- RANKINITE - Ca₃Si₂O₇

Theoretical atomic positions and lattice parameters at experimental volum from 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:	1 2 2
number of shifts:	1
shifts:	0 0 0
Kinetic energy cut-off:	40 Ha [=1088.464 eV ]
eXchange-Correlation functional:	LDA pw90

Pseudopotentials:
Ca:	calcium, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 0 local
Si:	silicon, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 2 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):

Ca:	2.2588	0.1588	-0.0533
	0.1135	2.2202	0.1066
	-0.0582	0.1374	2.2552
Eig. Value:	2.3944	2.0278	2.3120
Ca:	2.1806	-0.1828	0.0242
	-0.2407	2.2214	0.1015
	-0.0055	0.0628	2.1617
Eig. Value:	1.9677	2.4254	2.1707
Ca:	2.4170	-0.1239	-0.0159
	-0.1860	2.2321	0.1111
	0.0090	0.0760	2.1696
Eig. Value:	2.5125	2.0738	2.2325
Si:	2.6555	0.1133	-0.0298
	0.0527	2.6953	0.0341
	0.0668	-0.0988	3.0378
Eig. Value:	2.5873	2.7601	3.0411
Si:	2.5816	0.1550	0.1174
	0.1564	2.8570	-0.0703
	0.0513	0.0943	2.9547
Eig. Value:	2.4999	2.8977	2.9957
O:	-1.6128	-0.3605	0.0424
	-0.3631	-2.1106	0.0705
	0.0281	-0.0081	-1.4996
Eig. Value:	-1.4190	-2.3033	-1.5007
O:	-2.0202	-0.0140	0.2176
	0.0059	-1.5234	-0.0947
	0.2771	-0.1270	-1.6870
Eig. Value:	-2.1556	-1.4364	-1.6385
O:	-1.7303	0.2974	-0.2006
	0.2390	-1.7472	0.0940
	-0.2229	0.1657	-1.7195
Eig. Value:	-1.4477	-2.1450	-1.6043
O:	-1.1529	-0.0320	-0.2250
	-0.0326	-1.4128	-0.0419
	-0.2972	-0.0391	-2.8722
Eig. Value:	-1.1118	-1.4138	-2.9123
O:	-1.4446	-0.0299	-0.0151
	-0.0084	-2.1709	-0.1548
	0.0137	-0.0965	-1.5966
Eig. Value:	-1.4440	-2.1976	-1.5704
O:	-2.0601	0.1243	0.3560
	0.1970	-1.6751	-0.2157
	0.3982	-0.2201	-1.5955
Eig. Value:	-2.3610	-1.6310	-1.3387
O:	-2.0726	-0.2277	-0.2178
	-0.2067	-1.5860	0.0420
	-0.2602	-0.0037	-1.6087
Eig. Value:	-2.2324	-1.4189	-1.6159
Ca:	2.2588	-0.1588	-0.0533
	-0.1135	2.2202	-0.1066
	-0.0582	-0.1374	2.2552
Eig. Value:	2.3944	2.0278	2.3120
Ca:	2.1806	0.1828	0.0242
	0.2407	2.2214	-0.1015
	-0.0055	-0.0628	2.1617
Eig. Value:	1.9677	2.4254	2.1707
Ca:	2.4170	0.1239	-0.0159
	0.1860	2.2321	-0.1111
	0.0090	-0.0760	2.1696
Eig. Value:	2.5125	2.0738	2.2325
Si:	2.6555	-0.1133	-0.0298
	-0.0527	2.6953	-0.0341
	0.0668	0.0988	3.0378
Eig. Value:	2.5873	2.7601	3.0411
Si:	2.5816	-0.1550	0.1174
	-0.1564	2.8570	0.0703
	0.0513	-0.0943	2.9547
Eig. Value:	2.4999	2.8977	2.9957
O:	-1.6128	0.3605	0.0424
	0.3631	-2.1106	-0.0705
	0.0281	0.0081	-1.4996
Eig. Value:	-1.4190	-2.3033	-1.5007
O:	-2.0202	0.0140	0.2176
	-0.0059	-1.5234	0.0947
	0.2771	0.1270	-1.6870
Eig. Value:	-2.1556	-1.4364	-1.6385
O:	-1.7303	-0.2974	-0.2006
	-0.2390	-1.7472	-0.0940
	-0.2229	-0.1657	-1.7195
Eig. Value:	-1.4477	-2.1450	-1.6043
O:	-1.1529	0.0320	-0.2250
	0.0326	-1.4128	0.0419
	-0.2972	0.0391	-2.8722
Eig. Value:	-1.1118	-1.4138	-2.9123
O:	-1.4446	0.0299	-0.0151
	0.0084	-2.1709	0.1548
	0.0137	0.0965	-1.5966
Eig. Value:	-1.4440	-2.1976	-1.5704
O:	-2.0601	-0.1243	0.3560
	-0.1970	-1.6751	0.2157
	0.3982	0.2201	-1.5955
Eig. Value:	-2.3610	-1.6310	-1.3387
O:	-2.0726	0.2277	-0.2178
	0.2067	-1.5860	-0.0420
	-0.2602	0.0037	-1.6087
Eig. Value:	-2.2324	-1.4189	-1.6159
Ca:	2.2588	0.1588	-0.0533
	0.1135	2.2202	0.1066
	-0.0582	0.1374	2.2552
Eig. Value:	2.3944	2.0278	2.3120
Ca:	2.1806	-0.1828	0.0242
	-0.2407	2.2214	0.1015
	-0.0055	0.0628	2.1617
Eig. Value:	1.9677	2.4254	2.1707
Ca:	2.4170	-0.1239	-0.0159
	-0.1860	2.2321	0.1111
	0.0090	0.0760	2.1696
Eig. Value:	2.5125	2.0738	2.2325
Si:	2.6555	0.1133	-0.0298
	0.0527	2.6953	0.0341
	0.0668	-0.0988	3.0378
Eig. Value:	2.5873	2.7601	3.0411
Si:	2.5816	0.1550	0.1174
	0.1564	2.8570	-0.0703
	0.0513	0.0943	2.9547
Eig. Value:	2.4999	2.8977	2.9957
O:	-1.6128	-0.3605	0.0424
	-0.3631	-2.1106	0.0705
	0.0281	-0.0081	-1.4996
Eig. Value:	-1.4190	-2.3033	-1.5007
O:	-2.0202	-0.0140	0.2176
	0.0059	-1.5234	-0.0947
	0.2771	-0.1270	-1.6870
Eig. Value:	-2.1556	-1.4364	-1.6385
O:	-1.7303	0.2974	-0.2006
	0.2390	-1.7472	0.0940
	-0.2229	0.1657	-1.7195
Eig. Value:	-1.4477	-2.1450	-1.6043
O:	-1.1529	-0.0320	-0.2250
	-0.0326	-1.4128	-0.0419
	-0.2972	-0.0391	-2.8722
Eig. Value:	-1.1118	-1.4138	-2.9123
O:	-1.4446	-0.0299	-0.0151
	-0.0084	-2.1709	-0.1548
	0.0137	-0.0965	-1.5966
Eig. Value:	-1.4440	-2.1976	-1.5704
O:	-2.0601	0.1243	0.3560
	0.1970	-1.6751	-0.2157
	0.3982	-0.2201	-1.5955
Eig. Value:	-2.3610	-1.6310	-1.3387
O:	-2.0726	-0.2277	-0.2178
	-0.2067	-1.5860	0.0420
	-0.2602	-0.0037	-1.6087
Eig. Value:	-2.2324	-1.4189	-1.6159
Ca:	2.2588	-0.1588	-0.0533
	-0.1135	2.2202	-0.1066
	-0.0582	-0.1374	2.2552
Eig. Value:	2.3944	2.0278	2.3120
Ca:	2.1806	0.1828	0.0242
	0.2407	2.2214	-0.1015
	-0.0055	-0.0628	2.1617
Eig. Value:	1.9677	2.4254	2.1707
Ca:	2.4170	0.1239	-0.0159
	0.1860	2.2321	-0.1111
	0.0090	-0.0760	2.1696
Eig. Value:	2.5125	2.0738	2.2325
Si:	2.6555	-0.1133	-0.0298
	-0.0527	2.6953	-0.0341
	0.0668	0.0988	3.0378
Eig. Value:	2.5873	2.7601	3.0411
Si:	2.5816	-0.1550	0.1174
	-0.1564	2.8570	0.0703
	0.0513	-0.0943	2.9547
