- CORUNDUM - Al₂O₃

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:	167		R-3c
Lattice parameters (Å):	2.5190	2.5190		6.8758
Angles (°):	90.0	90.0		120.0

Symmetry (theoretical):

Space group:	167		R-3c
Lattice parameters (Å):	5.0460	5.0460		5.0460
Angles (°):	55.3	55.3		55.3

Cell contents:

Number of atoms:	10
Number of atom types:	2
Chemical composition:	0

Atomic positions (theoretical):

Al:	0.3520	0.3520	0.3520
Al:	0.8520	0.8520	0.8520
Al:	0.6480	0.6480	0.6480
Al:	0.1480	0.1480	0.1480
O:	0.5563	0.9437	0.2500
O:	0.2500	0.5563	0.9437
O:	0.9437	0.2500	0.5563
O:	0.4437	0.0563	0.7500
O:	0.7500	0.4437	0.0563
O:	0.0563	0.7500	0.4437

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.

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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	A2g	305	305	305	305
5	Eg	377	377	377	377	5.579e+38 9.5	9.079e+38 15.5	1.466e+39 25.0
6	Eg	377	377	377	377	5.579e+38 9.5	6.263e+38 10.7	1.184e+39 20.2
7	Eu	384	384	384	384
8	Eu	384	387	387	384
9	A2u	395	395	395	418
10	A1g	418	418	418	432	5.722e+39 97.7	1.365e+38 2.3	5.858e+39 100.0
11	Eg	432	432	432	432	2.854e+38 4.9	4.295e+38 7.3	7.149e+38 12.2
12	Eg	432	432	432	439	2.854e+38 4.9	3.870e+38 6.6	6.723e+38 11.5
13	Eu	439	439	439	439
14	Eu	439	446	446	446
15	Eg	446	446	446	446	1.228e+38 2.1	1.594e+38 2.7	2.822e+38 4.8
16	Eg	446	481	481	504	1.228e+38 2.1	1.709e+38 2.9	2.937e+38 5.0
17	A2g	535	535	535	535
18	Eu	570	570	570	570
19	Eu	570	575	575	570
20	Eg	575	575	575	575	1.480e+38 2.5	1.969e+38 3.4	3.449e+38 5.9
21	Eg	575	580	580	575	1.480e+38 2.5	1.176e+38 2.0	2.655e+38 4.5
22	A2u	580	599	599	599
23	A1u	599	630	630	634
24	Eu	634	634	634	634
25	Eu	634	644	644	644
26	A1g	644	696	696	696	8.933e+38 15.2	5.679e+38 9.7	1.461e+39 24.9
27	A1u	696	753	753	753
28	Eg	753	753	753	753	7.762e+38 13.2	7.489e+38 12.8	1.525e+39 26.0
29	Eg	753	754	754	754	7.762e+38 13.2	8.200e+38 14.0	1.596e+39 27.2
30	A2g	754	901	901	872

No.

Char.

ω TO

ω LOx

ω LOy

ω LOz

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