Grain-refining effects and mechanism of novel Al-Nb-B refiner on Al-Mg-Si alloy: phase-field simulation and experiment study

In this paper, the grain-refining effect of Al-Nb-B refiner in wrought Al alloys and corresponding refining mechanism was investigated using phase-field simulation and experiment methods. Through experimental statistics and data correction, the seed radius introduced by Al-Nb-B refiner into Al alloy melt and the corresponding quantitative density distribution data were obtained, and a seed density model (SDM) model has been established. On this basis, a multi-phase field method (MPFM) combined with the calculation of phase diagram (CALPHAD) has been employed to simulate the α-Al grain evolution of Al-Mg-Si alloy during the solidification process with the help of thermodynamic database. Experimental studies showed that the addition of 0.03 wt% Nb (Adding by Al-1.93Nb-0.22B master alloy) significantly reduced the grain size from 956.4 μm to about 219.4 μm, and the grain size slowly decreased to 192.3 μm by continuing to add refiner to 0.09 wt% Nb. Meanwhile, the simulation results demonstrated that after the addition of refiners, dendrite morphology transformed from the relatively developed dendrites with secondary and tertiary dendrites to a fine and uniform equiaxed shape. Simulation and experimental studies showed quantitative agreement. In addition, the results also prove that the addition of Al-Nb-B refiner can provide high-quality and stable heterogeneous nucleation particles.


Introduction
Al-Mg-Si commercial wrought Al alloys have been widely employed in aerospace and automobile, due to their competitive strength-to-weight ratio and excellent weldability. Hot deformation is an essential procedure for process optimization and mechanical properties improvement. Flow stress is the most important parameter for characterizing plastic deformation properties of metallic materials. The flow stress of the alloy with coarse grains was higher than that with fine grains at elevated temperatures [1][2][3]. Grain refinement is one of the most effective ways for the wrought Al alloy to improve its plastic deformation properties.
Adding master alloys (inoculants) to the melts is the most frequently used method to achieve alloys with fine grains. Al-Ti-B refiner is widely used in industry to refine Al alloys, which can improve the microstructure and properties of ingots [4]. However, Al-Ti-B refiners have poor refinement effect in alloys with high Si content (2.0 wt%) due to the interaction between Si and Ti which leads to the formation of titanium silicides depleting the melt of Ti. This phenomenon, which is called the Si-poisoning effect, is well known and has been proved by many researchers [5,6]. Nowak [5] reported that Nb-based compounds are highly effective in refining the α-Al dendrites grains in Al-Si alloys. The Al 3 Nb and NbB 2 phases in the refiner acted as nucleating seeds and existed stably in the melt [7]. The possibility of forming niobium silicide in Al alloy melt at 700°C-800°C is less than that of titanium silicide due to the lower reaction kinetics of niobium silicide [5], which [8,9] resisted the Si-poisoning by Al-Nb-B refiner (Adding in the form of master alloy) in Al-Si alloys. In recent years, Al-Nb-B refiner has gradually become a research hotspot in the field of Al alloy grain refinement. In addition, Narducci [10] found that the morphological Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
transformation of the Fe-rich phase occurs in the material with the addition of the Nb+B inoculant. Therefore, the newly refiner has a comprehensive effect in refining the grain, eutectic structure [5,11] and the second phase (Fe-rich phase) [12] in Al-Si cast Al alloy. However, there are still some shortcomings in the current research on Al-Nb-B refiners, e.g., can Al-Nb-B achieve the same grain refinement effect as cast in wrought Al alloys with lower Si content? Thereby expanding its scope of application. On the other hand, the model between inoculating particle size, distribution density, and nucleation undercooling of Al-Nb-B refiner has not been established. And the effect of Al-Nb-B refiner addition on the dynamic growth behavior of α-Al dendrites has not yet been revealed.
The current experimental dynamic characterization methods are limited. The In-situ synchrotron radiation technique can only characterize the solidification behavior of aluminum alloys with high copper content. Due to the difficulties in experiments, the phase-field method, which can accurately depict the dendritic morphology based on the diffusion interface, has become the best choice for studying the dynamic evolution of Si-containing aluminum alloy dendrites. The multi-phase field method (MPFM) is an advanced formulation for multiphase or multigrain systems that employed the phase field method for two-phase systems [13,14]. Wei et al [14] simulated the distribution of Cu-containing phases in the solidification structure of A2214 Al alloys by the phase field method and obtained the distribution and formation process of different Cu-containing phases. Bunck M et al [15] simulated the microstructure evolution of A356 Al alloy during the semi-solid solidification process. Nomoto et al [16] combined MPFM and calculation of phase diagram (CALPHAD) based to simulate the grain size of the solidification process of Al-Si-Ti-B quaternary alloy. All these researches indicated that MPFM is very suitable for microstructure simulation for metal materials with high precision.
In this study, the refining effect and mechanism of the Al-Nb-B refiner in Al-Mg-Si wrought alloy was firstly carried out. An SDM model describing nucleation particles was established by experimental statistical methods, and then it was introduced into the phase-field method to study the effect of Al-Nb-B refiner on morphology evolution during solidification. Finally, the principle of refinement is revealed by analyzing the cooling curve and combining experiments. The significance of this work lies in in-depth understanding of the relationship between the characteristics of particles (e.g. inoculating particle size, distribution density, amount added, and nucleation undercooling) incubated by Al-Nb-B refiner in wrought Al alloys of Al-Nb-B refiner, as well as their impact on crystal growth behavior, and enriching the grain refinement theory of Al-Nb-B refiner.

Material and procedures
In this paper, the Al-Mg-Si (0.8wt% Mg and 1.0wt% Si) alloy was used as raw material. Al-1.93Nb-0.22B (wt%) master alloy, provided by CITIC Metals Co., Ltd, was used as refiner. The casting process was conducted as the following process: First, put all raw materials (including Al-Nb-B refiner) into the furnace of vacuum induction melting furnace, and start vacuuming to 6-7 Pa. Then fill in argon and adjust the power to 30 kw to start smelting. After melting, reset the power to 20 kw, and start electromagnetic stirring refining for 3-5 min Finally, keep the temperature at about 750°C for 15 min and pour into the cylindrical mold (diameter = 95 mm, height = 100 mm), and cool it to room temperature in air. Four groups of alloy samples with different Nb contents (0 Nb, 0.03 Nb, 0.06 Nb and 0.09 Nb) were obtained. The actual compositions of Al-Mg-Si alloy with different Nb were monitored by ICP (Inductive Coupled Plasma Emission Spectrometer) and the results are shown in table 1.
The specimen used for metallographic structure analysis were prepared according to the process of grinding mechanical polishing erosion. Kohler reagent (mixed solution of hydrofluoric acid + hydrochloric acid + nitric acid + water, volume ratio of 2:3:5:190) was used to erode the specimen. The grain size analysis sample shall be eroded with 5% HF solution. The metallographic structure was observed with an OLS4100 laser confocal microscope. The Quanta 450FEG thermal field emission environmental scanning electron microscope (FE-SEM) and its energy dispersive spectroscopy (EDS) were used for the microstructure morphology and composition analysis respectively. The X-ray diffractometer (XRD) was used for the phase analysis.  [17] firstly proposed that Seed density model (SDM) could be used in the phase field method. SDM is the input parameter for nucleation in the microstructure simulation of phase field method, nucleates and grows the grains under the influence of the subsequent temperature field and alloy element concentration field.
The model was developed based on the dendrite-free growth model for calculating grain evolution. The free growth model was proposed by Geer et al [18] in combination with the classical heterogeneous nucleation process. This model holds that the critical nucleation undercooling degree on the particle is negatively correlated with the size of the particle, the specific expression is as follows: Where σ, ΔS V , and d represent the solid-liquid interfacial energy, entropy of fusion per unit volume, and nucleant particle diameter, respectively. SDM data are defined by the distribution of number density versus the radius of seed, as shown in figure 1(a). The numerical procedure for modeling nucleation using the SDM is briefly explained as follows: At the initial time, the seed in the simulation area is virtually distributed at random positions in the liquid phase area according to the distribution data. At this time, no seeds nucleate, as shown in figure 1(b). When the heat loss starts, it is checked whether each virtually distributed seed can nucleate by comparing the temperature at its position, with the amount of undercooling estimated by classical nucleation theory. If the supercooling degree is met, the area of the nucleated seeds in the liquid phase will be converted into solid phase, and then enter the phase field calculation program. When a seed starts to nucleate, its growth will release the latent heat and immediately affect other seeds waiting for nucleation. Therefore, not every nucleation seed in the melt can participate in the nucleation process. Figure 2(a) shows the microstructure of Al-Nb-B refiner which was characterized with a large number of fine seeds distributed uniformly in the α-Al matrix. The backscatter SEM photos were detected to distinguish the Nb-based seeds from the matrix and other phases in figure 2(a) and the result is presented in figure 2(c).These seeds were Al 3 Nb and NbB 2 based on XRD and EDS analysis, as be seen in figures 2(b) and (c). The radius and number of seeds of the second phase were counted by 'Nano Measure' software and the calculation region size was about 500 × 500 μm 2 . As can be seen from figure 2(c), most of the Nb-based seeds were in the shape of irregular polygons. Therefore, half of the longest diagonal of a polygon was taken as the radius in this paper. Finally, 1636 seeds were counted within the statistical region. The quantity ratio distribution of statistical results was presented in figure 2(d), which indicated that the relationship between the radius and the number of Nb-based seeds conformed to equation (2).
where ND(r) is the distribution of the radius and the corresponding seed density, N was the total number of Nbbased seeds and V m is the volume of Al-Mg-Si alloy melt. V m was about 833.33 cm 3 based on the experimental ingots. According to the ingot melted in the experimental work, the N value can be calculated using equation (4).
is the volume of one Nb-based seed which can be calculated using equation (5) [18]. V Nb is the total volume of Nb-based seeds in Al-Mg-Si alloy melt.
In the present study, the Al-Mg-Si alloy with 0.09 Nb sample was taken as the research object. The stereology method [19] was used to determine the volume of Nb-based seed. The volume fraction of the Nb-based seed is 4.5% and the corresponding volume in the Al-Mg-Si alloy melt is 1.708 cm 3 . The value of N can be calculated to be 1.708 × 10 12 . The number density distribution Nd(r) of seeds in the melt can be obtained by introducing the values of N, V m , and y(r) into equation (3). For the Al-Mg-Si alloy with 0.09 Nb, the final ND(r) calculation result is shown in figure 3.
According to the nucleation procedure and condition, there was a maximum number of seeds that can be activated and participate in nucleation under a given degree of undercooling. The free growth model [18], showed that larger seeds preferentially nucleate. It was necessary to optimize the ND(r) distribution data. In the optimization process, the radius of seeds that was less than 1 μm was not included in the calculation. Therefore, the modified seed distribution data was shown in the yellow histogram in figure 3. It can be found that the distribution is closer to the log function, and its distribution function shows in equation (6).

MPFM and CALPHAD for solidification
Boettger et al [17] proposed a numerical method involving the combination of an MPFM with the CALPHAD and developed the corresponding MICROSS software package. It can be coupled with the detailed thermodynamic information of multicomponent and heterogeneous systems in 'Thermo-calc' thermodynamic database, and the multicomponent diffusion equation in the interface area can also be described by coupling the database of 'Dictra' diffusion simulation software. The software of MICRESS6.200 was used in the phase field method simulation in this paper. The thermodynamic calculation software of Thermo-calc2019b was applied to obtain thermodynamic information of Al alloy. The material database was COST507 database suitable for light alloy [20]. The Al alloy with Al-Nb-B refiner in this paper was Al-Mg-Si alloy with many other microalloy elements. If all the elements were brought into the phase field model, a large amount of calculation was required. Therefore, considering the calculation efficiency and effectiveness of the COST507 database, the effect of elements less than 0.25wt% was ignored due to their little growth inhibition factor [21]. In this study, the composition of the alloy was simplified as (Al-0.8Mg-1.0Si-0.7Cu, wt%) in the MPFM. The diffusion coefficient of alloy elements was set according to table 2 [22]. In the simulation process, only the evolution of α-Al phase grain is considered, and the free energy of α-Al phase in the Al-Mg-Si-Cu alloy was coupled to the MICRESS software with the help of 'Thermo-calc' software. The interface energy between liquid phase and α-Al solid phase was 1 × 10 −5 J cm −2 [23]. The interface mobility coefficient of the solid-liquid twophase M u was 5 × 10 −2 cm 4 /Js [24]. The calculation region size was 2000 μm square and the grid size was set as 4 μm square. The parameters of MPFM were optimized and determined as following. The interface width was defined as three times the length of the grid. The anisotropy coefficient of interface energy was δ σ * = 0.25. The anisotropic coefficient of interfacial mobility was δ μ = 0.05. The initial temperature in the simulation area was 930 K and the temperature gradient was 0. The heat extraction rate was −500 J s −1 ·cm −3 considering the release of crystallization latent heat. 5 positions were randomly regarded as the initial crystal nucleus and the initial crystal size was 0. The simulation starts from 0 s and the simulation results are output every 0.1 s. The values of the physical constants employed are summarized in table 3.   With the adding of Al-Nb-B refiner, the effect of Nb and B elements should be considered in the microstructure simulation of Al-Mg-Si alloy. In the alloy with 0.09 Nb, since the Nb-based seeds had stable chemical properties [7], the maximum solid solubility of Nb in Al at 750°C was only 0.034 wt% [4]. Due to the limitation of initial concentration and element properties, the contribution of Nb as solute atoms to the grain refining effect is not as good as that of ordinary Mg, Si, Cu and other alloy elements [21]. Nowak et al [4] have added Nb in the form of powder into pure aluminum to study the effect of Nb on grain refinement. The results show that the effect of Nb in the form of solute element on grain refinement was very small. Therefore, the diffusion of Nb as a solute element was considered in simulation process. And thus the effect of Nb in the form of Nb-based seeds on grain refinement was mainly studied. In addition, adjust the simulation area to 1000 μm square, and the grid division method was 2 μm square. The seed radius and corresponding numerical density distribution data of 0.09 Nb alloy optimized according to equation (5) were used as nucleation conditions. The settings of other phase field and calculation parameters according to tables 2 and 3. Figure 4 shows the α-Al grain distributions of Al-Mg-Si alloy at different cooling times. It can be seen that nucleation had occurred because the liquid phase temperature had met the supercooling requirement at a cooling time of 0.1 s. This was related to the decreased temperature caused by the heated area dissipates outward in the liquid. Then the α-Al grain grew continuously in a typical dendritic structure. The main axis of dendrite extended to the liquid and the secondary dendrite and tertiary dendrite gradually bulged during the growth process. The adjacent grains gradually contacted with each other, and the growth speed of the grains slowed down until α-Al grains filled the region.  Interface energy/J.cm −2 1 × 10 −5 [24] Interface mobility coefficient 5 × 10 −2 cm 4 /Js [24] Anisotropy coefficient of interface energy δσ * = 0.25 Anisotropic coefficient of interfacial mobility

Simulation results of Al-Mg-Si alloy without adding refiners
Heat extraction rate −500 J s −1 ·cm −3

4.2.
Simulation results of Al-Mg-Si alloy with 0.09 wt% Nb Figure 5 shows the microstructure evolution simulation results of Al-Mg-Si alloy during solidification with adding Al-Nb-B refiner. The content of Nb in the alloy was 0.09 wt%. In the simulated images, the red represented liquid phase, the white represented α-Al solid phase, and blue line was the boundary of solid phase contact. Many seeds appeared in the liquid phase according to the number and density distribution data of nucleating seeds in the early stage of the simulation. Under the combined influence of the release of crystallization latent heat, regional heat loss, and the diffusion of alloy elements, some can continue to grow, while others will disappear. At the same time, the shape of grains in the early stage was closed to equiaxed, and some grains can be observed to be swallowed up subsequently. With the continuous growth of grains and contact with each other, the boundary between them gradually flattens, and finally, the morphology of grains turns into fine equiaxed grains with uniform size.

Experimental and simulation results with different Nb contents
In this paper, it was assumed that the contents of refiners had no effect on the radius of nucleating seeds and their proportion in the melt. Only the total number of seeds in the melt was affected by the contents of refiners. The content of Nb in the previously melted samples was 0.028 wt% (0.03 Nb), 0.058 wt% (0.06 Nb), and 0.091 wt% (0.09 Nb), respectively. Therefore, the seed radius and density distribution data in 0.03 Nb and 0.06 Nb Al alloys only need to calculate the seed number density corresponding to each radius in equal proportion to the mass fraction based on 0.09 Nb Al alloy, while the radius distribution remains unchanged. Take the obtained seed radius in the melt and the corresponding number density distribution data as the input conditions for nucleation. The other simulation parameters were the same as those of 0.09 Nb alloy. Finally, the microstructure simulation diagram at 2.6 s was obtained, as shown in figures 6(b) and (c), respectively. As shown in figure 6, comparing the simulated and experimental microstructural results of Al-Mg-Si alloy, it can be found that the simulation results are consistent with the experimental ones not only in grain morphology but also in grain size. In the Al-Mg-Si alloy without Al-Nb-B refiner, the grains were coarse dendritic, and the secondary dendrites and tertiary dendrites were relatively developed. However, the alloy microstructure with Al-Nb-B refiner changed into fine and uniform equiaxed grains. The average grain size decreased slightly with the increase of refiner. Figure 7 shows the variation of average grain size of the simulated and experimental results with different Nb content. The experimental results showed the average grain size decreased significantly after the adding Al-Nb-B refiner, from 956.4 um down to 219.4 um, and the grain size slowly decreases to 192.3 μm by continuing to add refiner to 0.09 wt%. The simulated results showed the average grain size is 1100 um down to 190 um with the same addition Al-Nb-B refiner. The results indicated that a clear consistence between experiments and simulation. Figure 8 shows the simulation results of the regional temperature change curve with the cooling time of the four alloys. The important parameters in the nucleation process can be obtained from the temperature change curve. The nucleation temperature T N referred to the initial temperature point that deviates from the linearity on the cooling curve. In addition, T min and T G represented the lowest and highest temperature points for the first time after the nucleation of α-Al phase respectively, and the undercooling (ΔT = T G -T min ) can be found in figure8(a). After adding refiner, the nucleation temperature was significantly higher than that of the 0 Nb alloy. Importantly, the undercooling of the three alloys using the Al-Nb-B refiner was only around 0.8 K, which was less than 3.2 K for the Nb-free Al alloy. High-quality nucleation seeds can significantly reduce the activation energy required for nucleation process, and the undercooling degree can reflect whether the refiner can provide enough potential nucleation seeds to a certain extent. Therefore, the cooling curve of the simulation results can also show that Al-Nb-B refiner provided effective heterogeneous nucleation seeds in Al-Mg-Si alloy melt. From figure 8(b), it can be found that in the three alloys of simulation results of adding different amounts of Al-Nb-B refiner, the nucleation temperature and supercooling degree were kept at a constant level. This indicated that the addition of a small amount of Al-Nb-B refiner can provide sufficient and stable excellent heterogeneous nucleation seeds to the melt.

