- WALSTROMITE - Ca₂BaSi₃O₉

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:	2		P-1
Lattice parameters (Å):	3.5630	5.0886		3.5577
Angles (°):	69.6	102.3		96.9

Symmetry (theoretical):

Space group:	2		P-1
Lattice parameters (Å):	6.6598	9.5265		6.6281
Angles (°):	69.9	102.6		97.0

Cell contents:

Number of atoms:	30
Number of atom types:	4
Chemical composition:	0

Atomic positions (theoretical):

Ca:	0.2693	0.5085	0.7589
Ca:	0.4388	0.8272	0.9449
Ba:	0.0495	0.8502	0.3203
Si:	0.0947	0.2212	0.1508
Si:	0.2321	0.4813	0.2843
Si:	0.4404	0.1972	0.5138
O:	0.2313	0.2593	0.9691
O:	0.8984	0.1195	0.1004
O:	0.0423	0.3707	0.1972
O:	0.3733	0.5561	0.1074
O:	0.1278	0.5858	0.3654
O:	0.3569	0.3565	0.5074
O:	0.6152	0.2363	0.3707
O:	0.5088	0.0900	0.7557
O:	0.2288	0.1244	0.3920
Ca:	0.7307	0.4915	0.2411
Ca:	0.5612	0.1728	0.0551
Ba:	0.9505	0.1498	0.6797
Si:	0.9053	0.7788	0.8492
Si:	0.7679	0.5187	0.7157
Si:	0.5596	0.8028	0.4862
O:	0.7687	0.7407	0.0309
O:	0.1016	0.8805	0.8996
O:	0.9577	0.6293	0.8028
O:	0.6267	0.4439	0.8926
O:	0.8722	0.4142	0.6346
O:	0.6431	0.6435	0.4926
O:	0.3848	0.7637	0.6293
O:	0.4912	0.9100	0.2443
O:	0.7712	0.8756	0.6080

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:

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	54	54	54	54	2.327e+39 4.5	1.927e+39 3.7	4.254e+39 8.1
5	Au	64	69	68	64
6	Au	85	90	86	86
7	Ag	90	90	90	90	4.169e+38 0.8	2.211e+38 0.4	6.380e+38 1.2
8	Ag	90	91	90	90	1.091e+39 2.1	2.267e+38 0.4	1.317e+39 2.5
9	Ag	103	103	103	103	1.112e+39 2.1	1.036e+39 2.0	2.147e+39 4.1
10	Au	111	112	111	115
11	Ag	115	115	115	115	1.636e+39 3.1	9.086e+38 1.7	2.544e+39 4.9
12	Ag	123	123	123	123	2.875e+39 5.5	3.526e+39 6.8	6.401e+39 12.3
13	Ag	137	137	137	137
14	Au	137	139	140	137	8.248e+38 1.6	4.779e+38 0.9	1.303e+39 2.5
15	Au	149	151	150	151
16	Ag	151	154	151	156	1.745e+39 3.3	1.305e+39 2.5	3.050e+39 5.8
17	Au	156	161	158	159
18	Ag	167	167	167	167	8.982e+38 1.7	5.942e+38 1.1	1.492e+39 2.9
19	Au	176	180	178	177
20	Ag	184	184	184	184	8.108e+38 1.6	1.086e+39 2.1	1.897e+39 3.6
21	Au	189	195	190	194
22	Au	195	201	201	195
23	Ag	201	208	201	201	9.191e+38 1.8	9.839e+38 1.9	1.903e+39 3.6
24	Ag	214	214	214	214	1.118e+39 2.1	3.533e+38 0.7	1.471e+39 2.8
25	Au	214	216	214	215
26	Au	216	223	223	218
27	Ag	223	225	233	223	4.864e+38 0.9	1.415e+38 0.3	6.278e+38 1.2
28	Au	236	236	238	247
29	Ag	247	247	247	252	1.073e+39 2.1	3.181e+38 0.6	1.392e+39 2.7
30	Ag	255	255	255	255	3.844e+38 0.7	3.891e+38 0.7	7.734e+38 1.5
31	Au	268	268	268	268
32	Au	273	274	274	274
33	Ag	274	274	276	276	1.433e+39 2.7	1.825e+39 3.5	3.259e+39 6.2
34	Ag	283	283	283	283	1.335e+39 2.6	1.230e+39 2.4	2.565e+39 4.9
35	Ag	288	288	288	288	2.158e+39 4.1	1.266e+39 2.4	3.424e+39 6.6
36	Au	295	297	296	298
37	Au	298	302	301	303
38	Ag	303	303	303	303	2.678e+39 5.1	2.396e+39 4.6	5.074e+39 9.7
39	Au	307	309	309	309
40	Ag	309	312	315	310	4.616e+38 0.9	5.035e+38 1.0	9.651e+38 1.8
41	Au	337	338	337	338
42	Ag	338	340	338	342	1.306e+39 2.5	8.501e+38 1.6	2.157e+39 4.1
43	Ag	349	349	349	349	7.410e+38 1.4	5.652e+38 1.1	1.306e+39 2.5
44	Au	350	360	350	358
45	Ag	360	362	360	360	6.369e+39 12.2	4.492e+39 8.6	1.086e+40 20.8
46	Au	363	365	364	368
47	Ag	384	384	384	384	4.797e+39 9.2	1.861e+39 3.6	6.659e+39 12.7
48	Au	393	393	393	393
49	Ag	397	397	397	397	2.544e+39 4.9	1.815e+39 3.5	4.358e+39 8.3
50	Au	401	402	402	402
51	Ag	428	428	428	428
52	Au	428	432	433	429	2.760e+39 5.3	3.030e+39 5.8	5.790e+39 11.1
53	Ag	441	441	441	441	9.786e+38 1.9	1.013e+39 1.9	1.991e+39 3.8
54	Au	452	453	452	453
55	Au	453	459	460	458
56	Ag	460	460	462	460	2.680e+39 5.1	1.687e+38 0.3	2.848e+39 5.5
57	Au	462	470	472	470
58	Ag	479	479	479	479	2.331e+39 4.5	1.374e+39 2.6	3.705e+39 7.1
59	Au	488	491	489	492
60	Ag	492	492	492	493	1.428e+39 2.7	8.774e+38 1.7	2.305e+39 4.4
61	Au	493	493	493	493
62	Ag	493	494	499	501	5.065e+39 9.7	9.000e+38 1.7	5.965e+39 11.4
63	Au	503	507	507	507
64	Ag	507	510	519	515	6.059e+38 1.2	6.545e+38 1.3	1.260e+39 2.4
65	Au	563	564	564	564
66	Ag	570	570	570	570	1.486e+39 2.8	1.254e+39 2.4	2.739e+39 5.2
67	Ag	638	638	638	638	5.206e+40 99.7	1.779e+38 0.3	5.223e+40 100.0
68	Au	643	644	643	648
69	Au	677	687	678	692
70	Au	706	710	710	706
71	Ag	710	711	724	710	3.177e+38 0.6	2.257e+38 0.4	5.434e+38 1.0
72	Ag	724	724	731	724	2.217e+38 0.4	9.656e+37 0.2	3.182e+38 0.6
73	Au	822	822	822	823
74	Ag	823	823	823	823	4.861e+38 0.9	2.909e+37 0.1	5.152e+38 1.0
75	Au	894	897	894	899
76	Ag	899	899	899	900	1.524e+39 2.9	5.002e+38 1.0	2.024e+39 3.9
77	Au	900	906	914	905
78	Ag	914	914	914	914	4.945e+39 9.5	2.911e+39 5.6	7.856e+39 15.0
79	Ag	922	922	922	922	1.031e+39 2.0	4.494e+38 0.9	1.480e+39 2.8
80	Au	931	939	931	937
81	Ag	939	940	939	939	5.696e+39 10.9	5.013e+38 1.0	6.197e+39 11.9
82	Au	949	952	973	949
83	Au	973	983	983	983
84	Ag	983	990	990	993	3.965e+40 75.9	4.726e+38 0.9	4.012e+40 76.8
85	Ag	1013	1013	1013	1013	8.862e+38 1.7	9.738e+37 0.2	9.835e+38 1.9
86	Au	1015	1016	1016	1024
87	Au	1024	1026	1040	1028
88	Ag	1040	1040	1044	1040	1.002e+40 19.2	2.590e+39 5.0	1.261e+40 24.1
89	Au	1045	1064	1059	1064
90	Ag	1064	1088	1064	1079	6.245e+39 12.0	3.170e+39 6.1	9.414e+39 18.0

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 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 α_xz element. As you rotate the crystal you can sample other entries of the Raman tensor or various linear combineations.