-    Na2S2O4     -    Na2S2O4

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 ICSD database; code 16646 

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:  13  P1_2/c_1 
Lattice parameters (Å):  6.4040  6.5590  6.5860 
Angles (°):  90.0  119.51  90.0 

Symmetry (theoretical): 

Space group:  13  P1_2/c_1 
Lattice parameters (Å):  6.2328  6.1847  6.4269 
Angles (°):  90  120.07  90 

Cell contents: 

Number of atoms:  16 
Number of atom types:  3 
Chemical composition:  0 

Atomic positions (theoretical):

S:  0.1961  0.3590  0.9315 
Na:  0.2631  0.8523  0.9799 
O:  0.3204  0.1908  0.8566 
O:  0.1166  0.2514  0.0920 
S:  0.8039  0.3590  0.5685 
Na:  0.7369  0.8523  0.5201 
O:  0.6796  0.1908  0.6434 
O:  0.8834  0.2514  0.4080 
S:  0.8039  0.6410  0.0685 
Na:  0.7369  0.1477  0.0201 
O:  0.6796  0.8092  0.1434 
O:  0.8834  0.7486  0.9080 
S:  0.1961  0.6410  0.4315 
Na:  0.2631  0.1477  0.4799 
O:  0.3204  0.8092  0.3566 
O:  0.1166  0.7486  0.5920 
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: 38
k-points  
   grid: 4 4 4 
   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: 
O:  oxygen, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 2 local 
Na:  sodium, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 2 local 
S:  sulphur, 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): 

S: 1.7872 -0.8207 -0.6912 
-0.4095 1.0804 -0.0730 
-0.9729 -1.1494 1.4773 
Eig. Value: 2.4856 0.0563 1.8030 
Na: 1.1119 -0.0349 -0.0583 
-0.0111 1.2323 -0.0449 
-0.0669 -0.0098 1.0485 
Eig. Value: 1.1501 1.2381 1.0045 
O: -1.8717 1.2607 0.3565 
0.3983 -1.3013 -0.1243 
-0.2944 0.3396 -0.6820 
Eig. Value: -2.4645 -0.8019 -0.5887 
O: -1.0273 -0.1956 0.3930 
0.0075 -1.0114 0.1057 
1.3343 0.9625 -1.8438 
Eig. Value: -0.3937 -0.9329 -2.5558 
S: 1.7872 0.8207 -0.6912 
0.4095 1.0804 0.0730 
-0.9729 1.1494 1.4773 
Eig. Value: 2.4856 0.0563 1.8030 
Na: 1.1119 0.0349 -0.0583 
0.0111 1.2323 0.0449 
-0.0669 0.0098 1.0485 
Eig. Value: 1.1501 1.2381 1.0045 
O: -1.8717 -1.2607 0.3565 
-0.3983 -1.3013 0.1243 
-0.2944 -0.3396 -0.6820 
Eig. Value: -2.4645 -0.8019 -0.5887 
O: -1.0273 0.1956 0.3930 
-0.0075 -1.0114 -0.1057 
1.3343 -0.9625 -1.8438 
Eig. Value: -0.3937 -0.9329 -2.5558 
S: 1.7872 -0.8207 -0.6912 
-0.4095 1.0804 -0.0730 
-0.9729 -1.1494 1.4773 
Eig. Value: 2.4856 0.0563 1.8030 
Na: 1.1119 -0.0349 -0.0583 
-0.0111 1.2323 -0.0449 
-0.0669 -0.0098 1.0485 
Eig. Value: 1.1501 1.2381 1.0045 
O: -1.8717 1.2607 0.3565 
0.3983 -1.3013 -0.1243 
-0.2944 0.3396 -0.6820 
Eig. Value: -2.4645 -0.8019 -0.5887 
O: -1.0273 -0.1956 0.3930 
0.0075 -1.0114 0.1057 
1.3343 0.9625 -1.8438 
Eig. Value: -0.3937 -0.9329 -2.5558 
S: 1.7872 0.8207 -0.6912 
0.4095 1.0804 0.0730 
-0.9729 1.1494 1.4773 
Eig. Value: 2.4856 0.0563 1.8030 
Na: 1.1119 0.0349 -0.0583 
0.0111 1.2323 0.0449 
-0.0669 0.0098 1.0485 
Eig. Value: 1.1501 1.2381 1.0045 
O: -1.8717 -1.2607 0.3565 
-0.3983 -1.3013 0.1243 
-0.2944 -0.3396 -0.6820 
Eig. Value: -2.4645 -0.8019 -0.5887 
O: -1.0273 0.1956 0.3930 
-0.0075 -1.0114 -0.1057 
1.3343 -0.9625 -1.8438 
Eig. Value: -0.3937 -0.9329 -2.5558 
Atom type  X  Y  Z 

