- BRAZILIANITE - NaAl₃(PO₄)₂(OH)₄

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/n
Lattice parameters (Å):	11.2330	10.1420		7.0970
Angles (°):	90	97.37		90

Symmetry (theoretical):

Space group:	14		P2_1/n
Lattice parameters (Å):	11.0300	9.9346		6.9763
Angles (°):	90	97.73		90

Cell contents:

Number of atoms:	88
Number of atom types:	5
Chemical composition:	0

Atomic positions (theoretical):

P:	0.1788	0.3126	0.2331
P:	0.3088	0.3345	0.7518
Al:	0.0430	0.2169	0.5626
Al:	0.2656	0.0733	0.5098
Al:	0.4595	0.2590	0.4311
Na:	0.3084	0.0790	0.0455
O:	0.1049	0.0785	0.4474
O:	0.4239	0.1131	0.5724
O:	0.0016	0.3474	0.7250
O:	0.4967	0.3928	0.2685
O:	0.1162	0.2331	0.0619
O:	0.2888	0.2244	0.3209
O:	0.2211	0.2190	0.6769
O:	0.3851	0.2850	0.9354
O:	0.0924	0.3409	0.3844
O:	0.3895	0.3785	0.6000
O:	0.2225	0.4501	0.1789
O:	0.2278	0.4549	0.7865
H:	0.0685	0.0050	0.3590
H:	0.4707	0.1072	0.7026
H:	0.0735	0.4044	0.7657
H:	0.0488	0.0337	0.8316
P:	0.3212	0.8126	0.2669
P:	0.1912	0.8345	0.7482
Al:	0.4570	0.7169	0.9374
Al:	0.2344	0.5733	0.9902
Al:	0.0405	0.7590	0.0689
Na:	0.1916	0.5790	0.4545
O:	0.3951	0.5785	0.0526
O:	0.0761	0.6131	0.9276
O:	0.4984	0.8474	0.7750
O:	0.0033	0.8928	0.2315
O:	0.3838	0.7331	0.4381
O:	0.2112	0.7244	0.1791
O:	0.2789	0.7190	0.8231
O:	0.1149	0.7850	0.5646
O:	0.4076	0.8409	0.1156
O:	0.1105	0.8785	0.9000
O:	0.2775	0.9501	0.3211
O:	0.2722	0.9549	0.7135
H:	0.4315	0.5050	0.1410
H:	0.0293	0.6072	0.7974
H:	0.4265	0.9044	0.7343
H:	0.4512	0.5337	0.6684
P:	0.8212	0.6874	0.7669
P:	0.6912	0.6655	0.2482
Al:	0.9570	0.7831	0.4374
Al:	0.7344	0.9267	0.4902
Al:	0.5405	0.7410	0.5689
Na:	0.6916	0.9210	0.9545
O:	0.8951	0.9215	0.5526
O:	0.5761	0.8869	0.4276
O:	0.9984	0.6526	0.2750
O:	0.5033	0.6072	0.7315
O:	0.8838	0.7669	0.9381
O:	0.7112	0.7756	0.6791
O:	0.7789	0.7810	0.3231
O:	0.6149	0.7150	0.0646
O:	0.9076	0.6591	0.6156
O:	0.6105	0.6215	0.4000
O:	0.7775	0.5499	0.8211
O:	0.7722	0.5451	0.2135
H:	0.9315	0.9950	0.6410
H:	0.5293	0.8928	0.2974
H:	0.9265	0.5956	0.2343
H:	0.9512	0.9663	0.1684
P:	0.6788	0.1874	0.7331
P:	0.8088	0.1655	0.2518
Al:	0.5430	0.2831	0.0626
Al:	0.7656	0.4267	0.0098
Al:	0.9595	0.2410	0.9311
Na:	0.8084	0.4210	0.5455
O:	0.6049	0.4215	0.9474
O:	0.9239	0.3869	0.0724
O:	0.5016	0.1526	0.2250
O:	0.9967	0.1072	0.7685
O:	0.6162	0.2669	0.5619
O:	0.7888	0.2756	0.8209
O:	0.7211	0.2810	0.1769
O:	0.8851	0.2150	0.4354
O:	0.5924	0.1591	0.8844
O:	0.8895	0.1215	0.1000
O:	0.7225	0.0499	0.6789
O:	0.7278	0.0451	0.2865
H:	0.5685	0.4950	0.8590
H:	0.9707	0.3928	0.2026
H:	0.5735	0.0956	0.2657
H:	0.5488	0.4663	0.3316

