- APATITE-F - Ca₅F(PO₄)₃

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:	176		P6_3/m
Lattice parameters (Å):	4.9711	4.9711		3.6496
Angles (°):	90.0	90.0		120.0

Symmetry (theoretical):

Space group:	176		P6_3/m
Lattice parameters (Å):	9.3755	9.3755		6.9240
Angles (°):	90.0	90.0		120.0

Cell contents:

Number of atoms:	42
Number of atom types:	4
Chemical composition:	0

Atomic positions (theoretical):

Ca:	0.6667	0.3333	0.0000
Ca:	0.9929	0.2427	0.2500
P:	0.3667	0.3977	0.2500
O:	0.4807	0.3240	0.2500
O:	0.4657	0.5874	0.2500
O:	0.2551	0.3425	0.0714
F:	0.0000	0.0000	0.2500
Ca:	0.3333	0.6667	0.5000
Ca:	0.7503	0.9929	0.7500
P:	0.9690	0.3667	0.7500
O:	0.1566	0.4807	0.7500
O:	0.8784	0.4657	0.7500
O:	0.9126	0.2551	0.5714
F:	0.0000	0.0000	0.7500
Ca:	0.7573	0.7503	0.2500
P:	0.6023	0.9690	0.2500
O:	0.6760	0.1566	0.2500
O:	0.4126	0.8784	0.2500
O:	0.6575	0.9126	0.0714
Ca:	0.0071	0.7573	0.7500
P:	0.6333	0.6023	0.7500
O:	0.5193	0.6760	0.7500
O:	0.5343	0.4126	0.7500
O:	0.7449	0.6575	0.5714
Ca:	0.2497	0.0071	0.2500
P:	0.0310	0.6333	0.2500
O:	0.8434	0.5193	0.2500
O:	0.1216	0.5343	0.2500
O:	0.0874	0.7449	0.0714
Ca:	0.2427	0.2497	0.7500
P:	0.3977	0.0310	0.7500
O:	0.3240	0.8434	0.7500
O:	0.5874	0.1216	0.7500
O:	0.3425	0.0874	0.5714
Ca:	0.3333	0.6667	1.0000
O:	0.7449	0.6575	0.9286
Ca:	0.6667	0.3333	0.5000
O:	0.0874	0.7449	0.4286
O:	0.3425	0.0874	0.9286
O:	0.2551	0.3425	0.4286
O:	0.9126	0.2551	0.9286
O:	0.6575	0.9126	0.4286

