Introduction

Aluminum is an ideal material to produce the housing and industrial materials, and they should possess both good castability and excellent mechanical properties. Die casting is the most common processing technology to produce Al-based alloys with thin-walled structures in industrial production. Pure aluminum has relatively poor mechanical properties, and thus, alloying is effective to enhance the mechanical properties of pure aluminum.

The Al–Si eutectic alloy is the mostly used as aluminum cast alloys in the transportation industry with their strong corrosion behavior, high ratio of strength to weight and castability. The melting conditions, temperature gradient, solidification rate, composition of the alloy and heat treatment that can be applied during and after casting are considered as the main control parameters to obtain the desired microstructure and mechanical properties of aluminum alloys (Ref 1,2,3,4,5).

Recently, the researchers have found new external solidification control parameters which are the semi-solid compaction, agitation, ultrasonic vibration, selective laser melting, alternative current, direct current and DC voltage. They have concluded that the desired mechanical properties of alloys might be obtained by controlling these parameters during the solidification of alloy. In addition to these, there are extra cost-effective processes such as grain refinement and heat treatment to improve the mechanical properties of alloys (Ref 6, 7).

Vibration, compression and semi-solid shaping progresses are commonly preferred to break the secondary dendrite arms and change the morphology of Si during the solidification in the Al-Si eutectic alloy. The strength property of the material was improved by producing small secondary dendrite arm spacings(SDAS) and the changing the morphology of the Si (Ref 2, 8,9,10,11,12).

Alternative current, direct current and magnetic field as a new alternative external control parameters have been extensively applied into the molten alloys, and their effects on the microstructure and mechanical properties of the alloys were clearly observed (Ref 12,13,14,15,16,17,18,19,20). In addition, the electrical pulse effects on the distribution of the elements in the electro pulsing alloy (Ref 14) are determined. The molten Bi–Mn eutectic alloy was solidified with the alternating current, static electric field and magnetic field (Ref 15). Manuwong et al. (Ref 16) have concluded that the externally applied electro pulsing is more effective a control parameter than the magnetic flux and Lorentz force parameters in magnetic refinement.

Zhang et al. (Ref 17) have investigated the distribution of electric currents on the grain size of solidified Al–Si hypoeutectic (Al–7wt.%Si) alloy under the application of electric current with constant parameters flowing through two parallel electrodes into the melt within a cylindrical mold and found that the mechanism of grain refinement driven by electric current is dendrite fragmentation induced by forced flow.

J, Li et al. (Ref 18) have solidified the Al–Si hypereutectic (Al–28.51 wt.%Si) alloy by applying direct electric current and examined the distribution of silicon. Electric current generates a Joule heat, which slows down the cooling rate and the precipitated area of primary silicon decreases with the increasing the current density. Direct current causes a convection leading to the migration of primary silicon in the opposite direction of electric field, which forms the accumulation area.

Räbiger et al. (Ref 19) have examined the effect of both direct current (DC) and rectangular current pulses (ECP) by applying electric current in their study. After the interaction between the applied current and the self-induced magnetic field, the Lorentz Force is formed, which produces an electro eddy flux and the Lorentz force acts as grain refiner.

The direction of DC electrical current and thus electrical field was normal to the S–L interface growth direction, and the electrical field force acting on the liquid atom does not influence on the atomic mass flux of liquid atoms at the S–L interface in the Al–Si hypoeutectic and Al–Si hypereutectic alloys (Ref 17,18,19). The magnetic field force and thus Lorentz force affect the atomic mass flux of liquid atoms at the S–L interface. But the magnitudes of applied Lorentz force acting on the liquid Al and Si atoms were not determined or not given for the Al–Si hypoeutectic and Al–Si hypereutectic alloys (Ref 17,18,19). Joule heating exists in the presence of current in these works (Ref 17,18,19).

The influences of static external electrical field on the microstructure were clearly seen in the Al–Cu eutectic system, but the researchers could not fully explain the effect of magnitude and direction of external static electrical field on microstructure (Ref 22). The dependence of microstructure parameter on E+ and E− was also not identified, and they (Ref 22) have just observed that the E+ and E− have affected on the lamellar structure and grain sizes.

