The Effect of Gradient Cooling Behavior on the Microstructure and Mechanical Properties of Al-2at.% Nd Alloy in a Vacuum Environment

Abstract

Al-2at.% Nd alloy with a gradient cooling rate was prepared using a wedge-shaped mold in a vacuum environment. The relationship between gradient cooling behavior and the microstructure and properties of the Al-2at.% Nd alloy was investigated. The stability of the Al₁₁Nd₃ phase and the mechanical properties were confirmed through first-principles calculations. The results indicated that as the cooling rate decreased, the transformation of grain morphology in Al-2at.% Nd occurred as follows: a mixture of columnar grains and equiaxed grains→equiaxed grains. The grain size of the alloy increased. Discontinuous skeletal eutectic phases, α-Al and Al₁₁Nd₃, formed within the alloy, resulting in a reduction in the number of phase boundaries and grain boundaries. The hardness of the alloy decreased by 25.53%, and this pattern of change closely aligned with the calculated results.

1. Introduction

Aluminum alloys have garnered significant attention from researchers due to their low density, commendable corrosion resistance, and exceptional formability. These materials are extensively utilized in various sectors, including aerospace, rail transportation, automotive, maritime applications, and national defense technology [1,2,3]. However, with the rapid advancement of technology, the performance requirements for aluminum alloys are becoming increasingly stringent. Consequently, certain aluminum alloys can no longer meet specific application areas’ demands. Therefore, there is a pressing need to develop new aluminum alloys that exhibit superior properties, such as high strength, enhanced corrosion resistance, and elevated temperature resistance, to satisfy the evolving requirements of both production and everyday life [4,5,6,7].

In recent years, the Al-Nd binary alloy system has gained significant attention among researchers as a target material in sputtering coating processes. However, the production and preparation of Al-Nd target materials present considerable challenges. To ensure the quality and performance of the target material, it is essential to use high-purity raw materials and employ precise processing techniques. Alloying represents a critical method for the development of new high-performance aluminum alloys. Research indicates that incorporating rare earth elements into aluminum and aluminum alloys can significantly modify the alloy composition and substantially enhance the microstructure of these material [8,9,10,11,12]. However, there is currently limited literature on Al-Nd target materials. One study indicates that the Al-2at.% Nd alloy is predominantly utilized in advanced thin-film transistor liquid crystal displays (TFT-LCDs) due to its exceptional resistance to hillock and whisker formation, alongside its having a low resistivity (<5 μΩcm) [13]. Therefore, conducting in-depth research on the preparation processes and performance characteristics of Al-Nd target materials is highly significant for advancing the development and progress of related industries. The challenge of homogenizing the microstructure of Al-Nd target materials lies in the formation and distribution of Al-Nd intermetallic compounds. In Al-Nd target materials, Nd primarily exists in the form of the eutectic compound Al₁₁Nd₃ [14]. Unlike the research on other Al-Nd intermetallic compounds, little is currently known about the Al₁₁Nd₃ phase. Xiao et al. [15] investigated the crystallization process of rapidly solidified Al-Nd-Ni alloys, which include Al₁₁Nd₃, Al₃Ni, and several unidentified phases. Liu et al. [16] examined the stability and mechanical properties of Al-RE intermetallic compounds (Al₂RE, Al₃RE, AlRE, Al₁₁RE₃, AlRE₂, and AlRE₃), demonstrating that these intermetallic compounds can act as strengthening phases, enhancing the properties of Al alloys. Therefore, it is essential to investigate the thermodynamic stability and mechanical properties of the Al₁₁Nd₃ phase to design and produce high-quality Al-Nd target materials and to advance the development of large-sized liquid crystal display panels.

