- 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

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:
Lattice parameters (Å):
Angles (°):

Symmetry (theoretical):

Space group:
Lattice parameters (Å):	7.6555	7.4439	7.0043
Angles (°):	105.8	101.3	114.6

Cell contents:

Number of atoms:	26
Number of atom types:	3
Chemical composition:	0

Atomic positions (theoretical):

Na:	0.2450	0.2880	0.1045
Si:	0.8396	0.1682	0.2197
Si:	0.1882	0.8220	0.2299
Si:	0.5663	0.7930	0.3230
Si:	0.8075	0.5721	0.3581
O:	0.8676	0.1251	0.9841
O:	0.5893	0.5739	0.2788
O:	0.6951	0.9190	0.1927
O:	0.9576	0.6851	0.2362
O:	0.7399	0.3179	0.2902
O:	0.3141	0.6865	0.2141
O:	0.0822	0.2871	0.3808
O:	0.3364	0.0584	0.4243
Na:	0.7550	0.7120	0.8955
Si:	0.1604	0.8318	0.7803
Si:	0.8118	0.1780	0.7701
Si:	0.4337	0.2070	0.6770
Si:	0.1925	0.4279	0.6419
O:	0.1324	0.8749	0.0159
O:	0.4107	0.4261	0.7212
O:	0.3049	0.0810	0.8073
O:	0.0424	0.3149	0.7638
O:	0.2601	0.6821	0.7098
O:	0.6859	0.3135	0.7859
O:	0.9178	0.7129	0.6192
O:	0.6636	0.9416	0.5757

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):

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