Mechanical and Electronic Properties of Fe(II) Doped Calcite: Ab Initio Calculations

Abstract

Calcite (CaCO₃), a widely used mineral in materials science and environmental engineering, exhibits excellent stability but has limited mechanical strength and a wide electronic band gap, restricting its broader functional applications. To address these limitations, we systematically investigated the effects of Fe(II) doping on the electronic and mechanical properties of calcite using density functional theory calculations. The results reveal that Fe atoms preferentially form a layered distribution within the lattice and significantly alter the electronic structure, notably reducing the band gap through the introduction of Fe 3d-derived states near the Fermi level. Concurrently, the incorporation of Fe strengthens the elastic constants and enhances the shear resistance, especially in directions aligned with the dopant layering. These improvements are attributed to the strong Fe-O bonding and localized lattice distortions. Furthermore, the interplay between the dopant distribution and magnetic ordering suggests that spin polarization could serve as a potential handle for property tuning. This study highlights Fe-doped calcite as a promising candidate for functional mineral-based materials and provides theoretical insights into the magnetic and structural design of carbonate systems.

1. Introduction

Calcium carbonate, one of the most abundant minerals on Earth, exists mainly in three primary polymorphs: calcite, aragonite, and vaterite [1]. Among these, calcite is the thermodynamically stable phase, while aragonite transforms into calcite at temperatures exceeding 573 K [2,3], and vaterite persists only in biogenic systems like fish otoliths [4]. Calcite dominates geological and industrial applications owing to its thermodynamic stability [5]. As a critical component of cement and concrete [6,7], the mechanical and electronic properties of calcite directly influence the durability of the material [8]. However, its intrinsic wide bandgap (~6 eV) [9] and moderate mechanical strength limit its advanced functional utilization in electronics or high-stress environments.

Recently, iron (Fe) doping has emerged as a promising strategy for enhancing the properties of various minerals. The complex d-orbital electron interactions and multivalent characteristics of Fe enable versatile modulation of the mechanical, optical, and catalytic behaviors across material systems [10,11,12]. For example, Wang et al. demonstrated that ferromagnetic ordering in Fe-TiO₂ spin catalysts enhanced ammonia electrosynthesis by optimizing the spin-polarized charge transfer and intermediate adsorption energetics [13]. These findings suggest that Fe doping could similarly unlock the latent functionality of calcite, enabling its application in spin-based devices and corrosion-resistant materials. However, existing studies on calcite doping have predominantly focused on thermodynamic stability and electronic properties, while the interplay between magnetic ordering and macroscopic mechanical characteristics, such as rigidity and fracture toughness, has been insufficiently explored [14]. This gap in knowledge presents critical challenges in fully understanding and exploiting the effects of doping in the practical design of materials. Two notable challenges remain in exploring the Fe doping effects in calcite. First, there is a significant lack of comprehensive theoretical models linking microscopic spin states to macroscopic mechanical properties, which severely limits the predictive material design. Second, current experimental methods struggle to capture real-time spin-state dynamics under realistic operational conditions, especially in extreme environments involving high pressures or intense magnetic fields, which often disrupt magnetic ordering.

Density functional theory (DFT) is a powerful tool for addressing these gaps. By accurately resolving the electronic structure, bandgap characteristics, and spin-polarized density of states of calcite, DFT provides atomic-scale insights into Fe-induced lattice distortions and orbital hybridization [11,15]. Its predictive capability for elastic constants and compatibility with in silico spin-polarized simulations make DFT indispensable for decoding spin-property relationships. This computational approach not only provides clarity on experimental observations but also facilitates the rational design of calcite-based functional materials for environmental and industrial applications. In this work, we use DFT calculations to investigate the effects of Fe (II) doping on the electronic structure, mechanical properties, and magnetic ordering of calcite.