More recently, Al–33.0 wt.% Cu and Al–6.4 wt.%Ni, which are well-known eutectic systems, were solidified with different magnitudes of E+ and E− (7.0-10.0 kV cm-1) with none current or none joule heating to investigate the influences of E+ and E− on λ, HB and σUTS by Basit et al (Ref 22, 23). They (Ref 22, 23) have observed that lamellar and rod structures, grain sizes and mechanical properties have been significantly influenced by the magnitudes of E+ and E− (7.0-10.0 kV cm-1) with none current or none joule heating in the Al–Cu and Al–Ni eutectic systems when the direction of E is same or opposite with the growth direction of S–L interface (Ref 22, 23). According their investigations (Ref 22, 23), the external high DC voltage applied into molten alloy has charged the Al, Cu and Ni atoms as +3 and +2 cations, respectively. Thus, Al+3, Cu+2 and Ni+2 cations were accelerated by the positive and negative electrical forces, F+ and F−, respectively, during the solidification. Therefore, the F+ and F− increase and decrease, respectively, the atomic mass flux of liquid Al, Cu and Ni atoms at S–L interface.

The other well-known binary eutectic system is Al–12.6 wt.% Si eutectic system, which has irregular eutectic structure. After the recent work done by Basit et all (Ref 22, 23), the influences of E+ and E− on the irregular eutectic microstructure and mechanical properties of Al–Si eutectic alloy were wondered. So how the E+ and E− influence on the λ, HB and σUTS values in the Al–Si eutectic system? It is because the alloying element of Si is semiconductive and the microstructure of Al–Si eutectic system is the irregular eutectic. For this purpose, the Al–Si molten alloy is directionally solidified with different E+ and E− values by keeping the existing solidification control parameters at same conditions and the λ, HB and σUTS are measured with standard measurement techniques.

Materials and Methods

Experimental Apparatus

An experimental apparatus originally designed by Basit et al (Ref 22) was used to solidify the Al–Si eutectic alloy with different magnitudes of E+ and E− in the present work. The details of experimental setup and procedures are given in the literature (Ref 22). The experimental apparatus is schematically illustrated in Fig. 1, and it consists of the external static electrical field system, cooling tank and preheating furnace.

Fig. 1
figure 1

Schematic representation of experimental apparatus for solidification of alloy under the static electric field

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The preheating furnace was build up to prevent immediately solidification of molten alloy into graphite crucible, prepared in the vacuum melting furnace.

20-mm-long cylindrical cooling tank was made of stainless steel, and the water was circulated through to cooling tank to solidify the molten alloy. A 10-mm part of the cooling tank was inserted into hot zone at the bottom of preheating furnace to solidify the molten alloy from bottom to top, and the temperature of cooling tank is kept constant at 291 K using a heating/refrigerating circulator.

An external static electrical field system was set up by connecting the output of FUG HCP 1400-35000 type DC high voltage source terminal to sample and a spacing of 4-6 mm between the sample and the earthed disc as shown in Fig. 2. DC high voltage source supplies the DC voltage up to 35 kV by a maximum 40 mA output current.

Fig. 2
figure 2

Schematic illustration of irregular eutectic structure growth under the static electrical field at different directions (a) positive and (b) negative

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The experimental error in the measurements of the space between the sample and stainless steel disc is determined as 2.7% (Ref 22).

Solidification of the Al–Si Eutectic Alloy Under Static Electrical Field

Al–12.6 wt.% Si eutectic master alloy was prepared by melting the required quantities of Al and Si with 4N and 5N purity of Al and Si, respectively, into a graphite pot (30 mm ID× 40 mm OD and 150 mm in length) under the vacuum. After allowing time to get homogenous melt, the Al–Si molten alloy into the graphite pot was cool down spontaneously under vacuum. Then, the Al–Si master alloy was cut into small pieces and sufficient amount of the Al–Si master alloy was re-melted into another graphite melting crucible (10 mm ID × 40 mm OD, 80 mm in deep and 100 mm long) under vacuum. The molten Al–Si alloy was homogenized by mixing with one end closed an alumina tube with a 25-minute time interval at least 4 times. The preheating furnace was heated up to the melting temperature of alloy while the Al–Si molten alloy was prepared. After homogenization, the graphite pot contains the Al–Si molten alloy, was taken from the vacuum furnace and then placed into the preheated furnace.

The E+ and E− were utilized into melts as shown in Fig. 2. The Al–Si molten alloy kept under the high external static electrical field was solidified from bottom to top by turning the cooling water on and the preheating furnace input power off until the preheating furnace temperature was fell down 50 degree below the Al–Si melting temperature. When the melting furnace temperature was 50 degree below the eutectic temperature, the graphite pot was quickly taken out from the solidification furnace to prevent the heat treatment during the cooling its temperature to room temperature and the graphite pot was broken to remove the specimen. Then, the specimen was rapid quenched into water bath. The solidifications of Al–Si alloy with different E+ and E− values (14, 16 and 17.9 kV cm–1) were done. A reference specimen was also solidified without the electric field under existing solidification conditions.

The total experimental error in the determination of E is found be 3.0% (Ref 22, 23).

Microstructure Observation and Eutectic Spacings Measurements

The solidified sample was 10 mm ID and 80 mm in length. For metallography, 5-mm-thick layer from top of sample was cut out to remove the possible oxide layer, and then, remain part of sample was cut into two pieces of 10 mm in length. After cold mounting of cross sections of these pieces, the sample were grinded and polished by MiniTech263 polishing machine, and then, the specimens were etched with 0.5wt.% HF agent to display the microstructure of the specimens for 35-40s.

The images of microstructures for the Al–Si alloy at near the eutectic composition solidified with different E+ and E− magnitudes were photographed with an optical microscope, and the eutectic spacings (λ) were measured from the photographs of microstructure using a software supplied by Nikon Company. At least 10 measurements of λ for each sample were made into a central circle of 5 mm radius for statistical reliability, and then, the average value of λ was considered. The statistical error with standard division in the measurements of λ is about 10% (Ref 23).

Hardness Measurements

After analyzing of microstructures, the cross-sectional surfaces of specimens were roughly flat by grinding with SiC paper for hardness measurements. The Brinell hardness measurements were made using a BULUT RBOV-200 type hardness tester, which has 62.5 kilograms of load with 2.5 mm in diameter a steel ball. At least 10 HB measurements for each sample were carried out to get reliable hardness value. The estimated experiential error in the hardness measurements is 4% (Ref 23).

Tensile Test Measurements

10 mm length from each end of samples was cut out, and the remain part of specimens was machined to form a shape, which is shown in Fig. 3 for σUTS measurements.

Fig. 3
figure 3

Geometrical illustration of tensile test specimen

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The σUTS values for the Al–Si eutectic alloy solidified with different values of E+ and E− were measured by a strain rate of 1mm/min at room temperature using INSTRON 8872 type universal tensile testing machine, which has Bluehill software. The σUTS measurements were made on longitudinal section of specimen, which is same direction with growth direction of S–L interface, and were repeated at least 4 times. The experimental error in the σUTS measurements is estimated to be 2% (Ref 23).

Results and Discussions

Influence of the E + and E − on λ

Figure 4 shows the microstructures of the Al–Si eutectic alloy solidified with different E+ and E− magnitudes. As shown in Fig. 4, the Al–Si eutectic alloy has an irregular eutectic microstructure. It was wonder whether the irregular eutectic structure could become a regular structure or not with the applied external static electric field?

Fig. 4
figure 4

Optical images of irregular eutectic structure for Al–Si eutectic system solidified with different directions and magnitudes of E; (a) 0.0 kV cm1; (b) 14.0 kV cm−1; (c) 16.0 kV cm−1; (d) 17.09 kV cm−1; (e) −14.0 kV cm−1; (f) −16.0 kV cm−1; and (g) −17.09 kV cm−1

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As shown in Fig. 4, the static external electrical field did not affect the direction of S–L interface growth and the irregularity the Si phase. While E+ and E− greatly affected the size of Al matrix phase, it did not affect the Si phase much even though the E values applied into the Al-Si system are approximately three times the E values applied into the Al-Cu and Al-Ni eutectic systems. Thus, the E+ and E− did not affect the λ value in the Al-Si eutectic alloy as much as the λ values in the Al-Cu and Al-Ni eutectic alloys. The atomic mechanism causing these differences can be explained as follows.

From fundamental of physics, the i specie liquid cation can be accelerated by the F acting on i specie liquid atom, and thus, the acceleration of i specie cation can be expressed as

$$a_{i}^{E} = \frac{{F_{E,i} }}{{m_{i} }} = \frac{{q_{i}^{*} E}}{{m_{i} }} = \frac{{Z_{i}^{*} \left| e \right|E}}{{m_{i} }}$$
(1)

where mi is the atomic mass of i specie ion, \(F_{E,i} = q_{i}^{*} E\) is the static electrical force acting on i specie cation, \(q_{i}^{*} = Z_{i}^{*} \left| e \right|\) is the charge of i specie cation and \(E = \left| {\overrightarrow {E} } \right|\) is the static electrical field. When the direction of E is parallel or antiparallel to the S–L growth direction, the F+ and F− act on each kind of atoms, and thus, the atomic mass flux for each kind of atoms at the S–L interface was influenced by the F+ and F−. As can be seen from Eq 1, the magnitude of acceleration for i specie cation depends on \(Z_{i}^{*}\) and mi with a constant E. Therefore, the increment or decrement in the V of S–L interface depends on the F+ and F− values.

The E+ and E− magnitudes were in the range of 14.0-17.9 kV cm−1 in the present work. As shown in Fig. 4 and Table 1, while the thickness of Alα phase was enlarged and reduced by increasing the E+ and E− values, respectively, the thickness of Si phase was not sufficiently changed by increasing the E+ and E− values. It seems that the E+ and E− do not strongly affect the irregular structure of Si phase in Alα matrix. The mechanism of atomic transportation during the solidification under static electrical field might be explained as follows.

Table 1 λ, HB and σUTS values for Al–12.6 wt. pct. Si eutectic system solidified with variable values of E+ and E−
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Al and Si are metal that will always lose free electrons. The halogens all have seven valence electrons. Each one of these elements wants to gain one electron to achieve an octet. Metals will always lose electrons to form cations. As aluminum has 3 valence electrons, it tends to lose electrons; then, after losing these 3 electrons, it becomes cation, which has +3 charges. Silicon is also a metal, and it can lose its 4 valence electrons and becomes cation, which has +4 charges.

When E+ and E− are applied into the Al–Si molten eutectic alloy, it can be assumed that the liquid Al and Si atoms are charged as Al+3e and Si+4e cations, respectively. The magnitudes of F+ and F− affecting on Al+3e and Si+4e cations during the solidification must be higher than the sum of surface tension and fraction forces for liquid Al and Si atoms. The present experimental results show that while F+ and F− values affecting on liquid Al+3e cation are sufficient to increase or decrease the mass transfer of liquid Al atom, the F+ and F− values affecting on liquid Si+4e cation were not sufficient to increase or decrease the mass transfer of liquid Si atom during the solidification.

The critical E value required for changing the size of Al phase in Al-based binary alloy (\({E}_{critical}^{Al}\)) was found as 6 kVcm−1 (Ref 22). If liquid Si atom is charged as Si+4e cation with the applied E, the critical value of E required for changing the microstructure of Si phase in Al matrix (\({E}_{critical}^{Si}\)) can be estimated by writing Eq 1 for Al+3e and Si+4e cations and then comparing them into each other to get equal acceleration. The accelerations of Al+3e and Si+4e cations should be equal to see similar effects on each Al+3e and Si+4e cations. Therefore, the \({E}_{critical}^{Si}\) value can be estimated from Eq 1 by using the determined value of \({E}_{critical}^{Si},\) and it can be expressed as:

$$E_{{{\text{critical}}}}^{{{\text{Si}}}} = \frac{{q_{Al} }}{{q_{Si} }}\frac{{m_{Si} }}{{m_{Al} }}E_{critical}^{Al}$$
(2)

