- MALACHITE - Cu₂CO₃(OH)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/a
Lattice parameters (Å):	9.5020	11.9740		3.2400
Angles (°):	90	98.75		90

Symmetry (theoretical):

Space group:	14		P2_1/a
Lattice parameters (Å):	9.5955	12.1985		3.1729
Angles (°):	90	101.17		90

Cell contents:

Number of atoms:	40
Number of atom types:	4
Chemical composition:	0

Atomic positions (theoretical):

Cu:	0.4858	0.2888	0.9416
Cu:	0.2058	0.3913	0.4159
O:	0.1386	0.1178	0.2364
O:	0.3113	0.2329	0.5162
O:	0.3407	0.0549	0.6191
O:	0.0789	0.3475	0.9076
O:	0.3566	0.4077	0.8885
C:	0.2629	0.1346	0.4562
H:	0.9940	0.3979	0.8225
H:	0.3846	0.4867	0.8933
Cu:	0.0142	0.7888	0.0584
Cu:	0.2942	0.8913	0.5841
O:	0.3614	0.6178	0.7636
O:	0.1887	0.7329	0.4838
O:	0.1593	0.5549	0.3809
O:	0.4211	0.8475	0.0924
O:	0.1434	0.9077	0.1115
C:	0.2371	0.6346	0.5438
H:	0.5060	0.8979	0.1775
H:	0.1154	0.9867	0.1067
Cu:	0.5142	0.7112	0.0584
Cu:	0.7942	0.6087	0.5841
O:	0.8614	0.8822	0.7636
O:	0.6887	0.7671	0.4838
O:	0.6593	0.9451	0.3809
O:	0.9211	0.6525	0.0924
O:	0.6434	0.5923	0.1115
C:	0.7371	0.8654	0.5438
H:	0.0060	0.6021	0.1775
H:	0.6154	0.5133	0.1067
Cu:	0.9858	0.2112	0.9416
Cu:	0.7058	0.1087	0.4159
O:	0.6386	0.3822	0.2364
O:	0.8113	0.2671	0.5162
O:	0.8407	0.4451	0.6191
O:	0.5789	0.1525	0.9076
O:	0.8566	0.0923	0.8885
C:	0.7629	0.3654	0.4562
H:	0.4940	0.1021	0.8225
H:	0.8846	0.0133	0.8933

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):

