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

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:  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):  7.0540  7.3500  7.2375 
Angles (°):  90  120.36  90 

Cell contents: 

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

Atomic positions (theoretical):

Mg:  0.0000  0.0000  0.0000 
Al:  0.7350  0.2670  0.0109 
P:  0.2491  0.3923  0.2443 
O:  0.8016  0.0216  0.1182 
O:  0.6971  0.4939  0.8991 
O:  0.0454  0.2703  0.1170 
O:  0.4418  0.2300  0.8809 
O:  0.7403  0.1450  0.7610 
H:  0.6045  0.4295  0.1985 
Mg:  0.0000  0.5000  0.5000 
Al:  0.2650  0.7670  0.4891 
P:  0.7509  0.8923  0.2557 
O:  0.1984  0.5216  0.3818 
O:  0.3029  0.9939  0.6009 
O:  0.9546  0.7703  0.3830 
O:  0.5582  0.7300  0.6191 
O:  0.2597  0.6450  0.7390 
H:  0.3955  0.9295  0.3015 
Al:  0.2650  0.7330  0.9891 
P:  0.7509  0.6077  0.7557 
O:  0.1984  0.9784  0.8818 
O:  0.3029  0.5061  0.1009 
O:  0.9546  0.7297  0.8830 
O:  0.5582  0.7700  0.1191 
O:  0.2597  0.8550  0.2390 
H:  0.3955  0.5705  0.8015 
Al:  0.7350  0.2330  0.5109 
P:  0.2491  0.1077  0.7443 
O:  0.8016  0.4784  0.6182 
O:  0.6971  0.0061  0.3991 
O:  0.0454  0.2297  0.6170 
O:  0.4418  0.2700  0.3809 
O:  0.7403  0.3550  0.2610 
H:  0.6045  0.0705  0.6985 
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
95
95
95
95
5.566e+38
0.6
9.215e+38
1.0
1.478e+39
1.6
5
Ag
102
102
102
102
3.048e+39
3.2
2.052e+39
2.2
5.100e+39
5.4
6
Au
128
128
128
128
7
Bu
159
160
159
159
8
Ag
164
164
164
164
5.335e+39
5.7
3.724e+38
0.4
5.707e+39
6.0
9
Au
169
169
169
169
10
Au
175
175
175
175
11
Bu
176
181
176
180
12
Ag
186
186
186
186
5.161e+39
5.5
3.095e+37
0.0
5.192e+39
5.5
13
Bg
188
188
188
188
4.116e+38
0.4
6.001e+38
0.6
1.012e+39
1.1
14
Ag
220
220
220
220
2.940e+39
3.1
3.639e+38
0.4
3.304e+39
3.5
15
Au
220
220
225
220
16
Bg
225
225
225
225
1.095e+38
0.1
1.184e+38
0.1
2.279e+38
0.2
17
Bu
234
234
234
234
18
Bg
247
247
247
247
2.201e+38
0.2
2.554e+38
0.3
4.755e+38
0.5
19
Ag
252
252
252
252
4.085e+39
4.3
2.370e+38
0.3
4.322e+39
4.6
20
Bg
252
252
252
252
3.707e+37
0.0
4.438e+37
0.0
8.145e+37
0.1
21
Au
259
259
260
259
22
Au
266
266
269
266
23
Ag
269
269
270
269
5.921e+39
6.3
6.718e+38
0.7
6.592e+39
7.0
24
Bu
270
273
273
276
25
Bu
277
278
277
281
26
Bu
295
297
295
297
27
Au
297
297
298
301
28
Bg
301
301
301
308
1.711e+37
0.0
2.353e+37
0.0
4.064e+37
0.0
29
Ag
308
308
308
310
4.050e+39
4.3
5.291e+38
0.6
4.579e+39
4.8
30
Bg
318
318
318
318
2.173e+38
0.2
3.131e+38
0.3
5.304e+38
0.6
31
Bu
319
320
319
326
32
Bg
333
333
333
333
2.489e+38
0.3
3.162e+38
0.3
5.651e+38
0.6
33
Ag
334
334
334
334
1.133e+39
1.2
5.582e+38
0.6
1.691e+39
1.8
34
Au
343
343
344
343
35
Bu
347
349
347
355
36
Bg
362
362
362
362
2.252e+37
0.0
2.796e+37
0.0
5.048e+37
0.1
37
Au
363
363
364
363
38
Ag
365
365
365
365
4.617e+39
4.9
8.688e+38
0.9
5.486e+39
5.8
39
Au
368
368
368
368
40
Bu
368
369
373
378
41
Bg
378
378
378
385
3.469e+38
0.4
5.729e+38
0.6
9.197e+38
1.0
42
Bu
388
388
388
389
43
Au
397
397
398
397
44
Ag
398
398
400
398
4.658e+39
4.9
3.468e+39
3.7
8.126e+39
8.6
45
Bu
402
417
402
403
46
Ag
417
421
417
417
1.110e+39
1.2
5.087e+38
0.5
1.619e+39
1.7
47
Au
425
425
428
425
48
Bu
428
429
437
437
49
Ag
437
437
445
445
8.108e+38
0.9
3.924e+38
0.4
1.203e+39
1.3
50
Bg
445
445
463
445
4.092e+38
0.4
6.894e+38
0.7
1.099e+39
1.2
51
Bu
463
466
466
466
52
Ag
466
482
477
475
3.442e+39
3.6
1.495e+39
1.6
4.937e+39
5.2
53
Bg
482
486
482
482
1.879e+38
0.2
1.999e+38
0.2
3.878e+38
0.4
54
Au
486
492
486
486
55
Ag
494
494
494
494
1.008e+39
1.1
1.076e+38
0.1
1.115e+39
1.2
56
Au
494
494
495
494
57
Bu
498
498
498
498
58
Bg
498
501
498
501
8.715e+37
0.1
1.042e+38
0.1
1.913e+38
0.2
59
Au
501
513
520
528
60
Bu
528
551
528
551
61
Au
551
562
559
562
62
Bg
562
564
562
566
1.804e+39
1.9
2.209e+39
2.3
4.013e+39
4.2
63
Au
570
570
584
570
64
Bg
584
584
584
584
2.175e+39
2.3
2.666e+39
2.8
4.840e+39
5.1
65
Bu
584
584
593
593
66
Ag
593
593
594
594
7.303e+38
0.8
3.828e+38
0.4
1.113e+39
1.2
67
Bg
603
603
603
603
1.818e+39
1.9
2.970e+39
3.1
4.789e+39
5.1
68
Au
615
615
615
615
69
Ag
616
616
616
616
4.956e+39
5.2
1.776e+39
1.9
6.732e+39
7.1
70
Bu
620
622
620
620
71
Ag
629
629
629
629
5.304e+39
5.6
5.187e+38
0.5
5.823e+39
6.2
72
Bu
631
635
631
631
73
Au
635
645
645
635
74
Bg
645
649
646
645
6.248e+37
0.1
1.047e+38
0.1
1.672e+38
0.2
75
Ag
790
790
790
790
5.455e+39
5.8
3.005e+39
3.2
8.460e+39
9.0
76
Bg
793
793
793
793
9.782e+38
1.0
1.546e+39
1.6
2.524e+39
2.7
77
Au
807
807
838
807
78
Bu
838
875
841
843
79
Au
969
969
969
969
80
Ag
969
969
982
969
1.461e+39
1.5
1.465e+39
1.6
2.926e+39
3.1
81
Bg
982
982
987
982
1.788e+39
1.9
2.248e+39
2.4
4.035e+39
4.3
82
Bu
994
1003
994
994
83
Au
1015
1015
1020
1015
84
Ag
1020
1020
1025
1020
4.944e+40
52.4
1.902e+37
0.0
4.946e+40
52.4
85
Bu
1034
1039
1034
1049
86
Bg
1049
1049
1049
1058
1.468e+39
1.6
2.263e+39
2.4
3.731e+39
4.0
87
Ag
1058
1058
1058
1070
3.052e+39
3.2
1.088e+39
1.2
4.140e+39
4.4
88
Bg
1070
1070
1070
1071
2.734e+39
2.9
3.935e+39
4.2
6.669e+39
7.1
89
Bu
1074
1088
1074
1088
90
Au
1088
1111
1111
1105
91
Au
1111
1121
1121
1111
92
Bg
1121
1122
1122
1121
1.082e+39
1.1
1.231e+39
1.3
2.313e+39
2.4
93
Ag
1122
1139
1144
1122
1.044e+40
11.1
3.714e+38
0.4
1.081e+40
11.5
94
Bu
1144
1155
1156
1159
95
Ag
1168
1168
1168
1168
2.072e+39
2.2
8.492e+38
0.9
2.921e+39
3.1
96
Bu
1169
1178
1169
1178
97
Au
1178
1195
1195
1201
98
Bg
1210
1210
1210
1210
3.869e+38
0.4
5.882e+38
0.6
9.751e+38
1.0
99
Ag
3273
3273
3273
3273
8.426e+40
89.2
1.016e+40
10.8
9.442e+40
100.0
100
Au
3278
3278
3278
3278
101
Bg
3278
3278
3284
3278
9.113e+39
9.7
1.065e+40
11.3
1.976e+40
20.9
102
Bu
3284
3305
3284
3287
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.