Ab Initio Studies on Hematite Surface and the Adsorption of Phosphate
This investigation explores the ab initio DFT method for understanding surface structure of hematite and the nature and energetics of phosphate adsorption. Using the full potential linearized plane wave method (FP-LAPW), we derived the structure and energies of various magnetic forms of hematite. The antiferromagnetic (AFM) form was observed to be the most stable. Hematite surfaces with Fe-termination, O-termination, or OH-termination were studied. The OH-terminated surface was the most stable. Stability of hematite surfaces follows the order OH-termination > Fe-termination > O-termination. Thus, surface reaction with hematite would occur with the OH at the surface and not with Fe atoms. The structure of phosphate adsorbed on hematite was derived. Bonding is through the H atom of the OH at the surface. An alternative mechanism of phosphate adsorption on hematite has been derived. Adsorption energy is high and suggests chemisorption rather than physisorption of phosphate on hematite.
Hematite is ubiquitous in all soils but is predominant in soils of the tropical and subtropical regions. Due to large surface area and high reactivity, hematite influences several physical and chemical properties. Modelling the reactivity of hematite surfaces is, therefore, based on its bulk crystal structure and particularly on the surface arrangement of atoms. Hematite, -Fe2O3, belongs to the space group 167 R-3c with either two or six formula units in the primitive rhombohedral and in the conventional hexagonal unit cells, respectively. Hexagonal close-packed layers of O atoms are present, with Fe atoms filling 2/3rd of the octahedral holes, which are all in a high-spin d5 electronic configuration . The stable phase is antiferromagnetic (AFM) below the Neel temperature, at 955 K .
Catti et al.  studied the electronic, magnetic, and structural properties of hematite by periodic unrestricted Hartree-Fock method and showed that the band gap is of p-d rather than d-d type, confirming the charge-transfer-insulator nature of hematite. Rollmann et al.  studied hematite by using density functional theory (DFT) and the generalized gradient approximation (GGA) and observed that the ground state is antiferromagnetic. Analysis of the density of states confirms the strong hybridization between Fe 3d and O 2p states. Spin-density functional theory was used for the calculation of slab geometry in the surface study of hematite . They observed that, depending on the ambient oxygen partial pressure, either the iron terminated surface or the oxygen terminated surface may be stable under thermal equilibrium. Rohrbach et al.  presented a detailed ab initio investigation of the structural, electronic, and magnetic properties of the (0 0 0 1) surfaces of hematite by GGA and (GGA + ) approaches. They observed that O-terminated surfaces are energetically unfavourable compared to the Fe-terminated surface. Using DFT methods, Souvi et al.  showed that outermost iron atoms of hematite would be almost fully hydroxylated. This would decrease the Lewis acidity of the surface and domination by hydrogen bonds. Experimental studies using crystal truncation rod (CTR) X-ray diffraction, however, showed that the unreacted -Fe2O3 (0 0 0 1) surface consists of both an O-layer terminated domain and a hydroxylated Fe-layer terminated domain . Trainor et al.  also used CTR XRD to study hematite surfaces and observed that surface is dominated by hydroxyls which are either singly or doubly coordinated with Fe.
Studies on adsorption of small molecules by hematite surfaces using DFT methods are now being increasingly used and have been reported to be quite reliable . DFT supercell calculations revealed that, regardless of nature of surface terminations, the adsorption of methyl radical was strong in all cases. Fe vacancy in hematite showed increased reactivity towards H2O .
