- CROCOITE - PbCrO₄

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. Tetter norm-conserving pseudopotential for Cr.

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/n
Lattice parameters (Å):	7.1200	7.4300		6.7900
Angles (°):	90	102.42		90

Symmetry (theoretical):

Space group:	14		P2_1/n
Lattice parameters (Å):	7.0193	7.3464		6.7203
Angles (°):	90	102.70		90

Cell contents:

Number of atoms:	24
Number of atom types:	3
Chemical composition:	0

Atomic positions (theoretical):

Pb:	0.2228	0.1448	0.3995
Cr:	0.2016	0.1659	0.8808
O:	0.0277	0.0987	0.6799
O:	0.1217	0.3504	0.9851
O:	0.2476	0.5064	0.4366
O:	0.3914	0.2154	0.7782
Pb:	0.2772	0.6448	0.1005
Cr:	0.2984	0.6659	0.6192
O:	0.4723	0.5987	0.8201
O:	0.3783	0.8504	0.5149
O:	0.2524	0.0064	0.0634
O:	0.1086	0.7154	0.7218
Pb:	0.7772	0.8552	0.6005
Cr:	0.7984	0.8341	0.1192
O:	0.9723	0.9013	0.3201
O:	0.8783	0.6496	0.0149
O:	0.7524	0.4936	0.5634
O:	0.6086	0.7846	0.2218
Pb:	0.7228	0.3552	0.8995
Cr:	0.7016	0.3341	0.3808
O:	0.5277	0.4013	0.1799
O:	0.6217	0.1496	0.4851
O:	0.7476	0.9936	0.9366
O:	0.8914	0.2846	0.2782

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:	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:
Pb:	Tetter norm-conserving pseudopotential
Cr:	chromium, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 1 local
O:	oxygen, fhi98PP : Trouiller-Martins-type, GGA Perdew/Burke/Ernzerhof (1996), 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:	3.7026	-0.0619	0.1559
	-0.0227	3.8637	-0.0123
	-0.0231	0.8162	4.0536
Eig. Value:	3.7313	3.5159	4.3727
Cr:	2.7986	-0.0610	-0.2152
	-0.0994	3.2314	0.2012
	0.1509	-0.3495	3.7042
Eig. Value:	2.7820	3.2362	3.7160
O:	-1.5659	-0.6571	-0.8184
	-0.8511	-1.2019	-0.7501
	-1.3422	-0.9469	-2.6734
Eig. Value:	-1.0191	-0.6081	-3.8140
O:	-1.6046	0.5578	0.2050
	0.6500	-2.9110	-1.0140
	0.2870	-1.1662	-0.9826
Eig. Value:	-1.3938	-3.6135	-0.4909
O:	-0.5154	-0.2013	0.2486
	-0.0916	-2.2781	-1.0727
	0.1098	-1.4192	-2.7526
Eig. Value:	-0.4501	-1.3117	-3.7843
O:	-2.8153	-0.7500	0.4241
	-0.7399	-0.7042	0.0307
	0.8176	0.1608	-1.3491
Eig. Value:	-3.2543	-0.4553	-1.1591
Pb:	3.7026	0.0619	0.1559
	0.0227	3.8637	0.0123
	-0.0231	-0.8162	4.0536
Eig. Value:	3.7313	3.5159	4.3727
Cr:	2.7986	0.0610	-0.2152
	0.0994	3.2314	-0.2012
	0.1509	0.3495	3.7042
Eig. Value:	2.7820	3.2362	3.7160
O:	-1.5659	0.6571	-0.8184
	0.8511	-1.2019	0.7501
	-1.3422	0.9469	-2.6734
Eig. Value:	-1.0191	-0.6081	-3.8140
O:	-1.6046	-0.5578	0.2050
	-0.6500	-2.9110	1.0140
	0.2870	1.1662	-0.9826
Eig. Value:	-1.3938	-3.6135	-0.4909
O:	-0.5154	0.2013	0.2486
	0.0916	-2.2781	1.0727
	0.1098	1.4192	-2.7526
Eig. Value:	-0.4501	-1.3117	-3.7843
O:	-2.8153	0.7500	0.4241
	0.7399	-0.7042	-0.0307
	0.8176	-0.1608	-1.3491
Eig. Value:	-3.2543	-0.4553	-1.1591
Pb:	3.7026	-0.0619	0.1559
	-0.0227	3.8637	-0.0123
	-0.0231	0.8162	4.0536
Eig. Value:	3.7313	3.5159	4.3727
Cr:	2.7986	-0.0610	-0.2152
	-0.0994	3.2314	0.2012
	0.1509	-0.3495	3.7042
Eig. Value:	2.7820	3.2362	3.7160
O:	-1.5659	-0.6571	-0.8184
	-0.8511	-1.2019	-0.7501
	-1.3422	-0.9469	-2.6734
Eig. Value:	-1.0191	-0.6081	-3.8140
O:	-1.6046	0.5578	0.2050
	0.6500	-2.9110	-1.0140
	0.2870	-1.1662	-0.9826
Eig. Value:	-1.3938	-3.6135	-0.4909
O:	-0.5154	-0.2013	0.2486
	-0.0916	-2.2781	-1.0727
	0.1098	-1.4192	-2.7526
Eig. Value:	-0.4501	-1.3117	-3.7843
O:	-2.8153	-0.7500	0.4241
	-0.7399	-0.7042	0.0307
	0.8176	0.1608	-1.3491
Eig. Value:	-3.2543	-0.4553	-1.1591
Pb:	3.7026	0.0619	0.1559
	0.0227	3.8637	0.0123
	-0.0231	-0.8162	4.0536
Eig. Value:	3.7313	3.5159	4.3727
Cr:	2.7986	0.0610	-0.2152
	0.0994	3.2314	-0.2012
	0.1509	0.3495	3.7042
Eig. Value:	2.7820	3.2362	3.7160
O:	-1.5659	0.6571	-0.8184
	0.8511	-1.2019	0.7501
	-1.3422	0.9469	-2.6734
Eig. Value:	-1.0191	-0.6081	-3.8140
O:	-1.6046	-0.5578	0.2050
	-0.6500	-2.9110	1.0140
	0.2870	1.1662	-0.9826
Eig. Value:	-1.3938	-3.6135	-0.4909
O:	-0.5154	0.2013	0.2486
	0.0916	-2.2781	1.0727
	0.1098	1.4192	-2.7526
Eig. Value:	-0.4501	-1.3117	-3.7843
O:	-2.8153	0.7500	0.4241
	0.7399	-0.7042	-0.0307
	0.8176	-0.1608	-1.3491
Eig. Value:	-3.2543	-0.4553	-1.1591

Atom type

Dielectric tensors:

	X	Y	Z
Ɛ_∞:	5.0925	0.0000	0.0000
	0.0000	5.3057	0.0000
	0.0000	0.0000	6.3080
Eig. Value:	5.0925	5.3057	6.3080
Refractive index (N):	2.2567	0.0000	0.0000
	0.0000	2.3034	0.0000
	0.0000	0.0000	2.5116
Eig. Value:	2.2567	2.3034	2.5116
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	43	43	43	43	1.986e+40 0.7	2.115e+40 0.7	4.101e+40 1.4
5	Ag	46	46	46	46	5.848e+40 2.0	3.010e+40 1.0	8.858e+40 3.0
6	Bu	49	49	49	49
7	Ag	52	52	52	52	3.772e+39 0.1	1.820e+39 0.1	5.592e+39 0.2
8	Ag	57	57	57	57	6.314e+40 2.1	4.076e+40 1.4	1.039e+41 3.5
9	Au	59	59	59	59
10	Bg	59	59	59	59	1.266e+38 0.0	1.929e+38 0.0	3.195e+38 0.0
11	Bu	59	60	60	59	1.234e+40 0.4	1.881e+40 0.6	3.115e+40 1.1
12	Bg	65	65	65	65	9.000e+39 0.3	1.089e+40 0.4	1.989e+40 0.7
13	Bg	77	77	77	77	4.672e+39 0.2	7.735e+39 0.3	1.241e+40 0.4
14	Bu	83	83	85	83
15	Au	85	92	93	87
16	Ag	93	93	96	93	2.977e+40 1.0	2.064e+40 0.7	5.041e+40 1.7
17	Au	96	99	99	99
18	Ag	99	101	99	101	1.953e+40 0.7	1.036e+39 0.0	2.057e+40 0.7
19	Bu	101	109	109	108
20	Ag	109	115	111	109	5.836e+40 2.0	4.232e+40 1.4	1.007e+41 3.4
21	Bg	115	117	115	115	1.747e+40 0.6	2.129e+40 0.7	3.876e+40 1.3
22	Bu	117	119	119	117
23	Au	119	122	124	120
24	Au	124	126	126	126
25	Bg	126	138	137	138	1.496e+40 0.5	1.605e+40 0.5	3.101e+40 1.1
26	Bu	138	143	142	143
27	Ag	143	143	143	153	1.858e+41 6.3	4.258e+40 1.4	2.284e+41 7.7
28	Bg	153	153	153	154	5.547e+40 1.9	5.954e+40 2.0	1.150e+41 3.9
29	Bg	157	157	157	157	3.368e+39 0.1	5.556e+39 0.2	8.924e+39 0.3
30	Au	161	162	161	162
31	Bu	162	164	164	164
32	Ag	164	174	178	178	1.288e+40 0.4	1.527e+40 0.5	2.815e+40 1.0
33	Bu	178	178	185	182
34	Au	185	191	188	191
35	Bg	191	195	191	195	1.455e+40 0.5	2.376e+40 0.8	3.832e+40 1.3
36	Ag	195	197	195	200	1.075e+41 3.6	5.899e+40 2.0	1.665e+41 5.6
37	Au	300	300	300	300
38	Bu	304	304	305	304
39	Bg	310	310	310	310	1.702e+41 5.8	1.986e+41 6.7	3.688e+41 12.5
40	Ag	323	323	323	323	4.199e+41 14.2	2.953e+41 10.0	7.152e+41 24.3
41	Bu	325	325	327	325
42	Au	336	337	336	336
43	Ag	339	339	339	339	4.383e+41 14.9	3.491e+41 11.8	7.874e+41 26.7
44	Bg	340	340	340	340	8.585e+40 2.9	1.139e+41 3.9	1.998e+41 6.8
45	Bu	345	345	346	345
46	Ag	346	346	346	346	1.080e+42 36.6	7.193e+41 24.4	1.799e+42 61.0
47	Bu	356	356	356	356
48	Bg	361	361	361	361	1.161e+40 0.4	1.243e+40 0.4	2.404e+40 0.8
49	Ag	365	365	365	365	3.117e+41 10.6	8.946e+40 3.0	4.012e+41 13.6
50	Au	367	369	367	368
51	Au	373	374	373	373
52	Bg	374	378	374	374	4.822e+40 1.6	5.327e+40 1.8	1.015e+41 3.4
53	Au	385	385	385	385
54	Ag	390	390	390	390	1.801e+41 6.1	9.897e+40 3.4	2.791e+41 9.5
55	Bg	390	390	390	390	6.196e+40 2.1	6.925e+40 2.3	1.312e+41 4.5
56	Bu	411	411	411	411
57	Au	897	899	897	903
58	Bu	903	903	903	903
59	Ag	903	903	905	903	2.143e+42 72.7	1.515e+41 5.1	2.294e+42 77.9
60	Bg	905	905	906	905	2.018e+39 0.1	2.669e+39 0.1	4.686e+39 0.2
61	Au	906	907	906	906
62	Ag	907	907	907	907	9.176e+41 31.1	1.784e+40 0.6	9.354e+41 31.7
63	Bu	907	908	909	907	2.891e+42 98.1	5.621e+40 1.9	2.947e+42 100.0
64	Au	909	917	920	920
65	Ag	920	920	923	924	9.178e+41 31.1	6.899e+40 2.3	9.868e+41 33.5
66	Bu	924	924	929	929
67	Bg	929	929	933	932	1.215e+41 4.1	1.366e+41 4.6	2.581e+41 8.8
68	Ag	933	933	941	933	1.245e+42 42.2	5.814e+40 2.0	1.303e+42 44.2
69	Bg	941	941	952	941	7.565e+40 2.6	8.832e+40 3.0	1.640e+41 5.6
70	Au	952	956	956	956
71	Bg	956	959	958	959	3.978e+40 1.3	5.104e+40 1.7	9.082e+40 3.1
72	Bu	959	997	981	1001

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.