Uncovering the Phase and Surface Stability of New Aluminoferrite C₄AM (M = Sc–Zn): Ab Initio Calculations

Abstract

Securing heavy metals within cement clinker phases is a sustainable strategy for solid waste upcycling, yet the atomic‐scale mechanisms governing the stability and surface properties of these phases remain elusive. This study systematically investigates the phase stability and surface properties of transition metal‐bearing tetracalcium aluminoferrite solid solutions Ca₂AlMO₅ (C₄AM, M = Sc–Zn) using DFT + U calculations. Electronic strong correlation proves essential for correctly describing the insulating behavior and spin states of these minerals. Notably, a spin‐state transition of Fe³⁺ and Co³⁺ in the octahedral field induces lattice contraction and reverses the energetic stability between I‐type and P‐type unit cells. Thermodynamic analysis reveals that while all C₄AM phases possess negative formation energies, only Cr, Mn, Fe, Ni, and Co are absolutely stable against decomposition into their respective binary oxides. Unstable systems exemplified by Cu and Zn are destabilized by substantial antibonding orbital occupancy at the E _F. Furthermore, Mn and Cr exhibit anomalous surface anisotropy, preferring cleavage along the (110) plane over the (001) plane to release Jahn–Teller strain. These findings provide critical theoretical insights for the long‐term sequestration of heavy metals in cementitious materials.

First‐principles calculations reveal how 3d‐electron filling regulates site preference, magnetic order, oxide‐referenced bulk stability, and facet‐dependent surface stability in C4AF‐derived brownmillerite Ca2AlMO5.

1. Introduction

The rapid acceleration of global industrialization has led to the generation of vast quantities of hazardous solid wastes, including electroplating sludge, mine tailings, fly ash, and cement dust. These residues are commonly enriched in transition metals such as Zn, Cu, Cr, Ni, and Mn, which pose persistent environmental risks due to their toxicity and limited natural attenuation [1, 2]. Within the framework of sustainable development and circular economy strategies, the utilization of such wastes as alternative raw materials in cement clinker production has emerged as an effective pathway for long‐term heavy metal immobilization [3, 4, 5]. In this approach, hazardous elements are incorporated into the crystalline lattice of clinker minerals, enabling both detoxification and resource conservation while reducing the demand for virgin raw materials and associated CO₂ emissions [6, 7].

The effectiveness of this mineralogical sequestration strategy is fundamentally governed by the interactions between transition metals and individual clinker phases. Extensive experimental studies have demonstrated that the influence of transition metal ions on cement hydration and performance is highly element‐specific [8]. Certain metals, such as Zn and Cd, can be readily incorporated into clinker phases but often induce pronounced retardation of hydration reactions, particularly through suppression of calcium silicate hydrate formation [9]. In contrast, Pb exhibits limited solubility in most clinker minerals and exerts a comparatively minor influence on hydration kinetics [10]. Chromium presents a more complex behavior, as Cr³⁺ substitution may accelerate setting and enhance early strength, while the potential formation of Cr⁶⁺ remains an environmental concern. These diverse macroscopic responses indicate that the atomic‐scale accommodation mechanisms of transition metals within clinker structures are highly nontrivial [11].

Systematic investigations into the effects of various transition metal oxides have further revealed that most metal species act as hydration retardants [12], although the degree of retardation varies widely depending on ionic size, valence state, and coordination preference [13]. Such findings highlight the intrinsic limitations of conventional silicate phases, particularly alite and belite, whose relatively rigid crystal frameworks exhibit restricted configurational tolerance toward multielement substitution [14, 15]. Excessive incorporation of heterovalent or size‐mismatched cations often leads to lattice strain, destabilization of key hydration products, and deterioration of early‐age performance [16], thereby constraining the overall sequestration capacity for complex hazardous wastes [17, 18].

In contrast to the silicate phases, the ferrite phase Ca₂AlFeO₅ (C₄AF) has been increasingly recognized as a structurally versatile host for transition metals. C₄AF adopts a brownmillerite‐type structure composed of alternating layers of corner‐sharing MO₆ octahedra and ordered MO₄ tetrahedral chains, giving rise to an intrinsically anisotropic and flexible lattice [19, 20]. This layered architecture accommodates a broad range of cation substitutions through local polyhedral tilting, distortion, and reorientation, without catastrophic framework collapse [21]. Experimental observations have shown that transition metals such as Cu, Zn, Pb, and Mn preferentially partition into the ferrite phase during clinker formation [22, 23, 24], underscoring its potential role as a primary sink for hazardous elements [25, 26]. However, existing studies have predominantly focused on dilute substitution regimes, leaving the intrinsic structural and thermodynamic limits of transition metal incorporation largely unexplored.