Eig. Value:	2.4999	2.8977	2.9957
O:	-1.6128	0.3605	0.0424
	0.3631	-2.1106	-0.0705
	0.0281	0.0081	-1.4996
Eig. Value:	-1.4190	-2.3033	-1.5007
O:	-2.0202	0.0140	0.2176
	-0.0059	-1.5234	0.0947
	0.2771	0.1270	-1.6870
Eig. Value:	-2.1556	-1.4364	-1.6385
O:	-1.7303	-0.2974	-0.2006
	-0.2390	-1.7472	-0.0940
	-0.2229	-0.1657	-1.7195
Eig. Value:	-1.4477	-2.1450	-1.6043
O:	-1.1529	0.0320	-0.2250
	0.0326	-1.4128	0.0419
	-0.2972	0.0391	-2.8722
Eig. Value:	-1.1118	-1.4138	-2.9123
O:	-1.4446	0.0299	-0.0151
	0.0084	-2.1709	0.1548
	0.0137	0.0965	-1.5966
Eig. Value:	-1.4440	-2.1976	-1.5704
O:	-2.0601	-0.1243	0.3560
	-0.1970	-1.6751	0.2157
	0.3982	0.2201	-1.5955
Eig. Value:	-2.3610	-1.6310	-1.3387
O:	-2.0726	0.2277	-0.2178
	0.2067	-1.5860	-0.0420
	-0.2602	0.0037	-1.6087
Eig. Value:	-2.2324	-1.4189	-1.6159

Atom type

Dielectric tensors:

	X	Y	Z
Ɛ_∞:	2.7368	0.0000	0.0000
	0.0000	2.7217	0.0000
	0.0000	0.0000	2.7622
Eig. Value:	2.7365	2.7217	2.7625
Refractive index (N):	1.6543	0.0000	0.0000
	0.0000	1.6498	0.0000
	0.0000	0.0000	1.6620
Eig. Value:	1.6542	1.6498	1.6621
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	60	60	61	60
5	Ag	72	72	72	72	1.358e+39 2.4	2.775e+38 0.5	1.635e+39 2.9
6	Bg	95	95	95	95	3.090e+38 0.6	4.571e+38 0.8	7.661e+38 1.4
7	Bu	109	109	109	117
8	Ag	122	122	122	122	6.488e+38 1.2	4.948e+37 0.1	6.983e+38 1.3
9	Bg	123	123	123	123	6.885e+37 0.1	1.155e+38 0.2	1.844e+38 0.3
10	Au	129	129	130	129
11	Ag	131	131	131	131	2.061e+38 0.4	1.017e+38 0.2	3.078e+38 0.6
12	Bu	137	138	137	138
13	Ag	138	138	138	138	9.044e+38 1.6	1.571e+37 0.0	9.201e+38 1.7
14	Au	139	139	139	139
15	Bu	142	142	142	142
16	Bu	142	144	142	143
17	Ag	149	149	149	149	8.851e+38 1.6	2.800e+37 0.1	9.131e+38 1.6
18	Bu	150	150	150	152
19	Bg	155	155	155	155	1.403e+38 0.3	2.315e+38 0.4	3.717e+38 0.7
20	Bu	156	156	156	156
21	Bu	156	156	157	158
22	Au	159	159	162	159
23	Ag	168	168	168	168	6.707e+38 1.2	6.256e+37 0.1	7.332e+38 1.3
24	Bg	169	169	169	169	8.730e+37 0.2	1.473e+38 0.3	2.346e+38 0.4
25	Au	172	172	173	172
26	Bg	173	173	174	173
27	Ag	176	176	176	176	6.120e+37 0.1	5.711e+37 0.1	1.183e+38 0.2
28	Au	181	181	181	181
29	Bg	188	188	188	188	4.110e+38 0.7	4.369e+38 0.8	8.479e+38 1.5
30	Bu	189	190	189	189
31	Au	191	191	192	191
32	Bu	192	193	193	192
33	Ag	195	195	195	195	3.865e+38 0.7	2.711e+38 0.5	6.576e+38 1.2
34	Ag	203	203	203	203	9.119e+37 0.2	4.961e+37 0.1	1.408e+38 0.3
35	Au	203	203	205	203
36	Bg	212	212	212	212	1.459e+38 0.3	1.908e+38 0.3	3.368e+38 0.6
