- PLAGIOCLASE - (Na,Ca)(Si,Al)₄O₈

BYTOWNITE - Theoretical structure, term in the plagioclase series treated as ideal solid solution using alchemical pseudopotentials. 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:	4 4 4
number of shifts:	1
shifts:	0.5 0.5 0.5
Kinetic energy cut-off:	38 Ha [=1034.0408 eV ]
eXchange-Correlation functional:	LDA pw90

Pseudopotentials:
Na:	sodium, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 2 local
Ca:	silicon, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 2 local
Al:	oxygen, 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:	1.9915	0.0360	0.0055
	0.0183	2.0290	0.0382
	-0.0155	0.0427	2.0047
Eig. Value:	2.0009	2.0643	1.9600
Si:	2.8536	0.2979	0.0033
	0.0773	2.6305	0.0639
	-0.0848	0.0593	2.9949
Eig. Value:	2.9598	2.5125	3.0067
Si:	2.8711	-0.2899	-0.0318
	-0.0889	2.7371	-0.0266
	-0.0150	-0.1343	3.0670
Eig. Value:	2.9964	2.5900	3.0888
Si:	2.8395	-0.1893	0.1076
	-0.0712	3.0593	0.0433
	0.1269	0.0463	2.7339
Eig. Value:	2.8835	3.1201	2.6292
Si:	2.7853	0.1066	0.0045
	0.0222	3.1248	-0.0507
	0.0758	0.0573	2.7592
Eig. Value:	2.8058	3.1369	2.7266
O:	-1.4418	-0.0761	0.4932
	-0.0787	-1.3712	0.1459
	0.5397	0.1462	-2.3810
Eig. Value:	-1.2124	-1.3506	-2.6310
O:	-1.4326	0.0361	-0.1645
	0.0523	-2.4523	0.0914
	-0.1727	0.0767	-1.2512
Eig. Value:	-1.5263	-2.4613	-1.1485
O:	-2.3679	-0.2784	0.2510
	-0.2862	-1.3021	-0.0720
	0.3131	-0.0601	-1.3918
Eig. Value:	-2.4988	-1.1434	-1.4196
O:	-2.3892	0.3330	0.3254
	0.3142	-1.3156	0.0102
	0.3632	-0.0121	-1.4277
Eig. Value:	-2.5757	-1.1758	-1.3810
O:	-1.4475	-0.4551	-0.1536
	-0.3895	-2.1739	-0.2892
	-0.1316	-0.2845	-1.2859
Eig. Value:	-1.2553	-2.4554	-1.1966
O:	-1.5150	0.3892	-0.2288
	0.3261	-2.1773	0.1203
	-0.2434	0.1127	-1.3100
Eig. Value:	-1.4868	-2.3728	-1.1427
O:	-1.3797	0.1539	-0.2399
	0.2336	-1.4227	0.2036
	-0.3119	0.2001	-2.2070
Eig. Value:	-1.1994	-1.4520	-2.3582
O:	-1.3672	-0.0639	-0.3719
	-0.1295	-1.3656	-0.2782
	-0.4438	-0.2504	-2.3051
Eig. Value:	-1.2146	-1.2974	-2.5259
Na:	1.9915	0.0360	0.0055
	0.0183	2.0290	0.0382
	-0.0155	0.0427	2.0047
Eig. Value:	2.0009	2.0643	1.9600
Si:	2.8536	0.2979	0.0033
	0.0773	2.6305	0.0639
	-0.0848	0.0593	2.9949
Eig. Value:	2.9598	2.5125	3.0067
Si:	2.8711	-0.2899	-0.0318
	-0.0889	2.7371	-0.0266
	-0.0150	-0.1343	3.0670
Eig. Value:	2.9964	2.5900	3.0888
Si:	2.8395	-0.1893	0.1076
	-0.0712	3.0593	0.0433
	0.1269	0.0463	2.7339
Eig. Value:	2.8835	3.1201	2.6292
Si:	2.7853	0.1066	0.0045
	0.0222	3.1248	-0.0507
	0.0758	0.0573	2.7592
Eig. Value:	2.8058	3.1369	2.7266
O:	-1.4418	-0.0761	0.4932
	-0.0787	-1.3712	0.1459
	0.5397	0.1462	-2.3810
Eig. Value:	-1.2124	-1.3506	-2.6310
O:	-1.4326	0.0361	-0.1645
	0.0523	-2.4523	0.0914
	-0.1727	0.0767	-1.2512
Eig. Value:	-1.5263	-2.4613	-1.1485
O:	-2.3679	-0.2784	0.2510
	-0.2862	-1.3021	-0.0720
	0.3131	-0.0601	-1.3918
Eig. Value:	-2.4988	-1.1434	-1.4196
O:	-2.3892	0.3330	0.3254
	0.3142	-1.3156	0.0102
	0.3632	-0.0121	-1.4277
Eig. Value:	-2.5757	-1.1758	-1.3810
O:	-1.4475	-0.4551	-0.1536
	-0.3895	-2.1739	-0.2892
	-0.1316	-0.2845	-1.2859
Eig. Value:	-1.2553	-2.4554	-1.1966
O:	-1.5150	0.3892	-0.2288
	0.3261	-2.1773	0.1203
	-0.2434	0.1127	-1.3100
Eig. Value:	-1.4868	-2.3728	-1.1427
O:	-1.3797	0.1539	-0.2399
	0.2336	-1.4227	0.2036
	-0.3119	0.2001	-2.2070
Eig. Value:	-1.1994	-1.4520	-2.3582
O:	-1.3672	-0.0639	-0.3719
	-0.1295	-1.3656	-0.2782
	-0.4438	-0.2504	-2.3051
Eig. Value:	-1.2146	-1.2974	-2.5259

