-    LAZULITE     -    MgAl2(PO4)2(OH)2

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/c 
Lattice parameters (Å):  7.1440  7.2780  7.2280 
Angles (°):  90  120.51  90 

Symmetry (theoretical): 

Space group:  14  P2_1/c 
Lattice parameters (Å):  7.7518  7.7518  4.3895 
Angles (°):  90  120.26  90 

Cell contents: 

Number of atoms:  34 
Number of atom types: 
Chemical composition: 

Atomic positions (theoretical):

Mg:  0.0000  0.0000  0.0000 
Al:  0.7335  0.2668  0.0099 
P:  0.2490  0.3897  0.2425 
O:  0.8001  0.0214  0.1182 
O:  0.6945  0.4975  0.9025 
O:  0.0424  0.2693  0.1129 
O:  0.4394  0.2363  0.8808 
O:  0.7374  0.1443  0.7607 
H:  0.6008  0.4321  0.1957 
Mg:  0.0000  0.5000  0.5000 
Al:  0.2665  0.7668  0.4901 
P:  0.7510  0.8897  0.2575 
O:  0.1999  0.5214  0.3818 
O:  0.3055  0.9975  0.5975 
O:  0.9576  0.7693  0.3871 
O:  0.5606  0.7363  0.6192 
O:  0.2626  0.6443  0.7393 
H:  0.3992  0.9321  0.3043 
Al:  0.2665  0.7332  0.9901 
P:  0.7510  0.6103  0.7575 
O:  0.1999  0.9786  0.8818 
O:  0.3055  0.5025  0.0975 
O:  0.9576  0.7307  0.8871 
O:  0.5606  0.7637  0.1192 
O:  0.2626  0.8557  0.2393 
H:  0.3992  0.5679  0.8043 
Al:  0.7335  0.2332  0.5099 
P:  0.2490  0.1103  0.7425 
O:  0.8001  0.4786  0.6182 
O:  0.6945  0.0025  0.4025 
O:  0.0424  0.2307  0.6129 
O:  0.4394  0.2637  0.3808 
O:  0.7374  0.3557  0.2607 
H:  0.6008  0.0679  0.6957 
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
Bg
72
72
72
72
8.452e+38
0.9
1.422e+39
1.5
2.267e+39
2.3
5
Ag
84
84
84
84
4.081e+39
4.2
2.985e+39
3.1
7.066e+39
7.3
6
Au
128
128
128
128
7
Bu
146
149
146
146
8
Au
158
158
158
158
9
Ag
168
168
168
168
4.461e+39
4.6
4.006e+38
0.4
4.862e+39
5.0
10
Bu
184
186
184
186
11
Ag
186
187
186
187
4.722e+39
4.9
2.737e+37
0.0
4.749e+39
4.9
12
Au
187
189
188
188
13
Bg
198
198
198
198
3.714e+38
0.4
5.570e+38
0.6
9.284e+38
1.0
14
Ag
229
229
229
229
3.145e+39
3.2
4.146e+38
0.4
3.560e+39
3.7
15
Bg
229
229
229
229
1.491e+38
0.2
1.592e+38
0.2
3.084e+38
0.3
16
Au
233
233
236
233
17
Bu
251
251
251
251
18
Bg
258
258
258
258
2.106e+38
0.2
2.323e+38
0.2
4.429e+38
0.5
19
Ag
261
261
261
261
4.849e+39
5.0
2.737e+38
0.3
5.123e+39
5.3
20
Bg
263
263
263
263
3.005e+37
0.0
5.038e+37
0.1
8.043e+37
0.1
21
Au
272
272
273
272
22
Bu
280
281
280
280
23
Au
286
286
287
286
24
Ag
287
287
289
287
4.639e+39
4.8
5.602e+38
0.6
5.200e+39
5.3
25
Bu
289
290
291
293
26
Bu
306
309
306
309
27
Au
309
310
309
315
28
Ag
315
315
315
315
1.809e+37
0.0
2.094e+37
0.0
3.902e+37
0.0
29
Bg
315
315
315
319
3.684e+39
3.8
4.502e+38
0.5
4.135e+39
4.3
30
Bu
322
323
322
333
31
Bg
333
333
333
338
1.940e+38
0.2
3.119e+38
0.3
5.059e+38
0.5
32
Bg
343
343
343
343
3.613e+38
0.4
4.968e+38
0.5
8.582e+38
0.9
33
Ag
347
347
347
347
2.399e+39
2.5
1.148e+39
1.2
3.547e+39
3.6
34
Au
356
356
356
356
35
Bu
364
367
364
369
36
Bg
369
369
369
372
1.097e+38
0.1
1.509e+38
0.2
2.606e+38
0.3
37
Au
378
378
379
378
38
Ag
379
379
383
379
4.217e+39
4.3
7.306e+38
0.8
4.948e+39
5.1
39
Au
383
383
386
383
40
Bu
386
389
387
390
41
Bg
390
390
390
398
3.436e+38
0.4
5.627e+38
0.6
9.063e+38
0.9
42
Ag
403
403
403
403
5.121e+39
5.3
3.714e+39
3.8
8.836e+39
9.1
43
Bu
405
405
405
408
44
Au
410
410
412
410
45
Bu
421
435
421
423
46
Ag
436
436
436
436
1.051e+39
1.1
4.283e+38
0.4
1.479e+39
1.5
47
Bu
441
447
441
449
48
Au
449
449
459
459
49
Ag
459
459
469
460
1.351e+39
1.4
9.574e+38
1.0
2.308e+39
2.4
50
Bg
469
469
477
469
3.908e+38
0.4
6.588e+38
0.7
1.050e+39
1.1
51
Bu
477
480
480
480
52
Ag
480
500
496
497
3.129e+39
3.2
1.299e+39
1.3
4.428e+39
4.6
53
Bg
500
500
500
500
2.484e+38
0.3
2.641e+38
0.3
5.125e+38
0.5
54
Au
500
509
500
500
55
Au
514
514
523
514
56
Au
528
528
528
528
57
Bg
528
528
536
528
1.070e+38
0.1
1.472e+38
0.2
2.542e+38
0.3
58
Ag
536
536
538
536
1.221e+39
1.3
2.786e+37
0.0
1.249e+39
1.3
59
Bu
538
547
538
545
60
Bu
549
568
549
568
61
Au
568
576
576
576
62
Bg
576
580
576
589
2.606e+39
2.7
3.255e+39
3.3
5.861e+39
6.0
63
Au
589
589
595
591
64
Bg
595
595
602
595
1.293e+39
1.3
1.505e+39
1.5
2.799e+39
2.9
65
Bu
602
603
605
605
66
Ag
605
605
612
614
1.343e+39
1.4
5.917e+38
0.6
1.935e+39
2.0
67
Bg
614
614
614
617
2.100e+39
2.2
3.462e+39
3.6
5.563e+39
5.7
68
Au
625
625
625
625
69
Ag
627
627
627
627
5.099e+39
5.2
1.976e+39
2.0
7.075e+39
7.3
70
Bu
635
639
635
636
71
Ag
646
646
646
646
5.720e+39
5.9
5.883e+38
0.6
6.308e+39
6.5
72
Bu
647
650
647
647
73
Au
650
666
665
650
74
Bg
666
670
666
666
6.887e+37
0.1
1.148e+38
0.1
1.837e+38
0.2
75
Ag
807
807
807
807
6.070e+39
6.2
3.618e+39
3.7
9.688e+39
10.0
76
Bg
810
810
810
810
1.084e+39
1.1
1.704e+39
1.8
2.789e+39
2.9
77
Au
826
826
861
826
78
Bu
861
900
864
867
79
Au
1004
1004
1005
1004
80
Ag
1005
1005
1015
1005
1.296e+39
1.3
1.160e+39
1.2
2.455e+39
2.5
81
Bg
1015
1015
1022
1015
1.341e+39
1.4
1.672e+39
1.7
3.013e+39
3.1
82
Bu
1024
1031
1024
1025
83
Au
1047
1047
1050
1047
84
Ag
1050
1050
1057
1050
5.191e+40
53.4
6.293e+37
0.1
5.198e+40
53.4
85
Bu
1067
1075
1067
1075
86
Bg
1075
1075
1075
1087
1.485e+39
1.5
2.272e+39
2.3
3.757e+39
3.9
87
Ag
1087
1087
1087
1096
1.483e+39
1.5
1.018e+39
1.0
2.501e+39
2.6
88
Bu
1101
1104
1101
1104
89
Bg
1104
1117
1104
1117
2.637e+39
2.7
3.816e+39
3.9
6.453e+39
6.6
90
Au
1117
1139
1137
1138
91
Au
1139
1152
1152
1139
92
Bg
1152
1153
1153
1152
1.071e+39
1.1
1.225e+39
1.3
2.296e+39
2.4
93
Ag
1153
1164
1170
1153
9.372e+39
9.6
3.302e+38
0.3
9.703e+39
10.0
94
Bu
1170
1183
1183
1186
95
Ag
1194
1194
1194
1194
2.677e+39
2.8
1.020e+39
1.0
3.697e+39
3.8
96
Bu
1198
1204
1198
1204
97
Au
1204
1224
1224
1228
98
Bg
1236
1236
1236
1236
3.034e+38
0.3
4.540e+38
0.5
7.573e+38
0.8
99
Ag
3234
3234
3234
3234
8.647e+40
88.9
1.080e+40
11.1
9.728e+40
100.0
100
Au
3240
3240
3240
3240
101
Bg
3240
3240
3248
3240
9.133e+39
9.4
1.061e+40
10.9
1.974e+40
20.3
102
Bu
3248
3272
3248
3251
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.