- QUARTZ - SiO₂

The crystal structure is fully relaxed (both unit cell parameters and atomic positions under symmetry constraints)

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:	154		P3_221
Lattice parameters (Å):
Angles (°):	90.0	90.0		120.0

Symmetry (theoretical):

Space group:	154		P3_221
Lattice parameters (Å):	4.9134	4.9134		5.4042
Angles (°):	90.0	90.0		120.0

Cell contents:

Number of atoms:	9
Number of atom types:	2
Chemical composition:	0

Atomic positions (theoretical):

Si:	0.4727	0.0000	0.1667
Si:	0.0000	0.4727	0.8333
Si:	0.5273	0.5273	0.5000
O:	0.4151	0.2623	0.2904
O:	0.7377	0.1528	0.9570
O:	0.8472	0.5849	0.6237
O:	0.2623	0.4151	0.7096
O:	0.1528	0.7377	0.0430
O:	0.5849	0.8472	0.3763

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	E	120	120	120	120	1.661e+39 2.6	1.718e+39 2.7	3.379e+39 5.4
5	E	120	120	120	120	1.661e+39 2.6	2.801e+39 4.4	4.462e+39 7.1
6	A1	182	182	182	182	3.097e+40 49.1	1.905e+37 0.0	3.099e+40 49.2
7	E	252	252	252	252	3.860e+38 0.6	5.120e+38 0.8	8.980e+38 1.4
8	E	252	253	253	252	3.860e+38 0.6	4.661e+38 0.7	8.521e+38 1.4
9	A1	345	345	345	345	1.726e+39 2.7	6.950e+38 1.1	2.421e+39 3.8
10	A2	358	358	358	380
11	E	382	382	382	382	4.156e+38 0.7	3.217e+38 0.5	7.374e+38 1.2
12	E	382	391	391	382	4.156e+38 0.7	6.214e+38 1.0	1.037e+39 1.6
13	E	433	433	433	433	3.711e+38 0.6	4.990e+38 0.8	8.701e+38 1.4
14	E	433	445	445	433	3.711e+38 0.6	5.601e+38 0.9	9.312e+38 1.5
15	A1	445	474	474	445	6.302e+40 100.0	1.779e+35 0.0	6.302e+40 100.0
16	A2	474	492	492	532
17	E	680	680	680	680	3.175e+38 0.5	3.025e+38 0.5	6.199e+38 1.0
18	E	680	682	682	680	3.175e+38 0.5	5.294e+38 0.8	8.469e+38 1.3
19	A2	766	766	766	776
20	E	780	780	780	780	4.695e+38 0.7	6.184e+38 1.0	1.088e+39 1.7
21	E	780	793	793	780	4.695e+38 0.7	5.605e+38 0.9	1.030e+39 1.6
22	E	1063	1063	1063	1063	3.162e+38 0.5	4.183e+38 0.7	7.345e+38 1.2
23	E	1063	1070	1070	1063	3.162e+38 0.5	3.801e+38 0.6	6.963e+38 1.1
24	A2	1070	1078	1078	1078
25	A1	1078	1152	1152	1155	3.455e+38 0.5	2.391e+38 0.4	5.846e+38 0.9
26	E	1155	1155	1155	1155	6.575e+38 1.0	5.617e+38 0.9	1.219e+39 1.9
27	E	1155	1225	1225	1234	6.575e+38 1.0	1.057e+39 1.7	1.715e+39 2.7

No.

Char.

ω TO

ω LOx

ω LOy

ω LOz

I ∥

I ⊥