- TOPAZ - Al₂SiO₄F₂

Experimental structure

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):	4.6499	8.7968		8.3909
Angles (°):	90.0	90.0		90.0

Symmetry (theoretical):

Space group:	62		Pbnm
Lattice parameters (Å):	4.6499	8.7968		8.3909
Angles (°):	90.0	90.0		90.0

Cell contents:

Number of atoms:	36
Number of atom types:	4
Chemical composition:	0

Atomic positions (theoretical):

Al:	0.9035	0.1310	0.0824
Si:	0.3978	0.9405	0.2500
O:	0.7961	0.5321	0.2500
O:	0.4569	0.7562	0.2500
O:	0.7893	0.0106	0.9079
F:	0.9018	0.7526	0.0572
Al:	0.4035	0.3690	0.9176
Si:	0.8978	0.5595	0.7500
O:	0.2961	0.9679	0.7500
O:	0.9569	0.7437	0.7500
O:	0.2893	0.4894	0.0921
F:	0.4018	0.7474	0.9428
Al:	0.0965	0.8690	0.5824
Si:	0.6022	0.0595	0.7500
O:	0.2039	0.4679	0.7500
O:	0.5431	0.2438	0.7500
O:	0.2107	0.9894	0.4079
F:	0.0982	0.2474	0.5572
Al:	0.5965	0.6310	0.4176
Si:	0.1022	0.4405	0.2500
O:	0.7039	0.0321	0.2500
O:	0.0431	0.2563	0.2500
O:	0.7107	0.5106	0.5921
F:	0.5982	0.2526	0.4428
Al:	0.0965	0.8690	0.9176
O:	0.2107	0.9894	0.0921
F:	0.0982	0.2474	0.9428
Al:	0.5965	0.6310	0.0824
O:	0.7107	0.5106	0.9079
F:	0.5982	0.2526	0.0572
Al:	0.9035	0.1310	0.4176
O:	0.7893	0.0106	0.5921
F:	0.9018	0.7526	0.4428
Al:	0.4035	0.3690	0.5824
O:	0.2893	0.4894	0.4079
F:	0.4018	0.7474	0.5572

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	A1g	152	152	152	152	4.970e+38 3.0	7.534e+36 0.0	5.046e+38 3.0
5	B3g	162	162	162	162	9.424e+37 0.6	1.296e+38 0.8	2.238e+38 1.3
6	Au	167	167	167	167
7	B1u	177	177	177	177
8	B3u	180	181	180	180
9	B2g	181	182	181	181	9.701e+36 0.1	1.334e+37 0.1	2.304e+37 0.1
10	Au	182	182	182	182
11	B2u	206	206	206	206
12	B1g	229	229	229	229	2.050e+38 1.2	2.819e+38 1.7	4.869e+38 2.9
13	A1g	229	229	229	229	3.845e+39 22.9	1.418e+38 0.8	3.987e+39 23.8
14	Au	234	234	234	234
15	B2g	235	235	235	235	9.188e+36 0.1	1.263e+37 0.1	2.182e+37 0.1
16	B3g	242	242	242	242	1.530e+37 0.1	2.103e+37 0.1	3.633e+37 0.2
17	B1g	255	255	255	255	7.108e+37 0.4	9.774e+37 0.6	1.688e+38 1.0
18	B2u	259	259	261	259
19	A1g	261	261	262	261	1.184e+40 70.6	1.471e+38 0.9	1.199e+40 71.5
20	B1g	265	265	265	265	1.123e+38 0.7	1.544e+38 0.9	2.668e+38 1.6
21	A1g	272	272	272	272	8.965e+39 53.5	1.602e+38 1.0	9.125e+39 54.4
22	B3g	273	273	273	273	1.560e+38 0.9	2.145e+38 1.3	3.706e+38 2.2
23	B1u	277	277	277	279
24	Au	279	279	279	282
25	B2g	282	282	282	282	1.218e+37 0.1	1.675e+37 0.1	2.893e+37 0.2
26	B3u	285	286	285	285
27	Au	295	295	295	295
28	B2u	295	295	301	295
29	B3u	303	303	303	303
30	B3g	306	306	306	306	1.718e+38 1.0	2.362e+38 1.4	4.080e+38 2.4
31	A1g	318	318	318	318	2.596e+39 15.5	9.729e+37 0.6	2.693e+39 16.1
32	B1u	320	320	320	323
33	B3u	324	325	324	324
34	B1g	326	326	326	326	2.114e+36 0.0	2.907e+36 0.0	5.022e+36 0.0
35	B2g	339	339	339	339	1.369e+37 0.1	1.882e+37 0.1	3.251e+37 0.2
36	B1g	342	342	342	342	1.923e+38 1.1	2.644e+38 1.6	4.567e+38 2.7
37	B3g	346	346	346	346	2.093e+37 0.1	2.877e+37 0.2	4.970e+37 0.3
38	B1u	349	349	349	351
39	B2g	351	351	351	352	1.094e+38 0.7	1.505e+38 0.9	2.599e+38 1.6
40	B3u	355	357	355	355
41	B1g	362	362	362	362	7.349e+36 0.0	1.011e+37 0.1	1.745e+37 0.1
42	B2u	370	370	379	370
43	A1g	388	388	388	388	2.001e+39 11.9	7.921e+37 0.5	2.081e+39 12.4
44	B3g	403	403	403	403	4.518e+37 0.3	6.212e+37 0.4	1.073e+38 0.6
45	B2u	404	404	408	404
46	B2g	409	409	409	409	1.577e+37 0.1	2.169e+37 0.1	3.746e+37 0.2
47	B3u	417	419	417	417
48	Au	419	425	419	419
49	B1u	425	431	425	431
50	B2u	431	432	432	432
51	B2g	432	435	435	435	1.421e+36 0.0	1.954e+36 0.0	3.374e+36 0.0
52	A1g	435	440	440	439	1.776e+39 10.6	2.546e+38 1.5	2.031e+39 12.1
53	B1u	440	444	444	444
54	Au	444	449	448	449
55	B2u	449	450	450	450
56	B1g	450	450	452	452	1.527e+36 0.0	2.100e+36 0.0	3.627e+36 0.0
57	Au	452	452	454	454
58	B3u	454	454	454	454
59	B2g	454	458	460	460	1.277e+38 0.8	1.755e+38 1.0	3.032e+38 1.8
60	A1g	460	460	461	461	2.165e+38 1.3	2.708e+37 0.2	2.436e+38 1.5
61	B1g	461	461	463	463	5.804e+37 0.3	7.980e+37 0.5	1.378e+38 0.8
62	B3g	463	463	476	476	1.181e+38 0.7	1.624e+38 1.0	2.805e+38 1.7
63	B3g	476	476	482	479	9.284e+36 0.1	1.277e+37 0.1	2.205e+37 0.1
64	B3u	482	486	485	482
65	B1u	486	490	486	490
66	B3g	490	494	490	494	1.664e+37 0.1	2.288e+37 0.1	3.953e+37 0.2
67	A1g	494	514	494	500	8.159e+38 4.9	4.350e+38 2.6	1.251e+39 7.5
68	B1u	514	521	514	521
69	Au	521	525	521	525
70	B1g	525	527	525	527	1.577e+38 0.9	2.169e+38 1.3	3.746e+38 2.2
71	B2u	527	531	528	531
72	A1g	531	532	531	535	1.203e+39 7.2	1.262e+38 0.8	1.330e+39 7.9
73	B2g	543	543	543	543	5.882e+36 0.0	8.087e+36 0.0	1.397e+37 0.1
74	B3g	547	547	547	547	2.083e+37 0.1	2.864e+37 0.2	4.946e+37 0.3
75	B2u	548	548	550	548
76	B3u	550	550	551	550
77	B1g	551	551	554	551	4.542e+37 0.3	6.246e+37 0.4	1.079e+38 0.6
78	A1g	554	554	562	554	4.537e+37 0.3	2.664e+37 0.2	7.201e+37 0.4
79	B3u	563	564	563	563
80	Au	564	573	564	564
81	B2u	573	575	575	573
82	B1u	575	594	594	594
83	B1g	594	602	602	602	2.427e+37 0.1	3.336e+37 0.2	5.763e+37 0.3
84	B2g	602	612	612	612	3.602e+37 0.2	4.953e+37 0.3	8.554e+37 0.5
85	A1g	612	626	626	626	3.323e+38 2.0	7.331e+37 0.4	4.056e+38 2.4
86	B1u	626	626	633	635
87	B2g	635	635	635	636	8.350e+37 0.5	1.148e+38 0.7	1.983e+38 1.2
88	B1g	640	640	640	640	1.366e+36 0.0	1.878e+36 0.0	3.244e+36 0.0
89	Au	653	653	653	653
90	B2u	656	656	664	656
91	B3u	666	667	666	666
92	B3g	667	667	667	667	8.782e+37 0.5	1.208e+38 0.7	2.086e+38 1.2
93	B2u	809	809	809	809
94	A1g	809	809	810	809	2.741e+39 16.4	8.241e+38 4.9	3.565e+39 21.3
95	B1u	810	810	810	810
96	Au	810	810	826	826
97	B3u	826	843	846	846
98	B3u	846	856	856	856
99	B1g	856	863	858	863	2.815e+38 1.7	3.870e+38 2.3	6.685e+38 4.0
100	B2u	863	872	872	872
101	A1g	872	877	877	877	1.652e+40 98.5	2.475e+38 1.5	1.676e+40 100.0
102	B1g	877	887	886	887	4.022e+38 2.4	5.530e+38 3.3	9.552e+38 5.7
103	A1g	887	891	887	891	2.794e+39 16.7	1.429e+39 8.5	4.223e+39 25.2
104	B2u	891	933	934	934
105	B2g	934	934	955	955	1.598e+39 9.5	2.198e+39 13.1	3.796e+39 22.6
106	B3u	955	959	959	959
107	B3g	959	963	963	963	3.042e+38 1.8	4.183e+38 2.5	7.225e+38 4.3
108	B1g	963	1001	975	964	5.244e+38 3.1	7.211e+38 4.3	1.246e+39 7.4

No.

Char.

ω TO

ω LOx

ω LOy

ω LOz

I ∥

I ⊥