-    PHENAKITE     -    Be2SiO4

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:  148  R-3 
Lattice parameters (Å):  6.5817  6.5817  4.3558 
Angles (°):  90  90  120 

Symmetry (theoretical): 

Space group:  148  R-3 
Lattice parameters (Å):  7.5742  7.5742  7.5742 
Angles (°):  108.03  108.03  108.03 

Cell contents: 

Number of atoms:  42 
Number of atom types: 
Chemical composition: 

Atomic positions (theoretical):

Be:  0.0000  0.6098  0.4311 
Be:  0.2057  0.2786  0.1027 
Si:  0.8723  0.9455  0.7664 
O:  0.5379  0.9594  0.6284 
O:  0.6629  0.0849  0.7493 
O:  0.4157  0.0380  0.0056 
O:  0.7059  0.7049  0.6706 
Be:  0.3742  0.4311  0.2057 
Be:  0.6098  0.1027  0.8723 
Si:  0.2786  0.7664  0.5379 
O:  0.9455  0.6284  0.6629 
O:  0.9594  0.7493  0.4157 
O:  0.0849  0.0056  0.7059 
O:  0.0380  0.6706  0.3742 
Be:  0.7049  0.2057  0.6098 
Be:  0.4311  0.8723  0.2786 
Si:  0.1027  0.5379  0.9455 
O:  0.7664  0.6629  0.9594 
O:  0.6284  0.4157  0.0849 
O:  0.7493  0.7059  0.0380 
O:  0.0056  0.3742  0.7049 
Be:  0.6706  0.3902  0.5689 
Be:  0.7943  0.7214  0.8973 
Si:  0.1277  0.0545  0.2336 
O:  0.4621  0.0406  0.3716 
O:  0.3371  0.9151  0.2507 
O:  0.5843  0.9620  0.9944 
O:  0.2941  0.2951  0.3294 
Be:  0.6258  0.5689  0.7943 
Be:  0.3902  0.8973  0.1277 
Si:  0.7214  0.2336  0.4621 
O:  0.0545  0.3716  0.3371 
O:  0.0406  0.2507  0.5843 
O:  0.9151  0.9944  0.2941 
O:  0.9620  0.3294  0.6258 
Be:  0.2951  0.7943  0.3902 
Be:  0.5689  0.1277  0.7214 
Si:  0.8973  0.4621  0.0545 
O:  0.2336  0.3371  0.0406 
O:  0.3716  0.5843  0.9151 
O:  0.2507  0.2941  0.9620 
O:  0.9944  0.6258  0.2951 
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.

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
Eg
159
159
159
159
1.959e+38
0.4
2.171e+38
0.4
4.129e+38
0.8
5
Eg
159
159
159
159
1.959e+38
0.4
1.981e+38
0.4
3.940e+38
0.7
6
Ag
222
222
222
222
2.391e+39
4.4
2.244e+37
0.0
2.413e+39
4.5
7
Au
227
227
227
227
8
Eg
229
229
229
229
1.462e+38
0.3
1.503e+38
0.3
2.965e+38
0.5
9
Eg
229
229
229
229
1.462e+38
0.3
2.382e+38
0.4
3.844e+38
0.7
10
Eu
237
237
237
237
11
Eu
237
237
237
237
12
Au
239
239
239
239
13
Ag
250
250
250
250
3.108e+37
0.1
7.215e+36
0.0
3.830e+37
0.1
14
Eg
254
254
254
254
3.621e+37
0.1
5.517e+37
0.1
9.138e+37
0.2
15
Eg
254
254
254
254
3.621e+37
0.1
5.260e+37
0.1
8.881e+37
0.2
16
Ag
259
259
259
259
1.700e+37
0.0
1.089e+37
0.0
2.788e+37
0.1
17
Au
270
270
270
270
18
Ag
272
272
272
272
7.184e+37
0.1
1.440e+37
0.0
8.624e+37
0.2
19
Eg
278
278
278
278
1.598e+38
0.3
2.606e+38
0.5
4.204e+38
0.8
20
Eg
278
278
278
278
1.598e+38
0.3
1.458e+38
0.3
3.056e+38
0.6
21
Eu
292
292
292
292
22
Eu
292
292
292
292
23
Au
295
295
295
295
24
Ag
295
295
295
295
6.852e+37
0.1
5.068e+37
0.1
1.192e+38
0.2
25
Eu
316
316
316
316
26
Eu
316
316
316
316
27
Au
343
343
343
346
28
Eg
346
346
346
346
1.798e+38
0.3
2.450e+38
0.5
4.247e+38
0.8
29
Eg
346
346
346
356
1.798e+38
0.3
2.784e+38
0.5
4.581e+38
0.8
30
Eu
357
357
357
357
31
Eu
357
358
358
357
32
Eu
372
372
372
372
33
Eu
372
372
372
372
34
Eg
382
382
382
382
5.724e+38
1.1
5.502e+38
1.0
1.123e+39
2.1
35
Eg
382
382
382
382
5.724e+38
1.1
5.743e+38
1.1
1.147e+39
2.1
36
Ag
407
407
407
407
9.050e+36
0.0
1.863e+34
0.0
9.069e+36
0.0
37
Eu
415
415
415
415
38
Eu
415
425
425
415
39
Au
425
426
426
426
40
Ag
426
430
430
426
8.063e+37
0.1
5.753e+36
0.0
8.638e+37
0.2
41
Eu
437
437
437
437
42
Eu
437
438
438
437
43
Eg
444
444
444
444
7.987e+38
1.5
7.407e+38
1.4
1.539e+39
2.8
44
Eg
444
444
444
444
7.987e+38
1.5
1.286e+39
2.4
2.084e+39
3.9
45
Ag
446
446
446
446
2.136e+38
0.4
1.651e+35
0.0
2.138e+38
0.4
46
Eg
462
462
462
462
1.007e+38
0.2
1.282e+38
0.2
2.289e+38
0.4
47
Eg
462
462
462
462
1.007e+38
0.2
9.958e+37
0.2
2.003e+38
0.4
48
Au
470
470
470
470
49
Ag
481
481
481
481
1.099e+38
0.2
1.511e+37
0.0
1.250e+38
0.2
50
Ag
486
486
486
486
7.958e+37
0.1
3.301e+37
0.1
1.126e+38
0.2
51
Eu
518
518
518
518
52
Eu
518
519
519
518
53
Eg
523
523
523
523
5.915e+38
1.1
5.369e+38
1.0
1.128e+39
2.1
54
Eg
523
523
523
523
5.915e+38
1.1
6.594e+38
1.2
1.251e+39
2.3
55
Au
544
544
544
544
56
Eu
557
557
557
557
57
Eu
557
557
557
557
58
Au
572
572
572
575
59
Eg
578
578
578
578
7.941e+37
0.1
8.934e+37
0.2
1.687e+38
0.3
60
Eg
578
578
578
578
7.941e+37
0.1
1.227e+38
0.2
2.021e+38
0.4
61
Eu
590
590
590
590
62
Eu
590
596
596
590
63
Ag
596
598
598
596
3.645e+38
0.7
2.299e+38
0.4
5.944e+38
1.1
64
Eg
620
620
620
620
2.155e+38
0.4
2.828e+38
0.5
4.983e+38
0.9
65
Eg
620
620
620
620
2.155e+38
0.4
3.344e+38
0.6
5.499e+38
1.0
66
Au
647
647
647
652
67
Ag
678
678
678
678
1.486e+38
0.3
1.858e+37
0.0
1.672e+38
0.3
68
Eg
680
680
680
680
1.450e+38
0.3
1.399e+38
0.3
2.849e+38
0.5
69
Eg
680
680
680
680
1.450e+38
0.3
1.459e+38
0.3
2.909e+38
0.5
70
Au
682
682
682
683
71
Eu
688
688
688
688
72
Eu
688
690
690
688
73
Au
699
699
699
700
74
Eu
700
700
700
700
75
Eu
700
702
702
701
76
Eg
702
702
702
702
2.525e+37
0.0
2.912e+37
0.1
5.437e+37
0.1
77
Eg
702
707
707
702
2.525e+37
0.0
3.924e+37
0.1
6.449e+37
0.1
78
Ag
707
714
714
707
5.171e+38
1.0
1.242e+38
0.2
6.414e+38
1.2
79
Ag
716
716
716
716
5.812e+37
0.1
8.035e+36
0.0
6.616e+37
0.1
80
Eu
721
721
721
721
81
Eu
721
723
723
721
82
Eg
723
723
723
723
1.944e+38
0.4
3.242e+38
0.6
5.186e+38
1.0
83
Eg
723
724
724
723
1.944e+38
0.4
2.048e+38
0.4
3.992e+38
0.7
84
Au
724
736
736
725
85
Au
736
737
737
737
86
Eg
737
737
737
737
1.102e+38
0.2
1.676e+38
0.3
2.778e+38
0.5
87
Eg
737
745
745
747
1.102e+38
0.2
1.346e+38
0.2
2.448e+38
0.5
88
Eu
747
747
747
747
89
Eu
747
759
759
753
90
Au
759
775
775
779
91
Ag
779
779
779
786
1.253e+39
2.3
8.905e+36
0.0
1.262e+39
2.3
92
Eg
786
786
786
786
4.879e+38
0.9
6.590e+38
1.2
1.147e+39
2.1
93
Eg
786
786
786
790
4.879e+38
0.9
7.396e+38
1.4
1.228e+39
2.3
94
Eu
790
790
790
790
95
Eu
790
797
797
797
96
Ag
797
801
801
800
2.439e+39
4.5
1.018e+36
0.0
2.440e+39
4.5
97
Eu
801
801
801
801
98
Eu
801
802
802
801
99
Au
802
814
814
816
100
Eg
816
816
816
816
2.532e+37
0.0
2.382e+37
0.0
4.914e+37
0.1
101
Eg
816
816
816
821
2.532e+37
0.0
2.999e+37
0.1
5.532e+37
0.1
102
Ag
821
821
821
847
5.586e+38
1.0
1.707e+37
0.0
5.756e+38
1.1
103
Ag
868
868
868
868
5.397e+40
99.8
1.251e+38
0.2
5.409e+40
100.0
104
Eu
892
892
892
892
105
Eu
892
896
896
892
106
Au
896
913
913
905
107
Eg
913
913
913
913
1.177e+39
2.2
1.149e+39
2.1
2.326e+39
4.3
108
Eg
913
917
917
913
1.177e+39
2.2
1.499e+39
2.8
2.677e+39
4.9
109
Ag
918
918
918
918
1.127e+39
2.1
2.311e+38
0.4
1.358e+39
2.5
110
Au
923
923
923
932
111
Eu
932
932
932
932
112
Eu
932
936
936
936
113
Eg
936
936
936
936
7.938e+38
1.5
1.296e+39
2.4
2.090e+39
3.9
114
Eg
936
947
947
947
7.938e+38
1.5
8.922e+38
1.6
1.686e+39
3.1
115
Ag
947
963
963
970
3.296e+39
6.1
1.575e+39
2.9
4.871e+39
9.0
116
Eu
970
970
970
970
117
Eu
970
996
996
996
118
Eg
996
996
996
996
2.188e+38
0.4
3.319e+38
0.6
5.507e+38
1.0
119
Eg
996
1003
1003
1002
2.188e+38
0.4
2.843e+38
0.5
5.030e+38
0.9
120
Au
1003
1008
1008
1008
121
Ag
1008
1019
1019
1019
6.708e+38
1.2
4.609e+36
0.0
6.755e+38
1.2
122
Eg
1019
1019
1019
1019
6.659e+38
1.2
6.329e+38
1.2
1.299e+39
2.4
123
Eg
1019
1022
1022
1022
6.659e+38
1.2
7.595e+38
1.4
1.425e+39
2.6
124
Eu
1022
1022
1022
1022
125
Eu
1022
1026
1026
1025
126
Au
1026
1117
1117
1110
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.