- LAZULITE - MgAl₂(PO₄)₂(OH)₂

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:	14		P2_1/c
Lattice parameters (Å):	7.1440	7.2780		7.2280
Angles (°):	90	120.51		90

Symmetry (theoretical):

Space group:	14		P2_1/c
Lattice parameters (Å):	7.0540	7.3500		7.2375
Angles (°):	90	120.36		90

Cell contents:

Number of atoms:	34
Number of atom types:	5
Chemical composition:	0

Atomic positions (theoretical):

Mg:	0.0000	0.0000	0.0000
Al:	0.7350	0.2670	0.0109
P:	0.2491	0.3923	0.2443
O:	0.8016	0.0216	0.1182
O:	0.6971	0.4939	0.8991
O:	0.0454	0.2703	0.1170
O:	0.4418	0.2300	0.8809
O:	0.7403	0.1450	0.7610
H:	0.6045	0.4295	0.1985
Mg:	0.0000	0.5000	0.5000
Al:	0.2650	0.7670	0.4891
P:	0.7509	0.8923	0.2557
O:	0.1984	0.5216	0.3818
O:	0.3029	0.9939	0.6009
O:	0.9546	0.7703	0.3830
O:	0.5582	0.7300	0.6191
O:	0.2597	0.6450	0.7390
H:	0.3955	0.9295	0.3015
Al:	0.2650	0.7330	0.9891
P:	0.7509	0.6077	0.7557
O:	0.1984	0.9784	0.8818
O:	0.3029	0.5061	0.1009
O:	0.9546	0.7297	0.8830
O:	0.5582	0.7700	0.1191
O:	0.2597	0.8550	0.2390
H:	0.3955	0.5705	0.8015
Al:	0.7350	0.2330	0.5109
P:	0.2491	0.1077	0.7443
O:	0.8016	0.4784	0.6182
O:	0.6971	0.0061	0.3991
O:	0.0454	0.2297	0.6170
O:	0.4418	0.2700	0.3809
O:	0.7403	0.3550	0.2610
H:	0.6045	0.0705	0.6985