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):

P:	3.5151	0.0505	0.0818
	0.1403	3.3778	-0.2872
	0.1218	-0.3622	3.4587
Eig. Value:	3.5557	3.0496	3.7464
P:	3.5980	-0.1215	0.0856
	0.0874	3.2738	0.2272
	0.0199	0.3409	3.4475
Eig. Value:	3.5872	3.0598	3.6723
Al:	3.2378	0.1936	0.0466
	0.2417	2.6343	0.0907
	0.1196	-0.1285	3.1509
Eig. Value:	3.3373	2.5608	3.1250
Al:	2.7404	0.0077	-0.0661
	0.0455	3.5803	0.0593
	-0.0127	-0.0175	2.8798
Eig. Value:	2.7289	3.5817	2.8900
Al:	3.3209	-0.0768	-0.1548
	-0.1222	2.5601	-0.2186
	0.0324	0.0579	3.1696
Eig. Value:	3.3487	2.5352	3.1667
Na:	1.0197	-0.0018	0.0183
	0.0185	1.2382	0.0030
	-0.0061	-0.0325	1.1415
Eig. Value:	1.0190	1.2407	1.1397
O:	-1.6602	-0.1381	-0.1911
	-0.0432	-1.9045	-0.3767
	-0.1391	-0.2979	-1.4563
Eig. Value:	-1.6343	-2.1389	-1.2479
O:	-1.7159	-0.1379	-0.2842
	-0.1995	-1.5037	0.0313
	-0.2383	0.0810	-1.4538
Eig. Value:	-1.9115	-1.5402	-1.2216
O:	-1.5439	-0.2328	0.1304
	-0.0963	-1.4808	-0.0922
	0.1172	-0.1069	-1.5030
Eig. Value:	-1.6888	-1.2487	-1.5902
O:	-1.3128	-0.0378	-0.0227
	-0.0581	-1.9966	0.1464
	0.0169	0.1792	-1.6308
Eig. Value:	-1.3088	-2.0611	-1.5703
O:	-1.6753	-0.2062	-0.5020
	-0.2025	-1.2994	-0.3460
	-0.5035	-0.3472	-1.9235
Eig. Value:	-1.2994	-1.1436	-2.4552
O:	-2.0791	0.3806	-0.4257
	0.2308	-1.6026	0.3995
	-0.4643	0.4699	-1.5953
Eig. Value:	-2.5911	-1.5383	-1.1477
O:	-1.8979	-0.4010	-0.3053
	-0.4099	-1.8652	-0.4996
	-0.3295	-0.5106	-1.4989
Eig. Value:	-2.5975	-1.5211	-1.1433
O:	-1.8019	0.2309	-0.6452
	0.1112	-1.1583	0.1561
	-0.5827	0.2111	-1.9898
Eig. Value:	-1.2754	-1.1129	-2.5617
O:	-1.8422	0.0539	0.3690
	-0.0197	-1.2822	0.1763
	0.3426	0.2146	-1.9232
Eig. Value:	-1.5862	-1.2016	-2.2598
O:	-1.7324	-0.1835	0.5249
	-0.1799	-1.5849	-0.0730
	0.5021	-0.1625	-1.7386
Eig. Value:	-1.1242	-1.6795	-2.2522
O:	-1.2520	-0.4840	0.2260
	-0.4144	-2.2618	0.5456
	0.1875	0.5715	-1.4318
Eig. Value:	-1.0808	-2.7102	-1.1546
O:	-1.7675	0.5008	0.1558
	0.3664	-1.9416	-0.4283
	0.1138	-0.4806	-1.3822
Eig. Value:	-1.5050	-2.4765	-1.1098
H:	0.5951	0.3419	0.3057
	0.2642	1.0761	0.5341
	0.2358	0.5016	0.7698
Eig. Value:	0.4515	1.6226	0.3669
H:	0.7580	0.0876	0.4409
	0.0985	0.4960	0.1471
	0.3034	0.0904	0.6789
Eig. Value:	1.1276	0.4663	0.3389
H:	0.9577	0.2146	0.0765
	0.1444	0.5475	0.0987
	0.0624	0.0882	0.3873
Eig. Value:	1.0400	0.5085	0.3440
H:	0.5383	-0.3707	0.1357
	-0.3341	1.0976	-0.2214
	0.1008	-0.1457	0.4432
Eig. Value:	0.3508	1.3213	0.4069
P:	3.5151	-0.0505	0.0818
	-0.1403	3.3778	0.2872
	0.1218	0.3622	3.4587
Eig. Value:	3.5557	3.0496	3.7464
P:	3.5980	0.1215	0.0856
	-0.0874	3.2738	-0.2272
	0.0199	-0.3409	3.4475
Eig. Value:	3.5872	3.0598	3.6723
Al:	3.2378	-0.1936	0.0466
	-0.2417	2.6343	-0.0907
	0.1196	0.1285	3.1509
Eig. Value:	3.3373	2.5608	3.1250
Al:	2.7404	-0.0077	-0.0661
	-0.0455	3.5803	-0.0593
	-0.0127	0.0175	2.8798
Eig. Value:	2.7289	3.5817	2.8900
Al:	3.3209	0.0768	-0.1548
	0.1222	2.5601	0.2186
	0.0324	-0.0579	3.1696
Eig. Value:	3.3487	2.5352	3.1667
Na:	1.0197	0.0018	0.0183
	-0.0185	1.2382	-0.0030
	-0.0061	0.0325	1.1415
Eig. Value:	1.0190	1.2407	1.1397
O:	-1.6602	0.1381	-0.1911
	0.0432	-1.9045	0.3767
	-0.1391	0.2979	-1.4563
Eig. Value:	-1.6343	-2.1388	-1.2479
O:	-1.7159	0.1379	-0.2842
	0.1995	-1.5036	-0.0313
	-0.2383	-0.0810	-1.4538
Eig. Value:	-1.9115	-1.5402	-1.2216
O:	-1.5439	0.2328	0.1304
	0.0963	-1.4808	0.0922
	0.1172	0.1069	-1.5030
Eig. Value:	-1.6888	-1.2487	-1.5902
O:	-1.3128	0.0378	-0.0227
	0.0581	-1.9966	-0.1464
	0.0169	-0.1792	-1.6308
Eig. Value:	-1.3088	-2.0611	-1.5703
O:	-1.6753	0.2061	-0.5020
	0.2025	-1.2994	0.3460
	-0.5035	0.3472	-1.9235
Eig. Value:	-1.2994	-1.1436	-2.4552
O:	-2.0791	-0.3806	-0.4257
	-0.2308	-1.6026	-0.3995
	-0.4643	-0.4699	-1.5953
Eig. Value:	-2.5911	-1.5383	-1.1477
O:	-1.8979	0.4010	-0.3053
	0.4099	-1.8652	0.4996
	-0.3295	0.5106	-1.4989
Eig. Value:	-2.5975	-1.5211	-1.1433
O:	-1.8019	-0.2309	-0.6452
	-0.1112	-1.1583	-0.1561
	-0.5827	-0.2111	-1.9898
Eig. Value:	-1.2754	-1.1129	-2.5617
O:	-1.8422	-0.0539	0.3690
	0.0197	-1.2822	-0.1763
	0.3426	-0.2146	-1.9232
Eig. Value:	-1.5862	-1.2016	-2.2598
O:	-1.7324	0.1835	0.5249
	0.1799	-1.5849	0.0730
	0.5021	0.1625	-1.7386
Eig. Value:	-1.1242	-1.6796	-2.2522
O:	-1.2520	0.4839	0.2260
	0.4144	-2.2618	-0.5456
	0.1876	-0.5715	-1.4318
Eig. Value:	-1.0808	-2.7101	-1.1546
O:	-1.7675	-0.5008	0.1558
	-0.3664	-1.9416	0.4283
	0.1138	0.4806	-1.3822
Eig. Value:	-1.5050	-2.4765	-1.1098
H:	0.5951	-0.3419	0.3057
	-0.2642	1.0761	-0.5341
	0.2358	-0.5016	0.7698
Eig. Value:	0.4515	1.6226	0.3669
H:	0.7580	-0.0876	0.4409
	-0.0985	0.4960	-0.1471
	0.3034	-0.0904	0.6789
Eig. Value:	1.1276	0.4663	0.3389
H:	0.9577	-0.2146	0.0765
	-0.1444	0.5475	-0.0987
	0.0624	-0.0882	0.3873
Eig. Value:	1.0400	0.5085	0.3440
H:	0.5383	0.3707	0.1357
	0.3341	1.0976	0.2214
	0.1008	0.1457	0.4432
