- SEIFERTITE - SiO₂

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:	60		Pbcn
Lattice parameters (Å):	2.1680	2.6703		2.3784
Angles (°):	90	90		90

Symmetry (theoretical):

Space group:	60		Pbcn
Lattice parameters (Å):	4.0315	4.9803		4.4419
Angles (°):	90	90		90

Cell contents:

Number of atoms:	12
Number of atom types:	2
Chemical composition:	0

Atomic positions (theoretical):

Si:	0.0000	0.1524	0.2500
O:	0.7316	0.6174	0.9197
Si:	0.5000	0.3476	0.7500
O:	0.7684	0.8826	0.4197
O:	0.2684	0.6174	0.5803
O:	0.2316	0.8826	0.0803
Si:	0.0000	0.8476	0.7500
O:	0.2684	0.3826	0.0803
Si:	0.5000	0.6524	0.2500
O:	0.2316	0.1174	0.5803
O:	0.7316	0.3826	0.4197
O:	0.7684	0.1174	0.9197

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.

Parameters of the Calculation

All the calculations have been done using the ABINIT software. This is a list of the most representative parameteres used during the Raman calculation.

Number of electronic bands:	26
k-points
grid:	6 6 6
number of shifts:	1
shifts:	0.5 0.5 0.5
Kinetic energy cut-off:	40 Ha [=1088.464 eV ]
eXchange-Correlation functional:	LDA_pw90

Pseudopotentials:
Si:	silicon, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 2 local
O :	oxygen, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 2 local

Dielectric Properties

We define:

The Born effective charges, also called dynamical charges, are tensors that correspond to the energy derivative with respect to atomic displacements and electric fields or, equivalently, to the change in atomic force due to an electric field: The sum of the Born effective charges of all nuclei in one cell must vanish, element by element, along each of the three directions of the space.
The dielectric tensors are the energy derivative with respect to two electric fields. They also relate the induced polarization to the external electric field.

Born effective charges (Z):

Si:	3.8001	0.0000	-0.1398
	-0.0000	3.9543	0.0000
	-0.0719	-0.0000	4.0127
Eig. Value:	3.7564	3.9543	4.0564
O :	-1.9000	-0.4651	0.3412
	-0.4895	-1.9771	0.0195
	0.2580	-0.0769	-2.0064
Eig. Value:	-1.3655	-2.4941	-2.0240
Si:	3.8001	0.0000	0.1398
	-0.0000	3.9543	-0.0000
	0.0719	0.0000	4.0127
Eig. Value:	3.7564	3.9543	4.0564
O :	-1.9000	-0.4651	-0.3412
	-0.4895	-1.9771	-0.0195
	-0.2580	0.0769	-2.0064
Eig. Value:	-1.3655	-2.4941	-2.0240
O :	-1.9000	0.4651	0.3412
	0.4895	-1.9771	-0.0195
	0.2580	0.0769	-2.0064
Eig. Value:	-1.3655	-2.4941	-2.0240
O :	-1.9000	0.4651	-0.3412
	0.4895	-1.9771	0.0195
	-0.2580	-0.0769	-2.0064
Eig. Value:	-1.3655	-2.4941	-2.0240
Si:	3.8001	-0.0000	-0.1398
	0.0000	3.9543	-0.0000
	-0.0719	0.0000	4.0127
Eig. Value:	3.7564	3.9543	4.0564
O :	-1.9000	-0.4651	0.3412
	-0.4895	-1.9771	0.0195
	0.2580	-0.0769	-2.0064
Eig. Value:	-1.3655	-2.4941	-2.0240
Si:	3.8001	-0.0000	0.1398
	0.0000	3.9543	0.0000
	0.0719	-0.0000	4.0127
Eig. Value:	3.7564	3.9543	4.0564
O :	-1.9000	-0.4651	-0.3412
	-0.4895	-1.9771	-0.0195
	-0.2580	0.0769	-2.0064
Eig. Value:	-1.3655	-2.4941	-2.0240
O :	-1.9000	0.4651	0.3412
	0.4895	-1.9771	-0.0195
	0.2580	0.0769	-2.0064
Eig. Value:	-1.3655	-2.4941	-2.0240
O :	-1.9000	0.4651	-0.3412
	0.4895	-1.9771	0.0195
	-0.2580	-0.0769	-2.0064
Eig. Value:	-1.3655	-2.4941	-2.0240

