Dispersion of TiB₂ Particles in Al–Ni–Sc–Zr System Under Rapid Solidification

Abstract

The dispersion behavior of ceramic particles in aluminum alloys during rapid solidification critically affects the resulting microstructure and mechanical performance. In this study, we investigated the nucleation and growth of Al₃(Sc,Zr) on TiB₂ surfaces in a 2TiB₂/Al–8Ni–0.6Sc–0.1Zr alloy, fabricated via wedge-shaped copper mold casting and laser surface remelting. Thermodynamic calculations were employed to optimize alloy composition, ensuring sufficient nucleation driving force under rapid solidification conditions. The results show that the formation of Al₃(Sc,Zr)/TiB₂ composite interfaces is highly dependent on cooling rate and plays a pivotal role in promoting uniform TiB₂ dispersion. At an optimal cooling rate (~1200 °C/s), Al₃(Sc,Zr) nucleates heterogeneously on TiB₂, forming core–shell structures and enhancing particle engulfment into the α-Al matrix. Orientation relationship analysis reveals a preferred (111)α-Al//(0001)TiB₂ alignment in Sc/Zr-containing samples. A classical nucleation model quantitatively explains the observed trends and reveals the critical cooling-rate window for composite interface formation. This work provides a mechanistic foundation for designing high-performance aluminum-based composites with uniformly dispersed reinforcements for additive manufacturing applications.

1. Introduction

Ceramic particles such as TiB₂, TiC, Al₂O₃, and Y₂O₃ are instrumental in refining the solidification microstructure of aluminum alloys [1,2]. Compared to the individual addition of M elements or ceramic particles, the simultaneous incorporation of both (e.g., Sc and Zr as M elements, and TiB₂ as the ceramic phase) offers three distinct advantages. First, TiB₂ exhibits high chemical stability in liquid Al, and its high volume fraction ensures an adequate number of nucleation sites to promote the columnar-to-equiaxed grain transition during rapid solidification. Second, the formation of intermediate Al₃(Sc,Zr) phases significantly enhances the nucleation potency of TiB₂ particles, potentially reducing the lattice mismatch at the TiB₂/α-Al interface from 4.22% to as low as 1% [3,4]. Third, TiB₂ promotes the precipitation of Al₃(Sc,Zr) by lowering its nucleation barrier and incubation time, thereby enhancing the grain refinement efficiency of Sc/Zr under rapid solidification conditions. Additionally, the low-mismatch TiB₂/α-Al interface facilitates the incorporation of TiB₂ particles into the growing α-Al grains, thereby mitigating their agglomeration at grain boundaries. If the heterogeneous nucleation rate of Al₃(Sc,Zr) is sufficiently high while its growth is effectively suppressed, these intermetallics may uniformly encapsulate TiB₂ particles. The nucleation and growth behavior of Al₃(Sc,Zr) is strongly influenced by the concentrations of Sc and Zr, as well as the applied cooling rate [5,6].

In this study, the Al–Ni system was chosen as the base alloy due to its widely recognized potential for enhancing mechanical properties over a wide temperature range [7]. Al-Ni alloys, particularly those containing high Ni content, derive significant strengthening from the in situ formation of stable Al₃Ni intermetallic phases during solidification [8]. This endows them with promising room-temperature strength and, critically, good elevated-temperature properties, making them attractive candidates for structural applications demanding thermal stability, such as components in aerospace or automotive sectors [9,10]. However, a significant challenge hindering the wider utilization of these alloys, especially in near-net-shape manufacturing processes like laser powder bed fusion (LPBF), is their inherent solidification behavior under rapid cooling conditions. Rapid solidification of Al-Ni alloys often results in the development of highly directional, coarse columnar grain structures [11]. This pronounced columnar grain growth leads to marked anisotropy in mechanical properties, meaning the material’s performance (e.g., strength, ductility) varies significantly depending on the direction relative to the solidification direction. Such anisotropy is undesirable as it can compromise the structural integrity and reliability of fabricated parts [12,13]. Consequently, for effectively controlling the solidification microstructure to suppress columnar growth and promote a more uniform, equiaxed grain morphology remains a critical research gap for realizing the full potential of high-performance Al-Ni based alloys in advanced manufacturing. Building upon our prior work in a 5TiB2/Al-4.5Mg-0.7Sc-0.2Zr model system [14], where precise cooling-rate control (~1000 °C/s) enabled the formation of a coherent 10–30 nm Al₃(Sc,Zr) 3DC interphase at TiB2/α-Al interfaces, reducing lattice mismatch to <1%, the present study extends this interfacial design strategy to Al-Ni alloys. The established principle that critical cooling rates govern the transition between strained 2DCs and coherent 3DCs directly informs our investigation of TiB₂/Al₃(Sc,Zr) nucleation kinetics in the Al-8Ni matrix. Specifically, we probe whether Ni’s influence on liquidus depression and atomic diffusion modifies the optimal cooling window (previously~1000 °C/s for Al-Mg) needed to achieve low-misfit multi-structural interfaces under rapid solidification.

This study investigated the heterogeneous nucleation and growth of Al₃(Sc,Zr) at the TiB₂ interface under rapid solidification conditions and evaluated the effect of the Al₃(Sc,Zr)/TiB₂ composite interface on TiB₂ particle dispersion. Based on the Al–Ni system, a model alloy (2TiB₂/Al–8Ni–0.6Sc–0.1Zr) was designed through thermodynamic calculations to facilitate the formation of such composite interfaces. Subsequently, both 2TiB₂/Al–8Ni–0.6Sc–0.1Zr and 2TiB₂/Al–8Ni alloys were fabricated via wedge-shaped copper mold casting and laser surface remelting to examine the nucleation and growth kinetics of Al₃(Sc,Zr) on TiB₂ surfaces in the 2TiB₂/Al–8Ni–0.6Sc–0.1Zr system. Finally, the mechanism by which the Al₃(Sc,Zr)/TiB₂ interface promotes TiB₂ dispersion was systematically analyzed.

2. Materials Design

Figure 1 shows the Al-rich end of the Al–xSc–yZr system, where the ratio of Sc to Zr is fixed at 3:1. All compositions in this work are given in mass fractions unless otherwise stated. The contour lines demonstrate the driving force for Al₃(Sc,Zr) precipitation from the undercooled melt. Under equilibrium solidification conditions, the precipitation of the Al₃(Sc,Zr) phase must occur before the formation of α-Al (660 °C), which requires the total content of Sc and Zr to exceed 0.03 wt.%. Under rapid solidification, however, the solute trapping effect [14,15,16] markedly increases the solubility of Sc and Zr in the α-Al matrix, thereby necessitating a higher overall concentration of these elements for Al₃(Sc,Zr) precipitation. A key prerequisite for achieving uniform encapsulation of each TiB₂ particle by Al₃(Sc,Zr) is an elevated heterogeneous nucleation rate of the intermetallic phase on the TiB₂ substrate. According to classical nucleation theory [5], the intrinsic factors governing the nucleation rate of Al₃(Sc,Zr) include the volumetric driving force, interfacial energy, and solute diffusivity. Among these, the driving force is the primary controlling factor when varying the Sc and Zr concentrations in the melt. Specifically, when the total Sc and Zr content increases from 0.3 wt.% to 0.9 wt.%, the nucleation driving force for Al₃(Sc,Zr) in a supersaturated Al–Sc–Zr melt (undercooled to 800 °C) increases sevenfold from 500 J/mol to 3500 J/mol, as depicted in Figure 1. Therefore, under rapid solidification conditions, a practical and efficient strategy for ensuring the formation of sufficient Al₃(Sc,Zr) to encapsulate TiB₂ particles is to increase the Sc and Zr content in the melt.

Another essential prerequisite for the encapsulation of TiB₂ particles by Al₃(Sc,Zr) is the complete dissolution of Sc and Zr atoms in the melt prior to solidification. If not achieved, these atoms will preferentially precipitate onto existing Al₃(Sc,Zr) particles, consuming the available Sc and Zr in the melt and leading to the formation of coarse primary Al₃(Sc,Zr) phases. Therefore, for a given alloy composition, the casting temperature of the melt must exceed the melting point of the Al₃(Sc,Zr) phase. In conventional casting processes, to minimize elemental evaporation and burn-off, the casting temperature is typically limited to temperatures below 1000 °C. This study adheres to this limitation to guide the selection of Sc and Zr content. Given the high mechanical performance of LPBF Al–Ni-Sc-Zr alloys [17], the 2TiB₂/Al–8Ni–Sc–Zr system is selected to investigate the proposed strategy for enhancing performance. High-throughput calculations of nucleation driving force and solidification path (based on the Scheil model) were conducted to determine the optimal Sc and Zr concentrations. These calculations were performed using CALPHAD (CALculation of PHAse Diagram) method in conjunction with a thermodynamic database of the Al–Ni–Sc–Zr–Ti–B system established by this work (see Section 3). The liquid phase and the relevant MB₂ (M = Ti, Sc, Zr) compounds were set as active, while the competing L1₂ variants, including Al₃(Sc,Zr), Al₃(Zr,Sc), Al₇₅Sc₁₆Zr₉ (τ₁), and Al₇₅Sc₁₀Zr₁₅ (τ₂), were suppressed, thereby yielding the nucleation driving force envelope for the L1₂ phases (Figure 2a). For the specific melt, only Zr-stabilized L1₂-Al₃Sc was treated as dormant to match the observed precipitation of Al₃(Sc,Zr) phases on TiB₂ particles [14]. Figure 2a illustrates the nucleation driving forces of the L1₂ phases from supersaturated melts at 600 °C, whereas Figure 2b presents a contour map of their dissolution temperatures. Unlike the Al–Mg database used in prior work [14], this database explicitly parameterizes the strong Ni–Sc and Ni–Zr interactions critical to the Al-8Ni matrix. The calculated liquidus projection (Figure 2a) and 600 °C isothermal section (Figure 2b) reveal that Ni (i) expands the nucleation temperature window for L1₂-Al₃(Sc,Zr) by approximately 15 °C (890–905 °C vs. 733–890 °C in Al–Mg), extending the integration bounds in Equations (4) and (5); and (ii) reduces the maximum thermodynamic driving force (ΔGᵥ) for nucleation by ~12% at equivalent undercoolings, thereby directly impacting the nucleation-rate integrals defined in Section 4. These quantitative distinctions—inaccessible with Mg-system databases—directly perturb nucleation kinetics and necessitate model recalibration for Ni-dominated alloys.

Although adding equal amounts of Sc and Zr most effectively enhances the precipitation driving force of the Al₃(Sc,Zr) phase, this strategy also substantially raises its melting temperature with increasing solute content. For instance, when both Sc and Zr are set at 0.4 wt.%, the melting point of Al₃(Sc,Zr) increases to approximately 1010 °C (Figure 2b), which exceeds the practical limits of conventional aluminum alloy processing. Moreover, at equal Sc and Zr concentrations, multiple Al₃(Sc,Zr) sub-phases, such as Al₇₅Sc₁₀Zr₁₅ (τ₂) and Al₇₅Sc₁₆Zr₉ (τ₁), are likely to form in the melt, complicating phase identification and analysis. To balance the requirements of maintaining a sufficiently high precipitation driving force, controlling the melt casting temperature, and minimizing compositional complexity, this study adopts a target composition of 0.6 wt.% Sc and 0.1 wt.% Zr.

3. Materials and Methods

3.1. Materials Fabrication

A 2TiB₂/Al–8Ni–0.6Sc–0.1Zr ingot was fabricated in a custom-designed wedge-shaped copper mold (Figure 3a). To measure the cooling rates at different positions within the wedge-shaped copper mold, K-type thermocouples were placed at the center of each section at heights of 42 mm, 32 mm, 22 mm, 12 mm, and 2 mm, as shown in Figure 3b. Data were collected at a frequency of 50 Hz. The measured cooling rates were then fitted to reflect the continuous variation of cooling rates across all regions. The raw materials included high-purity aluminum (>99.999%), an Al–10Ni master alloy, and an Al–11.8TiB₂ master alloy [17,18]. The preparation process was as follows: (1) The raw materials were weighed and thoroughly dried; (2) a graphite crucible was used for melting; (3) the crucible was internally cleaned, preheated, and coated with boron nitride; (4) the crucible was charged with high-purity aluminium (base layer), Al–10 Ni master alloy, Al–11.8 TiB₂ master alloy, Al–2 wt % Sc master alloy and Al–10 wt % Zr master alloy; the charge was pre-mixed to ensure macroscopic homogeneity; (5) the furnace was heated to 970 °C and held for 10 min to guarantee complete dissolution of all master alloys and to eliminate undissolved Sc/Zr-rich phases. After full melting, the melt was mechanically stirred with a graphite rod and skimmed; (6) a fluxing agent (Foseco) was added to the melt surface, followed by refining with a graphite bell jar for 3 min, maintaining the melt at 750 °C; (7) the crucible was transferred to a vacuum furnace preheated to 760 °C, where vacuum degassing was conducted for 10 min. Simultaneously, the copper and graphite molds were preheated to 150 °C; (8) after degassing, residual slag was removed. When the melt temperature stabilized at 740 ± 5 °C, it was poured into the wedge mold, and the remaining melt was cast into a cylindrical graphite mold (30 mm in diameter). The ingots were allowed to cool naturally after complete solidification. The chemical composition of the resulting 2TiB₂/Al–8Ni–0.6Sc–0.1Zr alloy was analyzed using an iCAP 6300 inductively coupled plasma optical emission spectrometer (ICP-OES) from Thermo Fisher Scientific (Waltham, MA, USA). The analysis was conducted with a detection limit of 0.1 mg/kg and an upper limit of 20%. The results are summarized in

Table 1. Chemical composition of the 2TiB₂/Al–8Ni–0.6Sc–0.1Zr alloy (wt.%).

Alloy	Ni	Sc	Zr	Ti	B	Al
2TiB2/Al–8Ni–0.6Sc–0.1Zr	8.40 ± 0.32	0.57 ± 0.06	0.13 ± 0.02	1.55 ± 0.09	0.69 ± 0.06	Bal.

.

The cylindrical ingots were machined into substrates with a diameter of 30 mm and a thickness of 1 cm for subsequent laser-directed energy deposition (L-DED) single-track remelting experiments. The laser power was fixed at 1200 W, and the scanning speeds were set to 20, 40, 60, and 80 mm/s. All experiments were conducted in an argon-shielded atmosphere.

3.2. Characterization Methods

A TESCAN MAIA3 scanning electron microscope (SEM, Brno, Czech Republic) was used to observe the microstructures. Depending on the specific requirements, secondary electron (SE) and backscattered electron (BSE) modes were employed. Energy-dispersive X-ray spectroscopy (EDS), electron backscatter diffraction (EBSD), and transmission Kikuchi diffraction (TKD) were used to determine elemental distributions and crystallographic features. Samples for SEM were prepared using standard metallographic polishing procedures. EBSD samples underwent additional surface preparation via ion polishing using a Leica EM TIC 3X triple ion beam system with the following settings: 5 kV, 10.5°, 20 min; 4.5 kV, 4.5°, 45 min; 3.5 kV, 4.5°, 15 min. TKD specimens were prepared as thin films using focused ion beam (FIB) milling. SEM imaging was conducted at an accelerating voltage of 10–20 kV and a working distance of 5–10 mm, while EBSD and TKD were performed at 20 kV and a working distance of 15–20 mm. EBSD/TKD data were processed using AZtecCrystal 2.1 software (Oxford, UK). Surface morphologies were also reconstructed in 3D using a VK-X3000 laser scanning confocal microscope (LSCM).

3.3. Thermodynamic Calculation

Phase equilibria and solidification paths for the Al–Ni–Sc–Zr–Ti–B system were calculated using the Pandat2023 software (CompuTherm LLC, USA) [19,20], employing a high-throughput approach. The thermodynamic data were derived from binary and ternary subsystems, including Al–Ni [21], Al–Sc [22], Ni–Sc [23,24], Al–Zr [25], Ni–Zr [26], Sc–B [27], Ni–Al–B [28], Al–Sc–Zr [29], Al–Ni–Sc [30,31], Al–Ni–Zr [32], and Al–Ti–B [33].

4. Results

4.1. Microstructure of Wedge-Cast Samples

Figure 4 illustrates the distribution of TiB₂ particles and the morphology of Al₃(Sc,Zr) in different regions of the 2TiB₂/Al–8Ni–0.6Sc–0.1Zr sample fabricated using the wedge-shaped copper mold. Elemental mapping results for the regions at D = 30 mm and D = 23 mm are shown in Figure 5. In the D = 30 mm region (cooling rate ≈ 700 °C/s), square-shaped primary phases are observed. EDS mapping (Figure 5) confirms that these are Al₃(Sc,Zr) phases, surrounded by clusters of TiB₂ particles. In contrast, in the D = 23 mm region (cooling rate ≈ 1200 °C/s), these primary Al₃(Sc,Zr) phases disappear and are replaced by numerous core–shell structured particles. The core is identified as TiB₂ and the shell as Al₃(Sc,Zr) (Figure 5e–h), suggesting that Al₃(Sc,Zr) nucleated and grew on the TiB₂ surface. TiB₂ particles in this region exhibit improved dispersion. At D = 20 mm (cooling rate ≈ 1750 °C/s), no core–shell structures are observed, and TiB₂ agglomeration becomes more pronounced. However, in the D = 0 mm region (cooling rate ≈ 6800 °C/s), the extent of TiB₂ agglomeration is reduced compared to that at D = 20 mm. Further increasing the cooling rate, primary Al₃Ni disappears, and the microstructure evolves into a fully eutectic structure at ~1200 °C s⁻¹ (Figure 4(b1,b2)); further increases in the cooling rate yield a slightly hypoeutectic morphology (Figure 4(c1,c2)), confirming the suppression of primary intermetallic formation. This is because, under rapid solidification, Al-8Ni gradually enters the eutectic coupling zone or even the hypereutectic zone due to competition between the growth kinetics of each phase [34,35].

4.2. Microstructure of Laser-Remelted Samples

Figure 6 presents LSCM images of the melt pool morphologies in the 2TiB₂/Al–8Ni and 2TiB₂/Al–8Ni–0.6Sc–0.1Zr alloys subjected to laser surface remelting under a constant laser power of 1200 W and varying scanning speeds (20, 40, 60, and 80 mm/s). The 2TiB₂/Al–8Ni samples are labeled A1–A4 and the 2TiB₂/Al–8Ni–0.6Sc–0.1Zr samples B1–B4. In both alloys, the scanning speed determines the average cooling rate during melt pool solidification. At a given scanning speed, the TiB₂ particles in the B-series samples exhibit significantly improved dispersion compared to those in the A-series. Notably, TiB₂ dispersion in sample B2 (40 mm/s) is optimal, consistent with the trend observed in the wedge-cast samples. The cooling-rate range of the L-DED process (10²–10⁴ °C/s [14]) is comparable to that of the wedge mold.

Figure 7(a1) shows a HAADF image of a TiB₂ particle near the bottom of the melt pool in sample B2. The corresponding HRTEM image (Figure 7(a2)) and its FFT (Figure 7(a3)) confirm that the phase coating the TiB₂ particle is Al₃(Sc,Zr). In Figure 7(b1–b3) and 7(c1–c3), HAADF and elemental maps of Sc and Zr are shown for TiB₂ particles in samples B2 and B4, respectively. The Al₃(Sc,Zr) coating thickness is ~20 nm in B2 and ~3 nm in B4, indicating that higher cooling rates (B4: 80 mm/s) reduce the growth of the Al₃(Sc,Zr) shell.

4.3. Orientation Relationship Between TiB₂ and α-Al

Segregation of Sc/Zr at the TiB₂/α-Al interface enhances lattice matching and facilitates specific orientation relationships (ORs). To validate this, EBSD analysis was conducted on the melt pool regions of samples A2 and B2. Twenty TiB₂ particles from within the grains and twenty from the grain boundaries were selected in each sample to analyze their orientation relationships with neighboring α-Al. Figure 8 shows one representative TiB₂–α-Al orientation relationship from the grain interior and one from a grain boundary in sample B2. Equal-area projections of the {001}α-Al plane are used to mark the poles of the {0001}TiB₂ planes.

Due to the fourfold symmetry of α-Al along the <001> axis, the {0001}TiB₂ poles are projected into the first quadrant. Figure 9a indicates ideal ORs: (111)α-Al//(0001)TiB₂ (red cross), (110)α-Al//(0001)TiB₂ (yellow cross), and (001)α-Al//(0001)TiB₂ (white cross). Figure 9b–e present the density distributions of these projections for samples A2 and B2. In sample A2, no reproducible ORs are observed between TiB₂ and α-Al, regardless of location. In contrast, sample B2 shows a preferential OR of (111)α-Al//(0001)TiB₂, particularly for TiB₂ particles within grains. Other parallel close-packed plane relationships are not observed. Based on the EBSD analysis of forty TiB₂ particles in B2, the (111)α-Al//(0001)TiB₂ interface emerges as the preferred orientation.

5. Discussion

5.1. Nucleation and Growth of Al₃(Sc,Zr) on TiB₂ Surfaces

To elucidate the formation of Al₃(Sc,Zr)/TiB₂ composite interfaces and their dependence on cooling rate, classical heterogeneous nucleation theory [36,37] was applied. The nucleation and growth of Al₃(Sc,Zr) on TiB₂ particles were evaluated using this framework with the following parameters:

-

Interfacial energy between Al₃(Sc,Zr) and liquid Al (γ)

Direct measurements of γ are unavailable. However, since Al₃(Sc,Zr) acts as a potential nucleation site for α-Al, its interfacial energy can be estimated based on values reported for α-Al/liquid Al (0.093–0.158 J/m²) [38,39]. Given the structural similarity between D0₂₂–Al₃Ti and L1₂–Al₃(Sc,Zr), the Al₃Ti/liquid Al interfacial energy is also relevant. DFT studies by Wearing et al. [40] showed that the difference in γ between Al₃Ti/liquid Al and α-Al/liquid Al is <0.35 J/m² (estimated at 0.31 J/m²). Hence, the γ value used here is set at 0.43 J/m².

-

Volumetric Gibbs free energy change (ΔGᵥ)

ΔGᵥ is typically approximated using the relationship ΔGᵥ = ΔHₘ(Tₘ–T)/Tₘ, where ΔHₘ is the latent heat of fusion and Tₘ is the melting point. However, for Al₃(Sc,Zr), which nucleates from a multicomponent melt, this is not valid. Instead, ΔGᵥ corresponds to the maximum thermodynamic driving force for forming Al₃(Sc,Zr) nuclei from clusters of Al, Sc, and Zr atoms. The driving force curve for the 2TiB₂/Al–8Ni–0.6Sc–0.1Zr system is shown in Figure 10.

-

Wetting angle (θ)

Al₃(Sc,Zr) preferentially nucleates on the (0001) plane of TiB₂. The value is set as 30° [14].

-

Nucleation site density (N)

Assuming each (0001) surface of a TiB₂ particle provides a single nucleation site, and given that there are two such surfaces per particle, N is calculated as:

$$N={\displaystyle \frac{2f_w\left(\mathrm{Ti}{\mathrm{B}}_2\right){\rho }_L}{{\rho }_{\mathrm{Ti}{\mathrm{B}}_2}{V}_{\mathrm{Ti}{\mathrm{B}}_2}}}$$

(1)

where $f_w\left(\mathrm{Ti}{\mathrm{B}}_2\right)$ is the TiB₂ mass fraction (0.02), ${\rho }_L$ and ${\rho }_{\mathrm{Ti}{\mathrm{B}}_2}$ are the densities of liquid Al and TiB₂, respectively; $V_{\mathrm{Ti}{\mathrm{B}}_2}$ is the average TiB₂ particle volume, estimated using a particle diameter of 800 nm [14].

-

Diffusion coefficient (D)

Based on the CALPHAD approach, the diffusion coefficient of an element in the liquid phase can be described using atomic mobility parameters. The mobility parameters for the Al–Sc liquid phase were obtained from Ref. [41]. According to the TEM-EDS mappings of Sc and Zr around the TiB₂ particle at 850 °C/s (Figure 7), the Al₃(Sc,Zr) precipitated from the liquid is Sc-rich and contains a small amount of Zr atoms. Therefore, the diffusion coefficients D_L used in our nucleation analysis is assigned to the trace diffusion coefficient of Sc in the Al–8Ni–0.6Sc–0.1Zr melt. In this study, the D_L as a function of temperature were calculated based on thermodynamic and mobility parameters for the Al–Ni–Sc–Zr–Ti–B system using the CALPHAD method, as illustrated in Figure 11.

-

Interfacial concentration ($x_{\mathit{L},\mathit{eff}})$

x_L,eff is the effective interfacial concentration at the solidification front, reflecting the number of Al₃(Sc,Zr) clusters that can form at this location. This term refers to the molar volume of Al₃(Sc,Zr) clusters near the solidification front. Prior to casting, all Sc and Zr atoms are fully dissolved in the melt; therefore, the molar volume is assumed to correspond to the total molar fraction of Al₃(Sc,Zr) clusters precipitated from the melt. According to equilibrium phase diagram calculations at 600 °C, the corresponding value in the 2TiB₂/Al–8Ni–0.6Sc–0.1Zr melt was calculated to be 1.7 wt% (Sc + Zr).

-

Incubation time

According to Klein et al. [42], the effective incubation time for nucleation is given by

$$\tau ={\displaystyle \frac{16\times k\times f\left(\theta \right)}{1-\cos \left(\theta \right)}}\times {\displaystyle \frac{1}{a^2\times x_{l,eff}}}\times {\displaystyle \frac{{\gamma }_{S/L}\times T}{D_L\times {∆G}_v^2}}$$

(2)

where θ is the wetting angle, γ_S/L is the interface energy between the solid and liquid, and ΔG_v is the driving force for precipitation.

Table 2. Model parameters used for the calculations in the heterogeneous nucleation model.

Parameter	Value	Unit	Parameter	Value	Unit
TL	932	°C	$x_{L,eff}$	0.017
γS/L	0.43	J⸱m−3	$W_{m,{Al}_{3}Sc}$	31.5	g/mol
θ	30	°	${\rho }_L$	2.61 × 103	kg⸱m−3
N	5.0 × 1017		${\rho }_{{Al}_{3}Sc}$	3.02 × 103	kg⸱m−3
a	2.6 × 10−10	m	${\rho }_{{TiB}_2}$	4.49 × 103	kg⸱m−3

summarizes the key parameters used in the heterogeneous nucleation model. In addition to the parameters described in items (1)–(7), the table additionally includes the average molar mass of the Al₃Sc phase ($W_{\mathrm{m},\mathrm{A}{\mathrm{l}}_3\mathrm{Sc}}$), the interfacial atomic spacing (a), and the density of the Al₃Sc phase (${\rho }_{\mathrm{A}{\mathrm{l}}_3\mathrm{Sc}}$). Moreover, the Gibbs free energy per unit volume of Al₃(Sc,Zr) and the diffusion coefficient D of Sc in the Al–8Ni–0.6Sc–0.1Zr melt are presented in Figure 10 and Figure 11, respectively. Since the first atomic layer of the Al₃(Sc,Zr) crystal consists of pure Al₃Sc, the value of a is calculated using the following equation:

$$a=\left({\displaystyle \frac{W_{\mathrm{m},\mathrm{A}{\mathrm{l}}_3\mathrm{Sc}}}{{\mathrm{N}}_{\mathrm{A}}\times {\rho }_{\mathrm{A}{\mathrm{l}}_3\mathrm{Sc}}}}\right)$$

(3)

where M is the molar mass of Al₃Sc, ρ is its density, and N_A is Avogadro’s number.

Figure 12 presents the temperature-dependent curves of the nucleation rate and the critical height of cap-shaped Al₃(Sc,Zr) nuclei. When the temperature drops below 805 °C, the nucleation rate of Al₃(Sc,Zr) increases significantly, reaching a peak at 550 °C. As the temperature decreases further, the diffusion of Sc and Zr in the undercooled liquid becomes limited, leading to a reduction in the nucleation rate of Al₃(Sc,Zr). However, when the temperature is substantially higher than 550 °C, the nucleation of Al₃(Sc,Zr) ceases. This phenomenon can be attributed to three main factors. First, due to solute trapping effects, the rapidly solidified α-Al grains formed at 643 °C inhibit the precipitation of Al₃(Sc,Zr). Second, the (111) plane of Al₃Sc, which is an atomically close-packed plane, is parallel to the (0001) plane of TiB₂. When the critical height of the cap-shaped nucleus is smaller than the interplanar spacing of Al₃Sc (2.3 × 10⁻¹⁰ m), Sc and Zr atoms stack directly onto the existing Al₃(Sc,Zr) crystal surface, preventing the formation of a three-dimensional nucleus. The intersection point between the green solid line and the black dashed line in the figure indicates that the critical temperature for the termination of Al₃(Sc,Zr) nucleation is 765 °C. Third, prior to reaching 765 °C, once the number of Al₃(Sc,Zr) nuclei reaches a critical level, the precipitation mode of the primary Al₃(Sc,Zr) phase shifts from nucleation-controlled to growth-controlled. Therefore, in the 2TiB₂/Al–8Ni–0.6Sc–0.1Zr melt, the nucleation of Al₃(Sc,Zr) occurs within the temperature range of 765–923 °C and terminates at 643 °C.

The extent of Al₃(Sc,Zr) coverage on TiB₂ surfaces is strongly correlated with the nucleation number density of Al₃(Sc,Zr) generated during rapid solidification. Given the abundance of TiB₂ particles in the melt serving as effective nucleation sites, it is assumed that Al₃(Sc,Zr) crystals nucleate upon undercooling of the liquid. The number density of Al₃(Sc,Zr) nucleation cores can be calculated using the following expression:

$$N_n^c={\int }_{T_L}^{T_c}J\times {\displaystyle \frac{dT}{\dot{T}}}$$

(4)

where J denotes the nucleation rate, and T_c represents the critical temperature (ranging from 765 to 923 °C) at which Al₃(Sc,Zr) transitions from nucleation to growth. Additionally, the mole fraction of Al₃(Sc,Zr) formed via heterogeneous nucleation can be estimated using the following expression:

$$f_n^c={\displaystyle \frac{1}{n_t}}{\int }_{T_L}^{T_c}J\times n^{*}\times {\displaystyle \frac{dT}{\dot{T}}}$$

(5)

where n_t denotes the total number of atoms that constitute the Al₃(Sc,Zr) phase under equilibrium conditions, whereas n^⁎ represents the number of atoms in a critical Al₃(Sc,Zr) nucleus at a given temperature. The value of n_t can be determined as follows:

$$n_t={\mathrm{N}}_{\mathrm{A}}\times {\displaystyle \frac{f_t^w}{W_{\mathrm{m},\mathrm{A}{\mathrm{l}}_3\mathrm{Sc}}}}\times {\rho }_L$$

(6)

where $f_t^w$ denotes the total mass fraction of Al₃(Sc,Zr) in the 2TiB₂/Al–8Ni–0.6Sc–0.1Zr system after equilibrium solidification, as determined by thermodynamic calculations. The critical nucleus size, n⁎, can be calculated using the following expression:

$$n^{*}=-{\displaystyle \frac{32\pi }{3a^3}}\times ({\displaystyle \frac{{\gamma }_{\mathrm{S}/\mathrm{L}}}{\mathsf{\Delta }{G}_V}}{)}^3\times f(\theta )$$

(7)

Equations (4) and (5) show that, under a fixed cooling rate, T_c governs both J and n^⁎. However, the exact value of T_c remains unknown. Accordingly, T_c is treated as an independent variable in the following analysis.

Figure 13 presents the variation curve of $N_c^n$ with respect to the cooling rate. If the transition of Al₃(Sc,Zr) from nucleation to growth does not occur before the liquid phase cools to 765 °C, the nucleation number density decreases monotonically with increasing cooling rate. This scenario defines the upper limit of the achievable nucleation number density. Assuming the transition from nucleation to growth occurs at T_c > 765 °C, the nucleation number density initially increases to a maximum with increasing cooling rate, and then gradually decreases and converges toward the upper limit. The intrinsic cause of this initial increase in nucleation number density is the reduction in the critical nucleus size with increasing cooling rate. Given that the coverage of Al₃(Sc,Zr) on TiB₂ surfaces reaches a maximum at a cooling rate of 1200 °C/s (as shown in Figure 4 and Figure 5), the actual value of $f_n^c$ for the nucleation-to-growth transition of Al₃(Sc,Zr) is expected to be approximately 2%.

Once nucleation is complete, Al₃(Sc,Zr) precipitates on the TiB₂ surface and proceeds to the growth stage. In the 2TiB₂/Al–8Ni–0.6Sc–0.1Zr system, a cooling rate of 1200 °C/s defines the threshold for forming a three-dimensional Al₃(Sc,Zr) coating on TiB₂ surfaces (Figure 5e). Above this threshold, the growth of Al₃(Sc,Zr) is significantly suppressed (Figure 7c). In a study of the 5TiB₂/Al–4.5Mg–0.7Sc–0.2Zr system [14], at a cooling rate of 6800 °C/s, the thickness of Al₃(Sc,Zr) decreases to approximately 1 nm, corresponding to a two-dimensional atomic layer. Below the 1200 °C/s threshold, the growth window of Al₃(Sc,Zr) extends, resulting in a rapid increase in total thickness.

In summary, the precipitation sequence of Al₃(Sc,Zr) on TiB₂ for the 2TiB₂/Al–8Ni–0.6Sc–0.1Zr system can be divided into three stages.

-

Stage I (805–923 °C, low undercooling): Al₃(Sc,Zr) nucleation is negligible; Sc/Zr atoms segregate onto the (0001) TiB₂ surface and construct a two-dimensional cluster (2DC) whose lattice must expand to achieve edge-to-edge matching with TiB₂. The resulting elastic strain suppresses subsequent α-Al nucleation.

-

Stage II (765–805 °C): the 2DC transforms into three-dimensional cap-shaped embryos (3DC) whose formation rate rises explosively (Figure 7b). These 3DC embryos spread over the TiB₂ surface to form a continuous shell; the process is most complete near 1200 °C/s (Figure 4b). Once the shell exceeds a critical thickness, lattice mismatch at the Al₃(Sc,Zr)/TiB₂ interface is fully relaxed, enabling coherent matching with α-Al.

