- GROSSULAR - Ca₃Al₂(SiO₄)₃

Theoretical atomic positions and lattice parameters at experimental volum from AMCSD

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:	230		Ia-3d
Lattice parameters (Å):	11.8063	11.8063		11.8063
Angles (°):	90	90		90

Symmetry (theoretical):

Space group:	230		Ia-3d
Lattice parameters (Å):	0.5292	0.5292		0.5292
Angles (°):	109.47	109.47		109.47

Cell contents:

Number of atoms:	80
Number of atom types:	4
Chemical composition:	0

Atomic positions (theoretical):

Si:	0.2500	0.6250	0.3750
Al:	0.0000	0.0000	0.0000
Ca:	0.2500	0.3750	0.1250
O:	0.6950	0.6897	0.0838
Si:	0.3750	0.2500	0.6250
Ca:	0.1250	0.2500	0.3750
O:	0.0838	0.6950	0.6897
Si:	0.7500	0.8750	0.1250
Al:	0.5000	0.0000	0.5000
Ca:	0.7500	0.1250	0.3750
O:	0.1059	0.6113	0.4162
Al:	0.0000	0.5000	0.5000
O:	0.3941	0.8103	0.5053
Si:	0.6250	0.7500	0.3750
Al:	0.5000	0.0000	0.0000
Ca:	0.3750	0.7500	0.1250
O:	0.8887	0.3941	0.0838
Si:	0.6250	0.3750	0.2500
Ca:	0.3750	0.1250	0.2500
O:	0.6897	0.0838	0.6950
Si:	0.1250	0.7500	0.8750
Al:	0.5000	0.5000	0.0000
O:	0.4162	0.1059	0.6113
O:	0.5053	0.3941	0.8103
Si:	0.3750	0.6250	0.7500
Al:	0.0000	0.5000	0.0000
Ca:	0.1250	0.3750	0.7500
O:	0.0838	0.8887	0.3941
O:	0.8050	0.8887	0.9947
Si:	0.8750	0.2500	0.1250
Al:	0.5000	0.5000	0.5000
O:	0.8103	0.8050	0.4162
O:	0.9947	0.8050	0.8887
O:	0.6897	0.1059	0.9947
Si:	0.7500	0.3750	0.6250
O:	0.1059	0.9947	0.6897
Al:	0.0000	0.0000	0.5000
O:	0.6113	0.6950	0.5053
Si:	0.8750	0.1250	0.7500
O:	0.6113	0.4162	0.1059
O:	0.8103	0.5053	0.3941
O:	0.3941	0.0838	0.8887
Si:	0.1250	0.8750	0.2500
O:	0.4162	0.8103	0.8050
O:	0.8887	0.9947	0.8050
O:	0.9947	0.6897	0.1059
O:	0.5053	0.6113	0.6950
Si:	0.2500	0.1250	0.8750
O:	0.8050	0.4162	0.8103
O:	0.6950	0.5053	0.6113
Ca:	0.7500	0.6250	0.8750
O:	0.3050	0.3103	0.9162
Ca:	0.8750	0.7500	0.6250
O:	0.9162	0.3050	0.3103
Ca:	0.2500	0.8750	0.6250
O:	0.8941	0.3887	0.5838
O:	0.6059	0.1897	0.4947
Ca:	0.6250	0.2500	0.8750
O:	0.1113	0.6059	0.9162
Ca:	0.6250	0.8750	0.7500
O:	0.3103	0.9162	0.3050
O:	0.5838	0.8941	0.3887
O:	0.4947	0.6059	0.1897
Ca:	0.8750	0.6250	0.2500
O:	0.9162	0.1113	0.6059
O:	0.1950	0.1113	0.0053
O:	0.1897	0.1950	0.5838
O:	0.0053	0.1950	0.1113
O:	0.3103	0.8941	0.0053
O:	0.8941	0.0053	0.3103
O:	0.3887	0.3050	0.4947
O:	0.3887	0.5838	0.8941
O:	0.1897	0.4947	0.6059
O:	0.6059	0.9162	0.1113
O:	0.5838	0.1897	0.1950
O:	0.1113	0.0053	0.1950
O:	0.0053	0.3103	0.8941
O:	0.4947	0.3887	0.3050
O:	0.1950	0.5838	0.1897
O:	0.3050	0.4947	0.3887

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.

