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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Mater.</journal-id>
<journal-title>Frontiers in Materials</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Mater.</abbrev-journal-title>
<issn pub-type="epub">2296-8016</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">1108308</article-id>
<article-id pub-id-type="doi">10.3389/fmats.2022.1108308</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Materials</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Impact of manganese diffusion into non-oriented electrical steel on power loss and permeability at different temperatures</article-title>
<alt-title alt-title-type="left-running-head">Elgamli et al.</alt-title>
<alt-title alt-title-type="right-running-head">
<ext-link ext-link-type="uri" xlink:href="https://doi.org/10.3389/fmats.2022.1108308">10.3389/fmats.2022.1108308</ext-link>
</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Elgamli</surname>
<given-names>Elmazeg</given-names>
</name>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1771796/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Anayi</surname>
<given-names>Fatih</given-names>
</name>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Shouran</surname>
<given-names>Mokhtar</given-names>
</name>
<uri xlink:href="https://loop.frontiersin.org/people/1770092/overview"/>
</contrib>
</contrib-group>
<aff>
<institution>Wolfson Centre for Magnetics</institution>, <institution>School of Engineering</institution>, <institution>Cardiff University</institution>, <country>United Kingdom</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1267729/overview">Fuyin Ma</ext-link>, Xi&#x2019;an Jiaotong University, China</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1788767/overview">Xudong Fan</ext-link>, Nanjing University of Science and Technology, China</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1561757/overview">Tadeusz Szumiata</ext-link>, Kazimierz Pu&#x142;aski University of Technology and Humanities in Radom, Poland</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Elmazeg Elgamli, <email>elgamlies@cardiff.ac.uk</email>
</corresp>
<fn fn-type="other">
<p>This article was submitted to Metamaterials, a section of the journal Frontiers in Materials</p>
</fn>
</author-notes>
<pub-date pub-type="epub">
<day>10</day>
<month>01</month>
<year>2023</year>
</pub-date>
<pub-date pub-type="collection">
<year>2022</year>
</pub-date>
<volume>9</volume>
<elocation-id>1108308</elocation-id>
<history>
<date date-type="received">
<day>25</day>
<month>11</month>
<year>2022</year>
</date>
<date date-type="accepted">
<day>21</day>
<month>12</month>
<year>2022</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2023 Elgamli, Anayi and Shouran.</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>Elgamli, Anayi and Shouran</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p>
</license>
</permissions>
<abstract>
<p>Minimising power losses and their consequences is a significant matter in electrical steel applications. Increasing the resistivity of the steel strips has been confirmed as a successful method to overcome the problem of power losses. To increase the resistivity of the strip, different effective methods have been proposed and tested. In this work, a new material has been proposed to achieve the objective of increasing the resistivity of the steel samples by adding Manganese (IV) oxide based on a diffusion technique. The surface of the samples is to be coated with the proposed Manganese oxide. This should guarantee an increase in the resistivity of the samples, which in turn reduces the power losses caused by the eddy current. The samples tested were of non-oriented electrical steels containing 2.4&#xa0;wt% Si-Fe (with a thickness of 0.305&#xa0;mm&#x2a;300&#xa0;mm&#x2a;30&#xa0;mm). It was measured for losses and permeability before and after treatment by a Single Strip Tester (SST) at 0.5&#x2013;1.7&#xa0;T using an Alternating Current magnetic properties measurement system under controlled sinusoidal at different frequencies. The obtained results revealed that the depth of Manganese oxide diffusion is inversely proportional to the increase in the temperature. It was demonstrated that the best amount of diffusion of the element into the strips was achieved at 525&#xb0;C, which was 60 weight % in comparison with 700&#xb0;C which was 20&#xa0;wt%. Likewise, at 800&#xb0;C it was 7&#xa0;wt%. However, the depth of diffusion of the manganese was the same at those tested temperatures, which were equal to 200&#xa0;&#xb5;m deep on each of the side strips. The diffusion of the material was investigated using Scanning Electron Microscope (SEM) coupled with Energy Dispersive X-ray Spectroscopy (EDS). Furthermore, from the results, it was concluded that the power losses in the coating samples were improved by 9% as compared with uncoated samples.</p>
</abstract>
<kwd-group>
<kwd>diffusion technique</kwd>
<kwd>energy-dispersive spectroscopy (EDS)</kwd>
<kwd>Single Strip Tester (SST)</kwd>
<kwd>power losses</kwd>
<kwd>different temperatures</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="s1">
<title>1 Introduction</title>
<p>Electrical steel is one of the most important soft magnetic materials for mechanical systems and transformers. It can be either Non-Oriented (NO) or grain-oriented (GO) (<xref ref-type="bibr" rid="B10">Godec et al., 1999</xref>; <xref ref-type="bibr" rid="B11">Heo, 2004</xref>; <xref ref-type="bibr" rid="B37">Tanaka and Yashiki, 2007</xref>; <xref ref-type="bibr" rid="B17">Ko et al., 2013</xref>). Non-Oriented Electrical Steels (NOES) are the most frequently used core materials for electric motors, generators and alternators because of their high magnetic permeability, high magnetisation saturation, minor core loss, and low cost (<xref ref-type="bibr" rid="B15">Jakubovics and Chen, 1979</xref>; <xref ref-type="bibr" rid="B24">Moses, 1990</xref>; <xref ref-type="bibr" rid="B9">Cullity and Graham, 2009</xref>; <xref ref-type="bibr" rid="B25">Moses, 2012</xref>; <xref ref-type="bibr" rid="B33">Silveyra et al., 2018</xref>). NO electrical steel is a type of soft magnetic material, that is, simply magnetised and demagnetised (<xref ref-type="bibr" rid="B29">Nakayama et al., 1996</xref>). Such steels are pluralist approaches in Alternating Current (AC) electromagnetic fields with a frequency of 50&#xa0;Hz and provide the basis for the manufacturing output of asynchronous motor cores, powerful electric rotating machines, limited generators, along with other electrical motors that transfer electrical energy to mechanical energy or vice-versa (<xref ref-type="bibr" rid="B22">Liu et al., 2016</xref>). Losses that contribute to the core loss of non-oriented electrical steels can be classified as the following: hysteresis loss, classical eddy-current loss and excess loss. It is recognised that the shape and behaviour of magnetic domains in external fields, in addition to the microstructure and texture of electrical steel, influence magnetic properties, namely hysteresis loss and excess loss (<xref ref-type="bibr" rid="B28">M&#x259;nescu et al., 2016</xref>; <xref ref-type="bibr" rid="B16">Kadyrzhanov et al., 2019</xref>; <xref ref-type="bibr" rid="B18">Kozlovskiy et al., 2019</xref>). One of the major contributors to total core losses is known as &#x201c;eddy current losses,&#x201d; which are induced by electrically conductive core material, producing currents. It is essential to find a mechanism to make the core more current-flow resistant while still enabling unrestricted magnetic flux flow (<xref ref-type="bibr" rid="B20">Leuning et al., 2018</xref>). This is accomplished in a mains transformer by adding approximately 3% silicon to the iron, increasing its resistance to 4.5 <inline-formula id="inf1">
<mml:math id="m1">
<mml:mrow>
<mml:mo>&#xd7;</mml:mo>
<mml:msup>
<mml:mn>10</mml:mn>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>7</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> [&#x2126; m]. The magnetic properties of a material are greatly affected by the size of its grains, inclusions, internal tensions and surface flaws. These microstructural variables influence the materials coercion, force and domain wall mobility, which determine how well it magnetises at medium and low external magnetic fields and contribute to hysteresis losses (<xref ref-type="bibr" rid="B2">Barros et al., 2008</xref>).</p>
<p>According to several previous scientific investigations, typical stress relief heat treatment improves the magnetic characteristics of punched, fully processed silicon steels (<xref ref-type="bibr" rid="B19">Landgraf and Emura, 2002</xref>; <xref ref-type="bibr" rid="B30">Paolinelli and da Cunha, 2006</xref>; <xref ref-type="bibr" rid="B6">Chiang et al., 2014</xref>). A similar annealing method, that is, often used in the industry involves heating at a gradual pace of 200&#xb0;C per hour, then soaking for an hour at a temperature between 700&#xb0;C and 800&#xb0;C (<xref ref-type="bibr" rid="B30">Paolinelli and da Cunha, 2006</xref>). The materials are cooled down in a similar way, although much more slowly. The entire conventional process, including heating, annealing and cooling, lasts for approximately 12&#xa0;h.</p>
<p>There have been several efforts to investigate the influence of manganese on high silicon alloyed electric steels with varying Mn contents (0.20, 0.69, and 1.38&#xa0;wt%). The effect of Mn on mechanical, microstructural, and magnetic properties has been thoroughly investigated in (<xref ref-type="bibr" rid="B32">Schulte et al., 2018</xref>). The addition of Mn reduced grain size while also improving electrical resistance, resulting in decreased core losses at higher frequencies. It was revealed that Mn (0.3%&#x2013;1.5% wt%) in electrical steel improves its magnetic characteristics. However, if the Mn concentration exceeds the range, the grains become smaller and the magnetic losses increase (<xref ref-type="bibr" rid="B31">Rastogi, 1977</xref>). Also; it was found that when Mn concentrations are high, core loss drops significantly, and magnetic flux density rises modestly (<xref ref-type="bibr" rid="B21">Liao, 1986</xref>).</p>
<p>The study conducted by (<xref ref-type="bibr" rid="B26">Moses and Thursby, 1983</xref>) has shown that using silicon as a diffusant may minimise the power loss of non-oriented silicon iron. Layer thickness is reduced when aluminium is placed unevenly across surface areas, including both in terms of content and thickness penetration. On both sides of the samples, there was evidence of a thin coating of porosity. When this method of diffusion is used, the composition changes the anisotropy constants very slightly, which is what possibly creates the right amount of internal stress (<xref ref-type="bibr" rid="B38">Tumanski, 2016</xref>). A significant drawback concerning this method is the creation of a permeable material on the side of the steel, the amount of diffusant that permeates the steel sheet from the paste can be regulated by means of restricting several diffusants, either by means of the structure of the paste and depth or by creating an appropriate paste to guarantee an excess of diffusant is always accessible. Prior to completely removing the remaining coating, the quantity of soft material can be modified by adjusting the duration and the heat of the fire. Additionally, by establishing a controlled resistivity gradient along the thickness of the sheet, it might be possible to increase the steel&#x2019;s effectiveness in distorted magnetisation conditions. To ascertain what happens to an electrical steel sheet&#x2019;s magnetic property when a distorted flux waveform is present, materials with different resistivities all the way through their thickness were made by diffusing tiny amounts of aluminium into silicon steel (<xref ref-type="bibr" rid="B1">Anayi et al., 2003</xref>).</p>
<p>This paper describes work where Manganese (IV) oxide has been coated on the surface of silicon iron and diffused into the laminations using comparable different temperature anneals. The diffusion technique and subsequent heat treatment enable the concentration of the diffused element to be varied through the thickness of the samples. The surface of the samples is to be coated with the proposed Manganese oxide. This should guarantee an increase in the resistivity of the samples, which in turn reduces the power losses caused by the eddy current. The experiment conducted for this study has two distinct stages. In the first step, the permeability and power loss of uncoated samples with Manganese (IV) oxide paste of NO electrical steel were measured. In the second step, the permeability and power loss of samples coated with Manganese (IV) oxide paste were measured and compared the uncoated samples. The term &#x201c;coating&#x201d; subsequently refers to applying MnO<sub>2</sub> paste to the coated Si-Fe strips.</p>
</sec>
<sec id="s2">
<title>2 Material and experimental procedure</title>
<sec id="s2-1">
<title>2.1 Materials</title>
<p>The material proposed in this paper is Manganese (IV) oxide (MnO<sub>2</sub>) powder activated, &#x223c;85% (Merck Life Science United Kingdom Limited), with particle size &#x3c;10&#xa0;&#x3bc;m (as analysed by the supplier). Similarly, this study made use of Silicone oil supplied by Merck Life Science United Kingdom Limited, which was utilised as the adhesive and diluted by way of using Aston as a pure solution. The adhesives physical characteristics are listed in <xref ref-type="table" rid="T1">Table 1</xref>.</p>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Characteristic of adhesive.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Adhesive type</th>
<th align="center">Density</th>
<th align="center">Melting point</th>
<th align="center">Boiling point (&#xb0;C)</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">Silicone oil</td>
<td align="center">0.967&#xa0;g/mL&#xa0;at 20&#xb0;C</td>
<td align="center">&#x2212;55&#xb0;C</td>
<td align="center">140</td>
</tr>
</tbody>
</table>
</table-wrap>
<sec id="s2-1-1">
<title>2.1.1 Mixing silicone oil into MnO2 powder</title>
<p>Powdered Manganese (IV) oxide (MnO2) and Silicone oil solution were combined to make a paste. Silicone oil comprised 0.5&#xa0;wt% of the paste composition per gramme of manganese (IV) oxide. The paste was then dried at 50&#xb0;C for 1&#xa0;hour to verify that the acetone had fully evaporated and the powdered Manganese had adhered sufficiently.</p>
</sec>
<sec id="s2-1-2">
<title>2.1.2 Preparation of samples without coating</title>
<p>The Non-Oriented Electrical Steel (NOES) &#x201c;2.4&#xa0;wt% Si-Fe&#x201d; 30 &#xd7; 0.305 &#xd7; 300&#xa0;mm (width &#xd7; thickness &#xd7; length) M330-35A was employed in this study. <xref ref-type="table" rid="T2">Table 2</xref> demonstrates in detail the variation in the chemical properties of the grade, which further contains minimal quantities of other components that are consistent between the grades. The steel was supplied by Tata Steel/Cogent Power and punched using new tooling by Wingard &#x26; Co., Baltimore, United States. Data from <xref ref-type="table" rid="T3">Table 3</xref>. Manufacturer-provided material data for the M330-35A samples (<xref ref-type="bibr" rid="B7">Cogent Power, 2008</xref>; <xref ref-type="bibr" rid="B8">Cogent Power, 2009</xref>).</p>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>Chemical composition of M330-35A samples.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Grade</th>
<th align="center">C%</th>
<th align="center">Si%</th>
<th align="center">Fe%</th>
<th align="center">Al%</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">M330</td>
<td align="center">0.0035a</td>
<td align="center">2.4000</td>
<td align="center">Balance</td>
<td align="center">0.3000</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="T3" position="float">
<label>TABLE 3</label>
<caption>
<p>Manufacturer-provided material data for M330-35A samples.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Grade</th>
<th align="center">Thickness (mm)</th>
<th align="center">Resistivity (&#x3bc;&#x3a9;cm)</th>
<th align="center">Elastic modulus, rd (N/m <inline-formula id="inf2">
<mml:math id="m2">
<mml:mrow>
<mml:msup>
<mml:mi>m</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula>)</th>
<th align="center">Elastic modulus, td (N/m <inline-formula id="inf3">
<mml:math id="m3">
<mml:mrow>
<mml:msup>
<mml:mi>m</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula>)</th>
<th align="center">Yield strength (N/m <inline-formula id="inf4">
<mml:math id="m4">
<mml:mrow>
<mml:msup>
<mml:mi>m</mml:mi>
<mml:mn>2</mml:mn>
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</mml:mrow>
</mml:math>
</inline-formula>)</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">M330</td>
<td align="center">0.35</td>
<td align="center">2.4000</td>
<td align="center">200 000</td>
<td align="center">210 000</td>
<td align="center">315</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>Prior to coating the samples, the power loss and permeability of the non-oriented steel were tested using the Single Strip Tester (SST) at inductions of 0.5T&#x2013;1.7&#xa0;T and magnetising frequencies of 50, 100, 200, 400, 500 and 700&#xa0;Hz up to 1&#xa0;kHz.</p>
</sec>
</sec>
<sec id="s2-2">
<title>2.2 Experimental procedure</title>
<sec id="s2-2-1">
<title>2.2.1 Heat treatment</title>
<p>The samples were annealed in an argon gas atmosphere in a fired furnace at a temperature rate increase of 200&#xb0;C/h to reach 800&#xb0;C after 4&#xa0;h and held for up to 2&#xa0;h. For stress relief, annealing at 800&#xb0;C was carried out downstream of the main annealing process. The temperature curve of the stress-relief annealing in relation to the recording of the furnace cycle is shown in <xref ref-type="fig" rid="F1">Figure 1</xref>.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Temperature and times for the diffusion annealing process.</p>
</caption>
<graphic xlink:href="fmats-09-1108308-g001.tif"/>
</fig>
<p>During the sintering process, argon gas was utilised as a protective environment. Prior to the annealing cycle, the furnace was cleansed for 30&#xa0;min with an Argon gas flow of 5&#xa0;L/min to remove any traces of the ambient air. The flow rate of Argon gas was set at 4&#xa0;L/min throughout the duration of the heat treatment.</p>
</sec>
<sec id="s2-2-2">
<title>2.2.2 Samples coated with MnO2</title>
<p>Manganese (IV) oxide (MnO<sub>2</sub>) powder was made with Silicone oil solution to form a paste. The sample particles were coated with MnO<sub>2</sub> <italic>via</italic> the surface diffusion technique, this was then coated on both sides of the non-oriented electrical steel strips.</p>
<p>In the next stage, the annealed samples were reheated after coating. These were then annealed at three distinct temperatures (535&#xb0;C, 700&#xb0;C, and 800&#xb0;C) and at three different times: 180, 60 and 45&#xa0;min. Subsequently, they were cooled in the furnace to room temperature.</p>
</sec>
</sec>
<sec id="s2-3">
<title>2.3 Magnetic property measurements by SST</title>
<p>Single Sheet Testers (SST) or Epstein frames are regularly used to determine the characteristics of electrical steel, as recommended by IEC-Standards (IEC 404-2) (<xref ref-type="bibr" rid="B35">S. Standard, 1996</xref>) and (IEC 404-3) (<xref ref-type="bibr" rid="B36">S. Standard, 1992</xref>). The significance of this type of measurement system is specific to the permeability and power loss (W/kg) at various magnetising frequencies. The &#x201c;Wolfson Centre for Magnetics&#x201d; at Cardiff University developed the Single Strip Tester (SST) system, which delivers highly accurate and automatic measurements. With the exception of the frame itself, the Epstein frame system is comparable to the (SST) (<xref ref-type="bibr" rid="B3">Bertotti, 1987</xref>). The system is shown in <xref ref-type="fig" rid="F2">Figure 2</xref> and comprises of a PC with LabVIEW version 2019 already installed, a DAQ (data acquisition Card) from NI PCI-6120, a power of amplifier, a 1&#xa0;&#x2126; shunt resistor (Rshunt), as well as an air flux adjusted SST (<xref ref-type="bibr" rid="B34">Somkun, 2010</xref>; <xref ref-type="bibr" rid="B13">Instruments, National, 2002</xref>). According to IEC 404-3, twin vertical yokes of GO silicon steel or nickel-iron alloy are employed. Furthermore, twin vertical yokes are made of GO silicon steel or nickel-iron alloy. The main coil of 865 turns (N1) is wrapped around the secondary winding, whilst a secondary coil of 250 turns (N2) is wrapped around the plastic frame. Between the yokes is a typical Epstein strip size sheet (305) mm long and 30&#xa0;mm wide. This setup provides a low reluctance path. AC tests were performed under comparable settings, with frequencies ranging from 50 to 1000&#xa0;Hz.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>AC magnetic property measurement system.</p>
</caption>
<graphic xlink:href="fmats-09-1108308-g002.tif"/>
</fig>
</sec>
<sec id="s2-4">
<title>2.4 Characterisation of microstructure</title>
<p>The samples were sliced and prepared (roughly 15&#x2013;20&#xa0;mm square) for examination under a scanning electron microscope to determine diffusion effects.</p>
<p>The final distribution relating to the effectiveness of the diffusion of the Manganese to both surfaces was investigated for strips of non-oriented electrical steel were tested as follows: concentration profiles measured Energy Dispersive X-ray Spectrometer (EDS) by using Scanning Electron Microscope (SEM).</p>
<p>Scanning Electron Microscope (SEM) was used to characterisation the sample&#x2019;s composite-coated steel. Inclusions were observed by Scanning Electron Microscope (SEM) and energy-dispersive spectroscopy (EDS) for elemental analysis.</p>
</sec>
<sec id="s2-5">
<title>2.5 Core loss separation method</title>
<p>The overall loss contains both hysteresis and eddy current loss components. The per-cycle hysteresis loss is presently determined using a different method. This approach measures core loss at various frequencies. When the magnetisation frequency curves at different flux densities are extrapolated to zero frequency, the hysteresis loss per cycle, which is the hysteresis energy loss per cycle, can be determined (<xref ref-type="bibr" rid="B27">Mthombeni and Pillay, 2006</xref>).<disp-formula id="e1">
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</mml:msub>
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<mml:mrow>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mi>f</mml:mi>
<mml:msubsup>
<mml:mi>B</mml:mi>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>k</mml:mi>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:msubsup>
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<mml:msub>
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<mml:mi>e</mml:mi>
</mml:msub>
<mml:msup>
<mml:mrow>
<mml:mi>f</mml:mi>
<mml:msub>
<mml:mi>B</mml:mi>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:math>
<label>(1)</label>
</disp-formula>
</p>
<p>The linear equation is the reason for the magnetising frequency using the maximum flux density B. Subsequently, the core loss data are applied with the aim of plotting the curves of Pc/f <italic>versus</italic> f. The curves are straight lines.<disp-formula id="e2">
<mml:math id="m6">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>A</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>B</mml:mi>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:math>
<label>(2)</label>
</disp-formula>Where A &#x3d; <italic>K</italic>&#x210e; <inline-formula id="inf5">
<mml:math id="m7">
<mml:mrow>
<mml:msubsup>
