-    WILLEMITE     -    Zn2SiO4

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):  4.7104  10.2718  8.7476 
Angles (°):  90  90  120 

Symmetry (theoretical): 

Space group:  148  R-3 
Lattice parameters (Å):  8.5641  8.5641  8.5641 
Angles (°):  107.88  107.88  107.88 

Cell contents: 

Number of atoms:  42 
Number of atom types:  4 
Chemical composition:  0 

Atomic positions (theoretical):

Zn:  0.3974  0.6252  0.2236 
Zn:  0.0585  0.2962  0.8895 
Si:  0.7333  0.9616  0.5540 
O:  0.8598  0.8563  0.5348 
O:  0.7476  0.0731  0.4331 
O:  0.8098  0.1014  0.7671 
O:  0.5262  0.8101  0.4754 
Zn:  0.6252  0.2236  0.3974 
Zn:  0.2962  0.8895  0.0585 
Si:  0.9616  0.5540  0.7333 
O:  0.8563  0.5348  0.8598 
O:  0.0731  0.4331  0.7476 
O:  0.1014  0.7671  0.8098 
O:  0.8101  0.4754  0.5262 
Zn:  0.2236  0.3974  0.6252 
Zn:  0.8895  0.0585  0.2962 
Si:  0.5540  0.7333  0.9616 
O:  0.5348  0.8598  0.8563 
O:  0.4331  0.7476  0.0731 
O:  0.7671  0.8098  0.1014 
O:  0.4754  0.5262  0.8101 
Zn:  0.6026  0.3748  0.7764 
Zn:  0.9415  0.7038  0.1105 
Si:  0.2667  0.0384  0.4460 
O:  0.1402  0.1437  0.4652 
O:  0.2524  0.9269  0.5669 
O:  0.1902  0.8986  0.2329 
O:  0.4738  0.1899  0.5246 
Zn:  0.3748  0.7764  0.6026 
Zn:  0.7038  0.1105  0.9415 
Si:  0.0384  0.4460  0.2667 
O:  0.1437  0.4652  0.1402 
O:  0.9269  0.5669  0.2524 
O:  0.8986  0.2329  0.1902 
O:  0.1899  0.5246  0.4738 
Zn:  0.7764  0.6026  0.3748 
Zn:  0.1105  0.9415  0.7038 
Si:  0.4460  0.2667  0.0384 
O:  0.4652  0.1402  0.1437 
O:  0.5669  0.2524  0.9269 
O:  0.2329  0.1902  0.8986 
O:  0.5246  0.4738  0.1899 
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
71
71
71
71
7.154e+39
13.5
2.025e+37
0.0
7.174e+39
13.5
5
Au
72
72
72
73
6
Eg
74
74
74
74
1.024e+39
1.9
9.287e+38
1.8
1.952e+39
3.7
7
Eg
74
74
74
74
1.024e+39
1.9
1.232e+39
2.3
2.255e+39
4.3
8
Eg
85
85
85
85
5.034e+38
0.9
6.921e+38
1.3
1.195e+39
2.3
9
Eg
85
85
85
85
5.034e+38
0.9
6.921e+38
1.3
1.195e+39
2.3
10
Eu
94
94
94
94
11
Eu
94
94
94
94
12
Ag
96
96
96
96
1.238e+38
0.2
7.138e+37
0.1
1.952e+38
0.4
13
Eg
107
107
107
107
1.718e+38
0.3
2.648e+38
0.5
4.366e+38
0.8
14
Eg
107
107
107
107
1.718e+38
0.3
2.076e+38
0.4
3.794e+38
0.7
15
Eu
108
108
108
108
16
Eu
108
108
108
108
17
Ag
111
111
111
111
1.692e+38
0.3
2.115e+37
0.0
1.903e+38
0.4
18
Au
121
121
121
121
19
Ag
131
131
131
131
6.843e+37
0.1
4.108e+37
0.1
1.095e+38
0.2
20
Eu
133
133
133
133
21
Eu
133
134
134
133
22
Au
135
135
135
136
23
Eg
136
136
136
136
1.792e+38
0.3
1.769e+38
0.3
3.561e+38
0.7
24
Eg
136
136
136
145
1.792e+38
0.3
1.674e+38
0.3
3.466e+38
0.7
25
Au
145
145
145
148
26
Ag
151
151
151
151
2.998e+38
0.6
1.131e+37
0.0
3.111e+38
0.6
27
Eu
154
154
154
154
28
Eu
154
158
158
154
29
Eg
158
158
158
158
7.441e+37
0.1
1.255e+38
0.2
1.999e+38
0.4
30
Eg
158
160
160
158
7.441e+37
0.1
7.770e+37
0.1
1.521e+38
0.3
31
Ag
167
167
167
167
4.901e+38
0.9
7.270e+37
0.1
5.628e+38
1.1
32
Au
182
182
182
182
33
Ag
185
185
185
185
1.314e+39
2.5
7.869e+34
0.0
1.314e+39
2.5
34
Eu
192
192
192
192
35
Eu
192
192
192
192
36
Eg
192
192
192
192
1.861e+37
0.0
2.850e+37
0.1
4.711e+37
0.1
37
Eg
192
192
192
192
1.861e+37
0.0
1.667e+37
0.0
3.527e+37
0.1
38
Eu
205
205
205
205
39
Eu
205
206
206
205
40
Eg
208
208
208
208
2.365e+38
0.4
1.779e+38
0.3
4.144e+38
0.8
41
Eg
208
208
208
208
2.365e+38
0.4
3.181e+38
0.6
5.546e+38
1.0
42
Au
210
210
210
213
43
Ag
213
213
213
217
1.115e+38
0.2
3.907e+37
0.1
1.506e+38
0.3
44
Eu
225
225
225
225
45
Eu
225
227
227
225
46
Eg
231
231
231
231
1.546e+38
0.3
1.981e+38
0.4
3.528e+38
0.7
47
Eg
231
231
231
231
1.546e+38
0.3
1.226e+38
0.2
2.772e+38
0.5
48
Au
244
244
244
246
49
Au
250
250
250
250
50
Eu
250
250
250
250
51
Eu
250
251
251
251
52
Au
251
259
259
259
53
Ag
259
266
266
264
3.581e+37
0.1
3.474e+35
0.0
3.615e+37
0.1
54
Eg
266
266
266
266
9.246e+37
0.2
1.007e+38
0.2
1.932e+38
0.4
55
Eg
266
281
281
266
9.246e+37
0.2
8.381e+37
0.2
1.763e+38
0.3
56
Ag
283
283
283
283
3.995e+38
0.8
3.159e+37
0.1
4.311e+38
0.8
57
Eu
284
284
284
284
58
Eu
284
287
287
284
59
Eg
287
287
287
287
6.322e+37
0.1
1.021e+38
0.2
1.653e+38
0.3
60
Eg
287
287
287
287
6.322e+37
0.1
5.416e+37
0.1
1.174e+38
0.2
61
Eu
382
382
382
382
62
Eu
382
384
384
382
63
Au
384
387
387
385
64
Ag
387
393
393
387
2.094e+38
0.4
6.134e+35
0.0
2.100e+38
0.4
65
Ag
393
393
393
393
3.004e+39
5.7
4.859e+37
0.1
3.052e+39
5.8
66
Au
395
395
395
399
67
Eg
399
399
399
399
3.044e+38
0.6
2.814e+38
0.5
5.857e+38
1.1
68
Eg
399
399
399
400
3.044e+38
0.6
3.039e+38
0.6
6.083e+38
1.1
69
Eu
400
400
400
400
70
Eu
400
403
403
404
71
Eg
404
404
404
404
2.864e+38
0.5
3.860e+38
0.7
6.724e+38
1.3
72
Eg
404
404
404
410
2.864e+38
0.5
4.358e+38
0.8
7.222e+38
1.4
73
Au
450
450
450
450
74
Eu
450
450
450
450
75
Eu
450
452
452
451
76
Eg
455
455
455
455
1.925e+38
0.4
2.171e+38
0.4
4.096e+38
0.8
77
Eg
455
455
455
455
1.925e+38
0.4
1.668e+38
0.3
3.594e+38
0.7
78
Ag
474
474
474
474
4.839e+38
0.9
1.395e+36
0.0
4.853e+38
0.9
79
Eu
491
491
491
491
80
Eu
491
491
491
491
81
Ag
502
502
502
502
6.136e+37
0.1
1.491e+37
0.0
7.626e+37
0.1
82
Eg
505
505
505
505
5.313e+37
0.1
6.955e+37
0.1
1.227e+38
0.2
83
Eg
505
505
505
505
5.313e+37
0.1
5.524e+37
0.1
1.084e+38
0.2
84
Au
515
515
515
516
85
Ag
556
556
556
556
8.747e+38
1.6
2.237e+37
0.0
8.970e+38
1.7
86
Eg
563
563
563
563
5.350e+37
0.1
7.062e+37
0.1
1.241e+38
0.2
87
Eg
563
563
563
563
5.350e+37
0.1
4.046e+37
0.1
9.396e+37
0.2
88
Au
575
575
575
579
89
Eu
579
579
579
579
90
Eu
579
587
587
587
91
Eu
587
587
587
587
92
Eu
587
593
593
592
93
Ag
593
593
593
593
3.823e+37
0.1
2.677e+37
0.1
6.500e+37
0.1
94
Eg
593
593
593
593
1.804e+38
0.3
2.183e+38
0.4
3.987e+38
0.8
95
Eg
593
597
597
593
1.804e+38
0.3
2.638e+38
0.5
4.442e+38
0.8
96
Au
598
598
598
602
97
Au
602
602
602
610
98
Eu
610
610
610
610
99
Eu
610
620
620
620
100
Ag
620
627
627
627
4.267e+38
0.8
1.597e+38
0.3
5.864e+38
1.1
101
Eg
627
627
627
627
9.604e+37
0.2
1.466e+38
0.3
2.427e+38
0.5
102
Eg
627
627
627
627
9.604e+37
0.2
8.788e+37
0.2
1.839e+38
0.3
103
Au
861
861
861
862
104
Eu
862
862
862
862
105
Eu
862
864
864
865
106
Eg
865
865
865
865
3.963e+38
0.7
4.973e+38
0.9
8.937e+38
1.7
107
Eg
865
865
865
865
3.963e+38
0.7
4.606e+38
0.9
8.570e+38
1.6
108
Ag
865
865
865
867
5.304e+40
100.0
7.288e+35
0.0
5.304e+40
100.0
109
Ag
884
884
884
884
2.382e+39
4.5
6.836e+37
0.1
2.450e+39
4.6
110
Eu
884
884
884
884
111
Eu
884
888
888
884
112
Au
888
895
895
891
113
Eg
895
895
895
895
4.241e+38
0.8
3.431e+38
0.6
7.672e+38
1.4
114
Eg
895
905
905
895
4.241e+38
0.8
6.035e+38
1.1
1.028e+39
1.9
115
Ag
905
906
906
905
4.090e+39
7.7
4.316e+38
0.8
4.522e+39
8.5
116
Au
906
906
906
906
117
Eg
906
906
906
906
4.798e+38
0.9
5.412e+38
1.0
1.021e+39
1.9
118
Eg
906
919
919
927
4.798e+38
0.9
7.294e+38
1.4
1.209e+39
2.3
119
Eu
927
927
927
927
120
Eu
927
944
944
944
121
Eg
944
944
944
944
1.651e+39
3.1
2.129e+39
4.0
3.780e+39
7.1
122
Eg
944
946
946
946
1.651e+39
3.1
1.346e+39
2.5
2.997e+39
5.7
123
Au
946
951
951
951
124
Ag
951
958
958
970
7.801e+38
1.5
1.919e+38
0.4
9.720e+38
1.8
125
Eu
970
970
970
970
126
Eu
970
998
998
991
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.