- AKERMANITE - Ca₂MgSi₂O₇

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:	113		P-42_1m
Lattice parameters (Å):	7.8338	7.8338		5.0082
Angles (°):	90	90		90

Symmetry (theoretical):

Space group:	113		P-42_1m
Lattice parameters (Å):	7.8435	7.8435		4.9958
Angles (°):	90	90		90

Cell contents:

Number of atoms:	24
Number of atom types:	4
Chemical composition:	0

Atomic positions (theoretical):

Ca:	0.3336	0.1664	0.5070
Mg:	0.0000	0.0000	0.0000
Si:	0.1397	0.3603	0.9345
O:	0.5000	0.0000	0.1844
O:	0.1387	0.3613	0.2537
O:	0.0809	0.1867	0.7885
Ca:	0.8336	0.3336	0.4930
Si:	0.6397	0.1397	0.0655
O:	0.0000	0.5000	0.8156
O:	0.6387	0.1387	0.7463
O:	0.8133	0.0809	0.2115
Ca:	0.1664	0.6664	0.4930
Mg:	0.5000	0.5000	0.0000
Si:	0.3603	0.8603	0.0655
O:	0.3613	0.8613	0.7463
O:	0.4191	0.6867	0.2115
Ca:	0.6664	0.8336	0.5070
Si:	0.8603	0.6397	0.9345
O:	0.8613	0.6387	0.2537
O:	0.9191	0.8133	0.7885
O:	0.3133	0.4191	0.7885
O:	0.6867	0.5809	0.7885
O:	0.1867	0.9191	0.2115
O:	0.5809	0.3133	0.2115

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	A2	37	37	37	37
5	E	75	75	75	75	3.749e+37 0.1	5.155e+37 0.1	8.904e+37 0.2
6	E	75	76	76	75	3.749e+37 0.1	5.155e+37 0.1	8.904e+37 0.2
7	B1	85	85	85	85	6.582e+38 1.1	4.936e+38 0.8	1.152e+39 2.0
8	A1	126	126	126	126	3.329e+38 0.6	3.401e+37 0.1	3.669e+38 0.6
9	E	129	129	129	129	3.094e+36 0.0	4.254e+36 0.0	7.348e+36 0.0
10	E	129	147	147	129	3.093e+36 0.0	4.253e+36 0.0	7.347e+36 0.0
11	B1	147	152	152	147	1.082e+38 0.2	8.116e+37 0.1	1.894e+38 0.3
12	E	158	158	158	158	8.042e+36 0.0	1.106e+37 0.0	1.910e+37 0.0
13	E	158	163	163	158	8.040e+36 0.0	1.106e+37 0.0	1.910e+37 0.0
14	E	163	163	163	163	4.695e+38 0.8	6.456e+38 1.1	1.115e+39 1.9
15	E	163	181	181	163	4.695e+38 0.8	6.456e+38 1.1	1.115e+39 1.9
16	B2	183	183	183	186	8.271e+36 0.0	1.137e+37 0.0	1.964e+37 0.0
17	E	186	186	186	186	1.686e+38 0.3	2.319e+38 0.4	4.005e+38 0.7
18	E	186	190	190	190	1.686e+38 0.3	2.318e+38 0.4	4.005e+38 0.7
19	A1	190	193	193	206	1.132e+38 0.2	7.121e+37 0.1	1.845e+38 0.3
20	B1	206	206	206	211	3.420e+38 0.6	2.565e+38 0.4	5.985e+38 1.0
21	A2	214	214	214	214
22	A1	217	217	217	217	1.894e+39 3.2	6.530e+36 0.0	1.900e+39 3.2
23	E	220	220	220	220	4.489e+38 0.8	6.172e+38 1.0	1.066e+39 1.8
24	E	220	221	221	220	4.489e+38 0.8	6.172e+38 1.0	1.066e+39 1.8
25	B2	242	242	242	242	1.719e+37 0.0	2.363e+37 0.0	4.082e+37 0.1
26	A2	243	243	243	243
27	E	260	260	260	260	2.145e+38 0.4	2.949e+38 0.5	5.094e+38 0.9
28	E	260	263	263	260	2.145e+38 0.4	2.949e+38 0.5	5.094e+38 0.9
29	B1	263	269	269	263	3.816e+37 0.1	2.862e+37 0.0	6.679e+37 0.1
30	B2	269	272	272	272	2.136e+37 0.0	2.938e+37 0.0	5.074e+37 0.1
31	A1	272	281	281	288	2.230e+38 0.4	9.043e+36 0.0	2.321e+38 0.4
32	E	305	305	305	305	2.209e+39 3.8	3.037e+39 5.2	5.246e+39 8.9
33	E	305	307	307	305	2.209e+39 3.8	3.037e+39 5.2	5.246e+39 8.9
34	A1	307	307	307	307	5.884e+37 0.1	3.881e+37 0.1	9.766e+37 0.2
35	B2	310	310	310	338	3.474e+38 0.6	4.777e+38 0.8	8.251e+38 1.4
36	E	352	352	352	352	3.050e+38 0.5	4.194e+38 0.7	7.244e+38 1.2
37	E	352	353	353	352	3.050e+38 0.5	4.194e+38 0.7	7.244e+38 1.2
38	B2	365	365	365	385	8.496e+35 0.0	1.168e+36 0.0	2.018e+36 0.0
39	E	389	389	389	389	6.446e+37 0.1	8.863e+37 0.2	1.531e+38 0.3
40	E	389	400	400	389	6.446e+37 0.1	8.863e+37 0.2	1.531e+38 0.3
41	B1	436	436	436	436	1.539e+39 2.6	1.154e+39 2.0	2.693e+39 4.6
42	A2	437	437	437	437
43	E	458	458	458	458	1.224e+36 0.0	1.683e+36 0.0	2.907e+36 0.0
44	E	458	465	465	458	1.224e+36 0.0	1.683e+36 0.0	2.907e+36 0.0
45	A1	465	471	471	465	4.013e+39 6.8	5.516e+37 0.1	4.068e+39 6.9
46	A2	471	480	480	471
47	B2	480	499	499	481	1.624e+37 0.0	2.232e+37 0.0	3.856e+37 0.1
48	E	501	501	501	501	7.975e+37 0.1	1.097e+38 0.2	1.894e+38 0.3
49	E	501	517	517	501	7.975e+37 0.1	1.097e+38 0.2	1.894e+38 0.3
50	B1	519	519	519	519	2.547e+37 0.0	1.911e+37 0.0	4.458e+37 0.1
51	E	570	570	570	570	2.973e+38 0.5	4.088e+38 0.7	7.062e+38 1.2
52	E	570	576	576	570	2.973e+38 0.5	4.088e+38 0.7	7.062e+38 1.2
53	A1	586	586	586	586	7.719e+39 13.1	1.145e+38 0.2	7.833e+39 13.3
54	E	604	604	604	604	1.043e+37 0.0	1.435e+37 0.0	2.478e+37 0.0
55	E	604	605	605	604	1.043e+37 0.0	1.435e+37 0.0	2.478e+37 0.0
56	B2	618	618	618	644	8.463e+35 0.0	1.164e+36 0.0	2.010e+36 0.0
57	A1	644	644	644	646	2.993e+40 50.9	2.161e+37 0.0	2.995e+40 50.9
58	B2	659	659	659	661	2.192e+38 0.4	3.014e+38 0.5	5.205e+38 0.9
59	E	829	829	829	829	6.782e+37 0.1	9.325e+37 0.2	1.611e+38 0.3
60	E	829	841	841	829	6.782e+37 0.1	9.325e+37 0.2	1.611e+38 0.3
61	A1	884	884	884	884	5.829e+40 99.1	5.210e+38 0.9	5.881e+40 100.0
62	B2	887	887	887	896	5.009e+38 0.9	6.888e+38 1.2	1.190e+39 2.0
63	B1	914	914	914	914	7.632e+36 0.0	5.724e+36 0.0	1.336e+37 0.0
64	E	919	919	919	919	7.646e+38 1.3	1.051e+39 1.8	1.816e+39 3.1
65	E	919	938	938	919	7.646e+38 1.3	1.051e+39 1.8	1.816e+39 3.1
66	E	945	945	945	945	1.761e+38 0.3	2.422e+38 0.4	4.183e+38 0.7
67	E	945	973	973	945	1.761e+38 0.3	2.422e+38 0.4	4.184e+38 0.7
68	A1	973	976	976	973	3.017e+39 5.1	1.941e+39 3.3	4.958e+39 8.4
69	B2	984	984	984	985	4.307e+38 0.7	5.921e+38 1.0	1.023e+39 1.7
70	A2	985	985	985	987
71	E	987	987	987	987	7.963e+36 0.0	1.095e+37 0.0	1.891e+37 0.0
72	E	987	1012	1012	1060	7.963e+36 0.0	1.095e+37 0.0	1.891e+37 0.0

No.

Char.

ω TO

ω LOx

ω LOy

ω LOz

I ∥

I ⊥