<mml:mi>B</mml:mi>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>k</mml:mi>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula> means hysteresis loss per cycle and B &#x3d; <inline-formula id="inf6">
<mml:math id="m8">
<mml:mrow>
<mml:msup>
<mml:msub>
<mml:mi>B</mml:mi>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula>.</p>
<p>More information for determining these coefficients is available in (<xref ref-type="bibr" rid="B5">Chen and Pillay, 2002</xref>; <xref ref-type="bibr" rid="B14">Ionel et al., 2006</xref>; <xref ref-type="bibr" rid="B12">Ibrahim and Pillay, 2012</xref>).</p>
<p>To obtain the overall hysteresis loss, multiply the static hysteresis power by the magnetising frequency. The hysteresis power loss per cycle is frequency independent. Having this knowledge is essential when applying the extrapolation method. Nevertheless, only at low frequencies is this supposition is valid. It would result in a non-uniform magnetic field throughout the lamination at higher frequencies, which would complicate the calculation.</p>
<p>Consequently, at every point within the lamination, each cycle&#x2019;s hysteresis loop and hysteresis power losses are distinct. On account of this, it is better to use the extrapolation method to determine the core loss separation at a low frequency; otherwise, the skin effect should indeed be considered (<xref ref-type="bibr" rid="B4">Boon and Robey, 1958</xref>).</p>
<sec id="s2-5-1">
<title>2.5.1 Core loss separation</title>
<p>The three-term formula follows the same approaches employed to separate losses into their eddy current and hysteresis components. However, in this instance, a third term reflecting the excess loss is provided.<disp-formula id="e3">
<mml:math id="m9">
<mml:mrow>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mi>C</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mi>e</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mi>a</mml:mi>
</mml:msub>
<mml:mtext>&#x2003;</mml:mtext>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi mathvariant="normal">W</mml:mi>
<mml:mo>/</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="normal">k</mml:mi>
<mml:mi mathvariant="normal">g</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mtext>&#x2009;</mml:mtext>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(3)</label>
</disp-formula>
</p>
<p>By dividing Eq. <xref ref-type="disp-formula" rid="e3">3</xref> by the magnetising frequency, we obtain Eq. <xref ref-type="disp-formula" rid="e4">4</xref> which represents the total power losses.<disp-formula id="e4">
<mml:math id="m10">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mi>f</mml:mi>
<mml:msubsup>
<mml:mi>B</mml:mi>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>k</mml:mi>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:msubsup>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>e</mml:mi>
</mml:msub>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>f</mml:mi>
<mml:msub>
<mml:mi>B</mml:mi>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>a</mml:mi>
</mml:msub>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>B</mml:mi>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mn>1.5</mml:mn>
</mml:msup>
</mml:mrow>
</mml:math>
<label>(4)</label>
</disp-formula>
</p>
<p>In this approach, which is similar to the two-term separation technique, the first right hand (P<sub>&#x210e;</sub>) represents the hysteresis loss component, the second (P<sub>e</sub>) represents the eddy current loss component, whereas the third (P<sub>a</sub>) represents the excess or anomalous loss component.</p>
<p>As the latter is influenced by micro-structural interaction, magnetic anisotropy and the non-homogeneous domestically driven eddy current (<xref ref-type="bibr" rid="B23">Mayergoyz and Serpico, 1999</xref>), the constant coefficients are as follows.<disp-formula id="e5">
<mml:math id="m11">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>A</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>B</mml:mi>
<mml:mi>f</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>C</mml:mi>
<mml:msqrt>
<mml:mi>f</mml:mi>
</mml:msqrt>
</mml:mrow>
</mml:math>
<label>(5)</label>
</disp-formula>
</p>
<p>An alternative viable method for finding the coefficients. The core loss per cycle is shown against the square root of frequency &#x221a; f rather than the frequency f for different levels of flux density B ranging from the smallest to the highest frequency (<xref ref-type="bibr" rid="B39">Williams et al., 1950</xref>).</p>
<p>Consequently, (6) may be adjusted by<disp-formula id="e6">
<mml:math id="m12">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>A</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>B</mml:mi>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msqrt>
<mml:mi>f</mml:mi>
</mml:msqrt>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>C</mml:mi>
<mml:msqrt>
<mml:mi>f</mml:mi>
</mml:msqrt>
</mml:mrow>
</mml:math>
<label>(6)</label>
</disp-formula>Where P<sub>c</sub>/f is shown on the y-axis and &#x221a;f is plotted on the x-axis, A, B and C may be determined using nominal curve fitting. A comparison of Eq. <xref ref-type="disp-formula" rid="e4">4</xref> and Eq. <xref ref-type="disp-formula" rid="e6">6</xref> gives<disp-formula id="e7">
<mml:math id="m13">
<mml:mrow>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
<mml:mi>f</mml:mi>
<mml:msubsup>
<mml:mi>B</mml:mi>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>k</mml:mi>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:math>
<label>(7)</label>
</disp-formula>
<disp-formula id="e8">
<mml:math id="m14">
<mml:mrow>
<mml:mi mathvariant="normal">B</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>e</mml:mi>
</mml:msub>
<mml:msup>
<mml:mrow>
<mml:mi>f</mml:mi>
<mml:msub>
<mml:mi>B</mml:mi>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:math>
<label>(8)</label>
</disp-formula>
<disp-formula id="e9">
<mml:math id="m15">
<mml:mrow>
<mml:mi mathvariant="normal">C</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>a</mml:mi>
</mml:msub>
<mml:msup>
<mml:mrow>
<mml:mi>f</mml:mi>
<mml:msub>
<mml:mi>B</mml:mi>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mn>1.5</mml:mn>
</mml:msup>
</mml:mrow>
</mml:math>
<label>(9)</label>
</disp-formula>Thus, when using this approach with certain flux densities, the loss coefficients <inline-formula id="inf7">
<mml:math id="m16">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>h</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf8">
<mml:math id="m17">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>e</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf9">
<mml:math id="m18">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>a</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> can be obtained.</p>
<p>In conclusion, Eq. <xref ref-type="disp-formula" rid="e1">1</xref> and Eq. <xref ref-type="disp-formula" rid="e6">6</xref> emphasise that the extrapolation technique is employed to determine that eddy currents cause a linear relationship between the frequency and the amount of power lost per cycle. Additionally, it is believed that hysteresis loss per cycle is frequency independent.</p>
</sec>
</sec>
</sec>
<sec sec-type="results|discussion" id="s3">
<title>3 Results and discussions</title>
<sec id="s3-1">
<title>3.1 Microstructure, grain size and texture</title>
<p>
<xref ref-type="fig" rid="F3">Figure 3</xref> explains the SEM and EDS analysis of typical inclusions in the final annealed samples. The samples were coated and polished using acetone. Scanning electron microscope and EDS was performed to analyse the Manganese inclusions. The EDS analysis revealed that a significant part of the sample that contains Manganese<bold>.</bold> The inclusions containing Manganese were predominantly (&#x3c;250&#xa0;&#xb5;m) in size. Inclusions with different Manganese contents can be seen in <xref ref-type="fig" rid="F3">Figures 3</xref>&#x2013;<xref ref-type="fig" rid="F5">5</xref>. The results of the EDS analysis are shown in the tables in relation to each figure.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Distribution of elements after heat treatment at 525&#xb0;C with Energy Dispersive System Analysis of X-rays using SEM. <bold>(A)</bold>. Energy dispersive X-ray (EDX) spectra of sample, <bold>(B)</bold> Table EDS analysis of inclusions from Figure <bold>(C)</bold>, <bold>(C)</bold> Complex inclusions in the sample of non-oriented electrical steel sheet containing % Mn.</p>
