Dendritic Spacing and Macrosegregation Affecting Microhardness of an Al-Si-Mg Alloy Solidified Under Unsteady State Conditions

The prediction of microstructure morphology is fundamental for the manufacture of metallic components, since the expected levels of mechanical properties will be associated with the final aspects of the microstructure. In this work, an Al-7wt.%Si-3wt.%Mg alloy was directionally solidified in unsteady state conditions in order to investigate the influence of the addition of 3wt.%Mg to an Al-7wt.%Si alloy on the solidification evolution. The microstructure of the examined alloy is shown to be characterized by a more complex arrangement of phases, as compared to that of the Al-7wt.%Si alloy, which includes the binary (α-Al+Mg 2 Si) and refined ternary (α-Al+Si+Mg 2 Si+Fe-rich IMC) eutectic mixtures. A higher Vickers hardness profile is shown to be associated with a more refined microstructural arrangement. However, for cooling rates lower than 2K/s the microhardness is shown to increase with the increase in the microstructural spacing, which is shown to occur caused by Si macrosegregation and higher content of free Mg.


Introduction
Al-Si cast alloys have been widely employed in the manufacture of engine components, such as cylinder heads and engine blocks. This class of alloys combines high strength to weight ratio, excellent thermal conductivity, wear and corrosion resistance. All these characteristics and properties make these alloys potential materials to the replacement of cast iron 1,2 . The engine represents on average, about 5% of the entire vehicle mass. One of the biggest challenges of the today's designers is to render high efficiency with low energy consumption and low gas emission. This scenario has been ideal for the development of light alloys, and particularly, the development of aluminum alloys is thus far from being finished. It is known that reducing weight is a very effective way to lower a vehicle´s fuel consumption. Therefore, the reduction of wall thickness without compromising the resistance to the stresses acting inside an engine is one of the main challenges facing aluminum casting industry. The A356 aluminum alloy is an important Al-Si-Mg structural material offering good specific strength associated with high levels of ductility, and excellent wear as well as corrosion resistances. Binary Al-Si alloys do not harden via heat treatment, but the addition of Mg improves the mechanical strength due to the precipitation of the Mg 2 Si intermetallics (IMC). This phase is very efficient to increase the mechanical strength at room temperature of 3xx.x and 6xxx series aluminum alloys [3][4][5][6][7] .
The use of the Al-7wt.%Si-0.3wt.%Mg alloy has been outstanding in the production of aluminum castings due to its excellent castability and excellent achievement of mechanical properties after heat treatment 4,5 . Although the literature contains several works on the influence of Si and the cooling rate on the microstructure of Al-Si alloys, there is not much information concerning the concomitant influence of the Mg content and the cooling rate on the morphology of as-solidified microstructures 5 . In order to form the Mg 2 Si IMC, Mg is usually added to Al-Si alloys in the range 0.3 to 0.6 wt.% 6 . In hypoeutectic alloys, this Mg content gives rise to the formation of Mg 2 Si in the form of fine needles in the ternary eutectic mixture (Al + Si + Mg 2 Si). The Mg 2 Si IMC (or β phase) is a face-centered cubic crystal (FCC), with melting point of 1087°C, specific mass of 1.88g/cm 3 and Vickers hardness of 456HV 6 . At room temperature, the microhardness of this IMC can reach 546HV whereas in one hour at 300°C this value drops to 180HV, revealing that the Mg 2 Si has low thermal stability. In this case, metastable coherent Mg 2 Si phases (β' and β'' phases), which can be achieved by appropriate heat treatments, may be very effective reinforcing phases 6,7 .
Recently, some studies have analyzed the effect of Mg contents above 3wt.% on the microstructure of Al-Si based alloys. According to Mandal and Makhlouf 8 , the addition of Mg (in the range from 1 to 5 wt.%) in hypereutectic Al-14wt.%Si-0.2wt.%Fe alloys induce the formation of a eutectic mixture of Si and Mg 2 Si particles surrounding the α-Al dendritic matrix. Tebib et al. 4 reported that an Al-15wt.%Si-14wt.%Mg-4wt.%Cu hypereutectic alloy can be considered a metal/matrix compound, where the primary phase Mg 2 Si (in the form of dendrites) acts as a homogeneously distributed hard reinforcement in a strong and ductile eutectic matrix (Al + Si + Mg 2 Si). In this microstructural pattern, the Mg 2 Si IMC would reinforce the matrix during its plastic deformation 4 . On the other hand, the literature is scarce on studies concerning the effect of Mg contents above 1wt.% on Al-Si-Mg hypoeutectic alloys.
Alloying elements such as Mg, Cu, Zn, Ni, Cr, Pb, Sn, Mn and Fe are generally added to Al-Si alloys in order to achieve mechanical properties and corrosion resistance for specific applications. However, care should be taken with the alloy Fe content, due to detrimental effects to mechanical and corrosion resistances caused by the formation of IMCs, such as the needle-like β-Al 5 FeSi 6,9-12 .
Iron has low solubility in Aluminum 6 , so Fe contents higher than 0.03wt.% led to the formation of Fe-rich IMCs, whose morphologies depend on the solidification cooling rate and the chemical composition of the alloy 13 . Basically, three patterns have been reported in the literature: acicular, Chinese script, and fishbone-like (or skeleton-like shape). The β-AlSiFe phase (Al 5 SiFe), due to its hard and brittle characteristics, is considered the most harmful for Al alloys. When Mg is present in Al-Si alloys containing Fe, the π-AlSiFeMg phase (Al 8 Mg 3 FeSi 6 ) is formed, which is also deleterious to the mechanical properties, responsible for reducing the ductility of Al-Si alloys 4 . In general, raw material is increasingly scarce due to the global consumption of limited resources. Currently, aluminum is the second most used metal in human activities. Due to the high cost production of primary aluminum, and due to the finite reserves of bauxite (main aluminum ore), the recycling of this metal is fundamental with a view to providing a growing share of total aluminum supply 14 . Efforts have been made to guarantee the quality of recycled aluminum in order to comply with the designed properties. Therefore, it is important to understand how the Fe content will influence the formation of IMCs in Al-Si-Mg castings, for determining the tolerances of Fe content in Al alloys when recycled aluminum is employed 4,15,16 .
Peres et al. 17 analyzed the microstructural morphology of Al-Si hypoeutectic alloys produced by a directional solidification technique. The authors observed for a wide range of solidification cooling rates, a microstructure composed essentially of a dendritic α-Al matrix with a eutectic mixture, formed by Al + Si, with Si in the shape of needles, located in the interdendritic regions. Canté et al. 14 evaluated the effects of the cooling rate (in the range of 0.5 to 28K/s) and of the Fe content on the microstructure of an Al-9wt%Si alloy. Coarsening of secondary (λ 2 ) and tertiary (λ 3 ) dendritic arms was observed to occur with decreasing cooling rates, as well as with decreasing incidence of acicular β-AlSiFe IMC (also associated with the decrease in cooling rate). The β-AlSiFe IMC particles are distributed between the dendritic arms, λ 2 and λ 3 , becoming coarser with the reduction in cooling rate. The coarsest microstructure was shown to be associated with the lowest ultimate tensile strength, and to a substantial 50% reduction in the elongation-to-fracture of this alloy.
Brito et al. 18 reported that the morphology of the Alrich matrix of an Al-3wt.%Mg-1wt.% Si alloy changes from cellular to dendritic for solidification cooling rates less than 1 K/s, and that a mixture of Mg 2 Si and β-AlFeSi IMCs were shown to be distributed in the intercellular and interdendritic regions as eutectic compounds. It was shown that the Vickers microhardness (HV) exhibited an increasing trend with the decrease in the cell spacing (λ C ), however, an inverse behavior with respect to the primary dendritic arm spacing, λ 1, was observed, where HV increased with the coarsening of λ 1 . The authors attributed the latter behavior to the better distribution of IMCs throughout the interdendritic regions. In a recent work, Brito et al. 18 have observed that a more refined microstructural arrangement (both matrix and IMCs) showed better corrosion resistance in a 0.06M NaCl solution. The mechanical properties showed similar behavior, and the best combination between ultimate tensile strength and elongation-to-fracture was obtained for the most refined cellular microstructural arrangement 19 .
The literature is still scarce of researches on the effects of solidification thermal parameters, macrosegregation, and the scale of microstructure dendritic arrays on the mechanical properties of hypoeutectic Al-Si alloys castings with Mg contents higher than 1wt.%. In order to obtain a directionally solidified (DS) casting under unsteady-state solidification conditions, a water-cooled solidification setup was used, which permitted a wide range of cooling rates to be investigated. The objective of the present work is to analyze the influence of the addition of 3wt.%Mg to an Al-7wt.%Si alloy on the dendritic growth of the Al-rich matrix, and to establish correlations between the dendritic scale of the microstructure, nature and fractions of precipitated IMCs, and the resulting microhardness along the length of the DS casting.

Materials and Methods
The Al-7wt.%Si-3wt.%Mg alloy was prepared from commercially pure Al, Si and Mg-Al master alloy. The alloy was directionally solidified in a solidification apparatus, in which heat was removed from a water-cooled bottom, promoting vertical upward unsteady-state solidification. Details concerning the solidification apparatus can be found in a previous study 20 and in Figure 1(a). When a melt temperature of about 35°C above the alloy liquidus temperature (T L ) was achieved, the heating system was switched off and at the same time the cooling system was activated, allowing the start of solidification. With a view to determining the cooling rate during solidification, eight (8) fine type K thermocouples (0.2 mm diameter wire) were placed in the geometrical center of the cylindrical mold cavity along its length. Figure 1(b) shows the Al-7%wt.Si-xMg pseudo binary phase diagram, calculated by the Thermo-Calc software, where a vertical dashed line indicates the nominal composition of the examined alloy.
The microstructural analysis was carried out on cross and longitudinal sections of samples extracted from the DS casting at the positions: 5, 10, 15, 20, 25, 30, 40, 50, 60, 70, 80, 90 and 100mm from the water-cooled bottom. Subsequently, the samples were ground with sandpapers, and polished with 1μm diamond paste. No chemical etching was required to reveal the microstructure. Optical microscopy was performed using an Olympus Inverted Metallurgical Microscope (model 41GX). The primary (λ 1 ), secondary (λ 2 ) and tertiary dendritic arm spacings (λ 3 ) were measured from optical images referring to the aforementioned sections along the length of the alloy casting. The triangle method 21 was used in order to perform the measurements of λ 1 at the cross sections. The intercept method 20 was adopted for measuring λ 2 and λ 3 at the longitudinal sections. At least 30 measurements were performed for each selected position along the length of the casting. The IMCs were characterized by SEM micrographs and microanalysis using a ZEISS Scanning Electron Microscope (ZEISS-EVO-MA15), equipped with an Energy Dispersive Spectrometer (EDS) model OXFORD X-MAX.
A detailed analysis of area fractions (AF) of the IMC particles have been determined for each sample associated with different positions along the length of the DS casting. Dimensionless shape factors (circularity-C and aspect ratio-AR) of the IMC particles were defined by a relation between the area of the particle surface (S) and its perimeter (C = 4πS/p 2 ) for circularity 14,21 . The circularity factor varies from 1.0 for a perfect circle, decreasing up to zero with the increasing complexity of the morphology of the examined particles.
X-Ray Fluorescence (XRF) analyses were carried out on cross-section samples, using a Rigaku device, model RIX3100, target area of 100mm². The patterns of X-ray Diffraction (XRD) analyses were obtained by a XRD diffractometer X'Pert Pro model MRD XL with a 2-theta range from 35 to 90 deg, Cu-Kα radiation with a wavelength of 0.15406 Å. Vickers microhardness tests were performed in a Shimadzu HRV-2 microdurometer according to the ASTM E384 standard 22 . Twenty indentations were performed for each sample. A 0.5 kgf load and a dwell time of 15 seconds of loading were used.   The solute partition coefficient (k 0 ) of all alloying elements is less than unity (k 0 < 1), which promotes the rejection of the solutes ahead of the solid/liquid interface. A negative segregation of Si, ranging from ~ 6wt.% (on the base) to ~ 8.5wt.% (at top of DS casting) was observed. Similar Si segregation behavior was reported for Al-Si-Sn 11 and Al-Si-Cu 23 alloys solidified in the same DS apparatus. The Mg profile was fairly constant along the entire DS casting length, and no significant segregation of this element occurred. The density of Mg (ρ Mg ) is lower than that of Al (ρ Al ); that is: ρ Mg ~ 70% ρ Al 24 . Due to this fact, increase in the Mg content ahead the solidification interface was expected to occur. However, this did not occur, as shown in Figure 2b. Brito et al. 17 have observed a similar behavior when analyzing compositions of samples extracted along the length of a DS Al-3wt.%Mg-1wt.%Si alloy casting. Vreeman and Incropera 25 have reported positive segregation at regions close to the cooled surface of the casting with an Al-6wt.%Mg alloy. They attributed this behavior to the effect of solidification shrinkage followed by interdendritic flow of the Mg-enriched melt. In the present study, it seems that an equilibrium has been established between upward gravity-driven Mg and downward shrinkage effects. Fe is normally a residual element of commercially pure Al. An average content of 0.15wt%Fe was observed along the entire DS casting length. A higher Fe content at the region immediately ahead the cooled bottom of the casting is shown in Figure 2(b). This enrichment of Fe is caused by Fe diffusion from the steel sheet that separates the casting from the cooling water 18 .

Results and Discussion
The cooling curves during solidification, shown in Figure 3(a), were obtained from a set of thermocouples placed in the geometrical center of the cylindrical mold cavity along its length. Figure 3(b) shows the plot of position (P) from the metal/mold interface and the corresponding time (t) of the liquidus front passing by each thermocouple. A P(t)=a.t b type function was fitted to the experimental data, being "a" and "b" constants. The derivatives of these functions with respect to time gave values for the growth rate (V L ), as shown in Figure 3(c). The cooling rate (Ṫ) was determined along the castings lengths, by considering the derivatives with respect to time of the thermal data recorded immediately after the passage of the liquidus front by each thermocouple. The resulting experimental Ṫ profile is shown in Figure 3(d).   17,23,26,27 . There are two types of eutectic mixtures in the interdendritic regions: 1) ternary eutectic: Al + Si particles + Mg 2 Si + Fe-rich IMC and 2) binary eutectic: Al + Mg 2 Si, as will be shown further. Close to the metal/mold interface, a more refined morphology can be observed due to the highest values of growth rates and cooling rates in this region. On the other hand, with the increase in distance from the cooled bottom of the casting, V L and Ṫ progressively decrease and the dendrite coarsening progresses. The results obtained in this research showed the beginning of the growth of tertiary dendritic arms (λ 3 ) for cooling rates lower than 6K/s, which stabilizes for cooling rates lower than 3K/s. It is possible to verify the regular presence of this type of dendritic arm in  analyzed the tertiary dendritic growth of binary hypoeutectic Al-Si alloys solidified in unsteady state conditions. The authors reported that a composition of 7wt% Si only showed stable λ 3 growth conditions to for cooling rates lower than 2K/s. The addition of 3wt% Mg seems to have anticipated the destabilization of the solid/liquid interface at the secondary dendritic arms favoring the growth of tertiary dendritic arms for higher values of cooling rate. Figure 5 shows the evolution of the microstructural parameters λ 1 , λ 2 and λ 3 as a function of the solidification thermal parameters V L and Ṫ. In the development of experimental power functions relating the growth of λ 1 in unsteady state conditions as a function of Ṫ, several authors 17,18,23,26,27 have derived a same exponent: -0.55. In the present study λ 1 has been correlated with Ṫ by a power function given by λ 1 =263 Ṫ -0.55 , as shown in Figure 5a. Peres et al. 16 obtained an experimental growth law of λ 1 as a function of Ṫ given by λ 1 =220 Ṫ -0.55 , for hypoeutectic Al-Si alloys. Comparing the growth of λ 1 for the DS Al-7wt%Si-3wt%Mg casting with that of an Al-7wt% Si 17 alloy, it was observed that the addition of 3wt.% Mg induced an increase in λ 1 for a same cooling rate range.
The experimental correlation λ 2 vs Ṫ for the DS Al-7wt%Si-3wt%Mg alloy casting, shown in Figure 5(b), is given by . For the Al-7wt.%Si 16 the literature reports . By comparing the aforementioned λ 2 growth laws, it can be seen that the addition of Mg to the Al-7wt.%Si alloy resulted on an opposite effect as compared to that associated with λ 1 , i.e. λ 2 decreases with the addition of Mg. In this work, the tertiary dendritic arms, λ 3 , were identified and measured accordingly, as depicted in Figure 5(a). The same exponent used for primary dendritic growth (-0.55) can represent the evolution of λ 3 with Ṫ, λ 3 =31 Ṫ -0.55 . The average λ 3 values varied from 16.5 to 34.4 µm. Rosa et al. 26 evaluated the value of λ 3 for hypoeutectic Al-Si alloys and proposed the following experimental growth law λ 3 =18 Ṫ -0.55 . In this case, the addition of Mg (similarly to the growth of λ 1 ) increases λ 3 for a same Ṫ, as compared to results of binary hypoeutectic Al-Si alloys. Secondary phases or intermetallic compounds (IMCs) were characterized by X-ray Diffraction and Scanning Electron Microscope (SEM) equipped with an Energy Dispersive Spectrometer (EDS). As shown in Figure 2(b) the Al-7wt. Si-3wt.%Mg alloy has a residual content of Fe of about 0.15wt.%. This content is enough to change the equilibrium pseudo-binary-phase diagram shown in Figure 1(a). Therefore, a Scheil-Gulliver (S-G) simulation was carried out in order to predict the new phases due to this residual Fe content. According to S-G computations performed by the Thermo-Calc Software, 0.15wt.%Fe enabled partial precipitations to occur during solidification, as shown in Figure 6(a). This is in agreement with the observations reported by Lima et al. 27 who identified on an Al-7wt.Si-0.3wt.%Mg alloy, the growth of α-Al, Si, Mg 2 Si, β-AlSiFe and π-AlSiMgFe. Figure 6(b) shows the XRD analysis that identified the following phases: α-Al, Si, Mg 2 Si and π-AlSiMgFe. Essentially, these are the same IMCs which were predicted by the Scheil-Gulliver computations.
The addition of 3wt.%Mg to the Al-7wt%Si alloy produced a more complex microstructure, with the formation of larger fraction of secondary phases. Figure 7(a) shows the morphology of the secondary phases for a cooling rate of 1.2K/s. In the region of binary eutectic, the morphology of the Mg 2 Si phase is a Chinese-script like 28 . This IMC occurred for the entire range of analyzed cooling rates, as part of the eutectic binary with Al, or still combined with Si and Fe-rich phase at the ternary eutectic mixture. The morphology of the Fe-rich phase was strongly influenced by the reduction in the cooling rate. For Ṫ> 3K/s these phases formed more frequently in the form of tertiary eutectic. For Ṫ lower than 1K/s, the tendency is to generate an acicular morphology. The composition of each phase was presented in a table inside Figure 7(b). Figure 7(c) shows SEM/EDS analyses with EDS elemental mapping indicating the composition and distribution of the elements in each phase. Liu and Kang 27 reported that the addition of Mg to Al-Mg-Si alloys has a strong influence on the formation of the solidification microstructures. The increase in the Mg content favors the increase in the fraction of Mg 2 Si particles. These authors also observed that the presence of Fe segregation to the final zone of solidification lead to the formation of a complex IMC (Al, Fe, Mg, Si), as well as of a tertiary eutectics, evidencing that even low Fe contents should not be neglected. Figure 8(a) shows a plot of the Mg content 19 in solid solution (Mg SS ) in the Al-rich matrix along the length of the DS Al-7wt.%Si-3wt.%Mg alloy casting, determined by SEM/EDS for three samples. A reduction in Mg SS can be observed from bottom to top of the casting thus allowing a higher content of free Mg (Mg F ) to be available, with the other alloy elements, to form the IMCs. Mg has a relatively high solubility in Al 29 . However, as the temperature is reduced a decrease in solubility occurs, and at room temperature Mg has a maximum solubility of approximately 0.4wt.%. In Al-Si-Mg alloys, Mg 2 Si formation occurs when Mg and Si are present at a Mg/Si ratio of 1.73, and its fraction will be proportional to the Mg content in the alloy 30 . According to Closset and Gruzleski 31 , the formation of iron-rich IMC is influenced by the Mg content. With more Figure 5. Correlations between dendrite arm spacings and solidification thermal parameters: a) λ 1 and λ 3 evolution as a function of cooling rate; and b) λ 2 evolution as a function of growth rate for the ternary Al-7wt.%Si-3wt.%Mg alloy casting.  Mg F at positions far from the cooled bottom of the casting, the volume fractions of Mg 2 Si and π-AlSiMgFe IMCs increase, as can be observed in Figure 8 (b). In order to confirm this reasoning, image analyses using the Image-J software were carried out. The mean values of area fractions and shape factors of the Mg 2 Si (dark particles) and π-AlSiMgFe IMCs (white particles) in the SEM images of Figure 7 have been determined for any cooling condition analyzed. In Figure 8(b) it can be observed a reduction in circularity of both IMCs with decreasing cooling rates (middle gray column). A reverse tendency can be observed for the fraction and aspect ratio, which increased with slower cooling conditions. Mg 2 Si and π-AlSiMgFe IMCs showed quite close values of circularity and aspect ratio along the entire length of the DS casting. The π-AlSiMgFe IMC shows higher aspect ratios associated with the decrease in cooling rate.  The higher fraction of Mg 2 Si IMC is related to the local contents of Mg and Si, since in Al-Si-Mg alloys the Mg 2 Si fraction is proportional to both Mg and Si contents of the alloy. It is worth noting that for positions in the casting associated with lower cooling rates a higher amount of Si is available due to macrosegregation effects (Figure 2), which combined with the higher Mg F amount (Figure8a) favors the formation of higher fractions of both IMCs.
Vickers microhardness tests were performed in transverse samples extracted along the entire DS casting length. Figure 9 shows the experimental measured values of Vickers microhardness as a function of the square root of λ 2 . Two different trends on the evolution of HV with λ 2 -1/2 can be observed (characterized by an inflection point at λ 2 -1/2 = 0.19µm -1/2 ). The adoption of two Hall-Petch type relationships seems to be appropriate for representing the hardness evolution with λ 2 for the examined alloy. Figure  4 showed stable growth of λ 3 from a lower cooling rate 3K/s. Despite the relatively small variation of λ 2 and λ 3 values along the monitored levels of cooling rates, other metallurgical features may interfere on hardness. In recent work, Kim et al. 32 , using compression and nanoindentation tests, have evaluated the deformation mechanism of an Al-Cu-Si alloy. A fractographic analysis carried out by using atomic force microscopy (AFM) showed that the enhancement of mechanical properties was due to the combined contributions of shear banding mechanisms associated with cooperative boundary sliding/rotation. Additionally, nanoindentation analyses confirmed that the interfacial sliding occurred during plastic deformation at the dendrite (soft)/eutectic (hard) interface.
Regions having higher values of λ 1 along the length of a DS casting are associated with higher values of λ 2 and λ 3 , which are generally associated with smaller values of hardness as compared to regions of smaller dendritic spacings 11 . As shown in Figure 9, this is so for the HV profile from the lowest λ 2 experimental value (highest λ 2 -1/2 value) up to the inflection point 11,18 , from which HV increases with decreasing dendritic spacings, that is for cooling rates lower than 2K/s, HV increases with the increase in λ 1 , λ 2 and λ 3 (decrease in λ 2 -1/2 ). Such increase in hardness even with increasing dendritic spacings can be attributed to the plastic constraint promoted by increasing fractions of hard π-AlSiFeMg and Mg 2 Si IMCs in regions closer to the top of the DS casting.