-

Stage III (≤765 °C): nucleation of new 3DC embryos ceases because their critical height falls below one atomic layer, and growth of the existing Al₃(Sc,Zr) shell dominates. For cooling rates ≤850 °C/s, the planar shell becomes morphologically unstable and evolves into seaweed/dendritic Al₃(Sc,Zr) (Figure 5a).

5.2. Effect of Composite Interface on TiB₂ Dispersion

Particle dispersion during solidification is governed by the interaction between particles and the advancing solid–liquid interface [43,44,45,46,47,48]. Ignoring gravity and convection, three forces are considered:

(1)

Interfacial tension (F_I): Dominates when the particle–interface gap is <0.2–0.4 nm [43]:

$$F_I=2\pi R_P\mathsf{\Delta }\gamma {\left({\displaystyle \frac{a_0}{a_0+d_{\mathrm{P}/\mathrm{S}}}}\right)}^n\alpha , n=2-7$$

(8)

where R_p is the particle radius; Δγ denotes the change in interfacial energy upon particle engulfment by the interface; a_o is the atomic spacing; d_p/s is the distance between the particle and the solidification front; and α is the interface shape factor. Given that the interfacial tension decays rapidly with increasing d_p/s, n is assigned a value of 7.

(2)

van der Waals force (Fᵥ): Dominates for gaps >0.4 nm: [43,44]:

$$F_V=-{\displaystyle \frac{A}{6}}{\displaystyle \frac{R_p\alpha }{{\left(a_0+h_{p/s}\right)}^2}}$$

(9)

where A is the Hamaker constant for the Al–TiB₂ system.

(3)

Viscous drag (F_D): The viscous force originates from the relative motion between the liquid phase and the particles displaced by the advancing solidification front. According to Stokes’ law, the viscous force is proportional to both the solidification rate and the viscosity of the liquid, and can be expressed as [43]:

$$F_D=6\pi \eta V{\displaystyle \frac{R_P}{h_{\mathrm{P}/\mathrm{S}}}}{\alpha }^2$$

(10)

where η is melt viscosity and V is particle velocity.

When the gap between the particle and the solidification front exceeds 0.4 nm, the condition required for particle engulfment is $F_D>F_V$. When the gap narrows to 0.2–0.4 nm, the condition for engulfment becomes $F_D>F_I$. When the repulsive and attractive forces reach equilibrium, an expression for the steady-state growth velocity can be derived. The corresponding critical velocities for these two cases are given as follows:

$$V_c^V={\displaystyle \frac{A}{432\pi \eta a_0{R}_P\alpha }}$$

(11a)

$$V_c^I={\displaystyle \frac{0.057a_0\mathsf{\Delta }\gamma }{3\eta R_P\alpha }}$$

(11b)

Given that $F_I$ is generally on the order of 10⁶ times greater than $F_V$, it significantly outweighs the latter in magnitude.

The influence of the Al₃(Sc,Zr)/TiB₂ composite interface on particle engulfment is manifested through the variation in $\mathsf{\Delta }\mathsf{\gamma }$. For uncoated TiB₂ particles, $\mathsf{\Delta }\mathsf{\gamma }$ can be described as follows:

$$\mathsf{\Delta }\mathsf{\gamma }={\gamma }_{\mathrm{Ti}{\mathrm{B}}_2/\mathsf{\alpha }\text{-}\mathrm{Al}}-({\gamma }_{\mathrm{Ti}{\mathrm{B}}_2/\mathrm{L}\text{-}\mathrm{Al}}+{\gamma }_{\mathsf{\alpha }\text{-}\mathrm{Al}/\mathrm{L}\text{-}\mathrm{Al}})$$

(12)

Upon coating of TiB₂ particles with Al₃(Sc,Zr), the $\mathsf{\Delta }\mathsf{\gamma }$ is altered as follows:

$$\mathsf{\Delta }\mathsf{\gamma }={\gamma }_{\mathrm{Ti}{\mathrm{B}}_2/\mathrm{A}{\mathrm{l}}_3\left(\mathrm{Sc},\mathrm{Zr}\right)/\mathsf{\alpha }\text{-}\mathrm{Al}}-({\gamma }_{\mathrm{Ti}{\mathrm{B}}_2/\mathrm{A}{\mathrm{l}}_3\left(\mathrm{Sc},\mathrm{Zr}\right)/\mathrm{L}\text{-}\mathrm{Al}}+{\gamma }_{\mathsf{\alpha }\text{-}\mathrm{Al}/\mathrm{L}\text{-}\mathrm{Al}})$$

(13)

where ${\gamma }_{\mathrm{Ti}{\mathrm{B}}_2/\mathsf{\alpha }\text{-}\mathrm{Al}}$ is the interfacial energy between TiB₂ and α-Al; ${\gamma }_{\mathrm{Ti}{\mathrm{B}}_2/\mathrm{L}\text{-}\mathrm{Al}}$ is the interfacial energy between TiB₂ and liquid Al; ${\gamma }_{\mathsf{\alpha }\text{-}\mathrm{Al}/\mathrm{L}\text{-}\mathrm{Al}}$ is the interfacial energy between α-Al and liquid Al; ${\gamma }_{\mathrm{Ti}{\mathrm{B}}_2/\mathrm{A}{\mathrm{l}}_3\left(\mathrm{Sc},\mathrm{Zr}\right)/\mathsf{\alpha }\text{-}\mathrm{Al}}$ is the interfacial energy at the junction of TiB₂, Al₃(Sc,Zr), and α-Al; ${\gamma }_{\mathrm{Ti}{\mathrm{B}}_2/\mathrm{A}{\mathrm{l}}_3\left(\mathrm{Sc},\mathrm{Zr}\right)/\mathsf{\alpha }\text{-}\mathrm{Al}}$ is the interfacial energy at the junction of TiB₂, Al₃(Sc,Zr), and liquid Al.

Table 3. Summary of interface energies used for calculation during particle engulfment process.

Interface	Symbol	Energy (J/m2)
α-Al/L-Al	${\gamma }_{\mathsf{\alpha }\text{-}\mathrm{Al}/\mathrm{L}\text{-}\mathrm{Al}}$	0.158
TiB2/α-Al	${\gamma }_{\mathrm{Ti}{\mathrm{B}}_2/\mathsf{\alpha }\text{-}\mathrm{Al}}$	2.72
TiB2/L-Al	${\gamma }_{\mathrm{Ti}{\mathrm{B}}_2/\mathrm{L}\text{-}\mathrm{Al}}$	2.39
Al3(Sc,Zr)/L-Al	${\gamma }_{\mathrm{A}{\mathrm{l}}_3\left(\mathrm{Sc},\mathrm{Zr}\right)/\mathrm{L}\text{-}\mathrm{Al}}$	4.3
Al3(Sc,Zr)/α-Al	${\gamma }_{\mathrm{A}{\mathrm{l}}_3\left(\mathrm{Sc},\mathrm{Zr}\right)/\mathsf{\alpha }\text{-}\mathrm{Al}}$	0.14
Al3(Sc,Zr)/TiB2	${\gamma }_{\mathrm{A}{\mathrm{l}}_3\left(\mathrm{Sc},\mathrm{Zr}\right)/\mathrm{Ti}{\mathrm{B}}_2}$	2.02

lists the values of the above interfacial energies, which are obtained from Ref. [14].

For TiB₂ particles not coated with Al₃(Sc,Zr), the system interfacial energy after engulfment is 0.172 J/m². For TiB₂ particles coated with Al₃(Sc,Zr), the corresponding $\mathsf{\Delta }\gamma$ is −0.448 J/m². The positive $\mathsf{\Delta }\mathsf{\gamma }$ value indicates that uncoated TiB₂ particles tend to be pushed away by the solidification front and accumulate at grain boundaries, a phenomenon commonly observed in conventional casting [49] and also reported in L-PBF processes [20]. For particles to be engulfed by the solidification front, the solidification velocity must exceed $V_c^I$. The negative value of $\mathsf{\Delta }\gamma$ implies that, once the gap between the particle and the solidification front decreases to 0.2–0.4 nm, the Al₃(Sc,Zr)-coated TiB₂ particles spontaneously enter the solid phase. In this case, the solidification velocity required for particle engulfment only needs to exceed $V_c^V$, which is lower than $V_c^I$.

Under different cooling rates, the engulfment behavior of TiB₂ particles by the solid/liquid interface varies significantly. At relatively low cooling rates, an overgrown Al₃(Sc,Zr) phase is observed around the TiB₂ particles. When the cooling rate increases to approximately 1200 °C/s, Al₃(Sc,Zr) precipitates on the surface of TiB₂ particles, resulting in a reduced critical velocity for particle engulfment, $V_c^V$. Consequently, the dispersion of TiB₂ particles is significantly improved (Figure 6). However, as the cooling rate further increases, the critical engulfment velocity rises back to $V_c^I$, and the precipitation of Al₃(Sc,Zr) on TiB₂ surfaces is suppressed, leading to the agglomeration of TiB₂ particles. When the cooling rate continues to increase beyond this point, the growth velocity of α-Al exceeds $V_c^I$, causing TiB₂ particles to be uniformly distributed within the α-Al matrix regardless of the presence of Al₃(Sc,Zr) precipitates on their surfaces (Figure 4(d1)–(d2)). The Al₃(Sc,Zr)/TiB₂ composite interface facilitates the dispersion of TiB₂ particles by reducing the interfacial barrier and lowering the critical engulfment velocity, enabling good dispersion of TiB₂ particles at cooling rates around 1200 °C/s (Figure 5e).

6. Conclusions

The heterogeneous nucleation and growth of Al₃(Sc,Zr) on TiB₂ surfaces under high cooling rates in the 2TiB₂/Al–Ni–Sc–Zr system were investigated through experiments and a nucleation model. The effect of the Al₃(Sc,Zr)/TiB₂ composite interface on TiB₂ particle dispersion was also assessed. The main conclusions are as follows:

(1)

The volumetric driving force for Al₃(Sc,Zr) precipitation, governed by the Sc and Zr contents in the melt, plays a critical role in determining the heterogeneous nucleation rate. Based on thermodynamic analysis, the Sc and Zr contents were set to 0.6 wt.% and 0.1 wt.%, respectively, balancing sufficient nucleation driving force, melt temperature control, and model simplicity.

(2)

The formation of the Al₃(Sc,Zr)/TiB₂ composite interface depends on the cooling rate and strongly influences TiB₂ dispersion. In wedge-cast samples, TiB₂ agglomeration occurred at 700 °C/s, with primary Al₃(Sc,Zr) forming around clusters. At 1200 °C/s, Al₃(Sc,Zr) precipitated on TiB₂ surfaces, forming core–shell structures and improving particle dispersion. At 1750 °C/s, these structures disappeared, and agglomeration reappeared.

(3)

In laser surface–remelted 2TiB₂/Al–8Ni samples, TiB₂ particles showed severe agglomeration and lacked a consistent orientation with the α-Al matrix. In contrast, the addition of Sc and Zr in the 2TiB₂/Al–8Ni–0.6Sc–0.1Zr alloy significantly improved dispersion. Dispersion first increased and then decreased with rising scanning speed. A reproducible orientation relationship of (111) α-Al//(0001) TiB₂ was observed.

(4)

The formation of the Al₃(Sc,Zr)/TiB₂ interface is closely linked to Al₃(Sc,Zr) nucleation under rapid solidification. Classical nucleation theory indicates that the highest nucleation density occurs near 1200 °C/s, at which the composite interface forms most effectively, thereby promoting uniform TiB₂ dispersion.