Adsorption reactions of phosphate are of particular interest due to its influence on phosphate availability to plants. The mechanisms of adsorption of phosphate on hematite surfaces have been derived mainly from experimental studies. Goldberg and Sposito  studied the kinetics of adsorption-desorption and proposed ligand exchange as the mechanism of phosphate-surface hydroxyl reaction. According to them, hydroxyl ion release and crystallographic calculations provided support for complexation of phosphate ions on the surface. Elzinga and Sparks  characterized phosphate adsorption on hematite as a function of pH and phosphate concentration by ATR-FTIR investigations and suggested that the surface complexes are monoprotonated. Rajan  measured phosphate adsorption on oxide surfaces by displacing ligands [M(OH)2 or M(OH)] and recording simultaneous reduction in the net surface charges. He inferred that phosphate was adsorbed on the hydrous oxides only and adsorption makes the oxide surface less positive. Barrón and Torrent  reported that surface hydroxyl configuration (SHC) of the hematite , , , , , , and faces determined the surface properties of oxides. Singly, doubly, and triply coordinated OH groups are involved in the specific adsorption of phosphate and other ions. Adsorption of phosphate and sulphate adsorption on ferric hydroxide simulated by DFT  showed that adsorption was most favored by bidentate, binuclear surface complexes. Phosphate complexes with iron hydroxides were also studied by quantum mechanical calculations which concluded that monoprotonated monodentate complex should be favored .
The objective here was to understand the nature of hematite surface that would be involved in surface reactions by theoretical studies of the structure using DFT-LPAW method. The subsequent goal was to study the geometry and energetics of phosphate adsorption on the surface. This involved (a) a derivation of the structure of the most stable magnetic form of hematite, (b) derivation of the most stable surface termination (Fe-termination, O-termination, or OH-termination) followed by derivation of the structure of this surface, and (c) derivation of the structure and orientation of the adsorbed phosphate and the energetics of the adsorption process. All derivations used ab initio methods based on the density functional theory  to derive electron densities and subsequent derivation of ground state properties.
2. Materials and Methods
2.1. Computational Methodology
Wien2k performs electronic structure calculations of solids using density functional theory. Here, Kohn-Sham equations for the ground state density and total energy are solved by the full potential linearized augmented plane wave (FP-LAPW) method  by introducing a basis set which is especially adapted to the problem . Kohn-Sham equations are solved self-consistently in an iterative process under the generalized gradient approximation with the Perdew-Burke-Ernzerhof functional for the exchange-correlation energy, subject to periodic lattice boundary conditions .
2.2. Geometry and Magnetic Nature of Unit Cell
Hematite belongs to the trigonal space group and can exist in three different magnetic forms, namely, nonmagnetic (NM), spin-polarized (SP), and antiferromagnetic (AFM). The rhombohedral structure was used for ground state calculations. Initially optimization of input parameters, -points, and was done. -points were studied over 200 to 1400 and observed to be optimum at 1400. value was optimum at 8.00. Energy cut-off between core and semicore was at −9.0 Ry. All three forms of hematite were optimized for volumes, / ratios, and atom positions. Total energies were derived for each of the optimized structures.
2.3. Supercell Calculations and Slab Geometry
Supercell calculations were done with the AFM form of hematite. The rhombohedral cell was transformed into a hexagonal cell using Cryscon. In the hexagonal cell, the O atoms approximately form a hexagonal close packing (hcp) lattice with Fe atoms occupying two-thirds of the octahedrally coordinated interstitial positions. The structure has a –O–Fe–Fe–O–Fe–Fe-stacking sequence in the direction, with ~2.20 Å between the O planes in the bulk configuration . Here, (0 0 0 1) plane was studied.
As the first step, an optimum vacuum slab was derived. A (1 × 1 × 1) hexagonal supercell was prepared and vacuum was added in the -direction. Here, the repeated slab model containing on average 12 atomic layers represents the surfaces. The optimum vacuum depth separating the slab in the direction was derived so that an intersurface interaction was negligible. The model was constructed such that the inversion symmetry was maintained; that is, both surfaces of the slab were identical. We used spin density functional theory calculations for the slab geometry. Optimized vacuum slab distance for AFM-hematite was at 29 Bohr. This agrees well with data obtained by previous workers .
Geometry optimization computations were performed in several stages. The surface atoms were relaxed layer by layer while fixing the rest of the system in order to obtain a good convergence. Towards the end of the convergence process, all atoms were relaxed. A modified tetrahedron integration scheme was used to generate the -mesh in the irreducible wedge of the hexagonal Brillouin zone on a special point grid . A (4 × 4 × 1) -mesh was required in the final stages of convergence. -mesh optimization followed by optimization was done. The muffin tin radius, , used was 1.70 Å for Fe and O atoms and 0.60 Å for H atoms. The energy cut-off between core and semicore was −9.00. The hematite surface was treated antiferromagnetically. In AFM-hematite surfaces, spin flipping for Fe (Fe1 and Fe2) was done, that is, inverting the spin up and dn (down). Rotational-translational matrix was added in AFM-hematite surfaces for the symmetry operation.
After deriving the optimized slab distance, cell optimization was done. For cell optimization, / optimization followed by volume optimization was performed . Using the computed lattice parameters in the direction parallel to the (0 0 0 1) surface, as obtained from bulk calculations, the atomic positions of all atoms in the slab were fully relaxed, resulting in optimized geometries and corresponding total energies.
Three different surface terminated states of hematite were studied. These were Fe-terminated, O-terminated, and OH-terminated. Each of these structures along with the surfaces was optimized for geometry and the most relaxed positions were derived. The total energies of the most relaxed structures were then derived.
2.4. Phosphate Adsorption
To calculate the adsorption energies and other properties of phosphate on the hematite, phosphate molecules were added to the protonated antiferromagnetic surface of the -Fe2O3 (0 0 0 1) on threefold oxygen site with the phosphate molecule located above the H-terminating oxide plane and the H–O bond length initially set at 0.130 nm. The phosphate molecules as well as the top Fe1–O1–Fe2 layers were then fully relaxed.
Calculations used the (4 × 4 × 1) -mesh, (Fe) = 1.60 Å, (O) = 1.10 Å, (P) = 1.50 Å, (H) = 0.60 Å, 13 GGA, , and mixing factor 0.01 (BROYD scheme). For symmetry operation, the rotational-translational matrix was
These strained systems contained huge amounts of forces. So the structures were minimized for forces by changing the atomic positions to derive the structure with minimum forces. Densities of states, electron density mappings, and so forth were plotted with both systems after optimizing the structures.
The adsorption energy was evaluated as where (adsorbed) is the total calculated energy of the unit cell containing the adsorbed phosphate molecule in its equilibrium position and (separated) is that of the system at a large separation of the phosphate molecules from the surface. The (separated) is equal to the sum of the calculated total energies of the partially optimized -Fe2O3 slab and a single phosphate molecule alone.
3. Results and Discussion
3.1. Cell Structure and Magnetization
Optimized cell dimensions and other cell properties of the three magnetic forms of hematite are shown in Table 1. Data show that the AFM form has the lowest energy and is, therefore, the most stable of all three forms. Stability follows the sequence AFM > SP > NM. The stability of the AFM form compared to other magnetic forms of hematite has been corroborated by previous workers [2, 3]. There appears to be an expansion of the cell in the /-axis from NM to SP to AFM form of hematite. The -axis is largest for AFM and smallest for the SP form. The derived cell parameters of AFM hematite are close to the experimental data (Table 1), namely, 5.035 Å and 13.72 Å, respectively . Other workers theoretically derived cell parameters as 5.025 Å and 13.671 Å  and 5.007 Å and 13.829 Å . Bulk modulus of NM, SP, and AFM hematite is in good agreement with the theoretical results by Bergermayer et al. .
The experimental band gap of hematite, a “Mott-Hubbard insulator”, is 2.0 eV. The theoretically derived band gap is not more than 0.50 eV due to strong interaction between 3d of Fe and 2p of oxygen. Since the theory of (DFT + LAPW) cannot deal completely with strongly correlated systems like hematite, (LDA + ) treatment was required . The value of used here was 4 eV in ground state calculations of hematite . Applying (LDA + ) on hematite, a band gap of 4.2450 eV and 1.5238 eV was observed for up and dn spins, respectively. The results are in good agreement with those reported earlier .
3.2. Surface Stability and Structure
In view of the stability of the AFM form of hematite, surface structural studies were carried out with the AFM hematite. There are basically two ways in which the surface of hematite may terminate, namely, Fe-terminating and O-terminating. However, in the presence of water (moisture from atmosphere), the oxygen terminating surface could get hydroxylated and thus become an OH surface. Such surfaces would not have dangling bonds. Therefore, for the purpose of these calculations, we also considered the OH-terminating surface.