Dielectric tensors: 

 X Y Z 
Ɛ∞: 3.1111 0.0000 0.3332 
0.0000 2.5754 0.0000 
0.3332 0.0000 3.6131 
Eig. Value: 2.9450 2.5754 3.7792 
Refractive index (N): 1.7638 0.0000 0.5772 
0.0000 1.6048 0.0000 
0.5772 0.0000 1.9008 
Eig. Value: 1.7161 1.6048 1.9440 
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
Bg
44
44
44
44
2.530e+40
1.4
4.227e+40
2.4
6.758e+40
3.8
5
Bg
76
76
76
76
2.631e+40
1.5
3.799e+40
2.1
6.430e+40
3.6
6
Bu
89
93
89
89
7
Au
94
94
106
94
8
Bg
106
106
110
106
3.292e+40
1.8
4.510e+40
2.5
7.802e+40
4.4
9
Ag
110
110
120
110
2.558e+40
1.4
2.622e+40
1.5
5.179e+40
2.9
10
Bu
120
122
122
122
11
Bg
122
124
127
122
4.591e+39
0.3
5.550e+39
0.3
1.014e+40
0.6
12
Au
137
137
141
137
13
Ag
148
148
148
148
8.913e+40
5.0
3.120e+40
1.8
1.203e+41
6.8
14
Ag
152
152
152
152
3.150e+40
1.8
2.567e+40
1.4
5.717e+40
3.2
15
Au
173
173
179
173
16
Ag
179
179
179
179
7.870e+40
4.4
3.882e+40
2.2
1.175e+41
6.6
17
Bu
186
188
186
186
18
Bg
200
200
200
200
3.913e+39
0.2
5.573e+39
0.3
9.485e+39
0.5
19
Ag
212
212
212
212
1.244e+41
7.0
6.112e+40
3.4
1.856e+41
10.4
20
Bu
221
221
221
227
21
Bg
227
227
227
230
3.198e+39
0.2
3.470e+39
0.2
6.668e+39
0.4
22
Au
230
230
247
237
23
Au
248
248
256
248
24
Bu
256
256
256
256
25
Ag
256
267
267
257
3.937e+39
0.2
4.001e+39
0.2
7.938e+39
0.4
26
Bg
267
272
275
267
7.614e+38
0.0
1.284e+39
0.1
2.046e+39
0.1
27
Bg
280
280
280
280
5.305e+39
0.3
6.613e+39
0.4
1.192e+40
0.7
28
Bu
280
290
280
283
29
Ag
290
291
290
290
6.012e+41
33.7
2.613e+41
14.7
8.625e+41
48.4
30
Au
291
292
293
291
31
Ag
316
316
316
316
1.776e+40
1.0
1.400e+40
0.8
3.176e+40
1.8
32
Au
316
316
316
316
2.030e+38
0.0
1.600e+38
0.0
3.630e+38
0.0
33
Ag
390
390
390
390
1.170e+42
65.6
6.122e+41
34.4
1.782e+42
100.0
34
Au
391
391
391
391
35
Bu
415
417
415
417
36
Bg
417
422
417
431
9.319e+39
0.5
1.062e+40
0.6
1.994e+40
1.1
37
Ag
497
497
497
497
1.058e+40
0.6
7.723e+39
0.4
1.831e+40
1.0
38
Au
498
498
511
498
39
Bu
532
533
532
533
40
Bg
533
533
533
533
2.329e+39
0.1
2.914e+39
0.2
5.243e+39
0.3
41
Bg
916
916
916
916
1.031e+40
0.6
1.399e+40
0.8
2.430e+40
1.4
42
Bu
918
928
918
941
43
Au
1016
1016
1026
1016
44
Ag
1026
1026
1030
1026
1.991e+41
11.2
5.232e+40
2.9
2.514e+41
14.1
45
Bu
1030
1037
1037
1037
46
Ag
1037
1055
1037
1055
2.907e+40
1.6
1.259e+40
0.7
4.166e+40
2.3
47
Au
1055
1068
1060
1068
48
Bg
1068
1092
1068
1072
1.894e+40
1.1
3.007e+40
1.7
4.902e+40
2.8
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: