Density functional theory study of the atomic and electronic structures of trans-vacant 1M Al-rich illite

Abstract

Illite is a common clay mineral that is found in a wide range of geological settings. The good thermal stability and non-swelling properties of illite make it valuable in ceramic materials, paints and coatings, drilling fluids, agriculture and geological studies. To gain a deeper understanding of the physical and chemical properties of illite, in the present paper the atomic and electronic structures of a typical trans-vacant 1M Al-rich illite were constructed and calculated using density functional theory. The calculated indirect band gap of Al-rich illite was 4.99 eV. The electronic analysis revealed that the interactions in the tetrahedral sheet were more stable than those in the octahedral sheet. The substitution of Al atoms noticeably reduced the stability of the tetrahedral sheet in Al-rich illite. Other properties of Al-rich illite, including the density of states, electron population/charge, electronic charge density and bonding interaction, are also discussed and analysed in detail.

Illite is a type of mica-like phyllosilicate clay mineral. Its name was introduced by Grim et al. (1937) and derived from the name of the state of Illinois, USA. Illite is a widespread mineral found in diverse geological environments, primarily originating from the weathering and alteration of other minerals such as micas and feldspars (Righi & Meunier, 1995; Shoval, 2023). The good thermal stability (He et al., 1995) and non-swelling properties (Ruiz Pestana et al., 2017) of illite make it valuable in a wide range of industrial and geological applications, including ceramic materials, paints and coatings, drilling fluids, agriculture and geological studies (Steiger, 1982; Feng et al., 1999; Sedmale et al., 2017; Li et al., 2018; Zhang et al., 2020; El Halim et al., 2022).

Existing experimental and theoretical data have confirmed the 2:1-type dioctahedral layered structure of illite, which consists of stacked layers primarily bound by van der Waals forces (Brigatti & Guggenheim, 2002). An individual 2:1 basic layer comprises two tetrahedral sheets sandwiching one octahedral sheet to form a T–O–T structure (Bergaya & Lagaly, 2013). The tetrahedral sheets are composed of Si–O tetrahedrons with some of the Si atoms substituted by Al atoms, whereas the octahedral sheet consists of Al, Mg or Fe cations coordinated with OH groups (Meunier & Velde, 2004). The interlayer space of illite primarily accommodates K ions, and the interlayer charge generally ranges between 0.60 and 0.85 per O₁₀(OH)₂ (Rieder et al., 1998). The octahedral sheet of illite exhibits two types of structure – cis-vacant and trans-vacant – determined by the configuration of the coordinating OH groups (Drits et al., 2006; Drits et al., 2012). In terms of polytypes, it has been observed that the 1M and 2M _l polytypes are most frequently encountered in illite species (Zoeller & Brockamp, 1997; Zviagina & Drits, 2019).

Due to the complexity of the chemical components, disordered stacking, cation substitutions, cation configurations and the small crystalline domain size of illite, measuring its atomic structure and crystal properties accurately through experiments remains challenging. With advancements in theoretical research, computational chemistry calculations based on density functional theory (DFT) have been proven to be effective and reliable for investigating clay minerals at the molecular level (Bridgeman, 1996; Beermann & Brockamp, 2005; Mercier et al., 2010; He et al., 2012; Teich-McGoldrick et al., 2012; Scholtzová & Tunega, 2019; Yuan et al., 2022; Zhao et al., 2023). A series of studies has investigated the structure of illite using DFT. Stixrude & Peacor (2002) discussed two avaliable competing models of illite smectite systems based on a first-principles study. The results revealed that differences in energy and structure between the two models can be understood in terms of local charge balance. Militzer et al. (2011) calculated the elastic constants of muscovite illite–smectite using DFT theory, and the differences indicated that there were variations in their crystal sturctures. Geatches & Wilcox (2014) modelled a variety of interlayer-deficient dioctahedral mica models of the 1M illite series based on crystallographic data and average formulae with DFT, and they analyzed the differences between cis-vacant and trans-vacant models. Escamilla-Roa et al. (2016) investigated the stability of the hydronium cation in the structure of illite. The results revealed that the hydronium cation remains in the interlayer of illite at high temperatures. Sánchez-Coronilla et al. (2019) investigated the inclusion of Fe, Cu and Zn in Illite. After analysing the stability and electronic effect of the inclusion system, illite presented good adsorption characteristics for Fe, Cu and Zn in the (1,0,0) site.

