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Electronic, optical and bonding properties of MgCO3 Faruque M. Hossain a,∗ , B.Z. Dlugogorski b , E.M. Kennedy b , I.V. Belova a , Graeme E. Murch a a

University Center for Mass and Thermal Transport in Engineering Materials, Priority Research Centre for Geotechnical and Materials Modelling, School of Engineering, The University of Newcastle, Callaghan, NSW 2308, Australia b

Priority Research Centre for Energy, School of Engineering, The University of Newcastle, Callaghan, NSW 2308, Australia

article

info

Article history: Received 7 September 2009 Received in revised form 8 February 2010 Accepted 8 February 2010 by J.R. Chelikowsky Available online 13 February 2010 Keywords: A. Inorganic compound B. Density functional theory D. Optical constants

abstract The electronic, optical and bonding properties of MgCO3 (magnesite, rhombohedral calcite-type structure) are calculated using a first-principles density-functional theory (DFT) method considering the exchange-correlation function within the local density approximation (LDA) and the generalized gradient approximation (GGA). The indirect band gap of magnesite is estimated to be 5.0 eV, which is underestimated by ∼1.0 eV. The fundamental absorption edge, which indicates the exact optical transitions from occupied valence bands to the unoccupied conduction band, is estimated by calculating the photon energy dependent imaginary part of the dielectric function using scissors approximations (rigid shift of unoccupied bands). The optical properties show consistent results with the experimental calcite-type structure and also show a considerable optical anisotropy of the magnesite structure. The density of states and Mulliken population analyses reveal the bonding nature between the atoms. © 2010 Elsevier Ltd. All rights reserved.

1. Introduction To control global climate change, it is essential to take the initiative in reducing the continued increase of CO2 , the major contributor from fossil fuel power plants. By capturing CO2 from the atmosphere, carbon sequestration is an effective method for greenhouse gas mitigation. Among the many different possible processes of CO2 sequestration, the chemical process of mineral storage is especially attractive provided a cost effective method can be developed. Carbon sequestration by reacting Mgcontaining silicate minerals with CO2 (mineral carbonation) to form carbonates has considerable advantages because the reaction is thermodynamically favourable and there are vast amounts of magnesium silicate minerals available worldwide. Furthermore, the carbon in the Earth’s mantle, that is at depths and pressures exceeding 33 km and 1 GPa, is probably stored in the form of magnesite. It appears that magnesite is the only stable carbonate mineral in the presence of silicates in the mantle [1]. A stability study of magnesite at pressure and temperature conditions close to the core-mantle boundary performed by Issiki et al. [2] showed that magnesite transforms to an unknown crystal form without any dissociation. These considerations clearly indicate the importance of magnesite as a host mineral for storing CO2 at the Earth’s surface, with application to sequestration of anthropogenic CO2 , and in the Earth’s mantle,

∗

Corresponding author. Tel.: +61 0383448744. E-mail address: [email protected] (F.M. Hossain).

0038-1098/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2010.02.008

to explain the mineralogical form of carbon in the interior of the Earth. It might also be added that MgCO3 is also very attractive for other applications such as in fire-extinguishing compositions, in cosmetics, in toothpaste and as a drying agent. Catti et al. [3] used an ab initio Hartree–Fock technique to calculate the electronic and bonding properties of magnesite. That study showed that the CO3 groups in the structure are rigidly bound with covalent bonding and that the Mg–O bonds showed ionic interaction. A first-principles calculation of Vočadlo [1] under the application of stress showed that the CO3 groups in MgCO3 are rigid and incompressible whilst the Mg–O bond undergoes significant compression without any chemical dissociation. An ab initio electronic structure calculation by Arapan et al. [4] on calcite (CaCO3 ) showed a new high-pressure phase transformation and explained the stability of calcite and magnesite in term of sp3 hybridized bonds under the Earth’s lower mantle pressure conditions. In this paper, we present an in-depth study of the electronic, optical and bonding properties of MgCO3 (magnesite) in order to provide an in-depth understanding of such minerals from an ab initio point of view. This will provide a bench-mark for other ab initio calculations in the search for new possible structures and phases of carbon containing minerals that can effectively capture CO2 for indefinite periods. 2. Method of calculation The magnesite polymorph of MgCO3 has a hexagonal crystal ¯ system with rhombohedral symmetry and space group R3c. Similar to calcite, the primitive cell (rhombohedral representation)

F.M. Hossain et al. / Solid State Communications 150 (2010) 848–851

contains two formula units. The calculations were performed using the hexagonal representation of the conventional unit cell instead of the primitive cell. The calculations were based on the ab initio plane wave pseudopotential DFT approach. The lattice parameters of magnesite were geometrically optimized and the ground-state electronic structure calculated using the CASTEP software code [5,6]. Optimization was performed with a convergence threshold for the maximum energy change of 5.0 × 10−6 eV/atom and for a maximum force of 0.01 eV/Å. The Vanderbilt ultrasoft pseudopotential (USP) method [7] with a plane wave basis set cut-off energy of 600 eV was used for the geometry optimization, band structure and density of states (DOS) calculations. The Monkhorst–Pack (MP) [8] mesh of 6 × 6 × 2 was used, which produces 10 k-points within the irreducible segment of the Brillouin zone (BZ). The effects of exchange and correlation energy were treated within the generalized gradient approximation (GGA) [9]. A norm-conserving pseudopotential method [10] with a plane wave basis set cut-off energy of 960 eV was used for the Mulliken charges and bond overlap population calculations and the optical properties calculations. The valence states for Mg, C, and O are 2p6 3s2 , 2s2 2p2 , and 2s2 2p4 respectively. The Mulliken charges and bond overlap populations were calculated by projecting the PW Khon–Sham eigenstates onto the atomic basis sets. Projection of the PW states on to LCAO basis sets [11] was used to perform the Mulliken population calculations. Population analysis of the resulting projected states was then performed using the Mulliken formalism [12]. 3. Results and discussion

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Fig. 1. Electronic band structure of magnesite along high symmetry directions in the first Brillouin zone using LDA (dotted lines) and GGA (solid lines) functionals. The dashed line at zero energy represents the Fermi level.

a b

3.1. Structural properties The optimized structural parameters of magnesite were obtained by searching for the stable structure for a minimum total energy with a suitable convergence criterion as mentioned in the method of calculation. The conventional cell of six formula units (Z = 6) with initial lattice parameters of a = b = 4.9901 Å, c = 17.061 Å is considered in this optimization calculation. Three interatomic angles (O–Mg–O) in the MgO6 octahedron of unoptimized structure are 87.452°, 92.548°, and 180.00° respectively. The optimized structural parameters are shown in Table 1 and compared with the experimental results. Our structural properties are consistent with the early experimental results. Structural optimization with LDA provides better results for a, b, V parameters and bond lengths, whilst the GGA provides better agreement for the three bond angles. Overall, the LDA functional shows better structural results. Both the LDA and GGA functionals are used for band structure calculations. 3.2. Energy band structure The electronic band structure of magnesite along highsymmetry directions in the Brillouin zone using both LDA and GGA functional is shown in Fig. 1. The indirect electronic band gap along Γ → M in the band structure is ∼5.0 eV, which is underestimated by ∼1.0 eV due to the limitation of LDA or GGA. Although the LDA functional shows better structural results, however, the indirect band gap is only ∼0.01 eV higher than the GGA functional. A noticeable energy shift occurs in the dispersive upper part of the conduction band. The valence band below the Fermi level extends to ∼8.0 eV and consists of three parts. The upper part just immediately below the Fermi level originated from the mixed contribution O 2p and Mg 2p/3s orbitals, which gives rise to the mainly ionic interaction between Mg and O. The lower two parts consist of sp hybridized orbitals produced from contribution of all three atoms, indicating the existence of some covalence in the structure. The conduction band above the Fermi level consists of two parts. The lower part

c d

Fig. 2. The total and partial density of states of magnesite. (a) Total density of states below and above the Fermi level (dashed line at zero energy), (b) partial density of states (2s and 2p orbital contribution) for O, (c) partial density of states (2s and 2p orbital contribution) for C, (d) partial density of states (2p and 3s orbital contribution) for Mg.

appears mainly from C 2p and slightly from O 2p and Mg sp orbitals. The upper part shows highly dispersive bands with most contribution from the Mg atom. The underestimated band gap is corrected in the optical properties calculations allowing the scissors operator of 0.9 eV, which rigidly shifts the unoccupied conduction band states with respect to the completely occupied valence band states. The scissors operator (0.9 eV) is chosen to adjust with the experimental band gap of calcite-type [15] structure. 3.3. Density of states (DOS) Fig. 2 shows the total and partial density of states (DOS) of magnesite. The projected density of states shows orbital contributions of magnesium, oxygen and carbon. Both LDA and GGA functionals are used for the DOS calculations. As we found no difference in atomic orbital contributions except spectral change in the upper conduction band, we show there only the GGA-derived results. The upper part of the valence band just immediately

