- KIESERITE - MgSO₄H₂O

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

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:	35 Ha [=952.406 eV ]
eXchange-Correlation functional:

Pseudopotentials:
Mg:	potassium, fhi98PP :
S:	aluminium, fhi98PP :
O:	silicon, fhi98PP :
H:	oxygen, fhi98PP :

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:	2.0753	0.2524	-0.0342
	0.2573	2.2548	-0.0873
	0.3295	-0.0932	2.1332
Eig. Value:	1.8042	2.4359	2.2233
S:	3.8330	-0.0000	0.1518
	-0.0000	3.2604	0.0000
	0.1201	-0.0000	3.4059
Eig. Value:	3.8726	3.2604	3.3663
O:	-1.4154	0.3777	-0.4897
	0.3794	-1.2817	0.4454
	-0.5066	0.4464	-1.4759
Eig. Value:	-2.2850	-0.9700	-0.9180
O:	-1.9741	-0.3982	0.2861
	-0.3114	-1.4384	0.4248
	0.2125	0.4218	-1.1771
Eig. Value:	-2.3101	-1.4148	-0.8647
O:	-1.8750	0.0000	-0.1631
	0.0000	-0.9494	-0.0000
	-0.0613	-0.0000	-1.1062
Eig. Value:	-1.8910	-0.9494	-1.0902
H:	1.3728	0.4446	0.2264
	0.2369	0.4372	0.0683
	0.1000	0.0288	0.4366
Eig. Value:	1.5107	0.3261	0.4098
Mg:	2.0753	-0.2524	-0.0342
	-0.2573	2.2548	0.0873
	0.3295	0.0932	2.1332
Eig. Value:	1.8042	2.4359	2.2233
O:	-1.4154	-0.3777	-0.4897
	-0.3794	-1.2817	-0.4454
	-0.5066	-0.4464	-1.4759
Eig. Value:	-2.2850	-0.9700	-0.9180
O:	-1.9741	0.3982	0.2861
	0.3114	-1.4384	-0.4248
	0.2125	-0.4218	-1.1771
Eig. Value:	-2.3101	-1.4148	-0.8647
H:	1.3728	-0.4446	0.2264
	-0.2369	0.4372	-0.0683
	0.1000	-0.0288	0.4366
Eig. Value:	1.5107	0.3261	0.4098
S:	3.8330	-0.0000	0.1518
	-0.0000	3.2604	0.0000
	0.1201	-0.0000	3.4059
Eig. Value:	3.8726	3.2604	3.3663
O:	-1.4154	0.3777	-0.4897
	0.3794	-1.2817	0.4454
	-0.5066	0.4464	-1.4759
Eig. Value:	-2.2850	-0.9700	-0.9180
O:	-1.9741	-0.3982	0.2861
	-0.3114	-1.4384	0.4248
	0.2125	0.4218	-1.1771
Eig. Value:	-2.3101	-1.4148	-0.8647
O:	-1.8750	0.0000	-0.1631
	0.0000	-0.9494	-0.0000
	-0.0613	-0.0000	-1.1062
Eig. Value:	-1.8910	-0.9494	-1.0902
H:	1.3728	0.4446	0.2264
	0.2369	0.4372	0.0683
	0.1000	0.0288	0.4366
Eig. Value:	1.5107	0.3261	0.4098
O:	-1.4154	-0.3777	-0.4897
	-0.3794	-1.2817	-0.4454
	-0.5066	-0.4464	-1.4759
Eig. Value:	-2.2850	-0.9700	-0.9180
O:	-1.9741	0.3982	0.2861
	0.3114	-1.4384	-0.4248
	0.2125	-0.4218	-1.1771
Eig. Value:	-2.3101	-1.4148	-0.8647
H:	1.3728	-0.4446	0.2264
	-0.2369	0.4372	-0.0683
	0.1000	-0.0288	0.4366
Eig. Value:	1.5107	0.3261	0.4098

Atom type

Dielectric tensors:

