-    APATITE-OH (ferroelectric)     -    Ca5(PO4)3OH

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:  Exp 176, Theo 173  Exp P6_3/m, Theo P6_3 
Lattice parameters (Å):  9.3940  9.3940  6.8967 
Angles (°):  90  90  120 

Symmetry (theoretical): 

Space group:  Exp 176, Theo 173  Exp P6_3/m, Theo P6_3 
Lattice parameters (Å):  9.3921  9.3921  6.8995 
Angles (°):  90  90  120 

Cell contents: 

Number of atoms:  44 
Number of atom types:  4 
Chemical composition:  0 

Atomic positions (theoretical):

Ca:  0.6667  0.3333  0.9957 
Ca:  0.9927  0.2474  0.2461 
P:  0.3659  0.3982  0.2472 
O:  0.4807  0.3258  0.2487 
O:  0.4642  0.5874  0.2417 
O:  0.2527  0.3387  0.0695 
O:  0.0000  0.0000  0.2841 
Ca:  0.3333  0.6667  0.4957 
Ca:  0.7453  0.9927  0.7461 
P:  0.9677  0.3659  0.7472 
O:  0.1549  0.4807  0.7487 
O:  0.8768  0.4642  0.7417 
O:  0.9140  0.2527  0.5695 
O:  0.0000  0.0000  0.7841 
Ca:  0.7526  0.7453  0.2461 
P:  0.6018  0.9677  0.2472 
O:  0.6742  0.1549  0.2487 
O:  0.4126  0.8768  0.2417 
O:  0.6613  0.9140  0.0695 
Ca:  0.0073  0.7526  0.7461 
P:  0.6341  0.6018  0.7472 
O:  0.5193  0.6742  0.7487 
O:  0.5358  0.4126  0.7417 
O:  0.7473  0.6613  0.5695 
Ca:  0.2547  0.0073  0.2461 
P:  0.0323  0.6341  0.2472 
O:  0.8451  0.5193  0.2487 
O:  0.1232  0.5358  0.2417 
O:  0.0860  0.7473  0.0695 
Ca:  0.2474  0.2547  0.7461 
P:  0.3982  0.0323  0.7472 
O:  0.3258  0.8451  0.7487 
O:  0.5874  0.1232  0.7417 
O:  0.3387  0.0860  0.5695 
Ca:  0.3333  0.6667  0.9950 
O:  0.7427  0.6506  0.9284 
Ca:  0.6667  0.3333  0.4950 
O:  0.0921  0.7427  0.4284 
O:  0.3494  0.0921  0.9284 
O:  0.2573  0.3494  0.4284 
O:  0.9079  0.2573  0.9284 
O:  0.6506  0.9079  0.4284 
H:  0.0000  0.0000  0.4254 
H:  0.0000  0.0000  0.9254 
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: 2 2 4 
   number of shifts: 1 
   shifts: 0 0 0.5 
Kinetic energy cut-off: 40 Ha  [=1088.464 eV ]
eXchange-Correlation functional: LDA pw90 

Pseudopotentials: 
Ca:  calcium, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 0 local 
P:  phosphorus, 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 
H:  hydrogen, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 2 local 
   