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F.M. Hossain et al. / Solid State Communications 150 (2010) 848–851

Table 1 Calculated structural parameters of magnesite for both LDA and GGA functionals compared with the early experimental results. Parameters

Experimental

Theoretical (this calculations) GGA

LDA

a = b (Å) c (Å)

4.637 , 4.635(2) 15.023a , 15.03(1)b

4.720 15.331

4.635 14.693

V (Å ) C–O bond (Å) Mg–O bond (Å) Three O–Mg–O bond angles (°)

279.7(3)b 1.283a 2.105a 88.252, 91.752, & 180a

295.8 1.298 2.149 88.263, 91.737, & 180

273.3 1.285 2.087 89.063, 90.937, & 180

a

3

a b

b

Ki Dong Oh et al. [Reference [13]]. G. Fiquet et al. [Reference [14]].

Table 2 Atomic Mulliken charges and effective valence charges in magnesite calculated from a PW electronic structure calculation. Species

s

p

Total charge (e)

Mulliken charge (e)

Effective valence (e)

C O Mg

0.88 1.77 0.26

2.52 4.91 0.26

3.4 6.68 0.55

+0.60 −0.68 +1.45

– –

+0.55

below the Fermi level consists mainly of O 2p states with some contributions from Mg sp, which is the origin of ionic bonds between Mg and O. The lower part of the valence band has almost a sp hybridized contribution mainly from both C and O atoms with a very small contribution from Mg sp, which is carrying covalent bonding information within the CO3 groups in the structure. The core level orbital states at around 20 eV below the Fermi level show a similar sp hybridized contribution from both C and O atoms, which determines the rigidity of CO3 groups. This DOS analysis predetermines the ionic and covalent bonding nature of the magnesite structure. The coexistence of such bonding will next be confirmed by a Mulliken population analysis. 3.4. Optical properties The optical properties were obtained by calculating the optical transition matrix elements between occupied eigenstates in the valence bands and unoccupied eigenstates in the conduction bands. We allow a vertical rigid shift of conduction band states (the scissors operator) of 0.9 eV during all optical properties calculations. Fig. 3 shows the frequency-dependent optical properties within the photon energy range of 0–20 eV. All optical properties (the imaginary part of the dielectric function ε2 (ω), the absorption α , the reflectivity, the refractive index n, and the extinction coefficient, (κ) were evaluated by polarizing the incoming light along two crystal directions (parallel and perpendicular to the c-axis of hexagonal unit cell). The fundamental absorption edge shows at ∼6.0 eV (as indicated by arrows) in the three spectra of ε2 (ω), α(ω), and κ(ω), which is consistent with the experimental band gap of the calcite-type [15] structure. Fig. 3 also shows different peaks arising from the allowed bandto-band transitions. The spectral plots along two different crystal directions show a significant optical anisotropy at the fundamental absorption edge (upper valence band to lower conduction band). A noticeable anisotropy (a sharp absorption peak at around 13.0 eV along [1] crystal direction] is also observed while transitions from the valence band to the upper part of the conduction band are due to the highly dispersive nature of the upper conduction band. This anisotropy information is required for designing a suitable interacting surface of the crystal which is sensitive to light and absorbing species. 3.5. Mulliken population analyses The Mulliken charge and overlap population are useful in evaluating the types of bonding (ionic, covalent or metallic) in a compound. The dominance of either covalent or ionic bonding may be determined from the ‘effective valence’, which is defined as

Fig. 3. The frequency-dependent optical properties (imaginary part of the dielectric function, ε2 (ω), absorption, α , reflectivity, refractive index, n, and extinction coefficient, κ calculated for the two directions (dashed and solid lines are along [001] and [100]) directions respectively) of incoming light with respect to the crystal axis of magnesite.

the difference between the formal ionic charge and the Mulliken charge on the cation species [16]. A value of zero indicates a perfectly ionic bond whilst values greater than zero indicate increasing levels of covalency. Table 2 lists the orbital charges and effective valence of the C, O, and Mg species of magnesite. The effective valence for Mg cations in MgCO3 is +0.55. This value represents the coexistence of both ionic and covalent bonding in magnesite. The type of bonding and its level may further be determined by calculating the Mulliken bond population.

