- NEIGHBORITE - NaMgF₃

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:	62		Pnma
Lattice parameters (Å):	5.3603	5.4884		7.6660
Angles (°):	90	90		90

Symmetry (theoretical):

Space group:	62		Pnma
Lattice parameters (Å):	4.8505	5.1169		7.0332
Angles (°):	90	90		90

Cell contents:

Number of atoms:	20
Number of atom types:	3
Chemical composition:	0

Atomic positions (theoretical):

Na:	0.9791	0.0686	0.2500
Mg:	0.0000	0.5000	0.0000
F:	0.1027	0.4718	0.2500
F:	0.6894	0.3038	0.0520
Na:	0.4791	0.4314	0.7500
Mg:	0.5000	0.0000	0.0000
F:	0.6027	0.0282	0.7500
F:	0.1894	0.1962	0.9480
Na:	0.0209	0.9314	0.7500
Mg:	0.0000	0.5000	0.5000
F:	0.8973	0.5282	0.7500
F:	0.3106	0.6962	0.5520
Na:	0.5209	0.5686	0.2500
Mg:	0.5000	0.0000	0.5000
F:	0.3973	0.9718	0.2500
F:	0.8106	0.8038	0.4480
F:	0.3106	0.6962	0.9480
F:	0.8106	0.8038	0.0520
F:	0.6894	0.3038	0.4480
F:	0.1894	0.1962	0.5520

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:	6 6 6
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:
Na:	sodium, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 0 local
Mg:	magnesium, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 0 local
F:	fluorine, 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):

Na:	1.0086	-0.0065	0.0000
	0.0008	0.9939	-0.0000
	0.0000	-0.0000	1.0298
Eig. Value:	1.0091	0.9933	1.0298
Mg:	1.8234	-0.0098	-0.0221
	0.0222	1.8360	0.0119
	0.0210	0.0000	1.8156
Eig. Value:	1.8219	1.8397	1.8134
F:	-0.8722	0.0019	-0.0000
	-0.0020	-0.8459	0.0000
	-0.0000	0.0000	-1.1046
Eig. Value:	-0.8722	-0.8459	-1.1046
F:	-0.9799	-0.1182	-0.0205
	-0.1162	-0.9920	-0.0031
	-0.0175	0.0044	-0.8704
Eig. Value:	-0.8549	-1.1040	-0.8834
Na:	1.0086	0.0065	-0.0000
	-0.0008	0.9939	0.0000
	-0.0000	0.0000	1.0298
Eig. Value:	1.0091	0.9933	1.0298
Mg:	1.8234	0.0098	0.0221
	-0.0222	1.8360	0.0119
	-0.0210	0.0000	1.8156
Eig. Value:	1.8219	1.8397	1.8134
F:	-0.8722	-0.0019	0.0000
	0.0020	-0.8459	-0.0000
	0.0000	-0.0000	-1.1046
Eig. Value:	-0.8722	-0.8459	-1.1046
F:	-0.9799	0.1182	0.0205
	0.1162	-0.9920	-0.0031
	0.0175	0.0044	-0.8704
Eig. Value:	-0.8549	-1.1040	-0.8834
Na:	1.0086	-0.0065	-0.0000
	0.0008	0.9939	-0.0000
	0.0000	-0.0000	1.0298
Eig. Value:	1.0091	0.9933	1.0298
Mg:	1.8234	-0.0098	0.0221
	0.0222	1.8360	-0.0119
	-0.0210	-0.0000	1.8156
Eig. Value:	1.8219	1.8397	1.8134
F:	-0.8722	0.0019	0.0000
	-0.0020	-0.8459	-0.0000
	0.0000	-0.0000	-1.1046
Eig. Value:	-0.8722	-0.8459	-1.1046
F:	-0.9799	-0.1182	0.0205
	-0.1162	-0.9920	0.0031
	0.0175	-0.0044	-0.8704
Eig. Value:	-0.8549	-1.1040	-0.8834
Na:	1.0086	0.0065	0.0000
	-0.0008	0.9939	-0.0000
	-0.0000	0.0000	1.0298
Eig. Value:	1.0091	0.9933	1.0298
Mg:	1.8234	0.0098	-0.0221
	-0.0222	1.8360	-0.0119
	0.0210	-0.0000	1.8156
Eig. Value:	1.8219	1.8397	1.8134
F:	-0.8722	-0.0019	0.0000
	0.0020	-0.8459	0.0000
	0.0000	0.0000	-1.1046
Eig. Value:	-0.8722	-0.8459	-1.1046
F:	-0.9799	0.1182	-0.0205
	0.1162	-0.9920	0.0031
	-0.0175	-0.0044	-0.8704
Eig. Value:	-0.8549	-1.1040	-0.8834
F:	-0.9799	-0.1182	-0.0205
	-0.1162	-0.9920	-0.0031
	-0.0175	0.0044	-0.8704
Eig. Value:	-0.8549	-1.1040	-0.8834
F:	-0.9799	0.1182	0.0205
	0.1162	-0.9920	-0.0031
	0.0175	0.0044	-0.8704
Eig. Value:	-0.8549	-1.1040	-0.8834
F:	-0.9799	-0.1182	0.0205
	-0.1162	-0.9920	0.0031
	0.0175	-0.0044	-0.8704
Eig. Value:	-0.8549	-1.1040	-0.8834
F:	-0.9799	0.1182	-0.0205
	0.1162	-0.9920	0.0031
	-0.0175	-0.0044	-0.8704
Eig. Value:	-0.8549	-1.1040	-0.8834

Atom type

Dielectric tensors:

	X	Y	Z
Ɛ_∞:	1.9611	0.0000	0.0000
	0.0000	1.9569	0.0000
	0.0000	0.0000	1.9592
Eig. Value:	1.9611	1.9569	1.9592
Refractive index (N):	1.4004	0.0000	0.0000
	0.0000	1.3989	0.0000
	0.0000	0.0000	1.3997
Eig. Value:	1.4004	1.3989	1.3997
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	Au	118	118	118	118
5	B1u	160	160	160	172
6	A1g	172	172	172	174	1.061e+38 13.7	7.050e+37 9.1	1.766e+38 22.8
7	B3u	174	174	174	176
8	A1g	188	188	188	188	4.641e+38 60.0	6.819e+37 8.8	5.323e+38 68.8
9	B1g	189	189	189	189	3.971e+37 5.1	5.461e+37 7.1	9.432e+37 12.2
10	B2u	192	192	200	192
11	B3g	200	200	200	200	1.019e+37 1.3	1.401e+37 1.8	2.420e+37 3.1
12	B1g	217	217	217	217	1.588e+38 20.5	2.183e+38 28.2	3.770e+38 48.7
13	Au	218	218	218	218
14	B3g	218	218	218	218	6.804e+36 0.9	9.356e+36 1.2	1.616e+37 2.1
15	B2g	224	224	224	224	5.264e+37 6.8	7.238e+37 9.4	1.250e+38 16.2
16	Au	231	231	231	231
17	B3u	239	246	239	239
18	B1u	246	247	246	247
19	A1g	247	248	247	248	5.342e+38 69.0	5.826e+37 7.5	5.925e+38 76.6
20	Au	248	252	248	257
21	B2u	263	263	266	263
22	B2u	266	266	275	266
23	B3u	275	276	276	275
24	B2g	276	276	276	276	1.036e+37 1.3	1.425e+37 1.8	2.461e+37 3.2
25	B1g	283	283	283	283	7.115e+36 0.9	9.783e+36 1.3	1.690e+37 2.2
26	A1g	283	283	283	283	1.406e+38 18.2	5.313e+37 6.9	1.937e+38 25.0
27	B2u	297	297	300	297
28	B1u	316	316	316	325
29	B3u	336	344	336	336
30	B1g	344	353	344	344
31	Au	355	355	355	355
32	B1u	359	359	359	368
33	B3g	368	368	368	390	2.524e+37 3.3	3.471e+37 4.5	5.995e+37 7.7
34	B3u	390	393	390	396
35	A1g	396	396	396	399	7.435e+38 96.1	3.036e+37 3.9	7.739e+38 100.0
36	B2u	399	399	403	403
37	B1g	403	403	406	408
38	B2u	408	408	410	410
39	B3u	410	413	413	413
40	B2g	413	421	421	414	1.937e+37 2.5	2.663e+37 3.4	4.599e+37 5.9
41	A1g	421	440	451	421	1.557e+38 20.1	9.910e+37 12.8	2.548e+38 32.9
42	B1g	451	451	462	451	2.490e+37 3.2	3.423e+37 4.4	5.913e+37 7.6
43	B3g	499	499	499	499	4.217e+37 5.4	5.799e+37 7.5	1.002e+38 12.9
44	A1g	504	504	504	504	1.243e+38 16.1	8.300e+37 10.7	2.073e+38 26.8
45	B2g	507	507	507	507	2.077e+38 26.8	2.856e+38 36.9	4.933e+38 63.7
46	B1u	510	510	510	515
47	B3u	515	517	515	517
48	Au	517	537	517	530
49	B2u	537	550	541	537
50	B3u	554	556	554	554
51	B2u	591	591	592	591
52	B3g	592	592	592	592	4.431e+36 0.6	6.092e+36 0.8	1.052e+37 1.4
53	B1g	596	596	596	596
54	B2g	619	619	619	619	3.507e+35 0.0	4.822e+35 0.1	8.328e+35 0.1
55	B1u	658	658	658	659
56	Au	660	660	660	660
57	B2u	662	662	664	662
58	B3u	664	682	682	664
59	Au	682	687	687	682
60	B1u	687	735	745	760

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.