Grain refining mechanism of Al-Nb-B refiner
The Nb element in Al-Nb-B refiner was mainly introduced into the liquid melt in the form of Al 3 Nb and NbB 2 particles as shown in figure 2. The refinement mechanism of this novel refiner is schematic presented in figure 9. The properties of these two kinds of particles were relatively stable. They can exist stably in the melt and  do not react with other alloy elements. The interfacial wettability between Al 3 Nb phase and α-Al was superior, and the mismatch between two-phase lattices was relatively low. At the same time, peritectic reaction (L+Al 3 Nb→α−Al) occurred on the surface of Al 3 Nb phase, which promoted the nucleation of Al alloy. The nucleation process can also occur on the surface of NbB 2 particles in a non-uniform manner, but Al 3 Nb particles play a leading role in the whole nucleation process. After the nucleation process of a large number of particles, the temperature field of the surrounding seeds will be affected due to the release of the latent heat of solidification. The grains grew in the form of equiaxed crystals until they meet the surrounding grains and stop growing. Finally, the liquid phase was also completely transformed into α-Al phase, while Al 3 Nb and NbB 2 phases are distributed in the interior of grains in the form of fine particles.
Al-Nb-B refiner played a role in heterogeneous nucleation by providing a large number of stable and excellent nucleation particles to the melt, thus promoting grain refinement. The experiments were conducted under the same smelting conditions which indicated that the difference between these alloys was the number of nucleating particles introduced into the melt. Due to the characteristics of Al-Nb-B refiner, the Al 3 Nb and NbB 2 particles in the structure can be stably present in the melt, both of which are excellent heterogeneous nucleation particles. However, due to the limitation of cooling conditions and elements in alloy, the temperature and solute field in the surrounding liquid region will be affected by the nucleation process under the given undercooling conditions. As can be seen from figure 10, the size of Nb-containing particles in the microstructure of the 0.09 Nb alloy sample was significantly larger than the nucleation particles in 0.03 Nb, which indicated the particles in 0.09 Nb alloy were more inclined to form larger nucleating particles. If Al-Nb-B refiner was added continuously, the amount of Nb dissolved into the matrix was limited. The refining effect of nucleation particles reached the threshold soon which resulted in the stagnation effect. This was consistent with the grain size in figure 7.

Conclusions
This paper investigated the refining mechanism of A-Nb-B refiner in deformed Al-Mg-Si alloy by combining SDM, MPFM, and experimental methods. The main conclusions are as follows:  (1) The distribution curve between the size and density of nucleation particles was statistically analyzed and fitted through experiments. Based on the free growth theory, an SDM was established for the relationship between the size density and nucleation undercooling of incubation particles. On this basis, the average grain size and size uniformity simulated by the MPFM were consistent with the experiment, which verifies the accuracy of the model.
(2) Addition of 0.03 wt% Nb (Adding by Al-1.93Nb-0.22B master alloy) significantly reduced the grain size from 956.4 μm to about 219.4 μm, and the grain size slowly decreased to 192.3 μm by continuing to add refiner to 0.09 wt% Nb. After the addition of refiners, dendrite morphology transformed from the relatively developed dendrites with secondary and tertiary dendrites to a fine and uniform equiaxed shape. The refinement stagnation effect was attributed to the release of solidification latent heat.
(3) Combining EDS analysis and cooling curves, the grain refinement mechanism of Al-Nb-B refiner was revealed: The low lattice misfit and good wettability between Al 3 Nb and α-Al can significantly reduce the activation energy required for the nucleation process, thereby lowering the nucleation undercooling.