- PARAKELDYSHITE - Na₂ZrSi₂O₇

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. Tetter norm-conserving pseudopotential for Zr.

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):	6.6600	8.8300		5.4200
Angles (°):	92.75	94.25		72.33

Symmetry (theoretical):

Space group:	2		P-1
Lattice parameters (Å):	6.4351	8.7176		5.3822
Angles (°):	92.60	94.32		71.03

Cell contents:

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

Atomic positions (theoretical):

Na:	0.8911	0.1066	0.2630
Na:	0.3479	0.4929	0.7585
Zr:	0.2947	0.2735	0.2193
Si:	0.6532	0.1455	0.7751
Si:	0.9407	0.3363	0.6817
O:	0.2808	0.0438	0.1746
O:	0.8926	0.1626	0.7122
O:	0.4903	0.2137	0.5394
O:	0.5795	0.2477	0.0288
O:	0.0026	0.3294	0.3960
O:	0.1331	0.3399	0.8818
O:	0.2841	0.5162	0.2852
Na:	0.1089	0.8934	0.7370
Na:	0.6521	0.5071	0.2415
Zr:	0.7053	0.7265	0.7807
Si:	0.3468	0.8545	0.2249
Si:	0.0593	0.6637	0.3183
O:	0.7192	0.9562	0.8254
O:	0.1074	0.8374	0.2878
O:	0.5097	0.7863	0.4606
O:	0.4205	0.7523	0.9712
O:	0.9974	0.6706	0.6040
O:	0.8669	0.6601	0.1182
O:	0.7159	0.4838	0.7148

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	58	58	58	58	1.994e+39 3.7	4.673e+38 0.9	2.461e+39 4.6
5	Ag	90	90	90	90	2.514e+39 4.7	2.273e+39 4.2	4.788e+39 8.9
6	Au	94	95	96	102
7	Ag	111	111	111	111	1.991e+39 3.7	8.951e+38 1.7	2.886e+39 5.4
8	Au	112	120	112	120
9	Ag	120	121	120	122	3.058e+39 5.7	2.100e+39 3.9	5.158e+39 9.6
10	Ag	126	126	126	126	4.879e+38 0.9	5.540e+38 1.0	1.042e+39 1.9
11	Ag	129	129	129	129	2.121e+39 4.0	7.847e+38 1.5	2.905e+39 5.4
12	Au	154	154	154	155
13	Ag	155	155	155	157	1.313e+39 2.5	5.769e+38 1.1	1.890e+39 3.5
14	Ag	170	170	170	170	3.045e+39 5.7	7.972e+38 1.5	3.843e+39 7.2
15	Au	173	173	173	173
16	Au	174	175	176	174
17	Ag	176	176	179	176	1.313e+39 2.5	2.189e+38 0.4	1.532e+39 2.9
18	Au	182	186	183	183
19	Ag	195	195	195	195	5.433e+39 10.1	4.878e+38 0.9	5.921e+39 11.1
20	Ag	198	198	198	198	1.084e+39 2.0	1.192e+39 2.2	2.275e+39 4.2
21	Au	199	203	199	201
22	Ag	216	216	216	216	1.719e+39 3.2	6.342e+38 1.2	2.353e+39 4.4
23	Au	217	217	217	217
24	Au	222	224	223	223
25	Au	224	227	228	225
26	Ag	233	233	233	233	8.446e+38 1.6	5.977e+38 1.1	1.442e+39 2.7
27	Ag	243	243	243	243
28	Au	243	243	244	245	3.150e+39 5.9	1.984e+39 3.7	5.134e+39 9.6
29	Ag	260	260	260	260	5.843e+39 10.9	1.448e+39 2.7	7.292e+39 13.6
30	Au	264	267	269	270
31	Ag	270	270	270	270	5.185e+39 9.7	2.022e+38 0.4	5.387e+39 10.1
32	Au	278	279	288	285
33	Au	288	289	298	308
34	Ag	308	308	308	311	3.203e+39 6.0	4.737e+38 0.9	3.677e+39 6.9
35	Au	319	319	319	323
36	Au	326	332	327	332
37	Ag	332	334	332	333	2.103e+40 39.3	3.341e+39 6.2	2.438e+40 45.5
38	Au	334	348	348	348
39	Ag	348	356	355	355	7.665e+39 14.3	1.913e+39 3.6	9.578e+39 17.9
40	Au	357	368	368	357
41	Ag	368	375	376	368	3.435e+38 0.6	2.211e+38 0.4	5.646e+38 1.1
42	Ag	376	376	382	376	2.817e+40 52.6	7.651e+39 14.3	3.583e+40 66.9
43	Au	410	411	410	411
44	Au	411	413	412	413
45	Ag	413	419	413	422	2.032e+40 37.9	5.151e+39 9.6	2.547e+40 47.6
46	Ag	422	422	422	436	1.605e+39 3.0	2.054e+39 3.8	3.659e+39 6.8
47	Au	448	469	466	465
48	Ag	469	471	469	469	9.702e+38 1.8	5.739e+38 1.1	1.544e+39 2.9
49	Au	490	499	499	494
50	Ag	499	503	508	499	5.383e+39 10.1	1.497e+39 2.8	6.880e+39 12.8
51	Au	540	541	541	541
52	Ag	541	541	543	541	4.304e+39 8.0	1.455e+39 2.7	5.758e+39 10.8
53	Au	554	563	556	554
54	Ag	568	568	568	568	7.780e+38 1.5	1.181e+39 2.2	1.959e+39 3.7
55	Au	591	595	595	591
56	Ag	595	598	599	595	1.962e+39 3.7	2.188e+39 4.1	4.151e+39 7.7
57	Au	689	692	696	690
58	Ag	718	718	718	718	1.043e+40 19.5	6.467e+38 1.2	1.108e+40 20.7
59	Ag	843	843	843	843	2.119e+39 4.0	2.385e+39 4.5	4.504e+39 8.4
60	Au	858	883	861	860
61	Au	891	900	901	901
62	Ag	901	901	917	905	2.759e+40 51.5	2.597e+40 48.5	5.356e+40 100.0
63	Ag	918	918	918	918	2.610e+39 4.9	2.134e+39 4.0	4.744e+39 8.9
64	Au	920	921	922	920
65	Au	922	931	931	929
66	Ag	931	951	943	931	1.214e+40 22.7	1.564e+40 29.2	2.779e+40 51.9
67	Au	966	972	972	972
68	Ag	972	975	975	975	3.426e+39 6.4	3.374e+39 6.3	6.800e+39 12.7
69	Ag	975	982	975	982	2.550e+40 47.6	2.749e+40 51.3	5.299e+40 98.9
70	Au	985	1017	1017	1017
71	Ag	1017	1030	1035	1080	1.780e+40 33.2	2.126e+40 39.7	3.906e+40 72.9
72	Au	1085	1092	1122	1112

No.

Char.

ω TO

ω LOx

ω LOy

ω LOz

I ∥

I ⊥