- TALC - Mg₃Si₄O₁₀(OH)₂

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:	2		P-1
Lattice parameters (Å):	5.2900	9.1730		9.4600
Angles (°):	90.46	98.68		90.09

Symmetry (theoretical):

Space group:	2		P-1
Lattice parameters (Å):	5.3307	10.2302		5.3298
Angles (°):	98.26	119.99		85.60

Cell contents:

Number of atoms:	21
Number of atom types:	4
Chemical composition:	0

Atomic positions (theoretical):

Mg:	0.0000	1.0000	0.0000
Mg:	0.6667	1.0000	0.3335
Mg:	0.3333	0.0000	0.6665
Si:	0.0040	0.7294	0.2606
Si:	0.6704	0.7294	0.5934
Si:	0.9960	0.2706	0.7394
Si:	0.3296	0.2706	0.4066
O:	0.6681	0.8907	0.6362
O:	0.3339	0.8976	0.9724
O:	0.0024	0.8907	0.3048
O:	0.8497	0.6748	0.9122
O:	0.8263	0.6743	0.4005
O:	0.3379	0.6743	0.4238
O:	0.3319	0.1093	0.3638
O:	0.6661	0.1024	0.0276
O:	0.9976	0.1093	0.6952
O:	0.1503	0.3252	0.0878
O:	0.1737	0.3257	0.5995
O:	0.6621	0.3257	0.5762
H:	0.3332	0.8028	0.9467
H:	0.6668	0.1972	0.0533

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:	50 Ha [=1360.58 eV ]
eXchange-Correlation functional:	LDA pw90

Pseudopotentials:
Mg:	magnesium, fhi98PP : Trouiller-Martins-type, GGA Perdew/Burke/Ernzerhof (1996), l= 2 local
Si:	silicon, fhi98PP : Trouiller-Martins-type, GGA Perdew/Burke/Ernzerhof (1996), l= 2 local
O:	oxygen, fhi98PP : Trouiller-Martins-type, GGA Perdew/Burke/Ernzerhof (1996), l= 2 local
H:	hydrogen, 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):

Mg:	1.9741	0.0670	0.0087
	0.1268	1.6785	-0.0444
	0.0163	-0.0450	2.0117
Eig. Value:	2.0030	1.6437	2.0176
Mg:	2.0092	-0.0346	-0.0043
	-0.0631	1.6781	-0.0402
	-0.0079	-0.0418	1.9828
Eig. Value:	2.0163	1.6656	1.9882
Mg:	2.0092	-0.0346	-0.0043
	-0.0631	1.6781	-0.0402
	-0.0079	-0.0418	1.9828
Eig. Value:	2.0163	1.6656	1.9882
Si:	3.4763	-0.0133	0.0316
	-0.0167	2.4957	-0.1273
	-0.0483	-0.1302	3.4707
Eig. Value:	3.4736	2.4788	3.4904
Si:	3.4838	0.0071	-0.0317
	0.0114	2.5058	-0.1331
	0.0481	-0.1326	3.4542
Eig. Value:	3.4871	2.4875	3.4692
Si:	3.4763	-0.0133	0.0316
	-0.0167	2.4957	-0.1273
	-0.0483	-0.1302	3.4707
Eig. Value:	3.4736	2.4788	3.4904
Si:	3.4838	0.0071	-0.0317
	0.0114	2.5058	-0.1331
	0.0481	-0.1326	3.4542
Eig. Value:	3.4871	2.4875	3.4692
O:	-1.5422	0.0010	0.0076
	-0.0096	-1.7303	-0.0091
	-0.0114	-0.0211	-1.5404
Eig. Value:	-1.5428	-1.7316	-1.5386
O:	-1.4757	0.0024	0.0005
	0.0128	-0.9703	0.0659
	0.0017	0.0665	-1.4679
Eig. Value:	-1.4758	-0.9615	-1.4766
O:	-1.5411	0.0016	-0.0068
	-0.0062	-1.7265	-0.0404
	0.0101	-0.0243	-1.5471
Eig. Value:	-1.5392	-1.7321	-1.5433
O:	-1.0529	0.0141	-0.0029
	0.0081	-1.1119	0.2249
	-0.0024	0.2275	-2.8539
Eig. Value:	-1.0495	-1.0864	-2.8828
O:	-2.4253	-0.1045	0.7850
	-0.1026	-1.0721	0.0633
	0.7863	0.0551	-1.5027
Eig. Value:	-2.8830	-1.0643	-1.0529
O:	-2.4203	0.0955	-0.7830
	0.0972	-1.0996	0.0580
	-0.7850	0.0633	-1.4973
Eig. Value:	-2.8758	-1.0928	-1.0485
O:	-1.5422	0.0010	0.0076
	-0.0096	-1.7303	-0.0091
	-0.0114	-0.0211	-1.5404
Eig. Value:	-1.5428	-1.7316	-1.5386
O:	-1.4757	0.0024	0.0005
	0.0128	-0.9703	0.0659
	0.0017	0.0665	-1.4679
Eig. Value:	-1.4758	-0.9615	-1.4766
O:	-1.5411	0.0016	-0.0068
	-0.0062	-1.7265	-0.0404
	0.0101	-0.0243	-1.5471
Eig. Value:	-1.5392	-1.7321	-1.5433
O:	-1.0529	0.0141	-0.0029
	0.0081	-1.1119	0.2249
	-0.0024	0.2275	-2.8539
Eig. Value:	-1.0495	-1.0864	-2.8828
O:	-2.4253	-0.1045	0.7850
	-0.1026	-1.0721	0.0633
	0.7863	0.0551	-1.5027
Eig. Value:	-2.8830	-1.0643	-1.0529
O:	-2.4203	0.0955	-0.7830
	0.0972	-1.0996	0.0580
	-0.7850	0.0633	-1.4973
Eig. Value:	-2.8758	-1.0928	-1.0485
H:	0.5011	-0.0029	-0.0004
	0.0051	0.1917	-0.0399
	0.0006	-0.0398	0.4958
Eig. Value:	0.5011	0.1866	0.5010
H:	0.5011	-0.0029	-0.0004
	0.0051	0.1917	-0.0399
	0.0006	-0.0398	0.4958
Eig. Value:	0.5011	0.1866	0.5010

Atom type

Dielectric tensors:

	X	Y	Z
Ɛ_∞:	2.5192	0.0000	0.0000
	0.0000	2.2380	0.0000
	0.0000	0.0000	2.5145
Eig. Value:	2.5193	2.2380	2.5144
Refractive index (N):	1.5872	0.0000	0.0000
	0.0000	1.4960	0.0000
	0.0000	0.0000	1.5857
Eig. Value:	1.5872	1.4960	1.5857
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	Ag	100	100	100	100	7.680e+38 1.7	9.933e+38 2.2	1.761e+39 3.9
5	Ag	102	102	102	102	9.628e+38 2.1	1.106e+39 2.4	2.069e+39 4.6
6	Au	146	146	146	146
7	Ag	146	146	146	146	3.261e+38 0.7	6.859e+37 0.2	3.947e+38 0.9
8	Au	159	161	159	159
9	Ag	169	169	169	169	3.388e+40 74.5	3.183e+39 7.0	3.706e+40 81.5
10	Au	170	170	170	171
11	Ag	222	222	222	222	3.855e+38 0.8	4.503e+38 1.0	8.358e+38 1.8
12	Au	226	226	226	226
13	Au	240	240	242	240
14	Ag	283	283	283	283	3.661e+39 8.1	2.234e+38 0.5	3.884e+39 8.5
15	Ag	286	286	286	286	2.423e+38 0.5	2.047e+38 0.5	4.469e+38 1.0
16	Au	287	287	287	288
17	Au	295	296	296	295
18	Ag	312	312	312	312	3.584e+38 0.8	4.448e+38 1.0	8.031e+38 1.8
19	Ag	312	312	312	312	4.324e+38 1.0	3.869e+38 0.9	8.194e+38 1.8
20	Au	331	331	331	332
21	Ag	336	336	336	336	6.807e+37 0.1	8.052e+37 0.2	1.486e+38 0.3
22	Ag	346	346	346	346	1.181e+40 26.0	1.550e+38 0.3	1.197e+40 26.3
23	Au	355	357	356	355
24	Au	357	358	357	357
25	Au	360	361	360	360
26	Ag	365	365	365	365	3.791e+38 0.8	2.697e+38 0.6	6.488e+38 1.4
27	Ag	366	366	366	366	6.240e+38 1.4	1.266e+38 0.3	7.506e+38 1.7
28	Au	373	373	373	380
29	Au	393	395	398	393
30	Ag	405	405	405	405	3.074e+39 6.8	3.634e+38 0.8	3.438e+39 7.6
31	Ag	406	406	406	406	4.727e+38 1.0	6.009e+38 1.3	1.074e+39 2.4
32	Au	415	416	416	416
33	Au	416	422	417	421
34	Ag	422	431	422	422	4.658e+38 1.0	6.846e+38 1.5	1.150e+39 2.5
35	Au	431	439	432	439
36	Ag	439	469	439	469	2.537e+39 5.6	7.451e+38 1.6	3.282e+39 7.2
37	Au	469	479	477	479
38	Ag	479	486	479	486	2.429e+38 0.5	3.184e+38 0.7	5.613e+38 1.2
39	Au	486	488	486	488
40	Ag	488	489	488	490	2.762e+38 0.6	1.595e+38 0.4	4.357e+38 1.0
41	Au	490	540	518	540
42	Au	576	577	576	576
43	Au	577	585	577	585
44	Ag	585	585	585	585	1.021e+39 2.2	1.302e+39 2.9	2.322e+39 5.1
45	Ag	585	593	585	596	9.581e+38 2.1	1.264e+39 2.8	2.222e+39 4.9
46	Ag	636	636	636	636	4.544e+40 99.9	2.274e+37 0.1	4.547e+40 100.0
47	Au	656	656	657	656
48	Au	738	738	738	738
49	Ag	739	739	739	739	7.106e+38 1.6	6.307e+38 1.4	1.341e+39 2.9
50	Au	741	741	741	741
51	Ag	742	742	742	742	7.374e+38 1.6	9.845e+38 2.2	1.722e+39 3.8
52	Ag	830	830	830	830
53	Au	830	830	830	830	6.751e+35 0.0	6.886e+35 0.0	1.364e+36 0.0
54	Au	884	884	919	884
55	Ag	920	920	920	920
56	Au	920	920	920	920	6.330e+38 1.4	7.906e+38 1.7	1.424e+39 3.1
57	Ag	920	920	920	920
58	Au	920	976	976	976	6.217e+38 1.4	9.043e+38 2.0	1.526e+39 3.4
59	Ag	976	1009	979	1009	5.194e+39 11.4	1.239e+39 2.7	6.433e+39 14.1
60	Ag	1009	1009	1009	1009
61	Au	1009	1060	1009	1059
62	Au	3752	3752	3752	3752
63	Ag	3752	3752	3754	3752	2.176e+40 47.9	5.480e+38 1.2	2.231e+40 49.1

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.