Atom type

Dielectric tensors:

	X	Y	Z
Ɛ_∞:	2.4788	0.0000	0.0000
	0.0000	2.5055	0.0000
	0.0000	0.0000	2.5001
Eig. Value:	2.4785	2.5084	2.4974
Refractive index (N):	1.5744	-0.0000	-0.0000
	-0.0000	1.5829	-0.0000
	-0.0000	-0.0000	1.5812
Eig. Value:	1.5743	1.5838	1.5803
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	68	68	68	68	1.121e+39 3.3	6.887e+38 2.0	1.809e+39 5.3
5	Au	79	83	84	84
6	Ag	84	84	87	85	1.662e+39 4.9	6.606e+38 1.9	2.323e+39 6.8
7	Ag	99	99	99	99	6.624e+38 1.9	2.765e+38 0.8	9.389e+38 2.8
8	Au	121	125	130	128
9	Ag	130	130	130	130	6.957e+38 2.0	1.043e+39 3.1	1.739e+39 5.1
10	Ag	146	146	146	146	2.176e+38 0.6	3.105e+38 0.9	5.281e+38 1.6
11	Au	155	156	163	156
12	Au	165	166	168	167
13	Ag	168	168	168	168	2.561e+39 7.5	6.821e+38 2.0	3.243e+39 9.5
14	Ag	172	172	172	172	5.241e+38 1.5	3.896e+38 1.1	9.138e+38 2.7
15	Ag	188	188	188	188	2.640e+39 7.8	7.914e+38 2.3	3.432e+39 10.1
16	Ag	199	199	199	199	2.670e+39 7.9	2.846e+38 0.8	2.954e+39 8.7
17	Au	203	207	204	208
18	Ag	215	215	215	215	7.032e+38 2.1	4.871e+38 1.4	1.190e+39 3.5
19	Au	228	232	229	228
20	Ag	232	233	232	232	1.313e+38 0.4	1.376e+38 0.4	2.689e+38 0.8
21	Au	234	237	238	239
22	Au	249	251	249	249
23	Ag	257	257	257	257	7.011e+38 2.1	6.439e+37 0.2	7.655e+38 2.3
24	Au	261	261	261	261
25	Ag	277	277	277	277	9.377e+39 27.6	3.077e+38 0.9	9.685e+39 28.5
26	Au	290	291	290	290
27	Ag	300	300	300	300	2.099e+38 0.6	6.253e+37 0.2	2.725e+38 0.8
28	Au	304	304	305	304
29	Ag	311	311	311	311	1.035e+38 0.3	9.149e+37 0.3	1.950e+38 0.6
30	Au	328	330	332	329
31	Ag	332	332	334	332	4.226e+38 1.2	6.108e+37 0.2	4.837e+38 1.4
32	Au	343	343	355	343
33	Ag	360	360	360	360	3.575e+38 1.1	2.321e+38 0.7	5.896e+38 1.7
34	Au	364	365	364	370
35	Au	375	378	378	389
36	Au	389	390	389	390
37	Au	390	391	391	391
38	Ag	391	394	394	394	1.735e+38 0.5	2.379e+38 0.7	4.114e+38 1.2