2. Computational Details

Periodic DFT calculations were performed using the Vienna Ab Initio Simulation Package [16,17]. Geometry optimizations and static calculations for all constructed models employed the projector-augmented wave (PAW) method [18] to describe the interaction between atomic cores and valence electron densities. The Perdew–Burke–Ernzerhof (PBE) functional—within the framework of the generalized gradient approximation—was used to approximate the exchange-correlation potential, accounting for electron-electron exchange and correlation interactions. The plane-wave cutoff energy was set to 520 eV to ensure complete convergence. Structural relaxations were conducted using the conjugate gradient method to simultaneously minimize the total energy and interatomic forces. The convergence criterion for the total energy was set to 10⁻⁵ eV, and the residual force on each atom was constrained to be less than 0.02 eV/Å. The Brillouin zone was sampled using the Monkhorst–Pack scheme with a k-point mesh of 2 × 2 × 1, which was found to be sufficient for achieving reliable accuracy in total energy evaluations and geometry optimizations.

To address the limitations of conventional DFT methods in accurately capturing the strong correlation effects of Fe 3d orbitals, which can significantly impact the reliability of the results, the DFT+U approach was applied. The effective Hubbard parameter U^d _(Fe) = 5.3 eV was obtained from the Materials Project database [19,20]. This value has been widely validated in the literature for iron-containing systems, as it effectively corrects the self-interaction errors in localized 3d orbitals and restores the correct energetic ordering between the different oxidation states. Moreover, using a physically justified and consistent U value across all Fe oxidation states ensures the reliability and transferability of the computational scheme. Arbitrary adjustment of the U parameter may lead to non-physical results and undermine the comparability of the calculation because the selection of U = 5.3 eV is not only based on theoretical demonstration and previous experimental calibration.

3. Results and Discussion

3.1. Relaxation of Structure

Calcite belongs to the trigonal crystal system with an R-3c space group [21]. The primitive unit cell contains 30 atoms. The calculated lattice parameters were as follows: a = b = 5.051 Å, c = 17.057 Å, α = β = 90°, and γ = 120°. These values are in excellent agreement with the experimental results (a = b = 4.989 Å and c = 17.061 Å, as reported by Stephen Campbell and Kristin M. Poduska [22]), validating the reliability of the first-principles calculations employed in this study. This consistency underscores the robustness of the computational methods in capturing the structural properties of calcite, laying a solid foundation for subsequent analyses involving doped systems.

To simulate Fe(II) doping in calcite, the site-occupancy disorder (SOD) method was employed [23]. This approach exploits lattice symmetry to minimize the redundant configurations arising from the disordered substitution of calcium atoms with Fe(II) ions. Configurations deemed equivalent through isometric operations were considered indistinguishable, leveraging the high symmetry and periodicity of the calcite crystal structure to simplify the configuration space while preserving the physical equivalence. This method enables the efficient identification of energetically favorable doped structures.

Figure 1a presents the formation energies for all possible doping configurations. Since all Ca sites are crystallographically equivalent, the initial distance between the Fe dopants is used as a distinguishing parameter. Figure 1b,c illustrate the dopant sites in the most stable configuration and highlight the layered distribution characteristics of these dopants within the structure.

The calcium-oxygen octahedron and the carbonate triangle are the fundamental structural units of calcite. Changes in these units effectively reflect alterations in the overall structure of calcite. The structural transformations of calcite can be directly characterized by analyzing the variations in the Ca-O and C-O bond lengths and O-Ca-O and O-C-O bond angles.

As illustrated in Figure 2a, Fe(II) doping induced notable changes in the bonding characteristics within calcite. The bond length of the C-O bond exhibited minimal variation, maintaining an average length of 1.298 Å with a highly concentrated distribution, indicating that the triangular symmetry of the carbonate ion (CO₃²⁻) was maintained. This further highlights the stability of the C-O bond under the local charge distribution. The average Ca–O bond length decreased slightly from 2.371 Å in pure calcite to 2.370 Å upon Fe(II) doping. Although the average change was minimal, the bond length distribution evolved from a concentrated to a more dispersed profile, indicating that Fe(II) incorporation disrupted the local symmetry of the [CaO₆] octahedra, leading to microscopic distortions in the bonding environment of calcium and surrounding oxygen atoms. Such distortions could be attributed to local lattice stress adjustments and charge redistribution resulting from the substitution of Ca(II) by Fe(II). In contrast, the Fe-O bond exhibited an average bond length of 2.191 Å, which was considerably shorter than that of the Ca-O bond. This reduction in bond length reflects the stronger chemical bonding between Fe(II) and oxygen atoms, implying a higher covalent character for the Fe-O bond than that of the Ca-O bond. Additionally, the Fe-O bond length distribution was narrower, further supporting the notion of a more stable local structure around the Fe(II) dopant.

Overall, the structural relaxation calculations successfully identified the most energetically favorable Fe-doping configurations in calcite, providing a robust and reliable model for subsequent theoretical analyses. The results indicate that the Fe dopants exhibit a distinct layered arrangement within the calcite lattice, which significantly affects the local structural characteristics, such as the bond lengths and bond angles. This comprehensive structural characterization not only validates the accuracy of our computational approach but also lays a critical foundation for accurately interpreting the changes in electronic and mechanical properties resulting from Fe doping.

As illustrated in Figure 2b, the average O-C-O remained fixed at 120° with a concentrated distribution, reinforcing the stability of the carbonate ion. In contrast, the average O-Ca-O bond angle increased from 92.932° to 95.316° upon doping, with the distribution becoming more dispersed. This change indicates localized distortions in the [CaO₆] octahedra. Moreover, the O-Fe-O bond angle exhibited a concentrated distribution centered at 90°, highlighting the symmetry and stability of the [FeO₆] octahedra. The incorporation of Fe(II) introduced localized lattice distortions, as evidenced by the dispersed Ca–O bond lengths and the altered O-Ca-O bond angles. Similarly, the formation of highly symmetrical [FeO₆] octahedra underscores the adaptability of the calcite lattice to accommodate Fe dopants.

3.2. Electronic Structure

The macroscopic properties of materials, such as their mechanical performance, optical behavior, and reactivity, are fundamentally derived from their electronic structures. Consequently, the electronic structure of calcite is a reliable indicator of its overall properties [24]. To investigate the influence of Fe(II) doping and its magnetic ordering on the electronic structure of calcite, the density of states (DOS) and the energy band structure were calculated for pristine calcite, as well as Fe-doped calcite in both ferromagnetic (FM) and antiferromagnetic (AFM) states. Since only two Fe atoms were introduced into the supercell, the ferromagnetic (FM) and antiferromagnetic (AFM) states were regulated by setting the two Fe atoms to have parallel or antiparallel spin orientations, respectively. The results are illustrated in Figure 3, Figure 4, Figure 5 and Figure 6.

The Fermi level (E_F) represents the highest occupied energy level in electron energy distribution at absolute zero temperature. Energy bands below the Fermi level are called valence bands, whereas those above the Fermi level are called conduction bands [25]. The energy difference between the lowest conduction band level and the highest valence band level is known as the bandgap. The band gap of pure calcite is 5 eV, with an experimental value of 6.0 ± 0.35 eV [26,27]. DFT calculations typically underestimate the bandgap, especially for wide-bandgap materials [17]. As shown in Figure 3a, the calculated band gap of calcite agrees with the expected values, exhibiting a typical underestimation trend.

Upon doping with Fe(II), significant modifications are observed in both the band dispersion and DOS profiles. The band gaps in the FM and AFM states are 1.722 eV and 2.531 eV. In Fe-doped calcite, new electronic states emerge within the original forbidden gap, which is primarily attributed to the Fe 3d orbitals. These states are clearly visible in the DOS as sharp peaks near the Fermi level. Further analysis of the electronic band structure (Figure 4) reveals that Fe doping not only reduces the band gap but also induces a transition from an indirect to a direct band gap at specific points in the Brillouin zone. Band unfolding confirms that this direct band gap is driven by Fe 3d orbital contributions, highlighting its potential implications for optoelectronic applications due to improved photon absorption and emission properties.

The influence of magnetic ordering on the electronic structure was also carefully examined. Our findings indicate that the magnetic orientation substantially affects the orbital interactions and electronic level splitting near the Fermi level. In the FM state, the parallel spin alignment of Fe ions enhances the electron orbital overlap, resulting in stronger exchange splitting and narrower band gaps. Conversely, the AFM state, characterized by antiparallel spins, exhibits a weaker orbital overlap and reduced splitting, leading to a comparatively larger band gap and enhanced insulating properties. However, given the relatively low doping concentration, the differences between the FM and AFM configurations manifest primarily at localized sites and thus have a limited impact on the macroscopic electronic properties.

DOS analysis revealed the electronic state distribution and band gap reduction in Fe-doped calcite, providing an overview of its electronic structure. However, it did not explicitly capture the interactions between the atoms underlying these changes. Consequently, to gain a better understanding of the mechanisms underlying the electronic interactions in Fe-doped calcite, we employed the LOBSTER program, a tool that examines synergistic oxygen-metal-ligand interactions, to perform crystal orbital Hamilton population (COHP) analysis [28,29]. The COHP between atomic orbitals i and j is defined as follows [28]:

$${\mathrm{COHP}}_{\mathit{ij}}\left(\mathrm{E}\right)={\sum }_{n,k}{c}_{i,\mathit{nk}}^{*} H_{\mathit{ij}} c_{j,\mathit{nk}} \mathrm{\delta }\left(E-E_{\mathit{nk}}\right),$$

(1)

where cᵢ,ₙₖ and cⱼ,ₙₖ are the coefficients of atomic orbitals i and j in the Bloch state ψₙₖ, Hᵢⱼ is the Hamiltonian matrix element between these orbitals, and δ(E − Eₙₖ) is the Dirac delta function. This definition projects the Hamiltonian onto atomic pairs in an energy-resolved manner, enabling the identification of bonding (negative values), antibonding (positive values), and nonbonding (near-zero) interactions. The COHP is dimensionless and fundamentally characterizes the relative bonding/antibonding weights rather than the absolute physical quantities. The integrated COHP (ICOHP), obtained by integrating the COHP curve over the energy, provides a quantitative measure of the total bonding strength between atomic pairs.

COHP analysis of the pure calcite, FM Fe-doped, and AFM Fe-doped phases revealed that the average -COHP for Ca-O remained relatively unchanged with Fe incorporation (Figure 5a), possibly owing to the low Fe concentration. Although the introduction of Fe affected the bonding of the local Ca-O bonds, the overall effect was minimal.

As shown in Figure 5c,d, the Fe 3d orbitals primarily contribute to the antibonding interactions in the Fe-O bonds, particularly near the Fermi level. These interactions arise from the repulsion between the Fe 3d and O 2p orbitals, which slightly weakens the Fe-O bond stability. However, due to the limited electron population in the Fe 3d orbitals at low doping concentrations, this antibonding effect remains weak and highly localized, exerting minimal influence on the overall electronic structure. In contrast, strong bonding interactions between the Fe 4s and O 2s/2p orbitals occur predominantly at deeper energy levels (below −6 eV), playing a crucial role in reinforcing the Fe-O bonding. This deeper-level bonding significantly enhances the structural stability near the dopant sites, allowing even low levels of Fe incorporation to exert a notable local structural impact on the calcite lattice.