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	T1u	0	0	0	0
2	T1u	0	0	0	0
3	T1u	0	0	0	0
4	T1u	156	156	156	156
5	T1u	156	156	156	156
6	T1u	156	157	157	157
7	T2u	157	157	157	157
8	T2u	157	157	157	157
9	T2u	157	157	157	157
10	Eg	177	177	177	177	2.819e+38 0.5	2.114e+38 0.4	4.933e+38 1.0
11	Eg	177	177	177	177	2.819e+38 0.5	2.114e+38 0.4	4.933e+38 1.0
12	T2g	184	184	184	184
13	T2g	184	184	184	184
14	T2g	184	184	184	184
15	T1u	185	185	185	185
16	T1u	185	185	185	185
17	T1u	185	187	187	187
18	T1g	187	187	187	187
19	T1g	187	187	187	187
20	T1g	187	189	189	189
21	T2u	190	190	190	190
22	T2u	190	190	190	190
23	T2u	190	190	190	190
24	T1g	194	194	194	194
25	T1g	194	194	194	194
26	T1g	194	194	194	194
27	A2g	197	197	197	197
28	A2u	197	197	197	197
29	T1u	203	203	203	203
30	T1u	203	203	203	203
31	T1u	203	204	204	204
32	T1g	233	233	233	233
33	T1g	233	233	233	233
34	T1g	233	233	233	233
35	Eu	234	234	234	234
36	Eu	234	234	234	234
37	T1u	242	242	242	242
38	T1u	242	242	242	242
39	T1u	242	244	244	244
40	T2g	244	244	244	244	1.079e+38 0.2	1.512e+38 0.3	2.590e+38 0.5
41	T2g	244	244	244	244	1.079e+38 0.2	1.814e+38 0.4	2.893e+38 0.6
42	T2g	244	247	247	247	1.078e+38 0.2	1.148e+38 0.2	2.226e+38 0.4
43	T2g	250	250	250	250	1.653e+38 0.3	1.992e+38 0.4	3.645e+38 0.7
44	T2g	250	250	250	250	1.653e+38 0.3	2.691e+38 0.5	4.344e+38 0.8
45	T2g	250	250	250	250	1.653e+38 0.3	2.136e+38 0.4	3.790e+38 0.7
46	T2u	252	252	252	252
47	T2u	252	252	252	252
48	T2u	252	252	252	252
49	T2g	279	279	279	279	3.700e+38 0.7	5.243e+38 1.0	8.943e+38 1.7
50	T2g	279	279	279	279	3.701e+38 0.7	6.192e+38 1.2	9.893e+38 1.9
51	T2g	279	279	279	279	3.697e+38 0.7	3.957e+38 0.8	7.654e+38 1.5
52	T1g	286	286	286	286
53	T1g	286	286	286	286
54	T1g	286	286	286	286
55	T2u	295	295	295	295
56	T2u	295	295	295	295
57	T2u	295	295	295	295
58	A2u	296	296	296	296
59	A1u	298	298	298	298
60	Eu	302	302	302	302
61	Eu	302	302	302	302
62	T1g	302	302	302	302
63	T1g	302	302	302	302
64	T1g	302	302	302	302
65	T1u	309	309	309	309
66	T1u	309	309	309	309
67	T1u	309	312	312	312
68	Eg	319	319	319	319	4.696e+37 0.1	3.522e+37 0.1	8.218e+37 0.2
69	Eg	319	319	319	319	4.696e+37 0.1	3.522e+37 0.1	8.218e+37 0.2
70	T2u	325	325	325	325
71	T2u	325	325	325	325
72	T2u	325	325	325	325
73	Eu	326	326	326	326
74	Eu	326	326	326	326
75	T2u	330	330	330	330
76	T2u	330	330	330	330
77	T2u	330	330	330	330
78	T1g	337	337	337	337
79	T1g	337	337	337	337
80	T1g	337	337	337	337
81	T2g	338	338	338	338	8.981e+37 0.2	9.927e+37 0.2	1.891e+38 0.4
82	T2g	338	338	338	338	8.981e+37 0.2	1.348e+38 0.3	2.246e+38 0.4
83	T2g	338	338	338	338	8.961e+37 0.2	1.341e+38 0.3	2.237e+38 0.4
84	T2g	345	345	345	345	5.093e+36 0.0	7.003e+36 0.0	1.210e+37 0.0
85	T2g	345	345	345	345	4.920e+36 0.0	6.765e+36 0.0	1.169e+37 0.0
