- TUITE - Ca₃PO₄

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:	166		R-3m
Lattice parameters (Å):	5.2487	5.2487		18.6735
Angles (°):	90	90		120

Symmetry (theoretical):

Space group:	166		R-3m
Lattice parameters (Å):	6.9527	6.9527		6.9527
Angles (°):	44.21	44.21		44.21

Cell contents:

Number of atoms:	13
Number of atom types:	3
Chemical composition:	0

Atomic positions (theoretical):

Ca:	0.0000	0.0000	0.0000
Ca:	0.2033	0.2033	0.2033
P:	0.4058	0.4058	0.4058
O:	0.3250	0.3250	0.3250
O:	0.2734	0.7537	0.2734
O:	0.7537	0.2734	0.2734
O:	0.2734	0.2734	0.7537
Ca:	0.7967	0.7967	0.7967
P:	0.5942	0.5942	0.5942
O:	0.6750	0.6750	0.6750
O:	0.7266	0.2463	0.7266
O:	0.2463	0.7266	0.7266
O:	0.7266	0.7266	0.2463

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.

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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	A2g	-58	-58	-58	-58
2	ac	0	0	0	0
3	ac	0	0	0	0
4	ac	0	0	0	0
5	Eu	35	35	35	35
6	Eu	35	64	64	35
7	A1u	114	114	114	114
8	Eu	130	130	130	130
9	Eu	130	157	157	130
10	Eg	157	157	157	157	1.387e+39 1.2	2.302e+39 2.0	3.689e+39 3.3
11	Eg	157	186	186	157	1.387e+39 1.2	1.560e+39 1.4	2.947e+39 2.6
12	Eg	186	186	186	186	2.286e+39 2.0	2.957e+39 2.6	5.242e+39 4.6
13	Eg	186	207	207	186	2.286e+39 2.0	1.741e+39 1.5	4.026e+39 3.6
14	A1g	207	217	217	207	8.552e+38 0.8	1.064e+38 0.1	9.616e+38 0.8
15	Eg	223	223	223	223	3.703e+37 0.0	3.948e+37 0.0	7.652e+37 0.1
16	Eg	223	223	223	223	3.703e+37 0.0	4.110e+37 0.0	7.813e+37 0.1
17	Eu	245	245	245	245
18	Eu	245	272	272	245
19	A2u	272	303	303	276
20	A2u	303	304	304	304
21	A1g	304	326	326	387	3.047e+39 2.7	1.526e+38 0.1	3.200e+39 2.8
22	Eg	396	396	396	396	1.038e+40 9.2	1.577e+40 13.9	2.615e+40 23.1
23	Eg	396	396	396	396	1.038e+40 9.2	1.378e+40 12.2	2.415e+40 21.3
24	Eu	447	447	447	447
25	Eu	447	448	448	447
26	Eu	540	540	540	540
27	Eu	540	551	551	540
28	Eg	551	551	551	551	2.361e+39 2.1	2.951e+39 2.6	5.311e+39 4.7
29	Eg	551	552	552	551	2.361e+39 2.1	1.822e+39 1.6	4.183e+39 3.7
30	A2u	552	556	556	593
31	A1g	620	620	620	620	3.107e+39 2.7	1.058e+39 0.9	4.165e+39 3.7
32	A2u	942	942	942	947
33	A1g	952	952	952	952	1.131e+41 99.9	1.268e+38 0.1	1.132e+41 100.0
34	Eg	982	982	982	982	6.350e+39 5.6	9.612e+39 8.5	1.596e+40 14.1
35	Eg	982	982	982	982	6.350e+39 5.6	5.052e+39 4.5	1.140e+40 10.1
36	Eu	992	992	992	992
37	Eu	992	1083	1083	992
38	A1g	1083	1088	1088	1083	1.709e+40 15.1	7.147e+39 6.3	2.424e+40 21.4
39	A2u	1089	1089	1089	1183

No.

Char.

ω TO

ω LOx

ω LOy

ω LOz

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