- TILLEYITE - Ca₅Si₂O₇(CO₃)₂

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:	14		P2_1/c
Lattice parameters (Å):	15.0820	10.2360		7.5720
Angles (°):	90	105.17		90

Symmetry (theoretical):

Space group:	14		P2_1/c
Lattice parameters (Å):	15.0354	10.2571		7.5753
Angles (°):	90	105.04		90

Cell contents:

Number of atoms:	88
Number of atom types:	4
Chemical composition:	0

Atomic positions (theoretical):

Ca:	0.0033	0.9948	0.7489
Ca:	0.1752	0.2101	0.0900
Ca:	0.1825	0.2075	0.6072
Ca:	0.1223	0.5885	0.0470
Ca:	0.1389	0.5766	0.5627
Si:	0.2023	0.9207	0.1389
Si:	0.2048	0.9151	0.5678
C:	0.0313	0.3090	0.3407
C:	0.0224	0.3031	0.8177
O:	0.0734	0.2083	0.2987
O:	0.0713	0.2061	0.7875
O:	0.0714	0.3741	0.4824
O:	0.0549	0.3739	0.9598
O:	0.0486	0.6612	0.7518
O:	0.0577	0.6767	0.2822
O:	0.2240	0.7744	0.0883
O:	0.2280	0.7661	0.6279
O:	0.1008	0.9789	0.0571
O:	0.1038	0.9733	0.5526
O:	0.2238	0.5288	0.8824
O:	0.2210	0.5216	0.3255
O:	0.2254	0.9166	0.3643
Ca:	0.4967	0.4948	0.2511
Ca:	0.3248	0.7101	0.9100
Ca:	0.3175	0.7075	0.3928
Ca:	0.3777	0.0885	0.9530
Ca:	0.3611	0.0766	0.4373
Si:	0.2977	0.4207	0.8611
Si:	0.2952	0.4151	0.4322
C:	0.4687	0.8090	0.6593
C:	0.4776	0.8031	0.1823
O:	0.4266	0.7083	0.7013
O:	0.4287	0.7061	0.2125
O:	0.4286	0.8741	0.5176
O:	0.4451	0.8739	0.0402
O:	0.4514	0.1612	0.2482
O:	0.4423	0.1767	0.7178
O:	0.2760	0.2744	0.9117
O:	0.2720	0.2661	0.3721
O:	0.3992	0.4789	0.9429
O:	0.3962	0.4733	0.4474
O:	0.2762	0.0288	0.1176
O:	0.2790	0.0216	0.6745
O:	0.2746	0.4166	0.6357
Ca:	0.9967	0.0052	0.2511
Ca:	0.8248	0.7899	0.9100
Ca:	0.8175	0.7925	0.3928
Ca:	0.8777	0.4115	0.9530
Ca:	0.8611	0.4234	0.4373
Si:	0.7977	0.0793	0.8611
Si:	0.7952	0.0849	0.4322
C:	0.9687	0.6910	0.6593
C:	0.9776	0.6969	0.1823
O:	0.9266	0.7917	0.7013
O:	0.9287	0.7939	0.2125
O:	0.9286	0.6259	0.5176
O:	0.9451	0.6261	0.0402
O:	0.9514	0.3388	0.2482
O:	0.9423	0.3233	0.7178
O:	0.7760	0.2256	0.9117
O:	0.7720	0.2339	0.3721
O:	0.8992	0.0211	0.9429
O:	0.8962	0.0267	0.4474
O:	0.7762	0.4712	0.1176
O:	0.7790	0.4784	0.6745
O:	0.7746	0.0834	0.6357
Ca:	0.5033	0.5052	0.7489
Ca:	0.6752	0.2899	0.0900
Ca:	0.6825	0.2925	0.6072
Ca:	0.6223	0.9115	0.0470
Ca:	0.6389	0.9234	0.5627
Si:	0.7023	0.5793	0.1389
Si:	0.7048	0.5849	0.5678
C:	0.5313	0.1910	0.3407
C:	0.5224	0.1969	0.8177
O:	0.5734	0.2917	0.2987
O:	0.5713	0.2939	0.7875
O:	0.5714	0.1259	0.4824
O:	0.5549	0.1261	0.9598
O:	0.5486	0.8388	0.7518
O:	0.5577	0.8233	0.2822
O:	0.7240	0.7256	0.0883
O:	0.7280	0.7339	0.6279
O:	0.6008	0.5211	0.0571
O:	0.6038	0.5267	0.5526
O:	0.7238	0.9712	0.8824
O:	0.7210	0.9784	0.3255
O:	0.7254	0.5834	0.3643

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.

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:	2.3055	-0.0480	-0.0183
	0.2044	2.2481	0.0877
	0.0452	0.1233	2.3013
Eig. Value:	2.4176	2.1461	2.2911
Ca:	2.2237	-0.0322	0.0211
	-0.0002	2.1839	-0.0197
	0.0315	-0.1573	2.3097
Eig. Value:	2.2169	2.1381	2.3622
Ca:	2.2347	0.0257	0.0468
	0.0421	2.3033	0.0236
	0.0711	-0.0635	2.1237
Eig. Value:	2.2510	2.3173	2.0934
Ca:	2.3998	-0.0815	0.0216
	0.0050	2.2745	0.0521
	-0.0065	0.1272	2.3902
Eig. Value:	2.4037	2.2180	2.4427
Ca:	2.3668	-0.1449	0.0807
	-0.0103	2.3947	0.0421
	0.1008	0.0157	2.2050
Eig. Value:	2.3510	2.4657	2.1497
Si:	2.7398	-0.1094	-0.0000
	-0.0543	2.8861	-0.0309
	0.1349	0.0024	2.8669
Eig. Value:	2.6854	2.9471	2.8603
Si:	2.8781	-0.1694	-0.0303
	-0.0983	2.9784	0.0499
	-0.0596	0.1735	2.7784
Eig. Value:	2.7958	3.1127	2.7263
C:	2.2240	-0.8785	1.0328
	-0.8474	2.0489	0.9522
	0.9102	0.8514	2.0992
Eig. Value:	2.9382	0.2983	3.1357
C:	2.2610	-0.9327	0.9576
	-0.8267	1.9424	0.9627
	0.8433	0.8683	2.1484
Eig. Value:	2.9310	0.3131	3.1077
O:	-1.4826	0.6496	0.0953
	0.5400	-1.9027	-0.4132
	0.0862	-0.3441	-1.1583
Eig. Value:	-1.1970	-2.4277	-0.9190
O:	-1.6404	0.7150	0.0764
	0.5851	-1.8090	-0.3092
	0.1041	-0.2560	-1.1486
Eig. Value:	-0.9633	-2.4380	-1.1968
O:	-1.1749	-0.1369	-0.4983
	-0.1234	-1.5257	-0.6788
	-0.4103	-0.6442	-1.7489
Eig. Value:	-0.8102	-1.1832	-2.4560
O:	-1.1261	-0.0294	-0.3913
	-0.0171	-1.5049	-0.7239
	-0.2340	-0.6770	-1.7745
Eig. Value:	-0.8076	-1.1929	-2.4050
O:	-1.9452	0.4978	-0.7117
	0.3905	-0.9888	0.0707
	-0.6337	0.1323	-1.5046
Eig. Value:	-2.5471	-0.7599	-1.1316
O:	-1.9184	0.3831	-0.7062
	0.2516	-0.9393	0.0155
	-0.7185	0.0992	-1.5115
Eig. Value:	-2.5091	-0.7806	-1.0795
O:	-1.5511	0.2362	0.0898
	0.1834	-2.1783	-0.1627
	0.0693	-0.3205	-1.5351
Eig. Value:	-1.4883	-2.3240	-1.4522
O:	-1.4549	0.0786	-0.0557
	0.0767	-2.3421	0.1741
	-0.0946	0.2293	-1.5707
Eig. Value:	-1.4174	-2.4009	-1.5494
O:	-2.0524	0.2652	-0.2603
	0.1564	-1.4932	0.1077
	-0.3548	0.1165	-1.6395
Eig. Value:	-2.2881	-1.4215	-1.4756
O:	-2.2361	0.3294	-0.0435
	0.1861	-1.5096	0.0008
	0.0155	-0.0873	-1.4690
Eig. Value:	-2.3182	-1.3982	-1.4982
O:	-1.9540	0.3408	0.0982
	0.3422	-1.8546	-0.0554
	0.0915	-0.1448	-1.5349
Eig. Value:	-2.2749	-1.5625	-1.5061
O:	-1.7189	0.2181	-0.2111
	0.2644	-1.9155	0.2438
	-0.3563	0.3228	-1.7534
Eig. Value:	-1.5940	-2.3435	-1.4504
O:	-1.3785	0.0281	0.4067
	0.0457	-1.2965	0.0497
	0.3649	-0.0145	-2.8737
Eig. Value:	-1.2502	-1.3311	-2.9674
Ca:	2.3055	0.0480	-0.0183
	-0.2044	2.2481	-0.0877
	0.0452	-0.1233	2.3013
Eig. Value:	2.4176	2.1461	2.2911
Ca:	2.2237	0.0322	0.0211
	0.0002	2.1839	0.0197
	0.0315	0.1573	2.3097
Eig. Value:	2.2169	2.1381	2.3622
Ca:	2.2347	-0.0257	0.0468
	-0.0421	2.3033	-0.0236
	0.0711	0.0635	2.1237
Eig. Value:	2.2510	2.3173	2.0934
Ca:	2.3998	0.0815	0.0216
	-0.0050	2.2745	-0.0521
	-0.0065	-0.1272	2.3902
Eig. Value:	2.4037	2.2180	2.4427
Ca:	2.3668	0.1449	0.0807
	0.0103	2.3947	-0.0421
	0.1008	-0.0157	2.2050
Eig. Value:	2.3510	2.4657	2.1497
Si:	2.7398	0.1094	-0.0000
	0.0543	2.8861	0.0309
	0.1349	-0.0024	2.8669
Eig. Value:	2.6854	2.9471	2.8603
Si:	2.8781	0.1694	-0.0303
	0.0983	2.9784	-0.0499
	-0.0596	-0.1735	2.7784
Eig. Value:	2.7958	3.1127	2.7263
C:	2.2240	0.8785	1.0328
	0.8474	2.0489	-0.9522
	0.9102	-0.8514	2.0992
Eig. Value:	2.9382	0.2983	3.1357
C:	2.2610	0.9327	0.9576
	0.8267	1.9424	-0.9627
	0.8433	-0.8683	2.1484
Eig. Value:	2.9310	0.3131	3.1077
O:	-1.4826	-0.6496	0.0953
	-0.5400	-1.9027	0.4132
	0.0862	0.3441	-1.1583
Eig. Value:	-1.1970	-2.4277	-0.9190
O:	-1.6404	-0.7150	0.0764
	-0.5851	-1.8090	0.3092
	0.1041	0.2560	-1.1486
Eig. Value:	-0.9633	-2.4380	-1.1968
O:	-1.1749	0.1369	-0.4983
	0.1234	-1.5256	0.6788
	-0.4103	0.6442	-1.7489
Eig. Value:	-0.8102	-1.1832	-2.4560
O:	-1.1261	0.0294	-0.3913
	0.0171	-1.5049	0.7239
	-0.2340	0.6770	-1.7744
Eig. Value:	-0.8076	-1.1929	-2.4050
O:	-1.9452	-0.4978	-0.7117
	-0.3905	-0.9888	-0.0707
	-0.6337	-0.1323	-1.5046
Eig. Value:	-2.5471	-0.7599	-1.1316
O:	-1.9184	-0.3831	-0.7062
	-0.2516	-0.9393	-0.0155
	-0.7185	-0.0992	-1.5115
Eig. Value:	-2.5091	-0.7806	-1.0795
O:	-1.5511	-0.2362	0.0898
	-0.1834	-2.1783	0.1627
	0.0693	0.3205	-1.5351
Eig. Value:	-1.4883	-2.3240	-1.4522
O:	-1.4549	-0.0786	-0.0557
	-0.0767	-2.3421	-0.1741
	-0.0946	-0.2293	-1.5707
Eig. Value:	-1.4174	-2.4009	-1.5494
O:	-2.0524	-0.2652	-0.2603
	-0.1564	-1.4933	-0.1077
	-0.3548	-0.1165	-1.6395
Eig. Value:	-2.2881	-1.4216	-1.4756
O:	-2.2361	-0.3294	-0.0435
	-0.1861	-1.5095	-0.0008
	0.0155	0.0873	-1.4690
Eig. Value:	-2.3182	-1.3982	-1.4982
O:	-1.9540	-0.3408	0.0982
	-0.3422	-1.8546	0.0554
	0.0915	0.1448	-1.5349
Eig. Value:	-2.2749	-1.5625	-1.5061
O:	-1.7189	-0.2181	-0.2111
	-0.2644	-1.9155	-0.2438
	-0.3563	-0.3228	-1.7535
Eig. Value:	-1.5940	-2.3435	-1.4504
O:	-1.3785	-0.0281	0.4067
	-0.0457	-1.2965	-0.0497
	0.3649	0.0145	-2.8737
