- PYROPE - Mg₃Al₂(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):	11.4545	11.4545		11.4545
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
Mg:	0.2500	0.3750	0.1250
O:	0.7021	0.6859	0.0817
Si:	0.3750	0.2500	0.6250
Mg:	0.1250	0.2500	0.3750
O:	0.0817	0.7021	0.6859
Si:	0.7500	0.8750	0.1250
Al:	0.5000	0.0000	0.5000
Mg:	0.7500	0.1250	0.3750
O:	0.1042	0.6204	0.4183
Al:	0.0000	0.5000	0.5000
O:	0.3958	0.8141	0.5162
Si:	0.6250	0.7500	0.3750
Al:	0.5000	0.0000	0.0000
Mg:	0.3750	0.7500	0.1250
O:	0.8796	0.3958	0.0817
Si:	0.6250	0.3750	0.2500
Mg:	0.3750	0.1250	0.2500
O:	0.6859	0.0817	0.7021
Si:	0.1250	0.7500	0.8750
Al:	0.5000	0.5000	0.0000
O:	0.4183	0.1042	0.6204
O:	0.5162	0.3958	0.8141
Si:	0.3750	0.6250	0.7500
Al:	0.0000	0.5000	0.0000
Mg:	0.1250	0.3750	0.7500
O:	0.0817	0.8796	0.3958
O:	0.7979	0.8796	0.9838
Si:	0.8750	0.2500	0.1250
Al:	0.5000	0.5000	0.5000
O:	0.8141	0.7979	0.4183
O:	0.9838	0.7979	0.8796
O:	0.6859	0.1042	0.9838
Si:	0.7500	0.3750	0.6250
O:	0.1042	0.9838	0.6859
Al:	0.0000	0.0000	0.5000
O:	0.6204	0.7021	0.5162
Si:	0.8750	0.1250	0.7500
O:	0.6204	0.4183	0.1042
O:	0.8141	0.5162	0.3958
O:	0.3958	0.0817	0.8796
Si:	0.1250	0.8750	0.2500
O:	0.4183	0.8141	0.7979
O:	0.8796	0.9838	0.7979
O:	0.9838	0.6859	0.1042
O:	0.5162	0.6204	0.7021
Si:	0.2500	0.1250	0.8750
O:	0.7979	0.4183	0.8141
O:	0.7021	0.5162	0.6204
Mg:	0.7500	0.6250	0.8750
O:	0.2979	0.3141	0.9183
Mg:	0.8750	0.7500	0.6250
O:	0.9183	0.2979	0.3141
Mg:	0.2500	0.8750	0.6250
O:	0.8958	0.3796	0.5817
O:	0.6042	0.1859	0.4838
Mg:	0.6250	0.2500	0.8750
O:	0.1204	0.6042	0.9183
Mg:	0.6250	0.8750	0.7500
O:	0.3141	0.9183	0.2979
O:	0.5817	0.8958	0.3796
O:	0.4838	0.6042	0.1859
Mg:	0.8750	0.6250	0.2500
O:	0.9183	0.1204	0.6042
O:	0.2021	0.1204	0.0162
O:	0.1859	0.2021	0.5817
O:	0.0162	0.2021	0.1204
O:	0.3141	0.8958	0.0162
O:	0.8958	0.0162	0.3141
O:	0.3796	0.2979	0.4838
O:	0.3796	0.5817	0.8958
O:	0.1859	0.4838	0.6042
O:	0.6042	0.9183	0.1204
O:	0.5817	0.1859	0.2021
O:	0.1204	0.0162	0.2021
O:	0.0162	0.3141	0.8958
O:	0.4838	0.3796	0.2979
O:	0.2021	0.5817	0.1859
O:	0.2979	0.4838	0.3796