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	E1g	19	19	19	19
5	E1g	19	19	19	19
6	Bg	72	72	72	72
7	Au	90	90	90	92
8	E1u	92	92	92	92
9	E1u	92	94	94	94
10	E2g	94	94	94	94	1.416e+38 0.1	1.935e+38 0.2	3.350e+38 0.3
11	E2g	94	105	105	98	1.416e+38 0.1	1.073e+38 0.1	2.489e+38 0.2
12	E2u	106	106	106	106
13	E2u	106	106	106	106
14	E1g	135	135	135	135	1.411e+38 0.1	1.717e+38 0.2	3.128e+38 0.3
15	E1g	135	135	135	135	1.411e+38 0.1	2.163e+38 0.2	3.574e+38 0.4
16	E2g	135	135	135	135	3.360e+38 0.3	2.894e+38 0.3	6.254e+38 0.6
17	E2g	135	135	135	135	3.360e+38 0.3	4.247e+38 0.4	7.607e+38 0.8
18	Au	142	142	142	142
19	Bu	142	142	142	142
20	E2u	149	149	149	149
21	E2u	149	149	149	149
22	Ag	155	155	155	155	1.061e+39 1.0	3.190e+37 0.0	1.093e+39 1.1
23	Bg	158	158	158	158
24	E2g	167	167	167	167	1.924e+38 0.2	1.474e+38 0.1	3.399e+38 0.3
25	E2g	167	167	167	167	1.924e+38 0.2	2.614e+38 0.3	4.538e+38 0.4
26	Ag	169	169	169	169	4.756e+38 0.5	1.633e+38 0.2	6.389e+38 0.6
27	Bg	175	175	175	175
28	Au	183	183	183	186
29	E1g	186	186	186	186	2.916e+38 0.3	3.368e+38 0.3	6.284e+38 0.6
30	E1g	186	186	186	186	2.916e+38 0.3	4.650e+38 0.5	7.566e+38 0.7
31	E1u	191	191	191	191
32	E1u	191	198	198	191
33	Bu	198	200	200	198
34	Bu	207	207	207	207
35	E2u	210	210	210	210
36	E2u	210	210	210	210
37	E2g	215	215	215	215	1.133e+38 0.1	1.211e+38 0.1	2.344e+38 0.2
38	E2g	215	215	215	215	1.133e+38 0.1	1.197e+38 0.1	2.331e+38 0.2
39	Ag	216	216	216	216	1.375e+39 1.4	1.852e+38 0.2	1.560e+39 1.5
40	E1u	217	217	217	217
41	E1u	217	226	226	217
42	Bg	226	229	229	226
43	Bu	229	234	234	229
44	E1g	234	234	234	234	2.410e+38 0.2	2.921e+38 0.3	5.331e+38 0.5
45	E1g	234	238	238	234	2.410e+38 0.2	3.706e+38 0.4	6.116e+38 0.6
46	E2u	238	238	238	238
47	E2u	238	239	239	238
48	Ag	239	239	239	239	5.962e+38 0.6	1.605e+38 0.2	7.567e+38 0.7
49	E1u	242	242	242	242
50	E1u	242	242	242	242
51	E2g	242	242	242	242	1.738e+38 0.2	2.012e+38 0.2	3.750e+38 0.4
52	E2g	242	256	256	242	1.738e+38 0.2	1.680e+38 0.2	3.418e+38 0.3
53	Bg	268	268	268	268
54	Ag	272	272	272	272	2.929e+39 2.9	3.624e+37 0.0	2.965e+39 2.9
55	Bu	273	273	273	273
56	Au	276	276	276	281
57	E2g	281	281	281	281	2.790e+38 0.3	3.153e+38 0.3	5.943e+38 0.6
58	E2g	281	281	281	281	2.790e+38 0.3	2.776e+38 0.3	5.565e+38 0.5
59	E1u	281	281	281	281
60	E1u	281	298	298	298
61	E2u	298	298	298	298
62	E2u	298	298	298	298
63	Bg	298	304	304	298
64	Ag	304	307	307	304	6.203e+38 0.6	4.117e+38 0.4	1.032e+39 1.0
65	E1g	308	308	308	308	7.356e+38 0.7	9.045e+38 0.9	1.640e+39 1.6
66	E1g	308	308	308	308	7.356e+38 0.7	1.203e+39 1.2	1.939e+39 1.9
67	Au	308	308	308	315
68	Bu	315	315	315	343
69	E2g	343	343	343	343	4.127e+38 0.4	5.654e+38 0.6	9.781e+38 1.0
70	E2g	343	343	343	347	4.127e+38 0.4	3.116e+38 0.3	7.243e+38 0.7
71	E1u	347	347	347	347
72	E1u	347	393	393	358
73	Bg	418	418	418	418
74	E1g	419	419	419	419	3.530e+39 3.5	5.639e+39 5.6	9.169e+39 9.1
75	E1g	419	419	419	419	3.530e+39 3.5	4.068e+39 4.0	7.598e+39 7.5
76	E2u	424	424	424	424
77	E2u	424	424	424	424
78	E2g	439	439	439	439	2.004e+39 2.0	1.926e+39 1.9	3.930e+39 3.9
79	E2g	439	439	439	439	2.004e+39 2.0	2.332e+39 2.3	4.335e+39 4.3
80	Ag	447	447	447	447	1.103e+39 1.1	8.179e+38 0.8	1.921e+39 1.9
81	E1u	454	454	454	454
82	E1u	454	455	455	454
83	Au	457	457	457	459
84	Bu	470	470	470	470
85	Au	546	546	546	547
86	E2u	547	547	547	547
87	E2u	547	547	547	555
88	E1u	555	555	555	555
89	E1u	555	558	558	559
90	E2g	559	559	559	559	1.269e+39 1.3	9.731e+38 1.0	2.242e+39 2.2
91	E2g	559	559	559	562	1.269e+39 1.3	1.724e+39 1.7	2.993e+39 3.0
92	Bu	562	562	562	570
93	Ag	570	570	570	571	2.429e+39 2.4	1.411e+39 1.4	3.839e+39 3.8
94	E1g	571	571	571	571	9.696e+38 1.0	1.092e+39 1.1	2.062e+39 2.0
95	E1g	571	571	571	578	9.696e+38 1.0	1.575e+39 1.6	2.544e+39 2.5
96	E1u	582	582	582	582
97	E1u	582	584	584	582
98	Bg	584	590	590	584
99	Ag	590	597	597	590	2.214e+39 2.2	8.994e+38 0.9	3.114e+39 3.1
100	Bu	597	598	598	597
101	E2g	598	598	598	598	2.427e+38 0.2	2.623e+38 0.3	5.050e+38 0.5
102	E2g	598	600	600	598	2.427e+38 0.2	2.534e+38 0.3	4.961e+38 0.5
103	Bu	934	934	934	934
104	E1u	935	935	935	935
105	E1u	935	935	935	935
106	Ag	935	936	936	935	1.013e+41 100.0	1.341e+36 0.0	1.013e+41 100.0
107	E2g	937	937	937	937	3.180e+38 0.3	4.025e+38 0.4	7.206e+38 0.7
108	E2g	937	937	937	937	3.180e+38 0.3	2.733e+38 0.3	5.914e+38 0.6
109	E2g	1011	1011	1011	1011	1.531e+39 1.5	1.264e+39 1.2	2.795e+39 2.8
110	E2g	1011	1011	1011	1011	1.531e+39 1.5	1.990e+39 2.0	3.521e+39 3.5
111	Au	1012	1012	1012	1012
112	E1u	1012	1012	1012	1012
113	E1u	1012	1025	1025	1025
114	E1g	1025	1025	1025	1025	1.482e+39 1.5	1.628e+39 1.6	3.110e+39 3.1
115	E1g	1025	1030	1030	1030	1.482e+39 1.5	2.448e+39 2.4	3.930e+39 3.9
116	Bu	1030	1033	1033	1033
117	Ag	1033	1038	1038	1038	6.851e+39 6.8	1.938e+39 1.9	8.789e+39 8.7
118	E2g	1038	1038	1038	1038	9.697e+38 1.0	1.085e+39 1.1	2.055e+39 2.0
119	E2g	1038	1039	1039	1039	9.697e+38 1.0	9.754e+38 1.0	1.945e+39 1.9
120	E2u	1039	1039	1039	1039
121	E2u	1039	1056	1056	1056
122	Ag	1056	1060	1060	1060	2.727e+39 2.7	1.820e+39 1.8	4.547e+39 4.5
123	Bg	1060	1062	1062	1069
124	E1u	1069	1069	1069	1069
125	E1u	1069	1104	1104	1100
126	Bu	1106	1106	1106	1106

No.

Char.

ω TO

ω LOx

ω LOy

ω LOz

I ∥

I ⊥