France



  Accelerated materials development has gained interest in the research community as this approach can generate large amount of data in short period of time, and models built from this data can optimize the properties of the material for specific engineering applications. One such material is soft magnetic material which are widely used in electric motors, generators, transformers, inductors, etc. To model and optimize the properties, machine learning can be deployed. We present preliminary findings of the data mining of the literature for the Fe-Co-Ni alloy system. The processing conditions, properties, and compositions were obtained from the literature. The use of a machine learning tool to predict the properties based on composition, processing parameters, and structural information is described.&lt;br/&gt;&lt;br/&gt;Introduction: Globally, in the past two decades, total energy consumption has increased exponentially and electric motors account for a significant fraction of the total power consumption[1]. Soft magnetic materials play an important role in energy conversion and are widely used in electric motors, transformer cores, electric vehicles, inductors, etc [2]. However, commercially available soft magnetic materials do not have the optimum balance of properties needed in high frequency electric motors operating in extreme environments. Hence, machine learning based magnetic property prediction, optimization and design of soft magnetic materials has gained attention [3-5]. We build a Fe-Co-Ni based metallic soft magnetic materials database from literature and use a neural network algorithm [6, 7] to optimize properties.&lt;br/&gt;&lt;br/&gt;Database and Machine Learning: A database of 891 data entries comprising magnetic, mechanical, and electrical properties of various composition of Fe-Co-Ni alloys processed at various conditions was compiled from relevant literature. To curate this database, 55 references were compiled, including standard books, handbooks, and relevant publications. The atomic % of other elements in the alloys was restricted to maximum of 10%. Further, the database was preprocessed to convert the weight % to atomic % of the elements, to convert alphanumeric type of material and processing condition entries to numerical, and to calculate grain size from coercivity and yield strength of the alloys. This preprocessed database was used to train the machine learning tool with input variables: (a) composition, (b) type of material (categorical), (c) processing parameters like treatment temperature and time, cooling rate, % reduction in area (% r.a.) either by cold rolling or hot rolling, reheating temperature and time, etc., (d) grain size, and (e) volume fraction of phases (FCC, BCC, HCP). The output properties were saturation magnetization, log(coercivity), log(maximum permeability), log(electrical resistivity), yield strength, tensile strength, log(elongation), Vickers hardness, and cost of the material. The quality of fit, coefficient of determination (R&lt;sup&gt;2&lt;/sup&gt;) values was determined through cross-validation. Using the trained model, properties of various compositions were predicted.&lt;br/&gt;&lt;br/&gt;Results and Discussion: Figure 1 shows the R&lt;sup&gt;2&lt;/sup&gt; values from cross-validation and the uncertainty in prediction for the output parameters. The algorithm was able to predict the properties in good agreement with the literature data. However, the prediction for electrical resistivity and elongation were not as good as that of other properties. This can be attributed to the lack of the data and complex behavior of the properties with the input parameters. The trained model was used to predict the properties of various Fe-Co-Ni alloys with the following conditions: cold rolled sheets with 95% r.a., annealed at 1000&lt;sup&gt;o&lt;/sup&gt;C for 2 hours, and furnace cooled. The predicted saturation magnetization for the above specified conditions reveals a complex interplay between the properties, hence there it could be possible to design a soft magnetic material with improved mechanical strength.&lt;br/&gt;&lt;br/&gt;Conclusion: Using this robust neural network model and data mining, preliminary results relevant to the development of a Fe-Co-Ni based soft magnetic material with optimal combination of properties could be obtained.&lt;br/&gt;&lt;br/&gt;Acknowledgement: This work is supported by the AME Programmatic Fund by the Agency for Science, Technology and Research, Singapore under Grant No. A1898b0043, and the Royal Society.

**References:**

[1] R. Saidur, Renewable and Sustainable Energy Reviews&lt;i&gt;,&lt;/i&gt; vol. 14, no. 3, p. 877-898 (2010)&lt;br/&gt;[2] V. Chaudhary, S.A. Mantri, R.V. Ramanujan, et. al., Progress in Materials Science&lt;i&gt;,&lt;/i&gt; vol. 114, p. 100688 (2020)&lt;br/&gt;[3] Y. Wang, Y. Tian, T. Kirk, et. al., Acta Materialia&lt;i&gt;,&lt;/i&gt; vol. 194, p. 144-155 (2020)&lt;br/&gt;[4] J. Nelson, and S. Sanvito, Physical Review Materials&lt;i&gt;,&lt;/i&gt; vol. 3, no. 10, p. 104405 (2019)&lt;br/&gt;[5] J. Konieczny, L. Dobrzañski, B. Tomiczek, et. al., Archives of Materials Science&lt;i&gt;,&lt;/i&gt; vol. 106, p. 106 (2008)&lt;br/&gt;[6] B.D. Conduit, N.G. Jones, H.J. Stone, et. al., Scripta Materialia&lt;i&gt;,&lt;/i&gt; vol. 146, p. 82-86 (2018)&lt;br/&gt;[7] B. Conduit, N.G. Jones, H.J. Stone, et. al., Materials &amp; Design&lt;i&gt;,&lt;/i&gt; vol. 131, p. 358-365 (2017)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/0143b4b4607cd37cafeda7e308e49281.jpg)
Figure 1: Coefficient of determination (R&lt;sup&gt;2&lt;/sup&gt;) values and the uncertainty in prediction of the properties, i.e., saturation magnetization (M&lt;sub&gt;s&lt;/sub&gt;), coercivity (H&lt;sub&gt;c&lt;/sub&gt;), Curie temperature (T&lt;sub&gt;c&lt;/sub&gt;), maximum permeability (&lt;sub&gt;m&lt;/sub&gt;), tensile strength (T.S.), yield strength (Y.S.), elongation (El.), Vickers hardness (H&lt;sub&gt;v&lt;/sub&gt;), and cost (from left to right).



INTERMAG 2021

 Data Mining based development of Fe-Co-Ni soft magnetic material

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Accelerated materials development has gained interest in the research community as this approach can generate large amount of data in short period of time, and models built from this data can optimize the properties of the material for specific engineering applications. One such material is soft magnetic material which are widely used in electric motors, generators, transformers, inductors, etc. To model and optimize the properties, machine learning can be deployed. We present preliminary findings of the data mining of the literature for the Fe-Co-Ni alloy system. The processing conditions, properties, and compositions were obtained from the literature. The use of a machine learning tool to predict the properties based on composition, processing parameters, and structural information is described. Introduction: Globally, in the past two decades, total energy consumption has increased exponentially and electric motors account for a significant fraction of the total power consumption[1]. Soft magnetic materials play an important role in energy conversion and are widely used in electric motors, transformer cores, electric vehicles, inductors, etc [2]. However, commercially available soft magnetic materials do not have the optimum balance of properties needed in high frequency electric motors operating in extreme environments. Hence, machine learning based magnetic property prediction, optimization and design of soft magnetic materials has gained attention [3-5]. We build a Fe-Co-Ni based metallic soft magnetic materials database from literature and use a neural network algorithm [6, 7] to optimize properties. Database and Machine Learning: A database of 891 data entries comprising magnetic, mechanical, and electrical properties of various composition of Fe-Co-Ni alloys processed at various conditions was compiled from relevant literature. To curate this database, 55 references were compiled, including standard books, handbooks, and relevant publications. The atomic % of other elements in the alloys was restricted to maximum of 10%. Further, the database was preprocessed to convert the weight % to atomic % of the elements, to convert alphanumeric type of material and processing condition entries to numerical, and to calculate grain size from coercivity and yield strength of the alloys. This preprocessed database was used to train the machine learning tool with input variables: (a) composition, (b) type of material (categorical), (c) processing parameters like treatment temperature and time, cooling rate, % reduction in area (% r.a.) either by cold rolling or hot rolling, reheating temperature and time, etc., (d) grain size, and (e) volume fraction of phases (FCC, BCC, HCP). The output properties were saturation magnetization, log(coercivity), log(maximum permeability), log(electrical resistivity), yield strength, tensile strength, log(elongation), Vickers hardness, and cost of the material. The quality of fit, coefficient of determination (R2) values was determined through cross-validation. Using the trained model, properties of various compositions were predicted. Results and Discussion: Figure 1 shows the R2 values from cross-validation and the uncertainty in prediction for the output parameters. The algorithm was able to predict the properties in good agreement with the literature data. However, the prediction for electrical resistivity and elongation were not as good as that of other properties. This can be attributed to the lack of the data and complex behavior of the properties with the input parameters. The trained model was used to predict the properties of various Fe-Co-Ni alloys with the following conditions: cold rolled sheets with 95% r.a., annealed at 1000oC for 2 hours, and furnace cooled. The predicted saturation magnetization for the above specified conditions reveals a complex interplay between the properties, hence there it could be possible to design a soft magnetic material with improved mechanical strength. Conclusion: Using this robust neural network model and data mining, preliminary results relevant to the development of a Fe-Co-Ni based soft magnetic material with optimal combination of properties could be obtained. Acknowledgement: This work is supported by the AME Programmatic Fund by the Agency for Science, Technology and Research, Singapore under Grant No. A1898b0043, and the Royal Society.

**References:**

[1] R. Saidur, Renewable and Sustainable Energy Reviews, vol. 14, no. 3, p. 877-898 (2010) [2] V. Chaudhary, S.A. Mantri, R.V. Ramanujan, et. al., Progress in Materials Science, vol. 114, p. 100688 (2020) [3] Y. Wang, Y. Tian, T. Kirk, et. al., Acta Materialia, vol. 194, p. 144-155 (2020) [4] J. Nelson, and S. Sanvito, Physical Review Materials, vol. 3, no. 10, p. 104405 (2019) [5] J. Konieczny, L. Dobrzañski, B. Tomiczek, et. al., Archives of Materials Science, vol. 106, p. 106 (2008) [6] B.D. Conduit, N.G. Jones, H.J. Stone, et. al., Scripta Materialia, vol. 146, p. 82-86 (2018) [7] B. Conduit, N.G. Jones, H.J. Stone, et. al., Materials & Design, vol. 131, p. 358-365 (2017)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/0143b4b4607cd37cafeda7e308e49281.jpg)
Figure 1: Coefficient of determination (R2) values and the uncertainty in prediction of the properties, i.e., saturation magnetization (Ms), coercivity (Hc), Curie temperature (Tc), maximum permeability (m), tensile strength (T.S.), yield strength (Y.S.), elongation (El.), Vickers hardness (Hv), and cost (from left to right).

technical paper

Recently, pearlitic wires, which experienced large drawing strains awoke the interest of material scientists due to their astonishing high strength of up to 7 GPa [1]. Because of the large amount of deformation applied during wire drawing, the grain size refines into the nanocrystalline regime and microstructural sizes of 10 nm and below are reported. The present study focusses on the capabilities to magnetically soften pearlitic steel by this “top-down”, conventional metal-forming process, as these length scales are already below the ferromagnetic exchange length of pure Fe. To do so, volume saturation magnetization and temperature dependent coercivities of wires experiencing high drawing strains (ε &gt; 5) were investigated. The results are compared to the ones of the initial wire, having more than twenty times the diameter and consequently a much coarser microstructure. To investigate the magnetic softening upon wire drawing, SQUID magnetometry and VSM measurements were performed. For the accurate determination of the volume saturation magnetization, the precise determination of the volume of the small samples is necessary. A confocal laser scanning microscope was used – the results allow the 3D reconstruction of the surfaces of the samples, for an example see inlay in Figure 1. From the surface reconstruction the volume can be calculated. It was found that the volume saturation magnetization is higher for the very thin wires in comparison to the initial state. While the thick, non-deformed wire shows a saturation magnetization very close to the one of pure pearlite, the saturation values for the thin wires are close to the one of pure body centred cubic (bcc) Fe (Figure 1). The slightly higher values, even in comparison to pure Fe, can be explained by C being supersaturated in the Fe matrix. The C necessary for supersaturation originates from the dissolution of cementite (Fe3C) during the wire drawing process [1]. Regarding the potential of wire drawing for magnetic softening, a decrease in coercivity was indeed found. The measured coercivities of the thin wires, determined with VSM, are smaller (24µm: 520 A/m, 36µm: 610 A/m) compared to the thick wire (1510 A/m). It is evident from magnetic measurements that there is a small but no substantial further refinement in grain size upon drawing the wire from 36 µm to 24 µm, although this constitutes a large degree of further deformation. Restoration mechanisms, as they are also known from other techniques involving severe deformation, seem to keep the grain size almost constant. For the thin wires, the grain size is calculated from the room temperature coercivity measurements. The grain size is found to be below the ferromagnetic exchange length of pure Fe, thus the random anisotropy model is applied. Using magnetic constants of pure Fe yields a grain size of 11 nm. This is in excellent agreement with atom probe tomography studies on the same material, where a subgrain size of 10 nm and below was found [2]. To further confirm the finding of dissolving cementite, the coercivity was determined as a function of temperature. Figure 2 includes calculated coercivities based on temperature dependent magnetocrystalline anisotropies for pure bcc Fe from [3–5]. Comparison reveals a very good match of measured and literature data; thus it can be safely assumed that the cementite has largely dissolved. Residual stresses, which might prevail from the drawing process would lead to an increased coercivity. Thus, a further softening of the drawn wires can be expected after thermal treatment, as it was the case for severe plastically deformed material, presented in [6]. One of the thin wires was annealed at 150°C for 30 min, which resulted in a decrease in coercivity by about 76 A/m or 12%. This proves the temperature stability of the microstructure at that temperature, as an increase in grain size would result in an increase in coercivity. The decrease in coercivity can be explained by reduced magneto-elastic effects, as residual stresses after wire drawing increase the effective anisotropy. In summary, pearlitic material was drawn to very high strains, resulting in very thin wires with nanocrystalline microstructure. Results of magnetic measurements indicate grain sizes close to 10 nm, the dissolution of cementite and a supersaturation of bcc Fe with C. It was possible to magnetically soften the coarse grained pearlitic steel from ~1500A/m to ~500A/m by this wire drawing process. However, the almost constant coercivity and grain size for very high drawing strains demonstrates that the magnetic softening seems to be maxed out. This project received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant No. 757333).

**References:**

[1] Y.J. Li, P. Choi, C. Borchers, et al., Atom probe tomography characterization of heavily cold drawn pearlitic steel wire, Ultramicroscopy. 111 (2011) 628–632. [2] Y. Li, D. Raabe, M. Herbig, et al., Segregation Stabilizes Nanocrystalline Bulk Steel with Near Theoretical Strength, Physical Review Letters. 113 (2014). [3] H.-P. Klein, E. Kneller, Variation of Magnetocrystalline Anisotropy of Iron with Field and Temperature, Phys. Rev. 144 (1966) 372–374. [4] B. Westerstrand, P. Nordblad, L. Nordborg, The Magnetocrystalline Anisotropy Constants of Iron and Iron-silicon Alloys, Phys. Scr. 11 (1975) 383–386. [5] I.M. Puzei, V.V. Sadchikov, Dependence of the magnetic-anisotropy energy in iron on the magnetic field, Sov. Phys. JETP. 70 (1990) 137–139. [6] M. Stückler, L. Weissitsch, S. Wurster, et al., Magnetic dilution by severe plastic deformation, AIP Advances. 10 (2020) 015210.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/6e4821f573e1bd315f9ff4211724fec7.jpg)
Figure 1: Saturation magnetization for all investigated wires, measured at applied fields ≥ 2 T, taking into account the individual sample volume determined by confocal laser scanning microscopy. The values of pure bcc Fe and pearlite are included. As an inlay, the 3D-reconstruction of the wire surface of a small section of one of the 36µm-wires is shown.

![](https://assets.underline.io/uploads/markdown_image/1/image/885834416e94cd889410edd26013c0ba.jpg)
Figure 2: Measured and corrected temperature-dependent coercivity of one of the 36µm-wire as a function of temperature. Results are compared with coercivities calculated according to literature [3–5] on temperature dependent magneto-crystalline anisotropy. The coercivity of the annealed 36µm-wire is also shown.

 Soft magnetic properties of severely drawn pearlitic-ferritic wires with nanocrystalline microstructure

Organophosphates (OP) have been used to kill insects in many areas such as homes and workplaces, especially in agricultural pest control [1]. In many people, the remains of OP can lead to many health problems to range from paralysis to death. For this reason, it is very important to detect OPs, which is the most important way of passage to the human organism, as a sensitive, fast, and cheap way. Nowadays, conventional OP detection is carried out by techniques such as mass spectroscopy, gas chromatography, and high-performance liquid chromatography. Although these methods give accurate and sensitive results, they require time-consuming processes such as sample preparation, solid-phase extraction, and comparison of sample peaks with references. Moreover, the cost of these methods is quite high. Therefore, the development of an alternative method as sensitive, fast, practical and cheap for detection of OPs was carried out in this study. The system used in the detection of OPs is a magnetoelastic sensor (MES). Magnetoelastic sensors are preferred because of their low cost, disposable application, wireless and easier to use. Magnetoelastic materials begin to vibrate (shorten and elongate) when exposed to a time-varying (AC) magnetic field. The vibration frequency of such samples varies depending on the geometry, elastic coefficient and mass (density) of the sample [2]. In magnetoelastic sensors, the amount of mass usually deposited on the sensor surface causes a shift in the resonance frequency and the shift in the magnetoelastic measurement system is measured. In this way, the mass accumulated on the sensor surface can be measured. It is important that the sensor surface is functionalized according to the type of molecule being detected. The magnetoelastic sensor will be more precise and superior if it measures a very low mass change. Therefore, enlarging the sensor surface area makes a significant contribution to the sensitivity of the sensor. In this context, electrospun nanofibers were coated on the sensor surface in order to increase the surface area of magnetoelastic sensors for the first time within this study. Within the scope of this project, 2826MB (Fe40Ni38Mo4B18) amorphous ferromagnetic ribbons with 35 mm long and 5 mm in width were used as MES. Then, the nanofibers were functionalized with glutaraldehyde (GA) in order to covalently bind acetylcholinesterase (AChE) enzyme to the surface. The resonance frequency of the functionalized amorphous strip was measured to be around 59 000 Hz. OP in the 10% EtOH solution was dripped with a micropipette on the surface of the functionalized MES then allowed drying. It was observed that the EtOH solution evaporate and the remaining OP covalently binds the acetylcholinesterase (AChE) enzyme. When 50 ppm OP in 10% EtOH solution were dropped, a decrease of approximately 22 Hz was observed in the resonance frequency at 500 A/m DC bias magnetic field. Figure 1 shows the measured resonance frequency change when different amounts of OP were dropped onto the MES. As can be seen, MES shows a linear change according to the amount of OP measured in the range of 0-150 ppm in 10% EtOH solution. To determine whether the frequency shift comes only from the OP, only 10% EtOH solution was dripped onto the functionalized MES surface in different amounts and it was found that no shift in the frequency had occurred. Acknowledgment This work was supported by TUBITAK with 119F144 project number.

**References:**

[1] M. Eddleston, M.R. Phillips, BMJ. 328, 42 (2004). [2] C.A. Grimes, P.G. Stoyanov, D. Kouzoudis, K.G. Ong, Rev. Sci. Instrum., 70, 4711 (1999).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c1ac49f02f0ff5add6db01a39b73119c.jpg)
Fig.1. Variation of resonance frequency as a function of diazinon organophosphates amount.

 Detection of Diazinon Organophosphates Using Magnetoelastic Sensor

Owing to the augmentation of wireless communication, the development of electromagnetic interference (EMI) shielding structures is an open area for research. The devices working at microwave frequencies are hazardous to human health and can also result in the malfunctioning of various sensitive equipments. Various techniques are reported by the researchers for the development of an efficient EMI shielding structure, some of them are composite materials, nanocomposites, metamaterials, and frequency selective surfaces (FSSs) [1]-[3]. FSSs are an array of periodic slots or apertures having excellent electromagnetic (EM) wave filtering properties. Major challenges across the research community are to create a miniaturized, angular stable, wideband, polarization-insensitive, and flexible EMI shielding structure. Multiband structures are often used by researchers to get a wide bandwidth. Whereas, miniaturization is attained either by techniques like 3-D, convoluted geometries, and lumped capacitances. All these methods of bandwidth improvement and miniaturization result in complex design and therefore fabrication becomes tedious. Almost all reported EMI shielding structures uses pure dielectric substrates like FR4 and Rogers. However, bandwidth and miniaturization can be improved by increasing the overall inductance of the shielding structure. The introduction of lumped inductors can be a solution but it not only increases the fabrication complexities but also may result in unwanted parasitic capacitance. Also introducing active or reactive components limits the conformal applications of shielding structures. One possible solution is to use magnetic substrates, which will increase the overall inductance of the shielding structure. Therefore, in this work electromagnetic properties of two magnetic substrates (Ferrite and magnetic silicon rubber) are measured and investigated to improve the bandwidth and miniaturization of an EMI shielding structure. Further, a polarization-insensitive, angular stable FSS is designed and the equivalent circuit model (ECM) is developed to have a physical insight into the structure. Moreover, a competent deep neural network (DNN) approach is employed for fast and accurate optimization of the shielding structure. At last, a prototype is developed and measured for validation of the proposed technique. The schematic of the proposed shielding structure is depicted in Figure 1(a). It comprises an array of periodic unit cells, a magnetic ferrite substrate, and a silicon rubber sheet. Figure 1(b) demonstrates an FSS unit cell with corresponding geometrical design variables. Here, ro is the radius of the outer circle and ri corresponds to the radius of the inner circle. d is the length of the patch, w is the width, and periodicity of the unit cell is represented by p. The electromagnetic properties of magnetic substrates are measured using a waveguide-based microwave measurement technique. Figure 1(c) depicts the measured relative permittivity (εr) and permeability (μr) of both the substrates. The real part of μr varies between 2.10 and 1.49 and the imaginary part varies between 0.34 and 0.0025 for magnetic silicon rubber when the frequency changes from 8.2 to 12.4 GHz. The real part of εr is 5.50 and the imaginary part varies between 0.20 and 0.005. On the other hand, the ferrite substrate real part of μr changes varies between 1.17 and 1.13 and the imaginary part varies between 0.04 and 0.001. Moving a step further, ECM of the FSS backed substrates is developed and the overall impedance is calculated. A huge database is created using the ECM and a deep neural network is trained using the Levenberg-Marquardt algorithm. The entire dataset is divided into three sections randomly for training, validation, and testing in the proportion of 70%, 15%, and 15%. Once the training, testing, and validation of the network is done, the shielding structure is optimized for resonant frequency and bandwidth. A prototype is then fabricated from the optimized parameters using the printed circuit board (PCB) technique. Figure 2(a) shows the image of the fabricated prototype. Meanwhile, the effect of the magnetic properties of the substrates on the transmission performance of the shielding structure is investigated. When the permittivity of the substrates dominates, a bandwidth of 2.75 GHz is obtained with resonant frequency at 10.42 GHz as shown in Figure 2(b). The bandwidth of surfaces with quite high impedance is directly proportional to the square root of overall inductance. To increase the bandwidth and to achieve miniaturization substrates with dominant magnetic properties are used. The overall inductance of the structure is increased by using substrates with dominant μr. Figure 2(b) depicts when substrates with dominant permeability are used in place of permittivity dominant substrates resonance shifts to lower value as the overall inductance of the structure increased. Also, the bandwidth obtained from such magnetic substrate increased to 3.37 GHz from 2.75 GHz. Therefore, it can be concluded that using magnetic substrates bandwidth enhancement and miniaturization of the shielding structure can be achieved.

**References:**

[1] M. Sonehara, T. Sato, M. Takasaki, H. Konishi, K. Yamasawa and Y. Miura, "Preparation and Characterization of Nanofiber Nonwoven Textile for Electromagnetic Wave Shielding," IEEE Transactions on Magnetics, vol. 44, no. 11, pp. 3107-3110, Nov. 2008. [2] J. Lee, B. M. Jung, S. B. Lee, S. Lee and K. H. Kim, "FeCoNi-Coated Glass Fabric/Polycarbonate Composite Sheets for Electromagnetic Absorption and Shielding," IEEE Transactions on Magnetics, vol. 53, no. 11, pp. 1-4, Nov. 2017. [3] R. Panwar, S. Puthucheri, D. Singh and V. Agarwala, "Design of Ferrite–Graphene-Based Thin Broadband Radar Wave Absorber for Stealth Application," IEEE Transactions on Magnetics, vol. 51, no. 11, pp. 1-4, Nov. 2015.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/cfe4cd73e62b6f4782155911aa08359e.jpg)
 
Figure 1. Proposed shielding structure (a) Schematic and FSS unit cell, and (b) Fabricated prototype

![](https://assets.underline.io/uploads/markdown_image/1/image/2627666b73e7db1a89ce3751c93f1ac6.jpg)
Figure 2. EMI shielding characteristics (a) Frequency-dependent electromagnetic characteristics of silicon rubber and ferrite substrates, and (b) Transmission performance for different configurations of FSS and substrates.

 Magnetic Substrate Coupled Broadband and Miniaturized Electromagnetic Interference Shielding Structure Using Deep Neural Network

Microwave absorbers are advanced electromagnetic structures that can competently deplete the incident electromagnetic (EM) wave, and widely utilized for stealth and electromagnetic interference mitigation applications. There have been enormous strides in the broadening of absorption bandwidth (BW) using thin and lightweight functional materials. Apart from functional materials, the shape and loading of the absorber are equally responsible for attenuating the EM wave. There are various potential structures capable of altering the equivalent EM properties of the material to achieve excellent absorption BW [1]-[2]. The simultaneous achievement of wide absorption bandwidth and lower coating thickness of the absorber layer is a very challenging task. In this work, an effort is made towards the design of thin and broadband triple-layer absorber by incorporating gradient air perforation into the absorbing sheets constituted of iron (Fe)-silicon carbide (SiC) composites synthesized by robust top-down fabrication technique. The gradient air perforation prompts viable absorption BW if the period and diameter of perforations are equivalent to the wavelength. Fe-SiC composites in distinct compositions (i.e., FS1, FS2, FS3, FS4, FS5, FS6, and FS7) have been utilized in the development of microwave absorber. The composites have been developed using a top-down fabrication technique accomplished via a high-energy planetary ball mill (Model: Insmart device, MBM-07, India). The milling process has been initiated by loading stainless steel containers with hard 20 mm and 10 mm diameter steel balls. The powder to ball weight ratio (PBR) of 1:10 was taken with the rotor speed to 400rpm. The EM properties of the composite were measured in the range of 8.2 to 12.4 GHz (i.e., X-band) using a waveguide-based microwave measurement technique. Further, Jaya’s-Grey Wolf based hybrid multiobjective optimization technique has been utilized for the modelling of a perforated multi-layered absorber using the measured EM parameters. The mathematical model of air perforation is integrated with the transmission line equations such that the developed structure appears like a gradient perforated triple-layer structure. The fitness function of maximum BW below -10dB with minimum thickness is organized in the hybrid optimization algorithm. An optimal sample has been fabricated using epoxy coating and drilling techniques based on the optimal design variables obtained using the algorithm. The schematic of 3D topology and fabricated porotype of perforated absorber constituted of Fe-SiC composites is shown in Figs. 1 (a) and (b), respectively. Fig. 2 shows the reflection coefficient curve (RC) of single-layer absorber at their optimal thicknesses. Among all Fe-SiC composite database, FS-7 composite achieves a minimum RC value of -24.7dB at 11.1 GHz at an optimal thickness of 1.7mm, covering an absorption BW of 3.1 GHz below -10dB threshold in X-band. Furthermore, FS-4 composite exhibits an absorption BW of 1.7GHz with a minimum RC value of -10.9 dB at 9.3 GHz at an optimal thickness of 1.7 mm. However, FS-3 composite achieves a minimum RC value of -9dB at 8.2 GHz demonstrating no absorption BW. In the proposed gradient structure, the hybrid optimization algorithm chooses composite FS-4 for layer 1 with an optimal thickness of 0.4 mm backed with a perfect electrical conductor. Consecutively, layers 2 and 3 (i.e., air absorber interface) are structured using FS-7 and FS-3 composites with an optimal thickness of 0.9 mm and 0.3 mm, respectively. The optimum air perforation diameter is 6 mm, 5mm, 4mm for FS-3, FS-7, and FS-4, respectively with a period of 20 mm. The magneto-dielectric properties of composite FS-3 are high as compared to FS-4 and FS-7 composites. Due to the larger diameter of air perforation, the effective magneto-dielectric properties are supervised to act as an impedance matching layer. A 1.6 mm multilayer structure (without hole) is compared with the proposed structure as shown in Fig. 2 (b). Due to gradient air perforation in the layered structure, the EM parameters are altered, which leads to the shift of resonance frequency. The obtained result reveals a better -10 dB absorption BW of 3.4 GHz with a minimum RC of -19.9 dB at 10.8 GHz. An exceptional microwave absorption is achieved in terms of peak RC and BW with a substantial reduction in the total coating thickness of 1.6 mm in comparison to a single-layer absorber. Moreover, due to perforation, the weight of the structure is also reduced. The gradient impedance alignment within the structure improves the other mechanisms of absorption, such as phase cancellation, internal reflection, and frequency dispersion within the structure which results in improved absorption BW.

**References:**

1. R. Panwar, S. Puthucheri, D. Singh and V. Agarwala, IEEE Transactions on Magnetics., vol. 51, no. 11, pp. 1-4 (2015). 2. L. Zhang, P. Zhou, H. Zhang, L. Lu, G. Zhang, H. Chen, H. Lu, J. Xie, and L. Deng, IEEE transactions on magnetics., vol. 50, no. 5, pp. 1-5 (2013).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a36d6e6475b0a7c1c80560119035c751.jpg)
Fig. 1. Schematic of perforated absorber (a) 3D topology and (b) fabricated porotype.

![](https://assets.underline.io/uploads/markdown_image/1/image/53df4f47bbf29bb3232a59d3911a61b0.jpg)
Fig. 2. Frequency-dependent RC curve of the absorber (a) single layer and (b) gradient perforated multilayered absorber in X-band.

 Fe-SiC Composite Constituted Multilayer Gradient Perforated Microwave Absorbing Structure for Stealth Applications

Yttrium Iron Garnet (YIG) is the benchmark material for ferromagnetic resonance; it is up to today the only magnetic material that is being integrated in on-shell electronic devices for its radiofrequency properties that combine high resonance quality factor (104) and frequency tunability. It is the goal of YIG magnonics to utilize this potential for a large variety of applications ranging from beyond complementary metal-oxide semiconductor (CMOS) computation to radiofrequency front-end and back-end analogue signal processing. YIG devices have however a severe drawback that is that they should include thermal stabilization. This is a necessity since YIG has a relatively low Curie temperature (∼550K) which results in a high sensitivity of its magnetization to temperature (∼4 Gauss/Kelvin). Here, we present a novel approach to solve this long standing issue by engineering the magnetic anisotropy in Bi substituted YIG. We evidence for those films that a vanishing effective magnetization yields high thermal stability over very wide temperature range: from 260K to 400K, where the frequency thermal drift is 50 times smaller than that of YIG. These types of properties can be leveraged for new applications where the temperature dependence of YIG is detrimental, while keeping the extremely low damping and insulating character of YIG[1]. For instance, this was key for the excitation of coherent spin-waves using SOT[2]. We anticipate that fabricating a material whose FMR frequency is temperature independent open new opportunities for the field of spintronics. In his seminal article[3] of 1948 Charles Kittel established the Ferromagnetic resonance (FMR) conditions of magnetic samples with arbitrary shapes stressing the importance of correcting the effective magnetic field that sets the Larmor frequency by taking into account the demagnetization field and the effect of uniaxial anisotropy. In today notations the FMR frequency can hence be written for a thin film in the in-plane magnetization configuration as: f=γ*(Ha*(Ha+(MS-Hu)))1/2. Where γ is the gyromagnetic factor, Ha is the applied magnetic field, MS is the saturation magnetization and Hu is the out-of-plane magnetization and the effective magnetization is defined as Meff = MS - Hu. It arises from this equation that the only temperature dependent terms are MS(T) and Hu(T). For most ferromagnetic materials Hu depends on MS with power law dependence defined by Callen and Callen theory[4]. Nonetheless, by engineering the magnetic anisotropy in Bi-YIG films, we were able to balance the saturation magnetization with the uniaxial anisotropy between 260K and 400K. These measurements were done on thin Bi1Y2Fe5O12 films of 21nm grown on (111)-oriented sGGG substrates with Pulsed Laser Deposition. We varied the substrate growth temperature within a range of 100°C and probed the films effective magnetization using FMR: we evidenced a magnetization state transition from in-plane to out-of-plane as the substrate growth temperature decreases from 500°C to 400°C. To ensure the nominal Bi content as well as the magneto-elastic anisotropy were maintained over all the growth temperature range, X-Ray Diffraction measurements were done and evidenced a perfect structural match between thin Bi1Y2IG films. Magneto-Optical Kerr Effect (MOKE) measurements were performed complementary to visualize not only the magnetic domains but also the magnetic anisotropy transition. With room temperature FMR measurements, we obtained the optimal substrate growth temperature range to be 420°C to 430°C: temperatures for which the effective magnetization Meff ≈ 0G. Interestingly, for thin films closest to the compensation, FMR measurements performed at lower temperatures evidenced that effective magnetization stay constant in a range of 140K: suggesting Hu(T)=Ms(T) contradictory with Callen and Callen theory[4]. Finally we measured the frequency thermal drift was about 1mT between 260K and 400K for films close to the compensation, FMR frequency is temperature independent.

**References:**

[1] L. Soumah, N. Beaulieu, L. Qassym, Nature Communication 9, 3355 (2018) [2] M. Evelt, L. Soumah, A.B. Rinkevich, Physical Review Applied 10, 041002 (2018) [3] C. Kittel, Physical Review 73, 155 (1948) [4] H. B. Callen and E. Callen, Journal of Physics and Chemistry of Solids 27, 1271 (1966).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e5e1e60b717ac1a92c59f4a6cb88abd2.jpg)
Fig. 1 Polar Magneto-Optical Kerr Effect (MOKE) measurement for a Bi-YIG thin film close to the compensation evidences the presence of magnetic domains.

![](https://assets.underline.io/uploads/markdown_image/1/image/7befc984861421507db377f3d886061b.jpg)
Fig. 2 Variation of the effective magnetization Meff(T) for Bi1YIG thin films within a range of 140K probed by Ferromagnetic Resonance (FMR) measurement.

 Fine tuning of the Magnetic Anisotropy results in Temperature Independent Ferromagnetic Resonance Frequency for Bi-YIG thin films grown by Pulsed Laser Deposition