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	T2g	68	68	68	68	7.569e+36 0.0	1.041e+37 0.0	1.798e+37 0.0
5	T2g	68	68	68	68	7.470e+36 0.0	1.027e+37 0.0	1.774e+37 0.0
6	T2g	68	68	68	68	7.924e+36 0.0	1.090e+37 0.0	1.882e+37 0.0
7	T2u	81	81	81	81
8	T2u	81	81	81	81
9	T2u	81	81	81	81
10	T1u	94	94	94	94
11	T1u	94	94	94	94
12	T1u	94	119	119	119
13	T1g	125	125	125	125
14	T1g	125	125	125	125
15	T1g	125	125	125	125
16	T1u	129	129	129	129
17	T1u	129	129	129	129
18	T1u	129	129	129	129
19	A2u	129	131	131	131
20	T1g	150	150	150	150
21	T1g	150	150	150	150
22	T1g	150	150	150	150
23	T2g	158	158	158	158	1.161e+37 0.0	1.362e+37 0.0	2.523e+37 0.0
24	T2g	158	158	158	158	1.162e+37 0.0	1.958e+37 0.0	3.120e+37 0.0
25	T2g	158	158	158	158	1.129e+37 0.0	1.231e+37 0.0	2.361e+37 0.0
26	T1u	169	169	169	169
27	T1u	169	169	169	169
28	T1u	169	184	184	184
29	T1g	184	184	184	184
30	T1g	184	184	184	184
31	T1g	184	191	191	191
32	T2g	191	191	191	191	1.148e+38 0.2	1.716e+38 0.3	2.864e+38 0.5
33	T2g	191	191	191	191	1.148e+38 0.2	1.124e+38 0.2	2.272e+38 0.4
34	T2g	191	194	194	194	1.147e+38 0.2	1.898e+38 0.3	3.045e+38 0.5
35	T2u	194	194	194	194
36	T2u	194	194	194	194
37	T2u	194	195	195	195
38	Eg	199	199	199	199	4.540e+37 0.1	3.405e+37 0.1	7.945e+37 0.1
39	Eg	199	199	199	199	4.540e+37 0.1	3.405e+37 0.1	7.945e+37 0.1
40	Eu	200	200	200	200
41	Eu	200	200	200	200
42	T1u	202	202	202	202
43	T1u	202	202	202	202
44	T1u	202	202	202	202
45	T2u	208	208	208	208
46	T2u	208	208	208	208
47	T2u	208	208	208	208
48	A2g	225	225	225	225
49	T1u	247	247	247	247
50	T1u	247	247	247	247
51	T1u	247	249	249	249
52	T2g	249	249	249	249	5.197e+37 0.1	6.593e+37 0.1	1.179e+38 0.2
53	T2g	249	249	249	249	5.198e+37 0.1	8.518e+37 0.1	1.372e+38 0.2
54	T2g	249	251	251	251	5.166e+37 0.1	6.017e+37 0.1	1.118e+38 0.2
55	T2u	255	255	255	255
56	T2u	255	255	255	255
57	T2u	255	255	255	255
58	T1g	260	260	260	260
59	T1g	260	260	260	260
60	T1g	260	260	260	260
61	T2u	272	272	272	272
62	T2u	272	272	272	272
63	T2u	272	272	272	272
64	T1g	272	272	272	272
65	T1g	272	272	272	272
66	T1g	272	272	272	272
67	Eu	281	281	281	281
68	Eu	281	281	281	281
69	Eg	286	286	286	286	1.150e+38 0.2	8.623e+37 0.1	2.012e+38 0.3
70	Eg	286	286	286	286	1.150e+38 0.2	8.623e+37 0.1	2.012e+38 0.3
71	A2g	287	287	287	287
72	A2u	290	290	290	290
73	A1u	291	291	291	291
74	T2g	303	303	303	303	1.083e+38 0.2	1.555e+38 0.2	2.637e+38 0.4
75	T2g	303	303	303	303	1.083e+38 0.2	1.480e+38 0.2	2.562e+38 0.4
76	T2g	303	303	303	303	1.082e+38 0.2	1.436e+38 0.2	2.519e+38 0.4
77	T1g	306	306	306	306
78	T1g	306	306	306	306
79	T1g	306	306	306	306
80	T1u	315	315	315	315
81	T1u	315	315	315	315
82	T1u	315	317	317	317
83	Eg	317	317	317	317	1.406e+38 0.2	1.054e+38 0.2	2.460e+38 0.4
