121	121
5	A1g	146	146	146	146	2.056e+39 12.0	1.038e+38 0.6	2.160e+39 12.6
6	B2u	147	147	147	147
7	Au	147	147	147	147
8	B1g	171	171	171	171	2.661e+36 0.0	3.659e+36 0.0	6.320e+36 0.0
9	B1g	189	189	189	189
10	B2u	193	193	194	193
11	B1u	199	199	199	202
12	B2g	202	202	202	211	1.940e+38 1.1	2.668e+38 1.6	4.608e+38 2.7
13	B3g	211	211	211	216	1.079e+38 0.6	1.484e+38 0.9	2.564e+38 1.5
14	Au	234	234	234	234
15	A1g	236	236	236	236	5.971e+39 34.9	2.260e+38 1.3	6.197e+39 36.3
16	Au	248	248	248	248
17	B2g	254	254	254	254	2.095e+37 0.1	2.881e+37 0.2	4.976e+37 0.3
18	B1g	258	258	258	258
19	B3u	258	260	258	258
20	B3g	260	265	260	260	2.644e+36 0.0	3.635e+36 0.0	6.279e+36 0.0
21	B1u	274	274	274	274
22	B3u	282	284	282	282
23	B1u	284	284	284	284
24	A1g	291	291	291	291	5.566e+38 3.3	1.066e+38 0.6	6.631e+38 3.9
25	Au	294	294	294	294
26	A1g	301	301	301	301	1.608e+40 94.1	1.014e+39 5.9	1.709e+40 100.0
27	B1u	305	305	305	306
28	B1g	306	306	306	306	1.146e+38 0.7	1.576e+38 0.9	2.723e+38 1.6
29	Au	307	307	307	307
30	B2u	319	319	326	319
31	B3u	326	326	326	326
32	B2u	328	328	329	328
33	B2g	330	330	330	330	8.669e+37 0.5	1.192e+38 0.7	2.059e+38 1.2
34	B3u	336	337	336	336
35	B1u	350	350	350	355
36	A1g	357	357	357	357	1.651e+38 1.0	5.993e+37 0.4	2.250e+38 1.3
37	Au	364	364	364	364
38	B3g	372	372	372	372	1.097e+38 0.6	1.508e+38 0.9	2.605e+38 1.5
39	B1g	375	375	375	375	6.828e+38 4.0	9.388e+38 5.5	1.622e+39 9.5
40	B2u	380	380	380	380
41	A1g	396	396	396	396	6.515e+38 3.8	6.560e+37 0.4	7.171e+38 4.2
42	B1g	401	401	401	401	1.587e+39 9.3	2.182e+39 12.8	3.768e+39 22.0
43	B3g	405	405	405	405	3.711e+36 0.0	5.103e+36 0.0	8.814e+36 0.1
44	B2u	405	405	411	405
45	B2g	411	411	413	411	2.981e+38 1.7	4.099e+38 2.4	7.080e+38 4.1
46	B3u	413	424	414	413
47	B2u	424	436	436	424
48	Au	436	439	439	436
49	B1g	439	441	441	439
50	A1g	441	452	452	441	7.270e+39 42.5	1.152e+39 6.7	8.422e+39 49.3
51	B1u	452	457	457	457
52	B2g	457	458	471	464	5.033e+38 2.9	6.920e+38 4.0	1.195e+39 7.0
53	B3u	471	494	490	471
54	B2u	494	496	496	494
55	B3g	496	503	503	496	1.046e+38 0.6	1.438e+38 0.8	2.484e+38 1.5
56	Au	503	504	510	503
57	B1u	510	510	522	522
58	B3u	522	535	536	562
59	A1g	562	562	562	564	4.804e+39 28.1	1.455e+38 0.9	4.950e+39 29.0
60	B3g	564	564	564	569	7.226e+37 0.4	9.935e+37 0.6	1.716e+38 1.0
61	B2u	569	569	571	577
62	B3u	577	577	577	577
63	B3u	586	586	586	586
64	B2u	587	587	592	587
65	B1u	592	592	593	593
66	Au	593	593	610	606
67	B2g	610	610	617	610	2.391e+36 0.0	3.287e+36 0.0	5.678e+36 0.0
68	B1g	617	617	622	617	5.395e+37 0.3	7.419e+37 0.4	1.281e+38 0.7
69	B2g	634	634	634	634	5.952e+35 0.0	8.183e+35 0.0	1.413e+36 0.0
70	Au	634	634	634	634
71	B1u	638	638	638	655
72	B3g	655	655	655	662	1.344e+39 7.9	1.848e+39 10.8	3.192e+39 18.7
73	A1g	662	662	662	669	1.732e+39 10.1	9.339e+38 5.5	2.666e+39 15.6
74	B3u	669	669	669	689
75	B2u	689	689	714	700
76	B1g	715	715	715	715	5.232e+37 0.3	7.194e+37 0.4	1.243e+38 0.7
77	B1g	725	725	725	725	1.658e+37 0.1	2.279e+37 0.1	3.937e+37 0.2
78	A1g	728	728	728	728	7.125e+37 0.4	5.343e+37 0.3	1.247e+38 0.7
79	B3u	746	750	746	746
80	B2u	750	806	774	750
81	A1g	825	825	825	825	5.994e+39 35.1	1.132e+39 6.6	7.126e+39 41.7
82	B3u	838	852	838	838
83	B2u	852	852	852	852
84	B2g	852	854	854	852	1.367e+38 0.8	1.879e+38 1.1	3.246e+38 1.9
85	Au	854	855	855	854
86	B1u	855	861	860	861
87	B1g	861	862	861	862	2.731e+38 1.6	3.755e+38 2.2	6.486e+38 3.8
88	B3g	862	874	862	904	2.577e+39 15.1	3.543e+39 20.7	6.120e+39 35.8
89	B3u	904	904	904	904
90	B2u	904	906	906	906
91	A1g	906	957	922	984	1.499e+40 87.7	5.047e+38 3.0	1.549e+40 90.6
92	B1g	984	984	984	987	5.801e+38 3.4	7.976e+38 4.7	1.378e+39 8.1
93	A1g	1086	1086	1086	1086	3.564e+39 20.9	1.709e+38 1.0	3.734e+39 21.9
94	B1g	1092	1092	1092	1092	4.754e+38 2.8	6.537e+38 3.8	1.129e+39 6.6
95	B2u	1122	1122	1131	1122
96	B3u	1131	1174	1185	1131

No.

Char.

ω TO

ω LOx

ω LOy

ω LOz

I ∥

I ⊥