-    WADEITE     -    K2ZrSi3O9

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:  176  P6_3/m 
Lattice parameters (Å):  6.6120  6.6120  9.5100 
Angles (°):  90  90  120 

Symmetry (theoretical): 

Space group:  176  P6_3/m 
Lattice parameters (Å):  6.4624  6.4624  9.9554 
Angles (°):  90  90  120 

Cell contents: 

Number of atoms:  30 
Number of atom types: 
Chemical composition: 

Atomic positions (theoretical):

K:  0.6667  0.3333  0.9792 
Zr:  0.0000  0.0000  0.0000 
Si:  0.3818  0.2887  0.2500 
O:  0.4582  0.0857  0.2500 
O:  0.2516  0.2743  0.1134 
K:  0.3333  0.6667  0.4792 
Zr:  0.0000  0.0000  0.5000 
Si:  0.0931  0.3818  0.7500 
O:  0.3725  0.4582  0.7500 
O:  0.9773  0.2516  0.6134 
Si:  0.7113  0.0931  0.2500 
O:  0.9143  0.3725  0.2500 
O:  0.7257  0.9773  0.1134 
Si:  0.6182  0.7113  0.7500 
O:  0.5418  0.9143  0.7500 
O:  0.7484  0.7257  0.6134 
Si:  0.9069  0.6182  0.2500 
O:  0.6275  0.5418  0.2500 
O:  0.0227  0.7484  0.1134 
Si:  0.2887  0.9069  0.7500 
O:  0.0857  0.6275  0.7500 
O:  0.2743  0.0227  0.6134 
K:  0.3333  0.6667  0.0208 
O:  0.7484  0.7257  0.8866 
K:  0.6667  0.3333  0.5208 
O:  0.0227  0.7484  0.3866 
O:  0.2743  0.0227  0.8866 
O:  0.2516  0.2743  0.3866 
O:  0.9773  0.2516  0.8866 
O:  0.7257  0.9773  0.3866 
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
E2u
-30
-30
-30
-30
2
E2u
-30
-30
-30
-30
3
Ac mode number 3 with char -90096.0
0
0
0
0
4
Ac mode number 4 with char -90096.0
0
0
0
0
5
Ac mode number 5 with char -90096.0
0
0
0
0
6
Bu
100
100
100
100
7
E1g
101
101
101
101
1.118e+39
2.9
1.667e+39
4.3
2.785e+39
7.1
8
E1g
101
101
101
101
1.118e+39
2.9
1.406e+39
3.6
2.524e+39
6.4
9
Ag
107
107
107
107
4.580e+39
11.7
1.051e+37
0.0
4.590e+39
11.7
10
Bg
113
113
113
113
11
Au
116
116
116
127
12
E2g
130
130
130
130
3.837e+38
1.0
5.248e+38
1.3
9.085e+38
2.3
13
E2g
130
130
130
130
3.836e+38
1.0
2.905e+38
0.7
6.741e+38
1.7
14
Bg
139
139
139
139
15
E2u
144
144
144
144
16
E2u
144
144
144
144
17
E1g
149
149
149
149
2.046e+39
5.2
3.137e+39
8.0
5.184e+39
13.2
18
E1g
149
149
149
149
2.046e+39
5.2
2.490e+39
6.4
4.536e+39
11.6
19
Au
151
151
151
151
20
E1u
160
160
160
160
21
E1u
160
166
166
160
22
E2u
166
166
166
166
23
E2u
166
169
169
166
24
E2g
194
194
194
194
2.593e+38
0.7
1.953e+38
0.5
4.546e+38
1.2
25
E2g
194
194
194
194
2.593e+38
0.7
3.556e+38
0.9
6.149e+38
1.6
26
Bu
204
204
204
204
27
E1g
217
217
217
217
7.473e+37
0.2
1.202e+38
0.3
1.949e+38
0.5
28
E1g
217
217
217
217
7.474e+37
0.2
8.535e+37
0.2
1.601e+38
0.4
29
E1u
232
232
232
232
30
E1u
232
232
232
232
31
E2u
232
232
232
232
32
E2u
232
238
238
232
33
Bg
244
244
244
244
34
Ag
254
254
254
254
2.190e+40
55.9
5.022e+37
0.1
2.195e+40
56.0
35
Au
256
256
256
291
36
E2g
291
291
291
291
8.377e+38
2.1
9.131e+38
2.3
1.751e+39
4.5
37
E2g
291
291
291
294
8.377e+38
2.1
8.671e+38
2.2
1.705e+39
4.4
38
E1u
294
294
294
294
39
E1u
294
298
298
298
40
Bu
298
307
307
307
41
Bu
307
307
307
311
42
Ag
311
311
311
313
7.159e+39
18.3
5.160e+37
0.1
7.210e+39
18.4
43
E1u
370
370
370
370
44
E1u
370
382
382
370
45
E2g
382
382
382
382
1.542e+38
0.4
2.001e+38
0.5
3.543e+38
0.9
46
E2g
382
386
386
382
1.542e+38
0.4
1.277e+38
0.3
2.819e+38
0.7
47
E2u
386
386
386
386
48
E2u
386
399
399
386
49
Au
401
401
401
406
50
E1g
406
406
406
406
3.286e+39
8.4
5.395e+39
13.8
8.681e+39
22.2
51
E1g
406
406
406
432
3.286e+39
8.4
3.640e+39
9.3
6.926e+39
17.7
52
Bg
432
432
432
439
53
E2g
476
476
476
476
2.361e+39
6.0
3.161e+39
8.1
5.522e+39
14.1
54
E2g
476
476
476
476
2.361e+39
6.0
1.856e+39
4.7
4.217e+39
10.8
55
E1u
483
483
483
483
56
E1u
483
493
493
483
57
Bu
493
525
525
493
58
Ag
525
526
526
525
2.255e+40
57.6
2.179e+38
0.6
2.277e+40
58.1
59
E1g
542
542
542
542
2.353e+39
6.0
3.432e+39
8.8
5.785e+39
14.8
60
E1g
542
542
542
542
2.353e+39
6.0
3.040e+39
7.8
5.393e+39
13.8
61
E2u
548
548
548
548
62
E2u
548
548
548
548
63
Ag
566
566
566
566
3.823e+40
97.6
9.504e+38
2.4
3.918e+40
100.0
64
Bu
570
570
570
570
65
Au
578
578
578
582
66
Bg
608
608
608
608
67
Ag
646
646
646
646
1.329e+40
33.9
1.385e+38
0.4
1.343e+40
34.3
68
Bu
651
651
651
651
69
E1u
756
756
756
756
70
E1u
756
758
758
756
71
E2g
758
758
758
758
6.879e+38
1.8
7.819e+38
2.0
1.470e+39
3.8
72
E2g
758
790
790
758
6.879e+38
1.8
6.798e+38
1.7
1.368e+39
3.5
73
E1u
953
953
953
953
74
E1u
953
960
960
953
75
E2g
960
960
960
960
1.659e+39
4.2
2.224e+39
5.7
3.883e+39
9.9
76
E2g
960
992
992
960
1.659e+39
4.2
1.300e+39
3.3
2.959e+39
7.6
77
Au
1004
1004
1004
1012
78
Bu
1012
1012
1012
1013
79
Ag
1013
1013
1013
1026
1.878e+38
0.5
1.315e+36
0.0
1.891e+38
0.5
80
E2u
1026
1026
1026
1026
81
E2u
1026
1026
1026
1028
82
E1g
1028
1028
1028
1028
1.525e+40
38.9
1.815e+40
46.3
3.340e+40
85.2
83
E1g
1028
1028
1028
1036
1.525e+40
38.9
2.378e+40
60.7
3.903e+40
99.6
84
Bu
1036
1036
1036
1059
85
E2g
1059
1059
1059
1059
5.900e+38
1.5
6.696e+38
1.7
1.260e+39
3.2
86
E2g
1059
1059
1059
1061
5.900e+38
1.5
5.842e+38
1.5
1.174e+39
3.0
87
E1u
1061
1061
1061
1061
88
E1u
1061
1065
1065
1065
89
Ag
1065
1137
1137
1163
6.863e+39
17.5
7.448e+38
1.9
7.608e+39
19.4
90
Bg
1184
1184
1184
1184
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.