- MIMETITE - Pb₅(AsO₄)₃Cl

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:	176		P6_3/m
Lattice parameters (Å):	10.2110	10.2110		7.4185
Angles (°):	90	90		120

Symmetry (theoretical):

Space group:	176		P6_3/m
Lattice parameters (Å):	10.1398	10.1398		7.2572
Angles (°):	90	90		120

Cell contents:

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

Atomic positions (theoretical):

Pb:	0.3333	0.6667	0.5044
Pb:	0.0098	0.2507	0.2500
As:	0.3797	0.4076	0.2500
O:	0.4925	0.3284	0.2500
O:	0.4844	0.6024	0.2500
O:	0.2627	0.3585	0.0640
Cl:	0.0000	0.0000	0.0000
Pb:	0.6667	0.3333	0.0044
Pb:	0.7591	0.0098	0.7500
As:	0.9721	0.3797	0.7500
O:	0.1640	0.4925	0.7500
O:	0.8819	0.4844	0.7500
O:	0.9042	0.2627	0.5640
Cl:	0.0000	0.0000	0.5000
Pb:	0.7493	0.7591	0.2500
As:	0.5924	0.9721	0.2500
O:	0.6716	0.1640	0.2500
O:	0.3976	0.8819	0.2500
O:	0.6415	0.9042	0.0640
Pb:	0.9902	0.7493	0.7500
As:	0.6203	0.5924	0.7500
O:	0.5075	0.6716	0.7500
O:	0.5156	0.3976	0.7500
O:	0.7373	0.6415	0.5640
Pb:	0.2409	0.9902	0.2500
As:	0.0279	0.6203	0.2500
O:	0.8360	0.5075	0.2500
O:	0.1181	0.5156	0.2500
O:	0.0958	0.7373	0.0640
Pb:	0.2507	0.2409	0.7500
As:	0.4076	0.0279	0.7500
O:	0.3284	0.8360	0.7500
O:	0.6024	0.1181	0.7500
O:	0.3585	0.0958	0.5640
Pb:	0.6667	0.3333	0.4956
O:	0.7373	0.6415	0.9360
Pb:	0.3333	0.6667	0.9956
O:	0.0958	0.7373	0.4360
O:	0.3585	0.0958	0.9360
O:	0.2627	0.3585	0.4360
O:	0.9042	0.2627	0.9360
O:	0.6415	0.9042	0.4360

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:	26
k-points
grid:	1 1 2
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:
Pb:	Tetter norm-conserving pseudopotential
As:	arsenic, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 2 local
O:	oxygen, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 2 local
Cl:	chlorine, 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):