Eig. Value:	-1.2502	-1.3311	-2.9674
Ca:	2.3055	-0.0480	-0.0183
	0.2044	2.2481	0.0877
	0.0452	0.1233	2.3013
Eig. Value:	2.4176	2.1461	2.2911
Ca:	2.2237	-0.0322	0.0211
	-0.0002	2.1839	-0.0197
	0.0315	-0.1573	2.3097
Eig. Value:	2.2169	2.1381	2.3622
Ca:	2.2347	0.0257	0.0468
	0.0421	2.3033	0.0236
	0.0711	-0.0635	2.1237
Eig. Value:	2.2510	2.3173	2.0934
Ca:	2.3998	-0.0815	0.0216
	0.0050	2.2745	0.0521
	-0.0065	0.1272	2.3902
Eig. Value:	2.4037	2.2180	2.4427
Ca:	2.3668	-0.1449	0.0807
	-0.0103	2.3947	0.0421
	0.1008	0.0157	2.2050
Eig. Value:	2.3510	2.4657	2.1497
Si:	2.7398	-0.1094	-0.0000
	-0.0543	2.8861	-0.0309
	0.1349	0.0024	2.8669
Eig. Value:	2.6854	2.9471	2.8603
Si:	2.8781	-0.1694	-0.0303
	-0.0983	2.9784	0.0499
	-0.0596	0.1735	2.7784
Eig. Value:	2.7958	3.1127	2.7263
C:	2.2240	-0.8785	1.0328
	-0.8474	2.0489	0.9522
	0.9102	0.8514	2.0992
Eig. Value:	2.9382	0.2983	3.1357
C:	2.2610	-0.9327	0.9576
	-0.8267	1.9424	0.9627
	0.8433	0.8683	2.1484
Eig. Value:	2.9310	0.3131	3.1077
O:	-1.4826	0.6496	0.0953
	0.5400	-1.9027	-0.4132
	0.0862	-0.3441	-1.1583
Eig. Value:	-1.1970	-2.4277	-0.9190
O:	-1.6404	0.7150	0.0764
	0.5851	-1.8090	-0.3092
	0.1041	-0.2560	-1.1486
Eig. Value:	-0.9633	-2.4380	-1.1968
O:	-1.1749	-0.1369	-0.4983
	-0.1234	-1.5257	-0.6788
	-0.4103	-0.6442	-1.7489
Eig. Value:	-0.8102	-1.1832	-2.4560
O:	-1.1261	-0.0294	-0.3913
	-0.0171	-1.5049	-0.7239
	-0.2340	-0.6770	-1.7745
Eig. Value:	-0.8076	-1.1929	-2.4050
O:	-1.9452	0.4978	-0.7117
	0.3905	-0.9888	0.0707
	-0.6337	0.1323	-1.5046
Eig. Value:	-2.5471	-0.7599	-1.1316
O:	-1.9184	0.3831	-0.7062
	0.2516	-0.9393	0.0155
	-0.7185	0.0992	-1.5115
Eig. Value:	-2.5091	-0.7806	-1.0795
O:	-1.5511	0.2362	0.0898
	0.1834	-2.1783	-0.1627
	0.0693	-0.3205	-1.5351
Eig. Value:	-1.4883	-2.3240	-1.4522
O:	-1.4549	0.0786	-0.0557
	0.0767	-2.3421	0.1741
	-0.0946	0.2293	-1.5707
Eig. Value:	-1.4174	-2.4009	-1.5494
O:	-2.0524	0.2652	-0.2603
	0.1564	-1.4932	0.1077
	-0.3548	0.1165	-1.6395
Eig. Value:	-2.2881	-1.4215	-1.4756
O:	-2.2361	0.3294	-0.0435
	0.1861	-1.5096	0.0008
	0.0155	-0.0873	-1.4690
Eig. Value:	-2.3182	-1.3982	-1.4982
O:	-1.9540	0.3408	0.0982
	0.3422	-1.8546	-0.0554
	0.0915	-0.1448	-1.5349
Eig. Value:	-2.2749	-1.5625	-1.5061
O:	-1.7189	0.2181	-0.2111
	0.2644	-1.9155	0.2438
	-0.3563	0.3228	-1.7534
Eig. Value:	-1.5940	-2.3435	-1.4504
O:	-1.3785	0.0281	0.4067
	0.0457	-1.2965	0.0497
	0.3649	-0.0145	-2.8737
Eig. Value:	-1.2502	-1.3311	-2.9674
Ca:	2.3055	0.0480	-0.0183
	-0.2044	2.2481	-0.0877
	0.0452	-0.1233	2.3013
Eig. Value:	2.4176	2.1461	2.2911
Ca:	2.2237	0.0322	0.0211
	0.0002	2.1839	0.0197
	0.0315	0.1573	2.3097
Eig. Value:	2.2169	2.1381	2.3622
Ca:	2.2347	-0.0257	0.0468
	-0.0421	2.3033	-0.0236
	0.0711	0.0635	2.1237
Eig. Value:	2.2510	2.3173	2.0934
Ca:	2.3998	0.0815	0.0216
	-0.0050	2.2745	-0.0521
	-0.0065	-0.1272	2.3902
Eig. Value:	2.4037	2.2180	2.4427
Ca:	2.3668	0.1449	0.0807
	0.0103	2.3947	-0.0421
	0.1008	-0.0157	2.2050
Eig. Value:	2.3510	2.4657	2.1497
Si:	2.7398	0.1094	-0.0000
	0.0543	2.8861	0.0309
	0.1349	-0.0024	2.8669
Eig. Value:	2.6854	2.9471	2.8603
Si:	2.8781	0.1694	-0.0303
	0.0983	2.9784	-0.0499
	-0.0596	-0.1735	2.7784
Eig. Value:	2.7958	3.1127	2.7263
C:	2.2240	0.8785	1.0328
	0.8474	2.0489	-0.9522
	0.9102	-0.8514	2.0992
Eig. Value:	2.9382	0.2983	3.1357
C:	2.2610	0.9327	0.9576
	0.8267	1.9424	-0.9627
	0.8433	-0.8683	2.1484
Eig. Value:	2.9310	0.3131	3.1077
O:	-1.4826	-0.6496	0.0953
	-0.5400	-1.9027	0.4132
	0.0862	0.3441	-1.1583
Eig. Value:	-1.1970	-2.4277	-0.9190
O:	-1.6404	-0.7150	0.0764
	-0.5851	-1.8090	0.3092
	0.1041	0.2560	-1.1486
Eig. Value:	-0.9633	-2.4380	-1.1968
O:	-1.1749	0.1369	-0.4983
	0.1234	-1.5256	0.6788
	-0.4103	0.6442	-1.7489
Eig. Value:	-0.8102	-1.1832	-2.4560
O:	-1.1261	0.0294	-0.3913
	0.0171	-1.5049	0.7239
	-0.2340	0.6770	-1.7744
Eig. Value:	-0.8076	-1.1929	-2.4050
O:	-1.9452	-0.4978	-0.7117
	-0.3905	-0.9888	-0.0707
	-0.6337	-0.1323	-1.5046
Eig. Value:	-2.5471	-0.7599	-1.1316
O:	-1.9184	-0.3831	-0.7062
	-0.2516	-0.9393	-0.0155
	-0.7185	-0.0992	-1.5115
Eig. Value:	-2.5091	-0.7806	-1.0795
O:	-1.5511	-0.2362	0.0898
	-0.1834	-2.1783	0.1627
	0.0693	0.3205	-1.5351
Eig. Value:	-1.4883	-2.3240	-1.4522
O:	-1.4549	-0.0786	-0.0557
	-0.0767	-2.3421	-0.1741
	-0.0946	-0.2293	-1.5707
Eig. Value:	-1.4174	-2.4009	-1.5494
O:	-2.0524	-0.2652	-0.2603
	-0.1564	-1.4933	-0.1077
	-0.3548	-0.1165	-1.6395
Eig. Value:	-2.2881	-1.4216	-1.4756
O:	-2.2361	-0.3294	-0.0435
	-0.1861	-1.5095	-0.0008
	0.0155	0.0873	-1.4690
Eig. Value:	-2.3182	-1.3982	-1.4982
O:	-1.9540	-0.3408	0.0982
	-0.3422	-1.8546	0.0554
	0.0915	0.1448	-1.5349
Eig. Value:	-2.2749	-1.5625	-1.5061
O:	-1.7189	-0.2181	-0.2111
	-0.2644	-1.9155	-0.2438
	-0.3563	-0.3228	-1.7535
Eig. Value:	-1.5940	-2.3435	-1.4504
O:	-1.3785	-0.0281	0.4067
	-0.0457	-1.2965	-0.0497
	0.3649	0.0145	-2.8737
Eig. Value:	-1.2502	-1.3311	-2.9674