- LAZULITE - MgAl₂(PO₄)₂(OH)₂

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.

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):	7.7518	7.7518		4.3895
Angles (°):	90	120.26		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:	0.7335	0.2668	0.0099
P:	0.2490	0.3897	0.2425
O:	0.8001	0.0214	0.1182
O:	0.6945	0.4975	0.9025
O:	0.0424	0.2693	0.1129
O:	0.4394	0.2363	0.8808
O:	0.7374	0.1443	0.7607
H:	0.6008	0.4321	0.1957
Mg:	0.0000	0.5000	0.5000
Al:	0.2665	0.7668	0.4901
P:	0.7510	0.8897	0.2575
O:	0.1999	0.5214	0.3818
O:	0.3055	0.9975	0.5975
O:	0.9576	0.7693	0.3871
O:	0.5606	0.7363	0.6192
O:	0.2626	0.6443	0.7393
H:	0.3992	0.9321	0.3043
Al:	0.2665	0.7332	0.9901
P:	0.7510	0.6103	0.7575
O:	0.1999	0.9786	0.8818
O:	0.3055	0.5025	0.0975
O:	0.9576	0.7307	0.8871
O:	0.5606	0.7637	0.1192
O:	0.2626	0.8557	0.2393
H:	0.3992	0.5679	0.8043
Al:	0.7335	0.2332	0.5099
P:	0.2490	0.1103	0.7425
O:	0.8001	0.4786	0.6182
O:	0.6945	0.0025	0.4025
O:	0.0424	0.2307	0.6129
O:	0.4394	0.2637	0.3808
O:	0.7374	0.3557	0.2607
H:	0.6008	0.0679	0.6957

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.

Parameters of the Calculation

All the calculations have been done using the ABINIT software. This is a list of the most representative parameteres used during the Raman calculation.

Number of electronic bands:	80
k-points
grid:	4 4 4
number of shifts:	1
shifts:	0.5 0.5 0.5
Kinetic energy cut-off:	40 Ha [=1088.464 eV ]
eXchange-Correlation functional:	LDA pw90

Pseudopotentials:
Mg:	magnesium, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 2 local
Al:	aluminium, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 2 local
P:	phosphorus, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 2 local
O:	oxygen, fhi98PP : Trouiller-Martins-type, GGA Perdew/Burke/Ernzerhof (1996), l= 2 local
H:	hydrogen, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 2 local

Dielectric Properties

We define:

The Born effective charges, also called dynamical charges, are tensors that correspond to the energy derivative with respect to atomic displacements and electric fields or, equivalently, to the change in atomic force due to an electric field: The sum of the Born effective charges of all nuclei in one cell must vanish, element by element, along each of the three directions of the space.
The dielectric tensors are the energy derivative with respect to two electric fields. They also relate the induced polarization to the external electric field.

Born effective charges (Z):

Mg:	2.1293	-0.0455	-0.0046
	-0.0244	2.1788	0.0345
	-0.1211	0.1123	1.9759
Eig. Value:	2.1132	2.2320	1.9387
Al:	3.2087	0.2040	-0.0135
	0.2819	3.1821	0.0126
	0.2146	-0.2488	3.0736
Eig. Value:	3.4389	2.8465	3.1790
P:	3.6885	0.0585	0.1457
	0.0279	3.5502	0.0152
	0.0649	0.0504	3.3016
Eig. Value:	3.7293	3.5378	3.2731
O:	-1.6561	-0.3404	0.3942
	-0.3900	-1.9450	0.5513
	0.4055	0.5911	-1.5814
Eig. Value:	-1.4080	-2.6487	-1.1258
O:	-1.7254	-0.3616	0.2918
	-0.2961	-1.8565	0.5426
	0.2777	0.5879	-1.5132
Eig. Value:	-1.4889	-2.5143	-1.0918
O:	-2.0315	-0.4688	-0.5532
	-0.4511	-1.6901	-0.4083
	-0.5898	-0.4200	-1.4835
Eig. Value:	-2.7459	-1.3706	-1.0885
O:	-1.8734	-0.4351	-0.5492
	-0.4381	-1.5331	-0.3940
	-0.5612	-0.3665	-1.5331
Eig. Value:	-2.5974	-1.2347	-1.1076
O:	-1.5574	-0.1106	0.1256
	-0.0737	-1.3437	0.0108
	0.1552	0.0119	-1.7091
Eig. Value:	-1.5048	-1.3051	-1.8002
H:	0.8821	-0.1726	0.1610
	-0.1402	0.5467	-0.0526
	0.0936	-0.0306	0.4572
Eig. Value:	0.9780	0.4860	0.4219
Mg:	2.1293	0.0455	-0.0046
	0.0244	2.1788	-0.0345
	-0.1211	-0.1123	1.9759
Eig. Value:	2.1132	2.2320	1.9387
Al:	3.2087	-0.2040	-0.0135
	-0.2819	3.1821	-0.0126
	0.2146	0.2488	3.0736
Eig. Value:	3.4389	2.8465	3.1790
P:	3.6885	-0.0585	0.1457
	-0.0279	3.5502	-0.0152
	0.0649	-0.0504	3.3016
Eig. Value:	3.7293	3.5378	3.2731
O:	-1.6561	0.3404	0.3942
	0.3900	-1.9450	-0.5513
	0.4055	-0.5911	-1.5814
Eig. Value:	-1.4080	-2.6487	-1.1258
O:	-1.7254	0.3616	0.2918
	0.2961	-1.8565	-0.5426
	0.2777	-0.5879	-1.5132
Eig. Value:	-1.4889	-2.5143	-1.0918
O:	-2.0315	0.4688	-0.5532
	0.4511	-1.6901	0.4083
	-0.5898	0.4200	-1.4835
Eig. Value:	-2.7459	-1.3706	-1.0885
O:	-1.8734	0.4351	-0.5492
	0.4381	-1.5331	0.3940
	-0.5612	0.3665	-1.5331
Eig. Value:	-2.5974	-1.2347	-1.1076
O:	-1.5574	0.1106	0.1256
	0.0737	-1.3437	-0.0108
	0.1552	-0.0119	-1.7091
Eig. Value:	-1.5048	-1.3051	-1.8002
H:	0.8821	0.1726	0.1610
	0.1402	0.5467	0.0526
	0.0936	0.0306	0.4572
Eig. Value:	0.9780	0.4860	0.4219
Al:	3.2087	0.2040	-0.0135
	0.2819	3.1821	0.0126
	0.2146	-0.2488	3.0736
Eig. Value:	3.4389	2.8465	3.1790
P:	3.6885	0.0585	0.1457
	0.0279	3.5502	0.0152
	0.0649	0.0504	3.3016
Eig. Value:	3.7293	3.5378	3.2731
O:	-1.6561	-0.3404	0.3942
	-0.3900	-1.9450	0.5513
	0.4055	0.5911	-1.5814
Eig. Value:	-1.4080	-2.6487	-1.1258
O:	-1.7254	-0.3616	0.2918
	-0.2961	-1.8565	0.5426
	0.2777	0.5879	-1.5132
Eig. Value:	-1.4889	-2.5143	-1.0918
O:	-2.0315	-0.4688	-0.5532
	-0.4511	-1.6901	-0.4083
	-0.5898	-0.4200	-1.4835
Eig. Value:	-2.7459	-1.3706	-1.0885
O:	-1.8734	-0.4351	-0.5492
	-0.4381	-1.5331	-0.3940
	-0.5612	-0.3665	-1.5331
Eig. Value:	-2.5974	-1.2347	-1.1076
O:	-1.5574	-0.1106	0.1256
	-0.0737	-1.3437	0.0108
	0.1552	0.0119	-1.7091
Eig. Value:	-1.5048	-1.3051	-1.8002
H:	0.8821	-0.1726	0.1610
	-0.1402	0.5467	-0.0526
	0.0936	-0.0306	0.4572
Eig. Value:	0.9780	0.4860	0.4219
Al:	3.2087	-0.2040	-0.0135
	-0.2819	3.1821	-0.0126
	0.2146	0.2488	3.0736
Eig. Value:	3.4389	2.8465	3.1790
P:	3.6885	-0.0585	0.1457
	-0.0279	3.5502	-0.0152
	0.0649	-0.0504	3.3016
Eig. Value:	3.7293	3.5378	3.2731
O:	-1.6561	0.3404	0.3942
	0.3900	-1.9450	-0.5513
	0.4055	-0.5911	-1.5814
Eig. Value:	-1.4080	-2.6487	-1.1258
O:	-1.7254	0.3616	0.2918
	0.2961	-1.8565	-0.5426
	0.2777	-0.5879	-1.5132
Eig. Value:	-1.4889	-2.5143	-1.0918
O:	-2.0315	0.4688	-0.5532
	0.4511	-1.6901	0.4083
	-0.5898	0.4200	-1.4835
Eig. Value:	-2.7459	-1.3706	-1.0885
O:	-1.8734	0.4351	-0.5492
	0.4381	-1.5331	0.3940
	-0.5612	0.3665	-1.5331
Eig. Value:	-2.5974	-1.2347	-1.1076
O:	-1.5574	0.1106	0.1256
	0.0737	-1.3437	-0.0108
	0.1552	-0.0119	-1.7091
Eig. Value:	-1.5048	-1.3051	-1.8002
H:	0.8821	0.1726	0.1610
	0.1402	0.5467	0.0526
	0.0936	0.0306	0.4572
Eig. Value:	0.9780	0.4860	0.4219

Atom type

Dielectric tensors:

	X	Y	Z
Ɛ_∞:	2.8146	0.0000	0.0336
	0.0000	2.7470	0.0000
	0.0336	0.0000	2.6884
Eig. Value:	2.8230	2.7470	2.6800
Refractive index (N):	1.6777	0.0000	0.1833
	0.0000	1.6574	0.0000
	0.1833	0.0000	1.6396
Eig. Value:	1.6802	1.6574	1.6371
Ɛ₀:	0.0000	0.0000	0.0000
	0.0000	0.0000	0.0000
	0.0000	0.0000	0.0000
Eig. Value:	0.0000	0.0000	0.0000

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	72	72	72	72	8.452e+38 0.9	1.422e+39 1.5	2.267e+39 2.3
5	Ag	84	84	84	84	4.081e+39 4.2	2.985e+39 3.1	7.066e+39 7.3
6	Au	128	128	128	128
7	Bu	146	149	146	146
8	Au	158	158	158	158
9	Ag	168	168	168	168	4.461e+39 4.6	4.006e+38 0.4	4.862e+39 5.0
10	Bu	184	186	184	186
11	Ag	186	187	186	187	4.722e+39 4.9	2.737e+37 0.0	4.749e+39 4.9
12	Au	187	189	188	188
13	Bg	198	198	198	198	3.714e+38 0.4	5.570e+38 0.6	9.284e+38 1.0
14	Ag	229	229	229	229	3.145e+39 3.2	4.146e+38 0.4	3.560e+39 3.7
15	Bg	229	229	229	229	1.491e+38 0.2	1.592e+38 0.2	3.084e+38 0.3
16	Au	233	233	236	233
17	Bu	251	251	251	251
18	Bg	258	258	258	258	2.106e+38 0.2	2.323e+38 0.2	4.429e+38 0.5
19	Ag	261	261	261	261	4.849e+39 5.0	2.737e+38 0.3	5.123e+39 5.3
20	Bg	263	263	263	263	3.005e+37 0.0	5.038e+37 0.1	8.043e+37 0.1
21	Au	272	272	273	272
22	Bu	280	281	280	280
23	Au	286	286	287	286
24	Ag	287	287	289	287	4.639e+39 4.8	5.602e+38 0.6	5.200e+39 5.3
25	Bu	289	290	291	293
26	Bu	306	309	306	309
27	Au	309	310	309	315
28	Ag	315	315	315	315	1.809e+37 0.0	2.094e+37 0.0	3.902e+37 0.0
29	Bg	315	315	315	319	3.684e+39 3.8	4.502e+38 0.5	4.135e+39 4.3
30	Bu	322	323	322	333
31	Bg	333	333	333	338	1.940e+38 0.2	3.119e+38 0.3	5.059e+38 0.5
32	Bg	343	343	343	343	3.613e+38 0.4	4.968e+38 0.5	8.582e+38 0.9
33	Ag	347	347	347	347	2.399e+39 2.5	1.148e+39 1.2	3.547e+39 3.6
34	Au	356	356	356	356
35	Bu	364	367	364	369
36	Bg	369	369	369	372	1.097e+38 0.1	1.509e+38 0.2	2.606e+38 0.3
37	Au	378	378	379	378
38	Ag	379	379	383	379	4.217e+39 4.3	7.306e+38 0.8	4.948e+39 5.1
39	Au	383	383	386	383
40	Bu	386	389	387	390
41	Bg	390	390	390	398	3.436e+38 0.4	5.627e+38 0.6	9.063e+38 0.9
42	Ag	403	403	403	403	5.121e+39 5.3	3.714e+39 3.8	8.836e+39 9.1
43	Bu	405	405	405	408
44	Au	410	410	412	410
45	Bu	421	435	421	423
46	Ag	436	436	436	436	1.051e+39 1.1	4.283e+38 0.4	1.479e+39 1.5
47	Bu	441	447	441	449
48	Au	449	449	459	459
49	Ag	459	459	469	460	1.351e+39 1.4	9.574e+38 1.0	2.308e+39 2.4
50	Bg	469	469	477	469	3.908e+38 0.4	6.588e+38 0.7	1.050e+39 1.1
51	Bu	477	480	480	480
52	Ag	480	500	496	497	3.129e+39 3.2	1.299e+39 1.3	4.428e+39 4.6
53	Bg	500	500	500	500	2.484e+38 0.3	2.641e+38 0.3	5.125e+38 0.5
54	Au	500	509	500	500
55	Au	514	514	523	514
56	Au	528	528	528	528
57	Bg	528	528	536	528	1.070e+38 0.1	1.472e+38 0.2	2.542e+38 0.3
58	Ag	536	536	538	536	1.221e+39 1.3	2.786e+37 0.0	1.249e+39 1.3
59	Bu	538	547	538	545
60	Bu	549	568	549	568
61	Au	568	576	576	576
62	Bg	576	580	576	589	2.606e+39 2.7	3.255e+39 3.3	5.861e+39 6.0
63	Au	589	589	595	591
64	Bg	595	595	602	595	1.293e+39 1.3	1.505e+39 1.5	2.799e+39 2.9
65	Bu	602	603	605	605
66	Ag	605	605	612	614	1.343e+39 1.4	5.917e+38 0.6	1.935e+39 2.0
67	Bg	614	614	614	617	2.100e+39 2.2	3.462e+39 3.6	5.563e+39 5.7
68	Au	625	625	625	625
69	Ag	627	627	627	627	5.099e+39 5.2	1.976e+39 2.0	7.075e+39 7.3
70	Bu	635	639	635	636
71	Ag	646	646	646	646	5.720e+39 5.9	5.883e+38 0.6	6.308e+39 6.5
72	Bu	647	650	647	647
73	Au	650	666	665	650
74	Bg	666	670	666	666	6.887e+37 0.1	1.148e+38 0.1	1.837e+38 0.2
75	Ag	807	807	807	807	6.070e+39 6.2	3.618e+39 3.7	9.688e+39 10.0
76	Bg	810	810	810	810	1.084e+39 1.1	1.704e+39 1.8	2.789e+39 2.9
77	Au	826	826	861	826
78	Bu	861	900	864	867
79	Au	1004	1004	1005	1004
80	Ag	1005	1005	1015	1005	1.296e+39 1.3	1.160e+39 1.2	2.455e+39 2.5
81	Bg	1015	1015	1022	1015	1.341e+39 1.4	1.672e+39 1.7	3.013e+39 3.1
82	Bu	1024	1031	1024	1025
83	Au	1047	1047	1050	1047
84	Ag	1050	1050	1057	1050	5.191e+40 53.4	6.293e+37 0.1	5.198e+40 53.4
85	Bu	1067	1075	1067	1075
86	Bg	1075	1075	1075	1087	1.485e+39 1.5	2.272e+39 2.3	3.757e+39 3.9
87	Ag	1087	1087	1087	1096	1.483e+39 1.5	1.018e+39 1.0	2.501e+39 2.6
88	Bu	1101	1104	1101	1104
89	Bg	1104	1117	1104	1117	2.637e+39 2.7	3.816e+39 3.9	6.453e+39 6.6
90	Au	1117	1139	1137	1138
91	Au	1139	1152	1152	1139
92	Bg	1152	1153	1153	1152	1.071e+39 1.1	1.225e+39 1.3	2.296e+39 2.4
93	Ag	1153	1164	1170	1153	9.372e+39 9.6	3.302e+38 0.3	9.703e+39 10.0
94	Bu	1170	1183	1183	1186
95	Ag	1194	1194	1194	1194	2.677e+39 2.8	1.020e+39 1.0	3.697e+39 3.8
96	Bu	1198	1204	1198	1204
97	Au	1204	1224	1224	1228
98	Bg	1236	1236	1236	1236	3.034e+38 0.3	4.540e+38 0.5	7.573e+38 0.8
99	Ag	3234	3234	3234	3234	8.647e+40 88.9	1.080e+40 11.1	9.728e+40 100.0
100	Au	3240	3240	3240	3240
101	Bg	3240	3240	3248	3240	9.133e+39 9.4	1.061e+40 10.9	1.974e+40 20.3
102	Bu	3248	3272	3248	3251

No.

Char.

ω TO

ω LOx

ω LOy

ω LOz

I ∥

I ⊥

I Total

You can define the size of the supercell for the visualization of the vibration.

Normalized

Raw

Options for intensity.

Single Crystal Raman spectra

Single crystal Raman spectrum

The Raman measurements performed on single crystals employ polarized lasers and allow for the selection of specific elements of the individual Raman tensors of the Raman-active modes.

By convention, in the following we assume a measurement as X(XZ)Z, i.e. incident laser polarized along the X axis, emergent light polarized along the Z axis. If the crystal is aligned with the xyz reference frame, we sample the α_xz element. As you rotate the crystal you can sample other entries of the Raman tensor or various linear combineations.