Eig. Value:	0.3508	1.3213	0.4069
P:	3.5151	0.0505	0.0818
	0.1403	3.3778	-0.2872
	0.1218	-0.3622	3.4587
Eig. Value:	3.5557	3.0496	3.7464
P:	3.5980	-0.1215	0.0856
	0.0874	3.2738	0.2272
	0.0199	0.3409	3.4475
Eig. Value:	3.5872	3.0598	3.6723
Al:	3.2378	0.1936	0.0466
	0.2417	2.6343	0.0907
	0.1196	-0.1285	3.1509
Eig. Value:	3.3373	2.5608	3.1250
Al:	2.7404	0.0077	-0.0661
	0.0455	3.5803	0.0593
	-0.0127	-0.0175	2.8798
Eig. Value:	2.7289	3.5817	2.8900
Al:	3.3209	-0.0768	-0.1548
	-0.1222	2.5601	-0.2186
	0.0324	0.0579	3.1696
Eig. Value:	3.3487	2.5352	3.1667
Na:	1.0197	-0.0018	0.0183
	0.0185	1.2382	0.0030
	-0.0061	-0.0325	1.1415
Eig. Value:	1.0190	1.2407	1.1397
O:	-1.6602	-0.1381	-0.1911
	-0.0432	-1.9045	-0.3767
	-0.1391	-0.2979	-1.4563
Eig. Value:	-1.6343	-2.1389	-1.2479
O:	-1.7159	-0.1379	-0.2842
	-0.1995	-1.5037	0.0313
	-0.2383	0.0810	-1.4538
Eig. Value:	-1.9115	-1.5402	-1.2216
O:	-1.5439	-0.2328	0.1304
	-0.0963	-1.4808	-0.0922
	0.1172	-0.1069	-1.5030
Eig. Value:	-1.6888	-1.2487	-1.5902
O:	-1.3128	-0.0378	-0.0227
	-0.0581	-1.9966	0.1464
	0.0169	0.1792	-1.6308
Eig. Value:	-1.3088	-2.0611	-1.5703
O:	-1.6753	-0.2062	-0.5020
	-0.2025	-1.2994	-0.3460
	-0.5035	-0.3472	-1.9235
Eig. Value:	-1.2994	-1.1436	-2.4552
O:	-2.0791	0.3806	-0.4257
	0.2308	-1.6026	0.3995
	-0.4643	0.4699	-1.5953
Eig. Value:	-2.5911	-1.5383	-1.1477
O:	-1.8979	-0.4010	-0.3053
	-0.4099	-1.8652	-0.4996
	-0.3295	-0.5106	-1.4989
Eig. Value:	-2.5975	-1.5211	-1.1433
O:	-1.8019	0.2309	-0.6452
	0.1112	-1.1583	0.1561
	-0.5827	0.2111	-1.9898
Eig. Value:	-1.2754	-1.1129	-2.5617
O:	-1.8422	0.0539	0.3690
	-0.0197	-1.2822	0.1763
	0.3426	0.2146	-1.9232
Eig. Value:	-1.5862	-1.2016	-2.2598
O:	-1.7324	-0.1835	0.5249
	-0.1799	-1.5849	-0.0730
	0.5021	-0.1625	-1.7386
Eig. Value:	-1.1242	-1.6795	-2.2522
O:	-1.2520	-0.4840	0.2260
	-0.4144	-2.2618	0.5456
	0.1875	0.5715	-1.4318
Eig. Value:	-1.0808	-2.7102	-1.1546
O:	-1.7675	0.5008	0.1558
	0.3664	-1.9416	-0.4283
	0.1138	-0.4806	-1.3822
Eig. Value:	-1.5050	-2.4765	-1.1098
H:	0.5951	0.3419	0.3057
	0.2642	1.0761	0.5341
	0.2358	0.5016	0.7698
Eig. Value:	0.4515	1.6226	0.3669
H:	0.7580	0.0876	0.4409
	0.0985	0.4960	0.1471
	0.3034	0.0904	0.6789
Eig. Value:	1.1276	0.4663	0.3389
H:	0.9577	0.2146	0.0765
	0.1444	0.5475	0.0987
	0.0624	0.0882	0.3873
Eig. Value:	1.0400	0.5085	0.3440
H:	0.5383	-0.3707	0.1357
	-0.3341	1.0976	-0.2214
	0.1008	-0.1457	0.4432
Eig. Value:	0.3508	1.3213	0.4069
