-    FARRINGTONITE     -    Mg3PO4

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:  14  P2_1/n 
Lattice parameters (Å):  5.0800  5.0800  11.7000 
Angles (°):  90  86.48  90 

Symmetry (theoretical): 

Space group:  14  P2_1/n 
Lattice parameters (Å):  8.2073  7.6488  5.0534 
Angles (°):  136.35  136.35  63.43 

Cell contents: 

Number of atoms:  26 
Number of atom types:  3 
Chemical composition:  0 

Atomic positions (theoretical):

Mg:  0.6422  0.0998  0.1082 
Mg:  0.0000  0.0000  0.0000 
P:  0.3031  0.3009  0.0257 
O:  0.1311  0.2438  0.9571 
O:  0.3079  0.3750  0.3063 
O:  0.3487  0.4404  0.8162 
O:  0.4213  0.1448  0.9952 
Mg:  0.8578  0.5998  0.3918 
Mg:  0.5000  0.5000  0.5000 
P:  0.1969  0.8009  0.4743 
O:  0.3689  0.7438  0.5429 
O:  0.1921  0.8750  0.1937 
O:  0.1513  0.9404  0.6838 
O:  0.0787  0.6448  0.5048 
Mg:  0.3578  0.9002  0.8918 
P:  0.6969  0.6991  0.9743 
O:  0.8689  0.7562  0.0429 
O:  0.6921  0.6250  0.6937 
O:  0.6513  0.5596  0.1838 
O:  0.5787  0.8552  0.0048 
Mg:  0.1422  0.4002  0.6082 
P:  0.8031  0.1991  0.5257 
O:  0.6311  0.2562  0.4571 
O:  0.8079  0.1250  0.8063 
O:  0.8487  0.0596  0.3162 
O:  0.9213  0.3552  0.4952 
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.
     

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
Au
110
110
110
110
5
Ag
118
118
118
118
6.653e+39
7.7
1.781e+38
0.2
6.831e+39
7.9
6
Bg
120
120
120
120
5.446e+37
0.1
5.877e+37
0.1
1.132e+38
0.1
7
Bu
146
147
146
147
8
Ag
150
150
150
150
8.516e+38
1.0
1.628e+38
0.2
1.014e+39
1.2
9
Bg
154
154
154
154
1.020e+37
0.0
1.402e+37
0.0
2.421e+37
0.0
10
Au
164
164
165
164
11
Bu
167
168
167
167
12
Ag
171
171
171
171
2.209e+39
2.5
1.933e+38
0.2
2.402e+39
2.8
13
Bg
197
197
197
197
1.247e+38
0.1
2.033e+38
0.2
3.280e+38
0.4
14
Ag
203
203
203
203
7.591e+39
8.8
8.801e+37
0.1
7.679e+39
8.9
15
Bu
209
210
209
209
16
Bg
211
211
211
211
2.105e+37
0.0
2.604e+37
0.0
4.709e+37
0.1
17
Au
216
216
218
216
18
Au
219
219
221
219
19
Bu
221
224
221
221
20
Ag
230
230
230
230
6.544e+38
0.8
1.159e+38
0.1
7.703e+38
0.9
21
Au
238
238
238
238
22
Ag
242
242
242
242
1.583e+39
1.8
3.742e+37
0.0
1.620e+39
1.9
23
Au
244
244
244
244
24
Bg
244
244
248
244
6.813e+37
0.1
8.741e+37
0.1
1.555e+38
0.2
25
Bg
256
256
256
256
3.060e+38
0.4
5.130e+38
0.6
8.190e+38
0.9
26
Bu
269
270
269
270
27
Au
279
279
279
279
28
Bu
282
292
282
289
29
Bu
294
295
294
295
30
Au
295
295
302
296
31
Bg
302
302
307
302
4.892e+38
0.6
8.061e+38
0.9
1.295e+39
1.5
32
Ag
307
307
314
307
1.610e+39
1.9
9.516e+38
1.1
2.562e+39
3.0
33
Ag
317
317
317
317
1.103e+39
1.3
1.276e+39
1.5
2.379e+39
2.7
34
Au
320
320
337
320
35
Bg
337
337
347
337
3.346e+38
0.4
5.495e+38
0.6
8.841e+38
1.0
36
Bu
347
348
355
355
37
Au
355
355
380
365
38
Bu
380
385
386
381
39
Bu
386
397
393
397
40
Au
397
405
397
405
41
Bg
405
420
405
420
9.210e+38
1.1
9.917e+38
1.1
1.913e+39
2.2
42
Ag
420
432
420
436
1.891e+39
2.2
9.664e+38
1.1
2.857e+39
3.3
43
Ag
438
438
438
438
1.712e+39
2.0
1.755e+39
2.0
3.467e+39
4.0
44
Bg
438
438
438
438
1.828e+38
0.2
1.994e+38
0.2
3.822e+38
0.4
45
Au
441
441
442
441
46
Bu
458
459
458
469
47
Ag
469
469
469
476
1.085e+39
1.3
3.898e+38
0.4
1.475e+39
1.7
48
Bg
476
476
476
481
1.922e+38
0.2
3.001e+38
0.3
4.923e+38
0.6
49
Au
494
494
494
494
50
Bu
499
501
499
508
51
Ag
546
546
546
546
1.710e+39
2.0
1.643e+39
1.9
3.353e+39
3.9
52
Bu
550
560
550
559
53
Au
568
568
568
568
54
Bg
570
570
570
570
2.564e+39
3.0
3.558e+39
4.1
6.122e+39
7.1
55
Au
588
588
596
588
56
Ag
596
596
602
596
1.401e+39
1.6
7.251e+38
0.8
2.126e+39
2.5
57
Bg
602
602
611
602
4.521e+37
0.1
7.561e+37
0.1
1.208e+38
0.1
58
Bu
611
624
613
619
59
Ag
624
625
624
624
1.440e+39
1.7
5.590e+38
0.6
1.998e+39
2.3
60
Bu
625
631
625
625
61
Bg
631
640
631
631
1.083e+39
1.2
1.515e+39
1.7
2.597e+39
3.0
62
Au
640
642
643
640
63
Bu
951
952
951
951
64
Au
961
961
962
961
65
Ag
962
962
964
962
8.583e+40
99.0
8.260e+38
1.0
8.665e+40
100.0
66
Bg
964
964
964
964
2.311e+36
0.0
3.868e+36
0.0
6.179e+36
0.0
67
Bu
1002
1004
1002
1002
68
Ag
1004
1018
1004
1004
1.168e+40
13.5
2.123e+39
2.4
1.380e+40
15.9
69
Au
1018
1024
1020
1018
70
Au
1024
1034
1034
1024
71
Bg
1034
1038
1038
1034
2.677e+39
3.1
4.045e+39
4.7
6.721e+39
7.8
72
Ag
1038
1043
1043
1038
3.447e+39
4.0
2.455e+39
2.8
5.902e+39
6.8
73
Bu
1043
1048
1059
1058
74
Bu
1059
1064
1064
1064
75
Au
1064
1064
1064
1064
1.878e+38
0.2
3.234e+37
0.0
2.201e+38
0.3
76
Ag
1064
1100
1100
1100
1.036e+39
1.2
1.785e+38
0.2
1.215e+39
1.4
77
Bg
1100
1113
1114
1114
1.949e+39
2.2
2.268e+39
2.6
4.218e+39
4.9
78
Bg
1114
1114
1122
1154
2.105e+39
2.4
3.261e+39
3.8
5.366e+39
6.2
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.