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 mode number 1 with char 106498.0
0
0
0
0
2
Ac mode number 2 with char 106498.0
0
0
0
0
3
Ac mode number 3 with char 106498.0
0
0
0
0
4
B
38
38
38
38
5
E2
38
38
38
38
1.508e+39
1.5
2.545e+39
2.5
4.053e+39
4.0
6
E2
38
41
41
38
1.508e+39
1.5
1.603e+39
1.6
3.111e+39
3.0
7
E1
92
92
92
92
1.018e+38
0.1
9.677e+37
0.1
1.986e+38
0.2
8
E1
92
92
92
92
1.018e+38
0.1
1.196e+38
0.1
2.214e+38
0.2
9
E2
95
95
95
95
5.753e+36
0.0
7.910e+36
0.0
1.366e+37
0.0
10
E2
95
105
105
95
5.753e+36
0.0
7.910e+36
0.0
1.366e+37
0.0
11
A
105
105
105
110
3.842e+38
0.4
3.505e+37
0.0
4.193e+38
0.4
12
E1
115
115
115
115
3.850e+37
0.0
3.401e+37
0.0
7.251e+37
0.1
13
E1
115
115
115
115
3.850e+37
0.0
4.781e+37
0.0
8.631e+37
0.1
14
E1
134
134
134
134
4.381e+38
0.4
5.008e+38
0.5
9.389e+38
0.9
15
E1
134
134
134
134
4.381e+38
0.4
4.302e+38
0.4
8.683e+38
0.8
16
E2
136
136
136
136
9.099e+37
0.1
1.503e+38
0.1
2.413e+38
0.2
17
E2
136
136
136
136
9.099e+37
0.1
9.989e+37
0.1
1.909e+38
0.2
18
B
136
136
136
136
19
E1
144
144
144
144
2.370e+37
0.0
2.552e+37
0.0
4.922e+37
0.0
20
E1
144
144
144
144
2.370e+37
0.0
2.485e+37
0.0
4.855e+37
0.0
21
A
153
153
153
153
1.385e+39
1.4
7.163e+37
0.1
1.456e+39
1.4
22
B
160
160
160
160
23
A
169
169
169
169
3.207e+38
0.3
1.879e+38
0.2
5.086e+38
0.5
24
E1
171
171
171
171
1.076e+38
0.1
1.334e+38
0.1
2.409e+38
0.2
25
E1
171
171
171
171
1.076e+38
0.1
9.524e+37
0.1
2.028e+38
0.2
26
B
172
172
172
172
27
A
181
181
181
183
7.254e+37
0.1
1.667e+34
0.0
7.256e+37
0.1
28
E2
183
183
183
183
3.529e+37
0.0
3.774e+37
0.0
7.303e+37
0.1
29
E2
183
191
191
183
3.529e+37
0.0
5.930e+37
0.1
9.459e+37
0.1
30
E2
191
191
191
191
2.895e+38
0.3
3.981e+38
0.4
6.876e+38
0.7
31
E2
191
196
196
191
2.895e+38
0.3
3.981e+38
0.4
6.876e+38
0.7
32
B
200
200
200
200
33
A
208
208
208
208
1.868e+39
1.8
2.547e+37
0.0
1.893e+39
1.8
34
B
208
208
208
208
35
E1
208
208
208
208
2.067e+37
0.0
2.685e+37
0.0
4.752e+37
0.0
36
E1
208
208
208
209
2.067e+37
0.0
1.708e+37
0.0
3.776e+37
0.0
37
E1
215
215
215
215
8.056e+37
0.1
1.033e+38
0.1
1.838e+38
0.2
38
E1
215
215
215
215
8.056e+37
0.1
6.794e+37
0.1
1.485e+38
0.1
39
A
216
216
216
216
2.504e+38
0.2
1.353e+38
0.1
3.858e+38
0.4
40
E2
217
217
217
217
6.205e+37
0.1
6.597e+37
0.1
1.280e+38
0.1
41
E2
217
228
228
217
6.205e+37
0.1
1.047e+38
0.1
1.667e+38
0.2
42
B
228
232
232
228
43
E2
234
234
234
234
2.647e+37
0.0
4.434e+37
0.0
7.081e+37
0.1
44
E2
234
236
236
234
2.647e+37
0.0
2.846e+37
0.0
5.494e+37
0.1
45
B
236
236
236
236
46
E1
236
236
236
236
2.226e+36