First-principles calculations, commonly referred to as ab initio calculations, are methodologies grounded in the principles of quantum mechanics that address the Schrödinger equation utilizing only fundamental physical constants, thereby eschewing any reliance on empirical parameters [17,18,19]. Researchers have undertaken comprehensive investigations into the phase structures of binary aluminum alloy systems through these first-principles calculations. By evaluating physical quantities such as electronic structure, energy, and mechanical properties of materials, they can predict the macroscopic properties of these materials. In recent years, significant advancements in material design, synthesis, and simulation calculations have emerged from integrating first-principles calculations based on density functional theory (DFT) with molecular dynamics, establishing it as a crucial foundation and primary methodology in computational materials science. Michael C. Gao [20] conducted a systematic study on the formation and stability of Al-RE intermetallic compounds. Similarly, Michal Jahnátek [21] systematically investigated the plastic deformation behavior of Al₃(Sc, Ti, and V) intermetallic compounds in the L12 and D022 structures, providing a comprehensive analysis of various elastic constants.

Adding the element Nd can further improve the thermal stability and enhance the mechanical strength of aluminum alloys. Furthermore, the Al-2at.% Nd alloy exhibits favorable casting properties and is easily processed into various shapes and sizes of components. Therefore, due to considerations of processing efficiency and economic viability, we have chosen to study the Al-2at.% Nd alloy. However, there is still limited research on Al-Nd target materials and the Al₁₁Nd₃ phase. The stability, morphological characteristics, and inherent mechanical properties of Al₁₁Nd₃ in Al-Nd target alloys are not yet fully understood, and this will be essential in order to comprehend the material’s properties. Therefore, to address this knowledge gap, this study employs wedge-shaped copper molds to cast an Al-2at.% Nd alloy. It examines the influence of cooling rate on the grain morphology, dendrite arm spacing, and eutectic phase morphology of the Al-2at.% Nd alloy. Furthermore, first-principles calculations are utilized to evaluate the alloy’s phase stability and elastic properties, thereby providing a theoretical foundation for the fabrication of Al-Nd alloy targets.

2. Experimental Methods

2.1. Sample Preparation

Samples were prepared utilizing a commercially available 4N-grade bulk Al-2at.% Nd alloy. Initially, a high-purity graphite crucible was positioned within the coil of a vacuum induction melting furnace, and the interstices were filled with magnesia sand. Subsequently, the magnesia sand was combined with water glass to achieve a paste-like consistency, which was then applied around the crucible and allowed to dry. After thoroughly cleaning the furnace chamber and crucible, we placed the Al-Nd alloy raw material into the crucible. The furnace was subsequently evacuated to establish a vacuum conducive to melting. Upon reaching a temperature of 700 °C, the melts were poured into a wedge-shaped copper mold with an inside diameter of 65 × 50 mm and a height of 120 mm. After cooling for 30 min, we extracted the ingot.

Figure 1a illustrates the internal structure of the wedge-shaped copper mold. The cast ingot is segmented into four distinct regions, designated as A, B, C, and D, arranged from the bottom to the top, as depicted in the diagram.

In order to observe the grain structure of the alloy, anodic oxidation was conducted for approximately 45 s utilizing a 10% HBF₄ solution at a voltage of 20 V and a current range of 0.3–0.5 mA. The microstructure of the anodic coating on the cast sample was examined using polarized light microscopy with a Leica DMI5000M optical microscope (Wetzlar, Germany). For deep etching, the 10% NaOH solution was employed at room temperature for a duration of 50 s. In order to study the phase composition of the alloy, rectangular samples measuring 15 mm × 15 mm × 10 mm were cut, polished, and analyzed using X-ray diffraction (XRD, Rigaku, DMAX-2500, Cu-Kα, 18 kW). The morphology and elemental composition of the phases within the cast alloy were characterized using a field emission scanning electron microscope (Tescan, Brno, Czechia, MIRA3) equipped with an X-ray spectrometer. The alloy’s grain size and secondary dendrite arm spacing were statistically analyzed using Image-Pro Plus software (6.0, Media Cybernetics, Rockville, MD, USA). Using wire cutting technology, rectangular samples measuring 20 mm × 15 mm × 10 mm were cut out of areas of ingots A, B, C, and D. The hardness of the alloy at various positions was measured using a microhardness tester (FUTURE TECH, Kawasaki, Japan).

2.2. First-Principles Calculations

All first-principles calculations conducted in this study, based on Density Functional Theory (DFT), were executed using Vienna ab initio Simulation Package software (VASP 6.3). The Projector Augmented Wave (PAW) [22] method was utilized to represent the atomic pseudopotentials, while the Perdew–Burke–Ernzerhof (PBE) [23] functional was applied to characterize the exchange-correlation energy. Each unit cell was fully optimized until the total energy and force reached the convergence standards of 1.0 × 10⁻⁵ eV and 0.01 eV/Å, respectively [24]. Furthermore, all calculations presented in this paper underwent rigorous convergence testing.

The formation enthalpy of a compound serves as a valuable metric for evaluating the stability of alloy compounds. It is typically negative and represents the energy absorbed or released during the formation of a compound from its stable elemental constituents. A smaller formation enthalpy indicates greater stability of the compound. The formula for calculating the formation enthalpy of an alloy is as follows [25]:

$$\Delta H=1/(x+y)(E_{tot}-x{E}_{bulk}^A-y{E}_{bulk}^B)$$

(1)

The Al_xNd_y alloy phase, $E_{\mathrm{tot}}$, represents the total energy of the system. $E_{bulk}^A$ and $E_{\mathrm{bulk}}^B$ are the energies of Al atoms and Cu atoms in the crystal structure, respectively. The variables x and y correspond to the quantities of Al and Nd atoms present in the crystal structure of the intermetallic compound, respectively.

Elastic constants are fundamental physical quantities that provide insight into the mechanical stability of materials. These constants characterize various mechanical properties, including strength, toughness, hardness, and brittleness. Within the linear deformation regime of materials, characterized by small strains, the relationship between stress and strain is linear, thereby conforming to Hooke’s Law [26]:

$${\mathsf{\sigma }}_i={\displaystyle \sum _{j=1}^6{C}_{ij}}{\mathsf{\epsilon }}_{ij}$$

(2)

In this context, σ and ε denote stress and strain, respectively, while C_ij represents the elastic stiffness constant. It is important to note that the indices 1 ≤ i ≤ 6 indicate that both strain and stress possess six independent components.

3. Results and Discussion

3.1. The Influence of Gradient Cooling Behavior on the Microstructure of Al-2at.% Nd Alloy

Figure 2a–d illustrate the microstructural grain morphology of samples A, B, C, and D. It is evident that samples A, B, and C comprise a combination of columnar grains and equiaxed grains. In contrast, sample D is exclusively composed of equiaxed grains. As indicated by the arrows in direction 2 of Figure 2a–d, samples A, B, and C display columnar grains adjacent to the mold wall, with the growth direction of these columnar grains oriented perpendicularly to the mold wall. This is because the heat dissipation direction near the mold wall is perpendicular to the mold wall, and the grain growth rate in this direction is higher than that in other directions, resulting in preferential growth. The latent heat released by the preferentially growing dendrites inhibits the growth of dendrites in alternative directions, leading to the solidification of columnar grains in the preferred direction [27]. In contrast, sample D solidifies at the upper section of the mold, where heat dissipation is slower and lacks a specific direction for rapid heat dissipation. Consequently, the grains do not exhibit a preferred growth direction, resulting in the absence of columnar crystals along the mold wall. When the undercooling of the components at the tips of the columnar grain exceeds the critical undercooling necessary for nucleation, equiaxed crystal nuclei will be formed in the melt (as depicted in direction 1 of Figure 2a–d). By studying the grain size of the Al-2at.% Nd alloy under various cooling rates, we can gain insights into the mechanisms of grain growth during solidification. Additionally, by controlling the cooling rate, the grain size of the Al alloy can be adjusted, allowing for the regulation of the alloy’s properties. The grain sizes of samples A, B, C, and D were statistically analyzed utilizing Image-Pro Plus software (6.0, Media Cybernetics, Rockville, MD, USA). For each sample, the grain sizes of 15 different regions were measured, and the average value was calculated. The results presented in Figure 2(a₁–d₁). Figure 2(a₁–d₁) illustrate the frequency distribution of grain sizes across the four sample regions: D, C, B, and A, respectively. As the cooling rate diminishes, the grain size progressively increases from 523.28 μm to 743.57 μm.

Figure 3 shows the microstructure of the Al-2at.% Nd alloy at different cooling rates. It is evident that a gradual decrease in the cooling rate results in a notable coarsening of the alloy’s structure. Furthermore, the secondary dendrite arm spacing of the Al-2at.% Nd alloy at different cooling rates was quantified, as depicted in Figure 4. The data indicate that, from region A to region D, the secondary dendrite arm spacing increases from 14.21 μm to 42.72 μm as the cooling rate decreases. This phenomenon occurs because when the alloy cools at a slower rate, the heat loss at the solidification front is slower, leading to a smaller degree of undercooling and a correspondingly reduced nucleation rate. As a result, fewer crystal nuclei are formed during the solidification process, and these nuclei have more time to grow, resulting in larger grains and increased secondary dendrite arm spacing. Conversely, when the cooling rate is rapid, the crystal nuclei do not have sufficient time to grow during solidification, leading to smaller grain sizes and decreased secondary dendrite arm spacing. The reduced secondary dendrite arm spacing results in a greater number of grain boundaries, which can more effectively impede the movement of dislocations and enhance the hardness of the alloy.

To thoroughly investigate the influence of cooling rate on the morphology of the eutectic phase in the Al-2at.% Nd alloy, scanning electron microscopy (SEM) was employed for observation. Based on the Al-Nd binary phase diagram (Figure 5), it is established that the predominant phase in the Al-2at.% Nd alloy is the eutectic Al₁₁Nd₃ phase. Using wire cutting technology, a square sample of 15 mm × 15 mm × 10 mm is extracted from the core of the solidified ingot. Point scanning and XRD detection were performed on various morphologies of the second phase to analyze its composition further. By integrating the results from point scanning and face scanning (Figure 6) with the XRD spectrum analysis (Figure 7), it is discernible that the black matrix (point B) corresponds to the α-Al phase. In contrast, the white eutectic phase (points A and C) is attributed to the Al₁₁Nd₃ phase.

Figure 8a–d illustrate the microstructure of the Al-2at.% Nd alloy following solidification at various cooling rates. Figure 8e–h correspond to the boxed portions in Figure 8a–d, respectively, illustrating the morphology of eutectic Al₁₁Nd₃ after deep etching with NaOH solution. The observations indicate that at higher cooling rates, the morphology of the eutectic Al₁₁Nd₃ exhibits a skeletal structure, which is embedded within the aluminum matrix. This phenomenon can be attributed to the high cooling rate and substantial undercooling, which result in an unstable growth interface of the lamellar eutectic, thereby producing a complex skeletal structure of Al₁₁Nd₃.

3.2. The Effect of Gradient Cooling Behavior on the Properties of Al-2at.% Nd Alloy

Figure 9 illustrates the evolution of hardness in Al-2at.% Nd at various cooling rates. Generally, the cooling rate has a positive influence on hardness [29]. The hardness of the Al-2at.% Nd alloy decreases with a decreasing cooling rate and increases by 25.53% with an increasing cooling rate. This is because, as the cooling rate increases, the number of alloy phases and grains also increases, leading to a higher number of phase boundaries and grain boundaries. The greater the resistance encountered during the dislocation process, the higher the hardness of the alloy. Additionally, the sub-eutectic grain refinement of Al-2at.% Nd, the finer eutectic Al₁₁Nd₃, and the reduced secondary dendrite arm spacing positively influence hardness.

3.3. Crystal Structure and Phase Stability

Figure 10a shows the crystal cell structure model of the Al matrix, which belongs to the Fm-3m space group and has a face-centered cubic structure, with a = b = c = 4.03893 Å and α = β = γ = 90°. Figure 10b presents the unit cell structure model of the Al₁₁Nd₃ phase, which has an orthorhombic structure. The space group of Al₁₁Nd₃ is Immm, with lattice constants a = 4.3565 Å, b = 10.0679 Å, c = 12.9989 Å, and α = β = γ = 90°. The lattice constants and formation enthalpy of Al and Al₁₁Nd₃ are listed in

Table 1. Lattice constants (a, b, and c/Å), angles (α, β, and γ/°), and formation enthalpy ΔH (eV/atom) of Al and Al₁₁Nd₃.

Compounds	a	b	c	α	β	γ	ΔH
Al11Nd3	4.43	9.99	12.94	90	90	90	−0.42
Al	4.04	4.04	4.04	90	90	90

. The setting of the lattice constant is consistent with the results obtained from experimental testing. The Monkhorst–Pack method is used to divide the simple Brillouin zone K-point grid of the unit cell model, with the K-point for the Al matrix set to 5 × 5 × 5 and the K-point for the Al₁₁Nd₃ phase set to 14 × 6 × 5. The plane wave cutoff energy (Ecut) is set to 400 eV for the structural optimization of the Al matrix and Al₁₁Nd₃. From Table 1, it is evident that the enthalpy of formation of Al₁₁Nd₃ is negative (−0.42 eV/atom), indicating that the Al₁₁Nd₃ phase can exist stably. This also confirms that the addition of the Nd element in the previous experiment can lead to the formation of a stable discontinuous eutectic phase at the grain boundary.

3.4. Mechanical Properties

The elastic constant is a significant physical parameter for investigating the mechanical properties of compounds and comprehending the microscopic mechanical properties of crystal structures. Additionally, to ensure the accuracy of the calculations, we set the ion movement step size to POTIM = 0.015. The face-centered cubic structure of the Al matrix is characterized by three independent elastic constants (C₁₁, C₂₂, and C₄₄). In contrast, the body-centered orthorhombic structure of the Al₁₁Nd₃ compound is defined by nine independent elastic constants (C₁₁, C₂₂, C₃₃, C₄₄, C₅₅, C₆₆, C₁₂, C₁₃, and C₂₃). The conditions for mechanical stability are calculated by the following expressions [30]:

Cubic crystal system:

$$\left\{\begin{array}{l}{C}_{11}>0\\ C_{44}>0\\ C_{11}>\left|C_{12}\right|\\ \left(C_{11}+2C_{12}\right)>0\end{array}\right\}$$

(3)

Orthorhombic crystal system:

$$\left\{\begin{array}{l}{C}_{ii}>0\left(i=1,2,3,4,5,6\right)\\ \left(C_{11}+C_{22}-2C_{12}\right)>0\\ \left(C_{11}+C_{33}-2C_{13}\right)>0\\ \left(C_{22}+C_{33}-2C_{23}\right)>0\\ \left[C_{11}+C_{22}+C_{33}+2\left(C_{12}+C_{13}+C_{23}\right)\right]>0\end{array}\right\}$$

(4)

This study calculates the elastic constants of the Al matrix and the Al₁₁Nd₃ phase to investigate the mechanical properties of the Al-Nd binary alloy. According to

Table 2. Elastic constants Cij (GPa) of Al and Al₁₁Nd₃ in the ground state.

Compounds	C11	C12	C13	C22	C23	C33	C44	C55	C66
Al	114	62					32
Al11Nd3	130.8	43.2	43.3	126.7	51.8	125.9	55.4	50.3	47.9

and Formula (4), it can be established that Al₁₁Nd₃ satisfies the stability criterion for orthorhombic crystal systems, thereby confirming its stability. The compressibility of the crystal along the x, y, and z axes is directly indicated by the values of the elastic constants C₁₁, C₂₂, and C₃₃; a higher value signifies greater resistance to compression in that particular direction. The crystal’s capacity to withstand pure shear deformation on the (100), (010), and (001) crystal planes is represented by the elastic constants C₄₄, C₅₅, and C₆₆. Table 2 presents the theoretically calculated elastic constants, revealing that C₁₁ > C₂₂ > C₃₃ for Al₁₁Nd₃ suggests that the material is more resistant to compression along the x-axis. Additionally, the relationship C₄₄ > C₅₅ > C₆₆ for Al₁₁Nd₃ indicates that it exhibits the highest resistance to shear deformation on the (100) crystal plane.

This article also determines the bulk modulus (B), shear modulus (G), Young’s modulus (E), and Poisson’s ratio (σ) of the crystalline compound utilizing the Voigt–Reuss–Hill (VRH) approximation method. The values can be computed using the following formulas [31]:

$$B_H={\displaystyle \frac{1}{2}}\left(B_V+B_R\right)$$

(5)

$$G_H={\displaystyle \frac{1}{2}}\left(G_V+G_R\right)$$

(6)

$$E={\displaystyle \frac{9B_H{G}_H}{\left(3B_H+G_H\right)}}$$

(7)

$$\mathsf{\sigma }={\displaystyle \frac{\left(3B_H-2G_H\right)}{\left[2\left(3B_H+G_H\right)\right]}}$$

(8)

In the formula, B_H, B_V, B_R, G_H, G_V, and G_R represent the bulk and shear modulus calculated using the Voigt–Reuss–Hill, Voigt, and Reuss approximation methods [32].

The bulk modulus is a physical property that quantifies the compressive strength of an alloy when subjected to external forces, and it is intrinsically linked to the chemical bonds within the material. The shear modulus represents the capacity of a material to resist shear strain; a lower shear modulus indicates a diminished ability of the material to withstand shear strain. Young’s modulus characterizes the stiffness or resistance to deformation of solid materials. Upon analyzing the data presented in Figure 11 and

Table 3. Volume modulus, shear modulus, Young’s modulus, Poisson’s ratio, and B/G of Al and Al₁₁Nd₃.

Compounds	B (Gpa)	G (Gpa)	E (Gpa)	σ	B/G
Al	79.2	29.3	71.1	0.34	2.70
Al11Nd3	70.2	46.0	113.2	0.23	1.53

, it is observed that the B value of Al₁₁Nd₃ is marginally lower than that of the Al matrix, suggesting that Al₁₁Nd₃ possesses inferior compressive strength relative to the Al matrix. Conversely, the G and E values of Al₁₁Nd₃ exceed those of the Al matrix, indicating that Al₁₁Nd₃ can resist deformation and shear strain. Generally, the plasticity and brittleness of materials within a crystalline structure can be inferred from the ratio of the bulk modulus to the shear modulus and Poisson’s ratio [33]. According to the Pugh criterion, the material is considered brittle if the Poisson’s ratio is less than 0.26 or the B/G ratio is less than 1.75. As illustrated in Figure 11b, the B/G ratio of the Al matrix exceeds 1.75, indicating that the Al matrix exhibits favorable ductility. In contrast, the B/G ratio of Al₁₁Nd₃ is below 1.75, signifying that the presence of Al₁₁Nd₃ contributes to the material’s brittleness. This also demonstrates the formation of Al₁₁Nd₃, which makes it difficult for Al-Nd alloys to undergo severe plastic deformation. The hardness changes observed in the previous experiments have been verified.

4. Conclusions

This article employs a wedge-shaped copper mold to fabricate Al-2at.% Nd alloy ingots and analyses the alloy’s microstructure and phase structure in conjunction with first-principles calculations. The findings lead to the following conclusions:

• Under varying cooling rates, the microstructure of the Al-2at.% Nd alloy displays distinct morphologies. The large grain morphology near the mold wall shows columnar crystals. Conversely, at the center of the ingot, a reduction in the cooling rate leads to a transition in grain morphology from a mixed structure of columnar and equiaxed grains to a predominantly equiaxed grain structure.
• As the cooling rate diminishes, there is a corresponding increase in grain size, which ranges from 523.28 μm to 743.57 μm. Additionally, the spacing between secondary dendrite arms expands from 14.21 μm to 42.72 μm.
• At higher cooling rates, the morphology of the Al₁₁Nd₃ phase is characterized as skeletal and embedded within the aluminum matrix. The eutectic phase of the alloy comprises α-Al and Al₁₁Nd₃. The hardness of the Al-2at.% Nd alloy decreases with a decreasing cooling rate and increases by 25.53% with an increasing cooling rate.
• According to first-principles calculations, the Al-Nd binary intermetallic compound’s formation enthalpy is negative, indicating that Al₁₁Nd₃ is thermodynamically stable. The Poisson’s ratio of Al₁₁Nd₃ is measured at 0.23, and the B/G value is calculated to be 1.53, suggesting that the compound exhibits intrinsic brittleness in its ground state.