Cu:	2.6268	-2.6022	4.2769
	-0.3772	2.8807	2.3388
	-4.7307	1.3448	-3.9830
Eig. Value:	1.4451	4.5285	-4.4491
Cu:	-0.9072	-2.4399	4.1010
	1.4978	2.9328	-0.9319
	4.5458	8.1966	-0.8621
Eig. Value:	-6.1838	5.8127	1.5346
O:	-4.1787	-4.9842	-0.2533
	0.6043	-1.9752	0.3066
	0.0222	8.5156	-3.6662
Eig. Value:	-4.1677	2.1735	-7.8259
O:	-1.8417	4.3613	0.6920
	-0.6528	-1.3615	0.5724
	4.2267	-5.9706	0.2539
Eig. Value:	0.2228	-5.6953	2.5232
O:	-2.6975	0.2225	-0.8955
	1.2435	-3.7945	0.9764
	-0.8486	3.1036	-1.2257
Eig. Value:	-2.3352	-5.3518	-0.0308
O:	-4.3159	0.9300	-3.2850
	-3.2473	-1.7556	2.4878
	0.8434	-8.6596	0.0535
Eig. Value:	-5.8604	-2.5350	2.3775
O:	5.4548	0.0613	-6.7912
	1.0907	-1.5067	-2.7180
	-4.1841	1.3652	7.2493
Eig. Value:	0.7916	-1.5653	11.9711
C:	1.7073	1.1997	0.6393
	-2.0697	3.0549	-2.3025
	6.4057	-3.8628	5.0302
Eig. Value:	-1.0507	2.1155	8.7276
H:	3.0309	-2.1748	2.1785
	0.2500	0.1648	-0.1405
	-1.9854	1.9303	-2.8460
Eig. Value:	3.3289	0.1333	-3.1124
H:	0.5807	-2.7233	-0.8117
	-0.2273	1.3615	0.5058
	-1.0478	3.9811	0.8881
Eig. Value:	-0.1625	4.2004	-1.2076
Cu:	2.6281	2.5773	4.2803
	0.3771	2.8803	-2.3388
	-4.7753	-1.2166	-4.0093
Eig. Value:	1.4387	4.5031	-4.4427
Cu:	-0.8988	2.5380	4.1321
	-1.4980	2.9324	0.9319
	4.4625	-8.7593	-1.0544
Eig. Value:	5.9549	1.4356	-6.4113
O:	-4.2485	4.8855	-0.2817
	-0.6044	-1.9752	-0.3067
	0.4198	-7.9536	-3.5048
Eig. Value:	-4.0231	1.8940	-7.5995
O:	-1.7803	-4.3077	0.7261
	0.6527	-1.3618	-0.5725
	3.8184	5.6543	0.0388
Eig. Value:	0.2190	-5.4938	2.1714
O:	-2.7317	-0.3466	-0.9004
	-1.2436	-3.7947	-0.9764
	-0.6693	-2.3503	-1.2018
Eig. Value:	-2.3097	-5.0885	-0.3300
O:	-4.4203	-0.7425	-3.3157
	3.2472	-1.7556	-2.4878
	1.4651	7.5776	0.2394
Eig. Value:	-5.5800	-2.3324	1.9759
O:	5.6221	0.0061	-6.7457
	-1.0908	-1.5069	2.7180
	-5.2075	-1.7805	6.9694
Eig. Value:	0.2859	-1.5480	12.3467
C:	1.6578	-1.2421	0.6194
	2.0696	3.0549	2.3024
	6.6772	4.1156	5.1430
Eig. Value:	-1.2098	2.1121	8.9534
H:	3.0348	2.2009	2.1810
	-0.2500	0.1648	0.1405
	-1.9998	-2.0756	-2.8588
Eig. Value:	3.3415	0.1630	-3.1637
H:	0.5921	2.7160	-0.8089
	0.2273	1.3615	-0.5058
	-1.1183	-3.9401	0.8709
Eig. Value:	-0.1875	4.1952	-1.1832
Cu:	2.8665	-2.9589	4.3221
	-0.3769	2.8803	2.3389
	-6.1118	3.3954	-4.2436
Eig. Value:	1.4472	5.3210	-5.2650
Cu:	-0.7223	-2.6650	4.1864
	1.4981	2.9319	-0.9319
	3.4460	9.4941	-1.3558
Eig. Value:	1.1911	5.9935	-6.3307
O:	-4.1525	-5.0991	-0.2527
	0.6043	-1.9752	0.3066
	-0.1283	9.1701	-3.6685
Eig. Value:	-4.2107	2.5154	-8.1008
O:	-1.5291	4.0549	0.7967
	-0.6525	-1.3623	0.5725
	2.4081	-4.2053	-0.3571
Eig. Value:	-4.5430	0.2191	1.0754
O:	-2.6378	0.1816	-0.8876
	1.2436	-3.7945	0.9764
	-1.1978	3.3216	-1.2728
Eig. Value:	-2.2985	-5.4875	0.0809
O:	-4.5136	0.6146	-3.3698
	-3.2475	-1.7555	2.4877
	1.9853	-6.8309	0.5451
Eig. Value:	-5.4415	-2.1360	1.8535
O:	5.9169	-0.1045	-6.6474
	1.0911	-1.5076	-2.7179
	-6.8685	2.3311	6.4116
Eig. Value:	-0.5483	-1.5736	12.9428
C:	1.7759	1.1216	0.6515
	-2.0696	3.0548	-2.3025
	6.0084	-3.4220	4.9605
Eig. Value:	-0.7595	2.1235	8.4272
H:	3.0035	-2.2025	2.1732
	0.2500	0.1648	-0.1405
	-1.8240	2.0890	-2.8151
Eig. Value:	3.3094	0.1828	-3.1390
H:	0.6197	-2.7026	-0.8021
	-0.2273	1.3615	0.5058
	-1.2744	3.8606	0.8321
Eig. Value:	-0.2381	4.1902	-1.1388
Cu:	2.7883	2.9748	4.3070
	0.3772	2.8807	-2.3388
	-5.6971	-3.5122	-4.1622
Eig. Value:	1.4622	5.2644	-5.2198
Cu:	-0.7474	2.5488	4.1685
	-1.4979	2.9323	0.9319
	3.5750	-8.8096	-1.2640
Eig. Value:	1.2836	5.7602	-6.1229
O:	-4.0672	5.1939	-0.2215
	-0.6042	-1.9752	-0.3066
	-0.6383	-9.7405	-3.8573
Eig. Value:	-4.3525	2.8106	-8.3578
O:	-1.6357	-4.1138	0.7487
	0.6528	-1.3616	-0.5724
	2.9830	4.5471	-0.0896
Eig. Value:	-4.8050	0.2169	1.5012
O:	-2.6367	-0.0252	-0.8906
	-1.2435	-3.7943	-0.9764
	-1.2281	-4.2108	-1.2608
Eig. Value:	-2.3578	-5.8020	0.4680
O:	-4.3513	-0.8066	-3.3271
	3.2473	-1.7554	-2.4878
	1.0428	7.9719	0.3007
Eig. Value:	-5.6979	-2.3190	2.2108
O:	5.6771	0.0280	-6.7285
	-1.0908	-1.5069	2.7179
	-5.5092	-1.9035	6.8760
Eig. Value:	0.1370	-1.5466	12.4558
C:	1.8116	-1.0703	0.6672
	2.0697	3.0549	2.3025
	5.7830	3.1260	4.8643
Eig. Value:	-0.6098	2.1308	8.2097
H:	3.0181	2.1862	2.1754
	-0.2500	0.1648	0.1405
	-1.9043	-1.9882	-2.8264
Eig. Value:	3.3189	0.1527	-3.1151
H:	0.6012	2.7086	-0.8067
	0.2273	1.3615	-0.5058
	-1.1696	-3.8997	0.8587
Eig. Value:	-0.2051	4.1870	-1.1605