86	T2g	345	345	345	345	5.076e+36 0.0	6.979e+36 0.0	1.206e+37 0.0
87	T1u	354	354	354	354
88	T1u	354	354	354	354
89	T1u	354	354	354	354
90	T2u	355	355	355	355
91	T2u	355	355	355	355
92	T2u	355	355	355	355
93	Eg	372	372	372	372	5.655e+38 1.1	4.241e+38 0.8	9.896e+38 1.9
94	Eg	372	372	372	372	5.655e+38 1.1	4.241e+38 0.8	9.896e+38 1.9
95	A1g	374	374	374	374	1.392e+40 26.9	6.448e+29 0.0	1.392e+40 26.9
96	A1u	380	380	380	380
97	T1u	390	390	390	390
98	T1u	390	390	390	390
99	T1u	390	391	391	391
100	T1g	391	391	391	391
101	T1g	391	391	391	391
102	T1g	391	392	392	392
103	T2g	392	392	392	392	9.799e+36 0.0	1.347e+37 0.0	2.327e+37 0.0
104	T2g	392	392	392	392	9.802e+36 0.0	1.348e+37 0.0	2.328e+37 0.0
105	T2g	392	396	396	396	9.937e+36 0.0	1.366e+37 0.0	2.360e+37 0.0
106	Eu	396	396	396	396
107	Eu	396	407	407	407
108	A2g	407	409	409	409
109	T2u	412	412	412	412
110	T2u	412	412	412	412
111	T2u	412	412	412	412
112	T1u	413	413	413	413
113	T1u	413	413	413	413
114	T1u	413	413	413	413
115	Eu	414	414	414	414
116	Eu	414	414	414	414
117	T1u	416	416	416	416
118	T1u	416	416	416	416
119	T1u	416	419	419	419
120	T2u	432	432	432	432
121	T2u	432	432	432	432
122	T2u	432	432	432	432
123	T1g	433	433	433	433
124	T1g	433	433	433	433
125	T1g	433	433	433	433
126	Eg	438	438	438	438	3.240e+38 0.6	2.430e+38 0.5	5.670e+38 1.1
127	Eg	438	438	438	438	3.240e+38 0.6	2.430e+38 0.5	5.670e+38 1.1
128	A2g	441	441	441	441
129	Eu	448	448	448	448
130	Eu	448	448	448	448
131	T1u	450	450	450	450
132	T1u	450	450	450	450
133	T1u	450	453	453	453
134	A2u	453	453	453	453
135	T2u	453	453	453	453
136	T2u	453	453	453	453
137	T2u	453	457	457	457
138	A1u	457	465	465	465
139	T1u	466	466	466	466
140	T1u	466	466	466	466
141	T1u	466	471	471	471
142	T1g	471	471	471	471
143	T1g	471	471	471	471
144	T1g	471	474	474	474
145	T2g	474	474	474	474	1.555e+38 0.3	2.282e+38 0.4	3.837e+38 0.7
146	T2g	474	474	474	474	1.556e+38 0.3	1.544e+38 0.3	3.101e+38 0.6
147	T2g	474	495	495	495	1.556e+38 0.3	2.614e+38 0.5	4.171e+38 0.8
148	T1u	495	495	495	495
149	T1u	495	495	495	495
150	T1u	495	497	497	497
151	A2u	497	500	500	500
152	T1g	500	500	500	500
153	T1g	500	500	500	500
154	T1g	500	506	506	506
155	T2g	506	506	506	506	3.744e+38 0.7	5.188e+38 1.0	8.932e+38 1.7
156	T2g	506	506	506	506	3.744e+38 0.7	5.039e+38 1.0	8.783e+38 1.7
157	T2g	506	516	516	516	3.744e+38 0.7	5.216e+38 1.0	8.960e+38 1.7
158	T2u	516	516	516	516
159	T2u	516	516	516	516
160	T2u	516	522	522	522
161	Eg	524	524	524	524	1.082e+38 0.2	8.113e+37 0.2	1.893e+38 0.4
162	Eg	524	524	524	524	1.082e+38 0.2	8.113e+37 0.2	1.893e+38 0.4
163	T1u	528	528	528	528
164	T1u	528	528	528	528
165	T1u	528	545	545	545
166	A1g	545	557	557	557	2.180e+38 0.4	4.739e+27 0.0	2.180e+38 0.4
167	Eu	557	557	557	557
