- FORSTERITE - Mg₂SiO₄

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):	4.7503	10.1870		5.9771
Angles (°):	90	90		90

Symmetry (theoretical):

Space group:	62		Pbnm
Lattice parameters (Å):	4.6846	10.0026		5.8725
Angles (°):	90	90		90

Cell contents:

Number of atoms:	28
Number of atom types:	3
Chemical composition:	0

Atomic positions (theoretical):

Mg:	0.0000	0.0000	0.0000
Mg:	0.9913	0.2761	0.2500
Si:	0.4270	0.0940	0.2500
O:	0.7685	0.0916	0.2500
O:	0.2222	0.4456	0.2500
O:	0.2754	0.1636	0.0314
Mg:	0.5000	0.5000	0.0000
Mg:	0.4913	0.2239	0.7500
Si:	0.9270	0.4060	0.7500
O:	0.2685	0.4084	0.7500
O:	0.7222	0.0544	0.7500
O:	0.7754	0.3364	0.9686
Mg:	0.0000	0.0000	0.5000
Mg:	0.0087	0.7239	0.7500
Si:	0.5730	0.9060	0.7500
O:	0.2315	0.9084	0.7500
O:	0.7778	0.5544	0.7500
O:	0.7246	0.8364	0.5314
Mg:	0.5000	0.5000	0.5000
Mg:	0.5087	0.7761	0.2500
Si:	0.0730	0.5940	0.2500
O:	0.7315	0.5916	0.2500
O:	0.2778	0.9456	0.2500
O:	0.2246	0.6636	0.4686
O:	0.7246	0.8364	0.9686
O:	0.2246	0.6636	0.0314
O:	0.2754	0.1636	0.4686
O:	0.7754	0.3364	0.5314

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	Au	105	105	105	105
5	B2u	147	147	148	147
6	B2g	178	178	178	178
7	Au	186	186	186	186
8	A1g	190	190	190	190	8.142e+37 0.1	5.258e+37 0.1	1.340e+38 0.2
9	B3g	197	197	197	197	4.476e+37 0.1	6.155e+37 0.1	1.063e+38 0.2
10	B1u	200	200	200	200
11	B3u	206	207	206	206
12	B1g	225	225	225	225
13	A1g	227	227	227	227	1.530e+39 2.5	1.835e+37 0.0	1.549e+39 2.6
14	B2g	250	250	250	250	1.334e+38 0.2	1.834e+38 0.3	3.167e+38 0.5
15	Au	251	251	251	251
16	B1g	258	258	258	258	3.018e+37 0.0	4.150e+37 0.1	7.168e+37 0.1
17	B3u	280	280	280	280
18	B1u	283	283	283	284
19	B2u	285	285	285	285
20	B3g	288	288	288	288	8.558e+36 0.0	1.177e+37 0.0	2.033e+37 0.0
21	B2u	297	297	299	297
22	B1u	299	299	301	301
23	B1u	301	301	301	301
24	B1u	301	303	314	311
25	B1u	316	316	316	318
26	A1g	318	318	318	321	1.680e+39 2.8	8.990e+37 0.1	1.769e+39 2.9
27	B3g	322	322	322	322	8.336e+37 0.1	1.146e+38 0.2	1.980e+38 0.3
28	B3u	323	325	323	323
29	B1g	328	328	328	328	2.076e+37 0.0	2.855e+37 0.0	4.932e+37 0.1
30	B2g	332	332	332	332	1.656e+37 0.0	2.277e+37 0.0	3.933e+37 0.1
31	A1g	336	336	336	336	7.153e+38 1.2	4.671e+38 0.8	1.182e+39 2.0
32	Au	349	349	349	349
33	A1g	357	357	357	357	7.555e+38 1.2	5.415e+38 0.9	1.297e+39 2.1
34	B2u	364	364	364	364	2.894e+37 0.0	3.979e+37 0.1	6.873e+37 0.1
35	B1g	364	364	374	364	1.151e+38 0.2	1.583e+38 0.3	2.734e+38 0.5
36	B2g	374	374	381	374	5.480e+37 0.1	7.536e+37 0.1	1.302e+38 0.2
37	B3g	387	387	387	387	8.131e+38 1.3	1.118e+39 1.8	1.931e+39 3.2
38	B1g	387	387	387	387	9.433e+36 0.0	1.297e+37 0.0	2.240e+37 0.0
39	Au	392	392	392	392
40	B3u	398	401	398	398
41	B2u	402	402	412	402
42	B3u	412	420	420	412
43	B3g	420	425	423	420	1.208e+36 0.0	1.661e+36 0.0	2.869e+36 0.0
44	B1u	425	429	425	428
45	B1u	429	430	429	430
46	B2u	430	436	436	436
47	A1g	436	438	438	438	9.905e+38 1.6	5.433e+38 0.9	1.534e+39 2.5
48	Au	438	446	446	446
49	B1g	446	451	447	451	3.519e+38 0.6	4.838e+38 0.8	8.357e+38 1.4
50	B2g	451	464	451	456	1.518e+38 0.3	2.087e+38 0.3	3.605e+38 0.6
51	B2u	464	473	480	464
52	B1u	480	480	483	483
53	B3u	483	484	484	484
54	Au	484	484	492	494
55	B1u	508	508	508	508
56	B2u	508	508	509	509
57	B3u	509	514	514	514
58	Au	514	532	522	532
59	B2u	532	533	534	534
60	B3u	534	540	540	540
61	A1g	540	552	573	578	7.493e+38 1.2	1.927e+38 0.3	9.419e+38 1.6
62	B1g	578	578	578	579	3.358e+38 0.6	4.618e+38 0.8	7.976e+38 1.3
63	B2g	579	579	579	581	6.414e+38 1.1	8.819e+38 1.5	1.523e+39 2.5
64	B3g	587	587	587	587	5.897e+38 1.0	8.109e+38 1.3	1.401e+39 2.3
65	B3u	603	606	603	603
66	A1g	606	628	606	606	6.589e+39 10.9	2.865e+38 0.5	6.876e+39 11.4
67	B2u	628	628	628	628
68	B1g	628	649	628	628	8.623e+37 0.1	1.186e+38 0.2	2.048e+38 0.3
69	A1g	819	819	819	819	5.994e+40 99.0	6.216e+38 1.0	6.056e+40 100.0
70	B2u	828	828	828	828
71	B3u	828	829	832	828
72	B1g	832	832	832	832	5.409e+38 0.9	7.437e+38 1.2	1.285e+39 2.1
73	A1g	849	849	849	849	3.454e+40 57.0	8.031e+38 1.3	3.534e+40 58.4
74	B1g	858	858	858	858	2.256e+39 3.7	3.102e+39 5.1	5.358e+39 8.8
75	B1u	867	867	867	867
76	B2u	867	867	875	875
77	B2g	875	875	904	904	3.287e+39 5.4	4.519e+39 7.5	7.806e+39 12.9
78	Au	904	904	914	914
79	B3g	914	914	956	956	2.269e+39 3.7	3.120e+39 5.2	5.389e+39 8.9
80	B3u	956	961	961	961
81	A1g	961	961	961	972	6.165e+39 10.2	3.373e+39 5.6	9.538e+39 15.7
82	B1g	972	972	972	973	1.617e+38 0.3	2.224e+38 0.4	3.841e+38 0.6
83	B3u	973	982	973	982
84	B2u	982	1072	989	988

No.

Char.

ω TO

ω LOx

ω LOy

ω LOz

I ∥

I ⊥