39	Ag	394	403	409	409	1.335e+39 3.9	1.630e+38 0.5	1.498e+39 4.4
40	Ag	409	409	411	410	1.398e+39 4.1	8.356e+37 0.2	1.482e+39 4.4
41	Au	411	411	417	415
42	Ag	446	446	446	446	4.141e+38 1.2	1.654e+38 0.5	5.796e+38 1.7
43	Au	454	455	456	454
44	Au	461	462	461	461
45	Ag	470	470	470	470	4.441e+38 1.3	4.095e+37 0.1	4.850e+38 1.4
46	Ag	474	474	474	474	5.285e+39 15.6	1.501e+38 0.4	5.435e+39 16.0
47	Ag	501	501	501	501	3.392e+40 99.8	5.107e+37 0.2	3.397e+40 100.0
48	Au	529	531	543	529
49	Ag	565	565	565	565	1.932e+39 5.7	6.939e+36 0.0	1.939e+39 5.7
50	Au	566	575	567	572
51	Au	586	597	590	605
52	Ag	621	621	621	621	1.590e+38 0.5	1.769e+38 0.5	3.359e+38 1.0
53	Ag	629	629	629	629	1.190e+39 3.5	2.848e+37 0.1	1.218e+39 3.6
54	Au	629	652	632	633
55	Au	722	722	723	724
56	Ag	724	724	724	724	2.524e+39 7.4	1.709e+38 0.5	2.695e+39 7.9
57	Au	727	728	727	727
58	Ag	744	744	744	744	1.008e+39 3.0	7.029e+38 2.1	1.711e+39 5.0
59	Au	747	747	753	750
60	Au	777	786	777	777
61	Ag	789	789	789	789	1.694e+39 5.0	2.489e+38 0.7	1.943e+39 5.7
62	Ag	792	792	792	792	6.793e+38 2.0	3.743e+38 1.1	1.054e+39 3.1
63	Au	901	901	904	904
64	Ag	904	904	915	907	9.408e+38 2.8	1.190e+39 3.5	2.131e+39 6.3
65	Ag	915	915	916	915	3.646e+38 1.1	4.483e+38 1.3	8.129e+38 2.4
66	Au	919	927	949	949
67	Ag	949	949	962	964	3.002e+38 0.9	2.120e+38 0.6	5.122e+38 1.5
68	Au	964	969	969	969
69	Ag	969	978	979	971	1.795e+38 0.5	1.957e+38 0.6	3.752e+38 1.1
70	Au	979	991	991	997
71	Ag	1012	1012	1012	1012	2.821e+38 0.8	3.390e+38 1.0	6.211e+38 1.8
72	Au	1028	1028	1028	1028
73	Au	1037	1045	1038	1041
74	Ag	1045	1060	1045	1045	1.657e+38 0.5	8.376e+37 0.2	2.495e+38 0.7
75	Ag	1060	1076	1060	1060	4.047e+38 1.2	3.643e+38 1.1	7.690e+38 2.3
76	Au	1077	1080	1080	1080
77	Ag	1080	1084	1099	1082	3.735e+38 1.1	3.594e+38 1.1	7.329e+38 2.2
78	Au	1099	1137	1126	1145

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.