37	Bu	215	215	215	215
38	Bu	215	216	215	220
39	Bg	220	220	220	222	1.699e+38 0.3	1.904e+38 0.3	3.603e+38 0.6
40	Ag	222	222	222	226	2.607e+39 4.7	1.561e+38 0.3	2.763e+39 5.0
41	Bg	226	226	226	232	2.263e+38 0.4	3.112e+38 0.6	5.375e+38 1.0
42	Bg	232	232	232	234	2.369e+37 0.0	3.258e+37 0.1	5.627e+37 0.1
43	Ag	234	234	234	237	3.033e+38 0.5	1.448e+38 0.3	4.481e+38 0.8
44	Ag	237	237	237	239	4.347e+38 0.8	5.304e+38 1.0	9.651e+38 1.7
45	Au	239	239	241	243
46	Au	243	243	244	243
47	Bu	244	248	249	249
48	Bg	249	249	250	250	2.535e+38 0.5	3.242e+38 0.6	5.778e+38 1.0
49	Bg	254	254	254	254	2.614e+38 0.5	3.448e+38 0.6	6.063e+38 1.1
50	Ag	255	255	255	255	5.804e+38 1.0	5.613e+37 0.1	6.366e+38 1.1
51	Au	259	259	262	259
52	Ag	262	262	264	262	4.867e+38 0.9	2.261e+38 0.4	7.128e+38 1.3
53	Bu	264	265	266	265
54	Au	266	266	267	266
55	Bg	267	267	270	267	3.124e+38 0.6	4.402e+38 0.8	7.526e+38 1.4
56	Bu	270	270	273	273
57	Au	273	273	280	273
58	Bu	280	284	282	281
59	Bg	284	284	284	284	5.951e+38 1.1	7.851e+38 1.4	1.380e+39 2.5
60	Ag	289	289	289	289	4.853e+38 0.9	3.000e+38 0.5	7.853e+38 1.4
61	Bg	290	290	290	290	3.691e+37 0.1	6.188e+37 0.1	9.878e+37 0.2
62	Au	295	295	295	295
63	Ag	295	295	297	295	8.169e+38 1.5	6.900e+38 1.2	1.507e+39 2.7
64	Bu	298	300	298	299
65	Au	300	301	301	300
66	Bg	301	308	308	301	1.980e+38 0.4	3.142e+38 0.6	5.123e+38 0.9
67	Bu	308	313	313	309
68	Ag	313	320	318	313	5.464e+38 1.0	2.868e+38 0.5	8.332e+38 1.5
69	Ag	320	327	320	320	9.976e+38 1.8	2.771e+38 0.5	1.275e+39 2.3
70	Au	327	329	328	327
71	Bg	329	331	329	329	1.755e+39 3.2	2.037e+39 3.7	3.791e+39 6.8
72	Bu	332	339	332	339
73	Au	339	347	348	340
74	Bu	348	350	352	352
75	Ag	352	352	353	353	3.508e+39 6.3	3.171e+39 5.7	6.679e+39 12.0
76	Au	353	353	353	353
77	Bg	353	353	358	353	2.418e+38 0.4	3.884e+38 0.7	6.302e+38 1.1
78	Bu	358	360	361	359
79	Bg	364	364	364	364	4.248e+38 0.8	6.873e+38 1.2	1.112e+39 2.0
80	Ag	370	370	370	370	4.488e+38 0.8	5.581e+38 1.0	1.007e+39 1.8
81	Bu	372	373	372	373
82	Au	373	373	373	373
83	Bg	373	377	384	373	2.397e+38 0.4	3.749e+38 0.7	6.146e+38 1.1
84	Ag	384	384	391	384	8.393e+38 1.5	4.603e+38 0.8	1.300e+39 2.3
85	Bg	410	410	410	410	2.818e+38 0.5	4.718e+38 0.8	7.536e+38 1.4
86	Ag	419	419	419	419	1.283e+39 2.3	9.826e+38 1.8	2.265e+39 4.1
87	Bu	420	423	420	421
88	Au	423	433	425	423
89	Ag	448	448	448	448	7.721e+38 1.4	2.451e+38 0.4	1.017e+39 1.8
90	Bg	450	450	450	450	5.492e+38 1.0	6.046e+38 1.1	1.154e+39 2.1
91	Au	452	452	456	452
92	Bu	456	456	457	457
