Theoretical structure and surface energy of the reconstructed {01.2} form of calcite (CaCO 3) crystal

Two different reconstructions of the (01.2) face (Ca or CO 3 terminated) of calcite (CaCO 3) were studied: (i) R1 reconstruction: the outermost layer is based on the [0 1 0] × 1/3[2 1 1] rectangular mesh, which is symmetrical with respect to the c glide plane of the crystal, thus fulfilling the 2D symmetry of the face and (ii) R2 reconstruction: the outermost layer is based on a 1 / 6 [ 4 2 1 ¯ ] × 1 / 6 [ 2 2 ¯ 1 ] lozenge shaped mesh that does not respect the 2D symmetry of the face. The ( 01.2 ) R 1 Ca , ( 01.2 ) R 1 CO 3 , ( 01.2 ) R 2 Ca and ( 01.2 ) R 2 CO 3 slabs geometry optimizations of calcite (CaCO 3) were performed either at DFT level or by using empirical potentials; the results obtained with these two different calculation methodologies are in good agreement. With respect to their arrangement in the bulk, the CO 3 groups of the outermost layer are significantly rotated about the crystallographic a-axis and about the normal to the 01.2 plane; further, the thickness of the outermost layer is significantly lower than that of the underneath ones. The surfaces energies ( γ) at 0 K, for relaxed and unrelaxed ( 01.2 ) R 1 Ca , ( 01.2 ) R 1 CO 3 , ( 01.2 ) R 2 Ca and ( 01.2 ) R 2 CO 3 faces, were determined either at DFT level or by using empirical potentials. Independently of the method of calculation employed, the stability order of the relaxed faces is ( 01.2 ) R 1 CO 3 < ( 01.2 ) R 2 Ca < ( 01.2 ) R 2 CO 3 < ( 01.2 ) R 1 Ca . Concerning the unrelaxed faces, whose energies were evaluated by using empirical potentials only, the stability order is instead ( 01.2 ) R 1 Ca < ( 01.2 ) R 2 Ca < ( 01.2 ) R 1 CO 3 < ( 01.2 ) R 2 CO 3 ; such different ordering shows the importance of geometry relaxation in the calculation of the surface energy. The values of the relaxed surface energies are γ ( 01.2 ) R 1 CO 3 ≈ 750 , γ ( 01.2 ) R 2 Ca ≈ 950 , γ ( 01.2 ) R 2 CO 3 ≈ 980 and γ ( 01.2 ) R 1 Ca ≈ 1050 erg/cm 2.