From a theoretical perspective, the accurate description of transition‐metal‐substituted ferrite phases remains challenging due to the presence of localized 3d electrons and strong electron correlation effects. Standard density functional theory approaches often fail to capture these features reliably, necessitating the use of Hubbard‐corrected methods to properly describe electronic localization, spin states, and crystal field effects [9, 27]. Moreover, the thermodynamic stability of heavily substituted ferrite phases must be assessed within a chemically consistent framework that considers both formation energetics and decomposition pathways relevant to the high‐temperature environment of cement kilns [17]. Despite their importance, such atomistic‐level investigations remain scarce in the context of cement chemistry.

In this work, a comprehensive first‐principles investigation of fully substituted ferrite phases Ca₂AlMO₅ (C₄AM, M = Sc–Zn) is presented. By adopting a complete substitution model rather than conventional dilute doping, this study aims to elucidate the intrinsic structural response, thermodynamic stability, and electronic characteristics of brownmillerite ferrites under extreme transition metal loading. Density functional theory with Hubbard corrections is employed in combination with energetic analyses to evaluate phase stability trends across the 3d series. Through this approach, the present work seeks to establish an atomistic foundation for understanding the sequestration limits of transition metals in ferrite‐rich clinker phases, thereby providing theoretical guidance for the design of environmentally resilient cementitious materials.

2. Computational Details

2.1. Electronic Structure Calculations

Spin‐polarized DFT calculations were conducted using the Vienna Ab initio Simulation Package (VASP). The interaction between valence electrons and atomic kernels was described by the Projector Augmented Wave (PAW) method, with the exchange‐correlation functional was treated via the Generalized Gradient Approximation (GGA) as parameterized by Perdew–Burke–Ernzerhof (PBE) [28, 29]. A plane‐wave kinetic energy cutoff was set to 500 eV. The convergence criteria for total energy and Hellmann–Feynman forces on each atom were established at 10^{− 5} eV and 0.02 eV/Å, respectively.

To account for the strong electronic correlation of the 3d transition metals (M = V, Cr, Mn, Fe, Co, Ni, Cu), the GGA + U calculations were performed using the Dudarev approach with effective Hubbard parameter U _eff [30]. The U _eff assigned were 3.25, 3.7, 3.9, 5.3, 3.32, 6.2, and 7.0 eV, respectively [31, 32, 33, 34]. The initial magnetic moments for all M ions were set to 5.0 μ_B, with the final spin states determined after geometric optimization and self‐consistent convergence. For the bulk phases, Brillouin zone integration was performed using a Γ‐centered Monkhorst–Pack k‐point grid of 5 × 4 × 2. For each M element, both ferromagnetic (FM) and antiferromagnetic (AFM) spin configurations were considered.

2.2. Structural Models and Thermodynamic Evaluation

Based on the Ibm2 (I‐type) and Pcmn (P‐type) prototypic structures of C₄AF, C₄AM models were constructed by completely substituting Fe sites with transition metals. The thermodynamic stability was evaluated using the formation energy E _form relative to pure elements and the decomposition energy E _decomp relative to most stable binary oxides. All optimized lattice parameters of the reference phases were compared with available experimental values, as summarized in Table S1. The calculations followed the formulas

$$E_{\mathrm{form}}=E_{\text{total}}\left(C_4\mathrm{AM}\right)-\mathit{\sum }_i{n}_i{\mu }_i$$

$$E_{\text{decomp}}=E_{\text{total}}\left(C_4\mathrm{AM}\right)-\mathit{\sum }_j{n}_j{E}_{\text{total}}\left({\text{stable phases}}_j\right)$$

where E _total(C ₄AM) is the optimized total energy, n _i and μ _i represent the number and chemical potential of constituent elements, and E _total(stable phases _j ) denotes the energy of the stable decomposition products.

2.3. Surface Modeling

Surface properties were investigated using I‐type C₄AM slab models for the (001) and (110) planes. For the (001)‐type surfaces, two nonequivalent terminations were constructed: the (001) surface corresponding to the CaO‐FeO2 termination and the OCa‐AlO termination. A vacuum layer of 15 Å was introduced along the surface‐normal direction to avoid interactions between periodic images. The k‐point meshes were set to 2 × 3 × 1 for the (110) surface and 2 × 2 × 1 for the (001) surface. The average surface energy γ _avg was decomposed into cleavage energy ΔE _cleave and relaxation energy ΔE _relax [35]

$${\gamma }_{\mathrm{avg}}=\mathrm{\Delta }{E}_{\text{cleave}}+\mathrm{\Delta }{E}_{\text{relax}}=\frac{E_{\text{unrelax}}-n{E}_{\mathrm{bulk}}}{2A}+\frac{E_{\mathrm{slab}}-E_{\text{unrelax}}}{2A}$$

where E _slab and E _unrelax is the energy of the unrelaxed and relaxed slab, respectively. E _bulk is the energy of the corresponding bulk unit, n is the number of formula units in the slab, and A is the surface area. Dipole corrections were applied during slab calculations to minimize artificial electrostatic interactions caused by asymmetric surface models. Electronic properties were further analyzed via Bader charge population and the Crystal Orbital Hamilton Population (COHP) analyses to quantify the charge transfer and bonding characteristics. Structural visualizations were generated using VESTA.

3. Results and Discussion

3.1. Crystal Structure Evolution and Spin‐State Induced Stability Reversal

The C₄AF phase is characterized by a distinctive layered framework where the network is composed of alternating corner‐sharing tetrahedral and octahedral units. In this structural matrix, the occupancy of cation sites is highly sensitive to the ionic species. As illustrated in Figure 1A,B, the I‐type C₄AM unit cell features transition metals in the octahedral coordination while Al atoms occupy the tetrahedral sites; conversely, the P‐type cell exhibits the inverse occupancy.

FIGURE 1.

(A) Crystal structure of I‐type C₄AF and the octahedral coordination environment of M ions. (B) Crystal structure of P‐type C₄AF and the tetrahedral coordination environment of M ions. (C) Distribution of ionic radii for M ions in various oxidation states. (D) Calculated energy differences ΔE between P‐type and I‐type C₄AM configurations with and without the inclusion of strong electronic correlation effects (DFT vs. DFT + U). The total energy was taken from the lowest‐energy magnetic state among the tested FM and AFM configurations.

The site preference is fundamentally governed by the match between ionic radii and coordination environments. According to the Shannon system, the radius of high‐spin (HS) Fe³⁺ is approximately 64.5 pm in octahedral sites and 49 pm in tetrahedral sites, values that align closely with the radius of Al³⁺ (53.5 and 39 pm for sixfold and fourfold coordination, respectively). This geometric compatibility underpins the experimental observation that transition metals preferentially substitute for Fe within the cement clinker lattice.

3.1.1. Thermodynamic Stability and the Hubbard U Effect

The chemical viability of incorporating TMs into the C₄AM lattice is fundamentally dictated by the competition between different crystalline symmetries and the thermodynamic resistance against phase separation. As illustrated in Figures 1D and S1, the energy difference ΔE between I‐type and P‐type configurations serves as a primary descriptor of structural preference. Under the standard PBE‐GGA framework, which often underestimates electron localization, all investigated C₄AM phases exhibit a lower total energy in the I‐type symmetry. This suggests a baseline preference for TMs to occupy the larger, higher‐coordination octahedral sites. However, this simplified view fails to account for the complex electronic environment of 3d orbitals.

The inclusion of the Hubbard U correction proves to be a decisive factor in evaluating the true thermodynamic landscape. For the V, Cr, and Mn systems, the DFT + U treatment enhances the energetic advantage of the I‐type structure, widening the stability gap relative to the P‐type. In sharp contrast, the Fe and Co systems display a dramatic stability reversal. The P‐type lattice for Ca₂AlFeO₅ and Ca₂AlCoO₅ becomes energetically more favorable than the I‐type under AFM and FM‐U, respectively. This reversal is a direct manifestation of the electronic instability of the Co³⁺ and Fe³⁺ ion in the strong crystal field of an octahedral environment, where the energy penalty for orbital reorganization or spin‐state transition outweighs the geometric benefits of the I‐type lattice.

Beyond structural preference, the absolute thermodynamic stability must be assessed via E _form and E _decomp. According to the calculated E _form, all C₄AM phases exhibit negative values relative to their constituent elements, indicating that their synthesis is theoretically feasible (Figure 2). However, a negative E _form is a necessary but insufficient condition for long‐term sequestration. The more rigorous criterion is the E _decomp relative to the most stable binary oxides (CaO, Al₂O₃, MO _x ).

FIGURE 2.

Formation and decomposition energy pathways and magnitudes calculated relative to (A,C) stable elemental substances and (B,D) stable binary oxides. Lower formation energies correspond to enhanced phase stability, whereas elevated decomposition energies reflect superior structural resistance to decomposition.

Thermodynamic robustness against phase separation is evident in the Ti, V, Cr, and Mn systems, as indicated by their consistently negative E _decomp values. This ensures their integrity during the high‐temperature clinkering process. Conversely, the Cu and Zn systems, despite having negative E _form, exhibit positive or near‐zero E _decomp. This thermodynamic vulnerability suggests that while these heavy metals can be incorporated into the lattice, they possess a strong tendency to undergo phase separation or remain in a metastable state. This finding rationalizes the experimental observations by Kakali et al., where CuO and ZnO act as potent retardants owing to their propensity for precipitation and poor lattice incorporation.

3.1.2. Anisotropic Lattice Distortion and Volume Changes

In the C₄AM system, the incorporation of TM ions does not merely represent a stoichiometric substitution; rather, it triggers a profound mechanical strain within the host lattice dictated by the unique 3d electronic configurations of the substituent. As illustrated in Figures 3 and S2, the evolution of unit cell volumes exhibits a distinct elemental dependency. For the I‐type configuration, the cell volume generally follows a decreasing trend as the atomic number of the transition metal increases, with the notable exception of the Zn system. This contraction is primarily governed by the effective ionic radii of the M ions occupying the octahedral sites. According to Shannon's theory, the radius of HS Fe³⁺ serves as the structural benchmark. As the 3d orbitals are progressively filled, the interplay between electron–electron repulsion and nuclear attraction results in a nonlinear evolution of lattice parameters.

FIGURE 3.

Lattice parameters of C₄AM with the lowest‐energy magnetic state. (A–C) Lattice parameters for I‐type and (D–F) P‐type C₄AM, calculated with and without the inclusion of strong electronic correlation effects.

The anisotropy of this lattice distortion is most prominently manifested in the evolution of the c‐axis. Within the layered brownmillerite framework, the c‐axis length is intrinsically coupled to the apical M—O_C bond lengths of the MO₆ octahedra. Notably, this structural dependency manifests as pronounced anomalies in the c‐axis parameters for the Mn and Ni systems, as revealed by DFT + U calculations. Specifically, the d ⁴ system in Mn³⁺ undergoes a pronounced axial expansion. This phenomenon is a classic manifestation of the Jahn–Teller effect: to lift the orbital degeneracy and minimize the total energy, the MnO₆ octahedron undergoes a tetragonal elongation. This causes the dz² orbital to stabilize at a lower energy level, which in turn pushes the bridging oxygen atoms O_C further apart along the c‐direction. Such orbital‐driven symmetry breaking is a primary source of internal stress in Mn‐doped ferrite phases, potentially influencing the long‐term structural integrity of the clinker.

Conversely, the Co system in the I‐type structure exhibits a dramatic c‐axis compression. This contraction serves as a macroscopic fingerprint of the HS to low‐spin (LS) transition of the Co³⁺ ion. When Co is subjected to the strong crystal field of the octahedral site, its 3d electrons redistribute from the higher‐energy e _g orbitals to the lower‐energy t _2g orbitals. This transition leads to a sharp reduction in the effective ionic radius, causing the octahedral cage to collapse inward. The resulting lattice shrinkage induces severe axial strain, which provides the structural explanation for the thermodynamic instability and the stability reversal of the I‐type Co phase. In the P‐type configuration, where M ions occupy tetrahedral sites, the impact on the overall cell volume is attenuated although localized distortions remain substantial. The d‐orbital arrangement within the MO₄ tetrahedra transmits strain to the neighboring AlO₆ octahedra via shared O_C atoms.

3.1.3. Local Coordination and RDF Analysis

To gain a deeper atomistic understanding of the structural distortions induced by transition metal substitution, a systematic analysis of the Radial Distribution Function (RDF) under FM magnetic states was conducted. As shown in Figures 4 and S3, the RDF profiles provide a direct visualization of the local coordination environment and the degree of structural disorder within the C₄AM lattice. The bond length distributions of M—O, Ca—O, and Al—O pairs serve as sensitive indicators of how electronic correlations, such as the Jahn–Teller effect and spin‐state transitions, propagate from the 3d orbital level to the long‐range crystalline framework.

FIGURE 4.

(A–C) Radial distribution functions (RDF) of Ca—O, Al—O, and M—O bonds in I‐type C₄AM under strong electronic correlation effects and FM magnetic states; (D) Structural configuration showing the connectivity between AlO₄ tetrahedra and MO₆ octahedra.

The M—O coordination shells exhibit the most pronounced variation across the transition metal series. In the prototypic I‐type Fe and Ti systems, the M—O RDF displays a characteristic doublet peak near 2.0 Å, corresponding to the equatorial M—O_M and apical M—O_C bonds within the MO₆ octahedra. However, this symmetrical distribution is severely disrupted in the Co and Mn systems. Specifically, for the I‐type Ca₂AlCoO₅ phase, the Co—O first‐shell RDF splits into four distinct sub‐peaks. This multipeak feature is a definitive geometric signature of the complex structural rearrangement accompanying the HS‐to‐LS transition. The collapse of the octahedral cage along the c‐axis, driven by the occupancy of t _2g orbitals, forces the oxygen ligands into an asymmetric configuration to minimize steric repulsion, thereby resulting in a highly distorted coordination environment that contributes to the thermodynamic instability of the I‐type Co phase.

The Ca—O and Al—O RDF profiles further elucidate the structural integrity of the interlayer and intralayer networks (Figures S4 and S5). Across the series, the Al—O tetrahedral bonds remain relatively rigid, with sharp, well‐defined peaks, suggesting that the AlO₄ network acts as a stable structural scaffold that resists appreciable deformation. In contrast, the Ca—O distribution is more sensitive to the identity of the M cation. The sharpest Ca—O peaks are observed in the I‐type Ti and P‐type Mn systems, indicating a high degree of structural order in the calcium‐oxygen sub‐lattices. Conversely, for the Cr system without the U correction, the Ca—O peak intensity is markedly diminished, implying that the absence of electronic localization leads to an artificial increase in lattice disorder and fluctuating electrostatic forces within the Ca layers.

Specifically, the Jahn–Teller active Mn³⁺ system exhibits a distinct RDF signature, where the M—O peak undergoes pronounced broadening with a tail extending toward longer bond lengths. This corresponds to the tetragonal elongation of the MnO₆ octahedra, where the apical Mn—O_C bonds are stretched to stabilize the dz² electrons. This local elongation is not isolated; it induces a compensatory shift in the Ca—O RDF, as the Ca ions must adjust their positions to accommodate the expanded MnO₆ units.

Quantifying these local distortions through RDF integration reveals that the coordination shell overlap is highest in Cu and Zn systems. The increased occupancy of antibonding orbitals weakens the primary M—O bonds, leading to a more fluid local environment where the distinction between the first and second coordination shells becomes blurred. This localized melting of structural order explains the experimental difficulty in achieving high‐purity crystalline phases for Cu and Zn substituted ferrites. In conclusion, the RDF analysis confirms that the 3d electronic state of the substituent acts as a structural template, where localized orbital physics dictates the symmetry, bond length distribution, and ultimate phase stability of the C₄AM mineral family.

3.2. Electronic Structure

The macroscopic stability and structural distortions observed in the C₄AM series are fundamentally rooted in the electronic configurations of the transition metal 3d orbitals. The DFT + U framework enables the accurate resolution of localized electronic states that standard PBE functionals fail to capture.

3.2.1. Magnetic Moments and Spin‐State Analysis

The magnetic moment serves as the most direct physical descriptor for characterizing the electronic configuration, oxidation state, and spin state of transition metal ions. In the C₄AM system, the degree of localization of the transition metal 3d orbitals fundamentally dictates the magnetic properties and thermodynamic stability of the mineral phase. By comparing the calculated magnetic moments under the standard PBE and the DFT + U frameworks as summarized in Table S2, the decisive role of strong electronic correlation in describing the electronic states of these systems becomes strikingly apparent.

In standard PBE calculations, the GGA functional suffers from an inherent self‐interaction error, which leads to an artificial over‐delocalization of the 3d electrons. This deviation is particularly pronounced in the V, Fe, Co, and Ni systems, where the calculated magnetic moments are typically nonintegers, and the systems erroneously exhibit metallic behavior. For instance, at the PBE level and FM magnetic state, the average magnetic moment of the Fe atom is only 3.66 μ_B, which is substantially lower than the theoretical expectation for a trivalent iron ion. However, upon the introduction of the Hubbard U correction, the magnetic moment of Fe is corrected to 5.00 μ_B. This result aligns perfectly with the characteristic HS d ⁵ configuration of the Fe³⁺ ion, demonstrating the superior accuracy of the DFT + U method in restoring electron localization and the correct spatial distribution of spin density.

For other elements in the C₄AM series, DFT + U similarly provides a more physically realistic description of the spin states. In the tetrahedral environment of the P‐type structure, where the crystal field splitting energy is relatively small, the M ions generally maintain a high‐spin state. Calculations show that the P‐type Co system possesses a magnetic moment of 4.00 μ_B, corresponding to the high‐spin Co³⁺ (d ⁶) configuration. However, a striking magnetic anomaly occurs in the octahedral environment of the I‐type structure. The magnetic moment of I‐type Co plummets from the PBE‐predicted value to 1.20 μ_B. This quantitative shift provides conclusive electronic evidence that Co³⁺, under the influence of the strong octahedral crystal field, undergoes a transition from a high‐spin state to a LS state. Due to the full or partial occupancy of the t _2g orbitals and the resulting electron pairing, the net magnetic moment decreases. This forced spin‐state flip not only alters the chemical bonding energy but also triggers the aforementioned macroscopic lattice collapse along the c‐axis.

More fundamentally, the magnetic properties of the Mn system provide key insights into the high‐spin state stability and its correlation with the Jahn–Teller effect. The calculated magnetic moment for Mn is approximately 4.0 μ_B, which is consistent with a d ⁴ configuration. This magnetic distribution supports the half‐metallic nature of the Mn system under strong correlation effects. The variations in spin polarization reflect the competition between crystal field splitting and M—O hybridization within different coordination polyhedra. In surface models, despite the presence of coordination defects, Co atoms continue to exhibit a low‐spin state. This suggests that the energy released through surface relaxation and coordination loss is insufficient to reverse the electronic occupancy priority driven by strong correlation.

3.2.2. Density of States (DOS) and Bandgap Engineering

The transition from metallic to insulating or semiconducting behavior represents a primary consequence of the Hubbard U correction within the C₄AM series. As shown in the projected density of states (PDOS) in Figures 5 and S6–S9, the electronic structure of the 3d transition metals is characterized by a complex interplay between M‐3d and O‐2p orbitals. Under the standard PBE‐GGA framework, several phases, including those containing V, Fe, Co, and Ni, are incorrectly predicted to be metallic, arising from the artificial delocalization of d‐electrons. However, the introduction of the DFT + U term localizes these electrons, effectively opening or widening the energy gaps at the Fermi level (E _F).

FIGURE 5.

Atom‐resolved PDOS for M—O bonds in I‐type C₄AM under strong electronic correlation effects and the lowest‐energy magnetic state. The M‐3d contributions are shown as colorful filled regions, while the O‐2p contributions are shown as gray filled regions. The Fermi level is shifted to 0 eV. Positive and negative values denote spin‐up and spin‐down PDOS, respectively.

For the V, Cr, and Fe substituted systems, the DFT + U treatment reveals a robust insulating character. In the Fe‐based system (C₄AF), the U correction of 4.0 eV pushes the occupied d‐states deep into the valence band and the unoccupied states into the conduction band, resulting in a clear bandgap that aligns with experimental observations of ferrite phases. A similar gap‐opening mechanism is observed for the Cr system, where the U term mitigates the self‐interaction error and stabilizes the Cr‐3d states. This bandgap engineering is critical for the thermodynamic persistence of these phases, as the presence of a finite gap minimizes the total electronic energy and enhances the chemical stability of the M—O polyhedral.

A particularly intriguing electronic state is observed in the Mn‐substituted system, which exhibits half‐metallic behavior under the DFT + U framework. While the spin‐down channel displays a wide insulating gap of 2.83 eV, the spin‐up channel remains metallic, with the DOS crossing the E _F. This spin‐polarized conductivity is a direct result of the specific d ⁴ configuration of Mn³⁺ in the octahedral field, where the Jahn–Teller effect further splits the e _g orbitals. The half‐metallicity of Ca₂AlMnO₅ implies a high degree of spin‐polarization at the mineral surface, which may have profound implications for its catalytic activity and its interaction with aqueous species during early‐age hydration.

In contrast, the Co and Ni systems maintain a metallic character even after the application of Hubbard U corrections in the I‐type structure. For the I‐type Co system, the DOS at E _F is predominantly contributed by the d _xy orbitals. This persistent metallicity, coupled with the previously discussed low‐spin transition, indicates that the I‐type Co lattice is in a state of high electronic tension. The high DOS at the E _F for Co and Ni suggests that these systems are electronically less stable compared to their Fe or Cr counterparts, as the lack of a bandgap allows for greater electron mobility.

Notably, the PDOS profiles further elucidate the orbital‐resolved M—O hybridization strength, confirming the enhanced covalency in late transition‐metal systems. Across the series from Ti to Cu, a gradual downward shift of the M‐3d states toward the O‐2p dominated valence band is observed. This shift represents an increase in the covalency of the M—O bonds, as the energy alignment between the metal and oxygen orbitals becomes more favorable. In the Cu and Zn systems, the 3d orbitals are almost entirely filled and localized at the bottom of the valence band, yet they exert a strong repulsion on the neighboring O‐2p electrons.

3.2.3. Bonding Nature: COHP and Bader Charge Analysis

To quantify the chemical bonding strength and the degree of ionicity versus covalency in the C₄AM lattice, COHP and Bader charge analyses were conducted. While the DOS provides a map of electronic levels, COHP allows for the partition of these states into bonding and antibonding contributions, offering a rigorous energetic perspective on structural stability [36].

The M—O bond lengths in Ca₂AlMO₅ split into long, medium, and short bonds, indicating a distorted local coordination environment around the transition‐metal cation (Figure 6A). The nonmonotonic variations of these bond lengths and the corresponding distortion index across the Sc–Zn series suggest that the local M—O geometry is governed not only by ionic size, but also by d‐electron filling and M—O bonding characteristics. For example, Cr shows a relatively low distortion, indicating a more uniform M—O coordination environment, whereas Mn, Co, and Zn exhibit larger distortions, reflecting stronger local structural accommodation within the brownmillerite framework. To further evaluate structural compatibility, the M—O bond lengths in Ca₂AlMO₅ were compared with those in the most stable oxides of each transition‐metal element. The long M—O bonds show larger positive mismatch values and stronger fluctuations than the medium and short bonds, indicating that the structural mismatch between the Ca₂AlMO₅ framework and the oxide reference environments is mainly accommodated by elongation of the long bonds. In contrast, the medium and short bonds remain closer to the oxide‐reference values, suggesting stronger local bonding constraints. The −ICOHP analysis further shows that short M—O bonds have the strongest bonding contribution, followed by medium and long bonds, while the overall −ICOHP values generally decrease from early to late 3d elements (Figure 6C). Consistently, Bader charge analysis reveals a gradual decrease in the net charge of the M cations, indicating reduced electron donation and a weakened ionic component of M—O bonding with increasing d‐electron filling. Overall, these results show that the stability of Ca₂AlMO₅ is closely associated with the combined evolution of local structural distortion, M—O bond strength, and charge transfer across the 3d series.

FIGURE 6.

Evolution of local geometry, bonding strength, and charge transfer of M‐centered O₆ octahedra in Ca₂AlMO₅ with the lowest‐energy magnetic orders. (A) Average M—O bond lengths classified as long, medium, and short bonds. (B) Distortion index of the M—O₆ octahedron. (C) Average −ICOHP values of long, medium, and short M—O bonds. (D) Bader charges of M and O atoms across the Sc–Zn series. The left and right y‐axes correspond to M and O, respectively.

As illustrated in Figure S10, the COHP profiles for the M—O bonds reveal a systematic evolution of bonding character across the 3d series. The −ICOHP values, which serve as a proxy for bond strength, generally exhibit a decreasing trend as the d‐electron count increases from Ti to Zn. A critical observation is the position of E _F relative to the bonding and antibonding regions. For the thermodynamically stable V, Cr, and Fe systems, the E _F is situated within a near‐zero COHP region, indicating that all bonding states are fully occupied while antibonding states remain vacant. In sharp contrast, for the Ti, Mn, Cu, and Zn systems, the E _F resides within antibonding regions. The occupancy of these antibonding orbitals destabilizes the M—O framework, forcing the lattice to undergo the anisotropic distortions and symmetry breaking to minimize the energy penalty associated with these unfavorable electronic states.

Bader charge population analysis (Figure S11) provides further insight into the charge transfer and the mixed ionic‐covalent nature of the bonds [37]. As the transition metal series progresses from Ti to Cu, there is a consistent decrease in the net positive charge of the M ions. This trend reflects a gradual increase in M—O covalency, as the d‐orbitals descend in energy and hybridize more effectively with the O‐2p ligands. A localized anomaly is observed for the Co ion, which exhibits a sharp jump in its Bader charge value. This discontinuity is the electronic hallmark of the spin‐state transition from high‐spin to low‐spin. The redistribution of electrons into the t _2g orbitals alters the effective shielding of the nucleus, thereby modifying the volume of the Bader basins.

The correlation between −ICOHP and the calculated E _form underscores the predictive power of electronic descriptors. For instance, the Cu and Zn systems exhibit the lowest −ICOHP values and the highest occupancy of antibonding states, which directly correlates with their poor thermodynamic stability and their experimental roles as hydration retardants. The weak Cu—O and Zn—O bonds are easily disrupted, potentially leading to the leaching of these heavy metals or the formation of amorphous phases that inhibit the growth of C–S–H.

3.3. Surface Properties: Stability and Cleavage Anisotropy

The surface characteristics of C₄AM phases are critical for understanding the early‐age hydration kinetics and the leaching resistance of sequestered heavy metals. The interaction between the structural symmetry of the bulk and the coordination environment at the mineral‐water interface dictates the preferred cleavage planes.

3.3.1. Surface Energetics and Cleavage Mechanisms

Figure 7 shows the optimized surface configurations of I‐type C₄AM on the (110) and (001) planes. As summarized in Table S3 and Figures S12 and S13, the majority of C₄AM systems satisfy the thermodynamic condition γ ₍₀₀₁₎ > γ ₍₁₁₀₎ , indicating a clear preference for cleavage along the (110) plane. In the I‐type lattice, the (001) cleavage involves breaking the M—O_C bridging bonds and Ca—O bonds parallel to the interlayer interface. However, the Ti system exhibit a clear inversion of surface stability, as γ ₍₁₁₀₎ surpasses γ ₍₀₀₁₎ in preference. For the Ti‐substituted system, the (001) surface energy reaches a maximum of 1.18 J/m², driven by an exceptionally low ΔE _cleave. This quantitative evidence confirms that the Ti—O_C bridging and Ca—O interactions form the strongest interlayer coupling among all studied transition metals, effectively locking the layered structure and resisting cleavage along the basal plane.

FIGURE 7.

Surface configuration of the (A) (110) plane and (B) (001) plane in I‐type C₄AM under strong electronic correlation effects.

The Mn system presents a unique case where the γ ₍₁₁₀₎ value is lower than Cr and Fe systems. This is attributed to the Jahn–Teller effect, which induces a significant tetragonal distortion in the MnO₆ octahedra. In the (001) orientation, the atomic relaxation is severely constrained by the rigid vertical alignment of the Mn—O_C bonds. In contrast, the (110) plane provides a lower‐symmetry environment that allows for more effective strain release during the cleavage process. Consequently, the (110) plane becomes the preferred cleavage surface for Ca₂AlMnO₅, as it better accommodates the structural distortions inherent to the Mn³⁺ electronic state.

3.3.2. Anisotropy of Electronic Charge Distribution

The property of C₄AM mineral surfaces is fundamentally governed by the localized charge density and the electrostatic potential at the outermost atomic layers. While surface energy defines thermodynamic stability, the spatial distribution of valence electrons dictates the kinetic pathways for water adsorption and ion exchange. Bader charge analysis (Figure 8) reveals a profound anisotropy in the electronic environment between the (001) and (110) surfaces, providing a microscopic basis for the varied hydration behaviors observed in heavy‐metal‐doped clinkers.

FIGURE 8.

Bader charges of surface‐layer (A) Ca and (B) O atoms at (110) plane, and (C) Ca and (D) O atoms at (001) plane.

A consistent trend observed across the entire 3d transition metal series is that the oxygen atoms on the (001) surface possess significantly higher negative charges compared to those on the (110) surface. This enhanced ionicity on the (001) plane is a direct consequence of the unsaturated coordination resulting from the cleavage of apical M—O_C bonds. To compensate for the loss of neighboring cations, these surface oxygen atoms attract more electron density from the underlying Ca and Al/M layers. This creates a more intense localized electrostatic field on the (001) facet, which acts as a strong driving force for the adsorption of polar water molecules. Consequently, the (001) surface is expected to be the primary site for initial hydroxylation, despite its generally lower surface energy compared to the (110) plane.

The charge of the calcium ions also exhibits marked anisotropy. For transition metals with d‐electron counts ranging from 1 to 5 (Ti to Mn), the Ca ions on the (110) surface exhibit higher positive Bader charges than those on the (001) surface. This increased ionicity implies that the Ca atoms on the (110) plane are more exposed and less shielded by the M—O framework. This phenomenon is particularly critical for the Mn‐substituted system, where the (110) plane is the preferred cleavage surface. The combination of high Ca ionicity and the Jahn–Teller‐driven distortion of the MnO₆ units suggests that the (110) surface of Ca₂AlMnO₅ is highly susceptible to leaching, as the Ca and Mn ions are less constrained by the covalent network than they are in the Fe‐based bulk.

Specifically, the charge redistribution accompanying the transition metal substitution modulates the active site density. In the Co, Ni, and Cu systems, the decrease in the net positive charge of the M ions leads to a more balanced sharing of electrons within the MO₄ or MO₆ units. However, on the (001) surface of the Co system, the dramatic relaxation releases structural stress, causing a localized charge jump that deviates from the linear trend seen in the bulk. This indicates that the property of the Co‐doped phase is not merely a function of its chemistry but is highly sensitive to the surface‐induced electronic phase transition into a low‐spin state. The high negative charge on the surface oxygens in the Co system suggests that while the bulk might be metastable, the surface remains highly reactive, potentially explaining the rapid initial interaction with hydration fluids.

4. Conclusion

In this work, the structural, electronic, and surface properties of 3d transition‐metal (TM) substituted C₄AF phases were systematically investigated using DFT + U calculations. By resolving the strong electronic correlation of 3d orbitals, a comprehensive theoretical framework has been established for the sequestration of heavy metals in cement clinker minerals. The key findings are summarized as follows:

• 1.Spin‐state induced stability reversal: We discovered that for most C₄AM phases, the I‐type structure characterized by octahedral M occupancy is energetically favored. However, for Ca₂AlCoO₅, a stability reversal occurs where the P‐type phase, featuring tetrahedral M occupancy, becomes more stable. This is driven by the Co³⁺ ion's transition to a low‐spin state in the octahedral field, which induces massive lattice strain and a dramatic c‐axis compression.
• 2.The Hubbard interaction effect: The Hubbard U correction is essential for accurately describing the insulating nature of these ferrite phases. While V, Cr, and Fe systems exhibit robust bandgaps, the Mn‐substituted system displays unique half‐metallic behavior. The persistence of metallic states in Co and Ni systems, despite U corrections, highlights their inherent electronic instability compared to the Fe‐based host.
• 3.Chemical bonding and antibonding occupancy: Combined COHP and Bader charge analyses reveal that thermodynamic stability is governed by the occupancy of antibonding states at the E _F. The filling of antibonding states induces electronic tension in systems such as Ti, Mn, Cu, and Zn, underpinning their propensity for phase separation and their roles as hydration retardants.
• 4.Anisotropy of surface energetics: A marked anomaly emerges in Cr and Mn systems, where the (110) plane replaces the (001) plane as the preferred cleavage surface. This is attributed to the strong interlayer coupling in the Cr system and the need for strain release from Jahn–Teller distortions in the Mn system.
• 5.Charge distribution at surfaces: Bader charge mapping reveals that the (001) surface acts as an ionic hotspot with highly negative oxygen sites, promoting water adsorption. In contrast, the (110) surface—particularly in Mn‐doped phases—exhibits enhanced cation ionicity, potentially increasing the risk of heavy metal leaching.

In summary, the successful sequestration of heavy metals in the ferrite phase of cement is not merely a geometric process but is profoundly dictated by orbital‐resolved physics. The bulk‐surface stability trade‐off is controlled by the spin‐state configurations and the occupancy of antibonding orbitals. These insights provide a robust theoretical basis for designing eco‐friendly cements and for predicting the long‐term environmental stability of clinkers containing hazardous transition metals.

Funding

This work was supported by the National Natural Science Foundation of China (U22A20122) and the Basic Research Program of Shenzhen (JCYJ20240813103559008).

Conflicts of Interest

The authors declare no conflicts of interest.

Supporting information

Supplementary Material

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.