93	Bu	465	466	465	470
94	Ag	470	470	470	470	9.855e+38 1.8	1.245e+39 2.2	2.230e+39 4.0
95	Ag	470	470	472	472	7.485e+37 0.1	9.398e+37 0.2	1.688e+38 0.3
96	Bu	472	472	472	472
97	Ag	472	472	472	476	4.478e+38 0.8	4.168e+38 0.7	8.646e+38 1.6
98	Bg	476	476	476	501	3.614e+38 0.6	5.987e+38 1.1	9.601e+38 1.7
99	Bg	501	501	501	509	5.559e+38 1.0	9.031e+38 1.6	1.459e+39 2.6
100	Ag	509	509	509	512	1.605e+39 2.9	1.784e+38 0.3	1.784e+39 3.2
101	Au	512	512	513	513
102	Bu	521	523	521	521
103	Au	523	523	523	523
104	Bg	523	524	523	523	3.645e+38 0.7	5.236e+38 0.9	8.882e+38 1.6
105	Bu	528	534	528	534
106	Ag	534	534	534	534	1.064e+39 1.9	1.391e+38 0.2	1.203e+39 2.2
107	Au	534	542	540	545
108	Bg	545	545	545	545	6.201e+38 1.1	9.433e+38 1.7	1.563e+39 2.8
109	Ag	545	545	545	545	1.522e+39 2.7	1.187e+39 2.1	2.709e+39 4.9
110	Au	548	548	550	548
111	Bu	550	551	551	551
112	Bg	551	560	554	567	8.480e+38 1.5	1.335e+39 2.4	2.183e+39 3.9
113	Au	641	641	649	641
114	Bg	651	651	651	651	2.321e+37 0.0	2.863e+37 0.1	5.184e+37 0.1
115	Ag	657	657	657	657	1.480e+40 26.6	1.578e+38 0.3	1.496e+40 26.9
116	Bu	668	668	668	668
117	Bu	832	833	832	833
118	Au	833	834	834	835
119	Ag	835	835	835	839	1.728e+39 3.1	4.078e+37 0.1	1.769e+39 3.2
120	Bg	839	839	839	854	1.271e+38 0.2	1.357e+38 0.2	2.628e+38 0.5
121	Ag	877	877	877	877	5.542e+40 99.6	2.400e+38 0.4	5.566e+40 100.0
122	Bg	884	884	884	884	9.623e+37 0.2	1.371e+38 0.2	2.334e+38 0.4
123	Bu	891	894	891	894
124	Au	897	897	901	897
125	Bu	920	921	920	927
126	Ag	930	930	930	930	3.480e+36 0.0	1.675e+36 0.0	5.155e+36 0.0
127	Ag	930	930	931	930	1.381e+38 0.2	6.251e+37 0.1	2.006e+38 0.4
128	Bu	933	933	933	933
129	Bg	933	933	933	935	3.378e+38 0.6	3.596e+38 0.6	6.974e+38 1.3
130	Ag	935	935	935	939	1.846e+39 3.3	6.057e+38 1.1	2.452e+39 4.4
131	Au	939	939	942	943
132	Bu	945	949	945	949
133	Au	949	958	955	958
134	Bg	958	958	958	958	7.893e+39 14.2	7.715e+38 1.4	8.664e+39 15.6
135	Bg	958	969	958	962	1.717e+39 3.1	3.946e+38 0.7	2.112e+39 3.8
136	Ag	969	970	969	969	6.491e+39 11.7	8.012e+38 1.4	7.292e+39 13.1
137	Au	973	973	973	973
138	Bu	973	981	981	981
139	Bg	981	989	988	989	4.756e+37 0.1	7.719e+37 0.1	1.247e+38 0.2
140	Au	989	992	994	989
141	Bu	994	1000	1000	1000
142	Ag	1000	1002	1002	1002	8.568e+38 1.5	9.146e+38 1.6	1.771e+39 3.2
143	Bg	1002	1029	1041	1005	5.174e+38 0.9	8.047e+38 1.4	1.322e+39 2.4
144	Bg	1041	1041	1045	1041	1.989e+39 3.6	2.640e+39 4.7	4.630e+39 8.3

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.