Compositional Design of Soft Magnetic High Entropy Alloys by Minimizing Magnetostriction Coefficient in ( Fe 0 . 3 Co 0 . 5 Ni 0 . 2 ) 100 − x ( Al 1 / 3 Si 2 / 3 ) x System

Developing cost-effective soft magnetic alloys with excellent mechanical properties is very important to energy-saving industries. This study investigated the magnetic and mechanical properties of a series of (Fe0.3Co0.5Ni0.2)100−x(Al1/3Si2/3)x high-entropy alloys (HEAs) (x = 0, 5, 10, 15, and 25) at room temperature. The Fe0.3Co0.5Ni0.2 base alloy composition was chosen since it has very the smallest saturation magnetostriction coefficient. It was found that the (Fe0.3Co0.5Ni0.2)95(Al1/3Si2/3)5 alloy maintains a simple face-centered cubic (FCC) solid solution structure in the states of as-cast, cold-rolled, and after annealing at 1000 ◦C. The alloy after annealing exhibits a tensile yield strength of 235 MPa, ultimate tensile strength of 572 MPa, an elongation of 38%, a saturation magnetization (Ms) of 1.49 T, and a coercivity of 96 A/m. The alloy not only demonstrates an optimal combination of soft magnetic and mechanical properties, it also shows advantages of easy fabrication and processing and high thermal stability over silicon steel and amorphous soft magnetic materials. Therefore, the alloy of (Fe0.3Co0.5Ni0.2)95(Al1/3Si2/3)5 holds good potential as next-generation soft magnets for wide-range industrial applications.


Introduction
Contrasted to the traditional alloy design concept that is based on one or two major elements, high-entropy alloys (HEAs) usually contain four or more major elements, and the content of each major element is above 5 at% [1][2][3][4][5][6][7][8][9][10].The high configurational entropy of the HEAs tends to promote forming the solid solution phases with the face-centered cubic (FCC) [11][12][13][14][15], body-centered cubic (BCC) [16,17], and hexagonal-close-packed (HCP) structures [18][19][20], as well as dual solid-solution phases [21][22][23].The composition of HEAs is generally near the center of the multi-component phase diagram, and hence it is difficult to distinguish the solvent from the solute.The following 5 characteristics are typically and have been verified for the HEAs [4,24,25]: (3).very low stacking-fault energy; (4).high irradiation resistance; (5).high corrosion resistance.Consequently, HEAs show promising potentials for wide ranges of industrial applications and the HEA concept is considered to be one of the three major breakthroughs in alloying theory [3].To date considerable research efforts on HEAs focus on their microstructures and mechanical properties [26][27][28][29][30][31] while there is rising interest in developing high-entropy soft magnetic materials [32][33][34][35][36][37][38][39][40].Magnetic materials play a fundamental role in transformers, motors, electromagnets, and other power industries [41].Common soft magnetic alloys include silicon steel, ferrite, iron-nickel alloys, and bulk metallic glasses.However, to date many challenges still remain for energy-saving and high-performance applications.For example, it is time-consuming to produce and process silicon-steels [42].Ferrite has low magnetization, iron-nickel alloy has low resistivity, and bulk metallic glass are inherently brittle and are also limited to small size [43,44].Recent studies have shown that FeCoNiAlSi-based and FeCoNiMnAl-based HEAs exhibit high saturation magnetization which open up new research directions of soft magnetic materials [45].However, the coercivity of HEAs is a bit high, for example, the coercivity of FeCoNi(Al,Si)0.2alloy is 1400 A/m [46].It is known that the magnetic properties of HEAs are sensitive to the alloy system and the composition, the phase crystal structures, and the microstructure.
In terms of soft magnetic materials, the most important characteristic is high permeability, high saturation induction, low core loss and low coercivity.In this study, ferromagnetic elements Fe, Co, and Ni were selected as the main constituents of the alloy system [47].The base alloy composition Fe0.3Co0.5Ni0.2 was chosen since the alloy has a close-to-zero saturation magnetostriction coefficient (λs) as shown in the Co-Fe-Ni ternary system (Figure 1).To balance soft magnetic and mechanical properties, Al and Si in small amount was added to Fe0.3Co0.5Ni0.2, and the resulting materials properties of the (Fe0.3Co0.5Ni0.2)100−X(Al1/3Si2/3)X(X = 0, 5, 10, 15, and 25) high entropy alloys were studied systematically.It was found that the (Fe0.3Co0.5Ni0.2)95(Al1/3Si2/3)5alloy exhibits excellent soft magnetic properties.The alloy has small coercivity of 96 A/m, and the saturation magnetic induction (Bs) and the saturation magnetization (Ms) reached 1.55 T and 1.49 T, respectively.The alloy in the as-cast state also shows an excellent tensile elongation up to 25% and a yield stress of 122 MPa at room temperature.

Alloys Preparation
Al, Co, Cr, Fe, and Ni elements with purities of greater than 99.5 wt.% were used to prepare (Fe 0.3 Co 0.5 Ni 0.2 ) 100−X (Al 1/3 Si 2/3 ) X alloys ingots using vacuum arc melting (VAM) and magnetic levitation melting (MLM).The alloys were remelted five times in order to improve the chemical homogeneity.The ingot of the maglev melted alloy is cut into a plate with a thickness of 6 mm.Then the plate was cold rolled to a thickness of 1 mm (i.e., thickness reduction of 83%) by multi-pass rolling, with 0.5 mm reduction for each step.Subsequent annealing heat treatment was performed at 1000 • C for 2 h followed by water quenching or furnace cooling.

Structural Characterization and Performance Experiments
The crystal structures of the ingots were measured by a Smart Lab X-ray diffractometer (Bruker D8, Karlsruhe, Germany), using Cu-Kα radiation.The electron backscatter diffraction (EBSD) was carried out by a field emission scanning electron microscope (ZEISS SUPRA 55, Jena, Germany).Room temperature compression and tensile tests were conducted on a CMT Model 4305 Universal Electronic Tester with a strain rate of 1 × 10 −3 min −1 .A hysteresis loop and hysteresis loss curve were obtained by PPMS (physical property measurement system) and VSM (Vibrating Sample Magnetometer) at room temperature.The four-point method was used for measuring the electrical resistance.

Results
Figure 2 shows the XRD profiles of (Fe 0.3 Co 0.5 Ni 0.2 ) 100−X (Al 1/3 Si 2/3 ) X HEAs, (X = 0, 5, 10, 15, and 25).When X = 0, 5, and 10, the alloys possess a simple FCC structure.When X reaches 15, BCC phase appears and the alloy exhibits an FCC + BCC dual-phase structure.When the (Al 1/3 Si 2/3 ) content increases to 25, the FCC phase disappears and only BCC phase was detected.Al has a much larger atomic radius than the transition metal elements of the alloys and it is known as a potent BCC phase stabilizer in steels.Figure 3 shows the hysteresis loops of the (Fe 0.3 Co 0.5 Ni 0.2 ) 100−X (Al 1/3 Si 2/3 ) X series alloys at room temperature.The saturation magnetization of these alloys decreases gradually from 168.06 Am 2 /kg to 116.48 Am 2 /kg with increasing (Al 1/3 Si 2/3 ) contents.The compression stress-strain behavior of (Fe0.3Co0.5Ni0.2)100−X(Al1/3Si2/3)Xalloys is shown in Figure 5, and the corresponding yield stress and plastic strain are summarized in Table 1.In general, the yield stress of the alloys increases with increasing the (Al1/3Si2/3) content.When X = 5, the alloy maintains good plasticity with certain work hardening ability, and no fracture occurred during compression test.When X ≥ 15, the yield stress increases rapidly with a large reduction in plasticity.
The variation of mechanical properties is attributed to the different phase structures and microstructures.Dissolution of Al and Si in the FCC lattice of transition metals of Fe, Co, and Ni causes severe lattice distortion, contributing to pronounced solid solution strengthening.However, excessive addition of Al and Si promotes the formation of BCC phase, and the strength of the alloy increases rapidly at the cost of significantly reduced plasticity.Similar trend on the effect of Al contents on the phase stability and mechanical properties of high entropy alloys is reported by Tang et al [48].The compression stress-strain behavior of (Fe 0.3 Co 0.5 Ni 0.2 ) 100−X (Al 1/3 Si 2/3 ) X alloys is shown in Figure 5, and the corresponding yield stress and plastic strain are summarized in Table 1.In general, the yield stress of the alloys increases with increasing the (Al 1/3 Si 2/3 ) content.When X = 5, the alloy maintains good plasticity with certain work hardening ability, and no fracture occurred during compression test.When X ≥ 15, the yield stress increases rapidly with a large reduction in plasticity.Table 1.The magnetic properties and compression behavior of (Fe0.3Co0.5Ni0.2)100−X(Al1/3Si2/3)Xhigh entropy alloys at room temperature.The variation of mechanical properties is attributed to the different phase structures and microstructures.Dissolution of Al and Si in the FCC lattice of transition metals of Fe, Co, and Ni causes severe lattice distortion, contributing to pronounced solid solution strengthening.However, excessive addition of Al and Si promotes the formation of BCC phase, and the strength of the alloy increases rapidly at the cost of significantly reduced plasticity.Similar trend on the effect of Al contents on the phase stability and mechanical properties of high entropy alloys is reported by Tang et al [48].

Alloys
For industrial applications, it is necessary for HEAs to possess not only good soft magnetic properties, but also acceptable plastic deformation ability.
The newly-designed (Fe 0.3 Co 0.5 Ni 0.2 ) 95 (Al 1/3 Si 2/3 ) 5 alloy in the present study has shown good potential for industrial application as high-performance soft magents.The saturation magnetization of the alloy reaches 153.45 Am 2 /kg and the resistivity is about 60.3 µΩ•cm.Besides, it also shows satisfactory ductility.A comprehensive characterization of the aloy is presented in the following sections.
Figure 6 shows the macroscopic appearance of (Fe 0.3 Co 0.5 Ni 0.2 ) 95 (Al 1/3 Si 2/3 ) 5 alloy by vacuum magnetic suspension melting and the sheet after cold-rolled.Figure 7 shows the X-ray diffraction pattern of the alloy in the as-cast, cold-rolled, water quenching, and furnace cooling states after heat treatment.A simple FCC structure can be clearly identified in all states while a small peak at around 30 degrees appears in the as-cast and furnace-cooled states.Table 1.The magnetic properties and compression behavior of (Fe0.3Co0.5Ni0.2)100−X(Al1/3Si2/3)Xhigh entropy alloys at room temperature.For industrial applications, it is necessary for HEAs to possess not only good soft magnetic properties, but also acceptable plastic deformation ability.The newly-designed (Fe0.3Co0.5Ni0.2)95(Al1/3Si2/3)5alloy in the present study has shown good potential for industrial application as high-performance soft magents.The saturation magnetization of the alloy reaches 153.45 Am 2 /kg and the resistivity is about 60.3 μΩ .cm. Besides, it also shows satisfactory ductility.A comprehensive characterization of the aloy is presented in the following sections.8a) alloy shows a coarse column grain microstructure with the column width of ~1000 µm.After cold-rolling (83% thickness reduction), the grains are significantly elongated (Figure 8b).Annealing at 1000 • C caused complete recrystallization and the resulting grain sizes were significantly smaller than in the as-cast and cold-rolled states (Figure 8c,d).Annealing also introduced the formation of a large number of annealing twins but there was no preferred grain orientation observed.Under the condition of furnace cooling, the average grain size is ~30 µm.