Pb:	3.3281	0.0066	-0.0000
	-0.0066	3.3281	0.0000
	-0.0000	-0.0000	3.8814
Eig. Value:	3.3281	3.3281	3.8814
Pb:	3.1383	-0.1447	-0.0000
	-0.1150	3.5813	0.0000
	-0.0000	-0.0000	3.8800
Eig. Value:	3.1030	3.6166	3.8800
As:	4.0751	-0.4466	-0.0000
	-0.2104	4.0343	0.0000
	-0.0000	-0.0000	2.9101
Eig. Value:	4.3838	3.7255	2.9101
O:	-3.2536	0.5091	-0.0000
	0.4483	-1.6016	-0.0000
	0.0000	0.0000	-1.7492
Eig. Value:	-3.3823	-1.4729	-1.7492
O:	-2.4019	-0.3196	-0.0000
	-0.5634	-2.9835	-0.0000
	0.0000	-0.0000	-1.5962
Eig. Value:	-2.1640	-3.2214	-1.5962
O:	-1.9803	-0.2047	-0.1852
	-0.2260	-1.9334	-0.3611
	-0.1281	-0.2716	-2.6634
Eig. Value:	-2.0207	-1.7161	-2.8401
Cl:	-1.7978	-0.1354	0.0000
	0.1354	-1.7978	-0.0000
	-0.0000	-0.0000	-2.1168
Eig. Value:	-1.7978	-1.7978	-2.1168
Pb:	3.3281	0.0066	0.0000
	-0.0066	3.3281	-0.0000
	0.0000	0.0000	3.8814
Eig. Value:	3.3281	3.3281	3.8814
Pb:	3.5830	-0.1417	0.0000
	-0.1120	3.1366	-0.0000
	-0.0000	-0.0000	3.8800
Eig. Value:	3.6166	3.1030	3.8800
As:	4.3290	0.0638	0.0000
	0.3000	3.7804	-0.0000
	-0.0000	-0.0000	2.9101
Eig. Value:	4.3838	3.7255	2.9101
O:	-2.4291	-0.9243	0.0000
	-0.9851	-2.4260	0.0000
	-0.0000	-0.0000	-1.7492
Eig. Value:	-3.3823	-1.4729	-1.7492
O:	-2.4558	0.5946	0.0000
	0.3507	-2.9296	-0.0000
	-0.0000	-0.0000	-1.5962
Eig. Value:	-2.1640	-3.2214	-1.5962
O:	-1.7586	0.0980	0.2201
	0.0767	-2.1551	-0.3410
	0.1712	-0.2467	-2.6634
Eig. Value:	-1.7161	-2.0207	-2.8401
Cl:	-1.7978	-0.1354	-0.0000
	0.1354	-1.7978	0.0000
	0.0000	-0.0000	-2.1168
Eig. Value:	-1.7978	-1.7978	-2.1168
Pb:	3.3581	0.2419	-0.0000
	0.2716	3.3615	-0.0000
	0.0000	-0.0000	3.8800
Eig. Value:	3.1030	3.6166	3.8800
As:	3.7600	0.0285	0.0000
	0.2647	4.3494	0.0000
	0.0000	0.0000	2.9101
Eig. Value:	3.7255	4.3838	2.9101
O:	-1.6000	0.5064	0.0000
	0.4456	-3.2551	-0.0000
	0.0000	-0.0000	-1.7492
Eig. Value:	-1.4729	-3.3823	-1.7492
O:	-3.2205	0.0908	-0.0000
	-0.1531	-2.1649	0.0000
	-0.0000	-0.0000	-1.5962
Eig. Value:	-3.2214	-2.1640	-1.5962
O:	-2.1316	0.1387	0.4053
	0.1173	-1.7821	0.0201
	0.2993	0.0249	-2.6634
Eig. Value:	-2.0207	-1.7161	-2.8401
Pb:	3.1383	-0.1447	0.0000
	-0.1150	3.5813	0.0000
	-0.0000	-0.0000	3.8800
Eig. Value:	3.1030	3.6166	3.8800
As:	4.0751	-0.4466	0.0000
	-0.2104	4.0343	0.0000
	-0.0000	-0.0000	2.9101
Eig. Value:	4.3838	3.7255	2.9101
O:	-3.2536	0.5091	0.0000
	0.4483	-1.6016	-0.0000
	0.0000	-0.0000	-1.7492
Eig. Value:	-3.3823	-1.4729	-1.7492
O:	-2.4019	-0.3196	-0.0000
	-0.5634	-2.9835	-0.0000
	0.0000	0.0000	-1.5962
Eig. Value:	-2.1640	-3.2214	-1.5962
O:	-1.9803	-0.2047	0.1852
	-0.2260	-1.9334	0.3611
	0.1281	0.2716	-2.6634
Eig. Value:	-2.0207	-1.7161	-2.8401
Pb:	3.5830	-0.1417	0.0000
	-0.1120	3.1366	-0.0000
	-0.0000	0.0000	3.8800
Eig. Value:	3.6166	3.1030	3.8800
As:	4.3290	0.0638	0.0000
	0.3000	3.7804	0.0000
	-0.0000	-0.0000	2.9101
Eig. Value:	4.3838	3.7255	2.9101
O:	-2.4291	-0.9243	0.0000
	-0.9851	-2.4260	0.0000
	0.0000	0.0000	-1.7492
Eig. Value:	-3.3823	-1.4729	-1.7492
O:	-2.4558	0.5946	0.0000
	0.3507	-2.9296	-0.0000
	-0.0000	0.0000	-1.5962
Eig. Value:	-2.1640	-3.2214	-1.5962
O:	-1.7586	0.0980	-0.2201
	0.0767	-2.1551	0.3410
	-0.1712	0.2467	-2.6634
Eig. Value:	-1.7161	-2.0207	-2.8401
Pb:	3.3581	0.2419	-0.0000
	0.2716	3.3615	-0.0000
	-0.0000	0.0000	3.8800
Eig. Value:	3.1030	3.6166	3.8800
As:	3.7600	0.0285	-0.0000
	0.2647	4.3494	0.0000
	0.0000	0.0000	2.9101
Eig. Value:	3.7255	4.3838	2.9101
O:	-1.6000	0.5064	0.0000
	0.4456	-3.2551	0.0000
	0.0000	-0.0000	-1.7492
Eig. Value:	-1.4729	-3.3823	-1.7492
O:	-3.2205	0.0908	0.0000
	-0.1531	-2.1649	0.0000
	0.0000	0.0000	-1.5962
Eig. Value:	-3.2214	-2.1640	-1.5962
O:	-2.1316	0.1387	-0.4053
	0.1173	-1.7821	-0.0201
	-0.2993	-0.0249	-2.6634
Eig. Value:	-2.0207	-1.7161	-2.8401
Pb:	3.3281	0.0066	-0.0000
	-0.0066	3.3281	0.0000
	-0.0000	0.0000	3.8814
Eig. Value:	3.3281	3.3281	3.8814
O:	-1.9803	-0.2047	-0.1852
	-0.2260	-1.9334	-0.3611
	-0.1281	-0.2716	-2.6634
Eig. Value:	-2.0207	-1.7161	-2.8401
Pb:	3.3281	0.0066	0.0000
	-0.0066	3.3281	-0.0000
	0.0000	0.0000	3.8814
Eig. Value:	3.3281	3.3281	3.8814
O:	-1.7586	0.0980	0.2201
	0.0767	-2.1551	-0.3410
	0.1712	-0.2467	-2.6634
Eig. Value:	-1.7161	-2.0207	-2.8401
O:	-2.1316	0.1387	0.4053
	0.1173	-1.7821	0.0201
	0.2993	0.0249	-2.6634
Eig. Value:	-2.0207	-1.7161	-2.8401
O:	-1.9803	-0.2047	0.1852
	-0.2260	-1.9334	0.3611
	0.1281	0.2716	-2.6634
Eig. Value:	-2.0207	-1.7161	-2.8401
O:	-1.7586	0.0980	-0.2201
	0.0767	-2.1551	0.3410
	-0.1712	0.2467	-2.6634
Eig. Value:	-1.7161	-2.0207	-2.8401
O:	-2.1316	0.1387	-0.4053
	0.1173	-1.7821	-0.0201
	-0.2993	-0.0249	-2.6634
Eig. Value:	-2.0207	-1.7161	-2.8401

