1x2x1 super structure. The crystal structure is fully relaxed (both unit cell parameters and atomic positions under symmetry constraints) at 10GPa.
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:
Theo 14
Theo P2_1/n
Lattice parameters (Å):
6.7500
4.0633
6.8344
Angles (°):
90
90
90
Symmetry (theoretical):
Space group:
Theo 14
Theo P2_1/n
Lattice parameters (Å):
6.4543
7.7910
6.6941
Angles (°):
89.98
98.05
89.39
Cell contents:
Number of atoms:
48
Number of atom types:
2
Chemical composition:
0
Atomic positions (theoretical):
Si:
0.4998
0.9890
0.4942
Si:
0.0067
0.2431
0.0002
Si:
0.3510
0.5045
0.1118
Si:
0.1433
0.2469
0.3749
Si:
0.6423
0.9904
0.8806
Si:
0.8625
0.2501
0.6313
Si:
0.2769
0.2427
0.7591
Si:
0.7217
0.2155
0.2429
O:
0.3328
0.1166
0.3311
O:
0.1686
0.3664
0.1664
O:
0.6656
0.3851
0.6695
O:
0.8309
0.1361
0.8371
O:
0.4677
0.1125
0.7083
O:
0.0457
0.3588
0.7974
O:
0.5510
0.3862
0.2900
O:
0.9580
0.1382
0.2080
O:
0.2994
0.3646
0.5438
O:
0.2116
0.1224
0.9577
O:
0.7036
0.1333
0.4631
O:
0.7933
0.3770
0.0558
O:
0.4222
0.3800
0.9182
O:
0.0854
0.1439
0.5811
O:
0.5706
0.1172
0.0729
O:
0.9059
0.3695
0.4077
Si:
0.4878
0.5037
0.5058
Si:
0.9837
0.7600
0.0002
Si:
0.3657
0.9831
0.1249
Si:
0.1288
0.7622
0.3789
Si:
0.6378
0.5047
0.8737
Si:
0.8669
0.7588
0.6136
Si:
0.2658
0.7509
0.7577
Si:
0.7701
0.5356
0.2614
O:
0.3300
0.6112
0.3302
O:
0.1602
0.8686
0.1663
O:
0.6694
0.8838
0.6658
O:
0.8348
0.6291
0.8315
O:
0.4633
0.6183
0.7112
O:
0.0446
0.8615
0.7944
O:
0.5298
0.8833
0.2936
O:
0.9699
0.6331
0.2066
O:
0.3006
0.8654
0.5485
O:
0.2037
0.6301
0.9562
O:
0.7013
0.6245
0.4620
O:
0.7937
0.8800
0.0363
O:
0.4222
0.8751
0.9187
O:
0.0909
0.6345
0.5835
O:
0.5829
0.6116
0.0811
O:
0.9241
0.8703
0.4260
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:
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.
Parameters of the Calculation
All the calculations have been done using the ABINIT software. This is a list of the most representative parameteres used during the Raman calculation.
The Born effective charges, also called dynamical charges, are tensors that correspond to the energy derivative with respect to atomic displacements and electric fields or, equivalently, to the change in atomic force due to an electric field: The sum of the Born effective charges of all nuclei in one cell must vanish, element by element, along each of the three directions of the space.
The dielectric tensors are the energy derivative with respect to two electric fields. They also relate the induced polarization to the external electric field.
Born effective charges (Z):
Si:
3.8138
0.1808
0.1530
0.3902
3.7838
-0.1998
0.0382
-0.0628
3.9231
Eig. Value:
4.0883
3.4572
3.9752
Si:
3.8488
-0.0506
-0.0281
-0.1932
3.0772
0.4060
-0.0877
0.1571
3.8814
Eig. Value:
3.8085
2.9771
4.0218
Si:
3.9859
0.0002
0.0562
-0.1243
3.5291
-0.0366
-0.0337
0.0128
3.9307
Eig. Value:
3.9967
3.5206
3.9285
Si:
3.9768
-0.0631
0.0170
-0.3185
3.1715
0.0230
0.0976
-0.0333
3.9061
Eig. Value:
4.0434
3.1285
3.8824
Si:
3.9550
0.0084
0.0671
0.0420
3.8202
-0.0817
-0.1377
0.1214
3.8289
Eig. Value:
3.9668
3.7933
3.8440
Si:
3.8667
-0.0841
0.0753
-0.1724
3.1602
-0.1390
0.0151
-0.0364
4.0891
Eig. Value:
3.8733
3.1312
4.1115
Si:
3.9141
-0.0017
-0.0033
-0.0236
3.3807
-0.0391
-0.0151
-0.0049
4.0063
Eig. Value:
3.9136
3.3796
4.0079
Si:
3.7682
0.0756
-0.0230
0.2405
3.6933
0.0750
-0.0340
0.0288
3.7685
Eig. Value:
3.8940
3.5525
3.7834
O:
-1.9074
0.5201
-0.0078
0.5756
-1.9616
-0.1593
-0.0173
-0.1485
-1.9524
Eig. Value:
-1.3631
-2.5026
-1.9556
O:
-1.9524
-0.5646
0.0508
-0.5007
-1.8233
0.1744
-0.0033
0.1011
-1.9855
Eig. Value:
-2.4504
-1.3393
-1.9715
O:
-1.9268
0.4858
0.0199
0.5409
-1.8200
-0.1642
-0.0479
-0.1274
-2.0393
Eig. Value:
-2.4108
-1.3373
-2.0380
O:
-1.9144
-0.5549
-0.0202
-0.5441
-1.8207
0.1798
-0.0486
0.1083
-1.9641
Eig. Value:
-2.4306
-1.2910
-1.9776
O:
-1.9152
0.4886
0.0288
0.5193
-1.9010
-0.1784
-0.0302
-0.1079
-2.0042
Eig. Value:
-2.4358
-1.3868
-1.9977
O:
-1.9725
0.0395
-0.0334
0.0218
-1.3014
-0.0082
-0.0017
-0.0493
-1.9505
Eig. Value:
-1.9825
-1.2986
-1.9433
O:
-2.1367
0.3290
0.1027
0.3290
-1.9372
-0.1562
0.0705
-0.0576
-1.9563
Eig. Value:
-2.4192
-1.6883
-1.9227
O:
-2.0156
-0.0378
0.0142
0.0192
-1.2656
-0.0375
0.0077
-0.0550
-1.8916
Eig. Value:
-2.0166
-1.2620
-1.8942
O:
-1.9012
-0.5820
-0.0314
-0.5414
-1.8292
0.1442
-0.0674
0.1613
-2.0087
Eig. Value:
-2.4394
-1.2735
-2.0262
O:
-1.9224
0.4242
-0.0004
0.3826
-1.8227
0.4089
0.0665
0.3863
-1.9468
Eig. Value:
-2.4300
-1.2942
-1.9677
O:
-1.9035
-0.5811
-0.0890
-0.6040
-1.7838
0.1106
-0.0412
0.1034
-2.0044
Eig. Value:
-2.4405
-1.2286
-2.0226
O:
-1.8797
0.4690
0.0528
0.3747
-2.0517
0.1144
0.1028
0.1228
-2.1751
Eig. Value:
-1.5076
-2.4049
-2.1940
O:
-1.9538
-0.4245
-0.0179
-0.3773
-1.8469
-0.4236
0.0588
-0.3749
-1.9576
Eig. Value:
-2.4586
-1.3236
-1.9762
O:
-1.9855
0.0614
0.0094
0.0592
-1.2394
0.0162
0.0058
-0.0112
-1.9846
Eig. Value:
-1.9954
-1.2345
-1.9796
O:
-1.9445
-0.4177
0.0322
-0.4077
-1.8817
-0.4337
0.0753
-0.3532
-2.0254
Eig. Value:
-2.4779
-1.3339
-2.0398
O:
-2.0167
0.2988
-0.1167
0.2700
-1.8963
0.3190
-0.0845
0.2524
-2.0383
Eig. Value:
-2.4318
-1.5926
-1.9269
Si:
3.9140
0.0249
-0.1236
0.1502
3.4854
-0.0296
-0.0060
-0.0015
3.9768
Eig. Value:
3.8837
3.4682
4.0244
Si:
3.8813
-0.0330
-0.0014
-0.2419
3.4798
0.1951
0.2109
-0.1210
3.8886
Eig. Value:
4.0003
3.4274
3.8220
Si:
3.7286
0.1407
-0.1112
0.2253
3.7712
-0.0221
0.0129
-0.0311
4.0213
Eig. Value:
3.5649
3.9097
4.0466
Si:
3.7736
0.0043
-0.0117
-0.0683
3.4050
0.1602
-0.1163
0.1183
3.9804
Eig. Value:
3.7556
3.3724
4.0312
Si:
3.8023
0.1053
-0.0193
0.2357
3.4464
-0.2939
0.0631
-0.1273
4.0036
Eig. Value:
3.8563
3.3170
4.0790
Si:
3.9232
0.0586
-0.1246
-0.0509
3.4310
0.0564
0.0272
0.0656
3.8466
Eig. Value:
3.9480
3.4220
3.8309
Si:
3.8561
-0.0248
0.0461
0.0780
3.5116
-0.0035
-0.0099
0.0004
3.9738
Eig. Value:
3.8554
3.5096
3.9766
Si:
3.6841
0.0837
0.0458
0.1962
3.7023
0.0980
-0.0062
0.0342
3.7735
Eig. Value:
3.5485
3.8729
3.7384
O:
-1.9096
0.5668
-0.0211
0.5328
-1.8227
-0.1811
-0.0095
-0.1723
-2.0276
Eig. Value:
-2.4471
-1.2877
-2.0252
O:
-1.9227
-0.4815
-0.0118
-0.6236
-1.8389
0.1861
-0.1015
0.0923
-2.0461
Eig. Value:
-2.4424
-1.3001
-2.0653
O:
-1.9630
0.5094
-0.0469
0.5786
-1.8716
-0.1527
-0.0536
-0.1113
-1.9918
Eig. Value:
-2.4691
-1.3447
-2.0126
O:
-1.8936
-0.6020
0.0422
-0.5720
-1.9345
0.1786
0.0061
0.1786
-1.9883
Eig. Value:
-1.3094
-2.5403
-1.9666
O:
-1.9374
0.5097
0.0305
0.5481
-1.8264
-0.1670
-0.0660
-0.0982
-1.9766
Eig. Value:
-2.4267
-1.3310
-1.9827
O:
-1.9608
0.0258
0.0393
0.0074
-1.3734
-0.0572
0.0163
-0.0798
-1.9704
Eig. Value:
-1.9390
-1.3653
-2.0003
O:
-1.4689
0.0252
-0.1349
0.0224
-1.5407
0.0004
-0.1700
0.0132
-1.9737
Eig. Value:
-1.4227
-1.5441
-2.0165
O:
-1.9307
-0.5273
0.0283
-0.5565
-1.8482
0.1516
-0.0388
0.0865
-2.0698
Eig. Value:
-2.4489
-1.3347
-2.0651
O:
-1.9437
-0.5539
0.0005
-0.6297
-1.8202
0.1858
0.0289
0.1743
-1.9940
Eig. Value:
-2.5112
-1.2654
-1.9813
O:
-1.9253
0.4377
-0.0059
0.4161
-1.8824
0.4754
0.0694
0.4046
-1.9513
Eig. Value:
-2.5081
-1.2813
-1.9697
O:
-1.9923
-0.4695
0.0237
-0.4679
-1.8040
-0.4589
0.0639
-0.3517
-1.9414
Eig. Value:
-2.4894
-1.2423
-2.0060
O:
-1.9567
0.4960
-0.1657
0.5908
-1.8906
0.1282
-0.1397
0.1001
-1.4620
Eig. Value:
-2.5025
-1.3712
-1.4355
O:
-1.9575
-0.3976
0.0375
-0.4625
-1.9068
-0.4885
0.0972
-0.3363
-1.9636
Eig. Value:
-2.4958
-1.3042
-2.0279
O:
-1.9485
0.0417
-0.0444
0.0598
-1.4942
0.0106
-0.0388
-0.0483
-1.9237
Eig. Value:
-1.9814
-1.4873
-1.8977
O:
-1.9967
-0.0652
-0.0483
-0.0264
-1.3132
0.0210
-0.0223
0.0085
-1.9418
Eig. Value:
-2.0157
-1.3097
-1.9263
O:
-1.7369
0.1055
0.2690
0.1003
-1.4985
0.0929
0.2948
0.0691
-1.6917
Eig. Value:
-1.9980
-1.5979
-1.3311
Atom type
X
Y
Z
Dielectric tensors:
X
Y
Z
Ɛ∞:
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
Eig. Value:
0.0000
0.0000
0.0000
Refractive index (N):
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
Eig. Value:
0.0000
0.0000
0.0000
Ɛ0:
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
Eig. Value:
0.0000
0.0000
0.0000
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
0
0
0
0
2
0
0
0
0
3
0
0
0
0
4
0
229
229
229
5
0
249
249
248
6
0
264
265
264
7
0
272
272
273
8
0
279
281
279
9
0
292
292
292
10
0
305
308
306
11
0
314
315
314
12
0
320
320
320
13
0
322
322
322
14
0
324
324
325
15
0
335
336
335
16
0
337
337
337
17
0
353
353
353
18
0
355
355
355
19
0
360
359
359
20
0
364
364
364
21
0
368
368
368
22
0
376
377
376
23
0
378
378
378
24
0
390
389
390
25
0
390
391
391
26
0
397
396
398
27
0
403
403
403
28
0
413
413
413
29
0
416
417
416
30
0
419
422
420
31
0
424
425
424
32
0
429
428
428
33
0
434
434
434
34
0
437
438
437
35
0
442
442
442
36
0
446
447
447
37
0
460
457
457
38
0
462
460
463
39
0
467
468
469
40
0
473
472
473
41
0
478
477
477
42
0
487
488
488
43
0
489
490
490
44
0
492
494
492
45
0
497
497
497
46
0
500
500
500
47
0
506
511
506
48
0
512
513
512
49
0
521
515
514
50
0
523
524
523
51
0
524
527
526
52
0
534
535
534
53
0
536
540
539
54
0
546
548
547
55
0
555
552
550
56
0
556
556
556
57
0
566
564
560
58
0
567
567
567
59
0
572
571
571
60
0
577
575
572
61
0
581
578
578
62
0
587
583
583
63
0
590
589
590
64
0
594
596
591
65
0
599
598
598
66
0
602
600
601
67
0
607
606
606
68
0
608
610
610
69
0
622
618
617
70
0
625
623
624
71
0
630
628
629
72
0
633
632
632
73
0
640
638
639
74
0
651
644
645
75
0
653
651
651
76
0
654
655
655
77
0
658
656
655
78
0
664
666
664
79
0
674
674
672
80
0
679
679
677
81
0
685
684
681
82
0
690
685
689
83
0
694
691
690
84
0
697
696
696
85
0
701
700
699
86
0
705
706
709
87
0
714
712
711
88
0
720
719
717
89
0
727
730
729
90
0
731
732
732
91
0
734
737
737
92
0
739
739
746
93
0
750
748
752
94
0
754
754
755
95
0
757
760
765
96
0
767
768
772
97
0
775
776
775
98
0
777
777
778
99
0
783
783
791
100
0
791
792
791
101
0
794
795
797
102
0
801
801
806
103
0
809
807
809
104
0
816
814
814
105
0
826
818
827
106
0
828
833
829
107
0
837
837
837
108
0
843
843
841
109
0
846
846
846
110
0
849
850
851
111
0
856
854
853
112
0
862
862
862
113
0
864
866
866
114
0
870
871
871
115
0
881
875
881
116
0
887
886
883
117
0
891
892
893
118
0
902
898
902
119
0
905
904
905
120
0
906
907
907
121
0
918
918
918
122
0
922
919
926
123
0
926
926
926
124
0
935
933
937
125
0
943
943
943
126
0
947
950
951
127
0
953
954
954
128
0
957
956
961
129
0
968
966
969
130
0
971
971
973
131
0
981
980
979
132
0
989
987
987
133
0
994
995
992
134
0
1009
1009
1009
135
0
1012
1017
1018
136
0
1020
1021
1022
137
0
1030
1030
1030
138
0
1064
1061
1060
139
0
1065
1066
1066
140
0
1076
1075
1073
141
0
1081
1080
1087
142
0
1117
1112
1106
143
0
1133
1136
1152
144
0
1226
1211
1204
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.
Normalized
Raw
Options for intensity.
Single Crystal Raman spectra
Single crystal 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.
The Raman measurements performed on single crystals employ polarized lasers and allow for the selection of specific elements of the individual Raman tensors of the Raman-active modes.
By convention, in the following we assume a measurement as X(XZ)Z, i.e. incident laser polarized along the X axis, emergent light polarized along the Z axis. If the crystal is aligned with the xyz reference frame, we sample the αxz element. As you rotate the crystal you can sample other entries of the Raman tensor or various linear combineations.
Horizontal:
Xmin:
Xmax:
Vertical:
Ymin:
Ymax:
Choose the orientation of the crystal with respect to the reference system: