France



Due to their texture, the magnetic characteristics of grain oriented (GO) steels depend on the angle between the applied magnetic field and the rolling direction RD. These GO steels exhibit advantageous magnetic characteristics, such as high permeability in the RD and relatively poor properties in the transverse direction TD. In order to obtain a better electromagnetic modeling of the electrical energy conversion systems using GO steels, the dissipative phenomena and the anisotropy must be reliably represented. One example is the case of the GO electrical steels used in stators of turbo-generators. In order to create an appropriate model, the associated magnetic losses have to be taken into account for any angle between the applied field and the RD. However, the problem of computing iron losses whatever the angle between the applied field and the RD has remained unsolved especially within the finite element method (FEM) framework.&lt;br/&gt;&lt;br/&gt;In this paper, a phenomenological iron loss model, recently proposed in [1], taking into account the anisotropy and nonlinearity of GO sheets has been successfully implemented in the L2EP FEM software baptized code_Carmel [2]. The model relies on the ‘loss separation’ approach. In this approach, which is based on the traditional decomposition proposed by Bertotti [3], the total losses are decomposed into three terms (hysteresis, classical and excess losses). The originality of the model concerns the first loss term i.e., the quasi-static losses dissipated per magnetization cycle, depending on the polarization level J&lt;sub&gt;p&lt;/sub&gt; and on the angle θ between the applied field and RD. The proposed quasi-static loss model considers the magnetization process and the evolution of the domain wall structure (dws) with the angle θ [4]. It is built from the two sets of W-J&lt;sub&gt;p&lt;/sub&gt; quasi-static experimental data obtained in the principal directions RD and TD and is based on the interactions between the main classes of magnetic domains, 180° and 90° dws, known as “Néel phases” [5] through a single analytical relationship involving the volumic fraction occupied, for any direction of the magnetic field, by these classes. This same principle is applied for the determination of the excess losses. At this stage, the corresponding input data are the excess losses measured in both RD and TD. Concerning the classical loss term, it simply takes the expression resulting from the classical eddy current theory which is independent of the angle θ. Indeed, the case of an infinite sheet of thickness e, with a linear constitutive law (µ independent of H) and conductivity σ, under a sinusoidal field of frequency f, allows an entirely analytical resolution of the magnetic diffusion equation. Finally, we get a description of the total losses W(f,J&lt;sub&gt;p&lt;/sub&gt;) as a function of the angle θ, without any adjustable parameter. The model has been validated on industrial sheets of EDF turbo-generators by means of simple study cases under periodic (cyclic) waveforms. Thus, we dispose of an efficient and reliable tool for modeling the magnetic losses of GO sheets within the FEM simulation environment.&lt;br/&gt;&lt;br/&gt;In order to validate the implementation of the developed model, a finite element analysis (FEA) has been performed using code_Carmel. A 3D linear magnetostatic simulation has been done using the magnetic vector potential formulation. A diagonal permeability tensor has been used to represent the anisotropic properties of the GO material. This tensor is formed assuming non-diagonal terms. The values of the tensor for the axes x and y were obtained from the characterization of the industrial GO steel C150-35S in the RD and TD, while for the axis z a very low relative permeability of ≈ 30 is assumed, as measured in [6].&lt;br/&gt;&lt;br/&gt;Furthermore, the analyzed geometry corresponds to a GO sheet with dimensions of 10 cm x 10 cm and a thickness of 0.35 mm, surrounded by a coil along the x-axis. The iron loss calculation is performed in a section at the center of the sheet with an area of 1 cm x 1 cm. The elements at the center are subjected to a sinusoidal waveform of Jp of 0.5 T. Thirteen values of θ have been evaluated in this study (0°, 5°, 10°, 15°, 20°, 25°, 30°, 42°, 54.7°, 65°, 75°, 82.5° and 90°). They correspond to the angles characterized experimentally using the Epstein frame method with Epstein strips cut at different angles from the industrial GO steel sheet. Finally, from the distribution of H and J obtained in the FEA, the iron losses have been calculated in post-treatment. The main entries for the iron loss model were the hysteresis and excess losses in the RD and TD. In Table 1, an example comparing the static and dynamic losses obtained from the FEA against the experimental losses is given for some angles at 0.5 T. Further validations, analysis and discussions are envisaged in the extended version of the paper.

**References:**

[1] Carlo Appino, Enzo Ferrara, Fausto Fiorillo, et al., &lt;i&gt;Journal of Magnetism and Magnetic Materials&lt;/i&gt;, vol. 500, (2019).&lt;br/&gt;[2] code_Carmel. [Online]. Available: https://code-carmel.univ-lille.fr/?q=fr/ node/15, accessed 2021&lt;br/&gt;[3] G. Bertotti,&lt;i&gt; IEEE Transactions on Magnetics&lt;/i&gt;, vol. 24, no. 1, pp. 621–630, (1988)&lt;br/&gt;[4] F. Fiorillo, L. R. Dupré&lt;i&gt;, IEEE Trans. on Mag&lt;/i&gt;., vol. 38, no. 3, (2002)&lt;br/&gt;[5] L. Néel, &lt;i&gt;J. Phys. Rad&lt;/i&gt;., vol. 5, pp. 241, (1944)&lt;br/&gt;[6] N. Hihat, J. P. Lecointe, O. Ninet, et al., &lt;i&gt;International Journal of Applied Electromagnetics and Mechanics&lt;/i&gt;, vol. 46. pp. 349 - 354, (2014)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/0e5efc22699b2e5d1252a3fef02af167.png)
Table 1. Comparison of computed and experimental losses at 0.5 T



INTERMAG 2021

 Iron Loss Modeling of Anisotropic Soft Magnetic Steels in FEM Simulation Environment

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Due to their texture, the magnetic characteristics of grain oriented (GO) steels depend on the angle between the applied magnetic field and the rolling direction RD. These GO steels exhibit advantageous magnetic characteristics, such as high permeability in the RD and relatively poor properties in the transverse direction TD. In order to obtain a better electromagnetic modeling of the electrical energy conversion systems using GO steels, the dissipative phenomena and the anisotropy must be reliably represented. One example is the case of the GO electrical steels used in stators of turbo-generators. In order to create an appropriate model, the associated magnetic losses have to be taken into account for any angle between the applied field and the RD. However, the problem of computing iron losses whatever the angle between the applied field and the RD has remained unsolved especially within the finite element method (FEM) framework. In this paper, a phenomenological iron loss model, recently proposed in [1], taking into account the anisotropy and nonlinearity of GO sheets has been successfully implemented in the L2EP FEM software baptized code_Carmel [2]. The model relies on the ‘loss separation’ approach. In this approach, which is based on the traditional decomposition proposed by Bertotti [3], the total losses are decomposed into three terms (hysteresis, classical and excess losses). The originality of the model concerns the first loss term i.e., the quasi-static losses dissipated per magnetization cycle, depending on the polarization level Jp and on the angle θ between the applied field and RD. The proposed quasi-static loss model considers the magnetization process and the evolution of the domain wall structure (dws) with the angle θ [4]. It is built from the two sets of W-Jp quasi-static experimental data obtained in the principal directions RD and TD and is based on the interactions between the main classes of magnetic domains, 180° and 90° dws, known as “Néel phases” [5] through a single analytical relationship involving the volumic fraction occupied, for any direction of the magnetic field, by these classes. This same principle is applied for the determination of the excess losses. At this stage, the corresponding input data are the excess losses measured in both RD and TD. Concerning the classical loss term, it simply takes the expression resulting from the classical eddy current theory which is independent of the angle θ. Indeed, the case of an infinite sheet of thickness e, with a linear constitutive law (µ independent of H) and conductivity σ, under a sinusoidal field of frequency f, allows an entirely analytical resolution of the magnetic diffusion equation. Finally, we get a description of the total losses W(f,Jp) as a function of the angle θ, without any adjustable parameter. The model has been validated on industrial sheets of EDF turbo-generators by means of simple study cases under periodic (cyclic) waveforms. Thus, we dispose of an efficient and reliable tool for modeling the magnetic losses of GO sheets within the FEM simulation environment. In order to validate the implementation of the developed model, a finite element analysis (FEA) has been performed using code_Carmel. A 3D linear magnetostatic simulation has been done using the magnetic vector potential formulation. A diagonal permeability tensor has been used to represent the anisotropic properties of the GO material. This tensor is formed assuming non-diagonal terms. The values of the tensor for the axes x and y were obtained from the characterization of the industrial GO steel C150-35S in the RD and TD, while for the axis z a very low relative permeability of ≈ 30 is assumed, as measured in [6]. Furthermore, the analyzed geometry corresponds to a GO sheet with dimensions of 10 cm x 10 cm and a thickness of 0.35 mm, surrounded by a coil along the x-axis. The iron loss calculation is performed in a section at the center of the sheet with an area of 1 cm x 1 cm. The elements at the center are subjected to a sinusoidal waveform of Jp of 0.5 T. Thirteen values of θ have been evaluated in this study (0°, 5°, 10°, 15°, 20°, 25°, 30°, 42°, 54.7°, 65°, 75°, 82.5° and 90°). They correspond to the angles characterized experimentally using the Epstein frame method with Epstein strips cut at different angles from the industrial GO steel sheet. Finally, from the distribution of H and J obtained in the FEA, the iron losses have been calculated in post-treatment. The main entries for the iron loss model were the hysteresis and excess losses in the RD and TD. In Table 1, an example comparing the static and dynamic losses obtained from the FEA against the experimental losses is given for some angles at 0.5 T. Further validations, analysis and discussions are envisaged in the extended version of the paper.

**References:**

[1] Carlo Appino, Enzo Ferrara, Fausto Fiorillo, et al., Journal of Magnetism and Magnetic Materials, vol. 500, (2019). [2] code_Carmel. [Online]. Available: https://code-carmel.univ-lille.fr/?q=fr/ node/15, accessed 2021 [3] G. Bertotti, IEEE Transactions on Magnetics, vol. 24, no. 1, pp. 621–630, (1988) [4] F. Fiorillo, L. R. Dupré, IEEE Trans. on Mag., vol. 38, no. 3, (2002) [5] L. Néel, J. Phys. Rad., vol. 5, pp. 241, (1944) [6] N. Hihat, J. P. Lecointe, O. Ninet, et al., International Journal of Applied Electromagnetics and Mechanics, vol. 46. pp. 349 - 354, (2014)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/0e5efc22699b2e5d1252a3fef02af167.png)
Table 1. Comparison of computed and experimental losses at 0.5 T

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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

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).

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

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.

 Data Mining Approach to Development of Iron-Silicon Soft Magnetic Alloys

1Introduction Manufacturing of electrical machines, in general, involves cutting of electrical steel sheets to appropriate sizes. Different cutting techniques such as punching, electrical discharge machining (EDM) and laser cutting are popular. These methods cause damage inside the material close to the cutting edge, which results in deterioration of magnetic properties [1]. Existing studies are based on measurement result by Epstein frame, Ring sample and single-sheet tester. However, these methods do have problems, causing error when analyzing influence of manufacture on material properties[2]. For example, the such non-ideal factors as overlapping joint causes significant eddy current loss especially at high frequency, which may make effect of manufacture effect negligible. In order to obtain more accurate measurement results, this paper aims to propose a new method to clarify the cutting effect on magnetic properties of silicon steel, eliminating those non-ideal factors, and to find out mechanism behind the deterioration of magnetic properties based on macroscopic magnetic measurement and microstructure observation. 2Effect of Cutting Methods on Magnetic Properties of Electrical Steel 2.1Macroscopic Magnetic Measurement The effect of cutting on the electrical steel sheets is analyzed by magnetic measurement on steel strips of different widths. The magnetic test samples were 35WW270 electrical steel lamination (300 mm×30 mm×0.35 mm). Half of the samples were cut along rolling direction while the other half were in the transverse direction. Then the samples have been cut along their length into different width by shearing, EDM, laser cutting, and glued up with polyimide tapes. Magnetic measurements are usually performed on electrical steel samples with Epstein frame. Nevertheless, the Epstein frame has some intrinsic weaknesses. One of them is that the flux density and specific total loss is uneven near the corners. The Epstein frame can be divided as uniform area, transitional area and overlapping area. In order to eliminate the impact of overlapping area and transitional area, two Epstein frames were designed as Fig 1, E(25), 25cm (standard) and E(12.5), 12.5cm (non-standard) Epstein frames, which have identical corner areas and transitional areas. The only difference in size is that the uniform area of E(12.5) is shorter than E(25). The same steel sheet (300mm length *30mm width) were used in both Epstein frames and their total absolute loss was measured. Magnetic measurement are performed following standard IEC: 604004-2. It can be assumed the absolute loss of corner and affected area of E(25) and E(12.5) is equal because of the identical corners and affected area. Then the only difference in absolute power loss between the two Epstein frames is due to the difference in absolute loss of the different uniform areas. The magnetic properties of the samples were measured at 50-800 Hz, and the results at 50 Hz were shown in Fig 2. When B = 1 T and frequency is 50 Hz, compared with EDM, the iron loss of samples with shearing increased by 5.6% and that with laser cutting increased by 32.6%. It can be found that the difference decreased at a higher frequency.The iron loss can be divided into static loss and dynamic loss. With the frequency increasing, dynamic loss takes more share of total iron loss[3]. Therefore, it can be assumed that the effect of cutting stresses on static loss is greater than that on dynamic loss. 2.1.1Microstructure Observation The steel samples were prepared by grinding on 400, 800, and 1200 grit SiC papers and polishing using 3μm diamond paste to obtain a mirror-like surface. Specimen microstructure was examined by scanning electron microscopy (SEM). Fig 2 shows the microstructure of the samples with different cutting methods observed by SEM. There are different contrast effects due to the plastic deformation near the cutting edge. It can be seen that the width of damaged area of EDM is about 20 μm, smaller than that of shearing (83 μm). And it is obvious that there is melting or heat affect zone (108 μm) in the immediate proximity of the cut edge due to laser cutting procedure, which leads to the worst magnetic properties of samples with laser cutting. 3Conclusion This paper has compared and analyzed the effect of different cutting methods on the magnetic properties of electrical steel by double Epstein frames. It is found that EDM has the least influence on the sample, followed by shearing, and laser cutting has the greatest influence. The laser cutting effect is the worst, that is becacuse that there is no cooling in the cutting process, while EDM has coolant flow. The microstructure of the samples was observed by SEM. The results show that the macro measurement results are consistent with the micro observation results.

**References:**

&lt;!--[if supportFields]&gt;&lt;spanlang=EN-US&gt;&lt;span style='mso-element:field-begin'&gt;&lt;/span&gt;&lt;spanstyle='mso-spacerun:yes'&gt; &lt;/span&gt;ADDIN EN.REFLIST &lt;span style='mso-element:field-separator'&gt;&lt;/span&gt;&lt;/span&gt;&lt;![endif]--&gt;[1] H. Naumoski, "Investigation of the influence of different cutting procedures on the global and local magnetic properties of non-oriented electrical steel," Journal of Magnetism and Magnetic Materials, vol. 392, pp. 126-133, 2015. [2] Z. Xiaoyang, "Study on Measurement and Simulation Method of Magnetic Properties of Electrical Steel Sheets Considering Influence of Cutting Method," Shenyang University of Technology, 2016. [3] W. D. Chen J, Cheng S, "Modeling of Temperature Effects on Magnetic Property of Nonoriented Silicon Steel Lamination," IEEE Transactions on Magnetics, vol. 51, no. 11, pp. 1-4, 2015. &lt;!--[if supportFields]&gt;&lt;span lang=EN-US style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:宋体;mso-bidi-theme-font:minor-bidi;mso-ansi-language:EN-US;mso-fareast-language:ZH-CN;mso-bidi-language:AR-SA'&gt;&lt;spanstyle='mso-element:field-end'&gt;&lt;/span&gt;&lt;/span&gt;&lt;![endif]--&gt;

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/4befe7ab34ce100a7257c4a4004b0ad8.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/a40e5a0db3f0e78ca813dc19a706c8a2.jpg)

 Effect of Cutting Methods on Magnetic Properties of Electrical Steel

CoFeB is one of the most extensivity studied magnetic materials due to its atypical properties such as structurally smooth growth [1], soft magnetic properties [2], high spin polarization [3], and very low Gilbert damping [4], which makes it especially suitable for magnetic tunnel junction devices [5]. Numerous researches have proclaimed that thermal annealing is a decisive measure for a high performance of CoFeB based magnetic tunnel junction devices. Therefore, it is of utmost importance to understand the influence of thermal annealing on this alloy. In this work, the crystallisation of Co-Fe-B alloys triggered by thermal annealing was investigated by X-ray diffraction techniques and scanning electron microscopy, as well as spectroscopic ellipsometry and magneto-optical Kerr effect spectroscopy for annealing temperatures ranging from 300°C to 600°C. The transformation of ~100 nm thick CoxFe(80-x)B20 films from amorphous to polycrystalline was revealed by the sharpening of spectral features observed in optical and magneto-optical dielectric function spectra. These features are ascribed to direct inter-band transitions due to the hybridization of p- and d orbitals of Co-Fe alloys in bcc crystalline phase. Cross-sectional scanning electron microscopy of Co-Fe-B layers annealed at 600°C further confirmed that in the case of a Pt capping layer, the crystallization starts at the interface of CoFeB and Pt, and expands for a thickness, which is consistent with the vertical coherence length of the crystallites determined from XRD. The influence of B on the dielectric function was assessed both experimentally and by optical modelling. By analysing the Drude component of the optical dielectric function, a consistent trend between the charge carrier scattering time/resistivity and the annealing temperature was observed, in agreement with the electrical investigations by means of the four-point-probe method. The result obtained from this study were recently published in ref. [6].

**References:**

1. D. D. Djayaprawira, K. Tsunekawa, M. Nagai, H. Maehara, S. Yamagata, N. Watanabe, S. Yuasa, Y. Suzuki, and K. Ando, Appl. Phys. Lett. 86, 92502 (2005). 2. H. Hauser and R. Grössinger, J. Appl. Phys. 85, 5133 (1999). 3. S. X. Huang, T. Y. Chen, and C. L. Chien, Appl. Phys. Lett. 92, 242509 (2008). 4. C. Bilzer, T. Devolder, J.-V. Von Kim, G. Counil, C. Chappert, S. Cardoso, and P. P. Freitas, J. Appl. Phys. 100, 053903 (2006). 5. T. Devolder, J.-V. Kim, L. Nistor, R. Sousa, B. Rodmacq, and B. Diény, J. Appl. Phys. 120, 183902 (2016). 6. A. Sharma, M. A. Hoffmann, P. Matthes, O. Hellwig, C. Kowol, S. E. Schulz, D. R. T. Zahn, and G. Salvan, Phys. Rev. B 101, 054438 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c0dc6dc54b8645942697748105c792f5.jpg)
The polar Kerr effect measured polarisation rotation (θK) spectra for a Pt capped 100 nm thick Co40Fe40B20 film before and after annealing at various temperatures.

![](https://assets.underline.io/uploads/markdown_image/1/image/c008b8812afe925d41bc890b4fc5cea1.jpg)
SEM micrograph collage of substrate/ Co40Fe40B20/ Pt before and after annealing at 600°C, recorded in a FIB trench at 36° stage tilt.

 Crystallisation of optically thick films of CoxFe(80-x)B20: evolution of the (magneto-) optical and structural properties

Fe-Ga alloy is an advanced magnetostrictive material for actuators and sensors in terms of combining excellent mechanical and magnetostrictive properties. It is desirable to produce η(&lt;100&gt;//RD) textured Fe-Ga sheets due to the magnetostriction anisotropy with the largest coefficient along &lt;100&gt; direction and the serious eddy current loss in high-frequency use 1,2. The secondary recrystallization Goss ({110}&lt;001&gt;) texture and large magnetostriction coefficient were mainly achieved in Fe-Ga aaloy thin sheet with the thickness of 0.3~0.5mm, by the combination of micron-sized NbC particles and surface energy effect in high-temperature annealing 3,4, as well as the initial sharp &lt;100&gt;-oriented columnar grains by directional solidification 5. Since the eddy current loss is proportional to the square of the sheet thickness, the thinning of the sheet thickness can improve the energy conversion efficiency significantly. However, the secondary recrystallization of Goss texture significantly deteriorated in the Fe-Ga alloy sheet with a thickness of less than 0.3 mm due to the insufficient pinning force from the micron-sized NbC particles 6. The introduction of surface energy effect from H2S or S element, as well as the initial columnar crystals by directional solidification 7, cannot guarantee the complete secondary recrystallization in Fe-Ga alloy sheet with the thickness less than 0.3 mm. Qi et al 8 supposed the 0.10-mm Fe-Ga alloy ultra-thin sheets were prepared by rolling the 0.3 mm secondary recrystallized sheets, the strong cube texture and magnetostriction of 140 ppm were obtained after annealed for 2 h at 1200 °C under a flowing argon–hydrogen mixture. However, the preparation process is complicated and the incomplete secondary recrystallization restricts the magnetostriction coefficient. Therefore, it is necessary for the realization of complete secondary recrystallization in the Fe-Ga alloy sheet with a thickness of less than 0.3 mm. In the present study, the Fe-Ga ultra-thin sheets with the thickness of 0.10–0.25 mm were prepared via two-stage cold rolling method. The composite inhibitors composed of nanometer-sized sulfide and carbonitride are dispersedly precipitated during hot rolling and subsequent annealing, which provides effective pinning force for the normal growth of matrix grains. The gradually dissipated inhibition force during high-temperature annealing promotes a few exact Goss grains to grow abnormally by consuming primary recrystallized matrix grains textured by γ-fiber. Centimeter-sized secondary recrystallization Goss grains and large magnetostriction coefficient as high as 240 ppm is obtained in Fe-Ga alloy ultra-thin sheet without surface energy effect. The result indicates that complete secondary recrystallization can be realized based on the precise design and control of nano-sized composite precipitates and primary recrystallization microstructure/texture in Fe-Ga alloy ultra-thin sheet by conventional rolling and annealing methods.