Comparing the FM and AFM configurations, the FM state exhibits a parallel spin alignment of Fe atoms, which enhances the overlap between the Fe 3d and O 2p orbitals and strengthens the Fe-O bond. In contrast, the antiparallel spin alignment in the AFM state reduces the orbital overlap, leading to increased antibonding contributions near the Fermi level and weaker Fe-O bonding. However, due to the low Fe doping concentration and limited contribution of the Fe 3d orbitals, the overall differences in the electronic structure and macroscopic properties between the FM and AFM states remain negligible. To further investigate the local impact of Fe-O on Ca-O bonding and its underlying mechanism, we conducted a layer-by-layer COHP analysis of Ca-O (Figure 6a,b). The -ICOHP value for Ca-O in the Fe-doped layers increased considerably, indicating enhanced bonding interactions. The introduction of Fe appreciably strengthened the Ca-O bonding near the doped sites.

Overall, Fe doping markedly reduces the electronic band gap of calcite, induces a direct band gap transition, and modifies local orbital interactions through magnetic ordering and orbital hybridization effects. These electronic alterations provide a solid theoretical basis for understanding the doping-induced improvements in the mechanical properties of calcite, as discussed in the subsequent section.

3.3. Elastic Property

In the elastic regime, the stress (σ) response of a solid to an external strain (ε) satisfies the generalized Hooke’s law [30], expressed as follows:

$${\sigma }_i={\sum }_{j=1}^6{c}_{ij}{\epsilon }_{ij},$$

(2)

where both strain and stress can be expressed as vectors with six independent components (1 ≤ j ≤ 6, 1 ≤ i ≤6). The coefficients C_ij form a second-order elastic stiffness tensor, represented as a 6 × 6 symmetric matrix measured in GPa. The elastic stiffness tensor C_ij can be determined from the first derivative of the stress-strain curve.

Calcite crystals belong to the trigonal crystal system, which has six independent elastic constants: C₁₁, C₁₂, C₁₃, C₁₄, C₃₃, and C₄₄. The symmetry of the trigonal system imposes additional constraints, resulting in the following relationships among the elastic constants [31]:

C₂₂ = C₁₁, C₂₃ = C₁₃, C₂₄ = −C₁₄, C₅₅ = C₄₄, C₅₆ = C₁₄, C₆₆ = (C₁₁C₁₂)/2,

(3)

As listed in

Table 1. Comparison of the calculated main elastic constants C_ij (GPa) with the experimental values.

	Exp [34]	Exp [33]	Fe-Doped [34]	Pure	Fe-Doped	Siderite [35]
C11	149.4	144	93.0	146.9	160.9	278.0
C12	57.9	53.9	39.1	53.6	71.2	95.5
C13	53.5	51.1	26.5	57.0	60.3	84.1
C33	85.2	84	74.1	87.6	83.1	144.0
C44	34.1	33.5	25.5	30.5	35.7	48.0
C66	45.8	45.1	42.2	43.4	44.8	91.3

, the elastic constants of calcite obtained in this study were consistent with the experimental results reported by Chen [32] and Hearmon [33]. It is worth noting that the calculated elastic constants were obtained under idealized conditions at 0 K, which is typical for density functional theory simulations. In contrast, the experimental measurements were conducted at room temperature. The temperature dependence of the elastic constants in calcite, as in most materials, tends to show a slight decrease with increasing temperature due to lattice thermal expansion and anharmonic vibrations. Therefore, the slight discrepancy between the theoretical and experimental values can be attributed to this temperature difference. Despite this, the agreement remained very good, demonstrating the reliability and predictive power of this computational approach. Assuming that the calculation parameters were consistent with those of calcite and considering the strong correlation effects, the elastic constants of Fe-doped calcite could be predicted.

These results differ from those reported by Wang [34], who observed a decline in mechanical properties. By referencing Zhang’s [35] calculations on siderite, a mineral with a structure similar to that of calcite but differing only in cation type, and combining previous analyses of bond lengths and angles in the structure, it can be inferred that Fe doping can introduce local stress fields into the calcite structure. This behavior is analogous to the effect of Fe ions on the siderite lattice and can enhance the mechanical properties of calcite. The discrepancy with Wang’s findings could be because of the lack of consideration of strong correlation effects in their study, which can enormously influence the electronic structure and magnetic behavior of transition metals in crystals. The inclusion of the +U correction can more accurately reflect the structural changes induced by the incorporation of Fe into calcite.