Cohesive energies of all three terminating forms of hematite are shown in Table 2. The O-terminating surface has highest energy and is, therefore, the least stable; this is followed by the Fe-terminating surface. The OH-terminating surface has the lowest energy of all three forms and hence this is energetically the most stable form of the three. Therefore, the order of stability is OH-terminating hematite > Fe-terminating hematite > O-terminating hematite.
Other workers have also observed that the Fe-terminating surface is more stable than the O-terminating surface. Rohrbach et al.  observed that O-terminated surfaces are energetically unfavourable compared to the Fe-terminated surface. Other workers  also confirmed the greater stability of Fe-terminated surface over the O-terminating one. Another study has reported that the natural hematite surface consists of singly and doubly protonated layer of oxygen and that the p of the OH2 functional group is approximately 2 . It follows that, in aqueous medium at around neutral pH, the surface OH2 would dissociate to produce OH groups. This is in conformity with our own derivations. Our finding, on the stability of the OH-terminating surface, is significant because it suggests that surface reactions of hematite occur with the OH group at the surface and not with surface Fe or O.
3.3. Adsorption of Phosphate
Mechanism of phosphate adsorption is generally viewed as a direct interaction of with the O at the surface of oxide [28, 29], as shown in Figure 1(a). However, our derivations suggest that the stable hematite surface is OH-terminated and not O-terminated. Therefore, the mechanism of adsorption would be by H-bonding through the hydroxylated surface OH (Figure 1(b)). The adsorption energy for phosphate on hematite is joule/molecule or −62.2378 eV/molecule. Since the adsorption energy is quite large, the phenomenon is chemisorption and phosphate is not easily available to the plants.
Density of state (DOS) after phosphate adsorption shows remarkable changes for both spin up and dn states. In the total DOS (up), the range for valence band was 2.07 to −7.23 eV whereas in the DOS (dn) case, the range was 2.07 to −7.25 eV. A small shift in Fermi level is evident. Conduction band range was found to be above 3.05 eV for both total up and dn cases. For phosphate adsorbed hematite (Figures 2(c) and 2(d)), the band gaps were 0.925 and 0.952 eV for up and dn spins, respectively, whereas the hematite itself showed band gaps of 4.245 and 1.524 eV (Figures 2(a) and 2(b)).
Electron density plots are depicted in Figures 3(a) to 3(e). Electronic distributions around P and O of phosphate group are similar due to comparable electronegativity of P and O. Electronic distribution (Figure 3(e)) in O atoms shows uneven contribution of electron density from Fe and P. The extensive charge transfer from the O to Fe indicates a predominant ionic bonding resulting in a slightly polarized Fe charge density. This isolated electron distribution of phosphate group from the entire protonated hematite surface proves that the bond formation between phosphate group and hematite surfaces is through hydrogen only.
The antiferromagnetic (AFM) form has been shown to be the most stable form of hematite. Derivations suggest that the surface of hematite has a layer of OH and is neither O-terminated nor Fe-terminated. Accordingly, surface reactions occur with the OH at the surface. Adsorption of phosphate reveals a Fe–O–H–O–P mechanism for adsorption rather than a Fe–O–P mechanism. Adsorption energy is high suggesting chemisorption. This can explain the strong retention of phosphate by hematite.
Our study has demonstrated the feasibility of this new approach for reactivity of mineral surfaces. We have shown that it is possible to theoretically derive the surface structure of minerals, which is critical for understanding their reactivity. The geometry of surface adsorbed molecules can be derived and their adsorption energies could be calculated. Thus, reactivity and reaction mechanisms can be theoretically understood. Future work could be undertaken to study other minerals like gibbsite and goethite, using the methodologies that we have initiated here.
Conflict of Interests
The authors declare that there is no conflict of interests regarding the publication of this paper.
This research was supported by the Raman Centre for Applied and Interdisciplinary Sciences, Kolkata, West Bengal, India.
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