</caption>
<graphic xlink:href="fmats-09-1108308-g003.tif"/>
</fig>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Distribution of elements after heat treatment at 700&#xb0;C with Energy Dispersive System Analysis of X-rays using SEM. <bold>(A)</bold>. Energy dispersive X-ray (EDX) spectra of sample, <bold>(B)</bold> Table EDS analysis of inclusions from Figure <bold>(C)</bold>, <bold>(C)</bold> Complex inclusions in the sample of non-oriented electrical steel sheet containing % Mn.</p>
</caption>
<graphic xlink:href="fmats-09-1108308-g004.tif"/>
</fig>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>Distribution of elements after heat treatment at 800&#xb0;C with Energy Dispersive System Analysis of X-rays using SEM. <bold>(A)</bold>. Energy dispersive X-ray (EDX) spectra of sample, <bold>(B)</bold> Table EDS analysis of inclusions from Figure <bold>(C)</bold>, <bold>(C)</bold> Complex inclusions in the sample of non-oriented electrical steel sheet containing % Mn.</p>
</caption>
<graphic xlink:href="fmats-09-1108308-g005.tif"/>
</fig>
<p>In the table pertaining to <xref ref-type="fig" rid="F5">Figure 5</xref>, it can be noted that the inclusions that contain small amounts of Mn are exceedingly complex. The inclusions contain even more zirconium than Manganese. The high oxygen and carbon contents of the inclusions reveal the presence of Manganese oxides.</p>
<p>After coating the electrical steel with MnO2, the analysis of the deep elements was performed using EDS. During the EDS measurement, different areas were focused on. <xref ref-type="fig" rid="F3">Figure 3</xref> illustrates the identical peak. All of the MnO<sub>2</sub> can be noticed in the synthesised, nanostructures in the EDS spectrum. Where it was revealed that the major elements present were manganese, oxygen and carbon, in spectrum 55, the quantity of Mn, O<sub>2</sub> and C were 59.2, 25.79, and 10.18 weight %, respectively. Subsequently, after heat treatment, a small amount of impurity in conjunction with the presence of reduced titanium, was observed. However, while observed in spectrum 24, the values were noted to be 20.2, 28.95, and 2.68 measured in weight % for Mn, O<sub>2</sub> and C, respectively.</p>
<p>It was also observed that after mixing the Mn compound with Si oil particles followed by a heat treatment at 525&#xb0;C and 700&#xb0;C, the carbon amount was ascertained to increase, Similarly, the EDS graph in the figures indicates the presence of Fe that confirms the successful coating of the surface of the Mn with Si oil.</p>
<p>The elemental composition of the material was analysed using EDS to determine the nature of the composite, revealing that true functionalization occurred. Details of the three EDS spectra of the concentration (Mn) values measured in atomic and weight % are listed.</p>
</sec>
<sec id="s3-2">
<title>3.2 Effect of temperature on power losses</title>
<p>
<xref ref-type="fig" rid="F6">Figure 6</xref> describes the impact of temperature on the characteristics of the sample in terms of power losses at 400&#xa0;Hz and 1.5&#xa0;T. The power losses increase linearly when the temperature of the sample increases (uncoated or coated). The effect of temperature on the samples&#x2019; properties confirms that the highest increase in power loss at 52&#xa0;W/kg occurs at 700&#xb0;C when the firing time was 45&#xa0;min.</p>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>Power losses (400&#xa0;Hz, 1.5&#xa0;T) for coated and uncoated samples at different temperature.</p>
</caption>
<graphic xlink:href="fmats-09-1108308-g006.tif"/>
</fig>
<p>At the melting point of Mn at 525&#xb0;C, the following values were obtained: uncoated at 39&#xa0;W/kg and coated at 35&#xa0;W/kg when the firing time was 60&#xa0;min. Also, from <xref ref-type="fig" rid="F6">Figure 6</xref>, as can be seen, the maximum temperature of 800&#xb0;C has a slight reduction in power losses to 49&#xa0;W/kg when compared to 700&#xb0;C. Thus, its dissolving power is maximised.</p>
<p>
<xref ref-type="fig" rid="F6">Figure 6</xref> explains the power losses with different temperatures for the Manganese oxide sample both with and without coating whilst heating from 525&#xb0;C to 800&#xb0;C, respectively. In both cases, the power losses increased as the temperature increased from 525&#xb0;C to 700&#xb0;C. However, when the temperature reached 800&#xb0;C, there was an insignificant decrease in power losses. Furthermore, the peak of power losses appeared at 700&#xb0;C, indicating a significant increase in power losses, as shown in <xref ref-type="fig" rid="F6">Figure 6</xref> in both cases. Based on the results of the melting performance for manganese oxide, the annealing temperatures implemented in this study were 525&#xb0;C, 700&#xb0;C, and 800&#xb0;C. Therefore, the fact that the melting point of manganese oxide is 525&#xb0;C has contributed to improving the performance of samples and reducing power losses, is considered.</p>
</sec>
<sec id="s3-3">
<title>3.3 Effect of temperatures on permeability</title>
<p>
<xref ref-type="fig" rid="F7">Figure 7</xref> demonstrates permeability at 400&#xa0;Hz, 1.5&#xa0;T for coated and uncoated samples with manganese oxide contents at different temperatures during sintering times of 1&#xa0;hour, 45&#xa0;min, and 30&#xa0;min. It was observed that the permeability rose with the temperature and some of samples used (coated and uncoated). It was established that permeability decreased when the sample reached 525&#xb0;C but was high when used at the same temperature without being coated. It was observed that coated specimens had less permeability than the uncoated samples at 700&#xb0;C. Magnetic permeability decreases by increasing the temperature rate to 800&#xb0;C. This is caused by conditions brought on by an excess of lubricant that reduced permeability. Holding the sintering time had a visible impact on magnetic permeability, which will help minimise specimen flaws. It is apparent that specimens with an hour-long holding period have greater magnetic permeability than those with a 30-min holding period.</p>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>Permeability at 400&#xa0;Hz, 1.5&#xa0;T for coated and uncoated samples at different temperature.</p>
</caption>
<graphic xlink:href="fmats-09-1108308-g007.tif"/>
</fig>
<p>Consequently, the permeability of composites increases with increasing annealing temperature, whereas power loss diminishes when the annealing temperature is increased.</p>
</sec>
<sec id="s3-4">
<title>3.4 Power loss components</title>
<p>From the results obtained by applying the following method to calculate power loss separation, the power loss of the non-oriented electrical steel samples was measured using the SST system explained in (<xref ref-type="bibr" rid="B5">Chen and Pillay, 2002</xref>) and (<xref ref-type="bibr" rid="B12">Ibrahim and Pillay, 2012</xref>), in which all power loss measurements were made.</p>
<p>Typically, as shown in <xref ref-type="table" rid="T4">Table 4</xref>, at a maximum flux density of 1.5&#xa0;T and magnetising frequencies of 50, 100, 200, 400, 500, and 700&#xa0;Hz to 1&#xa0;kHz, the power loss of NO steel is calculated.</p>
<table-wrap id="T4" position="float">
<label>TABLE 4</label>
<caption>