In the present paper, a DFT study of a typical trans-vacant 1M Al-rich illite without octahedral substitution is reported by calculating its atomic and electronic structure, density of states (DOS), electron population/charge, electronic charge density and bonding interaction analysis. The current DFT results will contribute to a better understanding of the chemical, physical and mechanical properties of illite from a microscopic perspective.

Method of calculation

The periodic DFT calculations were conducted with the Vienna ab initio simulation package (VASP; Monkhorst & Pack, 1976; Kresse & Furthmüller, 1996). The interaction between the ions and valence electrons is described by the full-potential frozen-core all-electron projector augmented wave (PAW) method proposed by Blöchl (1994) and by Kresse & Joubert (1999). Plane-wave pseudopotentials and periodic boundary conditions were applied when solving the Kohn–Sham DFT equations. The electron exchange potential and correlation energy were calculated using the Perdew–Burke–Ernzerhof (PBE) form of the generalized gradient approximation (GGA; Perdew et al., 1996). In the present paper, a (3 × 4 × 3) Monkhorst–Pack k-point was utilized for Brillouin-zone integrations. The corresponding plane-wave basis cutoff energy was set at 450 eV. Geometry optimization was terminated when the Hellman–Feynman forces acting on each atom fell below 0.01 eV Å^–1, and the self-consistency iterations concluded once the total energies converged to within 10^–4 eV. The valence electron configurations of the elements in Al-rich illite were determined to be H 1s ¹, O 2s ²2p ⁴, Al 3s ²3p ¹, Si 3s ²3p ² and K 3s ²3p ⁶4s ¹. The accuracy of the calculations for weak interactions was ensured by employing the DFT-D3 dispersion correction method (Moellmann & Grimme, 2014).

The Mulliken population/charge calculations and crystal orbital Hamilton population (COHP) bonding analyses were conducted using the LOBSTER package (Hughbanks & Hoffmann, 1983; Dronskowski & Bloechl, 1993; Maintz et al., 2016; Ertural et al., 2019). Basis sets given by Koga and Maintz that fitted to the atomic VASP GGA-PBE wavefunctions were employed during the projection (Koga et al., 2000).

Results and discussion

The system of K_xAl₂(Si_4–xAl_x)O₁₀(OH)₂ was used to determine the chemical formula of Al-rich illite. The values of x ranged from 0.60 to 0.85, which conformed to the required layer charge and lattice substitution ratio. Based on the chemical composition analysis of Al-rich illite samples (Drits et al., 2010), in the present paper x = 0.75, for the ideal chemical formula of K_0.75Al₂(Si_3.25Al_0.75)O₁₀(OH)₂, was selected to represent a type of Al-rich illite. The initial cell configuration of the Al-rich illite was derived from the illite cells constructed by Drits et al. (2010) and consisted of a trans-vacant dioctahedral 1M polytype structure. K ions were introduced in the interlayer to balance the cell charge. Subsequently, Si atoms in the Si–O tetrahedrons were substituted with Al atoms to afford the K₃Al₈(Si₁₃Al₃)O₄₀(OH)₈ chemical formula. The configurations of the three substituted tetrahedral Al atoms were analysed comprehensively through calculations as presented in Table 1. To provide a clearer and more intuitive demonstration of the configurations of the three substituted Al atoms, a selection of representative configurations was chosen, and these are presented (arranged in order of energy) in Fig. 1. Lower energy corresponds to a more stable structure. The results revealed that the local aggregation of Al–O tetrahedrons result in reduced stability of the Al-rich illite cell, which was related to the partial local balance between the interlayer charge and the charge-deficient tetrahedral sheets (Stixrude & Peacor, 2002).

Table 1. The calculated total energy of the Al-rich illite with different configurations of the three substituted tetrahedral Al atoms.

Figure 1. A selection of representative configurations of 13 Si atoms and three substituted Al atoms (shown as tetrahedra) in the Al-rich illite unit cell. (a–l) Representative configurations of Al–O tetrahedra and Si–O tetrahedra arranged in order of energy. Yellow tetrahedra = Al–O tetrahedra; pink tetrahedra = Si–O tetrahedra.

The final optimized crystal structure model of Al-rich illite (with the most stable configuration of substituted tetrahedral Al atoms) is presented in Fig. 2a. The calculated structural parameters were: 2a = 10.454 Å, b = 9.021 Å, c = 10.316 Å, α = 89.93°, β = 101.99° and γ = 89.92°, which were in good agreement with the existing experimental data (Eberl et al., 1987; Drits & McCarty, 2007), as shown in Table 2. The major bond lengths of Al-rich illite are presented in Table 3. Considering the difference in symmetries and positions, as indicated in Fig. 2b, the Al atoms were divided into two kinds: Al_a was an Al atom in an octahedral sheet; and Al_b was a substituted Al atom in a tetrahedral sheet. The O atoms were divided into five kinds: O_a was an O atom of the hydroxyl in an octahedral sheet; O_b was an inner O atom shared by a Si–O tetrahedron and an Al–O octahedron; O_c was an inner O atom shared by an Al–O tetrahedron and an Al–O octahedron; O_d was an O atom in a tetrahedral sheet connected between Si and Al_b; and O_e was an O atom in a tetrahedral sheet connected between Si atoms. The results revealed that the length of the bonds in a octahedral sheet (Al_a–O_a, Al_a–O_b and Al_a–O_c) were all longer than those of the bonds in a tetrahedral sheet (Si–O_b, Al_b–O_c, Si–O_e, Al_b–O_d and Si–O_d), which implied that the bonding interactions in an octahedral sheet were weaker than those in a tetrahedral sheet. The lengths of the bonds in a Si–O tetrahedron (Si–O_e, Si–O_b and Si–O_d) were all shorter than those of the bonds in an Al–O tetrahedron (Al_b–O_c and Al_b–O_d), which indicated that the substitution of Al atoms reduced the connection strength of a tetrahedral sheet.

Figure 2. Crystal structures of the Al-rich illite K₃Al₈(Si₁₃Al₃)O₄₀(OH)₈. (a) Unit cell of Al-rich illite. (b) Characteristic atoms and bonds in Al-rich illite (back view). White spheres = hydrogen; red spheres = oxygen; yellow spheres = aluminium; pink spheres = silicon; purple spheres = potassium.

Table 2. Calculated and experimental lattice parameters of the Al-rich illite.

^a Eberl et al. (1987).

^b Drits & McCarty (2007).

Table 3. Calculated bond lengths in the optimized structure of the Al-rich illite.

Figure 3 displays the band structure of Al-rich illite near the Fermi level. The high-symmetry Brillouin-zone points were G(0,0,0), F(0,0.5,0), Q(0,0.5,0.5) and Z(0,0,0.5). The conduction-band minimum of Al-rich illite is at the G point and the valence-band maximum is at the F point. Thus, Al-rich illite was calculated to have an indirect band gap with a gap width of 4.99 eV. This characteristic illustrated that Al-rich illite can be treated as an insulator.

Figure 3. Calculated band structure for the Al-rich illite. The red and blue lines represent the bottom of the conduction band and the top of the valence band, respectively.

To further investigate the electronic properties of Al-rich illite, the electronic total DOS (TDOS) and electronic partial DOS (PDOS) for H, O, Al, Si and K atoms were calculated, and these are presented in Fig. 4. Five types of O atom and two types of Al atom were individually plotted, taking into account their symmetries and positions. The Fermi energy was set at 0. The TDOS within the energy range of –35 to 0 eV exhibited four prominent peaks, labelled as 1–4 in Fig. 4a,a′. It is clear that peaks 1 and 3 were solely contributed by the K s and p states. Peak 2 was mainly from the O 2s state, with a partial contribution of Si and Al 3s/3p and H 1s states. By contrast, peak 4 was almost entirely contributed by the 2p state of O atoms. After integrating the band structures in Fig. 3, it became evident that the top of the valence band is primarily composed of the 2p state of O atoms, whereas the bottom of the conduction band includes the 3s/3p states of Si and Al atoms. Five different types of O atom exhibited similar PDOS curves, which are attributed to the high ionicity of the oxygen, resulting in charge transfer from adjacent H, Al and Si atoms. As shown in Fig. 4b,c,g, the overlap between the O_b 2s state and H 1s state split into two peaks due to the hybridization with Al_a 3s/3p states in the octahedral sheet. Similarly, a particularly narrow peak of the O 1s state arose in the PDOS plot of O_c (Fig. 4c), which contributed peak 2′ of the TDOS plot. In the tetrahedral sheet, as shown in Fig. 4d,e,h–k, the substituted Al_b atom presented a different hybrid mode with adjacent O atoms compared to the Si atom. It is clear that the degree of hybridization between the Si 3p state and the adjacent O 2p state was stronger than that between the Al_b 3p state and adjacent the O 2p state.

Figure 4. The calculated electronic TDOS and electronic PDOS for the H, O, Al, Si and K atoms of the Al-rich illite. (a & á) TDOS of the Al-rich illite. (b) PDOS of the H atom in the hydroxyl. (c) PDOS of the Al_a atom in the octahedron. (d) PDOS of the substituted Al_b atom in the tetrahedron. (e) PDOS of the Si atom in the tetrahedron. (f) PDOS of the interlayer K atom. (g) PDOS of the O_a atom in the hydroxyl. (h) PDOS of the inner O_b atom. (i) PDOS of the inner O_c atom. (j) PDOS of the O_d atom connected between the Si and Al_b atoms. (k) PDOS of the O_e atom connected between Si atoms.

The atomic Mulliken population/charge analysis and the COHP bonding analysis for characteristic atoms and bonds in Al-rich illite were implemented using the LOBSTER package, and these are summarized in Tables 4 & 5. The Mulliken charge populations provide a comprehensive quantification of the charge transfers occurring within the crystals. The results revealed that five types of O atom gained 0.96–1.16 e, while the adjacent K lost 1.01 e, H lost 0.42 e, Si lost 2.18 e, Al_b lost 1.73 e and Al_a lost 1.62 e. In the tetrahedral sheet, the Si atom lost more electrons than the substituted Al_b atom, which indicated a stronger charge transfer between the Si atom and adjacent O atoms. Moreover, the residual electrons in the Al 3s/3p and Si 3s/3p states revealed the covalent character of the Si–O and Al–O bonds in the tetrahedrons and octahedrons. COHP can reveal the nature of covalent interactions between bonding atoms, whereas the integrated COHP (ICOHP) values up to the Fermi-level yields are the bond contributions to the band-structure energy, which provides clues as to the bond strength. The calculated ICOHP values of the bonds Al_a–O_a, Al_a–O_b, Si–O_b, Al_b–O_c, Si–O_e, Al_b–O_d and Si–O_d were –4.17, –3.96, –7.63, –5.47, –7.63, –5.83 and –8.36 eV, respectively, indicating that the bonding interaction strength of these bonds followed the order Si–O_d > Si–O_b > Si–O_e > Al_b–O_d > Al_b–O_c > Al_a–O_a > Al_a–O_b. The results revealed that, in the tetrahedral sheet, the Si–O bonds were significantly stronger than the Al–O bonds, suggesting that the substitution of Al_b weakened the stability of the silica tetrahedra. However, the Si–O and Al–O bonds in the tetrahedral sheet were all stronger than the Al–O bond in the octahedral sheet, indicating that the tetrahedral sheet was more stable than the octahedral sheet, even in the presence of substitution.

Table 4. Atomic Mulliken population/charge analysis and COHP bonding analysis for characteristic atoms and bonds in the Al-rich illite.

Table 5. Atomic Mulliken population analysis with specific orbitals for characteristic atoms of the Al-rich illite.

To gain a greater understanding of the bonding properties and charge distributions of the atoms in the tetrahedral sheet of Al-rich illite, the 3D and 2D electronic charge density contour plots (Fig. 5) were sampled within the plane containing the Si, Al_b and O_d atoms, which were positioned at the centre of the diagram. To better observe the charge density variation between atoms, regions with an electronic charge density exceeding 1 e Å^–3 were coloured white. The results revealed that the charge density around the O_d atom was substantial, indicating the high electronegativity of the O atom. The overlap of charge density within the Si–O_d and Al_b–O_d bond regions indicated covalent bonding properties. The dense contour lines within the Si–O_d bond region implied a stronger covalent bonding interaction compared to the Al_b–O_d bond, which is consistent with the conclusions presented above. Furthermore, the sparse contour lines around the Al_b atom revealed an ionic bonding characteristic of the Al_b–O_d bond. This mixed ionic/covalent bonding property has also been discovered in other clay minerals such as kaolinite and montmorillonite.

Figure 5. The sampled (a) 3D and (b) 2D electronic charge density contour plots of the Al-rich illite.

Further COHP analyses including main orbital-pair contributions were performed to investigate the bonding interactions of Si–O_d, Al_b–O_d and Al_a–O_b, as shown in Fig. 6. A comparison of the Si–O_d bond (ICOHP = –8.36 eV) and Al_b–O_d bond (ICOHP = –5.83 eV) in the tetrahedral sheet (Fig. 6a,b) revealed that all of the interactions (3s–2s, 3s–2p, 3p–2s and 3p–2p) of the Si–O_d bond were enhanced compared to the Al_b–O_d bond. Particularly noteworthy was the 3p–2p orbital pair (ICOHP = –2.94 eV), which reached a similar characteristic strength level as the 3p–2s orbital pair (ICOHP = –2.95 eV). The results revealed a high degree of hybridization between the orbitals of the Si and O_d atoms, especially the Si 3p and O_d 2s/2p states. Some 3p/3s–2s antibonding states were found in the energy range from –10 to –3 eV for the Si–O_d bond, which somewhat attenuated the interactions of the 3p–2s and 3s–2p bonding characteristics. Furthermore, a comparison of Al_a–O_b bond (ICOHP = –3.96 eV) interaction strengths and the main orbital-pair contribution is also presented in Fig. 6c. It was observed that the Al_a–O_b bond in octahedra presented weaker bonding interactions in all orbital pairs compared to the Al_b–O_d and Si–O_d bonds in tetrahedra, which resulted in lower structural stability of the octahedral sheet compared to the tetrahedral sheet.

Figure 6. The COHP analyses including the main orbital-pair contributions for three types of bonds of the Al-rich illite: (a) the Si–O_d bond in the tetrahedral sheet; (b) the Al_b–O_d bond in the tetrahedral sheet; and (c) the Al_a–O_b bond in the octahedral sheet.

Conclusion

In the present study, the atomic structure of a typical trans-vacant 1M Al-rich illite was constructed and systematically investigated using the DFT method. The calculated structural parameters were in good agreement with the available experimental values. The calculated indirect band gap of Al-rich illite was 4.99 eV, and as a result it can be treated as an insulator. The bond-length analyses indicated that the interactions in the tetrahedral sheet were more stable than those in the octahedral sheet. The ICOHP values of the Si–O and Al–O bonds in the tetrahedral sheet were –8.36 and –5.83 eV, respectively, which indicated that the substitutions of Al atoms reduced the stability of the tetrahedral sheet. The electronic charge density implied a mixed ionic/covalent bonding property in Al-rich illite. The present findings serve as a valuable reference for use in experimental and theoretical mineralogical investigations into illite.