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During the last decade, iron borate FeBO&lt;sub&gt;3 &lt;/sub&gt; based crystals have been attracting an increased interest of scientific community, mainly for the following reasons: (i) these materials can be applied in modern technical devices, &lt;i&gt;e.g&lt;/i&gt;. serving as sensitive instruments for measuring magnetic field, pressure, &lt;i&gt;etc&lt;/i&gt;., or as monochromators for use with synchrotron radiation [1]; (ii) mixed iron gallium borate Fe&lt;i&gt;&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;Ga&lt;sub&gt;1-&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;BO&lt;sub&gt;3&lt;/sub&gt; crystals are quite suitable objects for studying properties of trigonal weak ferromagnets with zero orbital moment [2, 3].&lt;br/&gt;We have recently shown that with decreasing iron contents the magnetic state of Fe&lt;i&gt;&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;Ga&lt;sub&gt;1-&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;BO&lt;sub&gt;3&lt;/sub&gt; crystals shows a gradual passage from easy-plane weak ferromagnet to diluted paramagnet, passing through magnetic clusters at intermediate iron contents [2]. Thus, by isomorphously substituting paramagnetic Fe&lt;sup&gt;3+&lt;/sup&gt; ions in iron borate, FeBO&lt;sub&gt;3&lt;/sub&gt;, by diamagnetic Ga&lt;sup&gt;3+&lt;/sup&gt; ions one can synthetize a series of isostructural single crystals allowing not only fine-tuning their magnetic characteristics, thus creating new materials with sought-for properties, but also studying the nature of magnetic state, magnetocrystalline anisotropy, &lt;i&gt;etc.&lt;/i&gt; [2, 3]. Such crystals can be synthesized using well-known flux growth technique [4]. However, obtaining high quality Fe&lt;i&gt;&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;Ga&lt;sub&gt;1-&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;BO&lt;sub&gt;3&lt;/sub&gt; crystals in wide range of substitutions, 0≤&lt;i&gt;x&lt;/i&gt;≤1, has required many trials in order to find out optimal regimes for crystallization at different concentrations and a considerable improvement of the standard synthesis technique [1].&lt;br/&gt;In this work, we have focused on microscopic characterization of certain magnetic properties of Fe&lt;i&gt;&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;Ga&lt;sub&gt;1-&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;BO&lt;sub&gt;3&lt;/sub&gt; borates by considering in detail &lt;i&gt;intracrystalline&lt;/i&gt; interactions in these materials. The density of the magnetic energy for Fe&lt;i&gt;&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;Ga&lt;sub&gt;1-&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;BO&lt;sub&gt;3&lt;/sub&gt; crystals can be expressed as follows [5]:&lt;br/&gt;&lt;i&gt;E&lt;/i&gt;=1/2&lt;i&gt; Em&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt;+&lt;i&gt;D &lt;/i&gt;(&lt;i&gt;l&lt;sub&gt;x&lt;/sub&gt;m&lt;sub&gt;y&lt;/sub&gt;&lt;/i&gt;-&lt;i&gt;l&lt;sub&gt;y&lt;/sub&gt;m&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;)+ 1/2&lt;i&gt; al&lt;sub&gt;z&lt;/sub&gt;&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt;+&lt;i&gt;d &lt;/i&gt;(3&lt;i&gt;l&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt;-&lt;i&gt;l&lt;sub&gt;y&lt;/sub&gt;&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt;) &lt;i&gt;l&lt;sub&gt;y&lt;/sub&gt;l&lt;sub&gt;z&lt;/sub&gt;&lt;/i&gt;+&lt;i&gt;e&lt;/i&gt; (&lt;i&gt;l&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;&lt;sup&gt;4&lt;/sup&gt;-14&lt;i&gt;l&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt;&lt;i&gt;l&lt;sub&gt;y&lt;/sub&gt;&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt;+&lt;i&gt;l&lt;sub&gt;y&lt;/sub&gt;&lt;/i&gt;&lt;sup&gt;4&lt;/sup&gt;) (&lt;i&gt;l&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt;-&lt;i&gt;l&lt;sub&gt;y&lt;/sub&gt;&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt;) (1)&lt;br/&gt;where &lt;i&gt;m&lt;/i&gt; and &lt;i&gt;l&lt;/i&gt; are reduced ferromagnetic and antiferromagnetic vectors, &lt;i&gt;D&lt;/i&gt; and &lt;i&gt;E&lt;/i&gt; are the Dzyaloshinskii-Moriya and exchange constants, is the uniaxial anisotropy constant, and &lt;i&gt;d&lt;/i&gt; and &lt;i&gt;e&lt;/i&gt; are the basal anisotropy constants. Different mechanisms responsible for the magnetic properties have different dependences on the concentration of paramagnetic ions and temperature; therefore, experimental studies of the latter dependences and a subsequent modelling based on eq. (1) could, on the one hand, single out dominating mechanisms of the magnetic transitions observed and, on the other hand, get better insight in the nature of intracrystalline interactions in trigonal weak ferromagnets.&lt;br/&gt;Since the Dzyaloshinskii-Moriya and exchange constants characterize pair interactions between paramagnetic ions, we have assumed that the corresponding &lt;i&gt;microscopic&lt;/i&gt; constants for a pair of Fe&lt;sup&gt;3+&lt;/sup&gt; ions in mixed crystals remain the same as those in unmixed crystal. Thus, we can express both constants for mixed iron-gallium borates through the &lt;i&gt;macroscopic&lt;/i&gt; &lt;i&gt;D&lt;/i&gt; and &lt;i&gt;E&lt;/i&gt; constants for unmixed iron borate and obtain an analytical expression of the macroscopic constants for mixed crystals. We have put forward a computer code modelling the diamagnetically diluted crystal lattice by the Monte-Carlo technique [6] and implementing a summation, first, over the nearest-neighbouring Fe&lt;sup&gt;3+&lt;/sup&gt; for a reference Fe&lt;sup&gt;3+&lt;/sup&gt; ion and, next, over all sites occupied by Fe&lt;sup&gt;3+&lt;/sup&gt; ions. As a result, we have shown that the dependences of both &lt;i&gt;D&lt;/i&gt; and &lt;i&gt;E&lt;/i&gt; constants on &lt;i&gt;x&lt;/i&gt; (at 0 K) follow a parabolic law.&lt;br/&gt;In calculating the magnetocrystalline anisotropy for Fe&lt;i&gt;&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;Ga&lt;sub&gt;1-&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;BO&lt;sub&gt;3&lt;/sub&gt; crystals one should take into account only crystal field and dipole-dipole contributions. Indeed, the 3&lt;i&gt;d&lt;/i&gt;&lt;sup&gt;5&lt;/sup&gt; electronic configuration of Fe&lt;sup&gt;3+&lt;/sup&gt; has zero orbital moment; therefore, the exchange energy in a good approximation is isotropic [7]. Recently we have calculated the dipole-dipole interaction energy in the model of “extended dipoles” [8], having non-negligible dipole size. Unlike the point dipoles, the extended dipoles bring a non-zero dipole-dipole contribution to the basal magnetocrystalline anisotropy, and earlier we have evaluated it for unmixed iron borate [3]. In the model of extended dipoles, a calculation of the Ampérian current,&lt;i&gt; i.e&lt;/i&gt;., a circular current loop of a radius &lt;i&gt;R,&lt;/i&gt; results in two possible sizes of the magnetic dipole represented by a Fe&lt;sup&gt;3+&lt;/sup&gt; ion: &lt;i&gt;R&lt;/i&gt;&lt;sub&gt;1 &lt;/sub&gt;= 0.2189 and &lt;i&gt;R&lt;/i&gt;&lt;sub&gt;2 &lt;/sub&gt;= 0.0797 Å [3]. In this work, we have applied the model of extending dipoles to evaluating the dipole-dipole contributions to the magnetocrystalline anisotropy constants of mixed iron-gallium borates. To this purpose, we have put forward a computer code implementing the lattice-sum method [3] and modelling the diamagnetically diluted crystal lattice using the Monte Carlo technique in the same way as in calculating &lt;i&gt;D&lt;/i&gt; and &lt;i&gt;E&lt;/i&gt; constants, &lt;i&gt;vide supra&lt;/i&gt; [6]. Resultantly, the dependences on &lt;i&gt;x&lt;/i&gt; of the dipole-dipole contribution to the magnetocrystalline constants for Fe&lt;i&gt;&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;Ga&lt;sub&gt;1-&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;BO&lt;sub&gt;3&lt;/sub&gt; crystals have been obtained, see Figures 1 and 2. The dipole-dipole contributions to the basal anisotropy constants have been calculated at 0 K for different &lt;i&gt;x&lt;/i&gt; using both possible effective dipole sizes, &lt;i&gt;R&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt; and &lt;i&gt;R&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;, determined for Fe&lt;sup&gt;3+&lt;/sup&gt; ions.&lt;br/&gt;This work was partially supported by the V.I. Vernadsky Crimean Federal University Development Program for 2015-2024 Grant no. VG04/2019; and by the RFBR projects Grants No. 19-32-90054 and 18-42-910008.

**References:**

1. E.S. Smirnova, N.I. Snegirev, I.S. Lyubutin &lt;i&gt;et al.&lt;/i&gt;, Acta Cryst., Vol. B76, p. 1100 (2020)&lt;br/&gt;2. K. Seleznyova, M. Strugatsky, S. Yagupov &lt;i&gt;et al.&lt;/i&gt;, J. Appl. Phys., Vol. 125, p. 223905 (2019)&lt;br/&gt;3. M. Strugatsky, K. Seleznyova, S. Yagupov &lt;i&gt;et al.&lt;/i&gt;, J. Magn. Magn. Mater., Vol. 442, p. 417 (2017)&lt;br/&gt;4. S. Yagupov, M. Strugatsky, K. Seleznyova &lt;i&gt;et al.&lt;/i&gt;, Appl. Phys. A, Vol. 121, p. 179 (2015)&lt;br/&gt;5. E.A. Turov and N.G. Guseinov, Soviet Physics JETP, Vol. 11, p. 955 (1960)&lt;br/&gt;6. L. Devroye, &lt;i&gt;Non-Uniform Random Variate Generation&lt;/i&gt;, Springer, 843 pp. (1986)&lt;br/&gt;7. J. Kanamori, in:&lt;i&gt; Magnetism&lt;/i&gt;, eds., G.T. Rado, H. Suhl, Acad. Press, Vol 1, pp. 127 (1963)&lt;br/&gt;8. K. Seleznyova, M. Strugatsky and J. Kliava, Eur. J. Phys., Vol. 37, p. 025203 (2016)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c80785883160de382473c88ba885d8ea.jpg)
Fig.1 Dipole-dipole contribution to &lt;i&gt;a&lt;/i&gt; &lt;i&gt;vs.&lt;/i&gt; &lt;i&gt;x&lt;/i&gt; in Fe&lt;i&gt;&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;Ga&lt;sub&gt;1-&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;BO&lt;sub&gt;3&lt;/sub&gt; crystals at 0 K.

![](https://assets.underline.io/uploads/markdown_image/1/image/530198f9d062fa644639968bd67c1f2b.jpg)
Fig.2 Dipole-dipole contributions to &lt;i&gt;d&lt;/i&gt; (left) and &lt;i&gt;e&lt;/i&gt; (right) &lt;i&gt;vs.&lt;/i&gt; &lt;i&gt;x&lt;/i&gt; in Fe&lt;i&gt;&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;Ga&lt;sub&gt;1-&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;BO&lt;sub&gt;3&lt;/sub&gt; crystals, calculated for two possible effective dipole sizes: &lt;i&gt;R&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt; (dashed curves) and &lt;i&gt;R&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt; (dash-dotted curves) at 0 K.

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During the last decade, iron borate FeBO3 based crystals have been attracting an increased interest of scientific community, mainly for the following reasons: (i) these materials can be applied in modern technical devices, e.g. serving as sensitive instruments for measuring magnetic field, pressure, etc., or as monochromators for use with synchrotron radiation [1]; (ii) mixed iron gallium borate FexGa1-xBO3 crystals are quite suitable objects for studying properties of trigonal weak ferromagnets with zero orbital moment [2, 3]. We have recently shown that with decreasing iron contents the magnetic state of FexGa1-xBO3 crystals shows a gradual passage from easy-plane weak ferromagnet to diluted paramagnet, passing through magnetic clusters at intermediate iron contents [2]. Thus, by isomorphously substituting paramagnetic Fe3+ ions in iron borate, FeBO3, by diamagnetic Ga3+ ions one can synthetize a series of isostructural single crystals allowing not only fine-tuning their magnetic characteristics, thus creating new materials with sought-for properties, but also studying the nature of magnetic state, magnetocrystalline anisotropy, etc. [2, 3]. Such crystals can be synthesized using well-known flux growth technique [4]. However, obtaining high quality FexGa1-xBO3 crystals in wide range of substitutions, 0≤x≤1, has required many trials in order to find out optimal regimes for crystallization at different concentrations and a considerable improvement of the standard synthesis technique [1]. In this work, we have focused on microscopic characterization of certain magnetic properties of FexGa1-xBO3 borates by considering in detail intracrystalline interactions in these materials. The density of the magnetic energy for FexGa1-xBO3 crystals can be expressed as follows [5]: E=1/2 Em2+D (lxmy-lymx)+ 1/2 alz2+d (3lx2-ly2) lylz+e (lx4-14lx2ly2+ly4) (lx2-ly2) (1) where m and l are reduced ferromagnetic and antiferromagnetic vectors, D and E are the Dzyaloshinskii-Moriya and exchange constants, is the uniaxial anisotropy constant, and d and e are the basal anisotropy constants. Different mechanisms responsible for the magnetic properties have different dependences on the concentration of paramagnetic ions and temperature; therefore, experimental studies of the latter dependences and a subsequent modelling based on eq. (1) could, on the one hand, single out dominating mechanisms of the magnetic transitions observed and, on the other hand, get better insight in the nature of intracrystalline interactions in trigonal weak ferromagnets. Since the Dzyaloshinskii-Moriya and exchange constants characterize pair interactions between paramagnetic ions, we have assumed that the corresponding microscopic constants for a pair of Fe3+ ions in mixed crystals remain the same as those in unmixed crystal. Thus, we can express both constants for mixed iron-gallium borates through the macroscopic D and E constants for unmixed iron borate and obtain an analytical expression of the macroscopic constants for mixed crystals. We have put forward a computer code modelling the diamagnetically diluted crystal lattice by the Monte-Carlo technique [6] and implementing a summation, first, over the nearest-neighbouring Fe3+ for a reference Fe3+ ion and, next, over all sites occupied by Fe3+ ions. As a result, we have shown that the dependences of both D and E constants on x (at 0 K) follow a parabolic law. In calculating the magnetocrystalline anisotropy for FexGa1-xBO3 crystals one should take into account only crystal field and dipole-dipole contributions. Indeed, the 3d5 electronic configuration of Fe3+ has zero orbital moment; therefore, the exchange energy in a good approximation is isotropic [7]. Recently we have calculated the dipole-dipole interaction energy in the model of “extended dipoles” [8], having non-negligible dipole size. Unlike the point dipoles, the extended dipoles bring a non-zero dipole-dipole contribution to the basal magnetocrystalline anisotropy, and earlier we have evaluated it for unmixed iron borate [3]. In the model of extended dipoles, a calculation of the Ampérian current, i.e., a circular current loop of a radius R, results in two possible sizes of the magnetic dipole represented by a Fe3+ ion: R1 = 0.2189 and R2 = 0.0797 Å [3]. In this work, we have applied the model of extending dipoles to evaluating the dipole-dipole contributions to the magnetocrystalline anisotropy constants of mixed iron-gallium borates. To this purpose, we have put forward a computer code implementing the lattice-sum method [3] and modelling the diamagnetically diluted crystal lattice using the Monte Carlo technique in the same way as in calculating D and E constants, vide supra [6]. Resultantly, the dependences on x of the dipole-dipole contribution to the magnetocrystalline constants for FexGa1-xBO3 crystals have been obtained, see Figures 1 and 2. The dipole-dipole contributions to the basal anisotropy constants have been calculated at 0 K for different x using both possible effective dipole sizes, R1 and R2, determined for Fe3+ ions. This work was partially supported by the V.I. Vernadsky Crimean Federal University Development Program for 2015-2024 Grant no. VG04/2019; and by the RFBR projects Grants No. 19-32-90054 and 18-42-910008.

**References:**

1. E.S. Smirnova, N.I. Snegirev, I.S. Lyubutin et al., Acta Cryst., Vol. B76, p. 1100 (2020) 2. K. Seleznyova, M. Strugatsky, S. Yagupov et al., J. Appl. Phys., Vol. 125, p. 223905 (2019) 3. M. Strugatsky, K. Seleznyova, S. Yagupov et al., J. Magn. Magn. Mater., Vol. 442, p. 417 (2017) 4. S. Yagupov, M. Strugatsky, K. Seleznyova et al., Appl. Phys. A, Vol. 121, p. 179 (2015) 5. E.A. Turov and N.G. Guseinov, Soviet Physics JETP, Vol. 11, p. 955 (1960) 6. L. Devroye, Non-Uniform Random Variate Generation, Springer, 843 pp. (1986) 7. J. Kanamori, in: Magnetism, eds., G.T. Rado, H. Suhl, Acad. Press, Vol 1, pp. 127 (1963) 8. K. Seleznyova, M. Strugatsky and J. Kliava, Eur. J. Phys., Vol. 37, p. 025203 (2016)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c80785883160de382473c88ba885d8ea.jpg)
Fig.1 Dipole-dipole contribution to a vs. x in FexGa1-xBO3 crystals at 0 K.

![](https://assets.underline.io/uploads/markdown_image/1/image/530198f9d062fa644639968bd67c1f2b.jpg)
Fig.2 Dipole-dipole contributions to d (left) and e (right) vs. x in FexGa1-xBO3 crystals, calculated for two possible effective dipole sizes: R1 (dashed curves) and R2 (dash-dotted curves) at 0 K.

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Fe-based soft magnetic materials have been widely used in electrical devices, such as motors, transformers, and inductors, due to their high saturation magnetic flux density. These Fe-based materials generally have a cubic crystal structure with the &lt;100&gt; easy axis of magnetization and fairly high intrinsic crystalline anisotropy constants. Thus, in order to improve their soft magnetic properties, nano-crystalline Fe-based alloy ribbons have been fabricated by rapid solidification and subsequent annealing processes. Because nano-crystalline grains with isotropic and homogeneous microstructures are known to reduce the coercivity (HC) effectively. However, the saturation magnetization (MS) of nano-crystalline alloy ribbons is reduced by adding glass forming elements. Thus it is always required to increase the Ms of the Fe-based alloy ribbons without deteriorating their coercivity. Our previous study showed that Fe84.3B13.7C1Cu1 amorphous ribbons could be fabricated by the rapid solidification process (RSP) and their crystallization procedures during the subsequent annealing process were discussed in terms of the nucleation and crystal growth of a-Fe grains [1]. In these ribbons, square shaped Fe grains were found to be formed and the growth rate of them were shown to be too fast to control the grain size below the exchange length of Fe [2]. Thus, despite their high Fe concentration, the permeability of the ribbons was limited by their HC. This means that it is required to develop the method for inhibiting the grain growth rate and controlling the morphology of annealed Fe grains. In this paper, Fe82.3B13.7C1Cu1Nb2 as-quenched ribbons were fabricated and annealed to understand the effect of Nb addition on the magnetic properties and microstructures during the annealing process. In this experiment, the ingots of Fe82.3B13.7C1Cu1Nb2 alloy were prepared by an arc melt process. As-quenched alloy ribbons were fabricated by the RSP under Ar atmosphere. The thermal properties of the as-quenched ribbons were analyzed by a differential thermogravimetric analyzer (DTA, TG-DTA2000SA) at a heating rate of 10 oC/min under Ar atmosphere. The annealing process was conducted using a rapid thermal process (RTP, IA-1240) equipment. During RTP, the ribbons were heated at a heating rate of 80 oC/min under Ar atmosphere. The MS and HC were measured by a vibrating sample magnetometer (VSM, LakeShore 7410). The microstructures of samples were analyzed by X-ray diffractometer (XRD, D/MAX-2500/PC) with CuKa radiation and atom probe tomography (APT, LEAP 4000X HR) analysis. The APT samples were prepared in the form of needles of 6060200 nm using a focused ion beam (FIB, Helios nanolab G3 UC). The XRD and compositional analysis of as-quenched ribbons confirmed the successful fabrication of Fe82.3B13.7C1Cu1Nb2 amorphous ribbons with a thickness of 21 μm and a width of 2 mm. The average MS and HC of the amorphous ribbons, measured at 10 kG, were 150.2 emu/g and 0.42 Oe, respectively. The DSC analysis of the amorphous ribbons showed that the first exothermic peak (Tx1) started at 400 oC and its maximum peak intensity appeared at 420 oC. In addition, the secondary crystallization temperature of the ribbons was increased up to 550 oC. Compared to Fe84.3B13.7C1Cu1 amorphous alloy, the higher peak temperatures indicate that the addition of Nb element improved the thermal stability of the ribbons. Figure 1 shows changes in the magnetic properties of Fe84.3B13.7C1Cu1 and Fe82.3B13.7C1Cu1Nb2 as-quenched ribbons annealed at their own Tx1 with increasing the annealing time. As shown in the figure, the low Ms of Fe-B-C-Cu-Nb as-quenched ribbon confirms that the Nb addition effectively stabilize the thermal stability of the Fe-B-C-Cu ribbon. Despite the high thermal stability, the MS and HC values of the Fe-B-C-Cu-Nb ribbon are shown to be sharply increased after annealing for 60 seconds. However, as the annealing time increased further, the increasing rate of the HC sharply drops, which is much lower than that of the Fe-B-C-Cu ribbon. These changes in magnetic properties should be caused by that the Nb addition changes the crystal nucleation and growth rate of the as-quenched ribbon and the crystalline shape of Fe grains during the annealing. In order to understand the microstructural effect of the Nb addition, the compositional changes at the interfaces of amorphous/crystalline grain during the annealing were measured by APT and their elemental distributions with the annealing time are shown in Figure 2. These figures confirm that B and C atoms, known as amorphous forming elements, were continuously pushed out of the a-Fe grain with increasing the annealing time. On the other hand, Cu atoms are known to act as nucleation sites of nanocrystals but evenly distributed in the a-Fe grain and the amorphous matrix. However, the diffusion of Nb atoms into the matrix is clearly observed when the annealing time is longer than 300 sec. This Nb diffusion behavior in the annealing time is in well accord with the coercivity change of the Fe82.3B13.7C1Cu1Nb2 ribbon. The change in the morphology of the a-Fe grain behavior was also confirmed by TEM. These results clearly show the role of Nb atoms in the fabrication of nanocrystalline a-Fe grains and more detailed analysis results will be presented.

**References:**

[1] K. Lee, M. Choi, G. Lee, M. Kim, and J. Kim, "Changes in Microstructure and Magnetic Properties of Fe–B–Cu–C Ribbons According to Annealing Conditions," IEEE Transactions on Magnetics, vol. 55, no. 2, pp. 1-4, 2019. [2] H. Lashgari, D. Chu, S. Xie, H. Sun, M. Ferry, and S. Li, "Composition dependence of the microstructure and soft magnetic properties of Fe-based amorphous/nanocrystalline alloys: a review study," Journal of Non-Crystalline Solids, vol. 391, pp. 61-82, 2014.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/6425dde224148ea7d23da2b73129c173.jpg)
Fig 1. Changes in the magnetic properties of Fe84.3B13.7C1Cu1 and Fe82.3B13.7C1Cu1Nb2 ribbons annealed at Tx1 for different annealing times

![](https://assets.underline.io/uploads/markdown_image/1/image/f44f6206d6b4f04273996415b8606716.jpg)
Fig 2. Changes in element distributions of the Fe82.3B13.7C1Cu1Nb2 ribbon at the interface during annealing

 Nb effects on the magnetic and microstructural properties of Fe-based nano-crystalline alloys

Due to high permeability, low coercivity, high resistivity, and low eddy current loss, amorphous and nanocrystalline materials with their excellent magnetic properties are attractive for high-frequency high-power applications, such as transformers, reactors and inverters to achieve high power density transmission. However, some electrical applications include inductors and transformers for multi-kilowatt power converters often necessary to add air gap in the magnetic core. The reasons are as follow: (a) reducing the equivalent permeability μre of the core, (b) increasing the excitation current for saturation, (c) effectively improve the anti-saturation ability of the core, (d) improve the capacity of the energy storage of magnetic components. The desired functions achieved from magnetic characteristic changes due to the air gap including: maintaining the stability of the inductance value of the reactor, increasing the power density of the inductor and the optimized design of the high frequency transformer, etc. Moreover, air gap may also increase the core loss. It is of great significance to study the magnetic properties of the cores with different air gaps. In this paper, dynamic magnetic properties of C-type amorphous (AMCC025) and nanocrystalline (F3CC0125) cores are measured with different air gap lengths (0-6mm) and frequencies (5-20 kHz) based on a novel designed magnetic tester. The tester can restrain the C-type core from six directions to ensure the stability of the testing sample. The air gap between the two cores can be accurately adjusted by the screw fixed on the precision displacement stage. The minimize air gap length can be fixed on 0.01mm. The effect of air gap length and frequency on the magnetic properties of different materials are compared. Moreover, the corresponding core losses of the samples in a wide range of frequency are analyzed. The traditional Steinmetz empirical formula is revised, and the core loss is calculated in sections according to the air gap length, and compared with experimental values. The hysteresis loops of the amorphous and nanocrystalline alloy cores at the same frequency of 20 kHz, different magnetic densities and different air gap lengths are shown in Fig. 1. As the air gap length increases, the slope of the B-H loops is reduced more and the slope of inclination is smaller slowly. Moreover, the effect of the air gap on the magnetic properties of nanocrystalline cores is more obvious than that of amorphous cores. It can be found that the nanocrystalline alloy is more sensitive to air gap than amorphous alloy due to its ultra-high relative permeability. According to the intensity of the fringing effect caused by the air gap length, two cases are concerned in the loss calculation. One is that the air gap is small enough to ignore the fringing effect, the other is that the air gap length is too large to ignore the fringing effect of the loss. Generally speaking, when lg/lc&lt;0.5%, where lg is the air gap length and lc is the equivalent magnetic circuit length, the influence of the fringing magnetic flux caused by the air gap on the inductance of the core can be ignored. But when lg/lc&gt;1.0%, due to the fringing diffusion of the air gap magnetic flux, the magnetic area of the air gap increases and the effective length of the air gap becomes shorter. Therefore, the influence of the fringing magnetic flux for core loss must be considered. Therefore, a modified Steinmetz empirical formula considering fringing flux is proposed, in which, the air gap length is used as a variable in the calculation and the precision is improved. Fig. 2. shows the variation in core loss density between the experimental and calculated results at given frequency with the different air gap lengths and magnetic flux densities. From the ratio of the air gap length to the magnetic circuit length, it can be seen that for amorphous core, the fringing effect does not need to be considered when the air gap length is less than 1 mm. Similarly, the air gap length boundary point of the nanocrystalline core is 1.6 mm. It can be seen that most of the calculated results well agree with the experimental results. The average percentage errors of the modified Steinmetz formular with fringing effect are all within 10% for amorphous and nanocrystalline core. It is proved that the influence of the fringing magnetic flux can be minimized under an optimized air gap length, and the loss will be reduced accordingly. Moreover, the modified Steinmetz formula can predict the core loss of the C-type core under different air gap lengths well. The modified core loss calculation model can provide theoretical guidance for the high frequency inductor and transformer cores design and optimization.

**References:**

[1] Ayachit, Agasthya, and M. K. Kazimierczuk, IET Circuits Devices & Systems, Vol. 11.3, p. 209-215(2017). [2] G. Calderon-Lopez, Y. Wang and A. J. Forsyth, IEEE Transactions on Power Electronics, vol. 34, p. 4656-4664, (2019). [3] Y. Wang, G. Calderon-Lopez, and A. J. Forsyth, IEEE Transactions on Power Electronics, vol. 32.6, p. 4683-4690(2019).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/5e253abb3cdfd1c7e01071e5e2cc67f1.jpg)
Fig. 1. The hysteresis loops of core under different air gap lengths (B = 0.1T, f = 10kHz).

![](https://assets.underline.io/uploads/markdown_image/1/image/b96a64a85226ae002049ed8fcad7189c.jpg)
Fig. 2. Core loss under different magnetic density and air gap lengths at fixed frequency.

 Magnetic Properties Measurement and Loss Calculation of the High-frequency Core with Air Gap

I. INTRODUCTION With the rapid development of the power electronics industry, electrical equipment is tending towards high-power, high-frequency, and miniaturization, in particular for the inductors, chokes, and transformers [1]. The magnetic material becomes a hinder to improve the device performance further [2]. At present, soft magnetic ferrite is widely used in high frequency applications due to the lower conductivity and core loss at the high operating frequency. However, the saturation flux density of ferrite is usually less than 0.5 T, which is much lower than that of alloy soft magnetic materials [3]. Nanocrystalline and amorphous alloys have excellent magnetic properties, such as low coercive force, high permeability, and saturation flux density, but these materials have high conductivity which causes great eddy current loss Ped. Magnetic cores fabricated by amorphous and nanocrystalline alloy powders can effectively reduce the Ped due to their lowered conductivity [4]. Consequently, these powder cores are gradually used in high-frequency and high-power applications. In fact, it is inevitable that the core and winding losses will lead to the temperature increase of the core, in particular, at high frequency [5]. Therefore, it is significant to study the temperature dependence of the magnetic properties of powder cores at high frequency. The results can be used to optimize the performance of electrical devices. II. MEASUREMENT PRINCIPLE AND SYSTEM In this article, the magnetic properties and loss characteristics of nanocrystalline powder core, amorphous powder core, ferrite, X-Flux (Fe-Si), and Kool-Mµ (Fe-Si-Al) are measured and analyzed in the range of 25 °C to 125 °C from 20 kHz to 100 kHz. The magnetic properties measurement system for the toroidal powder core sample is constructed, as shown in Fig.1. The toroidal powder core is placed in a thermotank for heating, and the internal temperature in the thermotank can be controlled by PID adjustment. The magnetic field intensity H and the magnetic flux density B are calculated by Ampere law and Faraday’s law of induction, respectively. The core loss is calculated by the Poynting equation and analyzed by the Steinmetz equation. III. EXPERIMENTAL RESULTS OF POWDER CORES The magnetic properties of the above materials as a function of temperature are investigated, such as coercive force, remanence, complex permeability, inductance factor, saturation flux density, and core loss. The properties are discussed using the micro-magnetism theory. Meanwhile, the material properties of the above materials are compared and summarized. A. Magnetic properties at different conditions The inductance factor, AL, of Kool-Mµ decreases with the increasing temperature. When the temperature rises from 25 °C to 50 °C, the AL of Kool-Mµ only changed by 0.383% from 156.7 nH/N2 to 156.1 nH/N2 at 100 kHz, 30 mT, which is a very little variation. But it decreased by 7.367% from 156.1 nH/N2 to 144.6 nH/N2 with the temperature rising from 50 °C to 125 °C. The saturation flux density Bs of the ferrite is also affected by temperature and frequency. The saturation flux density presents a downward trend with the increasing temperature or frequency, as shown in Fig.2 (a). The experimental results indicate that the saturation flux density of ferrite decreased from 0.479 T to 0.453 T while the operating frequency is from 20 kHz to 100 kHz at room temperature, which decreased by 5.428%. From 25 °C to 125 °C, the saturation flux density of ferrite decreased from 0.453 T to 0.319 T at 100 kHz, which decreased by 29.581%. B. Core loss analysis at different conditions When the temperature is increased from 25 °C to 125 °C, the loss of Kool-Mµ increases from 48.68 W/kg to 75.368 W/kg by 54.823% at operating frequency f = 100 kHz, and magnetic flux density B = 80 mT. However, the core loss of X-Flux and amorphous powder cores shows a decrease with increasing temperatures. The loss of X-Flux decreases from 199.708 W/kg at 25 °C to 175.805 W/kg at 125 °C by 11.969% while the loss of amorphous powder cores decreases from 118.165 W/kg at 25 °C to 107.127 W/kg at 125 °C. It is found that the amorphous powder cores have better temperature stability, as shown in Fig.2 (b). The nanocrystalline powder core shows the relative temperature stability compared with other samples since the loss values are similar at the experimental temperatures. On the other hand, the Kool-Mµ shows clearly temperature dependent loss property among the five samples. In addition, the core loss of the X-Flux is the largest, then followed by amorphous powder core, Kool-Mµ, nanocrystalline powder core, and ferrite at different frequencies over the experimental temperature range. In summary, the magnetic properties of five samples of different materials are measured at high frequencies over the temperature range from 25 °C to 125 °C. The physical characteristic of different materials exhibits an opposite trend with increasing temperature. The detailed comparison of results for five powder core materials will be shown in the full paper.

**References:**

[1] C. Jiang, X. Li, S. Ghosh, IEEE Transactions on Power Electronics., Vol. 35, p.10821-10830 (2020) [2] J. Millan, P. Godignon, X. Perpina, IEEE Transactions on Power Electronics., Vol. 29, p.2155-2163 (2014) [3] M. Yang, Y. Li, Q. Yang, IEEE Transactions on Applied Superconductivity., Vol. 30, p.1-5 (2020) [4] T. Suzuki, P. Sharma, L. Jiang, IEEE Transactions on Magnetics., Vol. 54, p.1-5 (2018) [5] N. Takahashi, M. Morishita, D. Miyagi, IEEE Transactions on Magnetics., Vol. 46, p.548-551 (2010)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d2b5dd3ec3b4878edd704526e47b46a8.jpg)
Fig. 1 Schematic diagram of experimental system for magnetic properties measurement with the effect of temperature.

![](https://assets.underline.io/uploads/markdown_image/1/image/20e4974e919b4bd9fa16021bb94c5041.jpg)
Fig. 2 The fundamental magnetization curve of TDK PC95 at different temperature (a), and core loss characteristic curves of amorphous (AM) and X-Flux powder cores at 100 kHz and different temperatures (b).

 Temperature Dependence of Powder Cores Magnetic Properties for High Frequency Applications

I. INTRODUCTION The wireless power transfer (WPT) systems，that is the contactless electrical power transfer, by electromagnetic coupling are of interest in charge of electric vehicles (EVs). However, a fraction of electromagnetic energy generated by the primary coil is lost due to loosely-coupled characteristics of the WPT system [1]. The stray flux will harm the human body and interfere with other electromagnetic equipment. Hence, it is necessary to effectively shield the leaking magnetic flux and improve the efficiency of coupling in the WPT system [2]. Generally, ferrite is used in WPT systems to concentrate the magnetic flux, and plays a role of shielding because of its high resistivity and permeability [3]. It is beneficial to reducing the core loss of the ferrite at high frequency. However, the effectiveness of shielding will be degraded by the low saturation flux density Bs of ferrite. And it is decreased drastically with the increasing temperature or frequency, usually between 0.2 and 0.5 T [4]. The thickness of the ferrite has to be increased for high power density WPT systems. Compared with ferrite, the nanocrystalline alloy has higher permeability and saturation flux density, which can improve the shielding effect. The use of alloy also reduces the weight and volume of the shielding pad. However, its high conductivity will lead to more eddy current losses, and the reduction of the power transmission efficiency. Conclusively, core material and structure are of importance to the transmission efficiency and power level of the WPT system. II. INVESTIGATION OF MAGNETIC MATERIAL PROPERTIES In this article, the nanocrystalline ribbons processed by the refinement crushing process and alternating seamless stitching process show an advantage in WPT since the eddies are restricted to the smaller areas and less eddy current loss of. Three types of ribbon with µ = 1000, 3000, 6000 respectively are simulated for the WPT system. The nanocrystalline ribbon of 1k107B, and PC95 ferrite are studied as well to optimize the design of WPT. The comparison involves permeability, conductivity, saturation flux density, and Curie temperature. The system performance, such as the leakage magnetic flux B, self inductances of secondary coil L2, mutual inductances M, coupling factor k, and transmission efficiency η are simulated using LCC-LCC topology and 1.5 kW at 85 kHz based on the above materials to summarize the influence of material characteristics on system performance. The results show that the PC95 pad shows the highest η of 98.07% among all the magnetic cores. The η of processed nanocrystalline alloy pad increases with the increased permeability, which is 96.10%, 97.86%, and 98.02%, respectively. The ferrite pad and nanocrystalline alloy pad with µ = 6000 have a similar η, but the latter shows a better shielding effect. The η of 1k107B pad is only 95.92%. The nanocrystalline alloy pad with µ = 1000 shows the lowest k value of 0.1002 due to its low permeability. III. OPTIMIZED DESIGN OF SHIELDING PAD To balance the efficiency of power transmission, shielding, and eddy current losses, the novel embedded magnetic shielding structure is proposed according to the magnetic flux distribution. It is composed of nanocrystalline alloy and ferrite, as shown in Fig.1. The ferrite pattern is designed to block the eddies. It found that the k and η of this novel structure show great improvement compared with the nanocrystalline ribbon cores. For example, the η of the embedded structure with 1k107B and PC95 is increased to 98.10% while it is 95.92% in pure 1k107B. In addition, ferrite frames with different heights are used in order to reduce the magnetic flux leakage at the edge of the shielding pad. The results using the 3-D finite element method indicate that the shielding effect and system performance are improved with the increasing the frame height Fig. 2 shows that flux densities along the centerline over 10 cm above the embedded pad decrease with increasing the height where the pad is composed of the nanocrystalline ribbon with µ = 6000 and ferrite. The L2 and M increased by 6.84% and 13.80% with a height of 5 cm while the L2 and M are 248.23 µH and 28.85 µH without the ferrite frame. However, η is almost unchanged, that is about 98.03%. The experimental WPT system for 85 kHz, 1.5 kW with a 24 cm air gap has been built to validate the simulation. The transmission performance with different shielding structures is compared, including PC 95 ferrite pad only and the novel structure composed of ferrite with the three nanocrystalline alloys with permeability µ = 1000, 3000, and 6000, respectively. Within the acceptable range of error, the experimental results are consistent with that of simulation. But the experimental efficiency η is lower than that of simulation due to the connecting line loss and switching loss. The former is generated by serious skin effect at a high operating frequency. The experimental results will be presented and discussed in detail in the full paper.

**References:**

[1] H. Kim, C. Song and D. Kim, IEEE Transactions on Microwave Theory and Techniques., Vol. 64, p.383-400(2016) [2] M. Pearce, G. A. Covic and J. T. Boys, IEEE Transactions on Power Electronics., Vol. 34, p. 6062-6075 (2019) [3] K. Elnail, X. Huang and C. Xiao, Energies., Vol. 11, p.1-17 (2018) [4] M. Yang, Y. Li, Q. Yang, IEEE Transactions on Applied Superconductivity., Vol. 30, p.1-5 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/9ddfed306a4f1401602c9edaa23bd65b.jpg)
Fig. 1 The gemometry of embedded shielding pattern.

![](https://assets.underline.io/uploads/markdown_image/1/image/36bcca415b77d73750db7ff8f521bf5d.jpg)
Fig. 2 Simulated the flux densities distributions along the centerline at 10 cm over the secondary shielding pattern, transmitting current i1 = 10√2sin(2π×85000t) A, t = 2.88×10-6 s.

 Comprehensive Analysis of Nanocrystalline Ribbon Cores in High-Power-Density WPT Pads for Electric Vehicles

Using Fe nanoparticles as raw material, we manufactured Fe16N2 nanoparticles by hydrogen reduction and ammonia nitriding process. XRD and Mossbauer spectroscopy analyses show that the prepared nanoparticles are composed of Fe16N2 and α-Fe. The proportion of Fe16N2 phase could reach 79%, and the saturation magnetization of the nanoparticles could reach 197emu/g. The Fe16N2 nanoparticles are mixed with paraffin, and the microwave absorption properties of the composites are measured. The reflection loss (RL) of the F16N2 nanoparticles can reach -18.3dB@4.82GHz, which shows it is a potential candidate for microwave absorbing materials. I. Introduction Fe16N2 is a special kind of FeN compound because its saturation magnetization can be higher than that of α-Fe. Depending on the preparing methods, F16N2 could have different morphologies including foils, wires, and nanoparticles. The saturation magnetization of F16N2 nanoparticles could reach 245emu/g as previous research reported, exceeding the saturation magnetization of Fe. The high saturation magnetization of F16N2 nanoparticles makes it possible for some practical use. In this work, the Fe16N2 nanoparticles are prepared and the microwave absorption properties were measured. II. Experimental Fe nanoparticles with average diameters of 65nm were used as the raw material. The Fe nanoparticles were firstly heated to 450°C in an H2 atmosphere and kept for 3h. Then, the samples ware then cooling down to 160°C and kept for 22h (sample S1) or 39h (sample S2) in NH3. Every three hours the sample has been flipped. III. Result and Discussion The XRD of S1 and S2 were measured using Cukα X-rays. Both S1 and S2 show the main peak of the Fe16N2 phase at 2θ=42.8°. The intensity of the main peak of S2 is higher than that of S1. Both samples have an XRD peak at 44.8° which is contributed by the overlap of the Fe16N2 secondary peak and the peak of α-Fe. So both samples are a mixture of Fe16N2 and α-Fe, and from the relative peak intensity, it can be inferred that the Fe16N2 phase content in S2 is higher than in S1. To determine the Fe16N2 phase content in S1 and S2 samples, the Mossbauer spectroscopy of the two samples are carried out. The experimental data and the fitting curve of the Mossbauer spectroscopy are shown in Fig. 1. The fitting result shows that S1 contains 69% Fe16N2 phase and S2 contains 79% Fe16N2 phase. This result is consistent with the judgment based on the relative peak intensity of XRD. The hysteresis loops of the samples are measured, and the saturation magnetization of S1 and S2 were 185emu/g and 197emu/g, respectively. As the Fe16N2 phase content increases, the saturation magnetization of the samples increase. This shows that Fe16N2 might have a higher saturation magnetization than α-Fe. The nanoparticles are mixed with paraffin with a mass ratio of 3:1 to form composites (also named S1 and S2). Then the composites are pressed into a toroidal shape with an inner diameter of 3.04 mm and an outer diameter of 7 mm. A vector network analyzer (VNA) is used to measure the high-frequency permittivity ε and permeability μ of the torus samples. Then, the reflection loss (RL) of the composite materials with different thicknesses is calculated by the transmission line theory depending on the measured ε and μ. The reflection losses of S1 and S2 are shown in Figure 2 (a) and (b), respectively. It can be seen that the microwave absorbing performance of S2 is slightly better than that of S1. When the thickness of the absorber is 2.2mm, the maximum RL of S2 could reach -18.5dB at 4.8GHz.

**References:**

1. J. P. Wang, Journal of Magnetism and Magnetic Materials., Vol. 497, p.165962 (2020) 2. Z. Liu, W. Yang, R. Wu, Journal of Magnetism and Magnetic Materials., Vol. 516, p.167332 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/8acd7adcb7907046654feeae46d173a6.jpg)
The Mossbauer Spectrum of sample S2 (a) and S1 (b).

![](https://assets.underline.io/uploads/markdown_image/1/image/c5133e2cdfa925e30b09f1561aa40c64.png)
The Reflection Loss (RL) of sample S1 (a) and S2 (b).

 The microwave absorption properties of Fe16N2 nanoparticles

0 Introduction As the operating frequency of the switching power supply continues to increase to MHz, the loss of various magnetic materials will increase rapidly with frequency and magnetic induction. The magnetization performance and the loss of magnetic materials limit the increase in power density. A metamaterial unit composed of resonant coils and resonant capacitors in series is printed on the FR-4 panel to form a metamaterial structure that can produce considerable equivalent permeability at a specific frequency. The relevant structural parameters and their optimization methods are analyzed, and the electromagnetic simulation software is used to verify the correctness of the electromagnetic metamaterial designed. Since the metamaterial unit only has a significantly increased equivalent permeability at a specific frequency, the metamaterial unit is designed to work at a fixed frequency or within a fixed frequency range. 1 Design and optimization of metamaterial units The metamaterial unit is printed on the FR4 board in the form of a matrix, and a total of 10 layers are printed to form a metamaterial structure, which is used to replace the central column part of the traditional transformer core. Figure 1 shows the two-dimensional model of the transformer based on the metamaterial structure and its flux distribution. This article uses controlled experimental methods to design and optimize the coil unit layout, size, shape, number of turns and resonant capacitance and other parameters. The window is defined as the ratio of the area of the FR4 board to the total area of the FR4 board after the metamaterial coil unit is removed. When only the arrangement of metamaterial units is changed, it is found through analysis that each metamaterial unit works independently instead of in series or parallel, and has better permeability and higher transmission efficiency. First, design the line width of the coil unit. The study found that as the line width increases, the line loss of the metamaterial unit will increase and the transmission efficiency of the transformer will decrease. Therefore, the wire width of the metamaterial unit should be as small as possible. Due to different technical levels, the minimum width of the coil is also different. The minimum line width used in this article is 0.3mm. When other parameters remain unchanged, when the number of turns n of the metamaterial unit is less than or equal to 3 or the window is greater than 72.25%, the energy transmission efficiency of the transformer will be much lower than that of the traditional transformer. When the number of turns of the coil is greater than 4, the metamaterial structure can provide a higher equivalent magnetic permeability, which can significantly improve the energy transmission efficiency compared with traditional transformers. When the value of n gradually increases, the equivalent permeability of the metamaterial continues to increase, and the transmission efficiency of the transformer also continues to increase. However, when the number of turns of the metamaterial unit is greater than 7, the transmission efficiency is basically unchanged. Blindly increasing the number of turns will increase the complexity of printing special material coil units. This leads to unnecessary waste of resources and increased costs. Therefore, when the number of coil turns is 7, the metamaterial structure has the best effect. Figure 2 is a graph of the dielectric parameters of the metamaterial when the number of coil turns is 7. Finally, the influence of different layers of the resonant capacitor on the metamaterial unit is studied. It is found that when the resonance capacitance of each layer is the same, the equivalent permeability coefficient of the intermediate metamaterial unit is lower than that of the mutual metamaterial unit. Therefore, the capacitance of the capacitors of the metamaterial units on both sides can be slightly enhanced, and the energy transmission efficiency of the transformer can be improved. 2. Simulation analysis of metamaterial unit Ansys electromagnetic simulation software is used to simulate the designed metamaterial unit structure. Based on the metamaterial structure and the 1:1 size of the traditional transformer, a two-dimensional model was established, and simulated and compared. The simulation parameters are not listed here. It is found through simulation that when the metamaterial coil unit has 7 turns, the transformer of the metamaterial structure has a higher equivalent permeability in the frequency range of 298-301kHz, and the degree of suppression of the magnetic flux is obvious. Compared with traditional magnetic cores, its energy efficiency is also higher. This verifies the correctness of the above-mentioned metamaterial structure design. 3. Conclusion This paper designs a metamaterial structure for high-frequency transformers. The new metamaterial structure design makes the transformer more efficient. The electromagnetic field simulation analysis of two different transformer models is carried out through the control experiment method. The results show that when the number of turns of the metamaterial unit is 7 turns and the operating frequency is about 300kHz, the equivalent permeability is higher and the energy transmission efficiency is better than that of the traditional transformer. Achieve the desired effect. The metamaterial structure designed in this paper does not require high circuit components and has obvious advantages in a certain frequency range.

**References:**

[1]SMITHDR, VIERDC, KOSCHNYT, etal. Electromagnetic parameter retrieval from inhomo-geneous metamaterials [J]. Physical Review E Statis-tical Nonlinear&Soft Matter Physics, 2005, 71 (3):036617.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c32cd8445ee34c56ff859dc3c579e8f3.jpg)
Fig.1

![](https://assets.underline.io/uploads/markdown_image/1/image/68ab4b8e5829e39f0f19c4cd83f19c04.jpg)
Fig.2

 Design and Simulation of Electromagnetic metamaterial Unit for High-frequency Transformer

I. Introduction Metasurfaces can be seen as two-dimensional metamaterial, which has been attracting attention for researchers these years [1]-[3]. In the early years, metasurfaces was considered as special frequency selective surfaces, the structure may be split-ring resonator, complementary split-ring resonator [4] or isotropic elements [5]. However, most researchers regard the metasurfaces as a novel periodic structure, that is different from frequency selective surfaces [2]. And metasurfaces can be using in many different and important applications such as reflection surface [2]–[4], perfect absorber [6]–[7] and holographic imaging. Polarization conversion surfaces are commonly used electromagnetic surfaces, which can be designed into reflective surfaces or transmissive surfaces [3], [4]. A traditional method to design polarization conversion surfaces is using birefringent materials, which can change the polarization state of incident wave and wavefront phase in each cardinal planes. Recently, research discovered that birefringent materials can be realized by anisotropic frequency selective surfaces. For all types of polarization conversion surfaces, the type which can converts linear polarization (LP) wave into circular polarization (CP) wave, is the most popular one. This type of metasurfaces converts an incident LP wave into a CP transmitted or reflected wave. In recent years, linear-to-circular polarization converter has great application prospect in satellite [5]-[6] and communication systems [7]. In this paper, a novel linear-to-circular polarization converter based on meander-line metasurfaces is presented. The proposed metasurfaces is a two-dimensional periodic structure which consists of two metallic layers separated by dielectric substrate. The structure of each unit is meander-line which is printed on the top and bottom metallic layers. By controlling different phase for vertical and horizontal electric field components of incident wave, the phase difference is 90° between two components, after passing through the metasurfaces. The metasurfaces converts the LP wave to CP wave with the bandwidth of 10.5~11.5 GHz. The simulation results show the metasurfaces is valuable for polarization conversion application. II. Metasurfaces Structure Design and Analysis A. Metasurfaces Structure The geometry of the metasurfaces is presented in Fig. 1. The structure is composed of two metallic layers and one dielectric substrate. The structure of two metallic layers is shown in Fig. 1(b). And the size of the metasurfaces unit is 6.2*6.2 mm2. Two metallic layers are printed on Rogers RT5880 substrate with the relative permittivity of εr =2.2 and the thickness of h=0.762 mm. The structure of the top metallic layer is meander-line which have different resonance characteristics to vertical and horizontal electric field components. And the bottom metallic layer is exactly the same as top layer. The geometric parameters of the metasurfaces are a=6.2 mm, p=0.9 mm and g=0.65 mm. B. Analysis of Metasurfaces To the vertical electric field, the meander-line can be equivalent to a shunt inductance. But, to the horizontal electric field, the meander-line will be equivalent to a shunt capacitance. Therefore, the incident wave with the 45° linear polarized, it can be divided into vertical and horizontal electric field components. Next, by controlling the phase difference between two components to 90°, the structure will convert LP wave to CP wave. The bandwidth of the metasurfaces can be increased by cascading several metasurfaces screen, and the additional dielectric layer can improve the oblique incidence stability. Equivalent circuit model (ECM) can be used to analyse the physical principle of the metasurfaces. Fig. 2(b) shows the ECM of the metasurfaces for vertical electric field. And Fig. 2(c) shows the ECM of the metasurfaces for horizontal E-field. Thus, adjusting the phase difference between two electric field components (|φ1-φ2|) is 90°, and a linear polarized wave can be converted into circular polarized wave. III. Simulation Results and Discussions The proposed metasurfaces can realize LP to CP conversion. For different electric field components, the metasurfaces has different functions. Fig. 3 and Fig. 4 show the simulated transmission coefficient of the metasurfaces with vertical and horizontal electric field. And TABLE I shows the amplitude and phase of transmission coefficient at 10.5 GHz and 11.5 GHz. Under two polarization waves and oblique incidence angles from 0° to 30°, the phase difference of vertical component and horizontal component is approximately 90°, and the transmissivity is over 50%. The polarization conversion bandwidth covers 10.5~11.5 GHz. The simulation results show that the proposed metasurfaces can convert linear polarization wave to circular polarization wave, and has good angular stability. IV. Conclusion A novel linear-to-circular polarization converter based on meander-line metasurfaces with angular stability is presented. The linear-to-circular polarization conversion bandwidth of the metasurfaces is 10.5~11.5 GHz for the transmissivity is over 50%. By controlling different phase for vertical and horizontal electric field components of incident wave, the phase difference between two electric field components can be adjusted to 90° after passing through the metasurfaces. The simulation results show the metasurfaces is valuable for linear-to-circular polarization conversion application.

**References:**

[1] J. Zhu and G. V. Eleftheriades, IEEE Antennas Wireless Propag. Lett., Vol. 8, pp. 295–298 (2009) [2] C. L. Holloway, E. F. Kuester and J. A. Gordon, IEEE Antennas Propag. Mag., Vol. 54, no. 2, pp. 10–35 (2012) [3] M. Euler, V. Fusco and R. Dickie, IEEE Trans. Antennas Propag., Vol. 59, no. 8, pp. 3103–3106 (2011) [4] B. A. Munk, Frequency Selective Surfaces: Theory and Design. Hoboken, NJ, USA: Wiley, 2005. [5] N. Yogesh, T. Fu, F. Lan and Z. Ouyang, IEEE Photon. J., Vol. 7, no. 3 (2015) [6] H. L. Zhu, S. W. Cheung and K. L. Chung, IEEE Trans. Antennas Propag., Vol. 61, no. 9, pp. 4615–4623 (2013) [7] M. Euler, V. Fusco and R. Cahill, IET Microw., Antennas Propag., Vol. 4, no. 11, pp. 1764–1772 (2010)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/54a372f181515a2c10a19b2098af8982.jpg)
Fig. 1. Geometry of the metasurfaces

![](https://assets.underline.io/uploads/markdown_image/1/image/fc59776639339ff41728641086a181f9.jpg)
Table 1. Amplitude and Phase for Two Electric Field Components

 Linear-to-Circular Polarization Converter Based on Meander-Line Metasurfaces

In recent years wireless systems have experienced a rapid and wide expansion. Although these services provide an expressive amount of electromagnetic energy in the environment, a large amount of this energy is actually wasted. Despite the low electromagnetic power density available ambient, it is permanent and can be harvested, by using a rectenna, in order to supply small electrical devices, such as Wireless Sensor Networks (WSNs) used in the Internet of Things (IoT) devices. The RF-based energy harvesting technology is especially suitable to power WSNs because if a compact rectenna is used it can be completely integrated in the distributed hosting sensors structure, reducing its cost, maintenance and environmental impact. The contribution of this work is to present a compact rectenna, which employs a patch antenna with a Metamaterial Unit Cell (MUC) as grounding plane, called Metamaterial Antenna (MA). The proposed rectenna is composed of a square patch antenna with a MUC operating as grounding plane and a double voltage rectifier circuit. Both were built by using a double-sided copper fiberglass substrate, FR-4, with thickness t=1.5mm and characterized relative electric permittivity εr=4.15 and tangent of losses δ=0.026. The initial antenna geometry was defined by using transmission line theory. The MUC geometry, composed of a Complementary Split Ring Resonator (CSRR) [1]-[2], was designed and optimized by using Computer Simulation Software (CST®) in order to obtain the value εr&lt;0 in 2.45GHz. Then, the antenna geometry was optimized together the obtained MUC geometry in order to find values of S11&lt;-10 dB in the range from 2.4 to 2.5GHz. The final topology of the optimized MA is shown in Fig. 1(a) and 1(b). A Conventional Antenna (CA), Fig. 1(c), with a perfect conductor grounding plane, also was designed and optimized by using the same goal of the MA, in order to process comparisons. The obtained results for CA and MA are 6.69dBi and 3.01dBi (simulated directivity) and -24.93dB and –20.58dB (measured S11 parameter), respectively. The rectifier circuit is composed of an open stub for impedance matching, a schottky diode HSMS-2852 and two 100uF capacitors. It was projected and optimized by using Advanced Design Software (ADS®) in order to obtain values of S11&lt;-10 dB in 2.45GHz for input power Pin= -20dBm. In order to experimentally evaluate the proposed rectenna performance it was positioned at a variable distance d from an internet router and a 10 kW resistive load was fed. The values of the measured voltage on the load (VL) are presented in Fig. 2. As can be observed the energy harvested by CA and MA rectennas is enough to supply low consumption loads, such as WSNs. As expected, CA is able to harvest more energy than MA, once it is more directive and larger (3.19 times bigger). However, since MA is more compact it can be more easily incorporated in the WSN structure. In the full paper, rectenna association results will be presented.

**References:**

[1] Y. Lee, Y. Hao, Characterization of microstrip patch antennas on metamaterial substrates loaded with complementary split-ring resonators, Microwave and Optical Technology Letters, vol. 50, no. 8, pp. 2131-2135, Aug. 2008. [2] P. D. Tung, P. H. Lam, N. T. Q. Hoa, A miniaturization of microstrip antenna using negative permitivity metamaterial based on csrr-loaded ground for wlan applications, Journal of Science and Technology, vol. 54 (6), pp.689-697, 2016.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/06e870b121ce4a323eef3a72c9a461aa.jpg)
Figure 1. Antennas Geometry: (a) MA, (b) MUC grounding plane and (c) CA.

![](https://assets.underline.io/uploads/markdown_image/1/image/cf2c1cf9b4f4b95ba3541d894bef05a6.jpg)
Figure. 2. Output voltage for CA and MA rectennas.

 Design of a Rectenna with Metamaterial Grounding Plane

1. INTRODUCTION A variety of smart materials have been focused on a broad range of engineering applications. Among several kinds of smart materials, magnetorheological (MR) fluids inducing a reversible change in rheological behavior under an external magnetic field are suspensions of soft-magnetic particles randomly dispersed in a non-magnetic liquid medium [1]. MR fluids enable rapid switching and proper control between a liquid-like and a solid-like structure by controlling the magnetic field strength. Soft-magnetic carbonyl iron (CI) microspheres have been extensively studied as a major material in MR fluids due to their appropriate particle size and magnetic properties but possess a serious sedimentation problem due to their high particle density [2]. On the other hand, spinel ferrites can be a good alternative to CI particles because of their low density [3]. In particular, spinel zinc ferrite of super-paramagnetic behavior with high magnetic susceptibility, saturation magnetization, low coercivity, and low remanent magnetization is seen as a promising candidate for the use as a dispersed particle in MR fluids [4]. In this work, ZnFe2O4 particles were coated with polyindole (PIn), a conducting polymer with high thermal stability, redox activity, and stable degradation rate [5]. By combining an inorganic with a conductive polymer, the density was lowered, showing better sedimentation improvement. Furthermore, these particles can be also responsive under an applied electric field strength in addition to magnetic fields. 2. EXPERIMENT ZnFe2O4 nanoparticles were synthesized by a solvothermal method, and the PIn was followed to be coated as a shell onto the core ZnFe2O4 nanoparticles during oxidation polymerization. A proper amount of ferric chloride hexahydrate and zinc chloride were mixed in ethylene glycol solvent by magnetic stirring. Sodium acetate and polyethylene glycol 400 were slowly poured into the solution. The vigorously stirred mixture was placed in an autoclave and heated at 200 °C for 12 h. After that, the product was washed several times and dried to obtain particles. In the next step, ZnFe2O4 was coated by a polymerization process of indole monomer using ammonium persulfate as an initiator. The final particles were collected using an external magnet. For rheological analysis, a smart fluid responding to both magnetic and electric fields was prepared by dispersing the synthesized ZnFe2O4/PIn particles in silicone oil (100cSt, 5 vol%) under sufficient sonication. Morphology and chemical elements of the ZnFe2O4/PIn were examined by the field emission transmission electron microscope in combination with an energy-dispersive X-ray spectroscopy, respectively. Rheological properties of the MR fluid were measured using a rotational rheometer via either a parallel-plate geometry under the magnetic field or a concentric cylinder geometry under the electric field. 3. RESULT AND DISCUSSION Figure 1 shows the FE-TEM image and line scan profiles of core/shell structured ZnFe2O4/Pin particles. The main elements of ZnFe2O4 were found abundantly in the center of the particle, and C was confirmed as the main element on the outside of the particle. This result definitively demonstrates that the particles consist of ZnFe2O4 as the core material and PIn composed of C and N as the shell material. In addition, as the detection amount of the core elements increased gradually toward the center of the line drawn along the particle diameter for line scan, it was clearly revealed that the ZnFe2O4 core had a spherical morphology. Figure 2 shows the shear stress as a function of shear rate for ZnFe2O4/PIn based on MR fluid under various magnetic field strengths up to 239 kA/m. Without the magnetic field strength, shear stress of MR fluids increased in proportion to shear rate showing a Newtonian fluid-like behaviour, but as the magnetic field was applied, shear stress was relatively maintained within a certain shear rate range and displayed non-Newtonian fluid-like behaviour. When the magnetic field strength was increased, the interaction between magnetic particles was formed more strongly compared to the hydrodynamic force, resulting in a strong chain-like structure of the particles leading to an increase in yield stress. The solid lines in Figure 2 were fitted by Herschel-Bulkley model expressed as τ=τ0+KÝn to explain the rheological behaviour of non-Newtonian fluids [6]. In the given model, τ0 is the yield stress of materials, K is the consistency factor and n is the flow behaviour index. The n of pseudo-plastic materials is generally known to be between 0 and 1. [7]. The chain-like structure of ZnFe2O4/PIn particles formed by the magnetic field is destroyed as the shear rate increases, resulting in a shear thinning behaviour. In addition to steady shear test, dynamic test was also performed to examine dynamic moduli under a magnetic field strength. Rheological properties of this smart fluid under an applied electric field strength were further tested to confirm the dual characteristics of the synthesized ZnFe2O4/PIn particles.

**References:**

[1] J. S. Oh and S. B. Choi, J. King Saud Univ. Sci., 29, 390 (2017). [2] B. Sim, H. S. Chae and H. J. Choi, Express Polym. Lett., 9, 736 (2015). [3] G. Wang, Y. Ma and Y. Tong, J. Intell. Mater. Syst. Struct., 28, 2331 (2017). [4] Y. Xu, D. Sun and H. Hao, RSC Adv., 6, 98994 (2016). [5] I. H. Park, S. H. Kwon and H. J. Choi, J. Magn., 24, 155 (2019). [6] G. Mullineux, Appl. Math. Model., 32, 2538 (2008). [7] C. H. Jeon and B. R. Hodges, Nat. Hazards Earth Syst. Sci., 18, 303 (2018).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/2c3c113e26171b2b321fc07d45e846b8.jpg)
Fig. 1 FE-TEM image of ZnFe2O4/PIn particle

![](https://assets.underline.io/uploads/markdown_image/1/image/43de2fa4ee266f281b0fd900148b2608.jpg)
Fig. 2 Shear stress curve of ZnFe2O4/PIn particle based MR fluid under various magnetic field strengths

 Fabrication of Polyindole Coated Zinc Ferrite Particles and Their Dual Rheological response under Magnetic and Electric Fields

1. INTRODUCTION While magnetorheological (MR) fluids consisting of soft-magnetic particles in non-magnetizable carrier fluid draw a huge attention with their active tune-ability under a magnetic field strength, electro/magnetorheolocial (E/MR) fluids prepared with conducting polymer and magnetic particle composite particles dispersed in a non-conducting carrier fluid exhibit a dual response under both magnetic and electric fields. The smart dual electro/magneto-responsive characteristics of fine tuning and the quick response make them appropriate candidates in wide engineering areas such as clutches, optical finishing systems, medical therapies, actuators, haptic master, micro-fluidic control which have been already adopted separately for either ER fluids or MR fluids [1]. Meanwhile, soft-magnetic carbonyl iron (CI) particles have been widely used in MR fluids, but possess several disadvantages such as their high density and low dispersion stability. Therefore, spinel ferrites with low density and sufficient magnetic behavior are also introduced as a new family of MR materials [2]. In this work, ZnFe2O4, a magnetic particle constituting the core, was synthesized in a spherical shape using the solvothermal method, and poly(diphenylamine) (PDPA), which has low density and suitable electrical conductivity, was coated through radical polymerization. ZnFe2O4/PDPA based MR fluid showed appropriate MR property due to the spinel structure of ZnFe2O4. Furthermore, it showed improved sedimentation stability because of the advantage of low density of particle [3]. 2. EXPERIMENT First of all, ZnFe2O4 was synthesized using the surfactant-assistant solvothermal method. 1.35g iron chloride hexahydrate (FeCl3.6H2O) (5mmol) and 0.34g Zinc chloride (ZnCl2) (2.5mmol) were added to 50ml of ethylene glycol, and agitation was performed using a magnetic bar. After stirring, sodium acetate of 3.6g (40mmol) as a weak base and polyethylene glycol 400 (1g) as a surfactant were slowly added to the prepared solution. After vigorously stirring the solution for about 1 h, it was transferred to a Teflon-lined stainless-steel autoclave, and the reacted at 200 for 12 h. After making the reactor to room temperature, black solid particles were obtained using magnets after several washing with ethanol and DI-water. Then, 0.75g ZnFe2O4 was added to a mixture of methanol and water 40ml/10ml, and then reaction was proceeded at 40 and 1ml of N-[(3-trimethoxysilyl)-propyl] aniline was added as a grafting agent, followed by stirring for 18 h. Modified ZnFe2O4 and diphenylamine (3mmol) were mixed with ethanol. Subsequently, HCl 1M 40ml was added and stirred at 5 for 30 min. Ammonium persulfate (4mmol) dissolved in 1M 10ml HCl was added to the solution, the reaction was carried out for 5 h, and the particles were obtained using a magnet and dried for 12h. 3. RESULT AND DISCUSSION TEM image of Fig. 1 for ZnFe2O4/PDPA particle synthesized shows that the size of synthesized material is about 300nm with its morphology of a core-shell structure. The thickness of the shell is about 14 nm, and by coating the polymer on the magnetic particle, the density of the particle is reduced, and the dispersion stability of its MR fluid can be improved. Figure 2 shows flow curve of MR fluid made by dispersing the synthesized core-shell particles in 100 cs silicone oil at 5 vol%. From the controlled shear rate test mode, the shear rate from 0.01s-1 to 200s-1 was applied, depending on the strength of the magnetic field up to 205kA/mm. In the absence of a magnetic field, the fluid behaves like a Newtonian fluid in which the shear stress increases lineary as the shear rate increases. This is because MR fluid behaves like a simple particle suspension following an Einstein equation behavior. On the other hand, when an external magnetic field is applied, the shear stress rises sharply and shows a certain specific yield. This behavior is due to the fact that the attractive force between magnetic particles becomes strong when a magnetic field is applied, and the particles form a chain-like structure in the fluid. As the strength of the magnetic field increases, the attractive force between particles also increases, so the shear stress value increases gradually [4]. To fit the curves representing non-Newtonian fluid properties of MR fluid, a solid line was drawn using the Herschel-Bulkley equation, which is expressed as τ=τ0+KÝn. Here, τ means shear stress and τ0 is the yield stress exhibited by the chain-like structure when a magnetic field is applied. The K value of the consisteny index refers to the viscosity of the fluid and n is the power law index [5]. As the solid lines fit well with the graph, it can be seen that Herschel-Bulkley equation interprets the behavior of MR fluid well over a wide shear rate range. In this work, we synthesized a core-shell structured magnetic particles and conducting polymer and confirmed MR properties such as yield stress and shear thinning under external magnetic field along with ER characteristics under an applied electric field.

**References:**

[1] M. T. Ramesan, Adv. Polym. Technol., 302, 21362 (2013) [2] G. S. Wang, Y. Y Ma, Yu Tong and J. Intell. Mater. Syst. Struct., 28, 2331 (2017) [3] J. H. Lee, H. J. Choi, Colloid Polym. Sci., 296, 1857 (2018) [4] Y. Z. Dong, H. J. Choi, IEEE Trans. Magn., 54, 4601004 (2018) [5] M. Zubieta, S. Eceolaza and M. J. Elejabarrieta, Smart Mater. Struct., 18, 095019 (2009)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/05763e8056ec6cf88c5358ef8935fc89.jpg)
Fig 1. TEM image of core shell structure coated with PDPA on ZnFe2O4

![](https://assets.underline.io/uploads/markdown_image/1/image/754b14d10e8ee19da44d563737667334.jpg)
Fig 2. Flow curve of ZnFe2O4 coated with PDPA under the external magnetic field of ZnFe2O4 coated with PDPA

Modelling of the Intracrystalline Interactions in Trigonal Weak Ferromagnets with Zero Orbital Moment

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