-    PROUSTITE     -    Ag3AsS3

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:  161  R3c 
Lattice parameters (Å):  10.7680  10.7680  8.7200 
Angles (°):  90  90  120 

Symmetry (theoretical): 

Space group:  161  R3c 
Lattice parameters (Å):  6.7582  6.7582  6.7582 
Angles (°):  102.72  102.72  102.72 

Cell contents: 

Number of atoms:  14 
Number of atom types:  3 
Chemical composition:  0 

Atomic positions (theoretical):

Ag:  0.4617  0.2426  0.9197 
As:  0.0151  0.0151  0.0151 
S:  0.5978  0.2603  0.2893 
Ag:  0.2426  0.9197  0.4617 
S:  0.2603  0.2893  0.5978 
Ag:  0.4197  0.7426  0.9617 
As:  0.5151  0.5151  0.5151 
S:  0.7893  0.7603  0.0978 
Ag:  0.9197  0.4617  0.2426 
S:  0.2893  0.5978  0.2603 
Ag:  0.7426  0.9617  0.4197 
S:  0.7603  0.0978  0.7893 
Ag:  0.9617  0.4197  0.7426 
S:  0.0978  0.7893  0.7603 
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: 56
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: 
Ag:  silver, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 1 local 
As:  arsenic, 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): 

Ag: 1.0879 0.0593 0.1754 
0.1343 0.7332 -0.0785 
-0.1067 -0.2093 0.8775 
Eig. Value: 1.1127 0.6226 0.9634 
As: 2.5445 0.1931 -0.0000 
-0.1931 2.5445 0.0000 
-0.0000 -0.0000 1.2918 
Eig. Value: 2.5445 2.5445 1.2918 
S: -2.1947 -0.5158 0.6249 
-0.5170 -1.3227 0.3507 
0.2491 0.4271 -1.3081 
Eig. Value: -2.6683 -1.2344 -0.9229 
Ag: 0.7380 0.0677 -0.1557 
0.1428 1.0831 -0.1127 
-0.1279 0.1971 0.8775 
Eig. Value: 0.6226 1.1127 0.9634 
S: -1.0935 -0.1187 -0.0087 
-0.1200 -2.4239 -0.7166 
0.2453 -0.4293 -1.3081 
Eig. Value: -1.2344 -2.6683 -0.9229 
Ag: 0.7380 -0.0677 0.1557 
-0.1428 1.0831 -0.1127 
0.1279 0.1971 0.8775 
Eig. Value: 0.6226 1.1127 0.9634 
As: 2.5445 -0.1931 -0.0000 
0.1931 2.5445 0.0000 
-0.0000 -0.0000 1.2918 
Eig. Value: 2.5445 2.5445 1.2918 
S: -1.0935 0.1187 0.0087 
0.1200 -2.4239 -0.7166 
-0.2453 -0.4293 -1.3081 
Eig. Value: -1.2344 -2.6683 -0.9229 
Ag: 0.9057 -0.2396 -0.0197 
-0.1645 0.9154 0.1912 
0.2346 0.0122 0.8775 
Eig. Value: 0.6226 1.1127 0.9634 
S: -1.9879 0.6364 -0.6162 
0.6351 -1.5295 0.3659 
-0.4944 0.0022 -1.3081 
Eig. Value: -2.6683 -1.2344 -0.9229 
Ag: 1.0879 -0.0593 -0.1754 
-0.1343 0.7332 -0.0785 
0.1067 -0.2093 0.8775 
Eig. Value: 1.1127 0.6226 0.9634 
S: -2.1947 0.5158 -0.6249 
0.5170 -1.3227 0.3507 
-0.2491 0.4271 -1.3081 
Eig. Value: -2.6683 -1.2344 -0.9229 
Ag: 0.9057 0.2396 0.0197 
0.1645 0.9154 0.1912 
-0.2346 0.0122 0.8775 
Eig. Value: 0.6226 1.1127 0.9634 
S: -1.9879 -0.6364 0.6162 
-0.6351 -1.5295 0.3659 
0.4944 0.0022 -1.3081 
Eig. Value: -2.6683 -1.2344 -0.9229 
Atom type  X  Y  Z 

Dielectric tensors: 

 X Y Z 
Ɛ∞: 11.0352 0.0000 0.0000 
0.0000 11.0352 -0.0000 
0.0000 -0.0000 9.3531 
Eig. Value: 11.0352 11.0352 9.3531 
Refractive index (N): 3.3219 0.0000 0.0000 
0.0000 3.3219 -0.0000 
0.0000 -0.0000 3.0583 
Eig. Value: 3.3219 3.3219 3.0583 
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
E
-23
-23
-23
-23
2
E
-23
-20
-20
-23
3
Ac
0
0
0
0
4
Ac
0
0
0
0
5
Ac
0
0
0
0
6
A2
6
6
6
6
7
E
29
29
29
29
1.146e+41
0.5
1.931e+41
0.8
3.077e+41
1.3
8
E
29
29
29
29
1.146e+41
0.5
1.192e+41
0.5
2.338e+41
1.0
9
A1
36
36
36
41
5.165e+41
2.2
5.611e+40
0.2
5.726e+41
2.5
10
E
42
42
42
42
1.004e+41
0.4
1.443e+41
0.6
2.447e+41
1.1
11
E
42
43
43
42
1.004e+41
0.4
1.419e+41
0.6
2.423e+41
1.0
12
A1
44
44
44
44
4.998e+42
21.5
3.240e+41
1.4
5.322e+42
22.9
13
A2
44
44
44
46
14
E
48
48
48
48
2.410e+41
1.0
2.898e+41
1.2
5.308e+41
2.3
15
E
48
50
50
48
2.410e+41
1.0
4.003e+41
1.7
6.412e+41
2.8
16
A2
59
59
59
59
17
E
67
67
67
67
2.794e+41
1.2
3.630e+41
1.6
6.423e+41
2.8
18
E
67
67
67
67
2.794e+41
1.2
4.415e+41
1.9
7.210e+41
3.1
19
E
106
106
106
106
6.292e+40
0.3
7.636e+40
0.3
1.393e+41
0.6
20
E
106
107
107
106
6.293e+40
0.3
9.498e+40
0.4
1.579e+41
0.7
21
E
124
124
124
124
1.617e+41
0.7
1.967e+41
0.8
3.584e+41
1.5
22
E
124
125
125
124
1.617e+41
0.7
1.261e+41
0.5
2.878e+41
1.2
23
A1
145
145
145
145
1.549e+42
6.7
1.385e+41
0.6
1.688e+42
7.3
24
A2
151
151
151
151
25
A1
213
213
213
213
4.504e+42
19.4
3.409e+41
1.5
4.845e+42
20.9
26
E
238
238
238
238
9.868e+39
0.0
1.606e+40
0.1
2.593e+40
0.1
27
E
238
239
239
238
9.804e+39
0.0
1.139e+40
0.0
2.119e+40
0.1
28
E
239
239
239
239
1.270e+41
0.5
1.228e+41
0.5
2.498e+41
1.1
29
E
239
239
239
239
1.269e+41
0.5
1.654e+41
0.7
2.923e+41
1.3
30
A2
257
257
257
257
31
E
271
271
271
271
6.143e+41
2.6
7.716e+41
3.3
1.386e+42
6.0
32
E
271
280
280
271
6.143e+41
2.6
4.885e+41
2.1
1.103e+42
4.7
33
A1
280
281
281
282
1.236e+42
5.3
2.642e+40
0.1
1.263e+42
5.4
34
A2
282
282
282
285
35
E
292
292
292
292
3.737e+40
0.2
4.877e+40
0.2
8.615e+40
0.4
36
E
292
292
292
292
3.737e+40
0.2
4.992e+40
0.2
8.729e+40
0.4
37
E
321
321
321
321
9.293e+41
4.0
1.513e+42
6.5
2.443e+42
10.5
38
E
321
328
328
321
9.293e+41
4.0
1.145e+42
4.9
2.075e+42
8.9
39
E
340
340
340
340
1.641e+41
0.7
2.006e+41
0.9
3.647e+41
1.6
40
E
340
344
344
340
1.641e+41
0.7
2.694e+41
1.2
4.335e+41
1.9
41
A1
344
344
344
350
2.321e+43
100.0
7.872e+39
0.0
2.322e+43
100.0
42
A2
354
354
354
354
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: