-    APATITE-F     -    Ca5F(PO4)3

Theoretical atomic positions and lattice parameters at experimental volum from 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):  4.9711  4.9711  3.6496 
Angles (°):  90.0  90.0  120.0 

Symmetry (theoretical): 

Space group:  176  P6_3/m 
Lattice parameters (Å):  9.3755  9.3755  6.9240 
Angles (°):  90.0  90.0  120.0 

Cell contents: 

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

Atomic positions (theoretical):

Ca:  0.6667  0.3333  0.0000 
Ca:  0.9929  0.2427  0.2500 
P:  0.3667  0.3977  0.2500 
O:  0.4807  0.3240  0.2500 
O:  0.4657  0.5874  0.2500 
O:  0.2551  0.3425  0.0714 
F:  0.0000  0.0000  0.2500 
Ca:  0.3333  0.6667  0.5000 
Ca:  0.7503  0.9929  0.7500 
P:  0.9690  0.3667  0.7500 
O:  0.1566  0.4807  0.7500 
O:  0.8784  0.4657  0.7500 
O:  0.9126  0.2551  0.5714 
F:  0.0000  0.0000  0.7500 
Ca:  0.7573  0.7503  0.2500 
P:  0.6023  0.9690  0.2500 
O:  0.6760  0.1566  0.2500 
O:  0.4126  0.8784  0.2500 
O:  0.6575  0.9126  0.0714 
Ca:  0.0071  0.7573  0.7500 
P:  0.6333  0.6023  0.7500 
O:  0.5193  0.6760  0.7500 
O:  0.5343  0.4126  0.7500 
O:  0.7449  0.6575  0.5714 
Ca:  0.2497  0.0071  0.2500 
P:  0.0310  0.6333  0.2500 
O:  0.8434  0.5193  0.2500 
O:  0.1216  0.5343  0.2500 
O:  0.0874  0.7449  0.0714 
Ca:  0.2427  0.2497  0.7500 
P:  0.3977  0.0310  0.7500 
O:  0.3240  0.8434  0.7500 
O:  0.5874  0.1216  0.7500 
O:  0.3425  0.0874  0.5714 
Ca:  0.3333  0.6667  1.0000 
O:  0.7449  0.6575  0.9286 
Ca:  0.6667  0.3333  0.5000 
O:  0.0874  0.7449  0.4286 
O:  0.3425  0.0874  0.9286 
O:  0.2551  0.3425  0.4286 
O:  0.9126  0.2551  0.9286 
O:  0.6575  0.9126  0.4286 
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.
     

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.

Horizontal:
Xmin:
Xmax:
Vertical:
Ymin:
Ymax:
 
Choose the polarization of the lasers.
I ∥ 
I ⊥ 
I Total 

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
19
19
19
19
5
E1g
19
19
19
19
6
Bg
72
72
72
72
7
Au
90
90
90
92
8
E1u
92
92
92
92
9
E1u
92
94
94
94
10
E2g
94
94
94
94
1.416e+38
0.1
1.935e+38
0.2
3.350e+38
0.3
11
E2g
94
105
105
98
1.416e+38
0.1
1.073e+38
0.1
2.489e+38
0.2
12
E2u
106
106
106
106
13
E2u
106
106
106
106
14
E1g
135
135
135
135
1.411e+38
0.1
1.717e+38
0.2
3.128e+38
0.3
15
E1g
135
135
135
135
1.411e+38
0.1
2.163e+38
0.2
3.574e+38
0.4
16
E2g
135
135
135
135
3.360e+38
0.3
2.894e+38
0.3
6.254e+38
0.6
17
E2g
135
135
135
135
3.360e+38
0.3
4.247e+38
0.4
7.607e+38
0.8
18
Au
142
142
142
142
19
Bu
142
142
142
142
20
E2u
149
149
149
149
21
E2u
149
149
149
149
22
Ag
155
155
155
155
1.061e+39
1.0
3.190e+37
0.0
1.093e+39
1.1
23
Bg
158
158
158
158
24
E2g
167
167
167
167
1.924e+38
0.2
1.474e+38
0.1
3.399e+38
0.3
25
E2g
167
167
167
167
1.924e+38
0.2
2.614e+38
0.3
4.538e+38
0.4
26
Ag
169
169
169
169
4.756e+38
0.5
1.633e+38
0.2
6.389e+38
0.6
27
Bg
175
175
175
175
28
Au
183
183
183
186
29
E1g
186
186
186
186
2.916e+38
0.3
3.368e+38
0.3
6.284e+38
0.6
30
E1g
186
186
186
186
2.916e+38
0.3
4.650e+38
0.5
7.566e+38
0.7
31
E1u
191
191
191
191
32
E1u
191
198
198
191
33
Bu
198
200
200
198
34
Bu
207
207
207
207
35
E2u
210
210
210
210
36
E2u
210
210
210
210
37
E2g
215
215
215
215
1.133e+38
0.1
1.211e+38
0.1
2.344e+38
0.2
38
E2g
215
215
215
215
1.133e+38
0.1
1.197e+38
0.1
2.331e+38
0.2
39
Ag
216
216
216
216
1.375e+39
1.4
1.852e+38
0.2
1.560e+39
1.5
40
E1u
217
217
217
217
41
E1u
217
226
226
217
42
Bg
226
229
229
226
43
Bu
229
234
234
229
44
E1g
234
234
234
234
2.410e+38
0.2
2.921e+38
0.3
5.331e+38
0.5
45
E1g
234
238
238
234
2.410e+38
0.2
3.706e+38
0.4
6.116e+38
0.6
46
E2u
238
238
238
238
47
E2u
238
239
239
238
48
Ag
239
239
239
239
5.962e+38
0.6
1.605e+38
0.2
7.567e+38
0.7
49
E1u
242
242
242
242
50
E1u
242
242
242
242
51
E2g
242
242
242
242
1.738e+38
0.2
2.012e+38
0.2
3.750e+38
0.4
52
E2g
242
256
256
242
1.738e+38
0.2
1.680e+38
0.2
3.418e+38
0.3
53
Bg
268
268
268
268
54
Ag
272
272
272
272
2.929e+39
2.9
3.624e+37
0.0
2.965e+39
2.9
55
Bu
273
273
273
273
56
Au
276
276
276
281
57
E2g
281
281
281
281
2.790e+38
0.3
3.153e+38
0.3
5.943e+38
0.6
58
E2g
281
281
281
281
2.790e+38
0.3
2.776e+38
0.3
5.565e+38
0.5
59
E1u
281
281
281
281
60
E1u
281
298
298
298
61
E2u
298
298
298
298
62
E2u
298
298
298
298
63
Bg
298
304
304
298
64
Ag
304
307
307
304
6.203e+38
0.6
4.117e+38
0.4
1.032e+39
1.0
65
E1g
308
308
308
308
7.356e+38
0.7
9.045e+38
0.9
1.640e+39
1.6
66
E1g
308
308
308
308
7.356e+38
0.7
1.203e+39
1.2
1.939e+39
1.9
67
Au
308
308
308
315
68
Bu
315
315
315
343
69
E2g
343
343
343
343
4.127e+38
0.4
5.654e+38
0.6
9.781e+38
1.0
70
E2g
343
343
343
347
4.127e+38
0.4
3.116e+38
0.3
7.243e+38
0.7
71
E1u
347
347
347
347
72
E1u
347
393
393
358
73
Bg
418
418
418
418
74
E1g
419
419
419
419
3.530e+39
3.5
5.639e+39
5.6
9.169e+39
9.1
75
E1g
419
419
419
419
3.530e+39
3.5
4.068e+39
4.0
7.598e+39
7.5
76
E2u
424
424
424
424
77
E2u
424
424
424
424
78
E2g
439
439
439
439
2.004e+39
2.0
1.926e+39
1.9
3.930e+39
3.9
79
E2g
439
439
439
439
2.004e+39
2.0
2.332e+39
2.3
4.335e+39
4.3
80
Ag
447
447
447
447
1.103e+39
1.1
8.179e+38
0.8
1.921e+39
1.9
81
E1u
454
454
454
454
82
E1u
454
455
455
454
83
Au
457
457
457
459
84
Bu
470
470
470
470
85
Au
546
546
546
547
86
E2u
547
547
547
547
87
E2u
547
547
547
555
88
E1u
555
555
555
555
89
E1u
555
558
558
559
90
E2g
559
559
559
559
1.269e+39
1.3
9.731e+38
1.0
2.242e+39
2.2
91
E2g
559
559
559
562
1.269e+39
1.3
1.724e+39
1.7
2.993e+39
3.0
92
Bu
562
562
562
570
93
Ag
570
570
570
571
2.429e+39
2.4
1.411e+39
1.4
3.839e+39
3.8
94
E1g
571
571
571
571
9.696e+38
1.0
1.092e+39
1.1
2.062e+39
2.0
95
E1g
571
571
571
578
9.696e+38
1.0
1.575e+39
1.6
2.544e+39
2.5
96
E1u
582
582
582
582
97
E1u
582
584
584
582
98
Bg
584
590
590
584
99
Ag
590
597
597
590
2.214e+39
2.2
8.994e+38
0.9
3.114e+39
3.1
100
Bu
597
598
598
597
101
E2g
598
598
598
598
2.427e+38
0.2
2.623e+38
0.3
5.050e+38
0.5
102
E2g
598
600
600
598
2.427e+38
0.2
2.534e+38
0.3
4.961e+38
0.5
103
Bu
934
934
934
934
104
E1u
935
935
935
935
105
E1u
935
935
935
935
106
Ag
935
936
936
935
1.013e+41
100.0
1.341e+36
0.0
1.013e+41
100.0
107
E2g
937
937
937
937
3.180e+38
0.3
4.025e+38
0.4
7.206e+38
0.7
108
E2g
937
937
937
937
3.180e+38
0.3
2.733e+38
0.3
5.914e+38
0.6
109
E2g
1011
1011
1011
1011
1.531e+39
1.5
1.264e+39
1.2
2.795e+39
2.8
110
E2g
1011
1011
1011
1011
1.531e+39
1.5
1.990e+39
2.0
3.521e+39
3.5
111
Au
1012
1012
1012
1012
112
E1u
1012
1012
1012
1012
113
E1u
1012
1025
1025
1025
114
E1g
1025
1025
1025
1025
1.482e+39
1.5
1.628e+39
1.6
3.110e+39
3.1
115
E1g
1025
1030
1030
1030
1.482e+39
1.5
2.448e+39
2.4
3.930e+39
3.9
116
Bu
1030
1033
1033
1033
117
Ag
1033
1038
1038
1038
6.851e+39
6.8
1.938e+39
1.9
8.789e+39
8.7
118
E2g
1038
1038
1038
1038
9.697e+38
1.0
1.085e+39
1.1
2.055e+39
2.0
119
E2g
1038
1039
1039
1039
9.697e+38
1.0
9.754e+38
1.0
1.945e+39
1.9
120
E2u
1039
1039
1039
1039
121
E2u
1039
1056
1056
1056
122
Ag
1056
1060
1060
1060
2.727e+39
2.7
1.820e+39
1.8
4.547e+39
4.5
123
Bg
1060
1062
1062
1069
124
E1u
1069
1069
1069
1069
125
E1u
1069
1104
1104
1100
126
Bu
1106
1106
1106
1106
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.