**References:**

1. S. M. Na and A. B. Flatau, Scripta Mater. Vol., 66, p.307-310 (2012). 2. J. H. Li, X. X. Gao, J. Zhu, T. Xia and M. C. Zhang, Scripta Mater. Vol., 63, p.246-249 (2010). 3. C. Yuan, J. H. Li, X. Q. Bao and X. X. Gao, J Magn Magn Mater. Vol., 391, p.145-150 (2015). 4. S. M. Na, K. M. Atwater and A. B. Flatau, Scripta Mater. Vol., 100, p.1-4 (2015). 5. C. Yuan, J. H. Li, X. G. Bao and X. X. Gao, J Magn Magn Mater. Vol., 374, p.459-462 (2015). 6. S. M. Na and A. B. Flatau, AIP Adv. Vol., 7, p.056406 (2017). 7. J. H. Li, C. Yuan, Q. L. Qi, X. Q. Bao and X. X. Gao, Metals. Vol., 7, p.36 (2017). 8. Q. Qi, J. Li, X. Mu, Z. Ding, X. Bao and X. Gao, J Mater Sci. Vol., 55, p.2226–2238 (2019).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/326557a3327ec6e86a0e54601fff5ed3.jpg)
Orientation image maps of Fe-Ga ultra-thin sheets annealed at 950°C (a), 1000°C (b), 1100°C (c), and macrostructure after final annealing (d), as well as the variation of magnetostriction coefficients (λ//, λ⊥) with magnetic field annealed at 1000°C and 1100°C (e)

 The secondary recrystallization texture and magnetostriction in Fe-Ga alloy ultra-thin sheet

Grain-oriented (GO) steel sheets increasingly face novel applications, like the ones enforced by the emerging smart grid technologies and the related medium-to-high frequencies conversion devices and those connected with the development of highly efficient low-noise rotating machines [1-3]. Comprehensive knowledge of the material behavior, going beyond the standard assessment of its properties at power frequencies along the rolling direction (RD), is therefore appreciated in the practice of machine design. This requires both experiments made upon broader than usual range of frequencies [4] and the investigation of the complex anisotropic response of the GO sheets and the related 2D magnetization process [5]. Such a process is shown to consists in the balanced contributions by moving [001] directed 180° domain walls (dws) and 90° dw transitions towards the [100] and [010] phases. It is then observed that, with the applied field leaving the RD, not only the magnetic losses suffer a sharp increase, but also a strong geometry dependent effect, under both static and dynamic regimes. This descends from the interference of the demagnetizing field, invariably arising in Fe-Si single crystals, but for closed samples cut along the &lt;100&gt;, &lt;110&gt;, and &lt;111&gt; axes. Consequently, the popular approach to GO characterization using Epstein strips cut at different angles θ to RD can provide the intrinsic properties of the material only for θ = 0° (RD) and θ = 90° (TD). This is ill-suited to straightforward use in those cases, like the rotating machine cores, where directions other than RD and TD are involved. However, the experimental knowledge of the geometry-independent RD and TD magnetization curves can be usefully exploited, following the lines of the Néel’s phase theory, to reconstruct the same curves measured on Epstein strips cut along a generic angle θ [6]. The same applies to the DC hysteresis loops and their area, once the fundamental role of the demagnetizing field is recognized. One can also emulate an infinitely extended sheet, the ideal configuration leading to the intrinsic material response, by adopting an X-stacked sheet configuration, where flux continuity across the sheet edges can be achieved, resulting in a net magnetization variation both along the applied field (i.e., the strip edges) and orthogonal to it. Also in this case the DC properties become predictable by starting from the RD and TD magnetic properties [6]. Any other sample geometry will then be fully represented by or will be intermediate between the Epstein and the X-stack configurations. In this work, we provide a general approach to DC and AC (1 Hz - 200 Hz) magnetic hysteresis loop and losses in Epstein and X-stacked HGO sheets. The experiments are made using either the standard Epstein frame or a single sheet tester, where 120 mm wide 300 mm long X-stacked sheet samples are inserted in a laminated flux-closing yoke. A phenomenological predicting method is devised, which relies on the pre-emptive knowledge of the behavior of hysteresis loop and energy loss independently measured under sinusoidal induction in the RD- and TD-cut Epstein strips. We treat, in accordance with magneto-optical observations, the magnetization process unfolding for generic angle θ as the result, dictated by applied, demagnetizing, and eddy current fields, of two mechanisms: 1) Displacement of the 180° dws, the process pertaining to the RD cut sheets and strips; 2) Motion of 90° dws, converting the antiparallel slab-like [001] domains into [010] and [100] domains, and vice versa. The frames in Fig. 1 qualitatively show an example of domain structure in an X-stacked sheet at two instants of time along a major hysteresis loop (peak polarization Jp = 1.45 T). The antiparallel [001] domain structure observed at J = 0, largely disappears upon attaining J = 0.87 T. With this configuration, only a faint demagnetizing field is expected to arise at the sample edges and a net 2D magnetization variation is observed. By taking then, for a given Jp, the experimental energy loss and the hysteresis loops pertaining to the RD and TD samples, obtained at JpRD = Jp cos(θ) and JpTD = Jp sin(θ), and realizing that the fractional sample volume v180(t) occupied by the [001] phase is related to the same quantity v90(t) = √2 JTD /Js associated with the [010] and [100] domains as v180(t ) = 1 – v90(t), we calculate loss and loop for any given θ value. An example of so-obtained energy loss W(f) at 50 Hz across a range of Jp values on 0.288 mm thick high-permeability GO Epstein strips cut at different angles θ to RD is provided in Fig. 2. The experiments show that W(θ) peaks around θ = 75°. The predicting approach to W(θ) is based on the experimental knowledge of the energy loss measured at the same frequency in the RD and TD strips for JpRD = Jp cos(θ) and JpTD = Jp sin(θ). This associates with the calculation of the hysteresis loop. A more involved approach is required by the W(θ) prediction in the X-stacked samples, where the simplifying assumption of zero magnetization across the sheet width does not hold.

**References:**

[1] T. Belgrand, R. Lemaître, A. Benabou, J. Blaszkowski et C. Wang, AIP Advances 8, 047611 (2018). [2] G. Parent, R. Penin, J. P. Lecointe, J. F. Brudny, and T. Belgrand, IEEE Trans. Magn. 49, 1977 (2013). [3] S. Lopez, B. Cassoret, J. Brudny, L. Lefebvre, and J. Vincent, IEEE Trans. Magn. 45, 4161(2009). [4] M. A. Shamsuddin, F. Rojas, R. Cardenas, J. Pereda, M. Diaz, and R. Kennel, Energies 13, 2319 (2020). [5] W. Pluta, IEEE Trans. Magn. 52, 6300912 (2016). [6] F. Fiorillo, L. R. Dupré, C. Appino, and A. M. Rietto, IEEE Trans. Magn. 38, 1467 (2002).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/6b5cb05f0e84b50643df6d3ceb985c44.jpg)
Fig. 1. X-stacked GO sheet, cut at 75° with respect to the RD. The [001] antiparallel slab-like domain structure found in the demagnetized state (J = 0) is converted by 90° dw motion into symmetric [100] and [010] structures under increasing applied field (Jp = 1.45 T).

![](https://assets.underline.io/uploads/markdown_image/1/image/853d1d39b26e5ad4a2c3c620a36c162b.jpg)
Fig. 2. Energy loss at 50 Hz measured versus Jp and θ in Epstein strips. Solid lines and symbols: experiments. Dashed lines: prediction by a weighted combination of the 50 Hz RD and TD loss figures.

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