84	Eg	317	319	319	319	1.406e+38 0.2	1.054e+38 0.2	2.460e+38 0.4
85	T2u	319	319	319	319
86	T2u	319	319	319	319
87	T2u	319	327	327	327
88	T2u	327	327	327	327
89	T2u	327	327	327	327
90	T2u	327	329	329	329
91	Eu	329	329	329	329
92	Eu	329	329	329	329
93	T2g	332	332	332	332	1.906e+38 0.3	2.697e+38 0.4	4.603e+38 0.7
94	T2g	332	332	332	332	1.905e+38 0.3	2.543e+38 0.4	4.449e+38 0.7
95	T2g	332	332	332	332	1.905e+38 0.3	2.620e+38 0.4	4.525e+38 0.7
96	T1u	334	334	334	334
97	T1u	334	334	334	334
98	T1u	334	334	334	334
99	A1g	334	334	334	334	1.002e+40 15.9	1.149e+27 0.0	1.002e+40 15.9
100	T1g	334	334	334	334
101	T1g	334	334	334	334
102	T1g	334	337	337	337
103	Eu	353	353	353	353
104	Eu	353	353	353	353
105	A1u	356	356	356	356
106	Eg	356	356	356	356	1.390e+37 0.0	1.039e+37 0.0	2.428e+37 0.0
107	Eg	356	356	356	356	1.393e+37 0.0	1.044e+37 0.0	2.437e+37 0.0
108	T2g	360	360	360	360	2.909e+38 0.5	2.756e+38 0.4	5.665e+38 0.9
109	T2g	360	360	360	360	2.909e+38 0.5	4.908e+38 0.8	7.817e+38 1.2
110	T2g	360	360	360	360	2.909e+38 0.5	4.335e+38 0.7	7.244e+38 1.1
111	T1u	362	362	362	362
112	T1u	362	362	362	362
113	T1u	362	364	364	364
114	T1g	364	364	364	364
115	T1g	364	364	364	364
116	T1g	364	374	374	374
117	A2u	376	376	376	376
118	T2u	379	379	379	379
119	T2u	379	379	379	379
120	T2u	379	379	379	379
121	T1u	401	401	401	401
122	T1u	401	401	401	401
123	T1u	401	404	404	404
124	Eu	413	413	413	413
125	Eu	413	413	413	413
126	A2g	423	423	423	423
127	T2u	427	427	427	427
128	T2u	427	427	427	427
129	T2u	427	427	427	427
130	T1u	432	432	432	432
131	T1u	432	432	432	432
132	T1u	432	439	439	439
133	A1u	439	452	452	452
134	T1u	454	454	454	454
135	T1u	454	454	454	454
136	T1u	454	454	454	454
137	T1g	454	454	454	454
138	T1g	454	454	454	454
139	T1g	454	465	465	465
140	T2g	465	465	465	465	2.893e+38 0.5	4.875e+38 0.8	7.768e+38 1.2
141	T2g	465	465	465	465	2.893e+38 0.5	3.229e+38 0.5	6.122e+38 1.0
142	T2g	465	475	475	475	2.892e+38 0.5	3.792e+38 0.6	6.683e+38 1.1
143	Eu	475	475	475	475
144	Eu	475	476	476	476
145	T2u	476	476	476	476
146	T2u	476	476	476	476
147	T2u	476	483	483	483
148	T1g	483	483	483	483
149	T1g	483	483	483	483
150	T1g	483	491	491	491
151	A2u	491	493	493	493
152	T2g	493	493	493	493	3.125e+38 0.5	4.941e+38 0.8	8.066e+38 1.3
153	T2g	493	493	493	493	3.125e+38 0.5	3.227e+38 0.5	6.352e+38 1.0
154	T2g	493	495	495	495	3.125e+38 0.5	4.724e+38 0.7	7.850e+38 1.2
155	Eg	495	495	495	495	6.408e+37 0.1	4.805e+37 0.1	1.121e+38 0.2
156	Eg	495	501	501	501	6.409e+37 0.1	4.807e+37 0.1	1.122e+38 0.2
157	T2u	504	504	504	504
158	T2u	504	504	504	504
159	T2u	504	504	504	504
160	T1u	506	506	506	506
161	T1u	506	506	506	506
162	T1u	506	526	526	526
163	Eu	526	526	526	526
164	Eu	526	532	532	532
165	A1g	532	532	532	532	9.721e+39 15.4	6.952e+26 0.0	9.721e+39 15.4