168	Eu	557	562	562	562
169	T1g	562	562	562	562
170	T1g	562	562	562	562
171	T1g	562	566	566	566
172	T2g	567	567	567	567	1.954e+37 0.0	2.687e+37 0.1	4.641e+37 0.1
173	T2g	567	567	567	567	1.982e+37 0.0	2.968e+37 0.1	4.950e+37 0.1
174	T2g	567	567	567	567	1.985e+37 0.0	2.665e+37 0.1	4.651e+37 0.1
175	A2g	568	568	568	568
176	T2u	578	578	578	578
177	T2u	578	578	578	578
178	T2u	578	578	578	578
179	Eg	587	587	587	587	2.020e+38 0.4	1.515e+38 0.3	3.536e+38 0.7
180	Eg	587	587	587	587	2.020e+38 0.4	1.515e+38 0.3	3.536e+38 0.7
181	T2u	598	598	598	598
182	T2u	598	598	598	598
183	T2u	598	598	598	598
184	T1u	609	609	609	609
185	T1u	609	609	609	609
186	T1u	609	616	616	616
187	T2g	616	616	616	616	6.906e+37 0.1	1.101e+38 0.2	1.792e+38 0.3
188	T2g	616	616	616	616	6.906e+37 0.1	6.185e+37 0.1	1.309e+38 0.3
189	T2g	616	616	616	616	6.906e+37 0.1	1.129e+38 0.2	1.820e+38 0.4
190	Eu	626	626	626	626
191	Eu	626	626	626	626
192	A1u	638	638	638	638
193	T1g	793	793	793	793
194	T1g	793	793	793	793
195	T1g	793	793	793	793
196	Eg	801	801	801	801	9.338e+35 0.0	7.004e+35 0.0	1.634e+36 0.0
197	Eg	801	801	801	801	9.337e+35 0.0	7.001e+35 0.0	1.634e+36 0.0
198	T2g	807	807	807	807	1.932e+39 3.7	2.245e+39 4.3	4.177e+39 8.1
199	T2g	807	807	807	807	1.932e+39 3.7	3.040e+39 5.9	4.972e+39 9.6
200	T2g	807	807	807	807	1.932e+39 3.7	2.679e+39 5.2	4.611e+39 8.9
201	T2u	810	810	810	810
202	T2u	810	810	810	810
203	T2u	810	810	810	810
204	T1g	819	819	819	819
205	T1g	819	819	819	819
206	T1g	819	819	819	819
207	T1u	820	820	820	820
208	T1u	820	820	820	820
209	T1u	820	826	826	826
210	A2u	826	827	827	827
211	T2g	827	827	827	827	8.238e+38 1.6	1.153e+39 2.2	1.977e+39 3.8
212	T2g	827	827	827	827	8.238e+38 1.6	1.163e+39 2.3	1.987e+39 3.8
213	T2g	827	834	834	834	8.238e+38 1.6	1.082e+39 2.1	1.906e+39 3.7
214	Eu	837	837	837	837
215	Eu	837	837	837	837
216	T1u	839	839	839	839
217	T1u	839	839	839	839
218	T1u	839	848	848	848
219	A1g	848	853	853	853	5.169e+40 100.0	1.150e+28 0.0	5.169e+40 100.0
220	T2u	853	853	853	853
221	T2u	853	853	853	853
222	T2u	853	855	855	855
223	Eg	855	855	855	855	1.027e+38 0.2	7.702e+37 0.1	1.797e+38 0.3
224	Eg	855	863	863	863	1.027e+38 0.2	7.702e+37 0.1	1.797e+38 0.3
225	Eu	863	863	863	863
226	Eu	863	866	866	866
227	T2u	877	877	877	877
228	T2u	877	877	877	877
229	T2u	877	877	877	877
230	T1u	885	885	885	885
231	T1u	885	885	885	885
232	T1u	885	910	910	910
233	T1g	910	910	910	910
234	T1g	910	910	910	910
235	T1g	910	950	950	950
236	A2g	950	954	954	954
237	A1u	954	978	978	978
238	T2g	987	987	987	987	6.244e+38 1.2	6.957e+38 1.3	1.320e+39 2.6
239	T2g	987	987	987	987	6.244e+38 1.2	1.053e+39 2.0	1.678e+39 3.2
240	T2g	987	987	987	987	6.244e+38 1.2	8.267e+38 1.6	1.451e+39 2.8

No.

Char.

ω TO

ω LOx

ω LOy

ω LOz

I ∥

I ⊥