Preparation of MgAl 2 O 4 -Coated Al 2 O 3np and Migration of Ceramic Nanoparticles during Ultrasonic Processing of Aluminum Matrix Composites

: Composites reinforced by nano-ceramic particles typically result in the formation of clustering and a weak interface. The spatial distribution of particles and the wetting behavior remarkably affect the targeted properties. Here, a surface modification combined spatial control solution was demonstrated to prepare nanocomposites with homogeneous micro-structures. Polycrystalline nano-MgAl 2 O 4 particles that possess a good crystallographic orientation relationship with Al were coated on the surface of ceramic particles, and they were macro- and then microscopically dispersed in the melt by ultrasonic vibration with variable frequency. The reason this is that the acoustic pressure distributed in the Al melt can induce the acoustic streaming and cavitation. A model for calculating equilibrium particle migration velocity was proposed, based on which the distribution of particles could be controlled by adjusting the solidification rate and the size of particle clustering. The experimental results were validated by the prediction of the model. In addition, it was found that the relationship of the maximum radius angle with the contact angle was  , and ultrasonic vibration could provide enough energy for the later stage entering of particles to overcome the


Introduction
Aluminum metal matrix composites reinforced by ceramic particles have emerged as an important structural material for using in the automotive and aerospace industries due to their high specific strength, high-temperature creep resistance, and excellent wear resistance [1][2][3]. In particular, the addition of nano-sized particles into the alloys can induce conspicuously improved mechanical properties [4]. In contrast, it is a challenging to well disperse and uniformly distribute the nanoparticles in the melts since they have larger specific surface area and poor wettability between ceramic phase and matrix alloy [3], which limits the strengthening effect of composites. A recent review reported that the surface modification of reinforcements was considered to be effective in promoting particle distribution and improving the wetting behavior [5].
Recently, MgAl2O4 spinel was used as reinforcements in lightweight alloys because of their important properties such as low density, high strength, high melting point, and thermal shock resistance [6,7]. Interestingly, there exists a good crystallographic orientation relationship between MgAl2O4 and Al matrix, and the lattice misfit of MgAl2O4 (100) and Al (100) is only 0.25% [8], indicating that MgAl2O4 particles can act as heterogeneous nucleating sites for Al alloys and promote the formation of fine equi-axed grains. Additionally, there is a relatively low contact angle between MgAl2O4 and Al melts [9]. In this context, it is an effective way to in-situ coat a nanolayer of MgAl2O4 on the surface of ceramic particles. Nevertheless, obtaining a uniform distribution of particles in the Al matrix is still key factor in manufacturing of composites due to van der Waals interactions between nanoparticles. Some studies have reported that the high intensity ultrasonic assisted casting method was successfully applied to fabricate nanocomposites since the cavitation and acoustic streaming by ultrasonic vibration in the melts could contribute to the wetting and dispersion of the reinforcement particles as well as the degassing of melts [10][11][12][13]. However, how ultrasonic vibration facilitates nanoparticles entering the melt and subsequently disperses them still needs to be clarified.
The size and distribution of nanoparticle clustering affect the microstructure and properties of composites [1,10,14]. When the solidification velocity is above the equilibrium particle migration velocity, the particles are engulfed by the solid-liquid interface, otherwise they are pushed toward the grain boundaries and eutectic regions [15]. In order to evaluate the distribution of nanoparticles in the matrix, it is necessary to clarify the relationship between solidification velocity and equilibrium particle migration velocity. Uhlmann et al. [16] first proposed the UCJ model, in which the critical velocity for steady state of pushing by introduction of the viscous drag force and the repulsive force was used for judging particle distribution in the matrix. After that, Stefanescu et al. [17] modified the UCJ model and the SAS model proposed by Shangguan et al. [18], which causes the increased accuracy of model prediction. However, these models can only explain the distribution of micronsized particles in the matrix. Therefore, based on the models by Stefanescu et al. [17] and Kim et al. [19], we considered Brownian motion and van der Waals interactions between particles and interfaces, proposed a concept of critical particle radius and then developed a model to calculate the equilibrium velocity for steady pushing of particles with different sizes [14]. It should be noted that the above models are aimed at the solidification process in static environment for the alloy melts containing suspended particles. Unfortunately, it is not clear whether these models can be applied for the solidification process under external field interference, and the migration of particles in the solidification process under the action of external field has been less reported. Thus, a model is needed to calculate the equilibrium migration velocity of nanoparticles during solidification of the nano-composites under ultrasonic vibration.
In this study, a polycrystalline layer of nano-MgAl2O4 spinel was in-situ coated on the surface of nano-sized alumina particles (Al2O3np) by electroless plating and calcination process, and the aluminum matrix composites reinforced with hybrid of MgAl2O4-coated Al2O3np and MgAl2O4 particles were prepared by high intensity ultrasonic assisted casting method. The aim of this study is to realize control of the size and distribution of nanoparticles in the matrix in order to make the composites with high-performance more possible, based on the studies on the influences of particle wetting and ultrasonic vibration on nanoparticle completely entering the melt and dispersion mechanism, and to establish a model of particle migration under ultrasound treatment. The experimental results were validated by the prediction of the model.

Preparation of MgAl2O4-Coated Al2O3np
Nano-sized α-Al2O3 powders (purity 99.99%) were kept at 600 °C for 1 h to remove impurities that may exist on particle surface, and then added to the distilled water under ultrasonic vibration with a power level of 150 W and frequency of 40 kHz. During ultrasonic processing, trisodium citrate was added and completely dissolved to form solution A, in which the molar ratio of trisodium citrate to alumina ranges from 0.01 to 0.03. Under the action of magnetic stirring, tin (II) chloride dihydrate was dissolved in the hydrochloric acid solution (2 mol/L), and then sodium chloride was added, finally obtaining solution B, in which the concentrations of stannous chloride and sodium chloride were 0.7 and 3.4 mol/L, respectively. The solutions A and B were mixed well and formed the solution C. Palladium chloride (purity 99.999%) was completely dissolved in the hydrochloric acid solution (2 mol/L) to obtain solution D, which contained 0.038 moles of palladium ion per liter. After the mixing of the solutions C and D by magnetic stirring, the nano-powders adsorbing σ ligands of tin-palladium were achieved by settlement and then centrifuge cleaning. The aqueous solution of potassium sodium tartrate was slowly introduced into the magnesium sulfate solution followed by adding a small amount of methanol, in which the molar ratio of potassium sodium tartrate to magnesium sulfate was 3.4 and the pH value of the solution was adjusted to 9 by using NaOH solution (0.017 mol/L). Then, the acquired nano-powders were ultrasonically distributed in the above solution at 150 W and a frequency of 40 kHz, slowly dropping formaldehyde in the meantime, wherein the molar ratio of formaldehyde to magnesium was 10 and the pH value should be controlled in the range of 11 to 12. After that, the new powders were obtained by centrifuge cleaning, and then drying in a vacuum oven at 80 °C for 3 h. Finally, the dried powders were air-heated to 930 °C at a rate of 18 °C/min, and then held for 1 h at this temperature.

Fabrication of MgAl2O4-Coated Al2O3np/Al7075 Composites
The commercial aluminum alloy 7075 in a clay-graphite crucible was completely melted under an argon atmosphere at 800 °C by using resistance furnace. The above MgAl2O4-coated Al2O3np after grinding was added into the melt at a rate of 0.3 g/min, while an ultrasonic vibration with 1 kW and a frequency of 10 kHz, was introduced into the melt to macroscopically disperse the nanoparticles. After addition was complete, the composite melts were ultrasonically vibrated at 1 kW and a frequency of 20 kHz for 10 min to achieve a full, microscopic dispersion. The composite slurry after ultrasonic processing was poured into a graphite crucible having an inner dimension of Φ40 mm × 115 mm and preheated to 550-600 °C. Then they were allowed to cool in a quiescent fashion to 700 °C. When the appropriate temperature was reached, the ultrasonic vibration was introduced into the composite slurry at 1 kW and 20 kHz, whereupon the slurry temperature was reduced to 620 °C at various cooling rates (0.36, 10, 33 and 117 °C/min). Then, they were quenched in water immediately. The mechanical vibration was also carried out during ultrasonic processing. To obtain nanoparticle clustering with different sizes, specimens containing 1.5 wt.% and 2.5 wt.% reinforcement particles were fabricated. Some Al7075 melts taken from the clay-graphite crucible were used to evaluate the wettability of Al2O3np coated with and without MgAl2O4 by the molten alloy via a sessile drop contact angle method.

Microstructural Characterization
The as-received ingots were cut axially along the centre line by a mechanical saw, and then a slice was transversely chosen in the central region of the ingots for observing microstructures of the composites. The microstructures and particle distribution in the matrix were examined by optical microscope (OM, eclipse, MA-200, Nikon, Tokyo, Japan) and scanning electron microscopy (SEM, Quanta-200F, FEI, OR, USA), equipped with X-ray mapping system. To identify the phase and microstructure of the MgAl2O4-coated Al2O3np, X-ray diffraction analysis (XRD, D8ADVANCE-A25, Bruker, Karlsruhe, Germany), scanning electron microscopy, and transmission electron microscopy (TEM, JEM-2100, Jeol, Tokyo, Japan) were performed. Figure 1 shows the schematic for the synthesis of MgAl2O4-coated Al2O3np. We proposed a method by which Mg-coated Al2O3np were firstly formed by electroless plating process, and then were calcined in air to obtain MgAl2O4-coated Al2O3np, as shown in Figure 1. It is well-known that ultrafine ceramic particles tend to agglomerate due to the van der Waals attraction force between them, which affects surface modification of particles, thus their well dispersion in the solution should be done during the coating processing. There, generally, are active hydroxyl groups (-OH) on the surface of Al2O3np to achieve a coordination number equilibrium by adsorption of hydrolyzed ions at room temperature. The trisodium citrate belongs to small molecular electrolyte, so that it could be grafted with these active hydroxyl groups to form an organic molecular membrane on the surface of Al2O3np, which facilitates dispersion of the particles through electrostatic and steric hindrance effects and provides favorable conditions for effective plating. To accelerate the reduction of magnesium ions, it is necessary to load catalytic point of Pd on the Al2O3np surface to reduce the activation energy of the initial reaction by embedding σ ligands of Sn-Pd, namely sensitization and activation treatment, where the appropriate acidity should be held in the SnCl and PdCl solutions to avoid hydrolysis of Sn and Pd ions. Free magnesium ions had a tendency to form magnesium hydroxide so the potassium sodium tartrate was used to form complex compound with them, finally adsorbing on the surface of ceramic particles. Meanwhile, a sufficient pH value (pH = 9) could make most of the ionized tartrate ions of potassium sodium tartrate, which was conducive to the formation of magnesium complex ions. Additionally, to avoid the formation of magnesium oxide due to incomplete reduction of magnesium ions, a small amount of stabilizer (methanol) should be added in the magnesium plating solution before adding reducing agent (formaldehyde). During calcination of Mg-coated Al2O3np, the substance of the outer layer of Mg coatings reacts with oxygen to form MgO and that of the inner layer reacts with Al2O3np to in-situ form MgAl2O4 spinel according to reactions (1) and (2):

MgAl2O4-Coated Al2O3np
The generated liquid Al in reaction (2) is infiltrated to the outer layer by the capillary action of Mg coatings, and reacts with oxygen to form Al2O3, as seen in reaction (3): These newly formed Al2O3 and MgO react with each other and form MgAl2O4 spinel as the following reaction: Based on thermodynamic data [20], the calculated standard Gibbs free energy values ( G   ) for reactions (1)-(4) were −940, −226, −914, and −37 kJ/mol, respectively, which means that MgAl2O4 phase can be produced in the view of thermodynamics. Figure 2 shows the XRD patterns for Al2O3np, Mg-coated Al2O3np and MgAl2O4-coated Al2O3np. The result of XRD analysis further confirms that the ceramic particles in the present work is α-Al2O3np with a hexagonal crystal structure (a = b = 0.4758 nm, c = 1.2991 nm). It can be seen from Figure 2 that compared to the raw Al2O3np, the intensity of diffraction peaks of treated Al2O3np are decreased obviously. Some researchers [21,22] reported that structure change taken place on the surface of Al2O3 when different solutions were used, finally causing the intensity change of diffraction peaks. However, the intensity of diffraction reflections from the matrix is not strongly affected by structural changes. Thus, the reduced diffraction intensity in the XRD patterns may be related to the crystal structure change of the Al2O3np surface due to the acidic substances in the sensitizing and activation solutions. However, the XRD pattern does not obviously show the diffraction peak of Mg and MgAl2O4 in our experiment. Maybe the content of these phases is lower [23]. The coated powders were detected by TEM to further observe their microstructures. Figure 3 shows the TEM images of these powders. It can be seen in Figure 3a that the flocculent poly-crystalline particles are attached to the surface of Al2O3np. The Energy Dispersive X-ray (EDX) (Figure 3b) analysis of selected region in Figure 3a indicates the presence of Mg. The energy peaks of C and Cu appear because of the use of copper carrier grid coated with carbon film. From the TEM image of the powders after calcination (Figure 3c), it can be obviously seen that, due to the flocculent poly-crystalline successfully generated, the surface of Al2O3np becomes very rough, and the coating thickness is in the range of about 10 to about 50 nm (Figure 3e,f). Figure 3d,h display EDX analysis and magnifying High-resolution transmission electron microscopy (HRTEM) image of frames A and B in the Figure  3c, respectively. It is worth noting that the intensity of Mg energy peak weakened compared to that in Figure 3b, which means the structure of the coatings have changed after calcination. The EDX result is the same as that reported by Zhou et al. [24] for the MgAl2O4 phase. The (Inverse Fast Fourier Transition) IFFT image is shown in Figure 3g by taking an inverse Fourier transform of the HRTEM of a single crystal in Figure 3h. Through IFFT analysis of the HRTEM, the interplanar crystal spacing of the single crystal was 0.2335 nm, corresponding to the (222) lattice plane of MgAl2O4. Also, the generated single MgAl2O4 was in the size range from about 5 to about 10 nm. Figure 3i Figure 4 shows the schematic diagram of nanoparticles entering the melt. In this study, MgAl2O4coated Al2O3np was treated as a spherical particle with radius R. The chemical potential and surface excess of solute are neglected since mass transfer does not occur in the interface between ceramic particle and liquid Al due to the transient ultrasound. The interface energy of particles before entering melt can be expressed by:

Thermodynamic Mechanism of Nanoparticles Entering Melt
For the particles on the surface of the melt, the interface energy is given as: where σ pl , σ pg , and lg σ are particle-liquid interface energy, particle-gas interface energy, liquidgas interface energy, respectively.  is the radius angle formed by the melt surrounding the particle, which changes from 0° to 180° during particle entering melt. The surface free energy changes from position a to b can be expressed as: Based on Young's equation, Equation (7) can be simplified to: ( ) where θ is the contact angle. According to Equation (8), when θ 90   , 0 surf E  , which indicates that the particles can spontaneously enter the melt; when θ 90   , the particles need to overcome the energy barrier in order to enter the melt. Therefore, for ceramic particles with poor wettability, wetting driving force should be applied to the particles/Al alloy system to realize the wetting.  Figure 5 shows the wettability of Al2O3np before and after coating treatment. As seen from Figure  5, the contact angle for the raw Al2O3np is 145°, while that of the MgAl2O4-coated Al2O3np is only 100° which is similar to the result reported by Guo et al. [9], indicating the coatings have improved the wetting between ceramic particle and Al melt. According to the results reported by Kaptay et al. [25] and Barin et al. [20], the lg σ value in this study was 0.7981 J/m 2 . Figure 6 shows the surface free energy change during particles with different sizes entering the melt. It can be found that at the minimum surface free energy change, the value of  (80°) can reflect the degree of ceramic particles spontaneously entering the melt and is independent of particle size, namely maximum radius angle ( 0  ), and its relation with contact angle is 0 180 θ =  −  . Also, when 0   , the particle can spontaneously enter the melt since the negative surface free energy change values are decreased with the increase of  , which indicates that the high value of 0  due to the good wettability makes the particles easily enter the melt. In addition, for a given  , the surface free energy change value is decreased with the increase of particle size, meaning the larger particles are easier to enter the melt. This is consistent with the fact that ultra-fine particles are difficultly added into the melt. When 0   , the particles need to overcome the energy barrier to make them completely enter the melt, and the larger the particle is, the higher the energy barrier is. Ultra-fine particles would difficultly enter the melt in the later stage of particle addition due to their agglomeration by the van der Waals force attraction. For the untreated Al2O3np (Figure 6b), the value of 0  was only 35° and the energy barrier approached 331.7273 × 10 −15 J, which is increased by 140.52% compared to that of the MgAl2O4coated Al2O3np. It is noted that the negative effect of van der Waals force can be eliminated by complete wetting of the particles, resulting in their spontaneous entering. Thus, improving the wettability of ceramic particles is an effective way to make them enter the melt smoothly.  Whether the particles can smoothly enter the melt in the later stage depends on the energy obtained by the surrounding. The ultrasonic intensity I in the melt was proposed by Eskin et al. [26], which can be given by: and the energy produced per unit time can be expressed by: where ρL is the density of Al melt, C is the sound speed in the melt, f is the frequency, A is the vibration amplitude, and S is the area of probe end. The nominal intensity at the probe-melt interface is above 15 × 10 3 W/cm 2 at A = 40 μm, where f = 20 kHz, ρL = 2700 kg/m 3 [14], and C = 4.58 × 10 3 m/s [27]. This value is two orders of magnitude greater than the required cavitation threshold (Ic) in the melt of light alloys (∽100 W/cm 2 [26]). Meanwhile, the energy produced per unit time (E) is 196.01 × 10 3 J. These indicate that high energy ultrasonic vibration can be generated in the melt and provides enough energy for ceramic particles entering the melt to overcome the energy barrier.

Ultrasonic Dispersion
The acoustic pressure at the probe-melt interface can be described by the following Equation [13]: Then, the high-energy ultrasonic wave is propagated to the melt and the acoustic pressure as a function of melt depth can be expressed by a wave equation:  (12) where P is the output power of ultrasonic vibration, D is the end face diameter of probe, and z is the distance from the end face of probe, namely melt depth. In this study, P = 1.0 kW, D = 40 mm, thus the acoustic pressure amplitude (PA) was 4.4375 × 10 6 Pa. The acoustic pressure in the actual state needs to be modified due to the impedance of metal melt, and a correction factor is introduced by [28]: where β is the nonlinear coefficient of fluid (β = 10), Ma is the Mach number, k is the wave number, and v0 is the effective vibration velocity at the probe end.  (14) Consequently, the formed gradient of acoustic pressure by its attenuation in the melt could lead to fluid jet, and then to a circulation flow, that is, acoustic streaming. The acoustic streaming velocity at the probe-melt interface depends on the following equation, which was given by Campbell et al. [29]: In this study, the U = 2.886 m/s, which is much higher than that induced by the thermal convection (10 −3 m/s [30]). Thus, the acoustic streaming plays an important role in dispersing particles. Figure 7 shows the distribution of acoustic pressure in the melt, based on Equations (12) and (14). Sauter et al. [31] revealed that the acoustic pressure that was above the threshold required for cavitation (Pc) could induce the collapse of cavitation bubbles, in which the melts absorbed the energy due to these collapses, thereby creating instantaneous shock waves. In this study, the cavitation taken place in the Al melts when P(z)mod ≥ Pc (∽10 bar [26]). Note that a large number of amorphous Al2O3np could act as the substrate for vapor-gas nuclei, which greatly reduced the cavitation threshold and facilitated the onset of cavitation. It can be found in Figure 7 that the acoustic pressure declines from the peak value to zero when the melt depth increases from 0 to 57.25 mm, and then returns to the peak value when the melt depth reaches 114.5 mm. The continuous process occurs with a further increase in the melt depth. Consequently, in some regions of the melt, the acoustic pressure is lower than the threshold required to produce cavitation for particle dispersion as shown in Figure 7b, leading to intermittent unsatisfaction. To overcome the above problem, the mechanical vibration along the axial direction was introduced at the bottom of the graphite crucible while ultrasonic treatment was carried out, which could make the total melts automatically tuned to the cavitation region by adjusting the distance from the end face of probe in melt. In addition, the acoustic pressure was reduced with the increase of melt depth because of the impedance of metal melt as shown in Figure 7b, which indicated that the depth of crucible should be suitably chosen.   [32] reported that for a given acoustic pressure, ultrasonic frequency was inversely proportional to vibration amplitude, and the ultrasonic vibration with a low frequency and high amplitude promoted the dispersion of micron-sized particles in the melt. During the addition of MgAl2O4-coated Al2O3np, for a given acoustic pressure, the ultrasonic vibration at a frequency of 10 kHz generated a wave with amplitude of 80 μm and its wavelength was two times higher than that for the ultrasound of 20 kHz, causing the formation of big vortex. The variable shear stress (τ) produced by liquid flow, destroyed the weak connection between particles in the aggregation, as shown in Figure 8a. Consequently, lots of small and medium-sized aggregations of nanoparticles were separated from the large ones, which led to the macroscopic dispersion of these particles, as shown in Figure 8b. In the small and medium-sized aggregations, there exist a strong van der Waals force attraction, which means that the minimum pressure for overcoming the van der Waals force needs to be provided in order to avoid particle agglomeration. When the cavitation bubbles collapse, the produced pressure can be expressed as [33]: (16) where Ph is the hydrostatic pressure, γ is the specific heat, and the internal pressure of the bubble (Pm) is PA + Ph. In this study, Ph = 0.1 × 10 6 Pa，Pm = 4.5375 × 10 6 Pa, and γ = 4/3, thereby giving a maximum theoretical value for Pc of about 5 GPa, which is more than sufficient to disperse single nanoparticles, as shown in Figure 8c. In addition, the pressure acting on the nanoparticles had a frequency of 20 kHz, namely, 20,000 cycles per second, finally leading to a fatigue break of attractions between nanoparticles. Simultaneously, single nanoparticles and small aggregations were well dispersed in the melt by acoustic streaming, as shown in Figure 8d.

Equilibrium Migration Velocity Model Prediction
The particle migration in the matrix is related to the size, equilibrium migration velocity of particles and solidification velocity, and affects their distribution. When the solidification velocity is greater than that of equilibrium migration of particles, these particles are engulfed by the solid-liquid interface, and thus distributed within the grain. Conversely, they are pushed toward the grain boundaries and eutectic regions. Thus, the model for calculating the equilibrium migration velocity of nanoparticles should be proposed to regulate the particle distribution. In this study, individual or small aggregations of nanoparticles, medium-sized aggregations and large aggregations are treated as a single spherical particle with different sizes. The high speed impacts of liquid molecules on particles owing to the instantaneous collapse of cavitation bubbles are neglected since the liquid molecules are relatively uniformly distributed around the particles, leading to counteracting of these forces. The buoyancy force that is produced due to the difference in density between the particles and the melt can be described by: where ρp is the density of Al2O3 particles (4050 kg/m 3 ), V is the volume of particle, and g is the gravitational acceleration (9.8 m/s 2 ). A viscous force is applied to the particles when the melt flows through them, which can be expressed by [34]: where vp is the migration velocity of particles and η is the viscosity coefficient of the melt (0.4 Pa s [14]). In addition, the particles are affected by scattering of the acoustic pressure wave corresponding to the radiation force, which is given by [35]: where ac  is the acoustic contrast factor and assumed as  (20) It can be seen from Equation (20) that the equilibrium velocity for particles migration increases with the increase of particle size, suggesting that larger particles have a greater tendency to be pushed toward grain boundaries and eutectic regions, and then act as obstacles against grain growth, accordingly leading to grain refinement. Whereas, fine particles are easily engulfed by solidification front due to their low equilibrium migration velocity, and thus distributed inside grain, which leads to the improved strength of the composites due to dispersion strengthening of ceramic particles, and simultaneously promotes the coordinated deformation between grains owing to the absence of nanoparticles on the grain boundaries. Thus, under the premise that the ceramic particles are well dispersed, lots of ultra-fine particles will be engulfed inside grains by using rapid solidification rates, such as laser surface cladding, cryogenic technology, etc., finally improving the comprehensive mechanical properties of composites. Thus, based on the proposed model, the required microstructures of composites could be obtained by controlling the size and distribution of nanoparticle clustering in the melt and the solidification rate. Figure 9 shows the average grain size of the composites (davg) containing 1.5 wt.% MgAl2O4coated Al2O3np vs cooling rate and corresponding microstructures. The result of Differential scanning calorimetry (DSC) analysis revealed that the liquidus temperature of the as cast Al7075 was 637.37 °C. Thus, the solidification time (ts) can be obtained. According to the modified solidification rate Equation [14]: where davg is the average grain diameter. The growth rate of crystal at different cooling rates, namely solidification rate, can be obtained, as listed in Table 1. For particle radii ranging from 50-10 μm, the equilibrium migration velocity as a function of particle size is shown in Figure 10, which is quantitatively shown for a given particle size. It can be found from Figure 10 that the equilibrium migration velocities under ultrasonic condition are one to two orders of magnitude greater than these obtained under static condition, which means that the ultrasonic vibration can accelerate the migration of particles. It is worth noting that the equilibrium migration velocity of particles with 3.0 μm under ultrasonic treatment is similar to that of particles with critical radius (2.77 μm, about 3 μm) under static solidification. This means that the particles with critical radius may not be affected by external force. In addition, it can be also seen from Figure 10 that under ultrasonic treatment, the particles within the range of 0-1 μm will be engulfed by the solidification front and thus distributed in the grains for a given solidification rate of 0.93 × 10 −6 m/s, while the particles above 1 μm are pushed toward the grain boundaries or eutectic regions; under static condition, the critical particle radius for particle pushing, however, reaches 2.4 μm for the same solidification rate, as shown in the shaded part of Figure 10. When the solidification rate is reduced to 0.78 × 10 −8 m/s, the particles in the range below 100 nm are engulfed, and other particles are pushed. Therefore, under ultrasonic condition, a higher solidification rate is needed to realize the engulfing and make particles distributed in the grains.    Figure 11 shows the distribution of nanoparticles in the composites with 1.5 wt.% ceramic reinforcements fabricated at the cooling rates of 0.36 and 117 °C/min, respectively. When the cooling was carried out slowly at 0.36 °C/min, many of ceramic particles below 100 nm were uniformly distributed in the grains of composites obtained under ultrasonic treatment (Figure 11a), while the nanoparticles with about 130 nm were found in the eutectic regions (Figure 11b). Figure 11c shows the distribution of nanoparticles at a rapid cooling rate of 117 °C/min. It can be found that the nanoparticles or their aggregations in the size range above 1 μm are pushed toward the grain boundaries. For static solidification, however, the nanoparticles or agglomerations below 2.5 μm were distributed in the grains and the large ones were located on the grain boundaries, as shown in (a) (b) (c) (d) (e) Figure 11d. Thus, only smaller particles can be captured by solidification front at a lower solidification rate, while other particles are pushed toward the grain boundaries or the final solidification regions because of the increased equilibrium particle migration velocity by ultrasonic treatment. The EDS results of particles distributed in the matrix further identify the MgAl2O4-coated Al2O3np presence and their distribution condition. The experimental results agree reasonably well with the calculation results obtained by the above model.

Conclusions
• The poly-crystalline nano-MgAl2O4 layer could be in-situ generated on the surface of Al2O3np by electroless plating and calcination.  • The acoustic streaming and instantaneous cavitation pressure of about 5 GPa resulted in the uniform distribution of particles in the melt when the ultrasonic vibration with variable frequency was introduced. • The established model reveals that ultrasonic vibration promotes particle migration in the melt and that greater solidification rates need to be selected for particle being engulfed inside grains.

Conflicts of Interest:
The authors declare no conflict of interest.