0.0
3.061e+36
0.0
5.286e+36
0.0
47
E1
236
238
238
236
2.226e+36
0.0
1.670e+36
0.0
3.896e+36
0.0
48
E2
239
239
239
239
1.925e+38
0.2
2.365e+38
0.2
4.290e+38
0.4
49
E2
239
245
245
239
1.925e+38
0.2
2.930e+38
0.3
4.855e+38
0.5
50
A
245
254
254
245
2.280e+38
0.2
1.252e+38
0.1
3.532e+38
0.3
51
E1
254
254
254
254
7.822e+37
0.1
9.535e+37
0.1
1.736e+38
0.2
52
E1
254
256
256
254
7.822e+37
0.1
7.086e+37
0.1
1.491e+38
0.1
53
B
271
271
271
271
54
A
275
275
275
276
5.592e+38
0.5
1.345e+37
0.0
5.726e+38
0.6
55
A
278
278
278
282
1.853e+38
0.2
1.621e+37
0.0
2.016e+38
0.2
56
B
282
282
282
284
57
E1
284
284
284
284
2.212e+38
0.2
2.875e+38
0.3
5.087e+38
0.5
58
E1
284
284
284
287
2.212e+38
0.2
1.825e+38
0.2
4.037e+38
0.4
59
E2
287
287
287
287
1.684e+37
0.0
2.809e+37
0.0
4.494e+37
0.0
60
E2
287
307
307
295
1.684e+37
0.0
1.822e+37
0.0
3.506e+37
0.0
61
E1
307
307
307
307
1.034e+36
0.0
7.754e+35
0.0
1.809e+36
0.0
62
E1
307
311
311
307
1.034e+36
0.0
1.422e+36
0.0
2.455e+36
0.0
63
A
311
313
313
313
7.214e+38
0.7
2.840e+38
0.3
1.005e+39
1.0
64
B
313
315
315
313
65
A
319
319
319
319
5.676e+38
0.6
9.339e+38
0.9
1.501e+39
1.5
66
E1
319
319
319
319
5.676e+38
0.6
6.270e+38
0.6
1.195e+39
1.2
67
E1
319
320
320
324
3.913e+37
0.0
3.950e+36
0.0
4.308e+37
0.0
68
B
324
324
324
367
69
E1
367
367
367
367
2.910e+38
0.3
3.040e+38
0.3
5.950e+38
0.6
70
E1
367
367
367
367
2.910e+38
0.3
3.144e+38
0.3
6.054e+38
0.6
71
E2
368
368
368
368
6.136e+36
0.0
8.436e+36
0.0
1.457e+37
0.0
72
E2
368
400
400
368
6.136e+36
0.0
8.436e+36
0.0
1.457e+37
0.0
73
B
420
420
420
420
74
E2
422
422
422
422
3.486e+39
3.4
3.958e+39
3.9
7.443e+39
7.3
75
E2
422
422
422
422
3.486e+39
3.4
5.628e+39
5.5
9.114e+39
8.9
76
E1
427
427
427
427
1.999e+37
0.0
2.010e+37
0.0
4.010e+37
0.0
77
E1
427
427
427
427
1.999e+37
0.0
2.238e+37
0.0
4.237e+37
0.0
78
E1
445
445
445
445
2.063e+39
2.0
2.259e+39
2.2
4.322e+39
4.2
79
E1
445
445
445
445
2.063e+39
2.0
2.124e+39
2.1
4.187e+39
4.1
80
A
453
453
453
453
1.043e+39
1.0
7.819e+38
0.8
1.825e+39
1.8
81
E2
458
458
458
458
1.262e+37
0.0
1.574e+37
0.0
2.836e+37
0.0
82
E2
458
459
459
458
1.262e+37
0.0
1.898e+37
0.0
3.160e+37
0.0
83
A
460
460
460
463
4.699e+37
0.0
5.874e+36
0.0
5.287e+37
0.1
84
B
474
474
474
474
85
A
546
546
546
546
7.570e+37
0.1
8.958e+37
0.1
1.653e+38
0.2
86
B2
546
546
546
546
7.570e+37
0.1
9.944e+37
0.1
1.751e+38
0.2
87
B2
546
546
546
550
8.892e+37
0.1
2.964e+37
0.0
1.186e+38
0.1
88
E2
550
550
550
550
5.733e+36
0.0
9.367e+36
0.0
1.510e+37
0.0
89
E2
550
556
556
560
5.733e+36
0.0
6.399e+36
0.0
1.213e+37
0.0
90
E1