The free electrons of Al and Si atoms are +3e and +4e, and the atomic mass of Al and Si atoms is 26.98 and 28.08, respectively. The surface tension of liquid Al and Si is also 0.896 and 0.784 N m−1 (Ref [23]), respectively, and they are also close to each other. From Eq 2, the \({E}_{critical}^{Si}\) value is determined to be 5 kV cm−1. The \({E}_{critical}^{Si}\) value of 5 kV cm−1 for Si+4e cation is one third of 14.1-17.9 kV cm−1 value applied into the Al–Si molten alloy in the present work. Thus, the applied E values (14.1-17.9 kV cm−1) are normally sufficient to increase or decrease the atomic mass flux of Si atoms at the S–L interface if liquid Si atom is charged as Si+4e cation. But the change of Si phase size in the Al matrix by E+ and E− was not clearly observed in the present work. From experimental observations, it can be concluded that the liquid Si atom was not charged as Si+4e cation because Si only occurs as ions on the gas phase and only at very high temperatures in a vacuum or inert gas. This means when E+ and E− are applied into the Al–Si molten alloy, the liquid Al atom was only charged as Al+3e cation by E+ and E−. Thus, the F+ and F− affect Al+3e cations and do not affect the uncharged Si atom. The mass transfer of liquid Al atom is affected by F+ and F−, and the mass transfer of liquid Si atom is not affected by F+ and F− during the solidification of Al–Si molten eutectic alloy under static electrical field. Therefore, the thickness of Alα phase is expanding by increasing the value of E+ or getting thinner by increasing the value of E−. However, the thickness of Si phase was not considerably changed with increasing the values of E+ and E−.

The eutectic spacing (λ) was measured with the triangle method (Ref 24). The λ values were measured from optical images taken from the cross sections of 2 different samples, and the average values of λ are given in Table 1. As shown in Fig. 4 and Table 1, an increment in the average value of \({\lambda }_{Ave}^{+}\) was observed with increasing E+ and a decrement in the average value of \({\lambda }_{Ave}^{-}\) was observed with increasing the E− in the Al–Si eutectic alloy. While the increment in the value of \({\lambda }_{Ave}^{+}\) is 100% at E+ =17.9 kV cm−1, the decrement in the value of \({\lambda }_{Ave}^{-}\) is 34% at E− =17.9 kV cm–1 in the Al–Si eutectic alloy.

The average λ versus the E+ and E− were plotted in logarithmic scale and are given in Fig. 5. The variation in λAve with E+ and E− is linear, and the relationships between them were determined from linear regression analysis as

$$\lambda_{{{\text{Average}}}}^{ + } (\mu m) = 0.01 \times E_{ + }^{2.56}$$
(3)
$$\lambda_{{{\text{Average}}}}^{ - } (\mu m) = 87.09 \times E_{ - }^{ - 1.11}$$
(4)
Fig. 5
figure 5

λ versus E+ and E− plots for the Al–Si eutectic system

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A comparison of λ dependence on E+ and E− for the Al–Si eutectic system obtained in the present work with the λ dependence on V, E+ and E− for the Al-based binary or ternary eutectic systems obtained in previous works (Ref 22, 23, 26, 30) is given in Table 2. The exponential 2.56 value of E+ for Al–Si eutectic system is very close to the exponentials 2.77 and 2.87 values of E+ for the Al–Cu and Al–Ni eutectic systems (Ref 22, 23), respectively. But the exponential 1.11 value of E− for Al–Si alloy is 44 and 21% is smaller than the exponentials 2.00 and 1.41 values of E− for the Al–Cu and Al–Ni eutectic systems (Ref 22, 23), respectively.

Table 2 A comparison of λ, HB and σUTS dependences on E+ and E− for Al–12.6 wt. pct
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The exponential values of E+ are close to each other for Al–Cu (Ref 22), Al–Ni (Ref 23) and Al–Si eutectic systems. But the exponential 1.4 and 2.0 values of E− for the Al–Cu and Al–Ni (Ref 22, 23) eutectic systems are bigger than the exponential 1.11 value of E− for the Al–Si eutectic system. The number of free electrons for Al and Cu, and Ni atoms is 3 and 2, respectively. The free electron number for Cu and Ni atoms is equal, and the atomic mass of Cu and Ni is 63.5 and 58.69, respectively. The free electron number for Al atom is 30% higher than the free electron numbers for Cu and Ni atoms, but the atomic mass of Al is one third of atomic mass of Cu and Ni. According to the results obtained for the Al–Si eutectic system, Si liquid atom which was not charged with E+ and E− or the F+ and F− affecting Si+4 liquid ion is not sufficient high to increase or decrease the atomic mass transfer of liquid Si atom at the S–L interface. The eutectic melting temperature of Al–Cu, Al–Si and Al–Ni systems is 821, 850 and 913 K, respectively. Therefore, the atomic mass flux due to the E+ and E− at the S–L interface is very complicate and depends on free electron numbers and atomic mass, alloy composition and melting temperature during the solidification.

Table 2 also shows the λ dependence on E+ is 4 times of the λ dependence on V and the λ dependence on E− is at least twice of the λ dependence on V in Al–Si binary or ternary alloys. The influences of E+ and E− on λ are higher than the influence of V on λ, and thus, the both magnitude and direction of E are an external control parameter for solidification when its direction is parallel or antiparallel to the S–L interface growth direction.

Dependence of HB on E+ and E−

The Brinell hardness measurements for the Al–Si alloy were made on the cross sections of samples, which are directionally solidified with different E+ and E−, and the average Brinell hardness (HB) values are given in Table 1. As mentioned above,\({\lambda }_{Ave}^{+}\) increases, and thus, the HB+ decreases with increasing the value of E+, but the \({\lambda }_{Ave}^{-}\) decreases and the HB– increases with increasing the value of E−. These decreases or increases in the HB values due to the changing of the Al phase size with E+ and E− are theoretically expected variations. The variations in HB with E are plotted in Fig. 6, and the relationships between them are found as:

$${\text{HB}}^{ + } = 91.20 \times E_{ + }^{ - 0.16}$$
(5)
$${\text{HB}}^{ - } = 25.11 \times E_{ - }^{0.32}$$
(6)
Fig. 6
figure 6

HB versus E+ and E− plots for the Al–Si eutectic system

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As shown in Table 1 and Fig. 6, the applied external static electric E+ and E− into the Al–Si molten alloy during the solidification seems to clearly influence the HB as well as the λ. The HB+ values for the sample solidified at 14.0, 16.0 and 17.9 kV cm–1 were measured to be 60.23, 63.25 and 65.27 kg mm–2, respectively, while the HB– values for the samples solidified at −14.0, −16.0 and −17.9 kV cm−1 were also measured as 58.79, 57.82 and 56.7 kg mm−2, respectively. The HB+ and HB- values measured in the present work are the average value of 10 hardness measurements for each sample.

The exponential 0.16 value of E+ is about half of exponential 0.32 value of E− in the Al–Si. This means that the E− is more effective than the E+ in the Al–Si eutectic system.

The HB+ and HB− dependences on E+ and E− for the Al–Si eutectic system determined in the present work were also compared with the HB dependences on V, E+ and E− for the Al-based binary and ternary eutectic systems determined in previous works (Ref 22, 23, 26, 30) and are given in Table 2. Exponential 0.16 value of E+ for the Al–Si eutectic system is about one fourth and one sixth of exponential 0.61 and 0.96 values of E+ for Al–Ni (Ref 23) and Al–Cu (Ref 22) eutectic systems, respectively. The exponential 0.32 value of E− for the Al–Si eutectic system is about half of the exponentials 0.63 and 0.51 values of E− for Al–Ni (Ref 23) and Al–Cu (Ref 22), respectively.

Additionally, Table 2 shows that HB dependence on E+ and E− is stronger than the HB dependence on V in the Al–Si binary and multicomponent systems.

Effects of E + and E − on σ UTS

Figure 7 shows the ultimate tensile stress versus strain curves for the Al–Si eutectic alloy directionally solidified with different E+ and E− values. The σUTS, YS and %El values for the Al–Si eutectic alloy were determined from stress–strain graphs and are given in Table 1.

Fig. 7
figure 7

Stress–strain curves for the Al–Si eutectic system solidified with different values of (a) E+ and (b) E−

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Figure 8 shows the variations in σUTS with E+ and E−. Figure 8 and Table 1 show the σUTS value decreases with increasing E+ while the σUTS value increases with increasing E− The reason for this difference is the exactly same reason with hardness variations. Again, the E+ and E− affected the atomic mass flux of liquid Al atoms at the S–L interface during the solidification and the growth rate of S–L interface increases or decreases. Thus, any increment or decrement in the V value due to E+ and E− affects the microstructure and thus the mechanical properties of alloys.

Fig. 8
figure 8

σUTS versus E+ and E− plots for the Al–Si eutectic system

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The relationships between σUTS and E+ and E− were determined with regression analysis as:

$$\sigma_{UTS}^{ + } = 251.18 \times E_{ + }^{ - 0.18}$$
(7)
$$\sigma_{UTS}^{ - } = 125.89 \times E_{ - }^{0.09}$$
(8)

The influences of E+ and E− on σUTS for the Al–Si irregular system are compared with the influences of E+, E− and V on σUTS for the Al-based binary or ternary alloys obtained in previous works (Ref 22,23,24,25,26) and given in Table 2. The exponential 0.18 and 0.09 values of E+ and E−, respectively, for the Al–Si irregular eutectic system are very close to the exponential 0.20 and 0.11values of V for the Al–Si–Mg (Ref 26) and Al–Si–Ni–Fe (Ref 27) irregular eutectic system, respectively. The exponential 0.18 value of E+ for the Al–Si irregular eutectic system is one fourth and one sixth of exponentials 0.77 and 1.31 values of E+ for Al–Cu (Ref 22) and Al–Ni (Ref 23) eutectic systems, respectively. Nevertheless, the exponential 0.09 value of E− for the Al–Si irregular eutectic system is one fifth and one tenth of exponentials 0.45 and 1.12 values of E+ for the Al–Cu (Ref 22) and Al–Ni (Ref 23) eutectic systems, respectively. From Table 2, it can be also concluded that the dependences of σUTS on E+ and E− for the Al–Si irregular eutectic system are not stronger than the dependence of σUTS on E+ and E− for the Al–Cu (Ref 22) and Al–Ni (Ref 23) regular eutectic systems.

As shown in Table 1, the YS and %El for the Al–Si eutectic alloy are also affected from E+ and E−. Increment in the YS value is about 6% with increasing E− while decrement in the YS value is about 10%. According to %El values shown in Table 1, the %El value increases about 4% and 2% by increasing E− and E+ values, respectively. It is expected that when the YS value increases, the %El value should be decreased or vice versa. But the %El also increased while YS value increased by increasing E+ value in the present work. This disparity might be coming from an error in the determination of %El value.

From the above discussion, it might be expressed that the microstructure and physical and mechanical properties for alloys produced by electrically chargeable metals can be controlled by the external control parameter of static E when its direction is parallel or antiparallel to the S–L growth direction.

Conclusions

Both the direction and magnitude of E applied into Al–Si molten alloy did not affect the S–L interface growth direction and the irregularity Si phase. While E+ and E− affect effectively the size of Al matrix phase, the size of Si phase was not affected by E+ and E− because liquid Si atom was not charged with the E+ and E− The F+ and F− acting on charged liquid Al atoms increase or decrease the acceleration of the liquid Al atoms at the S–L interface during the transformation from liquid to solid. Therefore, the F+ and F− lead an increment or decrement in the atomic mass flux of liquid Al atoms at the S–L interface when its direction is parallel or antiparallel to the S–L interface growth direction. Thus, the λ, HB and σUTS values in the Al-Si eutectic system are not affected as much as in the Al–Cu and Al–Ni eutectic systems by E+ and E− magnitudes. Therefore, dependence of λ, HB and σUTS on E+ and E− in the Al–Cu and Al–Ni eutectic alloys are stronger than dependence of λ, HB and σUTS on E+ and E− in the Al–Si eutectic alloy.

From experimental results, it can be concluded that the external static E plays an affective role to control the atomic mass flux for alloys at the S–L interface during the solidification of alloys produced by electrically chargeable metals when its direction is parallel or antiparallel with S–L interface growth direction.