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	Bg	95	95	95	95	5.566e+38 0.6	9.215e+38 1.0	1.478e+39 1.6
5	Ag	102	102	102	102	3.048e+39 3.2	2.052e+39 2.2	5.100e+39 5.4
6	Au	128	128	128	128
7	Bu	159	160	159	159
8	Ag	164	164	164	164	5.335e+39 5.7	3.724e+38 0.4	5.707e+39 6.0
9	Au	169	169	169	169
10	Au	175	175	175	175
11	Bu	176	181	176	180
12	Ag	186	186	186	186	5.161e+39 5.5	3.095e+37 0.0	5.192e+39 5.5
13	Bg	188	188	188	188	4.116e+38 0.4	6.001e+38 0.6	1.012e+39 1.1
14	Ag	220	220	220	220	2.940e+39 3.1	3.639e+38 0.4	3.304e+39 3.5
15	Au	220	220	225	220
16	Bg	225	225	225	225	1.095e+38 0.1	1.184e+38 0.1	2.279e+38 0.2
17	Bu	234	234	234	234
18	Bg	247	247	247	247	2.201e+38 0.2	2.554e+38 0.3	4.755e+38 0.5
19	Ag	252	252	252	252	4.085e+39 4.3	2.370e+38 0.3	4.322e+39 4.6
20	Bg	252	252	252	252	3.707e+37 0.0	4.438e+37 0.0	8.145e+37 0.1
21	Au	259	259	260	259
22	Au	266	266	269	266
23	Ag	269	269	270	269	5.921e+39 6.3	6.718e+38 0.7	6.592e+39 7.0
24	Bu	270	273	273	276
25	Bu	277	278	277	281
26	Bu	295	297	295	297
27	Au	297	297	298	301
28	Bg	301	301	301	308	1.711e+37 0.0	2.353e+37 0.0	4.064e+37 0.0
29	Ag	308	308	308	310	4.050e+39 4.3	5.291e+38 0.6	4.579e+39 4.8
30	Bg	318	318	318	318	2.173e+38 0.2	3.131e+38 0.3	5.304e+38 0.6
31	Bu	319	320	319	326
32	Bg	333	333	333	333	2.489e+38 0.3	3.162e+38 0.3	5.651e+38 0.6
33	Ag	334	334	334	334	1.133e+39 1.2	5.582e+38 0.6	1.691e+39 1.8
34	Au	343	343	344	343
35	Bu	347	349	347	355
36	Bg	362	362	362	362	2.252e+37 0.0	2.796e+37 0.0	5.048e+37 0.1
37	Au	363	363	364	363
38	Ag	365	365	365	365	4.617e+39 4.9	8.688e+38 0.9	5.486e+39 5.8
39	Au	368	368	368	368
40	Bu	368	369	373	378
41	Bg	378	378	378	385	3.469e+38 0.4	5.729e+38 0.6	9.197e+38 1.0
42	Bu	388	388	388	389
43	Au	397	397	398	397
44	Ag	398	398	400	398	4.658e+39 4.9	3.468e+39 3.7	8.126e+39 8.6
45	Bu	402	417	402	403
46	Ag	417	421	417	417	1.110e+39 1.2	5.087e+38 0.5	1.619e+39 1.7
47	Au	425	425	428	425
48	Bu	428	429	437	437
49	Ag	437	437	445	445	8.108e+38 0.9	3.924e+38 0.4	1.203e+39 1.3
50	Bg	445	445	463	445	4.092e+38 0.4	6.894e+38 0.7	1.099e+39 1.2
51	Bu	463	466	466	466
52	Ag	466	482	477	475	3.442e+39 3.6	1.495e+39 1.6	4.937e+39 5.2
53	Bg	482	486	482	482	1.879e+38 0.2	1.999e+38 0.2	3.878e+38 0.4
54	Au	486	492	486	486
55	Ag	494	494	494	494	1.008e+39 1.1	1.076e+38 0.1	1.115e+39 1.2
56	Au	494	494	495	494
57	Bu	498	498	498	498
58	Bg	498	501	498	501	8.715e+37 0.1	1.042e+38 0.1	1.913e+38 0.2
59	Au	501	513	520	528
60	Bu	528	551	528	551
61	Au	551	562	559	562
62	Bg	562	564	562	566	1.804e+39 1.9	2.209e+39 2.3	4.013e+39 4.2
63	Au	570	570	584	570
64	Bg	584	584	584	584	2.175e+39 2.3	2.666e+39 2.8	4.840e+39 5.1
65	Bu	584	584	593	593
66	Ag	593	593	594	594	7.303e+38 0.8	3.828e+38 0.4	1.113e+39 1.2
67	Bg	603	603	603	603	1.818e+39 1.9	2.970e+39 3.1	4.789e+39 5.1
68	Au	615	615	615	615
69	Ag	616	616	616	616	4.956e+39 5.2	1.776e+39 1.9	6.732e+39 7.1
70	Bu	620	622	620	620
71	Ag	629	629	629	629	5.304e+39 5.6	5.187e+38 0.5	5.823e+39 6.2
72	Bu	631	635	631	631
73	Au	635	645	645	635
74	Bg	645	649	646	645	6.248e+37 0.1	1.047e+38 0.1	1.672e+38 0.2
75	Ag	790	790	790	790	5.455e+39 5.8	3.005e+39 3.2	8.460e+39 9.0
76	Bg	793	793	793	793	9.782e+38 1.0	1.546e+39 1.6	2.524e+39 2.7
77	Au	807	807	838	807
78	Bu	838	875	841	843
79	Au	969	969	969	969
80	Ag	969	969	982	969	1.461e+39 1.5	1.465e+39 1.6	2.926e+39 3.1
81	Bg	982	982	987	982	1.788e+39 1.9	2.248e+39 2.4	4.035e+39 4.3
82	Bu	994	1003	994	994
83	Au	1015	1015	1020	1015
84	Ag	1020	1020	1025	1020	4.944e+40 52.4	1.902e+37 0.0	4.946e+40 52.4
85	Bu	1034	1039	1034	1049
86	Bg	1049	1049	1049	1058	1.468e+39 1.6	2.263e+39 2.4	3.731e+39 4.0
87	Ag	1058	1058	1058	1070	3.052e+39 3.2	1.088e+39 1.2	4.140e+39 4.4
88	Bg	1070	1070	1070	1071	2.734e+39 2.9	3.935e+39 4.2	6.669e+39 7.1
89	Bu	1074	1088	1074	1088
90	Au	1088	1111	1111	1105
91	Au	1111	1121	1121	1111
92	Bg	1121	1122	1122	1121	1.082e+39 1.1	1.231e+39 1.3	2.313e+39 2.4
93	Ag	1122	1139	1144	1122	1.044e+40 11.1	3.714e+38 0.4	1.081e+40 11.5
94	Bu	1144	1155	1156	1159
95	Ag	1168	1168	1168	1168	2.072e+39 2.2	8.492e+38 0.9	2.921e+39 3.1
96	Bu	1169	1178	1169	1178
97	Au	1178	1195	1195	1201
98	Bg	1210	1210	1210	1210	3.869e+38 0.4	5.882e+38 0.6	9.751e+38 1.0
99	Ag	3273	3273	3273	3273	8.426e+40 89.2	1.016e+40 10.8	9.442e+40 100.0
100	Au	3278	3278	3278	3278
101	Bg	3278	3278	3284	3278	9.113e+39 9.7	1.065e+40 11.3	1.976e+40 20.9
102	Bu	3284	3305	3284	3287

No.

Char.

ω TO

ω LOx

ω LOy

ω LOz

I ∥

I ⊥