- GEIKIELITE - MgTiO₃

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:	148		R-3
Lattice parameters (Å):	5.0567	5.0567		13.9034
Angles (°):	90.0	90.0		120.0

Symmetry (theoretical):

Space group:	148		R-3
Lattice parameters (Å):	5.3784	5.3784		5.3784
Angles (°):	55.3	55.3		55.3

Cell contents:

Number of atoms:	10
Number of atom types:	3
Chemical composition:	0

Atomic positions (theoretical):

Mg:	0.3547	0.3547	0.3547
Ti:	0.1446	0.1446	0.1446
O:	0.5605	0.9522	0.2289
O:	0.9522	0.2289	0.5605
O:	0.2289	0.5605	0.9522
Mg:	0.6453	0.6453	0.6453
Ti:	0.8554	0.8554	0.8554
O:	0.4395	0.0478	0.7711
O:	0.0478	0.7711	0.4395
O:	0.7711	0.4395	0.0478

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	Ag	232	232	232	232	1.020e+41 11.8	3.414e+39 0.4	1.054e+41 12.2
5	Eu	279	279	279	279
6	Eu	279	287	287	279
7	Eg	287	287	287	287	4.933e+40 5.7	5.208e+40 6.0	1.014e+41 11.8
8	Eg	287	295	295	287	4.933e+40 5.7	5.426e+40 6.3	1.036e+41 12.0
9	Ag	312	312	312	312	4.790e+40 5.6	6.349e+38 0.1	4.853e+40 5.6
10	Au	314	314	314	330
11	Eg	330	330	330	330	3.349e+40 3.9	5.139e+40 6.0	8.488e+40 9.8
12	Eg	330	330	330	335	3.349e+40 3.9	2.659e+40 3.1	6.008e+40 7.0
13	Eu	335	335	335	335
14	Eu	335	365	365	365
15	Eg	365	365	365	365	6.483e+40 7.5	6.292e+40 7.3	1.277e+41 14.8
16	Eg	365	393	393	380	6.483e+40 7.5	1.075e+41 12.5	1.724e+41 20.0
17	Ag	395	395	395	395	8.886e+40 10.3	2.313e+40 2.7	1.120e+41 13.0
18	Au	415	415	415	445
19	Eu	454	454	454	454
20	Eu	454	491	491	454
21	Eg	491	491	491	491	4.227e+40 4.9	4.039e+40 4.7	8.266e+40 9.6
22	Eg	491	507	507	491	4.227e+40 4.9	4.605e+40 5.3	8.832e+40 10.2
23	Ag	510	510	510	510	6.148e+40 7.1	1.976e+38 0.0	6.168e+40 7.2
24	Au	525	525	525	567
25	Eu	567	567	567	567
26	Eu	567	666	666	634
27	Eg	666	666	666	666	3.238e+40 3.8	4.846e+40 5.6	8.084e+40 9.4
28	Eg	666	717	717	666	3.238e+40 3.8	2.759e+40 3.2	5.996e+40 7.0
29	Au	717	720	720	720
30	Ag	720	817	817	784	8.606e+41 99.8	1.993e+39 0.2	8.626e+41 100.0

No.

Char.

ω TO

ω LOx

ω LOy

ω LOz

I ∥

I ⊥