-    NEIGHBORITE     -    NaMgF3

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:  63  Cmcm 
Lattice parameters (Å):       
Angles (°):  90  90  90 

Symmetry (theoretical): 

Space group:  63  Cmcm 
Lattice parameters (Å):  5.0685  5.0685  7.1249 
Angles (°):  90  90  33.24 

Cell contents: 

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

Atomic positions (theoretical):

Na:  0.2556  0.2556  0.7500 
Na:  0.7444  0.7444  0.2500 
Mg:  0.0000  0.0000  0.0000 
Mg:  0.0000  0.0000  0.5000 
F:  0.0691  0.0691  0.2500 
F:  0.9309  0.9309  0.7500 
F:  0.3730  0.3730  0.4433 
F:  0.3730  0.3730  0.0567 
F:  0.6270  0.6270  0.5567 
F:  0.6270  0.6270  0.9433 
Atom type  X  Y  Z 

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: 

Size:

 Nx:  Ny:  Nz: 
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 4 
   number of shifts: 1 
   shifts: 0 0 0 
Kinetic energy cut-off: 40 Ha  [=1088.464 eV ]
eXchange-Correlation functional: LDA pw90 

Pseudopotentials: 
Na:  sodium, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 0 local 
Mg:  magnesium, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 0 local 
F:  fluorine, 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): 

Na: 0.9935 0.0000 -0.0000 
0.0000 1.1079 0.0000 
-0.0000 -0.0000 1.0502 
Eig. Value: 0.9935 1.1079 1.0502 
Na: 0.9935 0.0000 0.0000 
0.0000 1.1079 -0.0000 
-0.0000 -0.0000 1.0502 
Eig. Value: 0.9935 1.1079 1.0502 
Mg: 1.9766 -0.0000 -0.0000 
-0.0000 1.7203 0.0147 
-0.0000 0.0408 1.8702 
Eig. Value: 1.9766 1.7153 1.8752 
Mg: 1.9766 -0.0000 0.0000 
-0.0000 1.7203 -0.0147 
-0.0000 -0.0408 1.8702 
Eig. Value: 1.9766 1.7153 1.8752 
F: -0.8742 -0.0000 -0.0000 
-0.0000 -0.8705 0.0000 
-0.0000 -0.0000 -1.1400 
Eig. Value: -0.8742 -0.8705 -1.1400 
F: -0.8742 0.0000 0.0000 
0.0000 -0.8705 -0.0000 
0.0000 -0.0000 -1.1400 
Eig. Value: -0.8742 -0.8705 -1.1400 
F: -1.0479 0.0000 -0.0000 
0.0000 -0.9788 -0.0489 
-0.0000 -0.0515 -0.8902 
Eig. Value: -1.0479 -1.0015 -0.8675 
F: -1.0479 0.0000 0.0000 
0.0000 -0.9788 0.0489 
0.0000 0.0515 -0.8902 
Eig. Value: -1.0479 -1.0015 -0.8675 
F: -1.0479 -0.0000 -0.0000 
0.0000 -0.9788 -0.0489 
-0.0000 -0.0515 -0.8902 
Eig. Value: -1.0479 -1.0015 -0.8675 
F: -1.0479 -0.0000 0.0000 
-0.0000 -0.9788 0.0489 
0.0000 0.0515 -0.8902 
Eig. Value: -1.0479 -1.0015 -0.8675 
Atom type  X  Y  Z 

Dielectric tensors: 

 X Y Z 
Ɛ∞: 1.9676 0.0000 0.0000 
0.0000 1.9409 0.0000 
0.0000 0.0000 1.9457 
Eig. Value: 1.9676 1.9409 1.9457 
Refractive index (N): 1.4027 0.0000 0.0000 
0.0000 1.3932 0.0000 
0.0000 0.0000 1.3949 
Eig. Value: 1.4027 1.3932 1.3949 
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
Au
118
118
118
118
5
B1g
146
146
146
146
3.026e+36
0.1
4.160e+36
0.1
7.186e+36
0.2
6
B1u
147
147
147
167
7
B3u
180
182
180
180
8
A1g
182
184
182
182
6.031e+37
1.7
4.141e+37
1.2
1.017e+38
2.9
9
B1u
188
188
188
189
10
B3g
189
189
189
211
2.128e+37
0.6
2.925e+37
0.8
5.053e+37
1.4
11
B3g
240
240
240
240
1.702e+37
0.5
2.340e+37
0.7
4.042e+37
1.1
12
B2u
241
241
246
241
13
A1g
246
246
253
246
1.450e+38
4.1
5.008e+37
1.4
1.951e+38
5.5
14
B1g
253
253
262
253
7.122e+36
0.2
9.792e+36
0.3
1.691e+37
0.5
15
B3u
262
274
262
262
16
B2u
274
289
289
274
17
B2g
289
295
298
289
18
B1g
298
298
305
298
7.011e+37
2.0
9.640e+37
2.7
1.665e+38
4.7
19
B1u
306
306
306
319
20
B2u
319
319
335
339
21
A1g
339
339
339
360
6.541e+37
1.8
4.186e+37
1.2
1.073e+38
3.0
22
B3g
381
381
381
381
2.267e+37
0.6
3.117e+37
0.9
5.384e+37
1.5
23
Au
405
405
405
405
24
B3u
409
413
409
409
25
A1g
413
429
413
413
3.472e+39
98.0
6.960e+37
2.0
3.542e+39
100.0
26
B1u
429
469
429
443
27
B2u
469
495
495
469
28
B3g
495
518
518
495
5.517e+37
1.6
7.585e+37
2.1
1.310e+38
3.7
29
B2u
518
539
539
518
30
B1u
539
572
584
633
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.

Nx: 
Ny: 
Nz: 
Normalized
Raw
Options for intensity.
 

Single Crystal Raman spectra

Single crystal 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.

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 αxz element. As you rotate the crystal you can sample other entries of the Raman tensor or various linear combineations.

Horizontal:
Xmin:
Xmax:
Vertical:
Ymin:
Ymax:
 


Choose the orientation of the crystal with respect to the reference system:

 
Rotation around X axis:
Rotation around Z axis:
Rotation around Y axis: