- TOPAZ - Al₂SiO₄F₂

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 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		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):	4.5849	8.6722		8.2651
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:	0.9039	0.1309	0.0826
Si:	0.3983	0.9404	0.2500
O:	0.7939	0.5320	0.2500
O:	0.4572	0.7551	0.2500
O:	0.7892	0.0105	0.9087
F:	0.9022	0.7522	0.0571
Al:	0.4039	0.3691	0.9174
Si:	0.8983	0.5596	0.7500
O:	0.2939	0.9680	0.7500
O:	0.9572	0.7449	0.7500
O:	0.2892	0.4895	0.0913
F:	0.4022	0.7478	0.9429
Al:	0.0961	0.8691	0.5826
Si:	0.6017	0.0596	0.7500
O:	0.2061	0.4680	0.7500
O:	0.5428	0.2449	0.7500
O:	0.2108	0.9895	0.4087
F:	0.0978	0.2478	0.5571
Al:	0.5961	0.6309	0.4174
Si:	0.1017	0.4404	0.2500
O:	0.7061	0.0320	0.2500
O:	0.0428	0.2551	0.2500
O:	0.7108	0.5105	0.5913
F:	0.5978	0.2522	0.4429
Al:	0.0961	0.8691	0.9174
O:	0.2108	0.9895	0.0913
F:	0.0978	0.2478	0.9429
Al:	0.5961	0.6309	0.0826
O:	0.7108	0.5105	0.9087
F:	0.5978	0.2522	0.0571
Al:	0.9039	0.1309	0.4174
O:	0.7892	0.0105	0.5913
F:	0.9022	0.7522	0.4429
Al:	0.4039	0.3691	0.5826
O:	0.2892	0.4895	0.4087
F:	0.4022	0.7478	0.5571

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	150	150	150	150	4.024e+38 2.6	9.083e+36 0.1	4.115e+38 2.7
5	B3g	162	162	162	162	1.016e+38 0.7	1.396e+38 0.9	2.412e+38 1.6
6	Au	169	169	169	169
7	B3u	174	176	174	174
8	B1u	178	178	178	180
9	B2g	186	186	186	186	8.051e+36 0.1	1.107e+37 0.1	1.912e+37 0.1
10	Au	188	188	188	188
11	B2u	211	211	212	211
12	B1g	230	230	230	230	1.914e+38 1.2	2.631e+38 1.7	4.545e+38 3.0
13	A1g	237	237	237	237	6.491e+39 42.2	1.954e+38 1.3	6.687e+39 43.5
14	Au	239	239	239	239
15	B2g	243	243	243	243	9.422e+36 0.1	1.296e+37 0.1	2.238e+37 0.1
16	B3g	247	247	247	247	2.117e+37 0.1	2.912e+37 0.2	5.029e+37 0.3
17	B1g	263	263	263	263	8.723e+37 0.6	1.199e+38 0.8	2.072e+38 1.3
18	B2u	264	264	265	264
19	A1g	265	265	269	265	8.744e+39 56.9	8.989e+37 0.6	8.834e+39 57.5
20	B1g	275	275	275	275	1.134e+38 0.7	1.560e+38 1.0	2.694e+38 1.8
21	A1g	282	282	282	282	7.577e+39 49.3	1.424e+38 0.9	7.719e+39 50.2
22	B2g	284	284	284	284	1.257e+37 0.1	1.729e+37 0.1	2.986e+37 0.2
23	B3g	287	287	287	287	1.453e+38 0.9	1.998e+38 1.3	3.451e+38 2.2
24	B3u	291	292	291	291
25	B1u	292	292	292	295
26	Au	295	295	295	297
27	Au	304	304	304	304
28	B2u	304	304	306	304
29	B3u	306	306	310	306
30	B3g	311	311	311	311	1.573e+38 1.0	2.162e+38 1.4	3.735e+38 2.4
31	B1u	327	327	327	330
32	B1g	330	330	330	330
33	A1g	330	330	330	334	1.878e+39 12.2	7.205e+37 0.5	1.950e+39 12.7
34	B3u	335	338	335	335
35	B2g	350	350	350	350	5.567e+36 0.0	7.654e+36 0.0	1.322e+37 0.1
36	B1g	353	353	353	353	1.746e+38 1.1	2.400e+38 1.6	4.146e+38 2.7
37	B1u	362	362	362	366
38	B3g	366	366	366	366	1.584e+37 0.1	2.178e+37 0.1	3.762e+37 0.2
39	B2g	372	372	372	372	8.888e+37 0.6	1.222e+38 0.8	2.111e+38 1.4
40	B3u	373	376	373	373
41	B1g	377	377	377	377	2.631e+37 0.2	3.618e+37 0.2	6.249e+37 0.4
42	B2u	382	382	395	382
43	A1g	398	398	398	398	1.775e+39 11.6	6.732e+37 0.4	1.843e+39 12.0
44	B2u	415	415	417	415
45	B3g	421	421	421	421	2.363e+37 0.2	3.249e+37 0.2	5.611e+37 0.4
46	Au	431	431	431	431
47	B3u	432	439	432	432
48	B2g	439	448	439	439	4.266e+37 0.3	5.866e+37 0.4	1.013e+38 0.7
49	B2u	448	449	449	448
50	A1g	449	451	451	449	1.571e+39 10.2	3.239e+38 2.1	1.895e+39 12.3
51	B1u	451	465	462	458
52	B1g	468	468	468	468	2.039e+36 0.0	2.803e+36 0.0	4.842e+36 0.0
53	B2u	469	469	472	469
54	B1u	472	472	472	472
55	B2g	472	472	478	478	2.900e+37 0.2	3.987e+37 0.3	6.887e+37 0.4
56	B2g	478	478	479	479	1.017e+38 0.7	1.399e+38 0.9	2.416e+38 1.6
57	B3u	479	483	483	483
58	Au	483	484	487	487
59	A1g	487	487	488	488	1.183e+38 0.8	6.121e+37 0.4	1.795e+38 1.2
60	Au	488	488	493	493
61	B3g	493	493	493	493	6.916e+37 0.5	9.510e+37 0.6	1.643e+38 1.1
62	B1g	493	493	496	500	1.094e+38 0.7	1.504e+38 1.0	2.598e+38 1.7
63	B3u	500	510	500	510
64	B3g	510	514	510	510	6.539e+37 0.4	8.991e+37 0.6	1.553e+38 1.0
65	A1g	514	525	514	514	6.413e+38 4.2	4.149e+38 2.7	1.056e+39 6.9
66	B1u	525	531	525	531
67	B3g	531	540	531	531	3.094e+37 0.2	4.254e+37 0.3	7.348e+37 0.5
68	B1g	540	546	540	540	1.443e+38 0.9	1.985e+38 1.3	3.428e+38 2.2
69	B2u	546	547	550	546
70	B1u	555	555	555	557
71	A1g	557	557	557	559	1.132e+39 7.4	5.262e+37 0.3	1.185e+39 7.7
72	Au	559	559	559	568
73	B1g	576	576	576	576	3.095e+37 0.2	4.255e+37 0.3	7.350e+37 0.5
74	B3u	577	582	577	577
75	B2u	585	585	588	585
76	B2g	589	589	589	589	3.916e+36 0.0	5.384e+36 0.0	9.300e+36 0.1
77	B3g	596	596	596	596	2.624e+37 0.2	3.608e+37 0.2	6.232e+37 0.4
78	B2u	602	602	606	602
79	B1u	606	606	607	607
80	A1g	607	607	610	610	5.632e+37 0.4	3.280e+37 0.2	8.912e+37 0.6
81	B3u	610	613	613	613
82	Au	613	628	628	628
83	B1g	628	633	633	633	2.490e+37 0.2	3.423e+37 0.2	5.913e+37 0.4
84	B2g	633	640	640	640	5.969e+37 0.4	8.207e+37 0.5	1.418e+38 0.9
85	A1g	640	665	669	668	2.471e+38 1.6	5.966e+37 0.4	3.068e+38 2.0
86	B1u	669	669	680	680
87	B2g	680	680	680	683	3.637e+37 0.2	5.001e+37 0.3	8.638e+37 0.6
88	B1g	683	683	683	683	7.731e+36 0.1	1.063e+37 0.1	1.836e+37 0.1
89	Au	684	684	684	684
90	B2u	697	697	700	697
91	B3u	706	707	706	706
92	B3g	707	709	707	707	6.226e+37 0.4	8.561e+37 0.6	1.479e+38 1.0
93	Ag	857	857	857	857	1.095e+38 0.7	2.867e+37 0.2	1.382e+38 0.9
94	Ag	857	857	863	857	2.469e+39 16.1	6.464e+38 4.2	3.115e+39 20.3
95	B1u	863	863	863	863
96	Au	863	863	873	873
97	B3u	873	885	890	890
98	B3u	890	902	902	902
99	B1g	902	911	906	911	1.867e+38 1.2	2.567e+38 1.7	4.434e+38 2.9
100	B2u	911	919	919	919
101	A1g	919	928	928	928	1.515e+40 98.6	2.124e+38 1.4	1.536e+40 100.0
102	B1g	928	940	936	940	3.530e+38 2.3	4.854e+38 3.2	8.384e+38 5.5
103	A1g	940	940	940	940	2.242e+39 14.6	1.280e+39 8.3	3.523e+39 22.9
104	B2u	940	977	984	984
105	B2g	984	984	1001	1001	1.311e+39 8.5	1.802e+39 11.7	3.113e+39 20.3
106	B3u	1001	1008	1008	1008
107	B3g	1008	1009	1009	1009	2.834e+38 1.8	3.896e+38 2.5	6.730e+38 4.4
108	B1g	1009	1049	1020	1012	4.421e+38 2.9	6.078e+38 4.0	1.050e+39 6.8

No.

Char.

ω TO

ω LOx

ω LOy

ω LOz

I ∥

I ⊥