-    MIMETITE     -    Pb5(AsO4)3Cl

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:  176  P6_3/m 
Lattice parameters (Å):  10.2110  10.2110  7.4185 
Angles (°):  90  90  120 

Symmetry (theoretical): 

Space group:  176  P6_3/m 
Lattice parameters (Å):  10.1398  10.1398  7.2572 
Angles (°):  90  90  120 

Cell contents: 

Number of atoms:  42 
Number of atom types: 
Chemical composition: 

Atomic positions (theoretical):

Pb:  0.3333  0.6667  0.5044 
Pb:  0.0098  0.2507  0.2500 
As:  0.3797  0.4076  0.2500 
O:  0.4925  0.3284  0.2500 
O:  0.4844  0.6024  0.2500 
O:  0.2627  0.3585  0.0640 
Cl:  0.0000  0.0000  0.0000 
Pb:  0.6667  0.3333  0.0044 
Pb:  0.7591  0.0098  0.7500 
As:  0.9721  0.3797  0.7500 
O:  0.1640  0.4925  0.7500 
O:  0.8819  0.4844  0.7500 
O:  0.9042  0.2627  0.5640 
Cl:  0.0000  0.0000  0.5000 
Pb:  0.7493  0.7591  0.2500 
As:  0.5924  0.9721  0.2500 
O:  0.6716  0.1640  0.2500 
O:  0.3976  0.8819  0.2500 
O:  0.6415  0.9042  0.0640 
Pb:  0.9902  0.7493  0.7500 
As:  0.6203  0.5924  0.7500 
O:  0.5075  0.6716  0.7500 
O:  0.5156  0.3976  0.7500 
O:  0.7373  0.6415  0.5640 
Pb:  0.2409  0.9902  0.2500 
As:  0.0279  0.6203  0.2500 
O:  0.8360  0.5075  0.2500 
O:  0.1181  0.5156  0.2500 
O:  0.0958  0.7373  0.0640 
Pb:  0.2507  0.2409  0.7500 
As:  0.4076  0.0279  0.7500 
O:  0.3284  0.8360  0.7500 
O:  0.6024  0.1181  0.7500 
O:  0.3585  0.0958  0.5640 
Pb:  0.6667  0.3333  0.4956 
O:  0.7373  0.6415  0.9360 
Pb:  0.3333  0.6667  0.9956 
O:  0.0958  0.7373  0.4360 
O:  0.3585  0.0958  0.9360 
O:  0.2627  0.3585  0.4360 
O:  0.9042  0.2627  0.9360 
O:  0.6415  0.9042  0.4360 
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: 

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: 1 1 2 
   number of shifts: 
   shifts: 0.5 0.5 0.5 
Kinetic energy cut-off: 40 Ha  [=1088.464 eV ]
eXchange-Correlation functional: LDA pw90 

Pseudopotentials: 
Pb:  Tetter norm-conserving pseudopotential 
As:  arsenic, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 2 local 
O:  oxygen, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 2 local 
Cl:  chlorine, 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): 

Pb: 3.3281 0.0066 -0.0000 
-0.0066 3.3281 0.0000 
-0.0000 -0.0000 3.8814 
Eig. Value: 3.3281 3.3281 3.8814 
Pb: 3.1383 -0.1447 -0.0000 
-0.1150 3.5813 0.0000 
-0.0000 -0.0000 3.8800 
Eig. Value: 3.1030 3.6166 3.8800 
As: 4.0751 -0.4466 -0.0000 
-0.2104 4.0343 0.0000 
-0.0000 -0.0000 2.9101 
Eig. Value: 4.3838 3.7255 2.9101 
O: -3.2536 0.5091 -0.0000 
0.4483 -1.6016 -0.0000 
0.0000 0.0000 -1.7492 
Eig. Value: -3.3823 -1.4729 -1.7492 
O: -2.4019 -0.3196 -0.0000 
-0.5634 -2.9835 -0.0000 
0.0000 -0.0000 -1.5962 
Eig. Value: -2.1640 -3.2214 -1.5962 
O: -1.9803 -0.2047 -0.1852 
-0.2260 -1.9334 -0.3611 
-0.1281 -0.2716 -2.6634 
Eig. Value: -2.0207 -1.7161 -2.8401 
Cl: -1.7978 -0.1354 0.0000 
0.1354 -1.7978 -0.0000 
-0.0000 -0.0000 -2.1168 
Eig. Value: -1.7978 -1.7978 -2.1168 
Pb: 3.3281 0.0066 0.0000 
-0.0066 3.3281 -0.0000 
0.0000 0.0000 3.8814 
Eig. Value: 3.3281 3.3281 3.8814 
Pb: 3.5830 -0.1417 0.0000 
-0.1120 3.1366 -0.0000 
-0.0000 -0.0000 3.8800 
Eig. Value: 3.6166 3.1030 3.8800 
As: 4.3290 0.0638 0.0000 
0.3000 3.7804 -0.0000 
-0.0000 -0.0000 2.9101 
Eig. Value: 4.3838 3.7255 2.9101 
O: -2.4291 -0.9243 0.0000 
-0.9851 -2.4260 0.0000 
-0.0000 -0.0000 -1.7492 
Eig. Value: -3.3823 -1.4729 -1.7492 
O: -2.4558 0.5946 0.0000 
0.3507 -2.9296 -0.0000 
-0.0000 -0.0000 -1.5962 
Eig. Value: -2.1640 -3.2214 -1.5962 
O: -1.7586 0.0980 0.2201 
0.0767 -2.1551 -0.3410 
0.1712 -0.2467 -2.6634 
Eig. Value: -1.7161 -2.0207 -2.8401 
Cl: -1.7978 -0.1354 -0.0000 
0.1354 -1.7978 0.0000 
0.0000 -0.0000 -2.1168 
Eig. Value: -1.7978 -1.7978 -2.1168 
Pb: 3.3581 0.2419 -0.0000 
0.2716 3.3615 -0.0000 
0.0000 -0.0000 3.8800 
Eig. Value: 3.1030 3.6166 3.8800 
As: 3.7600 0.0285 0.0000 
0.2647 4.3494 0.0000 
0.0000 0.0000 2.9101 
Eig. Value: 3.7255 4.3838 2.9101 
O: -1.6000 0.5064 0.0000 
0.4456 -3.2551 -0.0000 
0.0000 -0.0000 -1.7492 
Eig. Value: -1.4729 -3.3823 -1.7492 
O: -3.2205 0.0908 -0.0000 
-0.1531 -2.1649 0.0000 
-0.0000 -0.0000 -1.5962 
Eig. Value: -3.2214 -2.1640 -1.5962 
O: -2.1316 0.1387 0.4053 
0.1173 -1.7821 0.0201 
0.2993 0.0249 -2.6634 
Eig. Value: -2.0207 -1.7161 -2.8401 
Pb: 3.1383 -0.1447 0.0000 
-0.1150 3.5813 0.0000 
-0.0000 -0.0000 3.8800 
Eig. Value: 3.1030 3.6166 3.8800 
As: 4.0751 -0.4466 0.0000 
-0.2104 4.0343 0.0000 
-0.0000 -0.0000 2.9101 
Eig. Value: 4.3838 3.7255 2.9101 