P:	3.5151	-0.0505	0.0818
	-0.1403	3.3778	0.2872
	0.1218	0.3622	3.4587
Eig. Value:	3.5557	3.0496	3.7464
P:	3.5980	0.1215	0.0856
	-0.0874	3.2738	-0.2272
	0.0199	-0.3409	3.4475
Eig. Value:	3.5872	3.0598	3.6723
Al:	3.2378	-0.1936	0.0466
	-0.2417	2.6343	-0.0907
	0.1196	0.1285	3.1509
Eig. Value:	3.3373	2.5608	3.1250
Al:	2.7404	-0.0077	-0.0661
	-0.0455	3.5803	-0.0593
	-0.0127	0.0175	2.8798
Eig. Value:	2.7289	3.5817	2.8900
Al:	3.3209	0.0768	-0.1548
	0.1222	2.5601	0.2186
	0.0324	-0.0579	3.1696
Eig. Value:	3.3487	2.5352	3.1667
Na:	1.0197	0.0018	0.0183
	-0.0185	1.2382	-0.0030
	-0.0061	0.0325	1.1415
Eig. Value:	1.0190	1.2407	1.1397
O:	-1.6602	0.1381	-0.1911
	0.0432	-1.9045	0.3767
	-0.1391	0.2979	-1.4563
Eig. Value:	-1.6343	-2.1388	-1.2479
O:	-1.7159	0.1379	-0.2842
	0.1995	-1.5036	-0.0313
	-0.2383	-0.0810	-1.4538
Eig. Value:	-1.9115	-1.5402	-1.2216
O:	-1.5439	0.2328	0.1304
	0.0963	-1.4808	0.0922
	0.1172	0.1069	-1.5030
Eig. Value:	-1.6888	-1.2487	-1.5902
O:	-1.3128	0.0378	-0.0227
	0.0581	-1.9966	-0.1464
	0.0169	-0.1792	-1.6308
Eig. Value:	-1.3088	-2.0611	-1.5703
O:	-1.6753	0.2061	-0.5020
	0.2025	-1.2994	0.3460
	-0.5035	0.3472	-1.9235
Eig. Value:	-1.2994	-1.1436	-2.4552
O:	-2.0791	-0.3806	-0.4257
	-0.2308	-1.6026	-0.3995
	-0.4643	-0.4699	-1.5953
Eig. Value:	-2.5911	-1.5383	-1.1477
O:	-1.8979	0.4010	-0.3053
	0.4099	-1.8652	0.4996
	-0.3295	0.5106	-1.4989
Eig. Value:	-2.5975	-1.5211	-1.1433
O:	-1.8019	-0.2309	-0.6452
	-0.1112	-1.1583	-0.1561
	-0.5827	-0.2111	-1.9898
Eig. Value:	-1.2754	-1.1129	-2.5617
O:	-1.8422	-0.0539	0.3690
	0.0197	-1.2822	-0.1763
	0.3426	-0.2146	-1.9232
Eig. Value:	-1.5862	-1.2016	-2.2598
O:	-1.7324	0.1835	0.5249
	0.1799	-1.5849	0.0730
	0.5021	0.1625	-1.7386
Eig. Value:	-1.1242	-1.6796	-2.2522
O:	-1.2520	0.4839	0.2260
	0.4144	-2.2618	-0.5456
	0.1876	-0.5715	-1.4318
Eig. Value:	-1.0808	-2.7101	-1.1546
O:	-1.7675	-0.5008	0.1558
	-0.3664	-1.9416	0.4283
	0.1138	0.4806	-1.3822
Eig. Value:	-1.5050	-2.4765	-1.1098
H:	0.5951	-0.3419	0.3057
	-0.2642	1.0761	-0.5341
	0.2358	-0.5016	0.7698
Eig. Value:	0.4515	1.6226	0.3669
H:	0.7580	-0.0876	0.4409
	-0.0985	0.4960	-0.1471
	0.3034	-0.0904	0.6789
Eig. Value:	1.1276	0.4663	0.3389
H:	0.9577	-0.2146	0.0765
	-0.1444	0.5475	-0.0987
	0.0624	-0.0882	0.3873
Eig. Value:	1.0400	0.5085	0.3440
H:	0.5383	0.3707	0.1357
	0.3341	1.0976	0.2214
	0.1008	0.1457	0.4432
Eig. Value:	0.3508	1.3213	0.4069