Study on the Stability of Fe/Al₂O₃ Interface in Metal-Based Cermets Using Thermodynamic Modeling

Abstract

Iron-based cermet has the advantages of high-temperature resistance, low price, good performance, and so on. At present, most of the studies on cermets are focused on the measurement of macroscopic properties and optical microscopic characterization, while there are few microscopic studies on the interface structure. In this paper, based on density functional theory (DFT), the stability of the Fe/Al₂O₃ interface is studied, and the stability difference and interface formation mechanism of different end combinations are investigated. By calculating the surface energy, adhesion work, interface energy, density of states, charge density, differential charge density, and so on, it was concluded that the stability of the O-terminal interface was greater than that of the Al interface. It has a certain guiding role in the preparation of Fe/Al₂O₃ cermet materials.

1. Introduction

Iron-based cermet is a heterogeneous composite composed of metal iron as a matrix, adding one or more ceramic phases. It not only has certain thermal conductivity, electrical conductivity, and toughness but also has high hardness and wear resistance as well as good corrosion resistance and thermal stability [1]. Because of their excellent performance and high performance-to-price ratio, iron-based cermets have become widely used as high-temperature-resistant components in conductive environments, mechanical sealing rings, and sealing parts of agricultural submersible pumps. At the same time, iron has a high melting point; its strength, hardness, plasticity, heat resistance, and oxidation resistance can be adjusted by alloying, and iron-based friction materials have good economy and show better friction properties under high temperature and high load. Their high mechanical strength means they can bear large loads, so iron-based cermet friction materials are widely used in aviation, automobile, and construction machinery as well as other heavy-duty or overload braking or clutch equipment [2].

The research on the Fe/Al₂O₃ interface in the alloy system has become a research hotspot. As a typical heterogeneous structure [3], there are great differences in physical and chemical properties between metals and oxides, such as the crystal structure, electronic state, thermal expansion coefficient, and so on. It is difficult to form a common lattice between them. The binding mechanism at the interface is very complex, which is the result of many factors, such as electron orbital hybridization, charge transfer, chemical bond polarization, dispersion, and so on. Due to the difficulties in sample preparation, testing, and characterization, some important structural features are difficult to obtain using existing experimental methods. In recent years, computer simulation has also begun to emerge. However, the finite element simulation is not suitable for the microscopic model, and the strengthening mechanism cannot be studied in essence. It can only simulate the mechanical properties, temperature, speed, and other parameters of large parts in the process of forming or deformation. First-principles calculation, based on first-principles theory [4], is a technique used to study the electrical structure of multi-electronic systems in quantum mechanics, which can avoid the difficulties encountered in experiments. The interface is constructed by using the structural characteristics of each atom in the system, and the bonding of the interface is analyzed according to the principle of nuclear–electron interaction and its basic law of motion so as to explain the interface phenomenon. The difficulties encountered in interface testing and characterization are avoided [5]. In recent years, computer simulation software has been developed rapidly, and it has become possible to use it to study a variety of properties of cermets. Therefore, the computer simulation of composites has a very wide application prospect.

The interface of the composite is a key factor affecting the mechanical properties of the material, which directly affects the interaction between the matrix and the reinforced phase. At present, great progress has been made in the theoretical research of the solid–solid interface.

Zhang et al. [6] theoretically calculated the separation work of AlN (001)/Ti (001) and AlN (003)/Cr (110). It was found that the separation work of AlN-001 (001) was significantly higher than that of Cr (001) compared with the experimental data, which is basically consistent with the experimental results. The first principle can effectively solve the problem of adhesion between ceramic interfaces. Xiao [7] studied the electronic structure of the TiC (111)/Mg (0001) interface under four different bonding modes using the first-principles calculation. Through the comparison of adhesion work, it was found that the interface structure of the C terminal was more stable, and the structure of the heart interface was the most stable. Through the first-principles calculation method, we can deeply understand the interface bonding micromechanism of the TiC/Mg interface to understand the influence of the interface on the properties of composites. Zhang et al. [8] studied the structure and interaction between Al₂O₃/Al and Al₂O₃/Ag interfaces and the structure of the interfaces via first principles. It was found that in the interface mode of alumina, when the oxygen content was high, the interface stability was better, and the interface tension was larger. By using the first principle, the predicted bond energy sequence of metal, ceramic, and the metal/ceramic interface can be consistent with the results of monotone fracture, fatigue fracture, and drop experiments. Pilania et al. [9] studied the mixed-interface model of Al/α-Al₂O₃. In the coherent interface, the non-stoichiometric interfaces of Al and O at different atomic ends of the interface were studied, and their relative stability was determined. At the same time, the evolution process of the ceramic blade interface under a loading condition was studied using the molecular simulation method. This work was expected to provide new information about the formation of dislocation modes at the interface to adapt to mismatch strain and the factors that control the formation of these modes as well as understand and predict the macro-mechanical behavior of Al/α-Al₂O₃ composite structures. Shen Yufang et al. [10] performed an in-depth study on the interfacial-binding energy characteristics of cermets through the first-principles method, explored the interfacial structure, electronic state, and interfacial stability of cermets, and revealed the microscopic mechanism related to the interfacial properties.

In this study, based on density functional theory, the energy of a metal oxide system is calculated using first-principles and interface geometry theories, and the atomic and electronic structure of the interface as well as interface stability and adsorption strength are investigated. The properties of the Fe (111)/Al₂O₃ (0001) interface and Fe/Al₂O₃ structure stability are studied systematically. Different end faces were used to simulate the surface formation process, and the outermost O end, monolayer Al end, and double-layer Al end of the Al₂O₃ (0001) surface were tested and calculated. Al₂O₃ with different end faces was selected as the substrate to adsorb the face-centered cube (fcc)-Fe (111) crystal face in order to find the lowest point of energy and the most stable structure to achieve the best catalytic effect, and the microadhesion mechanism of the interface was studied by calculating the adsorption energy, density of states, and differential charge density.

2. Calculation Method and Model

2.1. Calculation Method

This study employs the CASTEP module within the MS software for computational purposes [11], grounded in density functional theory (DFT). The Kohn–Sham wave functions are computed using plane wave (PW) basis vector expansion. The interaction between the ion nucleus and the valence electrons is described using ultra-soft pseudopotentials (USPPs) in reciprocal space. Geometric optimization is performed utilizing the Broyden–Fletcher–Goldfarb–Shannon (BFGS) method. The exchange–correlation energy function is represented by the Perdew–Burke–Ernzerhof (PBE) form within the generalized gradient approximation (GGA). Prior to the simulation, the structures of the fcc-Fe and α-Al₂O₃ blocks are individually optimized. Following optimization, the chosen parameters must be evaluated. The control variable method is employed to determine the plane wave truncation energy and the k-point grid within the Brillouin zone. To maintain computational efficiency, each parameter is varied individually to assess its impact on the accuracy of the results.

2.2. Model Building

Generally, a stable heterogeneous interface system is characterized by crystal planes exhibiting the lowest surface energy. According to the literature [12], γ-Fe (111) and α-Al₂O₃ (0001) are among the surface structures with the lowest surface energy within the low-index planes. Consequently, the α-Al₂O₃ (0001)/γ-Fe (111) interface system is identified as the most stable among all possible structures. To ensure the rationality of the interface structure, four critical factors must be considered during the establishment of the Al₂O₃ (0001)/Fe (111) interface: lattice mismatch rate, surface termination atomic type, number of atomic layers, and stacking order. The detailed implementation process is illustrated in Figure 1.

(I)

Lattice mismatch rate

Typically, there are discrepancies in the length and angle of the boundary vectors within the surface lattice parameters of heterogeneous materials, resulting in lattice mismatch at the interface [12]. In general, lattice mismatch can be mitigated or resolved by expanding or reconstructing the crystal unit cell while preserving the original crystal structure. The docking mode of metal and ceramic surfaces can be determined by calculating the lattice mismatch (δ). The formula is shown in (1) [12]:

$$\delta ={\displaystyle \frac{a_1-a_2}{a_1}}\times 100\%$$

(1)

In the formula, $a_1$ denotes the lattice constant of the metal matrix, while $a_2$ denotes the lattice constant of the ceramic reinforcement phase.

When $\delta$ < 5%, it can be concluded that the surfaces of the two materials will align to form a coherent interface, and the mismatch stress induced by this alignment can be considered negligible.

As illustrated in Figure 1, the lattice parameters for the Al₂O₃ (0001) surface are $u$ = $v$ = 4.846 Å and $\alpha$ = 120°, while for the two-fold enlarged Fe (111) surface, they are $u$ = $v$ = 4.861 and $\alpha$ = 120°, respectively. Due to the differences in lattice vectors affecting the area, the lattice mismatch calculation, as given in Formula (1), reveals that the mismatch rate for the Al₂O₃ (0001)/Fe (111) interface is 0.3%. This value indicates a minimal crystal plane mismatch that can be considered negligible.

(II)

Surface atomic terminal category

The terminal category of surface atoms plays a crucial role in determining the surface chemical properties. Iron (Fe) is characterized by a non-polar surface, consisting solely of Fe atoms. In contrast, Al₂O₃ (0001) features a polar surface with three distinct types of atoms in the outermost layer: single-Al, double-Al, and O-terminal. According to the literature [13], the monolayer Al terminal structure on the Al₂O₃ (0001) surface is the most stable and facilitates the formation of a stable interface.

(III)

Number of surface atomic layers

Increasing the number of atomic layers on both sides of the interface can more accurately reflect the true properties of the material surface; however, this approach also results in a significant expenditure of computational resources. Thus, it is essential to optimize the number of surface layers for both Fe (111) and Al₂O₃ (0001). To ensure the stability of the interface model, it is preferable to use the surface configuration with the lowest surface energy. Prior to evaluating the performance of the Fe/Al₂O₃ interface, it is necessary to ensure that each side of the interface has a sufficient number of atomic layers to accurately capture the internal characteristics of the material. However, increased accuracy leads to longer computational times. Therefore, it is crucial to test for surface convergence to determine the minimum number of atomic layers required. In this study, the surface energies of Fe with layer numbers ranging from 3 to 9 were calculated. As indicated in

Table 1. Surface energy of Fe (111) surface with different thickness.

Atom Layers, n	3	5	7	9
Surface energy (σ) (J/m2)	2.51	2.63	2.65	2.64

, the surface energy starts to converge when the Fe (111) atomic layers reach 5, demonstrating stability. The surface energy was measured at 2.63 J/m², which aligns closely with values reported in other studies (2.78 J/m² [14] and 2.55 J/m² [15], respectively). To enhance the accuracy of the calculations, a 7-layer Fe (111) structure was selected for the interface model.

For the polar Al₂O₃ (0001) surface, the appropriate number of atomic layers is determined by analyzing the convergence of the rate of change in atomic interlayer distance before and after optimizing the surface structure. The rate of change in atomic interlayer distance ($\mathsf{\Delta }{\mathrm{d}}_{ij}$) is defined by Formula (2) [16]:

$$\mathsf{\Delta }{d}_{ij}={\displaystyle \frac{d_{ij}-d_{ij}^o}{d_{ij}^o}}\times 100\%$$

(2)

In the formula, $d_{ij}^o$ represents the layer spacing before surface structure optimization, and $d_{ij}$ represents the layer spacing after the surface structure is optimized.

Table 2. Variation in layer spacing on the surface of single Al-terminal Al₂O₃ (0001).

Surface Terminal	Rate of Change in Interlayer Spacing	Number of Surface Atomic Layers (N)
	(%)	9	12	15	18
Singl-Al	Δd12	−98.11	−90.30	−86.37	−89.03
	Δd23	+0.84	+0.72	+4.01	+6.62
	Δd34	−54.02	−39.34	−46.09	+7.56
	Δd45	+24.98	−13.32	+22.34	+23.23
	Δd56		+1.98	+3.02	+2.79
	Δd67			−2.89	−3.65
	Δd78				+2.47

,

Table 3. Variation in layer spacing on the surface of double Al-terminal Al₂O₃ (0001).

Surface Terminal	Rate of Change in Interlayer Spacing	Number of Surface Atomic Layers (N)
	(%)	11	14	17	20
Double-Al	Δd12	+18.09	+21.20	+18.96	+21.05
	Δd23	−0.99	−0.92	−3.08	−4.09
	Δd34	+0.39	+0.95	+3.05	+3.57
	Δd45	−3.97	−6.06	−4.69	−4.98
	Δd56	+3.79	+1.87	+1.64	+0.33
	Δd67		−0.71	+0.60	+1.65
	Δd78			−0.33	+0.70
	Δd89				−0.43

and

Table 4. Changes in layer spacing on the surface of Al₂O₃ (0001) at the O end.

Surface Terminal	Rate of Change in Interlayer Spacing	Number of Surface Atomic Layers (N)
	(%)	7	10	13	16
O	Δd12	+29.5	+16.98	+12.01	+26.23
	Δd23	−13.97	−21.12	−19.02	−23.21
	Δd34	+7.97	+3.01	+4.97	−0.41
	Δd45		−1.32	+1.55	−1.83
	Δd56			+0.89	+1.85
	Δd67				−1.23

present the α-Al₂O₃ (0001) surfaces for the three types of terminations: single-Al, double-Al, and O-terminal. The surface structures of single-Al, double-Al, and O-terminal Al₂O₃ (0001) reach stability with atomic layer counts of 12, 14, and 13 layers, respectively, at which point the interlayer spacing starts to converge, indicating structural stability. Consequently, monolayer-Al, bilayer-Al, and O-terminal surfaces of Al₂O₃ (0001) are assigned 12, 14, and 13 atomic layers, respectively, for the opposite faces of the interface structure.

(IV)

Stacking sequence of interfacial atoms

The stacking order of atoms at heterogeneous interfaces has a direct impact on both the bonding properties and the stability of the interface. Based on the docking characteristics of Al₂O₃ (0001) and Fe (111) surfaces, this study examines three types of high-symmetry sites, as illustrated in Figure 2. For instance, in the case of the single-Al termination of Al₂O₃ (0001), the outermost surface of Fe (0001) serves as the reference base. Here, an Al atom positioned directly above a Fe atom is referred to as the Top site, which is the center of a triangle formed by three Fe atoms, and it is also called the Hcp site. Alternatively, if the Al atom is situated between two Fe atoms, this configuration is referred to as the Bridge site. Consequently, each type of Fe/Al₂O₃ interface binding can exhibit three distinct stacking orders.

Based on the results of calculations and analyses regarding atomic layer number, surface terminal atomic types, interface mismatch rates, and stacking orders of Fe and Al₂O₃ surfaces, a 7-layer Fe (111) surface and three types of terminal Al₂O₃ (0001) surfaces (12-layer single-Al end, 14-layer double-Al end, and 13-layer O end) have been chosen to construct the interface, as illustrated in Figure 3. Each interface binding type encompasses three stacking sequences, resulting in a total of 9 distinct Al₂O₃/Fe interface structures for subsequent research.

2.3. Parameter Setting

The calculation in this article is based on the CASTEP software package based on the first principle. The specific parameters used are detailed and verified as follows.

The BFGS minimization algorithm is utilized to optimize the cell, surface, and interface structures. The convergence criteria are set as follows: atomic energy deviation is 0.01 meV/atom, maximum atomic force is 0.03 eV/Å, atomic stress deviation is 0.05 GPa, and maximum displacement is 0.001 Å.

The interactions between ionic nuclei and valence electrons are modeled using the ultra-soft pseudopotential (USPP). The valence electron configurations for the three elements are set as follows: O with 2s²2p⁴, Al with 3s²3p¹, and Fe with 3d⁶4s².

The process for determining exchange–correlation functionals is as follows. To select the most appropriate exchange–correlation functionals and ensure high computational accuracy, various functionals are evaluated and chosen. This study calculates the physical parameters (lattice parameters, bulk modulus, and enthalpy of formation) of Fe and Al₂O₃ using both the Local Density Approximation (LDA) and Generalized Gradient Approximation (GGA) functionals. These results are compared with other theoretical and experimental data, as shown in

Table 5. Lattice parameters, bulk modulus of Fe and Al₂O₃.

Cell Type		Method	a (Å)	c (Å)	B (GPa)
γ-Fe	This paper studies	GGA-PBE	3.437		255
	Other studies	GGA-PBE [15]	3.474		232
		GGA-PW91 [15]	3.472		240
		LDA-CAPZ [17]	3.428
	Experimental study		3.645 [18]
α-Al2O3	This paper studies	GGA-PBE	4.846	13.265	220
	Other studies	GGA-PBE [16]	4.759	12.991
		GGA-PBE [19]	4.812	13.133
	Experimental study		4.759 [14]	12.993	253

. The results indicate that the values calculated using the GGA-PBE functional are consistent with other theoretical values and more closely match experimental results. Therefore, GGA-PBE is selected as the exchange–correlation functional for the first-principles calculations in this study.

In addition, it is necessary to verify the energy convergence of Ecut and K-point settings. Theoretically, increasing the values of Ecut and K-point enhances calculation accuracy; however, this also consumes more computational resources and may lead to issues such as a non-convergence of energy. As shown in Figure 4 and Figure 5, when the Ecut value reaches 380 eV, the total energy of the atom starts to stabilize, indicating energy convergence. Therefore, Ecut is set to 380 eV. When the K-point value is increased to 8 × 8 × 8, the total energy of the atom also converges. Consequently, the bulk phase calculations for Fe and Al₂O₃ use a K-point grid of 8 × 8 × 8, while the surface and interface structures are calculated using a K-point grid of 8 × 8 × 1.

3. Results

3.1. Effect of Thermodynamic Parameters on Interfacial Stability

(1)

Interfacial adhesion work

Interfacial adhesion work is a direct thermodynamic parameter for assessing interfacial stability. Higher adhesion work indicates stronger interfacial bonding strength. To compare the bonding strength of Fe/Al₂O₃ interface structures across different bonding modes, the ideal adhesion work per unit area is calculated, as described in Formula (3) [20].

$$W_{ad}={\displaystyle \frac{E_{Fe}+E_{A{l}_2{O}_3}-E_{Fe/A{l}_2{O}_3}}{A}}$$

(3)

In the form, $E_{Fe/A{l}_2{O}_3}$ represents the total energy of the Fe/Al₂O₃ interface, $E_{A{l}_2{O}_3}$ represents the energy in the interface model where Al₂O₃ is replaced by a vacuum layer, $E_{Fe}$ represents the energy in which Fe in the interface model is replaced by the vacuum layer and $A$ represents the area of the interface.

This paper employs two methods to analyze the results of the $W_{ad}$ calculation. The first method is the minimum total energy approach, which is based on the principle that a lower total energy of the interface system corresponds to greater stability and higher adhesion work [20]. Figure 6 illustrates the curvilinear relationship between the interfacial spacing and $W_{ad}$ for three bonding types of Fe/Al₂O₃ interfaces across different stacking orders. The results indicate that the adhesion work of the Fe/Al₂O₃ interface follows the order: O-terminal > double-layer Al-terminal > single-layer Al-terminal, with the $W_{ad}$ value for the O-terminal interface being significantly higher than that for the Al terminals. Furthermore, for the same bonding mode, the interfacial adhesion work is directly related to the stacking order of the interfacial atoms, with $W_{ad}$ values initially increasing and then decreasing as the interfacial spacing increases. The maximum $W_{ad}$ values are observed at specific stacking orders: single-layer Al-Hcp (2.20 Å, 1.35 J/m²), double-layer Al-Hcp (1.90 Å, 3.62 J/m²), and O-Hcp (1.75 Å, 7.23 J/m²), respectively. The largest adhesion work for all three interface types occurs at the Hcp stacking position, which is consistent with findings in other metal–ceramic interface systems, such as Fe/WC [15] and NiTi/Al₂O₃ [16]. Therefore, it can be concluded that the interface stability is optimal when the atomic stacking order of the cermet interface is at the Hcp position.

The second approach involves structural optimization. Utilizing the results from the initial method, nine interface models exhibiting the maximum adhesion energy $W_{ad}$ were chosen for structural optimization.

Table 6. Adhesion work and interfacial spacing before and after Fe/Al₂O₃ interface optimization.

Interface	Interfacial Stacking Sequence	Without Structural Optimization		After Structural Optimization
		d0 (Å)	Wad (J/m2)	d0 (Å)	Wad (J/m2)
Single-Al	Top	2.40	1.28	2.52	0.43
	Hcp	2.20	1.35	2.38	0.58
	Bridge	2.25	1.33	2.43	0.56
Double-Al	Top	2.00	3.02	1.98	3.54
	Hcp	1.90	3.62	1.92	3.82
	Bridge	1.90	3.53	1.96	3.62
O	Top	1.75	7.13	1.31	9.30
	Hcp	1.75	7.23	1.37	9.35
	Bridge	1.60	7.12	1.35	9.03

presents the adhesion energy $W_{ad}$ and interface spacing results before and after the optimization process. Following atomic structure optimization, the maximum $W_{ad}$ for the three interfaces are observed as single-layer Al end Hcp (2.43 Å, 0.56 J/m²), double-layer Al end Hcp (1.92 Å, 3.82 J/m²), and O-end Hcp (1.37 Å, 9.35 J/m²), respectively. At this stage, these three models can be classified as the most stable interface structures. This method also leads to the conclusion that interface stability is optimized when the adhesion work for these three end faces is situated at the Hcp position.

The calculations above indicate that different terminal types and stacking positions significantly impact adhesion work with the O-terminal exhibiting higher adhesion work compared to both single-layer and double-layer Al terminals.

(2)

Interfacial energy

Changes in chemical bonds, grain boundary distortions, and variations in internal energy due to atomic interactions are critical parameters for assessing the thermodynamic stability of the interface. The interface energy should be positive with values closer to zero indicating better interface stability. The formula for calculating interface energy (σ) is provided in Formula (4) [20].

$$\sigma ={\gamma }_{Fe}+{\gamma }_{A{l}_2{O}_3}-W_{ad}$$

(4)

In the equation, ${\gamma }_{Fe}$ represents the surface energy of Fe, ${\gamma }_{A{l}_2{O}_3}$ represents the surface energy of Al₂O₃, and $W_{ad}$ represents the adhesion work of the Fe/Al₂O₃ interface.

Figure 7 illustrates the interface energy of the Al₂O₃/Fe interface structure across different bonding modes. For the monolayer Al end interface, the interface energy remains constant and independent of atomic chemical potential. The Hcp site structure exhibits the lowest interface energy, indicating that the Hcp stacking model is the most stable for the monolayer Al end interface. In contrast, the interface energy of the double-layer Al and O-terminal Al₂O₃/Fe interface structures varies linearly with the minimum interface energy also observed at the Hcp site. This consistency supports the alignment of the interface energy results with the previously mentioned adhesion work findings Additionally, the O-end Al₂O₃/Fe interface exhibits a transition from positive to negative interface energy. A negative interface energy suggests that the structure may spontaneously form under certain conditions [21]. This observation further indicates that the O-end interface demonstrates stronger interaction. Some studies [22] have shown that sufficiently negative interface energy can induce the diffusion of interface atoms and facilitate the formation of interface alloys.

Based on the research findings on interface thermodynamic parameters, it is evident that the structural stability of the Al₂O₃/Fe interface varies significantly with different bonding modes. The O-end interface exhibits the highest thermodynamic stability, while the monolayer Al interface, although the easiest to form, shows the weakest bonding strength. Following atomic structure optimization, the single-Al-Hcp, double-Al-Hcp, and O-Top models are identified as the most stable structures for each interface type and are chosen for further study.

3.2. The Influence of Electron Arrangement on the Properties of Interface

The redistribution and transfer of electrons at the interface fundamentally drive the breaking and rebonding of chemical bonds between atoms. To investigate the bonding mechanism of the Al₂O₃/Fe interface, we analyzed the charge density, differential charge density, and density of states for three binding modes (single Al-Hcp, double Al-Hcp, and O-Top). The charge density distribution map provides a direct view of the electron distribution at the interface, while the differential charge density map is derived from the difference between the charge densities of the bonded atoms and their isolated counterparts. This vividly illustrates electron transfer behavior and bonding polarization direction during atomic electron coupling at the interface [23]. The calculation formula for this is provided in Formula (5) [20].

$$\rho ={\rho }_{total}-{\rho }_{Fe}-{\rho }_{{Al}_2{O}_3}$$

(5)

In the form, ${\rho }_{total}$ represents the total charge density of the Al₂O₃/Fe interface, and ${\rho }_{{Al}_2{O}_3}$ represents the charge density of Al₂O₃ in the same interface system.

The electron density and differential charge density maps are collected perpendicular to the interface, passing through the plane with the highest atom density on the interface. Figure 8 illustrates the charge density map of the Al₂O₃/Fe interface structures for the three bonding modes. The color gradient from blue to red represents the increase in electron concentration ranging from 0 to 2 ų. In all three Al₂O₃/Fe interface structures, a charge-sharing region is evident at the interface. This region results from the transfer of electrons from outside the nuclei on either side of the interface, indicating that the atoms at the interface exhibit covalent bonding characteristics. The electron concentration in the charge-sharing region follows the order: O > double-Al > single-Al terminal Al₂O₃/Fe interface with the O-terminal interface showing a significantly higher concentration than the other two types. A higher concentration in the electron-sharing region indicates stronger interface interaction, which fundamentally determines interface bonding strength. Therefore, the order of interface stability is O > double-layer Al > monolayer Al end Al₂O₃/Fe interface. This explanation aligns with the $W_{ad}$ calculation results from an electronic perspective.

Figure 9 presents the electron density difference maps for the Al₂O₃/Fe interface structures across the three bonding modes. Blue regions denote electron dissipation, while red regions indicate electron aggregation. The Al₂O₃/Fe structures for all three bonding modes exhibit distinct local characteristics, which are predominantly around and at the interface. In the monolayer Al terminal interface (Figure 9), the electron dissipation region of the first-layer Fe atoms extends into the Al₂O₃ side, surpassing the interface. Concurrently, an electron aggregation region forms between two Fe atoms and O, indicating a typical polar covalent bond. In the double-layer Al terminal interface (Figure 9), the Al (1), Al (2), and Fe (1) atoms create electron aggregation regions at the interface, exhibiting strong non-directional and unsaturated metal covalent bonds. Additionally, the deepening red color around the Fe (1) atom signifies noticeable charge aggregation, primarily due to electron transfer from the Al atom, indicating Al-Fe ionic bonding characteristics. The ionic bonding characteristics observed between metals are not coincidental but are due to differences in the metals’ chemical reactivity. Similar phenomena have been reported in other studies [24]. In the O-terminal interface structure (Figure 9), the Fe (1) and Fe (2) atoms experience significant charge loss with the electron dissipation region extending into the Al₂O₃ side. Conversely, the O (1), O (2), and O (3) atoms exhibit clear electron aggregation characteristics, indicating that Fe atoms at the interface lose electrons to the O atoms, forming Fe-O ionic bonds. Based on the differential charge density results, it can be concluded that the three Al₂O₃/Fe interface structures have bonded at the interface to form new compounds, which are referred to as interface products.

Since electron density and electron density difference are semi-quantitative analysis methods, they cannot fully determine the atomic bonding mechanism at the interface. Therefore, additional analysis using the atomic density of states calculations is necessary. The partial density of states (PDOS) for the numerically labeled atoms in Figure 9 has been calculated, and the results are presented in Figure 10. Figure 10a illustrates the monolayer Al terminal Al₂O₃/Fe interface. At an energy state of −3.3 eV, the O (1)-2p and Al (1)-3p orbitals hybridize with the Fe (1)-3d orbitals, resulting in a minor overlap peak that indicates typical covalent bonding characteristics. Concurrently, the PDOS peak of Al (1) at the Fermi level (0 eV) shows a bulge compared to the internal Al-center atom of Al₂O₃ and is greater than 0. This indicates the formation of Fe-Al metal bonds at the interface albeit with very weak bonding strength. Consequently, the chemical bonding at the monolayer Al terminal interface predominantly features covalent bonds with a minor presence of metal bonds. Figure 8b depicts the double-layer Al terminal Al₂O₃/Fe interface. The PDOS peaks for Al (1) and Al (2) atoms at the Fermi energy are elevated and exceed 0, with peak intensities significantly stronger than those observed for the single-layer Al terminal interface. This indicates that the double-layer Al terminal interface forms more and stronger Fe-Al metal bonds compared to the single-layer Al terminal interface. Additionally, within the energy range from −3.5 eV to the Fermi level, the Al (1Magne2)-3p orbital exhibits a prominent peak, which aligns in shape with the Fe (1)-3p orbital. This suggests that electron orbital hybridization occurs between Al (1Magne2) and Fe (1) atoms, leading to the formation of a covalent metal bond. Previous research has established that a greater overlap of PDOS peaks at the interface correlates with stronger covalent bonding [24]. This suggests that the covalent bond strength at the double-layer Al terminal interface is significantly higher than at the single-layer Al terminal interface. Thus, it can be concluded that the stability of the double-layer Al terminal interface is greater than that of the single-layer Al terminal, which explains the observed differences in bonding strength between the two interface structures from an electronic perspective, aligning with the $W_{ad}$ calculation results. Figure 8c illustrates the O-terminal Al₂O₃/Fe interface. The PDOS peak for the O (1, 2, and 3)-2p orbitals at the Fermi level is slightly higher than that of the Fe (1)-3d orbitals with a significant increase in peak intensity. This indicates the formation of covalent metal bonds at the interface. Notably, three new sets of PDOS overlapping peaks are observed: Fe (2)-O (2) from −19.4 to −20.9 eV, Fe (2)-O (3) from −19.3 to −20.1 eV, and Fe (1)-O (1) from −16.8 to −19.1 eV. Compared to the Al-terminal interfaces, the O-terminal interface exhibits a greater number of hybridized electron orbitals, aligning with the observed maximum bonding strength at the O-terminal interface. Based on the discussion, it can be inferred that the electron distribution and hybridization of electron orbitals at the interface are the fundamental factors determining the bonding properties of the Al₂O₃/Fe interface.

4. Discussion

This paper investigates the surface properties of γ-Fe (0001) and α-Al₂O₃ (0001) as well as the bonding characteristics and mechanisms associated with three different bonding modes (monolayer Al end, bilayer Al end, and O end) at the α-Al₂O₃ (0001)/γ-Fe (111) interface. The specific conclusions drawn from this study are as follows:

• When the number of atomic layers in Fe reaches 5 or more, the surface energy stabilizes and converges to 2.63 J/m². The surface energy of Al₂O₃ is dependent on the type of surface atomic termination. The surface energy of monolayer Al-terminal Al₂O₃, which maintains a complete stoichiometric ratio, remains unaffected by the chemical potential of elements, yielding a constant value of 1.4 J/m². In contrast, the surface energies of bilayer Al-terminal and O-terminal Al₂O₃, which lack a complete stoichiometric ratio, vary linearly with the chemical potential of the oxygen element. As the concentration of oxygen increases, the surface energy of bilayer Al-terminal Al₂O₃ increases linearly, while the surface energy of O-terminal Al₂O₃ decreases.
• The Al₂O₃/Fe interface can be categorized into three types based on bonding configurations: single-Al, double-Al, and O-terminal. Prior to structural optimization, the maximum adhesion work is observed for single-Al (Hcp 1.35 J/m²), double-Al (Hcp 3.62 J/m²), and O-terminal (Hcp 7.23 J/m²). Following structural optimization, the maximum bonding energies are observed as single-Al (Hcp 0.56 J/m²), double-Al (Hcp 3.82 J/m²), and O-terminal (Top 9.35 J/m²). Thus, the order of interface bonding strength is O > double-layer Al > single-layer Al. Notably, the maximum adhesion work of the O-terminal interface structure, both before and after optimization, is significantly greater than that of the Al-terminal interfaces. This indicates that the bonding mode at the Al₂O₃/Fe interface substantially influences interface stability.
• The electronic structure analysis reveals that electron-sharing regions are present in all three Al₂O₃/Fe interface types. However, the charge concentration at the O-terminal interface is notably higher compared to the monolayer Al and bilayer Al interfaces. This indicates that the interaction at the O-terminal interface is stronger, which elucidates the variations in bonding strength across different binding modes from an electronic perspective. Differential charge density and partial density of states calculations reveal that Fe-Al covalent metal bonds predominantly characterize the interfaces of single-Al and double-Al. Conversely, both Fe-Al covalent metal bonds and Fe-O ionic bonds are present at the O-terminal interface. Additionally, the hybridization of interatomic electron orbitals at the O-terminal interface is markedly pronounced with a higher number of electron orbital hybrids compared to the monolayer Al and bilayer Al interfaces. This indicates that both the hybridization of electron orbitals and the type of chemical bonds significantly influence the interface bonding properties.

5. Conclusions

This study conducts a comparative analysis of the bonding properties of the Al₂O₃/Fe interface across various bonding modes based on its structural characteristics. The interfacial bonding properties were assessed by examining both the thermodynamic and electronic characteristics of the interface. The bonding properties of the Al₂O₃/Fe interface across different bonding modes are elucidated from an electronic perspective. Developing methods to experimentally fabricate the O-end bound Al₂O₃/Fe interface structure will be a key focus for future research.