First-Principle Investigation of the Interface Properties of the Core-Shelled L1₂-Al₃M (M = Sc, Zr, Er, Y) Phase

Abstract

The interface structure and segregation behavior of L1₂-Al₃M (M = Sc, Zr, Er, Y) phases were investigated based on first-principles calculations. The results showed that the order of the thermodynamically stable interface was Al₃Zr/Al > Al₃Sc/Al > Al₃Er/ Al > Al₃Y/Al. The interfaces of Al₃Sc/Al₃Zr, Al₃Er/Al₃Zr, and Al₃Y/Al₃Er obtained negative interfacial energies and low coherent strain energies and were favorable to form a clear interface. Zr atom tended to segregate to the first atomic layer on the Al side of the Al/Al₃Sc, Al/Al₃Er, and Al/Al₃Y interfaces. The driving effect of the Zr atom segregation to the Al₃Y shows was stronger than that to Sc and Er atoms, whereas the high coherent strain energy hindered the formation of Al₃Y/Al₃Zr interface. Er atom tended to segregate at the Al/Al₃Y interface and accelerated the formation of core-shelled Al₃Y/Al₃Er. Furthermore, the formation of the double core-shelled Al₃Y/Al₃Er/Al₃Zr was discussed.

1. Introduction

Aluminum alloys containing scandium had attracted the attention of researchers due to their high strength, corrosion resistance, and weldability [1,2,3]. The small addition of Sc to aluminum alloy formed a coherent Al₃Sc phase (L1₂ phase) [4]. The primary Al₃Sc phase can refine the grain of the as-cast Al alloy. The secondary Al₃Sc phase effectively inhibited the growth of recrystallized grains [5] and increased the recrystallization temperature [6]. However, Al₃Sc precipitate coarsened rapidly under high temperatures, reducing the strength of Al-Sc alloys. Moreover, the high price of Sc is prohibited from expanding commercial applications containing Sc aluminum alloys.

It was necessary to investigate new alloy elements to replace Sc elements and develop low-cost, high-performance aluminum alloys. Harada et al. [7] found that the atoms that replaced Sc to form the L1₂ microstructure should be located near Sc in the periodic table. Zr, Er, Yb, Y, and other elements may be good substitutes for Sc. Compared with the addition of Sc, the combined addition of Sc and Zr can precipitate a core-shelled Al₃(Sc, Zr) phase with a Sc-rich core and Zr-rich shell microstructure owing to the differences in diffusion rates between Sc and Zr atoms. The core-shelled Al₃(Sc, Zr) obtained better high-temperature stability (slower coarsening rate) [8]. The research of Er element alloying had attracted much attention due to the formation of L1₂-Al₃Er phase and its low cost. By partially replacing the Sc element with Er element, the alloy can precipitate core-shelled Al₃(Sc, Er) nano-phase with an Er-rich core and Sc-rich shell microstructure during homogenization [9], improving the creep resistance owing to its high lattice mismatch. Nie et al. [10] developed Al-Er alloys by completely replacing Sc with Er, and the alloys can also precipitate core-shelled Al₃(Er, Zr) phase similar to Al₃(Sc, Zr), displaying excellent thermal stability. Addition of Zr and Yb atoms into aluminum alloy promoted to precipitate L1₂-Al₃(Zr, Yb) nano-phase. The core-shelled microstructure was observed in Al-Yb-Zr alloys as the Zr atom was incorporated into the Al₃Yb nano-phase, thus displaying better thermal stability and inhibit-recrystallization ability [11]. The formation of the L1₂ nano-phase with core-shelled microstructure was usually attributed to the difference in element diffusion rate. The rapidly diffusing elements were enriched to form a core layer, and the slowly diffusing elements were segregated to form a shell layer.

Y and Sc were the congeners of the elements, and they had similar chemical properties. Zhang et al. [12] showed that Al-Y-Zr alloy can form L1₂-Al₃(Zr, Y) precipitate at 400 °C. The Al₃Y phase was first precipitated in the Al-Zr-Y alloy at the initial aging stage, which became the heterogeneous core of Al₃Zr precipitated by aging, accelerating the precipitation of Zr in solid solution in the alloy. Based on the atomic diffusion control mechanism, Al₃(Y, Zr) nano-phase should form a core-shelled microstructure with a Y-rich core and Zr-rich shell. However, Y and Zr atoms were evenly distributed in the precipitated phase, and no obvious segregation in the core/shell was observed in Al₃(Y, Zr) phase [13]. The mechanism of the L1₂-Al₃(Zr, Y) phase with no core-shelled microstructure had not been clearly understood.

The complex multilayer core-shelled microstructure provided a new idea for the structure design of nano-phase Al alloys. Christian Monachon et al. [14] performed a two-step aging treatment on the microalloyed Li, Sc, and Yb aluminum alloys, and high-density α-Al₃(Li_0.57Sc0_.33Yb_0.10) nano-sized precipitates were formed during aging treatment at 325 °C, exhibiting a Yb-enriched core and a Sc-enriched first shell with good stability due to the diffusivity ordering of D_Yb > D_Sc. During the second aging treatment at 170 °C, a second metastable δ’-Al₃Li shell presented around the Sc-enriched first shell, thus illustrating an Al₃Yb/Al₃Sc/Al₃Li bilayer core-shelled microstructure. Multilayer core-shelled microstructures had been observed in Al-Sc-Er-Zr alloys. After aging at 400 °C, Al₃Er/Al₃Sc/Al₃Zr precipitates containing an Er-enriched core surrounded by a Sc-enriched inner shell and a Zr-enriched outer shell were formed in Al-Zr-Sc-Er alloys, obtaining a high coarsening resistant and high strength [15]. The formation of the bilayer core-shelled microstructure was well agreed with the atomic diffusivity ordering of D_Er > D_Sc > D_Zr. However, the Al₃Zr/Al(Yb, Sc) phase of the Zr core layer and shell layer with randomly distributed Yb and Sc was observed in Al-Yb-Sc-Zr alloys [16], and there was no Al₃Yb/Al₃Sc/Al₃Zr bilayer core-shelled microstructure formed by the diffusion rate ordering of D_Yb > D_Sc > D_Zr. It implied that the diffusion rate did not control the formation of multilayer core-shelled microstructures.

First-principles thermodynamic calculation was an important method for understanding and predicting the structure and properties of the nanometer phases [17]. Based on first-principle thermodynamic calculations, Jiang et al. [18,19,20,21] calculated the interface formation energies and interfacial coherent strains on L1₂ nano-phases for Al-Sc/Er-Zr, Al-Sc-Er, and Al-Sc-Er-Zr alloys. These investigations showed that Sc, Er, or Zr strongly preferred to substitute the X sublattice sites in L1₂-Al₃X (X = Er or Sc), while the inter-substitution between L1₂-Al₃X was only weakly feasible. The (100)/(100) contacting facets were the most energy favored for the Al/Al₃X, Al/Al₃Zr, and Al₃X/Al₃ Zrinterfaces, and these interfaces were coherent with low formation energy. Zr segregation to the Al/Al₃X interface promoted the formation of a Zr-enriched shell. Thus, L1₂-Al₃(Re_x, Zr_1−x) precipitates tended to form the core-shelled microstructure.

As for L1₂-Al₃(Zr, Y) precipitate, there was few first-principles calculation of interface energy. Li et al. [22] investigated the interactions at the Al₃Y/Al interfaces based on first-principles calculation. However, first-principle calculations of the interfacial properties of multicomponent L1₂-phases containing Y atoms were rarely reported. In this paper, the interfacial properties of the Al₃M(Sc, Er, Zr, Y) phase were investigated based on first-principles calculations to reveal the mechanism of the L1₂-Al₃(Zr, Y) phase with no core-shelled microstructure. Furthermore, the complex multilayer core-shelled microstructure containing the Y atom was also discussed in this paper.

2. Computational Method

2.1. Calculation Details

This work was based on density functional theory (DFT) [23] and used VASP software [24] and the projection augmented wave (PAW) method [25] for first-principles calculations. The plane wave base cutoff energy used for structural optimization was 400 eV. The electron configuration was described by 3s²3p¹, 3s²3p⁶4s¹3d², 4s²4p⁶5s¹4d³, 6s²5p⁶5d¹, and 4s²4p⁶5s¹4d² valence states for Al, Sc, Zr, Er, and Y, respectively. The Perdew-Burke-Ernzer (PBE) [26,27] method of generalized gradient approximation (GGA) was used to describe the exchange-correlation energy functional between electrons. The total energy was calculated using the linear tetrahedron method with the Blöchl correction until the total energy converged to 10⁻⁴ eV/atom. In each periodic direction of reciprocal space, the Monkhorst-Pack k point grids with linear kmesh analytical values of less than 0.03 2π Å⁻¹ were used to integrate the Brilloin region, optimize the geometric structure, and calculate the follow-up result. The sandwich model with two interfaces without vacuum and the full optimization scheme including relaxation of atomic position, shape, and volume of the computational cell were used.

2.2. Interface Energy

To determine the appropriate interface structure, the interfacial energy and the coherent strain energy between the phase of L1₂-Al₃M (M = Sc, Zr, Er, Y) and Al matrix were calculated, respectively. To evaluate the formation of the different interfacial, the interface formation energy ΔG_f was calculated as follows [28]:

$$\mathit{\Delta }{G}_f=E{\mathrm{Al}}_{{\mathrm{Al}}_3\mathrm{M}}{}_{int}$$

(1)

where E_int was the total energy of the interface model; x denoted the phase fraction of Al; N was the total number of atoms in this interface model; and μ_Al and μ_Al3M were the fully relaxed energy per atom in Al and Al₃M structures, respectively.

The interface formation energy contained two parts of energy, one was the contribution of interfacial energy, and the other was the elastic strain energy from the lattice mismatch, so it can also be expressed as follows [29]:

$$\frac{\mathit{\Delta }{G}_f}{N}=\frac{2\cdot A\cdot \gamma }{N}+G_S$$

(2)

where A was the interface area. Since the calculation used a sandwich model with two interfaces (Figure 1), it was multiplied by a factor of two. G_s was the coherent strain energy per atom. γ was the interface energy per unit area without coherent strain energy.

In this calculation, the direct calculation method was used to calculate the energy of Al and Al₃M phases after the relaxation in the direction perpendicular to the interface by fixing the lattice, and the difference was made with the total energy of the interface supercell. The interface energy γ can be calculated by the following formula [30]:

$$\gamma =\frac{1}{2A}[{E\frac{N_{\mathrm{Al}}}{N_{total}}{E}_{\mathrm{Al}}^{\mathrm{fix}}\frac{N_{{\mathrm{Al}}_3\mathrm{M}}}{N_{total}}{E}_{{\mathrm{Al}}_3\mathrm{M}}^{\mathrm{fix}}}_{int}[]]$$

(3)

where N_Al and N_Al3M were the numbers of Al and Al₃M phases, respectively; N_total was the total number of phases in the interface model; and $E_{\mathrm{Al}}^{\mathrm{fix}}$ and $E_{{\mathrm{Al}}_3\mathrm{M}}^{\mathrm{fix}}$ were the energies of Al and Al₃M after the full relaxation perpendicular to the interface.

Based on Equation (3), the interface energy without the coherent strain can be obtained. The coherent strain energy can be calculated by applying Equations (1) and (2).

According to the research [18], the most energy-favored interface structures were determined as the Al-terminated and bridge-coordinated interface for the (100)Al/(100)Al₃M, the Al-terminated and hollow-coordinated interface for the (110)Al/(110)Al₃M, and the Al₃M-terminated and hollow-coordinated interface for the (111)Al/(111)Al₃M, respectively. The Al and Al₃M block consisted of more than five layers. After full relaxation of the interface to obtain the total energy of the interface E_int, the lattices parallel to the interface a and b direction were fixed, and the interface model was replaced with pure Al or pure Al₃M block of the same size, then relaxing in direction c to obtain $E_{\mathrm{Al}}^{\mathrm{fix}}$ and $E_{{\mathrm{Al}}_3\mathrm{M}}^{\mathrm{fix}}$. These models were employed for the calculation in this work, and the Al/Al₃M/Al interface models were shown in Figure 1. Directions a and b represent the interface plane, while direction c is perpendicular to the interface direction.

In order to analyze the formation of the core-shell structure from the perspective of thermodynamics, the interfacial energy and the coherent strain energy between the different L1₂ phases were also calculated, and the models were adopted as shown in Figure 2.

2.3. Interface Segregation Energy

The interfacial segregation of atoms had a thermodynamic driving force to take the place of the original atoms on the interface, thus forming a new interfacial structure [18,19]. In order to investigate the formation mechanism of the core-shelled L1₂ phase, the segregation energy of atoms at various atomic layers near the different Al₃M interfaces was further investigated, which was calculated as the total energy difference before and after N atom segregation to the Al/Al₃M interfaces. The segregation energy was expressed as [31]:

$$E_{seg}^{{\mathrm{Al}}_3\mathrm{M}/N}=\left(E_{\mathrm{inter}}^{{\mathrm{Al}}_3\mathrm{M}/N}+E_{\mathrm{bulk}}^{\mathrm{site}}\right)-\left(E_{\mathrm{inter}}^{{\mathrm{Al}}_3\mathrm{M}}+E_{\mathrm{bulk}}^N\right)$$

(4)

where Al₃M/N was the segregation of N atom from matrix to the Al₃M interfaces; $E_{\mathrm{inter}}^{{\mathrm{Al}}_3\mathrm{M}/N}$ was the total energy of the interface supercell after substitution by N atom in different layer or site; $E_{\mathrm{inter}}^{{\mathrm{Al}}_3\mathrm{M}}$ was the total energy of the original interface supercell; and $E_{\mathrm{bulk}}^{\mathrm{site}}$ and $E_{\mathrm{bulk}}^N$ were the atom chemical potential (site = Al or M) in the Al solid solution calculated using a 3 × 3 × 3 fcc supercell model.

3. Results and Discussion

3.1. Interface Energy

The direct calculation method was used to separate the interfacial energy and the coherent strain energy of Al₃M/Al and Al₃M/Al₃N. The calculation results were shown in

Table 1. The lattice parameter interface energy and strain energy of Al₃M/Al interface.

Interface		Lattice Parameter (Å)			Interface Energy γ (J/m2)	Strain Energy GS (meV/Atom)
		a	b	c
Al/Al3Sc	(100)	4.075	−	36.884	0.135	3.5
	(110)	4.077	5.818	34.608	0.204	3.2
	(111)	5.760	10.039	35.255	0.221	1.7
Al/Al3Zr	(100)	4.061	−	37.182	0.078	2.3
	(110)	4.063	5.824	34.693	0.109	1.3
	(111)	5.768	10.015	35.500	0.076	1.3
Al/Al3Er	(100)	4.177	−	37.064	0.181	8.8
	(110)	4.183	5.955	35.196	0.185	7.7
	(111)	5.933	10.239	35.452	0.227	9.0
Al/Al3Y	(100)	4.201	−	37.068	0.197	9.4
	(110)	4.203	5.986	35.355	0.185	9.6
	(111)	5.964	10.286	35.513	0.231	10.8

and

Table 2. The lattice parameter, interface energy, and strain energy of Al₃M/Al₃N interface.

Interface		Lattice Parameter (Å)			Interface Energy γ (J/m2)	Strain Energy GS (meV/Atom)
		a	b	c
Al3Sc/Al3Zr	(100)	4.102	-	36.982	−0.079	0.1
	(110)	4.099	5.798	34.913	−0.021	0.2
	(111)	5.801	10.050	35.579	−0.056	0.2
Al3Er/Al3Zr	(100)	4.247	-	38.218	−0.087	4.6
	(110)	4.249	6.028	35.868	−0.047	6.5
	(111)	6.007	10.398	36.709	−0.062	5.4
Al3Zr/Al3Y	(100)	4.171	-	37.554	−0.088	6.9
	(110)	4.171	5.899	35.511	−0.048	9.1
	(111)	5.895	10.216	36.112	−0.056	7.9
Al3Er/Al3Y	(100)	4.188	-	37.673	−0.018	0.1
	(110)	4.187	5.922	35.644	−0.004	0.2
	(111)	5.915	10.254	36.204	−0.0004	0.2

. Table 1 illustrated the interface energy and strain energy of the Al₃M/Al interface in the (100), (110), and (111) facets. The calculation values of interface energy and strain energy for the Al₃Er/Al, Al₃Sc/Al, and Al₃Zr/Al interfaces generally agreed with those in other literature [18,19] using linear fittings. For the Al₃Y/Al interface, the calculations of interface energy were lower than that of the investigation by Li [22], which was related to the difference between the calculation methods. However, the order of the interface energy of different crystal facets was consistent with the reference [22], that was, Al(111)/Al₃Y(111) > Al(100)/Al₃Y(100) > Al(110)/Al₃Y(110).

The order of the strain energy of the interface between the L1₂ phase and the Al matrix was Al₃Y > Al₃Er > Al₃Sc > Al₃Zr. However, the calculation values of strain energy in (110) facets for the Al₃Er/Al, Al₃Sc/Al, and Al₃Zr/Al interfaces were higher than those in other literature [18,19] using linear fittings. In particular, the coherent strain energy of the Al₃Y/Al and Al₃Er/Al interfaces was much higher than that of the Al₃Sc and Al₃Zr phases. The coherent strain energy of L1₂-Al₃M was related to the size mismatch in the lattice constant. Compared with the pure Al lattice constant 4.049 Å, the order of the size mismatch in the lattice constant was Al₃Y > Al₃Er > Al₃Sc > Al₃Zr (Table 1), which was well agreed with the order of the strain energy of the interface. Moreover, it can be inferred that Al₃Er and Al₃Y nano-phases obtained higher creep resistance than Al₃Sc and Al₃Zr nano-phases due to their higher coherent strain energy. The effect of the Er element on the creep resistance of aluminum alloy has been verified experimentally [32].

The order of the interface energy between the L1₂ phase and the aluminum interface was Al₃Y > Al₃Er > Al₃Sc > Al₃Zr. The results indicated that the order of formation for the thermodynamically stable interface was Al₃Zr > Al₃Sc > Al₃Er > Al₃Y. The low interface energy of Al₃M/Al implied the thermodynamic driving force for the formation of a stable L1₂-Al₃M nano-phases when the L1₂-Al₃M nano-phases precipitated from the Al matrix. The lowest interface energy of Al₃Zr indicated the low coarsening rate of the Al₃Zr phase. L1₂-Al₃Sc and Al₃Er nano-phases were thermodynamically stable in aluminum alloys containing Sc, Er elements, which was well agreed with the previous investigation [6,10]. L1₂-Al₃Y nano-phase was reported to form in the rapidly solidifying Al-Y alloys during solidification [33].

Furthermore, the crystal facets had a significant effect on the interface energy of Al₃M/Al. The interface energy of Al(100)/Al₃Sc(100) was the lowest, indicating that the Al₃Sc phase tended to precipitate at (100) facets. The interface energy of (100) and (111) in Al₃Zr was lower than that of the (110) facets, indicating that (100) and (111) facets were thermodynamically favored interfaces. Al₃Er was inclined to precipitate in (100) and (110) facets. The calculation results showed that the (110) facets of Al₃Y/Al were predicted as more energy favored than (100) and (111) facets.

Al₃Zr was considered to be the ideal shell for thermodynamically stable nano precipitates due to the low coarsening rate of the Al₃Zr phase and the low diffusion rate of the Zr element. However, the L1₂-Al₃Zr nano-phase was thermodynamically metastable and transformed into the equilibrium D0₂₃ structure above 475 °C [34]. It was expected to improve the thermodynamic stability of the L1₂-Al₃Zr nano-phase through Sc, Er elements microalloying. The interface energy and strain energy between L1₂-Al₃M (Sc, Er, Y)/ Al₃Zr in the (100), (110), and (111) facets were shown in Table 2. The calculation of L1₂-Al₃Sc/Al₃Zr and L1₂-Al₃Er/Al₃Zr were generally consistent with other literature [18,19] using linear fittings. The interface energies between different L1₂ phases were very small negative (essentially zero), and it indicated that such hetero-interfaces were thermodynamically stable.

However, the interface of L1₂-Al₃Y/Al₃Zr obtained the highest coherent strain energy in comparison with other L1₂ phase interfaces. It was difficult to form a good coherent interfacial relationship. Previous studies [12] showed that Al₃Y was first precipitated in Al-Y-Zr alloy at the early aging stage and accelerated the precipitation of Zr. However, after long aging, the precipitated phase failed to form an obvious Al₃Y core/Al₃Zr shell microstructure, which agreed with the calculation results. On the other hand, the interface of L1₂-Al₃Sc/Al₃Zr and L1₂-Al₃Er/Al₃Zr had lower interface energy and better interfacial structural relationships than that of Al₃Y/Al₃Zr, thus presenting a stable core-shelled microstructure [18,19]. It can be inferred that core-shelled Al₃Er/Al₃Zr nano-phases obtained higher creep resistances than Al₃Sc/Al₃Zr and Al₃Er/Al₃Y nano-phases due to their higher coherent strain energy. Furthermore, the Al₃Er/Al₃Y and Al₃Er/Al₃Zr phases tended to form the core-shelled microstructure due to their low coherent strain energy and negative interfacial energy. If the Al₃Er interlayer can be formed between Al₃Y/Al₃Zr, the stability of the double core-shelled Al₃Y/Al₃Er/Al₃Zr can be improved in comparison with that of Al₃Y/Al₃Zr.

On the other hand, the (100) facet was the most thermodynamic favored interface among the (100), (100), and (100) facets due to its low interface energy and strain energy. The interface energy of Al₃M(100)/Al₃N(100) was the lowest, indicating that L1₂-Al₃M (Sc, Er, Y)/Al₃Zr and L1₂-Al₃Er/Al₃Y phases tended to precipitate at (100) facets. The investigation by Wang [35] also revealed that Al₃Y(001)/Al(001) was the most stable interface. Moreover, L1₂-Al₃M (Sc, Er, Y)/Al₃Zr and L1₂-Al₃Er/Al₃Y phases maintained a good coherent interface at (100) facets owing to their lowest strain energy.

3.2. Segregation Energy

In order to clarify the formation mechanism of core-shell structure and the tendency of the second solute atom segregation to the interface, the segregation behavior of the second solute element on the interface was further investigated based on the interface calculation. The thermodynamic driving forces of atomic segregation at the interface were generally estimated by Equation (4).

The segregation energy of Zr atoms at various atomic layers near the different Al₃M (Zr, Sc, Er, Y)/Al interfaces were shown in Figure 3. The Zr atom preferentially occupied the first layer of the interface at the Al matrix side. Except for plane (100), the segregation energy at Al was greater than that at M, indicating that Zr always tended to be biased towards the M site in the first layer (the first layer) on the Al side. In particular, for the Al₃Sc(100)/Al(100) facet, there was a negative segregation energy for Zr occupying the Al position, indicating that Zr may precipitate at the Al position on the surface. Except for the (100) plane, Zr atoms did not occupy the Al position. It can be seen from the above results that Zr tended to form coherent structures during the segregation of the Al₃Sc/Al, Al₃Er/Al, and Al₃Y/Al interface.

In addition, it can be seen from Figure 3d, the segregation behavior of Er atom towards the A_l3Y/Al interface was similar to that of the Zr atom, suggesting that the mixture of Y and Er may be similar to Al₃(Sc, Zr) and Al₃(Er, Zr) to form a coherent interface of Al₃Y/Al₃Er.

The difference between the segregation energy at the interface and the energy dissolving in the Al matrix or Al₃M phase represented the driving ability of the atom to segregate at the Al₃M/Al interface. In order to see the numerical difference of segregation energy in Figure 3, the segregation energy of the Al₃M layer (layer −5) and Al layer (layer 5) was subtracted, respectively, and the interface (layer 1) obtained ΔE_Al3M and ΔE_Al. The results are shown in

Table 3. The difference of the segregation energy between interface and Al₃M phase and Al layer of each L1₂ phase.

Solute Atoms	Interface		ΔEAl3M (eV/Atom)	ΔEAl (eV/Atom)
Zr	Al3Sc/Al	(100)/(100)	0.552	0.464
		(110)/(110)	0.653	0.459
		(111)/(111)	0.644	0.457
	Al3Er/Al	(100)/(100)	0.615	0.540
		(110)/(110)	0.749	0.449
		(111)/(111)	0.810	0.617
	Al3Y/Al	(100)/(100)	0.898	0.530
		(110)/(110)	1.086	0.488
		(111)/(111)	1.131	0.653
Er	Al3Y/Al	(100)/(100)	0.807	0.354
		(110)/(110)	1.030	0.480
		(111)/(111)	0.991	0.659

. ΔE_Al was the segregation energy difference to migrate from the interface to the Al matrix. The larger the ΔE_Al, the greater the driving effect of the matrix-dissolved atoms’ segregation at the interface. ΔE_Al3M was the segregation energy to be overcome when atoms migrated from the interface into the Al₃M phase. The larger the value of ΔE_Al3M, the more difficult it was for atoms to migrate into the Al₃M phase.

Similarly, Table 3 showed that the ΔE_Al3M and ΔE_Al of the Zr atom were positive, indicating that the Zr atom was inclined to segregate at the Al/Al₃Sc, Al/Al₃Er, and Al/Al₃Y interfaces, and the interfacial segregation of Zr accelerated the formation of core-shelled microstructures. On the other hand, the order of the ΔE_Al3M and ΔE_Al was Al₃Y > Al₃Er > Al₃Sc. Al₃Er and Al₃Sc had a promoting effect on the segregation of the Zr atom. The Al₃Sc/Al₃Zr and Al₃Er/Al₃Zr interfaces can be formed owing to their small interfacial energy and strain energy. It indicated that, once the core-shelled microstructure was formed, it can stably maintain a clear core-shelled interface. The ΔE_Al3M and ΔE_Al of the Zr atom segregating to the Al/Al₃Y interface were most positive, and the driving effect of the Y atom was stronger than that of Er, Sc atoms. The Y atom can promote the diffusion of the Zr atom, whereas it was difficult to form a stable core-shelled Al₃Y/Al₃Zr due to the large coherency strain energy and high mismatch between the Al₃Y and Al₃Zr. These calculation results were well consistent with the previous investigation [12,13].

Table 3 also showed that the ΔE_Al3M and ΔE_Al of Er atom to Al₃Y were positive, and Er atom tended to segregate at the Al/Al₃Y interface and accelerated the formation of core-shelled Al₃Y/Al₃Er. Al₃Y had a precipitation-driving effect for Er atom. The diffusion rate of Er was higher than that of Zr, and the core-shelled Al₃Er/Al₃Zr can be formed. Therefore, as for Al-Y-Er-Zr alloys, they can obtain a thermodynamically stable Al₃Y/Al₃Er/Al₃Zr with double core-shelled microstructure.

4. Conclusions

The interface structure and segregation behavior of L1₂-Al₃M (M = Sc, Zr, Er, Y) phases were investigated based on first-principles calculations. The calculation results and conclusions were as follows:

(1)

The order of the thermodynamically stable interface was Al₃Zr/Al > Al₃Sc/Al > Al₃Er/Al > Al₃Y/Al. The interfaces of Al₃Sc/Al₃Zr, Al₃Er/Al₃Zr, and Al₃Y/Al₃Er obtained negative interfacial energies and low coherent strain energies and were favorable to form a clear interface. The high coherent strain energy hindered the formation of the Al₃Y/Al₃Zr interface.

(2)

Zr atoms tended to segregate to the first atomic layer on the Al side of the Al/Al₃Sc, Al/Al₃Er, and Al/Al₃Y interfaces and occupied the Sc, Er, and Y lattice positions on the layer. The driving effect of the Zr atom segregation to the Al₃Y was stronger than that of Al₃Sc and Al₃Er.

(3)

Er atoms tended to segregate at the Al/Al₃Y interface and accelerated the formation of core-shelled Al₃Y/Al₃Er. It can obtain double core-shelled Al₃Y/Al₃Er/Al₃Zr microstructure for Al-Y-Er-Zr alloys.