F.M. Hossain et al. / Solid State Communications 150 (2010) 848–851 Table 3 Mulliken bond populations, derived population ionicity, and bond lengths in magnesite. Bond

Bond population, P

Population ionicity, Pi

Bond length (Å)

C–O Mg–O O–O

0.89 0.18 −0.23

0.116 0.990 –

1.298 2.149 2.248

Table 3 lists the bond populations, population ionicity, and the bond lengths for C–O, Mg–O, and O–O bonds in the magnesite crystal. Positive and negative values indicate bonding and antibonding states, respectively. A high positive bond population indicates a high degree of covalency in the bond [16]. On the other hand, the population ionicity can be calculated from the definition of the ionicity scale of He et al. [17] as:

Pi = 1 − exp −

Pc − P P

,

where P is the overlap population of a bond and Pc is the bond population for a purely covalent bond. Pi = 0 indicates a purely covalent bond whilst Pi = 1 indicates a purely ionic bond. The C–O bonding within the CO3 group (shortest bond length) shows a high level of covalency and a low level of ionicity. Here, we assume that the value of Pc is equal to 1.0, representative of a purely covalent bond. The Mg–O bond shows a purely ionic nature with slight covalency, a similar result was found in our recent study on calcite (CaCO3 ) [18]. 4. Conclusion We have presented the energy band structure, density of states, optical properties, and bonding properties of rhombo-

851

hedral MgCO3 (magnesite) using a first-principles DFT calculation. The indirect energy gap for it is estimated to be ∼5.0 eV from the band structure calculations, whilst the fundamental absorption edge is estimated to be ∼6.0 eV from the photon energy dependent optical transition properties calculation using scissors approximations. The optical properties show consistent results with the experimental calcite-type structure. The rhombohedral magnesite structure is tested to be optically anisotropic. The density of states and Mulliken population analyses determines the presence of both ionic and covalent bonding in the magnesite. References [1] L. Vočadlo, Amer. Mineral. 84 (1999) 1627–1631. [2] M. Issiki, T. Irifune, K. Hirose, S. Ono, Y. Ohishi, T. Eatanuki, E. Nishibori, M. Takata, M. Sakata, Nature 427 (2004) 60. [3] M. Catti, A. Pavese, R. Dovesi, V.R. Saunders, Phys. Rev. B 47 (1993) 9189. [4] S. Arapan, J. Souza de Almedia, R. Ahuja, Phys. Rev. Lett. 98 (2007) 268501. [5] M.C. Payne, M.P. Teter, D.C. Allan, T.A. Arias, J.D. Joannopoulos, Rev. Modern Phys. 64 (1992) 1045. [6] L.J. Clarke, I. Stich, M.C. Payne, Comput. Phys. Commun. 72 (1992) 14. [7] D. Vanderbilt, Phys. Rev. B 41 (1990) 7892. [8] H. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188. [9] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [10] D.R. Hamann, M. Schluter, C. Chiang, Phys. Rev. Lett. 43 (1979) 1494–1497. [11] D. Sanchez-Portal, E. Artacho, J.M. Soler, Solid State Commun. 95 (1995) 685; J. Phys.: Condens. Matter. 8 (1996) 3859. [12] R.S. Mulliken, J. Chem. Phys. 23 (1955) 1833. [13] Ki Dong Oh, Hideki Morikawa, Shin’ichi Iwai, Hideki Aoki, Amer. Mineral. 58 (1973) 1029. [14] G. Fiquet, F. Guyot, Jean-Paul Itié, Amer. Mineral. 79 (1994) 15. [15] D.R. Baer, D.L. Blanchard Jr., Appl. Surf. Sci. 72 (1993) 295. [16] M.D. Segall, R. Shah, C.J. Pickard, M.C. Payne, Phys. Rev. B 54 (1996) 16317. [17] J. He, E. Wu, H. Wang, R. Liu, Y. Tian, Phys. Rev. Lett. 94 (2005) 015504. [18] F.M. Hossain, G.E. Murch, I.V. Belova, B.D. Turner, Solid State Commun. 149 (2009) 1201.