With the introduction of Fe, the C₁₁ constant increased considerably, whereas the C₃₃ constant decreased slightly, indicating enhanced resistance to deformation in the ab-plane direction, which was markedly stronger than that in the c-direction. Moreover, the resistance to deformation along the c-axis was slightly decreased. Both the C₄₄ and C₆₆ constants increased, with the C₄₄ constant exhibiting a particularly noticeable increase, suggesting that the shear resistance in the bc-plane and ac-plane increased considerably more than that in the ab-plane. Additionally, the C₁₂ and C₁₃ constants exhibited varying degrees of increase compared to those in the pure phase, indicating that the stress applied along the a-axis strengthened the coupling of deformation in the bc-plane direction. This enhanced coupling effect led to an increase in the material anisotropy, resulting in a less pronounced increase in the shear resistance within the ab-plane compared to the other directions.

The polycrystalline elastic constants were calculated using the elastic stiffness constants (C_ij) and elastic compliance constants (S_ij) based on the Voigt–Reuss–Hill approximation [36]. The Voigt approximation assumes an iso-strain condition, meaning that under macroscopic loading, all grains in the polycrystalline material experience a uniform strain [37]. The Reuss approximation assumes [38] an iso-stress condition, which means that under macroscopic loading, all grains experience uniform stress.

Hill proposed that the Voigt and Reuss methods could provide the upper and lower bounds of the elastic moduli for polycrystalline materials, respectively [36]. To obtain a more accurate estimate, Hill suggested using the arithmetic mean of the two. The relationships for the bulk modulus (B), shear modulus (G), Young’s modulus (E), and Poisson’s ratio (ν) are expressed as follows:

$$S_{ij}=C_{ij}^{-1},$$

(4)

$$A={\displaystyle \frac{C_{11}+C_{22}+C_{33}}{3}},B={\displaystyle \frac{C_{23}+C_{13}+C_{12}}{3}},C={\displaystyle \frac{C_{44}+C_{55}+C_{66}}{3}},$$

(5)

$$a={\displaystyle \frac{S_{11}+S_{22}+S_{33}}{3}},b={\displaystyle \frac{S_{23}+S_{13}+S_{12}}{3}},c={\displaystyle \frac{S_{44}+S_{55}+S_{66}}{3}},$$

(6)

$$B_V={\displaystyle \frac{A+2B}{3}},B_R={\displaystyle \frac{1}{3\mathrm{a}+6b}},B={\displaystyle \frac{1}{2}}\left(B_R+B_V\right),$$

(7)

$$G_V={\displaystyle \frac{A-B+3C}{5}},G_R={\displaystyle \frac{5}{4a-4b+3c}},G={\displaystyle \frac{1}{2}}\left(G_R+G_V\right),$$

(8)

$$E={\left({\displaystyle \frac{1}{3G}}+{\displaystyle \frac{1}{9B}}\right)}^{-1},v={\displaystyle \frac{1}{2}}\left(1-{\displaystyle \frac{3G}{3B+G}}\right)$$

(9)

Using Elastic Post [39,40] to visualize the three-dimensional elastic constants, the anisotropic effects of Fe doping on the mechanical properties of calcite were further analyzed. As illustrated in Figure 7a,e, with the introduction of Fe, the overall value of the bulk modulus of calcite increased; however, the anisotropy in its distribution remained relatively low, maintaining a nearly ellipsoidal distribution.

As illustrated in Figure 7b,f, the changes in the intensity and distribution characteristics of Young’s modulus were insignificant. This could be because of the compatibility of Fe doping with the Ca sites in calcite, which results in limited lattice distortion. Additionally, Fe doping tended to occur along the c-axis in a layered manner within the calcite structure, providing limited improvement in the tensile properties. The slight change in Young’s modulus further suggested that the enhancement of the overall mechanical properties of calcite by Fe doping was both directional and localized.