<p>Power loss of NO steel measured at various magnetising frequencies, with a total power loss per cycle uncoating at a peak flux density of 1.5&#xa0;T.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Magnetising frequency</th>
<th rowspan="2" align="center">Measured power loss (W/kg)</th>
<th rowspan="2" align="center">Power loss per cycle (W/kg).sec</th>
</tr>
<tr>
<th align="center">Hz</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">50</td>
<td align="center">1.921</td>
<td align="center">0.038</td>
</tr>
<tr>
<td align="center">100</td>
<td align="center">4.584</td>
<td align="center">0.045</td>
</tr>
<tr>
<td align="center">200</td>
<td align="center">12.505</td>
<td align="center">0.062</td>
</tr>
<tr>
<td align="center">400</td>
<td align="center">38.143</td>
<td align="center">0.095</td>
</tr>
<tr>
<td align="center">500</td>
<td align="center">56.428</td>
<td align="center">0.112</td>
</tr>
<tr>
<td align="center">700</td>
<td align="center">102.282</td>
<td align="center">0.146</td>
</tr>
<tr>
<td align="center">1000</td>
<td align="center">198.126</td>
<td align="center">0.198</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>
<xref ref-type="fig" rid="F8">Figure 8</xref> shows the measured power loss per cycle <italic>versus</italic> the frequency&#x2019;s square root. By fitting a polynomial curve to this curve in Microsoft Excel, we can find the coefficients of the power loss parts.</p>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>Total power loss per cycle of a magnetic sample made of non-oriented steel at a 1.5&#xa0;T flux density against the square root of frequency.</p>
</caption>
<graphic xlink:href="fmats-09-1108308-g008.tif"/>
</fig>
<p>The fitting equation&#x2019;s residual values are often very near to unity, or <inline-formula id="inf10">
<mml:math id="m19">
<mml:mrow>
<mml:msup>
<mml:mi>R</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 1, suggesting an accurate approximation.</p>
<p>
<xref ref-type="table" rid="T5">Table 5</xref> shows the results of determining the power loss components at various frequencies using the equations from <xref ref-type="fig" rid="F8">Figure 8</xref>.<disp-formula id="e10">
<mml:math id="m20">
<mml:mrow>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>h</mml:mi>
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<mml:mi>f</mml:mi>
<mml:msubsup>
<mml:mi>B</mml:mi>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>k</mml:mi>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:msubsup>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0.0321</mml:mn>
</mml:mrow>
</mml:math>
<label>(10)</label>
</disp-formula>
<disp-formula id="e11">
<mml:math id="m21">
<mml:mrow>
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</mml:mrow>
<mml:mn>2</mml:mn>
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<mml:mo>&#x3d;</mml:mo>
<mml:mn>0.0002</mml:mn>
</mml:mrow>
</mml:math>
<label>(11)</label>
</disp-formula>
<disp-formula id="e12">
<mml:math id="m22">
<mml:mrow>
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<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>k</mml:mi>
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</mml:msub>
</mml:mrow>
<mml:mn>1.5</mml:mn>
</mml:msup>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0.0005</mml:mn>
</mml:mrow>
</mml:math>
<label>(12)</label>
</disp-formula>
</p>
<table-wrap id="T5" position="float">
<label>TABLE 5</label>
<caption>
<p>Power loss components of SST of NO steel at various magnetising frequencies and a peak flux density of 1.5 (T) with uncoated samples.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="center">Frequency (Hz)</th>
<th rowspan="2" align="center">Measured power loss (W/kg)</th>
<th rowspan="2" align="center">P<sub>e</sub> (W/kg)</th>
<th rowspan="2" align="center">P<sub>h</sub> (W/kg)</th>
<th rowspan="2" align="center">P<sub>a</sub> (W/kg)</th>
<th align="center">P<sub>c</sub> &#x3d; P<sub>e</sub> &#x2b;</th>
<th rowspan="2" align="center">Error <inline-formula id="inf11">
<mml:math id="m23">
<mml:mrow>
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<mml:mrow>
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<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>c</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>u</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>d</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>P</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>m</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>s</mml:mi>
<mml:mi>u</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>d</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>P</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>u</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>d</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>100</mml:mn>
<mml:mo>%</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
</tr>
<tr>
<th align="center">P<sub>h</sub> &#x2b; P<sub>a</sub> (W/kg)</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">50</td>
<td align="center">1.921</td>
<td align="center">0.6</td>
<td align="center">1.605</td>
<td align="center">0.18</td>
<td align="center">1.921</td>
<td align="center">0.00</td>
</tr>
<tr>
<td align="center">100</td>
<td align="center">4.584</td>
<td align="center">2.2</td>
<td align="center">3.21</td>
<td align="center">&#x2212;0.5</td>
<td align="center">4.71</td>
<td align="center">&#x2212;0.02</td>
</tr>
<tr>
<td align="center">200</td>
<td align="center">12.505</td>
<td align="center">8.4</td>
<td align="center">6.42</td>
<td align="center">&#x2212;1.41</td>
<td align="center">13.01</td>
<td align="center">&#x2212;0.04</td>
</tr>
<tr>
<td align="center">400</td>
<td align="center">38.143</td>
<td align="center">32.9</td>
<td align="center">12.84</td>
<td align="center">&#x2212;4</td>
<td align="center">40.84</td>
<td align="center">&#x2212;0.07</td>
</tr>
<tr>
<td align="center">500</td>
<td align="center">56.428</td>
<td align="center">51</td>
<td align="center">16.05</td>
<td align="center">&#x2212;5.6</td>
<td align="center">58.45</td>
<td align="center">&#x2212;0.07</td>
</tr>
<tr>
<td align="center">700</td>
<td align="center">102.282</td>
<td align="center">99</td>
<td align="center">22.47</td>
<td align="center">&#x2212;9.26</td>
<td align="center">104.21</td>
<td align="center">&#x2212;0.08</td>
</tr>
<tr>
<td align="center">1000</td>
<td align="center">198.126</td>
<td align="center">202</td>
<td align="center">32.1</td>
<td align="center">&#x2212;15.81</td>
<td align="center">206.29</td>
<td align="center">&#x2212;0.09</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>The power loss components, as illustrated in <xref ref-type="table" rid="T5">Table 5</xref>, are calculated by applying these coefficients in Eq. <xref ref-type="disp-formula" rid="e6">6</xref>. <xref ref-type="fig" rid="F9">Figure 9</xref> demonstrates the relationship between the magnetising frequency and the hysteresis power loss and eddy current power loss at 1.5&#xa0;T. The static hysteresis loops are utilised to calculate hysteresis loss. However, an equation may be used to calculate eddy current power loss per cycle as a linear function of the magnetising frequency:<disp-formula id="e13">
<mml:math id="m24">
<mml:mrow>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mi mathvariant="bold-italic">e</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mi>&#x3c0;</mml:mi>
<mml:mrow>
<mml:mn>6</mml:mn>
<mml:mi>&#x3c1;</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:msup>
<mml:mi>d</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:msup>
<mml:mi>f</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:msup>
<mml:msub>
<mml:mi>B</mml:mi>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:math>
<label>(13)</label>
</disp-formula>Where <inline-formula id="inf12">
<mml:math id="m25">
<mml:mrow>
<mml:msub>
<mml:mi>B</mml:mi>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the peak flux density, (T); <italic>f</italic> is frequency, (Hz); <italic>&#x3c1;</italic> is resistivity (&#x3a9;. m); D is density, (kg/<inline-formula id="inf13">
<mml:math id="m26">
<mml:mrow>
<mml:msup>
<mml:mi>m</mml:mi>
<mml:mn>3</mml:mn>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula>); and <italic>d</italic> is the thickness of the lamination (m) (<xref ref-type="bibr" rid="B3">Bertotti, 1987</xref>).</p>
<fig id="F9" position="float">
<label>FIGURE 9</label>
<caption>
<p>Eddy current and hysteresis loss per cycle versus frequency.</p>
</caption>
<graphic xlink:href="fmats-09-1108308-g009.tif"/>
</fig>
<p>Power loss of non-oriented steel is measured at a peak flux density of 1.5&#xa0;T at different magnetizing frequencies with total power loss per cycle with coating as shown in <xref ref-type="table" rid="T6">Table 6</xref>.</p>
<table-wrap id="T6" position="float">
<label>TABLE 6</label>
<caption>
<p>Power loss of non-oriented steel is measured at a peak flux density of 1.5&#xa0;T at different magnetizing frequencies with total power loss per cycle with coating.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Magnetising frequency Hz</th>
<th align="center">Measured power loss (W/kg)</th>
<th align="center">Power loss per cycle (W/kg).sec</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">50</td>
<td align="center">1.912</td>
<td align="center">0.038</td>
</tr>
<tr>
<td align="center">100</td>
<td align="center">4.400</td>
<td align="center">0.045</td>
</tr>
<tr>
<td align="center">200</td>
<td align="center">12.00</td>
<td align="center">0.060</td>
</tr>
<tr>
<td align="center">400</td>
<td align="center">35.706</td>
<td align="center">0.089</td>
</tr>
<tr>
<td align="center">500</td>
<td align="center">52.680</td>
<td align="center">0.105</td>
</tr>
<tr>
<td align="center">700</td>
<td align="center">99.301</td>
<td align="center">0.141</td>
</tr>
<tr>
<td align="center">1000</td>
<td align="center">194.237</td>
<td align="center">0.194</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>The power loss separation findings for the same material with a coating are shown in <xref ref-type="table" rid="T7">Table 7</xref>.</p>
<table-wrap id="T7" position="float">
<label>TABLE 7</label>
<caption>
<p>Power loss components of an SST of NO steel at various magnetising frequencies and a peak flux density of 1.5 (T) with coated samples.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Frequency (Hz)</th>
<th align="center">Measured power loss (W/kg)</th>
<th align="center">P<sub>e</sub> (W/kg)</th>
<th align="center">P<sub>h</sub> (W/kg)</th>
<th align="center">P<sub>a</sub> (W/kg)</th>
<th align="center">P<sub>C</sub> &#x3d; P<sub>e</sub> &#x2b; P<sub>h</sub> &#x2b; P<sub>a</sub> (W/kg)</th>
<th align="center">Error <inline-formula id="inf14">
<mml:math id="m27">
<mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>P</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>c</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>u</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>d</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>P</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>m</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>s</mml:mi>
<mml:mi>u</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>d</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>P</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>u</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>d</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>100</mml:mn>
<mml:mo>%</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">50</td>
<td align="center">1.912</td>
<td align="center">0.5</td>
<td align="center">2.01</td>
<td align="center">&#x2212;0.56</td>
<td align="center">1.95</td>
<td align="center">&#x2212;0.01</td>
</tr>
<tr>
<td align="center">100</td>
<td align="center">4.400</td>
<td align="center">2</td>
<td align="center">4.02</td>
<td align="center">&#x2212;1.6</td>
<td align="center">4.42</td>
<td align="center">0.02</td>
</tr>
<tr>
<td align="center">200</td>
<td align="center">12.00</td>
<td align="center">8</td>
<td align="center">8.04</td>
<td align="center">&#x2212;4.5</td>
<td align="center">11.54</td>
<td align="center">0.04</td>
</tr>
<tr>
<td align="center">400</td>
<td align="center">35.706</td>
<td align="center">32</td>
<td align="center">16.08</td>
<td align="center">&#x2212;12.8</td>
<td align="center">35.28</td>
<td align="center">0.01</td>
</tr>
<tr>
<td align="center">500</td>
<td align="center">52.680</td>
<td align="center">50</td>
<td align="center">20.1</td>
<td align="center">&#x2212;17.88</td>
<td align="center">52.22</td>
<td align="center">0.00</td>
</tr>
<tr>
<td align="center">700</td>
<td align="center">99.301</td>
<td align="center">98</td>
<td align="center">28.14</td>
<td align="center">&#x2212;29.63</td>
<td align="center">96.51</td>
<td align="center">0.02</td>
</tr>
<tr>
<td align="center">1000</td>
<td align="center">194.237</td>
<td align="center">200</td>
<td align="center">40.21</td>
<td align="center">&#x2212;50.59</td>
<td align="center">211.68</td>
<td align="center">0.01</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>
<xref ref-type="fig" rid="F10">Figure 10</xref> shows the measured power loss per cycle versus the frequency&#x2019;s square root. By fitting a polynomial curve to this curve in Microsoft Excel, we can find the coefficients of the power loss parts with coating.</p>
<fig id="F10" position="float">
<label>FIGURE 10</label>
<caption>
<p>Shows the total power loss per cycle of a magnetic sample made of NO steel at a 1.5&#xa0;T flux density against the square root of frequency.</p>
</caption>
<graphic xlink:href="fmats-09-1108308-g010.tif"/>
</fig>
<p>
<xref ref-type="table" rid="T8">Table 8</xref> illustrates a comparison was made between the eddy current power loss obtained by the extrapolation method (experimental based) and eddy current calculated by the conventional formula (theory-based). This experiment indicated that the eddy current loss calculated in a sample at low induction and low frequency is virtually equal to that observed by the extrapolation method. Most of the extra loss changes with the frequency and strength of the field at the same eddy current power loss.</p>
<table-wrap id="T8" position="float">
<label>TABLE 8</label>
<caption>
<p>Results obtained using by extrapolation method and the comparison of Eq. <xref ref-type="disp-formula" rid="e13">13</xref> was used to figure out the eddy current power loss of an SST with a peak flux density of 1.5&#xa0;T and different frequencies.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Magnetising frequency Hz</th>
<th rowspan="2" align="center">Eddy current power loss (W/kg) by extrapolation method</th>
<th rowspan="2" align="center">Eddy current power loss (W/kg) by Eq. <xref ref-type="disp-formula" rid="e13">13</xref>
</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">50</td>
<td align="center">0.5</td>
<td align="center">0.39</td>
</tr>
<tr>
<td align="center">100</td>
<td align="center">2</td>
<td align="center">1.48</td>
</tr>
<tr>
<td align="center">200</td>
<td align="center">8</td>
<td align="center">7.44</td>
</tr>
<tr>
<td align="center">400</td>
<td align="center">32</td>
<td align="center">30.78</td>
</tr>
<tr>
<td align="center">500</td>
<td align="center">50</td>
<td align="center">47.16</td>
</tr>
<tr>
<td align="center">700</td>
<td align="center">98</td>
<td align="center">91.83</td>
</tr>
<tr>
<td align="center">1000</td>
<td align="center">200</td>
<td align="center">148.65</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>
<xref ref-type="table" rid="T9">Table 9</xref> displays the percentage reduction in power loss for uncoated and coated samples at various frequencies and verifies that the reduction in power loss occurs at a peak flux density of 1.5&#xa0;T. The diffusion of manganese (IV) oxide reduces losses by approximately 8% at 500Hz and 7% at 400&#xa0;Hz at the same value flux density. Moreover, as the internal effects of the internal flux distribution are greater even when AC magnetism was used, the unequal amount of Mn causes a resistivity gradient that lowers eddy current loss.</p>
<table-wrap id="T9" position="float">
<label>TABLE 9</label>
<caption>
<p>Illustrates the percent decrease in power loss on uncoated and coated samples at various frequencies at 1.5&#xa0;T.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Magnetising frequency (Hz)</th>
<th align="center">Measured power loss with uncoating (W/kg)</th>
<th align="center">Measured power loss with coating (W/kg)</th>
<th align="center">Reduction in power loss (%)</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">50</td>
<td align="center">1.921</td>
<td align="center">1.912</td>
<td align="center">1</td>
</tr>
<tr>
<td align="center">100</td>
<td align="center">4.584</td>
<td align="center">4.400</td>
<td align="center">5</td>
</tr>
<tr>
<td align="center">200</td>
<td align="center">12.505</td>
<td align="center">12.00</td>
<td align="center">5</td>
</tr>
<tr>
<td align="center">400</td>
<td align="center">38.143</td>
<td align="center">35.706</td>
<td align="center">7</td>
</tr>
<tr>
<td align="center">500</td>
<td align="center">56.428</td>
<td align="center">52.680</td>
<td align="center">8</td>
</tr>
<tr>
<td align="center">700</td>
<td align="center">102.282</td>
<td align="center">99.301</td>
<td align="center">3</td>
</tr>
<tr>
<td align="center">1000</td>
<td align="center">198.126</td>
<td align="center">194.237</td>
<td align="center">2</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>
<xref ref-type="table" rid="T10">Table 10</xref> displays the percentage reduction in permeability for coated and uncoated specimens at various frequencies. In the case of the uncoated samples, it can be observed that permeability on the samples is visibly effected by increased frequencies from 100 to 700&#xa0;Hz, while reducing in the case of the coated samples, which achieve higher magnetic permeability at 1&#xa0;KHz with coating and the highest percent decrease in permeability at 50&#xa0;Hz with coating at a peak flux density of 1.5&#xa0;T. The diffusion of manganese (IV) oxide reduces magnetic permeability at the same value of flux density. By the diffusion of MnO<sub>2</sub> into the Si-Fe strips, the texture of the material has been affected leading to a higher anisotropic coefficient, which was noticed when the relative permeability of the coating material has been reduced.</p>
<table-wrap id="T10" position="float">
<label>TABLE 10</label>
<caption>
<p>Illustrates the percent decrease in permeability for coated and uncoated specimens at various frequencies at 1.5&#xa0;T.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Magnetising frequency (Hz)</th>
<th align="center">Measured relative permeability (&#xb5;r) with uncoating</th>
<th align="center">Measured relative permeability (&#xb5;r) with coating</th>
<th align="center">Reduction in relative permeability (&#xb5;r) (%)</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">50</td>
<td align="center">784.798</td>
<td align="center">479.746</td>
<td align="center">39</td>
</tr>
<tr>
<td align="center">100</td>
<td align="center">652.928</td>
<td align="center">501.857</td>
<td align="center">24</td>
</tr>
<tr>
<td align="center">200</td>
<td align="center">670.574</td>
<td align="center">506.774</td>
<td align="center">25</td>
</tr>
<tr>
<td align="center">400</td>
<td align="center">795.923</td>
<td align="center">506.620</td>
<td align="center">38</td>
</tr>
<tr>
<td align="center">500</td>
<td align="center">875.002</td>
<td align="center">553.971</td>
<td align="center">37</td>
</tr>
<tr>
<td align="center">700</td>
<td align="center">937.858</td>
<td align="center">576.248</td>
<td align="center">39</td>
</tr>
<tr>
<td align="center">1000</td>
<td align="center">852.695</td>
<td align="center">620.494</td>
<td align="center">27</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="s3-5">
<title>3.5 Magnetic properties</title>
<p>The hysteresis loop of coated and uncoated samples is shown in <xref ref-type="fig" rid="F11">Figure 11</xref>. The diffusion and distribution of manganese are reflected by the size of the hysteresis loop, which is proportional to the amount of material stored in the samples. The hysteresis-loop area for coated is larger and has highest saturation flux density than the raw material. AC core losses were calculated at a frequency of 500&#xa0;Hz, and steel strips were magnetised to saturation. At saturation, the 500&#xa0;Hz flux density approaches 1.5&#xa0;T based on the magnetising current frequency. At low frequencies, the lowest core loss is measured at 525&#xb0;C, and the core loss increases gradually with increasing annealing temperature; at high frequencies, the minimum core loss is observed at 800&#xb0;C, and it decreases gradually with increasing annealing temperature. Consequently, a 500&#xa0;Hz and 1.5&#xa0;T hysteresis loop was used to investigate the magnetic properties.</p>
<fig id="F11" position="float">
<label>FIGURE 11</label>
<caption>
<p>The hysteresis loop at 500&#xa0;Hz and 1.5&#xa0;T <bold>(A)</bold> Uncoated sample, <bold>(B)</bold> coated sample.</p>
</caption>
<graphic xlink:href="fmats-09-1108308-g011.tif"/>
</fig>
</sec>
</sec>
<sec sec-type="conclusion" id="s4">
<title>4 Conclusion</title>
<p>In this paper, a new material Manganese (IV) oxide as a paste has been proposed to increase the resistivity of Si-Fe for the sake of reducing power losses. Manganese has been demonstrated to diffuse into steel from a paste consisting of the relevant element in powder form diluted silicone oil solution. With the addition of manganese, the power loss of non-oriented 2.4&#xa0;wt% silicon iron was reduced by up to 8% at 1.5&#xa0;T. The reason for the reduction appears to be a straightforward resistivity increase. In case of silicon diffusion, the degree of improvement was often silicon content at the surface. This layer was probably in effect virtually nonmagnetic and therefore brought about a reduction in saturation magnetization of the whole steel. The thickness of this layer was believed to be related to the relative rates of diffusion of manganese through the paste and metal and in consequence was dependent strongly on the composition of the paste. When applied to different temperature non-oriented steel material, the results obtained from three pasted samples were considerably different, power loss reduction be achieved using manganese. The best results obtained were reduction of up to 9% at 1.5&#xa0;T. Annealing achieved at 525&#xb0;C, 700&#xb0;C and 800<bold>&#xb0;</bold>C, power loss measurement before and after annealing are performed as shown, comparisons of power losses after annealing at different temperatures, 700&#xa0;C annealing sample-open annealed at 525&#xb0;C for 1&#xa0;h are presented in this paper.</p>
</sec>
</body>
<back>
<sec sec-type="data-availability" id="s5">
<title>Data availability statement</title>
<p>The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.</p>
</sec>
<sec id="s6">
<title>Author contributions</title>
<p>All authors listed have made a substantial, direct, and intellectual contribution to the work and approved it for publication.</p>
</sec>
<sec id="s7">
<title>Funding</title>
<p>This paper is part of the PhD study of the corresponding author, EE, who is sponsored by the Ministry of Higher Education and Scientific Research in Libya.</p>
</sec>
<ack>
<p>The authors would like to thank Cardiff University/School of Engineering for accepting to pay the APC towards publishing this paper.</p>
</ack>
<sec sec-type="COI-statement" id="s8">
<title>Conflict of interest</title>
<p>The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="disclaimer" id="s9">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
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