	X	Y	Z
Ɛ_∞:	2.6944	0.0000	0.0616
	0.0000	2.4420	0.0000
	0.0616	0.0000	2.4386
Eig. Value:	2.7085	2.4420	2.4246
Refractive index (N):	1.6415	0.0000	0.2482
	0.0000	1.5627	0.0000
	0.2482	0.0000	1.5616
Eig. Value:	1.6458	1.5627	1.5571
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-u	0	0	0	0
2	Ac-u	0	0	0	0
3	Ac-u	0	0	0	0
4	Bg	69	69	69	69	1.792e+38 0.1	2.282e+38 0.1	4.074e+38 0.2
5	Bu	118	118	118	119
6	Bg	123	123	123	123	5.005e+37 0.0	8.247e+37 0.0	1.325e+38 0.1
7	Au	128	128	130	128
8	Ag	146	146	146	146	1.636e+39 0.9	1.598e+39 0.9	3.235e+39 1.8
9	Bu	202	208	202	215
10	Bg	215	215	215	216	1.460e+39 0.8	2.123e+39 1.2	3.582e+39 2.0
11	Bu	227	227	227	232
12	Bg	241	241	241	241	1.625e+39 0.9	1.815e+39 1.0	3.440e+39 1.9
13	Ag	242	242	242	242	1.596e+40 8.9	4.810e+38 0.3	1.644e+40 9.2
14	Au	243	243	246	243
15	Ag	294	294	294	294	4.349e+39 2.4	8.481e+38 0.5	5.197e+39 2.9
16	Bg	305	305	305	305	1.545e+39 0.9	2.240e+39 1.3	3.785e+39 2.1
17	Bu	308	328	308	314
18	Au	328	332	338	328
19	Bu	338	343	349	352
20	Bg	366	366	366	366	7.486e+38 0.4	1.131e+39 0.6	1.879e+39 1.0
21	Au	383	383	387	383
22	Bu	387	409	393	391
23	Au	410	410	413	410
24	Bu	413	417	417	417
25	Ag	417	429	427	430	1.025e+40 5.7	6.681e+39 3.7	1.693e+40 9.5
26	Au	430	430	455	443
27	Ag	513	513	513	513	7.882e+39 4.4	6.604e+39 3.7	1.449e+40 8.1
28	Au	547	547	552	547
29	Bu	600	605	600	605
30	Bg	605	606	605	611	7.728e+39 4.3	1.270e+40 7.1	2.043e+40 11.4
31	Bg	616	616	616	616	3.603e+39 2.0	3.849e+39 2.2	7.452e+39 4.2
32	Ag	619	619	619	619	9.381e+39 5.2	4.856e+39 2.7	1.424e+40 8.0
33	Bu	622	625	622	623
34	Au	625	673	633	625
35	Bg	776	776	776	776	4.819e+38 0.3	5.533e+38 0.3	1.035e+39 0.6
36	Bu	782	801	782	800
37	Bu	963	1000	963	999
38	Au	1000	1004	1004	1000
39	Ag	1004	1020	1005	1004	1.172e+41 65.5	6.578e+38 0.4	1.179e+41 65.9
40	Bg	1020	1024	1020	1020	1.607e+39 0.9	2.086e+39 1.2	3.693e+39 2.1
41	Au	1024	1044	1027	1024
42	Ag	1044	1046	1044	1044	1.201e+40 6.7	2.010e+39 1.1	1.403e+40 7.8
43	Bg	1074	1074	1074	1074	3.870e+39 2.2	6.480e+39 3.6	1.035e+40 5.8
44	Bu	1105	1120	1105	1110
45	Ag	1120	1127	1120	1120	1.686e+40 9.4	6.044e+39 3.4	2.290e+40 12.8
46	Au	1146	1146	1201	1146
47	Bu	1201	1234	1216	1234
48	Bg	1234	1246	1234	1269	4.986e+39 2.8	5.331e+39 3.0	1.032e+40 5.8
49	Ag	1527	1527	1527	1527	3.396e+39 1.9	2.766e+39 1.5	6.162e+39 3.4
50	Au	1543	1543	1549	1543
51	Bu	2914	2919	2914	2919
52	Bg	2919	2966	2919	2919	1.560e+40 8.7	1.977e+40 11.0	3.537e+40 19.8
53	Ag	2966	2994	2966	2966	1.494e+41 83.5	2.961e+40 16.5	1.790e+41 100.0
54	Au	2994	3050	3014	2994

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.