As listed in

Table 2. Calculation values of mechanical performance parameters for pure and Fe-doped calcite. Bulk modulus (B), Young’s modulus (E), shear modulus (G), and Poisson’s ratio (ν).

	Exp	Pure	Fe-Doped	Fe-Doped [34]	Siderite [35]	Unit
B	74.6 ± 2.0	77.88	82.50	48.23	129.18	GPa
E	81.0 ± 0.8	82.55	87.56	72.21	154.67	GPa
G	30.7 ± 0.2	31.19	33.09	28.87	59.47	GPa
ν	0.32	0.32	0.32	0.25	0.30	/

, the effect of Fe doping on the average shear modulus was relatively small, whereas the isotropic increases, as observed in Figure 7c,g, indicated that Fe doping could have homogenized the bond strength and directional bonding within the lattice, reducing the directional differences in the shear modulus. This homogenizing effect could potentially improve the shear resistance of the doped calcite in practical applications, providing a more stable performance under multi-directional stresses.

Another important mechanical property of materials is their hardness, which is related to their plastic deformation and fracture resistance. However, hardness is a macroscopic concept typically characterized by indentation, which is dependent on the degree of plastic deformation. Despite the inherent differences between plastic and elastic deformations, the bulk and shear moduli are still used as preliminary predictors of hardness, and this prediction is reasonably reliable.

According to the literature, the elastic shear modulus (G) is proportional to the resistance to plastic deformation, whereas the bulk modulus (B) is proportional to the fracture strength. The ratio B/G, known as Pugh’s ratio, is an indicator of ductility. Consequently, a higher Pugh ratio indicates greater ductility, whereas a lower value suggests brittleness.

The critical value of B/G that defines the transition between ductile and brittle materials is approximately 1.75 [41]. As is well known in fracture theory, during the fracture process, part of the work done is converted into plastic deformation energy, part into elastic energy, and part into surface energy for newly created surfaces. Although some elastic energy can be recovered during fracture, most of it is dissipated, and the ease of plastic deformation is closely related to the ease of fracture. Another indicator of brittleness/ductility behavior can be calculated using Poisson’s ratio (ν). For brittle covalent materials, ν is typically small (~0.1), whereas for ductile metallic materials, ν is approximately 0.33. The Poisson’s ratios of pure calcite and Fe-doped calcite are both 0.32, suggesting that the elastic constants of calcite exhibit certain metallic characteristics [42].

4. Conclusions

In this study, we employed density functional theory to systematically investigate the structural, electronic, and mechanical properties of Fe(II) doped calcite. By simulating various doping configurations using the site-occupancy disorder method, we identified energetically favorable Fe-substitution models. The optimized structures revealed a characteristic layered distribution of Fe dopants, which introduced localized structural distortions and provided a reliable basis for further analyses of the electronic and mechanical properties.

Electronic structure calculations showed that Fe(II) doping significantly narrows the band gap of calcite and induces a transition from an indirect to a direct gap. This effect originates from the introduction of Fe 3d orbitals near the Fermi level and enhanced orbital hybridization, particularly in the FM state. Although differences between the FM and AFM states were observed, they were largely localized and had a minimal impact on the macroscopic properties due to the low doping concentration. COHP analysis further revealed that the Fe-O bonds exhibit moderate antibonding interactions near the Fermi level, while Fe doping also enhances the Ca-O bonding strength in the adjacent layers. Fe(II) doping leads to a moderate increase in the lattice stiffness and anisotropic reinforcement of the elasticity of calcite, which can be attributed to enhanced local bonding interactions and spin-mediated structural adjustments.

Overall, our results provide theoretical insights into the role of Fe(II) doping in modulating the properties of calcite and highlight its potential for functional mineral design in materials science and environmental applications.