The typical timescale for material discovery is remarkably long, taking between 10 – 20 years to propagate through idea conception, experimentation, optimisation, and deployment1. Existing global challenges such as the climate emergency require rapid development of new materials on timescales that are incompatible with the traditional linear material discovery approach. High-throughput approaches can be applied as a parallel material discovery methodology, for which a single sample contains a library of different material compositions that can be rapidly screened for the realisation of new magnetic materials. We apply the high-throughput material discovery approach to the new class of materials known as High Entropy Alloys (HEAs). HEAs often consist of five or more constituent elements mixed in near equal quantities. The name is owed to the resulting high configurational entropy of the alloy, which contributes to suppressing the formation of intermetallic phases and stabilises simple FCC and BCC solid solutions. HEAs occupy the unexplored central regions of phase diagrams, and as such, have potential to provide disruptive materials. Already HEAs have exhibited promising soft magnetic properties such as high saturation magnetisation alongside high electrical resistivity, as well as obtaining nanocrystalline textures2,3. However, the number of constituent elements and the various chemical compositions mean HEAs can be found in a very broad parameter space making it difficult to localise the search for useful compositions. This work has used combinatorial sputtering, to fabricate sample libraries containing composition variations of up to 35 at.% on a single Silicon wafer (Figure 1a). We investigate the (CoFeNi)1-x-yAxBy series, where A and B are 3d/4d transition metals (with the addition of Si and Al). Systems studied include CoFeNiMnAl, CoFeNiMnSi, and CoFeNiMnV. We implement a program to model the composition variation across a 3” Silicon wafer with three sputter sources at different incidence angles with concurrent deposition (Figure 1b). The resulting sample library is characterised using a high-throughput magneto-optical Kerr effect (MOKE) magnetometer which has been developed to automatically map the Kerr voltage (which is proportional to the magnetic moment) and coercive field across this sample library as function of HEA composition (Figure 1c). These can then be combined to achieve magnetic property mapping within the chemical composition space (Figure 1d). Following this, XRD, SQUID magnetometry, FMR and magneto-transport are used to generate a complete structural and functional property description of selected compositions. The resulting methodology not only provides a scalable process for magnetic HEA fabrication and characterisation, but can also be paired with data driven machine learning material discovery strategies such as Materials 4.04. The large datasets necessary for machine learning are costly to procure and so far lacking in functional magnetic properties (e.g. Ms, Hc) for which these high-throughput methods could provide.

**References:**

1. Y. Liu, T. Zhao, W. Ju and S. Shi, J. Materiomics 3, 159–177 (2017). 2. Y. Zhang, T. Zuo, Y. Cheng and P. K. Liaw, Sci. Rep. 3, 1455 (2013). 3. T. Zuo et al., Acta Mater. 130, 10–18 (2017). 4. R. Jose and S. Ramakrishna, Appl. Mater. Today 10, 127–132 (2018).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/646e3021d243cac1b425ee3cb6de2f04.jpg)
Schematic representation of the high-throughput thin film methodology applied to magnetic material discovery, including (a) combinatorial sputtering, (b) modelling the composition across the wafer, (c) a measured Kerr Voltage map, and (d) mapping of magnetic properties as a function of chemical composition.

 High-throughput studies of magnetic High Entropy Alloys

The accelerated development of new soft magnetic materials is urgently required to address the challenges of next generation high frequency rotating electrical machines. We used high-throughput experimental and characterization techniques as well as thermodynamic modeling and machine learning (ML) to develop novel soft magnetic materials based on the Fe-Co-Ni alloy system. The experimental methods include (i) Direct energy deposition based additive manufacturing of compositionally graded bulk materials, (ii) Magnetic thin films with a range of compositions, (iii) Chemical flow synthesis of magnetic nanoparticles, (iv) Spark plasma sintered compositionally graded magnetic alloys. The structural, magnetic, mechanical, and electrical properties were determined. The feasibility of our strategy to develop new soft magnetic alloys has been demonstrated. Introduction: Soft magnetic materials are the key component for various applications such as electric motors and generators, magnetic shielding, robotics, electromagnets, sensors, etc[1, 2]. Such systems utilize a significant fraction of the total energy consumption of the world, hence increasing their efficiency will have a significant impact on the urgent need for energy conservation. High frequency rotating electrical machines require magnetic materials with a balance of magnetic, mechanical, and electrical properties. The traditional methods of developing such materials are costly and time consuming, limiting the opportunity to discover new excellent materials. Hence, high throughput methods are of high demand for accelerated discovery of novel materials and to improve the properties of existing materials. We present experimental and computational high throughput approaches to design new magnetic materials. Methods: Compositionally graded Fe-xNi[3], Fe-xCo, Fe-xNi-yMo, Fe-xCo-yNi samples were prepared by a DED process. High purity spherical Fe, Co, Ni, Mo powders with sizes ranging from 50 to 150 mm were employed. Thin film libraries of Fe-Co-Ni were prepared by co-sputtering of Ni-21Fe and Co targets using magnetron sputtering at a base pressure of 10-8 torr. Thermodynamic modeling was found to be very helpful to identify the heat treatment conditions [4]. The following characterization methods were employed: XRD for crystal structure and phase fraction, EPMA-WBS and EDX for composition, PPMS and magnetic field assisted TGA for magnetic properties, four-point probe for electrical resistivities, and nono(micro)-indentation for mechanical properties. A neural network model was trained on the data to predict the magnetic, mechanical and electric properties. Figure 1 shows the methods and the properties of our interest. Results and discussion: Additive manufacturing was utilized to explore a range of compositions. Iron rich ternary Fe-Co-Ni (Fe&gt; 75%, Co&lt;20%, Ni&lt;25%) alloys exhibit saturation magnetization (Ms), coercivity (Hc), Curie temperature (Tc) and hardness values ranging from 167 to 218.4 emu/g, 19.6 to 10.2 Oe, 534 to 940 °C, 185 to 359 Hv, respectively. Fe-8Co-9.1Ni and Fe-7.4Co-11.3Ni were found to have optimum magnetic and mechanical properties with Ms of 218.4 and 217 emu/g, Hc of 10.2 and 13 Oe, Tc of 765 and 741 °C, hardness of 334 and 359 Hv, respectively. In spark plasma sintered compositionally graded Ni-21Fe-xCo alloys, the largest Ms, Hc, Tc and HV were observed in Co rich samples while the resistivity was found to be larger in Ni rich samples. As an example, the compositions along the diameter of 7.6 cm sample of a co-sputtered thin film is shown in figure 2. Thus, the feasibility to accelerate the development of novel soft magnets has been demonstrated in the Fe-Co-Ni system. Acknowledgement: This work is supported by the AME Programmatic Fund by the Agency for Science, Technology and Research, Singapore under Grant No. A1898b0043.

**References:**

[1] V. Chaudhary, S.A. Mantri, R.V. Ramanujan, R. Banerjee, Progress in Materials Science 114 (2020) 100688. [2] J.M. Silveyra, E. Ferrara, D.L. Huber, T.C. Monson, Science 362 (2018) eaao0195. [3] V. Chaudhary, N.M. Sai Kiran Kumar Yadav, S.A. Mantri, S. Dasari, A. Jagetia, R.V. Ramanujan, R. Banerjee, Journal of Alloys and Compounds 823 (2020) 153817. [4] S. Dasari, V. Chaudhary, B. Gwalani, A. Jagetia, V. Soni, S. Gorsse, R.V. Ramanujan, R. Banerjee, Materialia 12 (2020) 100755.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/920fbe1f51f6d92c3fa7416eceac2a0c.jpg)
Fig. 1 Soft magnetic materials development using accelerated (a) experimental, (b) computational and (c) characterization techniques, (d) measured/predicted properties

![](https://assets.underline.io/uploads/markdown_image/1/image/6b04517d314f4b720e708815ed8b0002.jpg)
Fig. 2 Change in composition across the diameter of circular graded thin film

 Accelerated development of soft magnetic alloys

Compositionally graded materials are attractive since the properties can be optimized according to the spatial requirement. We report the use of spark plasma sintering for the processing of compositionally graded magnetic materials. Magnetic, mechanical and electrical properties were screened using high throughput characterization techniques. A significant change in all these properties, e.g., saturation magnetization (Ms) ranging from 57 to 224 emu/g, Curie temperature (Tc) ranging from 358 to 1116 °C, and Vickers hardness ranging from 91 to 195 HV across the length of a single cylindrical sample was observed. Introduction: Elemental Fe, Co, Ni exhibit ferromagnetic behavior, and their alloys such as Fe-Co-2V (hiperco) and Ni-21Fe (permalloy) are well established commercially available soft magnetic materials. Fe-Co-2V exhibits an attractive combination of high saturation magnetization, high Curie temperature, high yield strength, and is very useful for high temperature magnetic applications. On the other hand, Permalloys exhibit low coercivity, high permeability, and moderate saturation magnetizations and are of high interest for transformers, electric motors and other electromagnetic devices. Magnetic components of a power electronic convertors functioning at high frequency can be &gt;50 % of total weight of the system[1]. It has been demonstrated that graded properties of soft magnetic materials are beneficial for next generation power convertors/generators[2, 3]. Therefore, developing magnetic components with spatially optimized properties is of high interest[1]. This work demonstrates the use of spark plasma sintering (SPS) for the accelerated preparation of a compositionally graded magnetic materials. Fe/Co/Ni/NiFe/FeCoV have been prepared using gas atomized spherical powders of Fe, Co, Ni, Ni-21Fe and Fe-Co-2V. This graded SPS technique produces a dense bulk metallic sample with discrete changes in composition, resulting in tunable, spatially optimized structural and functional properties. Experiment: Gas atomized prealloyed Fe-Co-2V and Ni-21Fe, and elemental Co, Fe and Ni, from Tosoh SMD Inc. were used as starting powders. The purity of all the powders is &gt;99.9%. The 5 compositions were loaded layer by layer in a graphite die. Sintering of compositionally graded Fe/Co/Ni/NiFe/FeCoV soft magnetic materials was performed using a Spark Plasma Sintering (SPS) equipment (Fuji Electronic Industrial, SPS-211LX) at a vacuum level below 8 Pa. The sample was vertically cut in two sections, one section was annealed at 800 °C for 4 h. The crystal structure of graded samples was determined by X-ray diffraction (XRD) using a Bruker D8 discover diffractometer (CuKa radiation). Elemental mapping was performed by an energy dispersive X-ray spectrometer attached to the SEM. The magnetic properties were measured using a physical property measurement system (PPMS) (EverCool-II, Quantum Design), equipped with a vibrating sample magnetometer. The microhardness of the graded samples was measured by a Vickers hardness tester (Future-Tech). Results and conclusion: Saturation magnetization (Ms), Curie temperature (Tc) and Vickers hardness (HV) of a typical compositionally graded Fe-Co-Ni-NiFe-FeCoV sample are shown in figure 1. Both ends (Fe and FeCoV) of the sample exhibit Ms of &gt;200 emu/g, while the central region, which is Ni, exhibits the minimum Ms of ~57 emu/g. The Curie temperature of the compositionally graded sample measured by employing a permanent magnet placed near the TGA pan. The Co region exhibits the highest Tc, with the Tc following the sequence of Co &gt; FeCoV &gt; Fe &gt; NiFe &gt; Ni. These Ms and Tc values closely matched with the values reported in earlier references. A significant change in mechanical properties across the sample was observed with a maximum Vickers hardness of 195 HV in the FeCoV region. Thus, SPS processed samples with spatially varying compositions were developed, relevant to the urgent need for magnetic components with spatially optimized properties. Acknowledgement: This work is supported by the AME Programmatic Fund by the Agency for Science, Technology and Research, Singapore under Grant No. A1898b0043.

**References:**

[1] D. Rodriguez-Sotelo, M.A. Rodriguez-Licea, A.G. Soriano-Sanchez, A. Espinosa-Calderon, F.J. Perez-Pinal, IEEE Access 8 56238-56252, (2020). [2] V. Chaudhary, S.A. Mantri, R.V. Ramanujan, R. Banerjee, Progress in Materials Science 114, 100688 (2020). [3] K. Byerly, P.R. Ohodnicki, S.R. Moon, A.M. Leary, V. Keylin, M.E. McHenry, S. Simizu, R. Beddingfield, Y. Yu, G. Feichter, R. Noebe, R. Bowman, S. Bhattacharya, JOM 70, 879-891 (2018).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/b66589666c74d5193a7c7b9a8854133b.jpg)
Fig. 1 Change in saturation magnetization (Ms), Curie temperature (Tc) and Vickers hardness (HV) across the length of a compositionally graded cylindrical sample

 Compositionally graded Fe/Co/Ni/NiFe/FeCoV soft magnetic materials

Alloy systems of the past tend towards single principal component alloy systems. In present research, the stoichiometry of alloy systems with large number of alloying components (&gt;4) can be adjusted to stabilise near-ideal solid solution phases (termed High-entropy alloys, HEAs due to their high configurational entropy), or to possess some mixture of ordered intermetallic phases and the near-ideal solid solution phase (termed Complex Concentrated Alloys, CCAs). HEA and CCA possess many design degree-of-freedoms. Precise control over stoichiometry and thermomechanical history lead to exciting magnetic properties; e.g. through the formation of nanocomposite microstructures [1] in CCAs can achieve good magnetic softness by allowing exchange averaging of the magnetic anisotropy. A major challenge to general application is the vast compositional design space; if ignoring stoichiometry: restricting the number of elements to 1) 3d transition metals, and 2) Si and B, there are 10C5 = 792 [RRR1] possible equimolar combinations. Millions more are possible if stoichiometry is relaxed. Appropriate strategies to filter out good candidate compositional families for study are thus essential. Alloy design can be generalised to two approaches: data-driven discovery (DDD) and functionality-driven discovery (FDD). For DDD experimental data obtained from exploratory and characterisation frameworks are extrapolated for design and prediction; in FDD search and optimisation methods are used to achieve targeted properties. Prediction models (e.g. ab-initio) are used in conjunction with FDD to determine microscopic parameters that govern material properties. FDD is useful in exploring materials with large numbers of degree-of-freedoms such as HEA/CCA systems as extrapolation from experimental data is not a good predictor of quantum mechanical behaviour (i.e. electronic structure interactions). Ab-initio models can calculate potential properties of new compositions, iterating over shedloads[RRR2] of stoichiometries using search and optimisation methods. Although computationally efficient, significant computational power is still required. Applying reasonably accurate low-fidelity pre-filters derived from quantum principles reduces the computational resources required. This work uses two such low-fidelity pre-filters using a parametric semi-empirical approach for determining the saturation magnetisation and mean Curie temperature of HEA/CCA systems. The Curie temperature can be expressed as a function alloyed system (i.e. the number of impurity atoms). At the electronic level these changes are due to 1) Variations of the local moments, and/or 2) Changes in interaction strength between moments represented by the molecular field coefficient (dependent on interatomic distances and local environment effects) [2]. Since the uniaxial pressure experienced by the valence electrons upon interatomic distance changes leads to electronic density compression [3], the rectangular band model [4] can be used to explore the onset of ferromagnetism by evaluating the bulk modulus, B with respect to the Stoner criterion. From this, the ratio B/EF (where the Fermi energy EF is approximated by the Mulliken electronegativity, XM) is used to predict the Curie temperature in HEAs and CCAs (cf. Fig. 1). The predictions are validated through synthesised as-cast HEA/CCA compositions that are characterised on a SQUID-VSM and are found to be dependent on the amount of antiferromagnetic Cr alloying in the system. The Bethe-Slater curve forms part of the early understanding of magnetism and the electronic-structure-driven magnetic ordering of 3d transition metals. Slater Rules [5] are used to evaluate the 4s:3d orbital radius ratio to reconstruct the Bethe-Slater curve (cf. Fig. 2a) using synthesised HEA/CCA compositions from literature, predictions, and our own experiments. Deviations in the 3d Bethe-Slater curve due to electronic interactions lead to curve shifts and model multiplicities, making predictions non-trivial. Orbital radius changes and valence symmetry-breaking are thus evaluated in a parametric function derived from rule-of-mixtures XM and valence electron values as a supplement to the modified Beth-Slater curve. Plotted using the same dataset, this function in Fig. 2b shows good parameterisation of MS with no model multiplicities making it suitable for design predictions. Both models show reasonable accuracies when compared to the experimental data and data from literature. One benefit of both models is that they are derived from common parameters (Bulk modulus, Mulliken electronegativity, atomic number, and d-electron count). This means that the predictive calculations can be obtained by using the rule-of-averages to determine the weighted mean of these parameters for various alloy systems. In order to further test the validity of these models, the models are used with an evolutionary algorithm to design a HEA/CCA with targeted Curie temperature and saturation magnetisation. The results of this prediction are synthesised and characterised through x-ray diffraction and SQUID-VSM and will be presented here.

**References:**

[1] N.A. Morley, B. Lim, J. Xi, A. Quintana-Nedelcos, Z. Leong, Sci. Rep., Vol. 10, 14506 (2020). [2] J.P. Gavigan, D. Givord, H.S. Li, , in: Concert. Eur. Action Magn. CEAM, p.163–173 (1989). [3] S.A. Serebrinsky, J.L. Gervasoni, J.P. Abriata, V.H. Ponce, J. Mater. Sci., Vol. 33, 167–171 (1998) [4] D.G. Pettifor, Bonding and structure of molecules and solids (1995). [5] J.C. Slater, Phys. Rev., Vol 36, p.57–64 (1930).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/32b4c926a5a2171a4d869a6d4bfa2874.jpg)
Fig. 1. Plot of a dimensionless number, B/XM against the Curie temperature for experimental values as well as values taken from literature. The lines represent a guide to the eye for the various amounts of Cr addition to the composition.

![](https://assets.underline.io/uploads/markdown_image/1/image/94cdfef7de161c197ef79ff1235b2407.jpg)
Fig. 2. Saturation magnetisation plotted against the 4s:3d ratio calculated using Slater Rules. *New results presented here **Experimental results from literature, ***Simulated results from literature.

 Parametric Semi-Empirical Design of Magnetic Properties in Complex Concentrated Alloys: Curie Temperature and Saturation Magnetisation

There has been renewed interest in recent years to accelerate materials development beyond traditional approaches. A combination of both machine learning and high-throughput experiments can be used for predicting material properties and designing compositions beyond what is currently known. Herein we report the use of a computational tool, Alchemite™, to mine for important processing parameters of Fe-Si-Al alloys from a data set curated from published experimental results. The preliminary calculations suggest that this is a viable method to develop new Fe-Si based alloys. Introduction: Silicon steels (Fe-Si) are an important class of materials as they are widely used in applications like electric motors and transformers. Currently, 3.2 wt.% Si is widely used due to (i) good balance of electrical and magnetic properties, and (ii) ductility requirements in traditional processing methods.1 Recent trends have pointed to higher Si content of up to 10 wt.%, with an addition of small amounts of aluminum (Al) to improve material performance. Due to the small literature, it is imperative that we use machine learning to explore higher Si compositions and their processing methods to obtain a good balance of soft magnetic properties, electrical properties and mechanical properties. Data Set and Machine Learning Model: A typical machine learning model comprises three parts: training data, attributes for describing the material, and the machine learning algorithm to map the attributes to properties. The Fe-Si-Al data set was compiled of reported experiment values from 40 references (IEEE Ferromagnetism Handbook2 and 39 journal references, published between 2000 – 2020), resulting in a total of 572 entries. The attributes that were selected as input parameters to describe the material were (i) Composition, (ii) Type of material – like ingots, sheets or powder etc., (iii) Final thickness of the material, heat treatment conditions (iv) Treatment temperature, (v) Treatment time and (vi) Cooling rate, (vii) Frequency and (viii) Magnetic flux density. The output parameters comprised various soft magnetic, electrical and mechanical properties. Alchemite™ is a machine learning technology commercialized for materials and industrial chemicals design through Intellegens.3 The artificial neural network trains from the data set provided and predicts the selected material properties. The coefficient of determination (R2) values was obtained to determine the consistency of the data and predictions. Results and Discussion: Figure 1 shows the R2 values for the input parameters. The machine learning tool showed good predictions for most properties, although mechanical properties were not as well predicted (R2&lt;0.8). This is expected as there is a gap in the reported literature. More work will be done to address this gap, by means of improving the data set through theoretical calculations and high-throughput experimental methods. We studied the machine learning model parameters to reveal the most important variables for each output parameter: The frequency of operation affects total core loss greatly, like observations in alternating current (AC) applications – core loss is higher at increased operating frequency. To mitigate such effects, electrical resistivity must be increased – by controlling material thickness, grain size, and composition. Next, the type of material strongly affects the coercivity. The coercivity is affected by the grain size and composition, and this is in turn is affected by the method of fabrication and subsequent processing. The tensile strength is sensitive to the cooling rate because it affects the formation of different phases (A2, B2, and D03). It is reported that the ordering of phases (in B2 and D03) can interact with dislocations, resulting in a strengthening effect which decreases ductility.1 The phases formed also depend on the Si content, as reflected by the correlation between yield strength and Si content. The above highlights how the various input attributes are interrelated in affecting the output properties, and physical insights this can deliver. This underpins the main difficulty in traditional trial and error experiments and the mammoth task to undertake if it is to be done manually. Conclusions: The results show that the use of Alchemite™ for the development of Fe-Si-Al alloys are robust and promising, as it can capture property-processing relationships and highlight gaps in the data set. More work will be focused on improving the data set and high-throughput experiments performed to compare the results obtained with the predicted values. This will enable us to add to knowledge on achieving optimized and balanced properties in Fe-Si based alloys. This work is supported by the AME Programmatic Fund by the Agency for Science, Technology and Research, Singapore under Grant No. A1898b0043 and the Royal Society.

**References:**

[1] G. Ouyang, X. Chen, and Y. Liang, Journal of Magnetism and Magnetic Materials, Vol. 481, p.234–250 (2019) [2] RM Bozorth, Ferromagnetism. (IEEE Press, 1993) [3] https://intellegens.ai/ (accessed January 2021)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/55c12021610e152d25b771cea3e2a50e.jpg)
Fig. 1: Coefficient of determination values of output properties from machine learning predictions. The properties from left to right are: W – Total core loss, μ – Permeability, Hc – Coercivity, Ms – Saturation magnetisation, Tc – Curie temperature, ρ – Electrical resistivity, T.S – Tensile strength, Y.S. – Yield strength, El. – Elongation, Hv – Hardness and Cost.

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