Using First-Principles Calculations to Investigate the Interfacial Properties of Ni(100)/Ni₃Al(100) Eutectic Structures

Abstract

In this paper, the interfacial stabilities of six different stacking interface configurations of Ni(100)/Ni₃Al(100) eutectic structures with AlNi termination and Ni termination are calculated by using first-principles methods. The calculated adhesion work and interface energy indicate that the “Center” site stacking interface configurations are more stable than the “Top” and “Bridge” site stacking interface models. The partial density of states (PDOS) and the charge density difference confirm that the bonding characteristic of the Ni-terminated “Center” site stacking interface of the Ni(100)/Ni₃Al(100) eutectic structure is metallic, while the bond at the AlNi-terminated “Center” site interface is a combination of covalent and metallic bonds. A comprehensive analysis of the interface energy, PDOS and charge density difference confirms that the AlNi-terminated “Center” site stacking interface configuration of the Ni(100)/Ni₃Al(100) eutectic structure is the most stable eutectic interface model.

1. Introduction

γ/γ’ eutectic structures consist of a face-centered cubic Ni solid solution matrix (γ) and an L1₂-type ordered face-centered cubic intermetallic Ni₃Al (γ’) phase. Ni/Ni₃Al eutectic structures have received considerable attention as typical structures in Ni-based superalloys, coatings and composites [1,2,3]. The performance of materials strongly depends on the morphology, volume fraction and interfacial characteristics of their Ni/Ni₃Al eutectic structures.

Many previous studies have been conducted on the solidification behavior and preferential growth orientation of Ni/Ni₃Al eutectic structures in Ni-based superalloys under different processing conditions [4]. Ni/Ni₃Al eutectic structures generally develop in the interdendritic regions of superalloys and eutectic composites, and they exhibit diversified morphologies, including isolated blocky, rosette-like, rod-like and continuous strip-like structures. The morphology and volume fraction of eutectic structures are closely related to the cooling rate, thermal gradient, alloy composition and external electromagnetic field [5,6,7,8]. In comparison to the Bridgman process, the downward directional solidification process enhances the cooling rate, refines the dendritic structure and decreases the Ni/Ni₃Al eutectic structure size to obtain a homogeneous microstructure [5]. A high thermal gradient increases the solid volume fraction and conforms to the Bower–Brody–Flemings model, promoting the development of a fine Ni/Ni₃Al eutectic structure in the center of interdendritic regions, which evolves into a petal-like coarse eutectic structure [6]. The addition of Re and Ru alloying elements increases the Ni/Ni₃Al eutectic fractions and the segregation degree of Al and Ta alloying elements [7]. An external high-density current causes the dissolution of Ni/Ni₃Al eutectic structures, promoting the transformation of the morphology of crisscrossed fine eutectic structures from block to bar shapes [8]. Therefore, in order to investigate the Ni/Ni₃Al eutectic structures in alloys with various chemical compositions under different cooling rates, thermal gradients and external electromagnetic fields are essential to improve the performance of materials containing eutectic structures. In particular, the two Ni and Ni₃Al phases under different conditions always have preferential growth orientations, and the orientation relationships (OR) of the Ni/Ni₃Al interface have been determined to be (100)_Ni||(100)_Ni3Al, (110)_Ni||(110)_Ni3Al and (111)_Ni||(111)_Ni3Al [9,10]. Moreover, the (100)_Ni||(100)_Ni3Al interface is taken in this study as a typical coherent interface, which universally exists in eutectic structures. Consequently, it is of significance to clarify the interfacial characteristic of Ni/Ni₃Al eutectic structures with preferential OR.

The interfacial characteristic between Ni and Ni₃Al, including atomic structures, electronic structures and interfacial stability, is often the controlling factor limiting their practical applications [11,12]. Thus, determining it and understanding its influence on the comprehensive properties of Ni/Ni₃Al eutectic structures are of great importance. For Ni-based single-crystal superalloys, the Ni matrix and Ni₃Al precipitates are coherent [13]. To date, first-principles calculations based on the density functional theory (DFT) have been used to establish supercell and cluster models of the Ni/Ni₃Al interface, further theoretically revealing the effects of alloying elements (Re, B, Cr, Ru, Co, Mo, W, Ta, Zr, Ti, Nb and Hf) on the thermodynamic stability and fracture strength of the interface between the Ni matrix and the precipitated Ni₃Al phase [14,15,16,17]. However, the previous studies mainly focus on one or two types of interfacial models. For the Ni/Ni₃Al eutectic structure in the interdendritic regions of superalloys and eutectic composites, the relationship of the interfacial characteristic with the preferential OR and eutectic structures, and the atomic and electronic structures and bonding characteristics of Ni/Ni₃Al eutectic structures with preferential growth orientation remain unclear. Therefore, a systematic study of Ni(100)/Ni₃Al(100) eutectic interfaces with diversified interface models is essential to clarify the interfacial properties of Ni/Ni₃Al eutectic structures.

This study investigates the interfacial stability and electronic structures of six different interface models of Ni(100)/Ni₃Al(100) eutectic structures calculated by employing first-principles calculations. The interface adhesion, interface energy and electronic structures of the diversified Ni(100)/Ni₃Al(100) interface configurations are determined, providing an enhanced understanding of the most stable structures and the bonding characteristics of the Ni(100)/Ni₃Al(100) eutectic interfaces with optimum stacking sites.

2. Computational Method

The first-principles calculations based on DFT were performed by using the Cambridge Sequential Total Energy Package (CASTEP) code [18]. The exchange and correlation energies of the bulk properties of pure Ni and Ni₃Al, including the lattice constants, elastic constants and bulk modulus, were calculated by using the Generalized Gradient Approximation (GGA) of the Perdew–Burke–Ernzerhof (PBE) functions [19]. The K-point sampling in the first irreducible Brillouin zone was conducted by using the Monkhorst–Pack scheme. The plane-wave cutoff energy was set to 450 eV, the Monkhorst–Pack k-point mesh with 13 × 13 × 13 k points was utilized for the bulk Ni and Ni₃Al, and 13 × 13 × 1 k points for the Ni/Ni₃Al interfaces were utilized in the Brillouin zone integration. For the interface calculations, the self-consistent field (SCF) convergence threshold was set to 2.0 × 10⁻⁷ eV/atom, and the mean atomic force was reduced to 0.01 eV/Å. The equilibrium stress for each atom was converged to 0.02 GPa, the displacement was lower than 5.0 × 10⁻⁵ Å, and the system was considered to converge. The Kohn–Sham equation with the self-consistent field procedure was solved to obtain the electronic minimization and the ground state. The Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm was employed to achieve the minimum energy state of the Ni/Ni₃Al eutectic interface. For the surface models and interface configurations, periodic boundary conditions were applied, and a vacuum layer with a thickness of 10 Å was added on the interface and surface structures to avoid the interaction between the two identical surfaces.

3. Results and Discussion

3.1. Bulk Properties of Ni and Ni₃Al

The calculated lattice parameters (a), elastic constants (C_ij) and bulk modulus (B) of the pure Ni and the pure Ni₃Al crystal are listed in

Table 1. The calculated lattice constants (a), elastic constants (C_ij) and bulk modulus (B) of pure Ni and Ni₃Al crystal.

		a(Å)	C11(GPa)	C12(GPa)	C44(GPa)	B(GPa)
Ni	PBE	3.529	283.78	178.75	110.95	203.76
	Exp. [20]	3.524	248.1	154.9	124.2	186
	Cal. [21]	3.526	303.4	205.7	136.3	196.8
Ni3Al	PBE	3.577	240.14	153.89	124.59	182.64
	Exp. [22]	3.567	224.5	148.6	124.4	173.9
	DFT [23]	3.58	243.8	148.7	123.4	182.4 [21]

. For the pure Ni, the space group is Fm-3m (225), and the lattice constant and bulk modulus are a = 3.529 Å and B = 203.76 GPa, respectively. The results calculated by using GGA-PBE agree well with the values reported in the previous references. The difference between the experimental and theoretical elastic constants and bulk modulus is attributed to the different computational and experimental conditions. The space group of Ni₃Al is Pm-3m (221), and the bulk structure of cubic Ni₃Al is shown in Figure 1. The crystal structure belongs to the Cu₃Au-type, and the Ni atoms occupy the 3c(0, 0.5, 0.5) Wyckoff positions, while the Al atoms occupy the 1a(0, 0, 0) positions. The lattice constant and bulk modulus calculated by using GGA-PBE are determined to be a = 3.577 Å and B = 182.64 GPa, respectively, which are in good agreement with the previous theoretical and experimental data. The comparison between the calculated and referenced values ensures the accuracy of the parameters and the precision in the calculation of the GGA-PBE functions. Therefore, the GGA-PBE functional is applied in the following calculations.

3.2. Surface Convergence

The required number of atomic layers for pure Ni and Ni₃Al in the surface slab models should be determined to ensure that the surface slab models exhibit bulk-like interior properties. To determine the number of atomic layers in the following calculations of interfacial characteristics, a surface convergence test is conducted on the Ni and Ni₃Al slabs versus slab thickness, and the results are listed in

Table 2. Calculated surface energies of different Ni(100) surfaces versus atomic layers.

	Atomic Layer (n)	Surface Energy (J/m2)
Ni (100)	3	2.24
	5	2.22
	7	2.21
	9	2.20
	11	2.19

. For the Ni(100) surface, the odd layers with two identical surfaces are chosen to calculate the surface energy. The surface energy (γ_s) for more than nine atomic layers can be determined by the following equation [24]:

$${\gamma }_s=\frac{1}{2A}\left(E_{\mathrm{surf}}-N{E}_{\mathrm{bulk}}\right)$$

(1)

where the factor 2 represents the two identical surfaces of the surface slab, A is the surface area, E_surf is the final energy of the Ni surface slab, E_bulk is the energy of each Ni atom in the bulk crystal, and N is the number of atoms in the surface slab. The Ni(100) surface energy is calculated and converges to 2.20 J/m² for the surface models with more than nine layers, which is consistent with a previous study [21]. Therefore, the Ni surface slab model with nine atomic layers is adopted in the following calculation of interfacial characteristics of the Ni(100)/Ni₃Al(100) eutectic structures.

For the Ni₃Al(100) surface, there are two kinds of Ni₃Al surfaces, namely, a Ni-terminated surface and a AlNi-terminated surface. The convergence test is conducted on the Ni₃Al surface slabs by using the method described in Ref. [25]. To avoid the dipole effect of the surface configurations, the two free surfaces of Ni₃Al(100) are identical. The odd layered slabs with 3, 5, 7, 9 and 11 layers are established to evaluate the convergences of the surfaces and to eliminate surface polarity. In the calculations, all of the atoms are relaxed to the local minimum positions. To quantitatively characterize the degree of relaxation during the calculations, the variation in the interlayer distance (Δ_ij) for the optimized configuration after relaxation is calculated as (d_i,j − d₀)/d₀ × 100%, where d₀ is the bulk interlayer distance, and d_i,j is the average distance between the ith and jth layer. A positive Δ_ij represents an increasing distance between the two layers and interlayer expansion, while a negative Δ_ij indicates a decreasing distance and interlayer reduction. The results are shown in

Table 3. Interlayer distance variation (Δ_ij) convergences of the two Ni-terminated and AlNi-terminated Ni₃Al(100) surfaces versus the number of atomic layers.

Termination	Interlayer	Slab Thickness
		3	5	7	9	11
Ni termination	Δ12	−3.93%	−4.14%	−4.25%	−4.32%	−4.24%
	Δ23		0.02%	−0.04%	−0.56%	−0.55%
	Δ34			0.05%	−0.39%	−0.45%
	Δ45				−0.64%	−0.75%
	Δ56					−0.003%
AlNi termination	Δ12	−3.22%	−3.02%	−3.08%	−3.02%	−3.02%
	Δ23		−0.21%	−0.44%	−0.39%	−0.39%
	Δ34			−0.36%	−0.31%	−0.26%
	Δ45				0.03%	0.02%
	Δ56					0.04%

. The two Ni-terminated and AlNi-terminated surfaces with more than nine layers converge well, indicating that nine layers are thick enough for the convergence of the two Ni-terminated and AlNi-terminated Ni₃Al(100) surfaces. Therefore, the nine-layered Ni and nine-layered Ni₃Al slabs are chosen to construct the Ni(100)/Ni₃Al(100) eutectic interfaces.

3.3. Surface Stability of Ni₃Al Surfaces

The Ni₃Al surface slab with symmetric terminations is non-stoichiometric, and the chemical potentials of the Ni and Al atoms should be considered for the calculation of the surface energy. The surface model is in equilibrium with the bulk and follows the relationships (${\mu }_{{\mathrm{Ni}}_3\mathrm{Al}}^{\mathrm{bulk}}={\mu }_{\mathrm{Al}}^{\mathrm{slab}}+3{\mu }_{\mathrm{Ni}}^{\mathrm{slab}}$) and (${\mu }_{{\mathrm{Ni}}_3\mathrm{Al}}^{\mathrm{bulk}}={\mu }_{\mathrm{Al}}^{\mathrm{slab}}+3{\mu }_{\mathrm{Ni}}^{\mathrm{slab}}+\Delta H_f^0$), where ${\mu }_{{\mathrm{Ni}}_3\mathrm{Al}}^{\mathrm{bulk}}$ is the chemical potential of bulk Ni₃Al; ${\mu }_{\mathrm{Al}}^{\mathrm{slab}}$ and ${\mu }_{\mathrm{Ni}}^{\mathrm{slab}}$ are the chemical potentials of the Al and Ni atoms, respectively; and $\Delta H_f^0$ is the formation enthalpy of bulk Ni₃Al. The surface energies (γ_s) of the different Ni₃Al surface models with non-stoichiometric characteristics can be determined by [26]

$${\gamma }_s=\frac{1}{2A}\left(E_{\mathrm{slab}}-\frac{N_{\mathrm{Ni}}}{3}{\mu }_{{\mathrm{Ni}}_3\mathrm{Al}}^{\mathrm{bulk}}+\left(\frac{N_{\mathrm{Ni}}}{3}-N_{\mathrm{Al}}\right){\mu }_{\mathrm{Al}}^{\mathrm{slab}}\right)$$

(2)

where A is the area of the surface; E_slab is the total energy of the different surface models; N_Ni and N_Al are the numbers of the Ni and Al atoms in the surface model, respectively. The Ni₃Al(100) surface equilibrates the Ni₃Al bulk and the chemical potentials of the Al and Ni atoms are less than the values in the bulk, indicating that stable atoms form the slab structures. In addition, ${\mu }_{\mathrm{Ni}}^{\mathrm{slab}}\le {\mu }_{\mathrm{Ni}}^{\mathrm{bulk}}$, and ${\mu }_{\mathrm{Al}}^{\mathrm{slab}}\le {\mu }_{\mathrm{Al}}^{\mathrm{bulk}}$; the range of ${\mu }_{\mathrm{Al}}^{\mathrm{slab}}-{\mu }_{\mathrm{Al}}^{\mathrm{bulk}}$ can be determined as follows:

$$\Delta H_f^0\le {\mu }_{\mathrm{Al}}^{\mathrm{slab}}-{\mu }_{\mathrm{Al}}^{\mathrm{bulk}}\le 0$$

(3)

The surface energy of Ni₃Al can be rewritten as follows:

$${\gamma }_s=\frac{1}{2A}\left(E_{\mathrm{slab}}-\frac{N_{\mathrm{Ni}}}{3}{\mu }_{{\mathrm{Ni}}_3\mathrm{Al}}^{\mathrm{bulk}}+\left(\frac{N_{\mathrm{Ni}}}{3}-N_{\mathrm{Al}}\right){\mu }_{\mathrm{Al}}^{\mathrm{bulk}}-\left(\frac{N_{\mathrm{Ni}}}{3}-N_{\mathrm{Al}}\right)\left({\mu }_{\mathrm{Al}}^{\mathrm{slab}}-{\mu }_{\mathrm{Al}}^{\mathrm{bulk}}\right)\right)$$

(4)

The surface energy variations of the Ni-terminated and AlNi-terminated surfaces versus the chemical potential difference of ${\mu }_{\mathrm{Al}}^{\mathrm{slab}}-{\mu }_{\mathrm{Al}}^{\mathrm{bulk}}$ are illustrated in Figure 2. There is a linear relationship between the surface energies and the chemical potential difference for the two surfaces. The Ni-terminated N₃Al(100) surface energy increases with the increase in the chemical potential difference, while the surface energy decreases for the AlNi-terminated N₃Al(100) surface. This is related to the different bonding characteristics of the Ni-terminated and AlNi-terminated Ni₃Al(100) surfaces, as discussed in the following section, which covers the electronic structures of the eutectic interface. The surface energy of the AlNi-terminated surface is smaller than that of the Ni-terminated surface, and the values of the surface energies of the AlNi-terminated and Ni-terminated surfaces range from 1.29 J to 2.11 J and from 2.3 J to 3.13 J, respectively. The smaller value of the surface energy for the AlNi-terminated Ni₃Al(100) surface indicates that it has better stability than the Ni-terminated Ni₃Al(100) surface.

4. Interfacial Properties

4.1. Atomic Structures of the Ni/Ni₃Al Eutectic Interface

The nine-layered Ni and nine-layered Ni₃Al surface slabs with periodic boundary conditions based on the surface convergence test were utilized to construct the Ni(100)/Ni₃Al(100) eutectic interface models. A vacuum layer of 10 Å was built on top of the interface models to eliminate the interaction between the free surfaces of the Ni₃Al and Ni slabs. The corresponding lattice mismatches (δ) for the interface models of Ni(100)/Ni₃Al(100) were calculated using δ = 2(α_Ni3Al − α_Ni)/(α_Ni3Al + α_Ni), where α_Ni3Al and α_Ni are the lattice constants of the Ni₃Al and Ni phases, respectively. The value of the lattice mismatches was determined to be 1.34%, indicating a coherent Ni(100)/Ni₃Al(100) interface and the neglect of the interfacial strain in the calculation of the interfacial characteristics. Three different stacking sequences of the Ni atoms in the layers of the Ni(100) surface on each of the Ni₃Al(100) Ni-terminated and AlNi-terminated surfaces were considered to build six different interface models of Ni(100)/Ni₃Al(100) eutectic structures, namely, the Ni-terminated and “Top” site stacking interface, the Ni-terminated and “Bridge” site stacking interface, the Ni-terminated and “Center” site stacking interface, the AlNi-terminated and “Top” site stacking interface, the AlNi-terminated and “Bridge” site stacking interface, and the AlNi-terminated and “Center” site stacking interface, as shown in Figure 3. For the Ni-terminated and AlNi-terminated surfaces, the “Top” site stacking interface shown in Figure 3a,d indicates that the interfacial Ni atoms in the first layer of the Ni(100) surface were placed right on the interfacial Ni or Al atoms of the Ni₃Al(100) slab. The “Bridge” site stacking interface shown in Figure 3b,e indicates that the interfacial Ni atoms in the first layer of the Ni(100) surface were located in the middle site between the Ni and Al atoms in the Ni₃Al(100) slab. The “Center” site stacking interface shown in Figure 3c,f indicates that the interfacial Ni atoms in the first layer of the Ni(100) surface were located right above the second layer of the Ni₃Al(100) slab. All the atoms in the interface models can be relaxed freely in the three dimensions.

4.2. Interfacial Stability

The interfacial adhesion work (W_ad) is commonly used to evaluate the interfacial stability of various Ni(100)/Ni₃Al(100) eutectic structures, and it is defined as the reversible energy required to separate the Ni/Ni₃Al interface into two free surfaces. A higher interfacial adhesion work represents a stable interface. The interfacial adhesion work of the Ni(100)/Ni₃Al(100) eutectic structure is determined via the energy of the Ni(100) surface slab (E_Ni), the energy of the Ni₃Al(100) surface slab ($E_{{\mathrm{Ni}}_3\mathrm{Al}}$) after relaxation and the interfacial energy of the Ni(100)/Ni₃Al(100) eutectic structure after full relaxation (E_interface):

$$W_{ad}=\frac{1}{A}\left(E_{\mathrm{Ni}}+E_{{\mathrm{Ni}}_3\mathrm{Al}}-E_{\mathrm{interface}}\right)$$

(5)

where A is the interfacial area of the Ni(100)/Ni₃Al(100) eutectic structure. After the atoms in the interface are fully relaxed to the equilibrium position, the variation of the total energy of the interface is calculated with the interfacial distance variation d₀, which is the distance between the first layer of the Ni and Ni₃Al slabs along the z direction. The optimal d₀ and W_ad are listed in the “Fully Relaxed” column in

Table 4. Adhesion work (W_ad) and interfacial distance variation (d₀) of the Ni-terminated and AlNi-terminated Ni(100)/Ni₃Al(100) interface models after relaxation.

Termination	Stacking	Fully Relaxed
		d0(Å)	Wad(J/m2)
Ni termination	Top	2.30	2.36
	Bridge	2.05	3.19
	Center	1.73	4.34
AlNi termination	Top	2.33	2.26
	Bridge	2.1	3.03
	Center	1.78	4.15

. Compared to the “Top” and “Bridge” site stacking configurations, the interfacial adhesion work of “Center” site stacking configuration is the highest for the both Ni-terminated and AlNi-terminated Ni(100)/Ni₃Al(100) eutectic interfaces. A larger adhesion work indicates a greater stability of the interface. This indicates that the Ni-terminated and AlNi-terminated “Center” (100) interfaces are more stable than the “Top” and “Bridge” site stacking interface models. Consequently, the Ni-terminated and AlNi-terminated “Center” site stacking interface configurations, rather than the “Top” and “Bridge” site stacking interface models, are further investigated in this study.

To further evaluate the interfacial stability of the different Ni(100)/Ni₃Al(100) eutectic interface configurations, the interfacial energies (γ) of the Ni-terminated and AlNi-terminated “Center” site stacking interface models are calculated by using the following equation [26].

$$\gamma =\frac{1}{A}\left(E_{\mathrm{interface}}-\frac{N_{\mathrm{Ni}}^{{\mathrm{Ni}}_3\mathrm{Al}}}{3}{\mu }_{{\mathrm{Ni}}_3\mathrm{Al}}^{\mathrm{bulk}}-\left(\frac{N_{\mathrm{Ni}}^{{\mathrm{Ni}}_3\mathrm{Al}}}{3}-N_{\mathrm{Al}}\right){\mu }_{\mathrm{Al}}^{\mathrm{slab}}-N_{\mathrm{Ni}}^{\mathrm{Ni}}{\mu }_{\mathrm{Ni}}^{\mathrm{bulk}}\right)-{\sigma }_{\mathrm{Ni}}-{\sigma }_{{\mathrm{Ni}}_3\mathrm{Al}}$$

(6)

where A is the interface area; E_interface is the interfacial energy of the Ni(100)/Ni₃Al(100) eutectic structure after full relaxation; N_Al is the number of Al atoms in the Ni₃Al(100) slab; $N_{\mathrm{Ni}}^{{\mathrm{Ni}}_3\mathrm{Al}}$ and $N_{\mathrm{Ni}}^{\mathrm{Ni}}$ are the number of Ni atoms in the Ni₃Al(100) and Ni(100) slabs, respectively; ${\mu }_{{\mathrm{Ni}}_3\mathrm{Al}}^{\mathrm{bulk}}$ is the chemical potential of Ni₃Al; ${\mu }_{\mathrm{Ni}}^{\mathrm{bulk}}$ is the chemical potential of the Ni atom in the Ni bulk; ${\mu }_{\mathrm{Al}}^{\mathrm{slab}}$ is the chemical potential of the Al atom in the interface; and ${\sigma }_{\mathrm{Ni}}$ and ${\sigma }_{{\mathrm{Ni}}_3\mathrm{Al}}$ are the surface energies of the Ni(100) and Ni₃Al(100) surfaces, respectively. For the two Ni-terminated and AlNi-terminated “Center” site stacking interface models, the interfacial energy variation versus the chemical potential difference of Al (${\mu }_{\mathrm{Al}}^{\mathrm{slab}}-{\mu }_{\mathrm{Al}}^{\mathrm{bulk}}$) is shown in Figure 4. The interface energy of the Ni-terminated “Center” site stacking interface monotonously increases from −0.07 to 0.7 J/m² with the increasing chemical potential difference, while the interface energy of the AlNi-terminated “Center” site stacking interface decreases from −0.06 to −0.84 J/m². The interfacial energy of the AlNi-terminated “Center” site stacking interface is lower than that of the Ni-terminated “Center” site stacking interface. This indicates that the AlNi-terminated “Center” site stacking Ni(100)/Ni₃Al(100) eutectic interface has a high stability and is more stable than the Ni-terminated “Center” site stacking interface model.

4.3. Electronic Structure

To further explore the interfacial characteristic and stability of the Ni-terminated and AlNi-terminated “Center” site stacking interface models of the Ni(100)/Ni₃Al(100) eutectic structures, the partial density of states (PDOS) and the charge density difference are calculated to elucidate the electronic structure and the bonding characteristics of the two different interface models. The obtained PDOS for the AlNi-terminated and Ni-terminated “Center” site stacking interfaces of the Ni(100)/Ni₃Al(100) eutectic structures are presented in Figure 5. The vertical dashed line represents the Fermi level. The 1st, 2nd and 3rd layers are the same as the layers in Figure 3, and the 3rd and higher layers of the Ni and Ni₃Al sides have similar bulk Ni and Ni₃Al properties. For the Ni-terminated “Center” site stacking Ni(100)/Ni₃Al(100) interface, the PDOS at the interface is different from that of the interior layers, indicating the electron redistribution of the interfacial atoms (Figure 5a). The interfacial Ni atoms have the same PDOS and occupy more states near the Fermi level with no depletion, indicating the metallic bonding characteristics of the Ni(100)/Ni₃Al(100) interface. For the AlNi-terminated “Center” site stacking Ni(100)/Ni₃Al(100) interface, the PDOS of the interfacial Al atoms are larger than the PDOS of those in the bulk or the interior one, and the first-layer Ni atoms in the Ni(100) slab have a weak depletion, as shown in Figure 5b. Based on the difference between the PDOS of the interface and the PDOS of the interior layers, the overlapping interfacial Ni and Al atoms near the Fermi level reflect the orbital hybridization and the formation of covalent bonds between Ni-3d and Al-2p. Therefore, the bonding characteristic of the AlNi-terminated “Center” site stacking interface of the Ni(100)/Ni₃Al(100) eutectic structures is covalent with metallic bonding.

Figure 6 shows the charge density difference for the fully relaxed Ni-terminated and AlNi-terminated “Center” site stacking interfaces of the Ni(100)/Ni₃Al(100) eutectic structures. The solid horizontal lines represent the interfaces of the two Ni(100)/Ni₃Al(100) eutectic interface models, the red area denotes the enrichment of electrons, and the blue area represents the loss of electrons. For the Ni-terminated “Center” site stacking interface, the charge depletion is mainly concentrated in the Al atoms in the Ni₃Al(100) slab and partially concentrated around the Ni atoms in the Ni(100) slab. The original interfacial charge distribution is similar to that in the Ni(100) slab and the Ni₃Al(100) slab, indicating no obvious charge transfer or redistribution near the interface and the metallic bonding characteristic at the Ni-terminated “Center” site stacking interface of the Ni(100)/Ni₃Al(100) eutectic structures, as shown in Figure 6a. For the AlNi-terminated “Center” site stacking interface, there is an obvious charge accumulation in the Ni atoms at the interface, and the charge accumulation region extends to the second layer of the Ni(100) slab. The interfacial charge distribution is similar to that in the Ni₃Al(100) slab, indicating the combined interaction of covalent and metallic bonding characteristics (Figure 6b). Additionally, the covalent bond is stronger than the metallic bond. Therefore, the bonding characteristic of the AlNi-terminated “Center” site stacking interface of the Ni(100)/Ni₃Al(100) eutectic structures is more stable than that of the Ni-terminated “Center” site stacking interface model. These results are consistent with the conclusion from the PDOS.

5. Conclusions

Six different Ni-terminated and AlNi-terminated interface models of Ni(100)/Ni₃Al(100) eutectic structures, containing “Top”, “Bridge” and “Center” site stacking configurations, were established for an investigation into the interfacial stability of eutectic structures. The interface adhesion, interface energy and electronic structures were calculated to determine the most stable interfacial configuration of the Ni(100)/Ni₃Al(100) eutectic structures. The main conclusions are summarized as follows:

• A nine-layered Ni(100) slab and a nine-layered Ni₃Al(100) slab with AlNi termination and Ni termination were utilized to establish six different interface models of Ni(100)/Ni₃Al(100) eutectic structures, namely, Ni-terminated and AlNi-terminated “Top” site stacking interface, Ni-terminated and AlNi-terminated “Bridge” site stacking interface, and Ni-terminated and AlNi-terminated “Center” site stacking interface configurations.
• The AlNi-terminated “Center” site stacking interface model of the Ni(100)/Ni₃Al(100) eutectic structure was determined to be the most stable interfacial configuration from a comprehensive analysis of the adhesion work, interfacial energy and electronic structures.
• The PDOS and charge density difference indicated the combined bonding characteristics of covalent and metallic bonds at the interface of the AlNi-terminated and “Center” site stacking interface of the Ni(100)/Ni₃Al(100) eutectic structure, which had a higher stability than the Ni-terminated and “Center” site stacking interfacial model.