-    HERDERITE     -    CaBe(PO4)F

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/a 
Lattice parameters (Å):  5.1859  4.0641  2.5401 
Angles (°):  90.0  90.1  90.0 

Symmetry (theoretical): 

Space group:  14  P2_1/a 
Lattice parameters (Å):  9.7332  7.6783  4.8347 
Angles (°):  90.0  91.0  90.0 

Cell contents: 

Number of atoms:  32 
Number of atom types:  5 
Chemical composition:  0 

Atomic positions (theoretical):

Ca:  0.0000  0.3293  0.1118 
Be:  0.9966  0.3366  0.4114 
P:  0.5413  0.0817  0.2678 
O:  0.4746  0.0416  0.3943 
O:  0.2476  0.4554  0.2828 
O:  0.6445  0.1933  0.3428 
O:  0.6767  0.1474  0.1037 
F:  0.3470  0.3230  0.4037 
Ca:  0.2227  0.1707  0.6118 
Be:  0.0034  0.1634  0.9114 
P:  0.4587  0.4183  0.7678 
O:  0.5254  0.4584  0.8943 
O:  0.7524  0.0446  0.7828 
O:  0.3555  0.3067  0.8428 
O:  0.3233  0.3526  0.6037 
F:  0.6530  0.1770  0.9037 
Ca:  0.7773  0.6707  0.8882 
Be:  0.0034  0.6634  0.5886 
P:  0.4587  0.9183  0.7322 
O:  0.5254  0.9584  0.6057 
O:  0.7524  0.5446  0.7172 
O:  0.3555  0.8067  0.6572 
O:  0.3233  0.8526  0.8963 
F:  0.6530  0.6770  0.5963 
Ca:  0.7773  0.8293  0.3882 
Be:  0.9966  0.8366  0.0886 
P:  0.5413  0.5817  0.2322 
O:  0.4746  0.5416  0.1057 
O:  0.2476  0.9554  0.2172 
O:  0.6445  0.6933  0.1572 
O:  0.6767  0.6474  0.3963 
F:  0.3470  0.8230  0.0963 
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
Ag
110
110
110
110
2.217e+38
0.4
1.008e+38
0.2
3.224e+38
0.6
5
Bu
122
122
128
122
6
Bg
128
128
129
128
2.154e+37
0.0
2.962e+37
0.1
5.116e+37
0.1
7
Ag
137
137
137
137
3.353e+38
0.6
6.355e+37
0.1
3.989e+38
0.8
8
Bu
139
139
140
139
9
Au
140
145
141
141
10
Bg
150
150
150
150
2.659e+38
0.5
3.948e+38
0.8
6.606e+38
1.3
11
Ag
156
156
156
156
1.749e+39
3.3
8.271e+37
0.2
1.832e+39
3.5
12
Bg
162
162
162
162
1.128e+38
0.2
1.202e+38
0.2
2.330e+38
0.4
13
Au
165
165
165
165
14
Ag
171
171
171
171
5.549e+38
1.1
2.208e+38
0.4
7.757e+38
1.5
15
Bu
178
178
178
178
16
Ag
189
189
189
189
3.031e+39
5.8
2.007e+38
0.4
3.232e+39
6.2
17
Bg
197
197
197
197
2.665e+37
0.1
3.963e+37
0.1
6.628e+37
0.1
18
Bu
199
199
201
199
19
Au
201
201
202
202
20
Ag
202
202
203
203
3.582e+37
0.1
1.194e+37
0.0
4.776e+37
0.1
21
Bg
203
203
208
209
1.951e+37
0.0
2.105e+37
0.0
4.056e+37
0.1
22
Bu
210
210
216
210
23
Bg
216
216
218
216
5.411e+37
0.1
5.900e+37
0.1
1.131e+38
0.2
24
Ag
218
218
218
218
1.090e+38
0.2
1.197e+38
0.2
2.287e+38
0.4
25
Bu
222
222
224
222
26
Au
224
229
231
231
27
Bg
231
231
235
233
3.445e+37
0.1
4.737e+37
0.1
8.181e+37
0.2
28
Au
235
238
238
238
29
Ag
238
242
239
241
4.518e+38
0.9
3.412e+38
0.7
7.930e+38
1.5
30
Au
243
244
243
244
31
Bu
244
253
245
258
32
Bg
258
258
258
261
4.198e+38
0.8
6.992e+38
1.3
1.119e+39
2.1
33
Bu
261
261
269
271
34
Au
271
271
271
272
35
Ag
272
272
272
276
4.182e+38
0.8
3.107e+38
0.6
7.289e+38
1.4
36
Ag
284
284
284
284
2.138e+38
0.4
2.764e+38
0.5
4.903e+38
0.9
37
Au
288
289
288
289
38
Bg
289
292
289
296
5.180e+38
1.0
6.625e+38
1.3
1.180e+39
2.3
39
Bg
296
296
296
303
7.779e+38
1.5
9.188e+38
1.8
1.697e+39
3.2
40
Bu
303
303
304
318
41
Ag
318
318
318
324
1.165e+39
2.2
7.744e+38
1.5
1.939e+39
3.7
42
Bg
324
324
324
325
8.950e+37
0.2
9.833e+37
0.2
1.878e+38
0.4
43
Bu
331
331
331
331
44
Ag
331
331
331
331
1.161e+39
2.2
7.641e+38
1.5
1.925e+39
3.7
45
Au
357
365
357
357
46
Au
397
402
397
398
47
Bu
404
404
409
404
48
Bg
412
412
412
412
6.791e+38
1.3
8.817e+38
1.7
1.561e+39
3.0
49
Au
432
433
432
433
50
Bg
436
436
436
436
8.262e+38
1.6
1.266e+39
2.4
2.092e+39
4.0
51
Ag
441
441
441
441
1.481e+39
2.8
1.324e+39
2.5
2.805e+39
5.4
52
Bu
446
446
454
446
53
Au
466
467
466
467
54
Bg
496
496
496
496
1.516e+38
0.3
2.515e+38
0.5
4.031e+38
0.8
55
Bu
497
497
497
497
56
Ag
502
502
502
502
3.179e+39
6.1
1.592e+39
3.0
4.771e+39
9.1
57
Bg
520
520
520
520
1.047e+39
2.0
1.735e+39
3.3
2.782e+39
5.3
58
Au
526
530
526
526
59
Bu
530
538
538
530
60
Ag
538
539
547
538
1.122e+39
2.1
1.447e+39
2.8
2.569e+39
4.9
61
Au
547
550
547
547
62
Bu
550
556
556
550
63
Bg
556
560
560
556
1.197e+39
2.3
1.284e+39
2.5
2.480e+39
4.7
64
Ag
560
573
561
560
1.014e+40
19.4
8.139e+38
1.6
1.095e+40
21.0
65
Ag
573
576
573
573
2.107e+39
4.0
1.293e+39
2.5
3.400e+39
6.5
66
Bg
590
590
590
590
2.908e+38
0.6
3.724e+38
0.7
6.633e+38
1.3
67
Au
600
600
600
600
68
Au
600
607
600
600
69
Au
694
702
694
695
70
Bu
702
715
707
702
71
Ag
715
727
715
715
2.035e+38
0.4
1.621e+38
0.3
3.656e+38
0.7
72
Bg
727
734
727
727
1.383e+38
0.3
1.725e+38
0.3
3.108e+38
0.6
73
Ag
735
735
735
735
4.218e+39
8.1
4.136e+38
0.8
4.631e+39
8.9
74
Bg
735
735
735
735
3.007e+38
0.6
4.639e+38
0.9
7.646e+38
1.5
75
Bu
747
747
757
747
76
Bu
757
757
761
757
77
Au
761
786
788
762
78
Au
788
790
792
797
79
Ag
797
797
797
822
4.249e+37
0.1
4.333e+37
0.1
8.582e+37
0.2
80
Bg
822
822
822
822
1.654e+37
0.0
2.274e+37
0.0
3.928e+37
0.1
81
Bu
932
932
934
932
82
Ag
934
934
941
934
1.644e+40
31.5
2.353e+39
4.5
1.879e+40
36.0
83
Au
959
964
959
964
84
Bg
964
974
964
967
2.816e+38
0.5
3.415e+38
0.7
6.231e+38
1.2
85
Ag
977
977
977
977
5.109e+40
97.8
1.138e+39
2.2
5.222e+40
100.0
86
Bu
984
984
989
984
87
Au
989
997
997
990
88
Ag
997
1005
1005
997
2.982e+39
5.7
1.519e+39
2.9
4.501e+39
8.6
89
Bg
1005
1016
1033
1005
6.530e+38
1.3
9.098e+38
1.7
1.563e+39
3.0
90
Au
1047
1055
1047
1047
91
Bg
1055
1066
1055
1055
1.082e+39
2.1
1.283e+39
2.5
2.364e+39
4.5
92
Bu
1066
1084
1084
1066
93
Au
1084
1099
1099
1099
94
Ag
1099
1115
1106
1115
5.618e+39
10.8
2.785e+39
5.3
8.403e+39
16.1
95
Bg
1115
1116
1115
1119
3.970e+39
7.6
5.805e+39
11.1
9.775e+39
18.7
96
Bu
1119
1119
1147
1157
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.