Atom type

Dielectric tensors:

	X	Y	Z
Ɛ_∞:	4.9199	0.0000	0.0000
	0.0000	4.9199	0.0000
	0.0000	0.0000	4.9662
Eig. Value:	4.9199	4.9199	4.9662
Refractive index (N):	2.2181	0.0000	0.0000
	0.0000	2.2181	0.0000
	0.0000	0.0000	2.2285
Eig. Value:	2.2181	2.2181	2.2285
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	E1g	3	3	3	3
5	E1g	3	3	3	3
6	Au	10	10	10	29
7	Bg	29	29	29	29
8	E2u	29	29	29	29
9	E2u	29	29	29	39
10	E1u	45	45	45	45
11	E1u	45	47	47	45
12	E1g	47	47	47	47	1.790e+39 0.2	2.670e+39 0.3	4.460e+39 0.5
13	E1g	47	48	48	47	1.790e+39 0.2	2.252e+39 0.3	4.042e+39 0.5
14	Bg	48	48	48	48
15	Bu	49	49	49	49
16	Ag	50	50	50	50	7.309e+40 8.3	8.601e+38 0.1	7.395e+40 8.4
17	E2g	51	51	51	51	1.381e+39 0.2	1.042e+39 0.1	2.424e+39 0.3
18	E2g	51	51	51	51	1.381e+39 0.2	1.892e+39 0.2	3.274e+39 0.4
19	E2u	58	58	58	58
20	E2u	58	58	58	58
21	E2g	63	63	63	63	6.867e+39 0.8	6.773e+39 0.8	1.364e+40 1.6
22	E2g	63	63	63	63	6.867e+39 0.8	7.820e+39 0.9	1.469e+40 1.7
23	Au	68	68	68	72
24	Bu	72	72	72	73
25	E1g	73	73	73	73	1.979e+40 2.3	3.271e+40 3.7	5.250e+40 6.0
26	E1g	73	73	73	74	1.979e+40 2.3	2.171e+40 2.5	4.151e+40 4.7
27	E1u	74	74	74	74
28	E1u	74	78	78	88
29	Ag	88	88	88	93	6.640e+40 7.6	6.796e+38 0.1	6.708e+40 7.6
30	Bg	93	93	93	93
31	E2g	93	93	93	93	1.530e+40 1.7	1.257e+40 1.4	2.788e+40 3.2
32	E2g	93	93	93	94	1.530e+40 1.7	1.994e+40 2.3	3.525e+40 4.0
33	E2u	94	94	94	94
34	E2u	94	94	94	96
35	Bu	99	99	99	99
36	E1g	100	100	100	100	1.242e+39 0.1	1.940e+39 0.2	3.182e+39 0.4
37	E1g	100	100	100	100	1.242e+39 0.1	1.477e+39 0.2	2.719e+39 0.3
38	Ag	102	102	102	102	3.313e+40 3.8	7.319e+37 0.0	3.320e+40 3.8
39	Au	105	105	105	106
40	E1u	106	106	106	106
41	E1u	106	112	112	112
42	E2g	112	112	112	112	1.746e+39 0.2	2.199e+39 0.3	3.944e+39 0.4
43	E2g	112	123	123	121	1.746e+39 0.2	1.511e+39 0.2	3.257e+39 0.4
44	Au	123	123	123	123
45	Bu	123	123	123	128
46	Ag	128	128	128	131	4.124e+39 0.5	2.459e+39 0.3	6.583e+39 0.8
47	E1u	131	131	131	131
48	E1u	131	132	132	132
49	E2u	132	132	132	132
50	E2u	132	142	142	142
51	E2g	142	142	142	142	5.814e+39 0.7	4.891e+39 0.6	1.070e+40 1.2
52	E2g	142	142	142	142	5.814e+39 0.7	7.465e+39 0.9	1.328e+40 1.5
53	Bg	142	142	142	143
54	Ag	143	143	143	146	7.968e+39 0.9	3.557e+39 0.4	1.152e+40 1.3
55	Bu	146	146	146	149
56	E1u	149	149	149	149
57	E1u	149	161	161	161
58	E2u	161	161	161	161
59	E2u	161	169	169	169
60	Bu	169	176	176	174
61	Ag	176	176	176	176	1.947e+40 2.2	1.410e+40 1.6	3.357e+40 3.8
62	Bu	176	182	182	176	1.073e+40 1.2	7.775e+39 0.9	1.851e+40 2.1
63	E2g	182	182	182	182	1.396e+40 1.6	1.918e+40 2.2	3.314e+40 3.8
64	E2g	182	183	183	182	1.396e+40 1.6	1.050e+40 1.2	2.446e+40 2.8
65	E1g	183	183	183	183	2.572e+40 2.9	3.047e+40 3.5	5.619e+40 6.4