166	T1g	550	550	550	550
167	T1g	550	550	550	550
168	T1g	550	550	550	550
169	T1u	550	550	550	550
170	T1u	550	550	550	550
171	T1u	550	565	565	565
172	A2g	565	571	571	571
173	T2g	571	571	571	571	3.250e+37 0.1	4.357e+37 0.1	7.606e+37 0.1
174	T2g	571	571	571	571	3.247e+37 0.1	4.860e+37 0.1	8.107e+37 0.1
175	T2g	571	586	586	586	3.249e+37 0.1	4.220e+37 0.1	7.469e+37 0.1
176	T2u	601	601	601	601
177	T2u	601	601	601	601
178	T2u	601	601	601	601
179	Eg	610	610	610	610
180	Eg	610	610	610	610
181	T2u	618	618	618	618
182	T2u	618	618	618	618
183	T2u	618	618	618	618
184	T2g	620	620	620	620	4.752e+38 0.8	6.533e+38 1.0	1.129e+39 1.8
185	T2g	620	620	620	620	4.752e+38 0.8	5.445e+38 0.9	1.020e+39 1.6
186	T2g	620	620	620	620	4.753e+38 0.8	7.624e+38 1.2	1.238e+39 2.0
187	Eu	633	633	633	633
188	Eu	633	633	633	633
189	T1u	641	641	641	641
190	T1u	641	641	641	641
191	T1u	641	642	642	642
192	A1u	679	679	679	679
193	T1g	815	815	815	815
194	T1g	815	815	815	815
195	T1g	815	815	815	815
196	Eg	828	828	828	828	2.388e+38 0.4	1.791e+38 0.3	4.180e+38 0.7
197	Eg	828	828	828	828	2.388e+38 0.4	1.791e+38 0.3	4.180e+38 0.7
198	T2g	830	830	830	830	2.567e+39 4.1	3.475e+39 5.5	6.042e+39 9.6
199	T2g	830	830	830	830	2.567e+39 4.1	4.298e+39 6.8	6.866e+39 10.9
200	T2g	830	830	830	830	2.567e+39 4.1	2.817e+39 4.5	5.384e+39 8.5
201	T1u	835	835	835	835
202	T1u	835	835	835	835
203	T1u	835	836	836	836
204	T2u	836	836	836	836
205	T2u	836	836	836	836
206	T2u	836	848	848	848
207	T1g	848	848	848	848
208	T1g	848	848	848	848
209	T1g	848	854	854	854
210	T2g	864	864	864	864	2.469e+38 0.4	2.660e+38 0.4	5.129e+38 0.8
211	T2g	864	864	864	864	2.469e+38 0.4	4.014e+38 0.6	6.483e+38 1.0
212	T2g	864	864	864	864	2.469e+38 0.4	3.511e+38 0.6	5.980e+38 0.9
213	T1u	864	864	864	864
214	T1u	864	864	864	864
215	T1u	864	868	868	868
216	A2u	868	871	871	871
217	Eu	871	871	871	871
218	Eu	871	874	874	874
219	T2u	874	874	874	874
220	T2u	874	874	874	874
221	T2u	874	885	885	885
222	A1g	885	900	900	900	6.316e+40 100.0	1.173e+27 0.0	6.316e+40 100.0
223	Eu	900	900	900	900
224	Eu	900	901	901	901
225	Eg	901	901	901	901	1.240e+38 0.2	9.302e+37 0.1	2.171e+38 0.3
226	Eg	901	905	905	905	1.240e+38 0.2	9.302e+37 0.1	2.171e+38 0.3
227	T2u	916	916	916	916
228	T2u	916	916	916	916
229	T2u	916	916	916	916
230	T1u	934	934	934	934
231	T1u	934	934	934	934
232	T1u	934	935	935	935
233	T1g	935	935	935	935
234	T1g	935	935	935	935
235	T1g	935	989	989	989
236	A2g	989	1005	1005	1005
237	A1u	1005	1015	1015	1015
238	T2g	1026	1026	1026	1026	1.129e+39 1.8	1.375e+39 2.2	2.505e+39 4.0
239	T2g	1026	1026	1026	1026	1.129e+39 1.8	1.855e+39 2.9	2.984e+39 4.7
240	T2g	1026	1026	1026	1026	1.129e+39 1.8	1.429e+39 2.3	2.558e+39 4.1

No.

Char.

ω TO

ω LOx

ω LOy

ω LOz

I ∥

I ⊥