560
560
560
560
1.095e+39
1.1
1.485e+39
1.4
2.580e+39
2.5
91
E1
560
560
560
562
1.095e+39
1.1
8.412e+38
0.8
1.936e+39
1.9
92
B
562
562
562
571
93
A
571
571
571
572
2.751e+39
2.7
1.578e+39
1.5
4.329e+39
4.2
94
E2
572
572
572
572
8.365e+38
0.8
1.150e+39
1.1
1.987e+39
1.9
95
E2
572
573
573
578
8.365e+38
0.8
1.150e+39
1.1
1.987e+39
1.9
96
E2
584
584
584
584
2.736e+37
0.0
3.069e+37
0.0
5.806e+37
0.1
97
E2
584
585
585
584
2.736e+37
0.0
4.455e+37
0.0
7.191e+37
0.1
98
B
585
592
592
585
99
A
594
594
594
594
2.583e+39
2.5
7.590e+38
0.7
3.342e+39
3.3
100
E1
601
601
601
601
2.476e+38
0.2
2.040e+38
0.2
4.516e+38
0.4
101
E1
601
601
601
601
2.476e+38
0.2
3.222e+38
0.3
5.699e+38
0.6
102
B
602
602
602
602
103
E2
608
608
608
608
1.857e+37
0.0
2.266e+37
0.0
4.123e+37
0.0
104
E2
608
628
628
608
1.857e+37
0.0
2.842e+37
0.0
4.699e+37
0.0
105
E1
675
675
675
675
5.113e+36
0.0
3.835e+36
0.0
8.948e+36
0.0
106
E1
675
675
675
675
5.113e+36
0.0
7.031e+36
0.0
1.214e+37
0.0
107
B
937
937
937
937
4.589e+35
0.0
6.310e+35
0.0
1.090e+36
0.0
108
E1
937
937
937
937
109
E1
937
938
938
937
110
A
938
939
939
938
1.025e+41
100.0
1.358e+37
0.0
1.025e+41
100.0
111
E1
939
939
939
939
2.064e+38
0.2
1.558e+38
0.2
3.622e+38
0.4
112
E1
939
939
939
939
2.064e+38
0.2
2.828e+38
0.3
4.892e+38
0.5
113
E1
1011
1011
1011
1011
1.410e+39
1.4
1.497e+39
1.5
2.907e+39
2.8
114
E1
1011
1011
1011
1011
1.410e+39
1.4
1.500e+39
1.5
2.910e+39
2.8
115
E2
1013
1013
1013
1013
4.854e+37
0.0
5.783e+37
0.1
1.064e+38
0.1
116
E2
1013
1016
1016
1013
4.854e+37
0.0
7.567e+37
0.1
1.242e+38
0.1
117
A
1016
1028
1028
1029
3.235e+37
0.0
5.693e+36
0.0
3.805e+37
0.0
118
E2
1029
1029
1029
1029
1.814e+39
1.8
2.411e+39
2.4
4.225e+39
4.1
119
E2
1029
1031
1031
1031
1.814e+39
1.8
2.579e+39
2.5
4.393e+39
4.3
120
B
1031
1034
1034
1034
121
A
1034
1038
1038
1038
6.068e+39
5.9
1.616e+39
1.6
7.685e+39
7.5
122
E1
1038
1038
1038
1038
1.023e+39
1.0
1.405e+39
1.4
2.428e+39
2.4
123
E1
1038
1047
1047
1047
1.023e+39
1.0
7.681e+38
0.7
1.791e+39
1.7
124
E1
1047
1047
1047
1047
9.489e+37
0.1
1.122e+38
0.1
2.071e+38
0.2
125
E1
1047
1055
1055
1055
9.489e+37
0.1
8.946e+37
0.1
1.843e+38
0.2
126
A
1055
1062
1062
1062
3.089e+39
3.0
1.578e+39
1.5
4.668e+39
4.6
127
B
1062
1062
1062
1069
128
E2
1069
1069
1069
1069
2.997e+37
0.0
3.945e+37
0.0
6.942e+37
0.1
129
E2
1069
1105
1105
1104
2.997e+37
0.0
4.297e+37
0.0
7.294e+37
0.1
130
B
1107
1107
1107
1107
131
A
3557
3557
3557
3558
2.716e+40
26.5
2.605e+39
2.5
2.977e+40
29.0
132
B
3564
3564
3564
3564
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.