66	E1g	183	183	183	183	2.572e+40 2.9	4.340e+40 4.9	6.912e+40 7.9
67	Au	183	187	187	185
68	E2u	200	200	200	200
69	E2u	200	200	200	200
70	E1u	207	207	207	207
71	E1u	207	213	213	207
72	Bg	215	215	215	215
73	E2u	276	276	276	276
74	E2u	276	276	276	276
75	Bg	281	281	281	281
76	E1g	298	298	298	298	5.080e+40 5.8	7.960e+40 9.1	1.304e+41 14.9
77	E1g	298	298	298	298	5.080e+40 5.8	6.010e+40 6.8	1.109e+41 12.6
78	Ag	302	302	302	302	5.104e+40 5.8	2.295e+40 2.6	7.399e+40 8.4
79	E2g	325	325	325	325	5.798e+39 0.7	7.588e+39 0.9	1.339e+40 1.5
80	E2g	325	325	325	325	5.798e+39 0.7	4.733e+39 0.5	1.053e+40 1.2
81	Bu	329	329	329	329
82	E1u	330	330	330	330
83	E1u	330	331	331	330
84	Au	331	335	335	344
85	E1g	347	347	347	347	2.285e+40 2.6	2.385e+40 2.7	4.669e+40 5.3
86	E2g	347	347	347	347	2.287e+40 2.6	2.387e+40 2.7	4.673e+40 5.3
87	E1u	347	347	347	347	2.290e+40 2.6	2.390e+40 2.7	4.680e+40 5.3
88	E1u	347	355	355	347	2.290e+40 2.6	2.476e+40 2.8	4.766e+40 5.4
89	E2u	355	355	355	355
90	E2u	355	356	356	355
91	Au	356	361	361	361
92	Bu	361	361	361	373
93	Ag	373	373	373	373	8.971e+39 1.0	1.474e+40 1.7	2.371e+40 2.7
94	E1g	373	373	373	373	8.971e+39 1.0	9.928e+39 1.1	1.890e+40 2.2
95	E1g	373	373	373	391	3.093e+40 3.5	1.498e+40 1.7	4.591e+40 5.2
96	E1u	391	391	391	391
97	E1u	391	403	403	398
98	Ag	403	408	408	403	1.364e+40 1.6	1.704e+39 0.2	1.534e+40 1.7
99	Bg	408	410	410	408
100	E2g	410	410	410	410	3.887e+39 0.4	4.863e+39 0.6	8.749e+39 1.0
101	E2g	410	416	416	410	3.887e+39 0.4	3.396e+39 0.4	7.283e+39 0.8
102	Bu	416	424	424	416
103	Ag	755	755	755	755	4.142e+40 4.7	2.312e+40 2.6	6.453e+40 7.4
104	Bu	758	758	758	758
105	E2g	761	761	761	761	4.273e+39 0.5	3.731e+39 0.4	8.004e+39 0.9
106	E2g	761	761	761	761	4.273e+39 0.5	5.349e+39 0.6	9.622e+39 1.1
107	E1u	765	765	765	765
108	E1u	765	771	771	765
109	E2u	771	771	771	771
110	E2u	771	773	773	771
111	Bg	773	777	777	773
112	E1g	777	777	777	777	1.194e+40 1.4	1.306e+40 1.5	2.500e+40 2.8
113	E1g	777	779	779	777	1.194e+40 1.4	1.977e+40 2.3	3.170e+40 3.6
114	Au	779	781	781	786
115	E1g	786	786	786	786	1.490e+40 1.7	1.309e+40 1.5	2.799e+40 3.2
116	E1g	786	786	786	786	1.490e+40 1.7	1.911e+40 2.2	3.401e+40 3.9
117	E2u	786	786	786	786
118	E2u	786	788	788	788
119	Ag	788	793	793	793	8.769e+41 99.9	7.156e+38 0.1	8.776e+41 100.0
120	Bu	793	793	793	799
121	E2g	799	799	799	799	4.699e+39 0.5	6.147e+39 0.7	1.085e+40 1.2
122	E2g	799	799	799	802	4.699e+39 0.5	3.838e+39 0.4	8.537e+39 1.0
123	E1u	802	802	802	802
124	E1u	802	808	808	808
125	Ag	808	837	837	825	3.233e+41 36.8	3.233e+40 3.7	3.556e+41 40.5
126	Bu	837	840	840	837

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.