Atom type

Dielectric tensors:

	X	Y	Z
Ɛ_∞:	3.3818	0.0000	0.0000
	0.0000	3.4702	0.0000
	0.0000	0.0000	3.5133
Eig. Value:	3.3818	3.4702	3.5133
Refractive index (N):	1.8390	0.0000	0.0000
	0.0000	1.8628	0.0000
	0.0000	0.0000	1.8744
Eig. Value:	1.8390	1.8628	1.8744
Ɛ₀:	0.0000	0.0000	0.0000
	0.0000	0.0000	0.0000
	0.0000	0.0000	0.0000
Eig. Value:	0.0000	0.0000	0.0000

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	B3g	354	354	354	354	3.984e+36 0.0	5.479e+36 0.1	9.463e+36 0.1
5	A1g	377	377	377	377	8.558e+39 81.7	1.591e+38 1.5	8.717e+39 83.3
6	B1u	378	378	378	381
7	B3g	400	400	400	400	2.089e+37 0.2	2.872e+37 0.3	4.960e+37 0.5
8	B1g	401	401	401	401	2.216e+38 2.1	3.047e+38 2.9	5.264e+38 5.0
9	B3u	450	458	450	450
10	B3u	458	491	458	458
11	B1g	491	493	491	491	1.355e+38 1.3	1.863e+38 1.8	3.217e+38 3.1
12	B2u	493	499	499	493
13	Au	499	505	505	499
14	B1u	505	509	509	509
15	A1g	509	522	531	531	1.039e+40 99.2	8.154e+37 0.8	1.047e+40 100.0
16	B1g	531	531	541	535	3.002e+38 2.9	4.128e+38 3.9	7.129e+38 6.8
17	B2g	541	541	548	541	1.423e+38 1.4	1.956e+38 1.9	3.379e+38 3.2
18	Au	548	548	559	548
19	A1g	559	559	608	559	1.554e+39 14.8	7.529e+37 0.7	1.629e+39 15.6
20	B3g	608	608	612	608	8.305e+37 0.8	1.142e+38 1.1	1.972e+38 1.9
21	B1u	621	621	621	642
22	B2g	642	642	642	645	2.222e+38 2.1	3.055e+38 2.9	5.277e+38 5.0
23	B1g	645	645	645	650	3.578e+36 0.0	4.920e+36 0.0	8.498e+36 0.1
24	B3u	650	678	650	678
25	B2u	678	693	693	693
26	Au	693	715	731	726
27	B2g	731	731	732	731	1.461e+39 14.0	2.010e+39 19.2	3.471e+39 33.2
28	B3u	732	741	741	732
29	B3g	741	751	751	741	2.758e+38 2.6	3.792e+38 3.6	6.550e+38 6.3
30	B1u	751	793	793	793
31	A1g	793	793	793	793	3.723e+39 35.6	1.029e+36 0.0	3.724e+39 35.6
32	Au	793	798	797	798
33	B2u	798	853	853	853
34	B3g	853	880	880	880	4.922e+38 4.7	6.768e+38 6.5	1.169e+39 11.2
35	B1g	880	924	924	924	3.588e+38 3.4	4.934e+38 4.7	8.522e+38 8.1
36	B2g	924	1017	1006	1035	1.955e+39 18.7	2.689e+39 25.7	4.644e+39 44.4

No.

Char.

ω TO

ω LOx

ω LOy

ω LOz

I ∥

I ⊥

I Total

You can define the size of the supercell for the visualization of the vibration.

Normalized

Raw

Options for intensity.

Single Crystal Raman spectra

Single crystal Raman spectrum

The Raman measurements performed on single crystals employ polarized lasers and allow for the selection of specific elements of the individual Raman tensors of the Raman-active modes.

By convention, in the following we assume a measurement as X(XZ)Z, i.e. incident laser polarized along the X axis, emergent light polarized along the Z axis. If the crystal is aligned with the xyz reference frame, we sample the α_xz element. As you rotate the crystal you can sample other entries of the Raman tensor or various linear combineations.