O: -3.2536 0.5091 0.0000 
0.4483 -1.6016 -0.0000 
0.0000 -0.0000 -1.7492 
Eig. Value: -3.3823 -1.4729 -1.7492 
O: -2.4019 -0.3196 -0.0000 
-0.5634 -2.9835 -0.0000 
0.0000 0.0000 -1.5962 
Eig. Value: -2.1640 -3.2214 -1.5962 
O: -1.9803 -0.2047 0.1852 
-0.2260 -1.9334 0.3611 
0.1281 0.2716 -2.6634 
Eig. Value: -2.0207 -1.7161 -2.8401 
Pb: 3.5830 -0.1417 0.0000 
-0.1120 3.1366 -0.0000 
-0.0000 0.0000 3.8800 
Eig. Value: 3.6166 3.1030 3.8800 
As: 4.3290 0.0638 0.0000 
0.3000 3.7804 0.0000 
-0.0000 -0.0000 2.9101 
Eig. Value: 4.3838 3.7255 2.9101 
O: -2.4291 -0.9243 0.0000 
-0.9851 -2.4260 0.0000 
0.0000 0.0000 -1.7492 
Eig. Value: -3.3823 -1.4729 -1.7492 
O: -2.4558 0.5946 0.0000 
0.3507 -2.9296 -0.0000 
-0.0000 0.0000 -1.5962 
Eig. Value: -2.1640 -3.2214 -1.5962 
O: -1.7586 0.0980 -0.2201 
0.0767 -2.1551 0.3410 
-0.1712 0.2467 -2.6634 
Eig. Value: -1.7161 -2.0207 -2.8401 
Pb: 3.3581 0.2419 -0.0000 
0.2716 3.3615 -0.0000 
-0.0000 0.0000 3.8800 
Eig. Value: 3.1030 3.6166 3.8800 
As: 3.7600 0.0285 -0.0000 
0.2647 4.3494 0.0000 
0.0000 0.0000 2.9101 
Eig. Value: 3.7255 4.3838 2.9101 
O: -1.6000 0.5064 0.0000 
0.4456 -3.2551 0.0000 
0.0000 -0.0000 -1.7492 
Eig. Value: -1.4729 -3.3823 -1.7492 
O: -3.2205 0.0908 0.0000 
-0.1531 -2.1649 0.0000 
0.0000 0.0000 -1.5962 
Eig. Value: -3.2214 -2.1640 -1.5962 
O: -2.1316 0.1387 -0.4053 
0.1173 -1.7821 -0.0201 
-0.2993 -0.0249 -2.6634 
Eig. Value: -2.0207 -1.7161 -2.8401 
Pb: 3.3281 0.0066 -0.0000 
-0.0066 3.3281 0.0000 
-0.0000 0.0000 3.8814 
Eig. Value: 3.3281 3.3281 3.8814 
O: -1.9803 -0.2047 -0.1852 
-0.2260 -1.9334 -0.3611 
-0.1281 -0.2716 -2.6634 
Eig. Value: -2.0207 -1.7161 -2.8401 
Pb: 3.3281 0.0066 0.0000 
-0.0066 3.3281 -0.0000 
0.0000 0.0000 3.8814 
Eig. Value: 3.3281 3.3281 3.8814 
O: -1.7586 0.0980 0.2201 
0.0767 -2.1551 -0.3410 
0.1712 -0.2467 -2.6634 
Eig. Value: -1.7161 -2.0207 -2.8401 
O: -2.1316 0.1387 0.4053 
0.1173 -1.7821 0.0201 
0.2993 0.0249 -2.6634 
Eig. Value: -2.0207 -1.7161 -2.8401 
O: -1.9803 -0.2047 0.1852 
-0.2260 -1.9334 0.3611 
0.1281 0.2716 -2.6634 
Eig. Value: -2.0207 -1.7161 -2.8401 
O: -1.7586 0.0980 -0.2201 
0.0767 -2.1551 0.3410 
-0.1712 0.2467 -2.6634 
Eig. Value: -1.7161 -2.0207 -2.8401 
O: -2.1316 0.1387 -0.4053 
0.1173 -1.7821 -0.0201 
-0.2993 -0.0249 -2.6634 
Eig. Value: -2.0207 -1.7161 -2.8401 
Atom type 

Dielectric tensors: 

 
Ɛ4.9199 0.0000 0.0000 
0.0000 4.9199 0.0000 
0.0000 0.0000 4.9662 
Eig. Value: 4.9199 4.9199 4.9662 
Refractive index (N): 2.2181 0.0000 0.0000 
0.0000 2.2181 0.0000 
0.0000 0.0000 2.2285 
Eig. Value: 2.2181 2.2181 2.2285 
Ɛ00.0000 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
E1g
3
3
3
3
5
E1g
3
3
3
3
6
Au
10
10
10
29
7
Bg
29
29
29
29
8
E2u
29
29
29
29
9
E2u
29
29
29
39
10
E1u
45
45
45
45
11
E1u
45
47
47
45
12
E1g
47
47
47
47
1.790e+39
0.2
2.670e+39
0.3
4.460e+39
0.5
13
E1g
47
48
48
47
1.790e+39
0.2
2.252e+39
0.3
4.042e+39
0.5
14
Bg
48
48
48
48
15
Bu
49
49
49
49
16
Ag
50
50
50
50
7.309e+40
8.3
8.601e+38
0.1
7.395e+40
8.4
17
E2g
51
51
51
51
1.381e+39
0.2
1.042e+39
0.1
2.424e+39
0.3
18
E2g
51
51
51
51
1.381e+39
0.2
1.892e+39
0.2
3.274e+39
0.4
19
E2u
58
58
58
58
20
E2u
58
58
58
58
21
E2g
63
63
63
63
6.867e+39
0.8
6.773e+39
0.8
1.364e+40
1.6
22
E2g
63
63
63
63
6.867e+39
0.8
7.820e+39
0.9
1.469e+40
1.7
23
Au
68
68
68
72
24
Bu
72
72
72
73
25
E1g
73
73
73
73
1.979e+40
2.3
3.271e+40
3.7
5.250e+40
6.0
26
E1g
73
73
73
74
1.979e+40
2.3
2.171e+40
2.5
4.151e+40
4.7
27
E1u
74
74
74
74
28
E1u
74
78
78
88
29
Ag
88
88
88
93
6.640e+40
7.6
6.796e+38
0.1
6.708e+40
7.6
30
Bg
93
93
93
93
31
E2g
93
93
93
93
1.530e+40
1.7
1.257e+40
1.4
2.788e+40
3.2
32
E2g
93
93
93
94
1.530e+40
1.7
1.994e+40
2.3
3.525e+40
4.0
33
E2u
94
94
94
94
34
E2u
94
94
94
96
35
Bu
99
99
99
99
36
E1g
100
100
100
100
1.242e+39
0.1
1.940e+39
0.2
3.182e+39
0.4
37
E1g
100
100
100
100
1.242e+39
0.1
1.477e+39
0.2
2.719e+39
0.3
38
Ag
102
102
102
102
3.313e+40
3.8
7.319e+37
0.0
3.320e+40
3.8
39
Au
105
105
105
106
40
E1u
106
106
106
106
41
E1u
106
112
112
112
42
E2g
112
112
112
112
1.746e+39
0.2
2.199e+39
0.3
3.944e+39
0.4
43
E2g
112
123
123
121
1.746e+39
0.2
1.511e+39
0.2
3.257e+39
0.4
44
Au
123
123
123
123
45
Bu
123
123
123
128
46
Ag
128
128
128
131
4.124e+39
0.5
2.459e+39
0.3
6.583e+39
0.8
47
E1u
131
131
131
131
48
E1u
131
132
132
132
49
E2u
132
132
132
132
50
E2u
132
142
142
142
51
E2g
142
142
142
142
5.814e+39
0.7
4.891e+39
0.6
1.070e+40
1.2
52
E2g
142
142
142
142
5.814e+39
0.7
7.465e+39
0.9
1.328e+40
1.5
53
Bg
142
142
142
143
54
Ag
143
143
143
146
7.968e+39
0.9
3.557e+39
0.4
1.152e+40
1.3
55
Bu
146
146
146
149
56
E1u
149
149
149
149
57
E1u
149
161
161
161
58
E2u
161
161
161
161
59
E2u
161
169
169
169
60
Bu
169
176
176
174
61
Ag
176
176
176
176
1.947e+40
2.2
1.410e+40
1.6
3.357e+40
3.8
62
Bu
176
182
182
176
1.073e+40
1.2
7.775e+39
0.9
1.851e+40
2.1
63
E2g
182
182
182
182
1.396e+40
1.6
1.918e+40
2.2
3.314e+40
3.8
64
E2g
182
183
183
182
1.396e+40
1.6
1.050e+40
1.2
2.446e+40
2.8
65
E1g
183
183
183
183
2.572e+40
2.9
3.047e+40
3.5
5.619e+40
6.4
66
E1g
183
183
183
183
2.572e+40
2.9
4.340e+40
4.9
6.912e+40
7.9
67
Au
183
187
187
185
68
E2u
200
200
200
200
69
E2u
200
200
200
200
70
E1u
207
207
207
207
71
E1u
207
213
213
207
72
Bg
215
215
215
215
73
E2u
276
276
276
276
74
E2u
276
276
276
276
75
Bg
281
281
281
281
76
E1g
298
298
298
298
5.080e+40
5.8
7.960e+40
9.1
1.304e+41
14.9
77
E1g
298
298
298
298
5.080e+40
5.8
6.010e+40
6.8
1.109e+41
12.6
78
Ag
302
302
302
302
5.104e+40
5.8
2.295e+40
2.6
7.399e+40
8.4
79
E2g
325
325
325
325
5.798e+39
0.7
7.588e+39
0.9
1.339e+40
1.5
80
E2g
325
325
325
325
5.798e+39
0.7
4.733e+39
0.5
1.053e+40
1.2
81
Bu
329
329
329
329
82
E1u
330
330
330
330
83
E1u
330
331
331
330
84
Au
331
335
335
344
85
E1g
347
347
347
347
2.285e+40
2.6
2.385e+40
2.7
4.669e+40
5.3
86
E2g
347
347
347
347
2.287e+40
2.6
2.387e+40
2.7
4.673e+40
5.3
87
E1u
347
347
347
347
2.290e+40
2.6
2.390e+40
2.7
4.680e+40
5.3
88
E1u
347
355
355
347
2.290e+40
2.6
2.476e+40
2.8
4.766e+40
5.4
89
E2u
355
355
355
355
90
E2u
355
356
356
355
91
Au
356
361
361
361
92
Bu
361
361
361
373
93
Ag
373
373
373
373
8.971e+39
1.0
1.474e+40
1.7
2.371e+40
2.7
94
E1g
373
373
373
373
8.971e+39
1.0
9.928e+39
1.1
1.890e+40
2.2
95
E1g
373
373
373
391
3.093e+40
3.5
1.498e+40
1.7
4.591e+40
5.2
96
E1u
391
391
391
391
97
E1u
391
403
403
398
98
Ag
403
408
408
403
1.364e+40
1.6
1.704e+39
0.2
1.534e+40
1.7
99
Bg
408
410
410
408
100
E2g
410
410
410
410
3.887e+39
0.4
4.863e+39
0.6
8.749e+39
1.0
101
E2g
410
416
416
410
3.887e+39
0.4
3.396e+39
0.4
7.283e+39
0.8
102
Bu
416
424
424
416
103
Ag
755
755
755
755
4.142e+40
4.7
2.312e+40
2.6
6.453e+40
7.4
104
Bu
758
758
758
758
105
E2g
761
761
761
761
4.273e+39
0.5
3.731e+39
0.4
8.004e+39
0.9
106
E2g
761
761
761
761
4.273e+39
0.5
5.349e+39
0.6
9.622e+39
1.1
107
E1u
765
765
765
765
108
E1u
765
771
771
765
109
E2u
771
771
771
771
110
E2u
771
773
773
771
111
Bg
773
777
777
773
112
E1g
777
777
777
777
1.194e+40
1.4
1.306e+40
1.5
2.500e+40
2.8
113
E1g
777
779
779
777
1.194e+40
1.4
1.977e+40
2.3
3.170e+40
3.6
114
Au
779
781
781
786
115
E1g
786
786
786
786
1.490e+40
1.7
1.309e+40
1.5
2.799e+40
3.2
116
E1g
786
786
786
786
1.490e+40
1.7
1.911e+40
2.2
3.401e+40
3.9
117
E2u
786
786
786
786
118
E2u
786
788
788
788
119
Ag
788
793
793
793
8.769e+41
99.9
7.156e+38
0.1
8.776e+41
100.0
120
Bu
793
793
793
799
121
E2g
799
799
799
799
4.699e+39
0.5
6.147e+39
0.7
1.085e+40
1.2
122
E2g
799
799
799
802
4.699e+39
0.5
3.838e+39
0.4
8.537e+39
1.0
123
E1u
802
802
802
802
124
E1u
802
808
808
808
125
Ag
808
837
837
825
3.233e+41
36.8
3.233e+40
3.7
3.556e+41
40.5
126
Bu
837
840
840
837
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: