Ab-Initio Studies of the Micromechanics and Interfacial Behavior of Al₃Y|fcc-Al

Abstract

In this paper, an Ab-initio study was employed to study the properties of interfaces of Al₃Y|Al. The interface strength, shear strength, structural stability, electronic density, bonding characteristics, stacking fault energy, and plasticity were all investigated. The interface with the stacking style of ABab or CBAcba has the greatest interface strength. The Al₃Y(111)|Al(111) interface has the highest tensile stress of 13.39 GPa for rigid stretching; and 9.39 GPa for relaxation stretching. In the stretching process, the Al₃Y(111)|Al(111) interface is prone to break on the Al₃Y side. However, the Al₃Y(010)|Al(010) and Al₃Y(110)|Al(110) interface systems tend to fracture at the interface and Al side, respectively. Moreover, the differential charge density, electron localization function, and partial density of states (PDOS) demonstrate the newly formed chemical bonds at the interface, and the chemical bonds were formed by s-p or s-p-d hybrid orbitals. According to the Rice ratio and shear stress, these interfaces were found to be plastic and the Al₃Y(111)|Al(111) interface has the best plasticity. This is significant because the formed interfaces are all advanced structure materials, which can be potentially used in automobile and aeronautical fields, even in some special industries.

1. Introduction

The lightweight, high strength, and excellent welding properties of Al and its alloys make them very popular materials for applications related to aeronautics and weapons [1,2,3,4]. However, the strength and toughness of Al for parts and equipment operated in extreme environments need to be significantly improved, which can be achieved by providing Al with transitional elements (e.g., V, Ti, Ag, Ni, Sc, Nb, and Y) to form tri-aluminide compounds [5,6,7,8,9,10,11,12,13].

In order to increase the thermal and oxidation resistance of Al alloys, it was found that adding traces of Y to the Al matrix was an extremely effective method of fine-tuning their physicochemical qualities [14,15,16,17]. Y addition to Al results in the formation of D0₁₉, D0₂₂, and L1₂ intermetallic structures, among which D0₁₉ is the most stable [18]. Yet, it is the L1₂ structure that improves the strength and plasticity of Al alloys the best. The precipitation of the L1₂-structured Al₃Y compound is very beneficial for the Al matrix: Al₃Y forms a coherent interface, and its presence enhances the creep resistance, prevents grain coarsening and inhibits dynamic recrystallization [19,20]. Another advantage is that the addition of Y increases the elastic modulus of the Al alloy effectively. To improve the ductility and strengthen Al alloys, scientists need to understand the atomic configuration and electronic structures within the modified Al matrix [21,22].

Typically, Al alloys contain various elements and precipitations. Thus, it is a challenge to explore the characteristics of every interface between L1₂ structured Al₃Y and the Al matrix experimentally. Al₃Y and bulk Al interactions may now be properly studied using density functional theory (DFT) ab-initio simulations, as condensed matter physics and computing technology continue to progress [23].

Currently, the published literature primarily focuses on properties of the single L1₂- or D0₂₂- phases in the bulk. Researchers successfully demonstrated the positive influence of the L1₂-structured Al₃Y on the Al alloy, which is even greater than the influence of the D0₂₂-Al₃Y phase [17,18,19,24]. However, data on the atomic interactions at the Al₃Y|Al interface are still limited. Therefore, in this work, we studied Al₃Y|Al interactions at the most common (010), (110), and (111) Al₃Y|Al interfaces using DFT. We believe that this analysis will help the scientific community in designing novel Al alloys with advanced properties.

The mechanical properties were analyzed using the R-W model [25,26] (which defines how the structural defects affect the overall energy of the system at the interface) and the first-principle computational tensile test [23,26] (FPCTT, (which is capable of mechanically “stretching” the interface perpendicularly to the interface). We selected two FPCTT methods to analyze the strength and fracture behavior of the matrix at its interface with the Al₃Y phase which are as follows: (1) a rigid method (widely used for the analysis of W, Ni, and Al alloy grain boundaries by modeling a pre-crack state at the corresponding interface); and (2) a relaxation method (capable of describing the fracture formation and propagation at the interface by allowing atoms in several layers to relax during the fracture-induced stretching).

Al₃Y|Al interfacial characteristics and interfacial interactions at low-indexed (010), (110), and (111) were further studied utilizing the Rice ratio and unstable stacking fault energy in various slip directions, respectively.

Furthermore, the electronic properties of different indexes at the Al₃Y|Al interface, as well as the plasticity, were also analyzed.

2. Computations

The Vienna Ab-initio Simulation Package was used to make the calculations (VASP) [27,28,29,30]. Bulk Al₃Y and Al were calculated using the Perdew–Burke–Ernzerhof [30,31] (PAW-GGA-PBE) scheme, Perdew–Wang-91 (PAW-GGA-PW91), and the local-density approximation (PAW-LDA) pseudopotential, respectively. K-mesh spacing’s sampling was set at 0.03 Å^–1. We used the Heyd–Scuseria–Ernzerhof (HSE06) technique to characterize the density of states with default settings since Y has d-electrons. The energy tolerance and force, as well as plane-wave cutoff energy, were set as 5 × 10^–8 eV/atom, 0.005 eV/Å, and 450 eV, respectively.

2.1. Optimization of Bulk Phases

We optimized the structures and calculated the lattice and elastic constants as well as formation enthalpy (ΔH^f) for the bulk Al and Al₃Y phases and compared the results with the literature data obtained experimentally (see

Table 1. ΔH^f and lattice constants calculated for the bulk Al₃Y phase using PW91, PBE, and LDA.

Bulk	Present Calculation			Previous Report
	LDA	PW91	PBE
a-Al3Y (Å)	4.231	4.242	4.229	4.233 [19], 4.259−4.324 [32]
ΔHf-Al3Y (kJ/mol)	–41.3	–44.2	–45.3	−45.2 [19], −46.4 [32], −49.4 [32]
a-Al (Å)	4.051	4.109	4.052	4.048, 4.049 [33]

and

Table 2. Elastic constants as well as Young’s (E), bulk (B), and shear(G) moduli.

		C11 (GPa)	C12 (GPa)	C44 (GPa)	B (GPa)	G (GPa)	E (GPa)
Al3Y	LDA	171.32	37.85	63.26	74.61	56.45	147.71
	GGA	164.24	36.66	61.81	76.85	61.88	144.58
	PBE	168.51	36.24	62.68	76.33	61.72	145.15
	Previous [17,32,33]	168.48	34.76–35.14	60.35–62.55	76.30	61.71	145.28
Al	LDA	99.10	55.67	29.76	70.15	26.54	70.71
	GGA	102.31	58.12	30.17	72.85	26.94	71.95
	PBE	101.87	54.38	30.05	70.21	25.53	73.04
	Previous [25]	95–108	44–62	28–33	61–77	30–31	69–82

). The ΔH^f of Al₃Y was calculated using Equation (1):

$$\Delta H^f=\frac{1}{4}\left({\mu }_{A{l}_{3}Y}^{bulk}-3{\mu }_{Al}^{bulk}-{\mu }_Y^{bulk}\right)$$

(1)

where ${\mu }_{Al}^{bulk}$, ${\mu }_{A{l}_{3}Y}^{bulk}$, and ${\mu }_Y^{bulk}$ are the chemical potentials of one atom in the corresponding bulk phases.

The elastic constants were calculated to ensure structural stability and are shown in Table 2, satisfying the generalized stability criteria for cubic crystals: C₁₁ + 2C₁₂ > 0, C₁₁ > |C₁₂|, and C₄₄ > 0. The shear (G), bulk (B), and Young’s (E) moduli were obtained using the Voigt–Reuss–Hill method. All values are in reasonable agreement with the literature values (see Table 2), confirming the reliability of our calculations and the stability of the optimized structure.

2.2. Low-Index Surfaces Properties

Several atomic layers of Al and Al₃Y were stacked to create the slab surface, which revealed the optimal arrangement with the lowest possible slab surface energies and the most stable structure. Figure 1 shows the stacked styles of the models.

The reasonable thickness of the surface model was judged by the change in the layer distance (Δ_ij(%), calculated using Equation (2)) of the relaxed models.

Table 3. Deviation of the layer distances after optimization.

Surface		Deviation (%) (010)			Deviation (%) (110)			Deviation (%) (111)
		5	7	9	5	7	9	5	7	9
Al3Y-Al	Δ12	2.7	1.8	1.9	−13.8	−26.6	−10.8	-	-	-
	Δ23	0.4	0.7	0.9	8.5	17.6	1.8	-	-	-
	Δ34	-	0.6	0.5	-	2.9	−0.9	-	-	-
	Δ45	-	-	0.4	-	-	0.4	-	-	-
					-	-	-	-	-	-
Al3Y-AlY	Δ12	−11.3	−8.9	−9.7	10.7	2.4	−5.1	1.6	1.2	2.1
	Δ23	2.2	2.9	3.1	16.9	1.8	6.9	1.3	1.5	1.3
	Δ34	-	−0.5	−1.1	-	−0.4	2.1	-	0.6	0.48
	Δ45	-	-	0.4	-	-	0.3	-	-	0.4
					-	-	-	-	-	-
Al	Δ12	4.3	3.8	−0.3	3.9	5.2	6.2	2.9	3.2	−0.6
	Δ23	5.6	1.9	2.8	−0.8	−1.7	5.5	−1.4	−0.3	1.4
	Δ34	-	2.2	0.9	-	2.7	−0.8	-	0.8	0.2
	Δ45	-	-	0.3	-	-	0.3	-	-	−0.1

shows the interlayer space before and after optimization.

$${\Delta }_{ij}\left(\%\right)=\frac{d_{ij}^{slab}-d_{in}^{slab}}{d_{in}^{sur}}\times 100\%$$

(2)

where $d_{ij}^{slab}$ (j = i + 1) and $d_{in}^{slab}$ are the atomic-layer spaces of the optimized and unoptimized surface models, respectively.

The Δ₄₅ values for the modelled (010) and (110) surfaces are <0.5% (see Table 3). Thus, nine atomic layers should be sufficient to demonstrate the bulk properties of material during the modeling of the internal interfaces. The Δ₃₄ values for the (111) surface were <0.5%. Therefore, a layer containing seven atomic layers should be sufficiently thick.

2.3. Interface Modeling

The interfaces Al₃Y(110)|Al(110), Al₃Y(111)|Al(111), and Al₃Y(010)|Al(010) were developed using data from prior papers. The vacuum in each model was 14 Å. Post-optimization misfits of these models accounted for 0.74% which was <1%; therefore, we concluded that the lattice distortion was too small to destabilize the interface stability [34,35]. Figure 2 shows the atom arrangements at these various interfaces.

3. Results and Discussion

The structural stability, electrical properties, interfacial strength, and plasticity of Al₃Y|Al surfaces are examined in this section.

3.1. Micromechanics and Separation Energies of Al₃|Y

To explain the Al₃Y|A interface’s fracture behavior and strength, we used (1) rigid and (2) relaxed methods, respectively. The interface considered by the rigid method was separated at the pre-cracked interface by the twenty 0.03 nm steps. A rupture in the interfacial area was ensured in this situation since all atoms’ locations were fixed. When using a relaxation strategy, only the locations of terminal atoms that were set to guarantee the systems were fractured at their weakest point. In this case, the separation energy (E_sep, calculated as shown in Equation (10)) and interfacial strength were calculated based on the relationship between separated (extended) distances (x) and corresponding energy.

$$E_{sep}=\frac{E_{sg}-E_{init}}{A_{in}}$$

(3)

where E_sg and E_init are the energies with and without interface separation, and A_in is the interfacial area. In order to determine the correlation between E_sep and x, techniques described in the literature were used [26]:

$$f\left(x\right)=E_{sep}-E_{sep}\times \left(1+\frac{x}{\lambda }\right)\times e^{-\frac{x}{\lambda }}$$

(4)

Originally, Equation (4) universally described the interactions between the atoms at the interface [26]. For metals, a better match between atomic spacing and micro stress might be achieved by varying f(x). In this case, the micro tensile stress can be expressed as:

$$f^{\prime }\left(x\right)=\frac{E_{sep}x}{{\lambda }^2}\times e^{-\frac{x}{\lambda }}$$

(5)

If x = λ in Equation (5), the theoretically micro tensile stress will reach its maximum (σ_max, see Equation (6). In general, the work of adhesion (W_ad) defines the interfacial wettability, which determines the maximum separation energy. The greater the work of adhesion, the easier the interface is to form

$${\sigma }_{max}=f^{\prime }\left(x\right)=\frac{E_{sep}x}{{\lambda }^2}\times e^{-\frac{x}{\lambda }}=\frac{E_{sep}}{\lambda e}$$

(6)

Separation energies and theoretically micro tensile stresses obtained by the rigid method are presented in Figure 3 and

Table 4. Separation distance (D_sep), work of adhesion (W_ad), fracture energy (E_fra), and maximum tensile stress (σ_max) of the interfaces.

Method	Interface	Wad (J/m2)	σmax (GPa)	Dsep (nm)
Rigid	Al3Y(010)/Al(010)	2.07	13.28	--
	Al3Y(110)/Al(110)	2.40	12.97	--
	Al3Y(111)/Al(111)	1.93	13.39	--

. The maximum adhesion work for different stacked types of (010), (110), and (111) interfaces is 2.07, 2.40, and 1.93 J/m², respectively.

For the Al₃Y(110)/Al(110), Al₃Y(010)/Al(010), and Al₃Y(111)/Al(111) interfaces, the σ_max were calculated to be equal to 12.97, 13.28 and 13.39 GPa, respectively. The interface with the second stacking style (Model2) yielded the highest adhesion value (W_ad) as well as theoretical tensile stress, which reflects good wettability and strength. Additionally, the atoms in this model were arranged similarly to the Al₃Y or bulk Al. Thus, the interfacial structure determines the interfacial strength of the same low-index interface.

3.2. Interface Energy

Because the second stacking style (Model2) provided the best wettability and highest strength, we selected it for further analysis and applied a relaxation method to understand the fracture of the relevant interfaces. To further understand the stability and rationality of these interfaces, the interface energy was calculated. First of all, we calculated the surface energy of Al and Al₃Y using Equations (7) and (8), respectively [36,37]:

$${\gamma }_{sur}=\frac{E_{Al}^{slab}-M\times {\mu }_{Al}^{bulk}}{2A}$$

(7)

$${\gamma }_{sur}=\frac{1}{2A}\left(E_{slab}-M_{Al}\times {\mu }_{Al}^{slab}-M_Y\times {\mu }_Y^{slab}\right)$$

(8)

where the E^slab is the surface energy, A is a single surface area, M expresses the amount of aluminum or the yttrium atom, and ${\mu }_i^{bulk}$ and ${\mu }_i^{slab}$ express the chemical potential of i atom in the bulk and slab, respectively.

Since the Al₃Y(111) surface is stoichiometric, Equation (4) can be simplified as follows:

$${\gamma }_{sur}=\frac{1}{2A}\left(E_{slab}-M_Y\times {\mu }_{A{l}_{3}Y}^{bulk}\right)$$

(9)

Since the surfaces of Al₃Y(010) and Al₃Y(110) are non-stoichiometric, Equation (9) should be expanded as shown in Equation (10) [37].

$${\gamma }_{sur}=\frac{1}{2A}\left(E_{slab}-M_Y\times {\mu }_{A{l}_{3}Y}^{slab}+\left(3M_Y-M_{Al}\right)\times {\mu }_{Al}^{slab}\right)$$

(10)

The following equations (Equations (11) and (12)) were obtained from a connection between bulk Al₃Y and its ΔH^f:

$$3{\mu }_{Al}^{slab}+{\mu }_Y^{slab}={\mu }_{A{l}_{3}Y}^{bulk}=3{\mu }_{Al}^{bulk}+{\mu }_Y^{bulk}+\Delta H^f$$

(11)

$${\mu }_{Al}^{slab}-{\mu }_{Al}^{bulk}<0\mathrm{and}{\mu }_Y^{bulk}-{\mu }_Y^{slab}>0$$

(12)

Thus, by combining Equations (11) and (12), we obtain:

$$\frac{1}{3}\Delta H^f<{\mu }_{Al}^{slab}-{\mu }_{Al}^{bulk}<0$$

(13)

The surface energy of Al and Al₃Y was calculated and is detailed in Figure 4 and

Table 5. Interfacial (γ_int) energy obtained using Model 2 and calculated surface energies (γ_sur) of Al and Al₃Y.

Energy (J/m2)	001	110	111
γsur(Al3Y-AlY)	0.727–1.374	1.041–1.428	1.122
γsur(Al3Y-Al)	1.229–1.755	1.182–1.569
γint(Al3Y/Al)	0.315	0.279	0.366

.

As shown in Figure 4, the values of the γ_sur for Al and Al₃Y (111) were constant and did not depend on the chemical environment, which was not the case for the (010) and (110) surfaces of Al₃Y. As the $\left({\mu }_{Al}^{slab}-{\mu }_{Al}^{bulk}\right)$ value increased, the γ_sur of Al₃Y-Al decreased, while it increased for the Al₃Y-AlY interface. Under Al-deficient conditions, the surface energies of Al₃Y adhere to the following sequence: Al₃Y-AlY(010) > Al₃Y-AlY(110) > Al₃Y(111) > Al₃Y-Al (110) > Al₃Y-Al (010); however, under the Al-rich conditions, it changes into Al₃Y-Al(110) > Al₃Y-Al(010) > Al₃Y-AlY(010) > Al₃Y-AlY(110) > Al₃Y(111). So, in the Al-rich environment, the structural stability of AlY surfaces from strong to weak is (111) > (110) > (010), which agrees well with the general rule mentioned in Ref. [34] and shows that the (111) surface is most stable.

The $\left({\mu }_{Al}^{slab}-{\mu }_{Al}^{bulk}\right)$ is zero because of the Al-rich ambiance at the interface. This resulted in γ_sur values for the AlY surface of 1.221, 1.185 and 1.132 J/m² for (010), (110) and (111) surfaces. According to Equation (14) [36,37], we computed the appropriate interface energies (γ_int) to be 0.315, 0.279, and 0.366 J/m², respectively.

$${\gamma }_{int}=\frac{1}{A}\left[E_{int}-M_Y\times {\mu }_{A{l}_{3}Y}^{bulk}+\left(3M_Y-M_{Al,AlY}\right)\times \left({\mu }_{Al}^{bulk}+\left({\mu }_{Al}^{slab}-{\mu }_{Al}^{bulk}\right)\right)-M_{Al,Al}\times {\mu }_{Al}^{bulk}\right]-{\gamma }_{s,Al\left(hkl\right)}-{\gamma }_{s,A{l}_{3}Y\left(hkl\right)}$$

(14)

M_Y, M_Al,AlY, and M_Al,Al indicate the amount of Y and Al atoms on the Al₃Y and Al sides, respectively. The surface energy of Al and Al₃Y-AlY are represented by ${\mathsf{\gamma }}_{s,Al}$ and ${\mathsf{\gamma }}_{s,AlY},$ respectively.

Further, we calculated electron migration according to the deformation charge density of these interfaces (see Figure 5). The blue cloud indicates electronic decreases; however, the yellow cloud represents the opposite. The results indicate Al and Y electrons migrated to the interface to form new chemical bonds to strengthen the interface and improve its wettability. The electrons at the interfaces of Al₃Y(010)|Al(010) and Al₃Y(110)|Al(110) gather closer to the Al side, while the electron cloud for the Al₃Y(111)|Al(111) system is more evenly distributed at the center plane of the interface (see Figure 5a–c). Then, we analyzed the type of chemical bond by calculating the electron localization functions (ELF). The value of the green part approximates 0.5 and the yellow part approximates 0.75; therefore, the formed chemical bond at the interface contains a covalent bond and metal bond. (see Figure 5a‘–c‘).

3.3. Partial Density and Bonding Nature of States

At the Al₃Y(010)|Al(010) interface, the projected partial density of states (PDOS) for Al and Y were equivalent to −1.72, 1.74, and 2.85 eV, which indicates the development of new chemical bonds and s-p or s-p-d hybrid orbitals. These data are also consistent with the data shown earlier in Figure 6. At E_f = 0, PDOS ≠ 0, it shows the system has significant conducting qualities and that there are several energy levels present at the Fermi level.

The PDOS for the Al, AlY-Al, and Y at the Al₃Y(110)|Al(110) interface was equal to −1.79, 1.11, and 2.76 eV (see Figure 7); this confirms the information in Figure 7 and also suggests the creation of novel chemical bonds and s-p-d hybrid orbitals (b). Similarly, for the Al₃Y(110)|Al(110) interface, PDOS ≠ 0 at E_f = 0. Thus, the system is a conductor.

In Figure 8, the PDOS for the Al, AlY-Al, and Y for the Al₃Y(111)|Al(111) interface were equal to −1.82, −0.37, and 1.51, and 2.15 eV, respectively, which indicates the formation of s-p-d hybrid orbitals.

3.4. Fracture Behavior and Toughness of The Interface

Although understanding the theoretical rigid tensile stress provides us with the tools to demonstrate interfacial strength, a deeper analysis of the interfacial fracture progression, consequently, is still needed to discover the weakest point. For this purpose, we graphed the fracture process for the Al₃Y(010)/Al(010) interface (see Figure 9). While a bilayer of Al atoms adhered to the Al₃Y side, the fracture path was concentrated on the Al side (see Figure 9a’–e’ for specific electronic configurations). The electron cloud density on the Al₃Y side drops due to the continuous stretching in response to the applied stress. Fractures begin to spread on the Al side as the straining proceeds.

No modifications to the atom configurations were seen in the electronic alterations of the Al₃Y(110)|Al(110) interface throughout the fracture propagation as determined by the relaxation approach (see Figure 10). During stretching, the interface electron cloud first decreases, forming electron-hole pairs at the interface. When the electronic hole cloud expands substantially, the interface breaks.

The electron density changes during the fracturing of the Al₃Y(111)|Al(111) interface obtained using the relaxation method are shown in Figure 11. The atomic arrangement of the Al₃Y side changed significantly with the fractured surface appearing on the Al₃Y side. The electron cloud density decreases substantially in several places (see Figure 11b). Upon continuous stretching, three of these places converted into electron holes (marked as blue dotted circles in Figure 11). Finally, a fracture surface formed along the electron-hole between the third and fourth layers on the Al₃Y side.

Then, we calculated the separation energy and tensile stress using the relaxation method and the results are shown in Figure 12 and

Table 6. Separation distance (D_sep), maximum separation energy (E_fra), and maximum tensile stress (σ_max) of the interfaces.

Method	Interface	Efra (J/m2)	σmax (GPa)	Dsep (nm)
relaxation	Al3Y(001)/Al(001)	2.90	8.59	0.311
	Al3Y(110)/Al(110)	2.23	9.34	0.432
	Al3Y(111)/Al(111)	3.76	9.39	0.513

.

Combing Figure 12b and Table 6, we can find the Al₃Y(111)|Al(111) system has the maximum tensile stress (9.39 GPa), and the tensile stress values for Al₃Y(001)|Al(001) and Al₃Y(110)|Al(110) systems are 8.59 Gpa and 9.34 Gpa, respectively. These results indicate that the Al₃Y(111)|Al(111) system greatly improves the strength and toughness of the alloy.

To comprehend the intrinsic characteristics of the toughness of different Al|Al₃Y interfaces, we investigated the stacking fault energies (γ_sf) and Rice ratios (D_R) [38,39,40]. Upon applied forced and during deformation, the interfaces were expected to either form (1) interfacial cleavage or (2) dislocations to propagate the interfacial slip [41]. It is reasonable to assume that the interfacial dislocation at critical energy (G_d) is lower than W_ad. The maximum γ_sf and critical energy (G_d) are often equivalent. The critical energy must be overcome during the slide.

$$G_d={\gamma }_{sf}=\frac{E_{sf}-E_0}{A}$$

(15)

where $E_{sf}$ is the interface system’s total energy with stacking faults, and E₀ is the energy without, respectively. Therefore, the Rice ratio (D_R) can be used to determine the plasticity of the interface system. The interface exhibits plasticity unless D_R < 1, in which case the interface is brittle. γ_ms is the maximum γ_sf.

$$D_R=\frac{G_c}{G_d}=\frac{W_{ad}}{{\gamma }_{ms}}$$

(16)

To better understand the investigated properties, we calculated two additional parameters (shear stress (F_S) and stress ratio (S_R)) according to Equations (17) and (18).

$$F_S=\frac{d{\gamma }_{sf}}{dx}$$

(17)

$$S_R=\frac{{\sigma }_{max}}{S_S}$$

(18)

where x is the displacement and S_S is the max value of the F_S.

Figure 13 shows the stacking fault energies we used to define the flexibility of our surfaces, and

Table 7. Maximum generalized unstable stacking fault energy, shear stress and corresponding Rice ratio (D_R) and stress ratio for Al₃Y(001)|Al(001), Al₃Y(110)|Al(110), and Al₃Y(111)|Al(111).

Interface System	Al3Y(010)/Al(010)		Al3Y(110)/Al(110)		Al3Y(111)/Al(111)
	<100>	<101>	<001>	<-110>	<-110>	<11-2>
${\gamma }_{ms}$(J/m2)	1.26	0.70	1.25	1.28	1.61	0.59/2.43
DR	1.64	2.95	1.92	1.87	1.20	3.27/0.79
SS(GPa)	10.95	8.71	15.38	15.37	20.08	32.31
SR	1.21	1.52	0.84	0.84	0.67	0.41

summarizes γ_ms, D_R, S_S and S_R. When the slippage at the Al₃Y(010)|(010) interface occurs in the <100> and <101> directions, γ_ms and D_R will be equal to 1.26 and 0.07 J/m², and 1.64 and 2.95, respectively, which indicates that the higher plasticity in the <101> direction. Additionally, the S_S in <101> direction is less than that in <100>; therefore, the slippage initiation will occur more easily in the <101> direction. γ_ms and D_R values for the Al₃Y(110)|Al(110) interface in the <001> and <1−10> directions will be equal to 1.25 J/m² and 1.28 J/m², and 1.92 and 1.87, respectively. Similar D_R values indicate a similar toughness along the <001>and <1−10> directions, and the S_S value also supports this conclusion.

Analysis of the stacking fault energy at the Al₃Y(111)|Al(111) interface (shown in Figure 13e,f) revealed that slippage will occur more easily in the <1−10> direction (since the corresponding max shear stress is 20.08 GPa).

All D_R values were greater than 1 (see Table 7). Thus, slippage at the Al₃Y|Al will occur more easily than cleavage. The best plasticity (judging by the corresponding D (equal to 3.27) and μ/b < 0.711) would be in the <11–2> direction. The max tensile strength of Al₃Y(010)|Al(010) is greater than the shear stress; however, the result of Al₃Y(110)|Al(110) and Al₃Y(111)|Al(111) is the opposite. Additionally, Al₃Y(111)|Al(111) has the largest shear stress in the <11−2> direction. The Al₃Y(111)|Al(111) interface is strongly recommended as it will increase the strength and improve the plasticity of Al alloys.

4. Conclusions

First-principles DFT simulations were used to develop an Al alloy with the required qualities by calculating the thermodynamics, mechanics, and electronic structure of the Al₃Y|Al interface. The simulation results and conclusions are outlined below.

• FPCTTs performed using the rigid method demonstrated the highest W_ad value for the Al₃Y|Al with a bulk-like stacked style. The Al₃Y(110)/Al(110) has the highest W_ad, which indicates that it is easiest to form.
• The Al₃Y(010)|Al(010) interface configuration would break on the Al side of the interface, while Al₃Y(110)|Al(110) and the Al₃Y(111)|Al(111) interfaces would very likely dissociate at the interface and on the Al₃Y side, respectively.
• The ELF and deformation charge density confirmed the existence of both metallic and covalent connections. The partial density of the states shows that s-p and s-p-d hybrid orbitals are formed among the Al and Y atoms at the interface.
• The D_R, FPCTT values validated the Al₃Y|Al interface’s superior toughness, tensile strength and shear strength. The results confirmed that Al₃Y(111)|Al(111) possessed the highest interfacial strength and plasticity. The results are significant because they can be potentially used in automobile and aeronautical fields, and even in some special industries.