Alloys
Figure 6 shows the macroscopic appearance of (Fe0.3Co0.5Ni0.2)95(Al1/3Si2/3)5alloy by vacuum magnetic suspension melting and the sheet after cold-rolled.Figure 7 shows the X-ray diffraction pattern of the alloy in the as-cast, cold-rolled, water quenching, and furnace cooling states after heat treatment.A simple FCC structure can be clearly identified in all states while a small peak at around 30 degrees appears in the as-cast and furnace-cooled states.Figure 8 presents the EBSD images of the (Fe0.3Co0.5Ni0.2)95(Al1/3Si2/3)5alloy in different conditions.The as-cast (Figure 8a) alloy shows a coarse column grain microstructure with the column width of ~1000 μm.After cold-rolling (83% thickness reduction), the grains are significantly elongated (Figure 8b).Annealing at 1000 °C caused complete recrystallization and the resulting grain sizes were significantly smaller than in the as-cast and cold-rolled states (Figures 8c and 8d).Annealing also introduced the formation of a large number of annealing twins but there was no preferred grain orientation observed.Under the condition of furnace cooling, the average grain size is ~30 μm.   Figure 9 shows the annular samples of the (Fe 0.3 Co 0.5 Ni 0.2 ) 95 (Al 1/3 Si 2/3 ) 5 alloy for magnetic induction-coercivity (B-H) measurement.Figure 10 shows the B-H and magnetization-coercivity (M-H) curves of the alloy in the states of as-cast (magnetic suspension melting), cold-rolled, water cooling, and furnace cooling after heat treatment, respectively.The soft magnetic properties of the alloy in the cold rolled variant are the worst.After the annealing treatment, the coercivity decreased from 510 A/m to 130 A/m due to internal stress release, and the saturation magnetic induction (Bs) improved from 1.14 T to 1.58 T.However, the saturation magnetization is almost constant under cold rolling and heat treatment conditions, which is about 1.49 T. Note that the coercivity of the alloy under vacuum magnetic suspension melting (96 A/m) is significantly lower than that of arc melting (>1000 A/m).The vacuum magnetic suspension melting method is cleaner than arc melting, and causes less oxide inclusions or other impurity in the ingot, and hence introduces much fewer magnetic domain pinning points in the alloy, leading to lower coercivity.
Figure 11 shows the hysteresis loss curve of the (Fe 0.3 Co 0.5 Ni 0.2 ) 95 (Al 1/3 Si 2/3 ) 5 alloy in different states.Under the power frequency conditions (50 Hz 1 T), the hysteresis loss (Ps) of the alloy in the states of as-cast, cold-rolled, water cooling, and furnace cooling after annealing is 3.13 W/kg, 8.91 W/kg, 4.26 W/kg, and 4.43 W/kg, respectively.In the application of soft magnetic materials, hysteresis loss energy will convert into heat, which will increase the temperature of the equipment and reduce working efficiency.Therefore, the hysteresis loss should be kept as small as possible.
Figure 12 presents the room temperature tensile stress-strain curves of the (Fe 0.3 Co 0.5 Ni 0.2 ) 95 (Al 1/3 Si 2/3 ) 5 alloy in the as-cast, cold-rolled, and annealed states.The specific values are listed in the Table 2.It shows that the as-cast alloy has the lowest strength, but with satisfactory ductility up to 25% elongation at room temperature.For the cold-rolled alloy, it has the lowest elongation of 1.3% but the highest yield and fracture stresses due to the work hardening.Figure 9 shows the annular samples of the (Fe0.3Co0.5Ni0.2)95(Al1/3Si2/3)5alloy for magnetic induction-coercivity (B-H) measurement.Figure 10 shows the B-H and magnetization-coercivity (M-H) curves of the alloy in the states of as-cast (magnetic suspension melting), cold-rolled, water cooling, and furnace cooling after heat treatment, respectively.The soft magnetic properties of the alloy in the cold rolled variant are the worst.After the annealing treatment, the coercivity decreased from 510 A/m to 130 A/m due to internal stress release, and the saturation magnetic induction (Bs) improved from 1.14 T to 1.58 T.However, the saturation magnetization is almost constant under cold rolling and heat treatment conditions, which is about 1.49 T. Note that the coercivity of the alloy under vacuum magnetic suspension melting (96 A/m) is significantly lower than that of arc melting (>1000 A/m).The vacuum magnetic suspension melting method is cleaner than arc melting, and causes less oxide inclusions or other impurity in the ingot, and hence introduces much fewer magnetic domain pinning points in the alloy, leading to lower coercivity.Magnetic materials have been developed for decades.As is well known, silicon steel is most widely used as soft magnetic material at relatively low price.However, the complex production process and large energy consumption restrict its application range [43].New materials, such as amorphous and nanocrystalline soft magnetic materials, also have excellent soft magnetic properties, but their applications are limited by their poor mechanical properties and thermal stability.In contrast, the high entropy soft magnetic material such as (Fe 0.3 Co 0.5 Ni 0.2 ) 95 (Al 1/3 Si 2/3 ) 5 as identified in the present study can make up for the deficiency of silicon steel and amorphous soft magnetic material.It has simple preparation process and stable crystal structure, and it also has balanced magentic and mechanical properties.It can be seen from Figure 13, the (Fe 0.3 Co 0.5 Ni 0.2 ) 95 (Al 1/3 Si 2/3 ) 5 alloy reported in this study (marked by the star) presents better magnetic properties than other soft magnetic high entropy alloys.Figure 11 shows the hysteresis loss curve of the (Fe0.3Co0.5Ni0.2)95(Al1/3Si2/3)5alloy in different states.Under the power frequency conditions (50 Hz 1 T), the hysteresis loss (Ps) of the alloy in the states of as-cast, cold-rolled, water cooling, and furnace cooling after annealing is 3.13 W/kg, 8.91 W/kg, 4.26 W/kg, and 4.43 W/kg, respectively.In the application of soft magnetic materials, hysteresis loss energy will convert into heat, which will increase the temperature of the equipment and reduce working efficiency.Therefore, the hysteresis loss should be kept as small as possible.2. It shows that the as-cast alloy has the lowest strength, but with satisfactory ductility up to 25% elongation at room temperature.For the cold-rolled alloy, it has the lowest elongation of 1.3% but the highest yield and fracture stresses due to the work hardening.
Magnetic materials have been developed for decades.As is well known, silicon steel is most widely used as soft magnetic material at relatively low price.However, the complex production process and large energy consumption restrict its application range [43].New materials, such as amorphous and nanocrystalline soft magnetic materials, also have excellent soft magnetic properties, but their applications are limited by their poor mechanical properties and thermal stability.In contrast, the high entropy soft magnetic material such as (Fe0.3Co0.5Ni0.2)95(Al1/3Si2/3)5as identified in the present study can make up for the deficiency of silicon steel and amorphous soft magnetic material.It has simple preparation process and stable crystal structure, and it also has balanced magentic and mechanical properties.It can be seen from Figure 13, the (Fe0.3Co0.5Ni0.2)95(Al1/3Si2/3)5alloy reported in this study (marked by the star) presents better magnetic properties than other soft magnetic high entropy alloys.
The relationship between magnetostrictive coefficient and coercivity of alloys for amorphous metals and HEAs reported in the literature is presented in Figure 14.This relationship indicates that identifying alloys with minimum saturation magnetostriction coefficient while optimizing the processing to lower coercivity is very important in developing soft magnetic materials.The relationship between magnetostrictive coefficient and coercivity of alloys for amorphous metals and HEAs reported in the literature is presented in Figure 14.This relationship indicates that identifying alloys with minimum saturation magnetostriction coefficient while optimizing the processing to lower coercivity is very important in developing soft magnetic materials.

Figure 1 .
Figure 1.The saturation magnetostriction (λs) of the Co-Fe-Ni bulk ternary alloys at room temperature.

Figure 1 .
Figure 1.The saturation magnetostriction (λs) of the Co-Fe-Ni bulk ternary alloys at room temperature.

Figure 3 .
Figure 3.The hysteresis loops of (Fe0.3Co0.5Ni0.2)100−X(Al1/3Si2/3)XHEAs at room temperature.Figure 3. The hysteresis loops of (Fe 0.3 Co 0.5 Ni 0.2 ) 100−X (Al 1/3 Si 2/3 ) X HEAs at room temperature.The variation of the coercivity (Hc) and saturation magnetization (Ms) are shown in Figure4.When X ≤ 10, the alloys maintain the FCC structure, and the coercivity increases with increasing Al and Si contents, increasing from 888 A/m to 1194 A/m.With higher Al and Si contents, the alloys become BCC dominant, and the Hc drops to 921 A/m when X = 15 but increases to 990 A/m when X = 25.Within a specific crystal structure, increasing Al and Si contents increase the atomic size difference and hence lattice distortion and coercivity.

Figure 8
Figure 8 presents the EBSD images of the (Fe 0.3 Co 0.5 Ni 0.2 ) 95 (Al 1/3 Si 2/3 ) 5 alloy in different conditions.The as-cast (Figure8a) alloy shows a coarse column grain microstructure with the column width of ~1000 µm.After cold-rolling (83% thickness reduction), the grains are significantly elongated (Figure8b).Annealing at 1000 • C caused complete recrystallization and the resulting grain sizes were significantly smaller than in the as-cast and cold-rolled states (Figure8c,d).Annealing also introduced the formation of a large number of annealing twins but there was no preferred grain orientation observed.Under the condition of furnace cooling, the average grain size is ~30 µm.

Figure 9 . 16 Figure 10 .
Figure 9.The annular samples that were machined for magnetic induction-coercivity (B-H) measurements: Inner diameter is 18 mm, outer diameter is 20 mm, and thickness is 0.3 mm.

Figure 12
Figure12presents the room temperature tensile stress-strain curves of the (Fe0.3Co0.5Ni0.2)95(Al1/3Si2/3)5alloy in the as-cast, cold-rolled, and annealed states.The specific values are listed in the Table2.It shows that the as-cast alloy has the lowest strength, but with satisfactory ductility up to 25% elongation at room temperature.For the cold-rolled alloy, it has the lowest elongation of 1.3% but the highest yield and fracture stresses due to the work hardening.Magnetic materials have been developed for decades.As is well known, silicon steel is most widely used as soft magnetic material at relatively low price.However, the complex production process and large energy consumption restrict its application range[43].New materials, such as amorphous and nanocrystalline soft magnetic materials, also have excellent soft magnetic properties, but their applications are limited by their poor mechanical properties and thermal stability.In contrast, the high entropy soft magnetic material such as (Fe0.3Co0.5Ni0.2)95(Al1/3Si2/3)5as identified in the present study can make up for the deficiency of silicon steel and amorphous soft magnetic material.It has simple preparation process and stable crystal structure, and it also has balanced magentic and mechanical properties.It can be seen from Figure13, the (Fe0.3Co0.5Ni0.2)95(Al1/3Si2/3)5alloy reported in this study (marked by the star) presents better magnetic properties than other soft magnetic high entropy alloys.The relationship between magnetostrictive coefficient and coercivity of alloys for amorphous metals and HEAs reported in the literature is presented in Figure14.This relationship indicates that identifying alloys with minimum saturation magnetostriction coefficient while optimizing the processing to lower coercivity is very important in developing soft magnetic materials.

Figure 13 .
Figure 13.The saturation magnetization and intrinsic coercivity of the ((Fe 0.3 Co 0.5 Ni 0.2 ) 95 (Al 1/3 Si 2/3 ) 5 alloy (marked by the red star) compared with other HEAs, amorphous metals and commercialized soft magnets compiled by Gao et al.Reproduced from [40] with permission of Cambridge University Press.