<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD Journal Publishing DTD v2.3 20070202//EN" "journalpublishing.dtd">
<article article-type="research-article" dtd-version="2.3" xml:lang="EN" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">
<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Chem.</journal-id>
<journal-title>Frontiers in Chemistry</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Chem.</abbrev-journal-title>
<issn pub-type="epub">2296-2646</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">1369937</article-id>
<article-id pub-id-type="doi">10.3389/fchem.2024.1369937</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Chemistry</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Kinetics of extracting valuable components from Ti-bearing blast furnace slag by acidolysis with sulphuric acid</article-title>
<alt-title alt-title-type="left-running-head">Wang 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/fchem.2024.1369937">10.3389/fchem.2024.1369937</ext-link>
</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Wang</surname>
<given-names>Yan</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/2628675/overview"/>
<role content-type="https://credit.niso.org/contributor-roles/conceptualization/"/>
<role content-type="https://credit.niso.org/contributor-roles/data-curation/"/>
<role content-type="https://credit.niso.org/contributor-roles/writing-original-draft/"/>
<role content-type="https://credit.niso.org/contributor-roles/Writing - review &#x26; editing/"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Gao</surname>
<given-names>Xin</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<role content-type="https://credit.niso.org/contributor-roles/conceptualization/"/>
<role content-type="https://credit.niso.org/contributor-roles/data-curation/"/>
<role content-type="https://credit.niso.org/contributor-roles/formal-analysis/"/>
<role content-type="https://credit.niso.org/contributor-roles/Writing - review &#x26; editing/"/>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>He</surname>
<given-names>Siqi</given-names>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="https://loop.frontiersin.org/people/2631530/overview"/>
<role content-type="https://credit.niso.org/contributor-roles/conceptualization/"/>
<role content-type="https://credit.niso.org/contributor-roles/data-curation/"/>
<role content-type="https://credit.niso.org/contributor-roles/formal-analysis/"/>
<role content-type="https://credit.niso.org/contributor-roles/investigation/"/>
<role content-type="https://credit.niso.org/contributor-roles/software/"/>
<role content-type="https://credit.niso.org/contributor-roles/Writing - review &#x26; editing/"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Guo</surname>
<given-names>Jun</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<role content-type="https://credit.niso.org/contributor-roles/conceptualization/"/>
<role content-type="https://credit.niso.org/contributor-roles/data-curation/"/>
<role content-type="https://credit.niso.org/contributor-roles/Writing - review &#x26; editing/"/>
</contrib>
</contrib-group>
<aff id="aff1">
<sup>1</sup>
<institution>College of Environment and Resources</institution>, <institution>Southwest University of Science and Technology</institution>, <addr-line>Mianyang</addr-line>, <addr-line>Sichuan</addr-line>, <country>China</country>
</aff>
<aff id="aff2">
<sup>2</sup>
<institution>Central Station of Ecological Environmental Monitoring in Mianyang</institution>, <addr-line>Mianyang</addr-line>, <addr-line>Sichuan</addr-line>, <country>China</country>
</aff>
<aff id="aff3">
<sup>3</sup>
<institution>College of Resources and Environmental Engineering</institution>, <institution>Mianyang Teachers&#x2019; College</institution>, <addr-line>Mianyang</addr-line>, <addr-line>Sichuan</addr-line>, <country>China</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/1392431/overview">Shifa Wang</ext-link>, Chongqing Three Gorges 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/1213838/overview">Jing Chen</ext-link>, Nanjing University of Posts and Telecommunications, China</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1497713/overview">Chao Liu</ext-link>, Northeast Petroleum University, China</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1431866/overview">Yougen Yi</ext-link>, Central South University, China</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Siqi He, <email>hemiaohesiqi@163.com</email>
</corresp>
</author-notes>
<pub-date pub-type="epub">
<day>08</day>
<month>02</month>
<year>2024</year>
</pub-date>
<pub-date pub-type="collection">
<year>2024</year>
</pub-date>
<volume>12</volume>
<elocation-id>1369937</elocation-id>
<history>
<date date-type="received">
<day>13</day>
<month>01</month>
<year>2024</year>
</date>
<date date-type="accepted">
<day>29</day>
<month>01</month>
<year>2024</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2024 Wang, Gao, He and Guo.</copyright-statement>
<copyright-year>2024</copyright-year>
<copyright-holder>Wang, Gao, He and Guo</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>Ti-bearing blast furnace slag is a kind of solid waste produced by Pangang Group Company through the blast furnace smelting method. A variety of valuable components can be extracted from the Ti-bearing blast furnace slag after acidolysis with concentrated sulphuric acid. In order to study the kinetics of acidolysis, this paper investigated the effects of the acidolysis temperature, acid-slag ratio and raw material particle size on the overall extraction rate of Ti<sup>4&#x2b;</sup>, Mg<sup>2&#x2b;</sup> and Al<sup>3&#x2b;</sup> components at different reaction times, and simulated the acidolysis process by using the unreacted shrinking core model. The results showed that the acidolysis process was controlled by internal diffusion with an apparent activation energy of 19.05&#xa0;kJ&#xa0;mol<sup>&#x2013;1</sup> and the semi-empirical kinetic equation of the acidolysis process was obtained.</p>
</abstract>
<kwd-group>
<kwd>Ti-bearing blast furnace slag</kwd>
<kwd>concentrated sulphuric acid</kwd>
<kwd>acidolysis</kwd>
<kwd>reaction process kinetics</kwd>
<kwd>sulphuric acid</kwd>
</kwd-group>
<custom-meta-wrap>
<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Chemical Physics and Physical Chemistry</meta-value>
</custom-meta>
</custom-meta-wrap>
</article-meta>
</front>
<body>
<sec sec-type="intro" id="s1">
<title>1 Introduction</title>
<p>Vanadium-titanium magnetite in the West Panzhi region produces an industrial solid waste, Ti-bearing blast furnace slag (TBFS), in the process of ironmaking, and the mass fraction of TiO<sub>2</sub> in the TBFS ranges from 18% to 22% (<xref ref-type="bibr" rid="B34">Zhang et al., 2007</xref>). Currently, the main disposal method for TBFS is to place it in a slag disposal pit, which has the disadvantages of requiring a large area, as well as the potential threat of environmental pollution and to human and animal health (<xref ref-type="bibr" rid="B10">Kuwahara et al., 2010</xref>). Therefore, it is essential to explore effective treatment methods for TBFS.</p>
<p>Due to the high titanium content in TBFS, it is difficult to use it directly for construction materials in the resource utilisation process (<xref ref-type="bibr" rid="B7">Huang et al., 2016</xref>; <xref ref-type="bibr" rid="B3">He et al., 2019</xref>). Therefore, researchers in China have focus on extracting valuable components from TBFS, which is considered to be more significant for research and economic value. As early as the &#x201c;seventh Five Year Plan&#x201d; and &#x201c;eighth Five Year Plan&#x201d; periods, Panzhihua Iron and Steel Research Institute conducted research on the extraction of titanium from TBFS. Currently, a production line for titanium extraction by chlorination with an annual treatment of 180,000 tons of TBFS has been established (<xref ref-type="bibr" rid="B6">Huang and Zhang, 1994</xref>). However, another industrial solid waste, titanium extraction tailings, is generated in the chlorination process (<xref ref-type="bibr" rid="B22">Peng et al., 2005</xref>). In addition, researchers have investigated the extraction of Ti, Si, Mg, Al and other elements from TBFS using alkalis, salts, acids, and other additives to prepare corresponding chemical products (<xref ref-type="bibr" rid="B38">Zhou et al., 1999</xref>; <xref ref-type="bibr" rid="B37">Zhou et al., 2013</xref>). Among the various extraction processes, sulphuric acidolysis has rapidly become a research hotspot because of its mature process technology, stable and easy-to-control reaction, simple operation and the ability to extract a variety of valuable components simultaneously. In the process of using sulfuric acid to hydrolyze TBFS, whether dilute or concentrated sulfuric acid as a reaction agent, or use one stage leaching (<xref ref-type="bibr" rid="B8">Jiang et al., 2010</xref>), or two stage leaching (<xref ref-type="bibr" rid="B20">Nie et al., 2023a</xref>), or roasting (<xref ref-type="bibr" rid="B4">He and Wang, 2023</xref>), or hydrothermal as reaction method, the extraction rate for titanium is high using this method (<xref ref-type="bibr" rid="B27">Valighazvini et al., 2013</xref>; <xref ref-type="bibr" rid="B33">Zhang et al., 2022</xref>; <xref ref-type="bibr" rid="B11">Li et al., 2024a</xref>). The acidolysis of TBFS using sulfuric acid can convert solid phase Ti, Mg, and Al into soluble Ti<sup>4&#x2b;</sup>, Mg<sup>2&#x2b;</sup> and Al<sup>3&#x2b;</sup>, which are then sequentially separated by boiling hydrolysis and stepwise precipitation (<xref ref-type="bibr" rid="B5">Hongjuan et al., 2015</xref>). Therefore, optimizing the acidolysis conditions, improving the extraction rate, and efficiently extracting the valuable components in TBFS are of great significance to achieve the dual purposes of waste treatment and resource utilisation.</p>
<p>At present, domestic and international studies on sulfuric acid hydrolysis of TBFS mainly focus on reaction processes and mechanisms (<xref ref-type="bibr" rid="B9">Ju et al., 2022</xref>), while there are fewer studies on the kinetic process of sulfuric acid hydrolysis. The following problems have arisen in actual process research: the acidolysis rate of each component in TBFS did not reach the equilibrium point of acidolysis kinetics, resulting in a high content of metal components in the remaining mud after acidolysis (<xref ref-type="bibr" rid="B30">Wang et al., 2022a</xref>). At the same time, the amount of mud increases and the component recovery decreases. This type of problem occurs not only in sulfuric acid hydrolysis of TBFS, but also in many sulfuric acid hydrometallurgy processes. Kinetic analysis can provide insight into the characteristics and mechanisms of sulphuric acid acidolysis of TBFS and predict the reaction rate, so as to effectively regulate the reaction conditions and improve the process efficiency. In order to provide a theoretical basis for the sulfuric acid acidolysis of TBFS, this study investigated the relationship between the total extraction rate of each component (i.e., all of Ti, Mg and Al) and the acidolysis time at different acidolysis temperatures, acid-slag ratios and raw material particle sizes. A kinetic model of the acidolysis process was fitted and the activation energy was calculated.</p>
</sec>
<sec id="s2">
<title>2 Experiment setup</title>
<sec id="s2-1">
<title>2.1 Mineralogical analysis of TBFS</title>
<p>The TBFS samples were dried at 106&#xb0;C for 24&#xa0;h and some TBFS samples were ground to a particle size of less than 0.074&#xa0;mm for XRD and XRF testing. The XRD results in <xref ref-type="fig" rid="F1">Figure 1</xref> show that the main mineral phase is perovskite with some amorphous phase (<xref ref-type="bibr" rid="B39">Zhu et al., 2023</xref>; <xref ref-type="bibr" rid="B13">Li et al., 2024b</xref>). <xref ref-type="table" rid="T1">Table 1</xref> shows the XRF analysis results of TBFS. The main chemical components are CaO, SiO2, TiO2, Al2O3 and MgO, with low contents of SO3, Fe2O3, K2O, MnO and Na2O, and the lowest contents of F, BaO, SrO and ZrO2.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>XRD patterns of TBFS.</p>
</caption>
<graphic xlink:href="fchem-12-1369937-g001.tif"/>
</fig>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Chemical composition of TBFS.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Compound</th>
<th align="center">wt%</th>
<th align="center">Compound</th>
<th align="center">wt%</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">CaO</td>
<td align="center">28.08</td>
<td align="center">K<sub>2</sub>O</td>
<td align="center">0.72</td>
</tr>
<tr>
<td align="center">SiO<sub>2</sub>
</td>
<td align="center">26.74</td>
<td align="center">MnO</td>
<td align="center">0.64</td>
</tr>
<tr>
<td align="center">TiO<sub>2</sub>
</td>
<td align="center">19.65</td>
<td align="center">Na<sub>2</sub>O</td>
<td align="center">0.53</td>
</tr>
<tr>
<td align="center">Al<sub>2</sub>O<sub>3</sub>
</td>
<td align="center">13.86</td>
<td align="center">F</td>
<td align="center">0.17</td>
</tr>
<tr>
<td align="center">MgO</td>
<td align="center">7.64</td>
<td align="center">BaO</td>
<td align="center">0.07</td>
</tr>
<tr>
<td align="center">SO<sub>3</sub>
</td>
<td align="center">1.05</td>
<td align="center">SrO</td>
<td align="center">0.04</td>
</tr>
<tr>
<td align="center">Fe<sub>2</sub>O<sub>3</sub>
</td>
<td align="center">0.79</td>
<td align="center">ZrO<sub>2</sub>
</td>
<td align="center">0.02</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>
<xref ref-type="fig" rid="F2">Figure 2</xref> shows the SEM and EDS results of TBFS. From <xref ref-type="fig" rid="F2">Figure 2A</xref>, it can be seen that the morphology of TBFS particles is an irregular structure with edges, smooth and dense surface, and uneven particle size. The EDS analysis was conducted on Ti, Mg, and Al elements in the A1 region. The distribution of each element is shown in <xref ref-type="fig" rid="F2">Figures 2B&#x2013;D</xref>. Ti, Mg, and Al elements are present on all visible particles and the enrichment zone boundary is not obvious, so the correlation between the three elements is well.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>SEM-EDS spectrum of TBFS <bold>(A)</bold> SEM of TBFS <bold>(B)</bold> Mg element distribution <bold>(C)</bold> Al element distribution <bold>(D)</bold> Ti element distribution.</p>
</caption>
<graphic xlink:href="fchem-12-1369937-g002.tif"/>
</fig>
<p>
<xref ref-type="fig" rid="F3">Figure 3</xref> shows the occurrence state of Ti, Mg and Al in TBFS determined by Tessier method. The percentage of Ti chemical form is residue state (58.5%) &#x3e; oxidation state (35.5%) &#x3e; organic state (4.8%) &#x3e; exchangeable state (1.2%) &#x3e; Ti carbonate state (0.0%). The percentage of Mg chemical form is residue state (91.3%) &#x3e; oxidation state (4.9%) &#x3e; organic state (1.5%) &#x3d; carbonate state (1.5%) &#x3e; exchangeable state (0.8%); The percentage of Al chemical form is residue state (96.2%) &#x3e; carbonate state (1.8%) &#x3e; organic state (1.4%) &#x3e; exchangeable state (0.6%) &#x3e; oxidation state (0.1%). The main occurrence of three components are residue state, indicating that their Chemical existence form is relatively stable.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Occurrence state of Ti, Mg and Al in TBFS <bold>(A)</bold> Ti; <bold>(B)</bold> Mg; <bold>(C)</bold> Al.</p>
</caption>
<graphic xlink:href="fchem-12-1369937-g003.tif"/>
</fig>
</sec>
<sec id="s2-2">
<title>2.2 Experimental procedure</title>
<p>
<list list-type="simple">
<list-item>
<p>a. Grind TBFS to the specific particle size shown in <xref ref-type="table" rid="T2">Table 2</xref>. Weigh the ground sample (10&#xa0;g) in a 100&#xa0;mL ceramic crucible with a lid and add concentrated sulfuric acid at the specific acid-slag mass ratio shown in <xref ref-type="table" rid="T2">Table 2</xref>.</p>
</list-item>
<list-item>
<p>b. After the acid and TBFS have been thoroughly mixed, the crucible is placed in a tubular program high-temperature furnace and the acidolysis reaction is carried out for a certain time at the specific temperature shown in <xref ref-type="table" rid="T2">Table 2</xref>. At the end of the reaction, the acidolysed slag was finely ground and 10&#xa0;g of the slag is placed in a 150&#xa0;mL conical flask, mixed with 60&#xa0;mL of deionised water and placed in a water bath at 60&#xb0;C with magnetic stirring at 20&#xa0;rpm for 60&#xa0;min.</p>
</list-item>
<list-item>
<p>c. After the water leaching, the leached slurry is vacuum filtered at 0.09&#xa0;MPa to separate the liquid from the solid and separated into leach residue and leachate. The content of Ti, Mg and Al in the leachate is determined by chemical titration and the percentages of components extracted (R) were calculated according to Eq. <xref ref-type="disp-formula" rid="e1">1</xref> (<xref ref-type="bibr" rid="B25">Shangguan et al., 2022a</xref>; <xref ref-type="bibr" rid="B18">Ma et al., 2023</xref>):</p>
</list-item>
</list>
<disp-formula id="e1">
<mml:math id="m1">
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>m</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>m</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>100</mml:mn>
<mml:mo>%</mml:mo>
</mml:mrow>
</mml:math>
<label>(1)</label>
</disp-formula>
</p>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>Design of kinetic experimental protocol.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Acidolysis temperature (&#xb0;C)</th>
<th align="center">Acid-slag ratio</th>
<th align="center">TBFS particle size (&#x3bc;m)</th>
<th align="center">Acidolysis time (min)</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">100, 110, 120, 130</td>
<td align="center">1.4</td>
<td align="center">Unclassified</td>
<td align="center">5, 10, 15, 20, 40, 60</td>
</tr>
<tr>
<td align="center">130</td>
<td align="center">1.0, 1.2, 1.4, 1.6</td>
<td align="center">Unclassified</td>
<td align="center">5, 10, 15, 20, 40, 60</td>
</tr>
<tr>
<td align="center">130</td>
<td align="center">1.4</td>
<td align="center">300, 200, 150, 74</td>
<td align="center">5, 10, 15, 20, 40, 60</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>Here, m<sub>1</sub> and m<sub>2</sub> are the total masses of Ti, Al, and Mg components in the TBFS and leachate, respectively.</p>
</sec>
</sec>
<sec sec-type="results|discussion" id="s3">
<title>3 Results and discussion</title>
<p>It can be seen from <xref ref-type="fig" rid="F1">Figure 1</xref> that the main phase of TBFS is an amorphous structure, and the analysis in <xref ref-type="fig" rid="F2">Figure 2</xref> shows the high correlation between occurrence of Ti, Mg, and Al. Therefore, Ti, Mg, and Al are considered as a whole to calculate the total extraction rate of the components in the dynamic simulation (<xref ref-type="bibr" rid="B19">Nie et al., 2020</xref>; <xref ref-type="bibr" rid="B21">Nie et al., 2023b</xref>). The correlation calculation is carried out by investigating the relationship between the total extraction rate and the acidolysis time at different reaction temperatures, acid-slag ratio, and raw material particle sizes. The acidolysis reaction of concentrated sulphuric acid with TBFS is a typical liquid-solid reaction. Since the surface of the TBFS particles is relatively dense, it can be considered a non-porous structure. The particles containing Ti, Mg and Al gradually shrank during the reaction, so the most suitable model for the reaction kinetic is the unreacted shrinking core model (<xref ref-type="bibr" rid="B1">Alkan and Do&#x11f;an, 2004</xref>; <xref ref-type="bibr" rid="B35">Zhang and Nicol, 2010</xref>; <xref ref-type="bibr" rid="B16">Liang et al., 2023a</xref>). The reaction started at the contact surface of concentrated H2SO4 and TBFS particles. The generated products (e.g., titanium sulphate) are wrapped around the surface of unreacted particles, and the H2SO4 diffused through the product layer to reach the unreacted interface to continue the acidolysis reaction. Thus, the overall rate of the reaction is affected by two steps: the internal diffusion step and the chemical reaction step (<xref ref-type="bibr" rid="B26">Sohn and Wadsworth, 2013</xref>; <xref ref-type="bibr" rid="B29">Wang et al., 2022b</xref>), the slower of which is the rate-controlling step during the acidolysis reaction process. <xref ref-type="table" rid="T3">Table 3</xref> shows the relationship between the extraction rate r and time t for the two control steps of the unreacted shrinking core model.</p>
<table-wrap id="T3" position="float">
<label>TABLE 3</label>
<caption>
<p>Integrated rate equation for unreacted shrinking core model.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Rate controlling step</th>
<th align="center">Rate equation</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">Internal diffusion</td>
<td align="center">1&#x2b;2(1 &#x2013; r) &#x2013; 3(1 &#x2013; r)<sup>2/3</sup> &#x3d; k<sub>r</sub>t</td>
</tr>
<tr>
<td align="center">Chemical reaction</td>
<td align="center">1 &#x2013; (1 &#x2013; r)<sup>1/3</sup> &#x3d; k<sub>r</sub>t</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>r: total extraction rate of Ti, Al or Mg; t: acidolysis time (min); kr: apparent rate constant.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<p>
<xref ref-type="fig" rid="F4">Figure 4</xref> shows the relationship between time and extraction rate at different acidolysis temperatures, acid-slag ratios and TBFS particle sizes. When the extraction rate tends to be stable, the acidolysis reaction is basically end, so only extraction rate before the end of acidolysis reaction can be used for calculation in the fitting calculation of the kinetic model. Therefore, the data before the reaction stabilizes in <xref ref-type="fig" rid="F4">Figure 4</xref> are fitted by substituting the equation in <xref ref-type="table" rid="T3">Table 3</xref> and the fitting results are shown in <xref ref-type="fig" rid="F5">Figures 5</xref>, <xref ref-type="fig" rid="F6">6</xref>. The kinetic fitting model is considered to be well fitted when the correlation coefficient (<italic>R</italic>
<sup>2</sup>) is greater than 0.85 (<xref ref-type="bibr" rid="B31">Wang et al., 2020</xref>; <xref ref-type="bibr" rid="B15">Li et al., 2023a</xref>), which shows that the <italic>R</italic>
<sup>2</sup> between the internal diffusion Equation <xref ref-type="disp-formula" rid="e1">(1)</xref> &#x2b; 2(1 &#x2013; r) &#x2013; 3(1 &#x2013; r)<sup>2/3</sup> and time t is greater than 0.85 for different acid-slag ratios, acidolysis temperatures and TBFS particle sizes. It can be assumed that the acidolysis reaction rate is mainly controlled by the internal diffusion of H<sub>2</sub>SO<sub>4</sub> in the product layer (<xref ref-type="bibr" rid="B36">Zhang et al., 2023</xref>). The related fitting equation and reaction rate constant k<sub>r</sub> are shown in <xref ref-type="table" rid="T4">Table 4</xref>.</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Variation in total extraction rate of components with acidolysis time under different process conditions: <bold>(A)</bold> acidolysis temperature; <bold>(B)</bold> acid-slag ratio; <bold>(C)</bold> TBFS particle size.</p>
</caption>
<graphic xlink:href="fchem-12-1369937-g004.tif"/>
</fig>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>The relationship between 1 &#x2b; 2(1 &#x2013; r) &#x2013; 3(1 &#x2013; r)<sup>2/3</sup> and t under different conditions: <bold>(A)</bold> acidolysis temperature, <bold>(B)</bold> acid-slag ratio and <bold>(C)</bold> TBFS particle size.</p>
</caption>
<graphic xlink:href="fchem-12-1369937-g005.tif"/>
</fig>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>The relationship between 1 &#x2013; (1 &#x2013; r)<sup>1/3</sup> and t under different conditions: <bold>(A)</bold> acidolysis temperature, <bold>(B)</bold> acid-slag ratio and <bold>(C)</bold> TBFS particle size.</p>
</caption>
<graphic xlink:href="fchem-12-1369937-g006.tif"/>
</fig>
<table-wrap id="T4" position="float">
<label>TABLE 4</label>
<caption>
<p>Fitting parameters of internal diffusion kinetic equations under different acidolysis conditions.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center"/>
<th align="center">Apparent rate <sup>constant</sup> k<sub>r</sub>
</th>
<th align="center">Fitting equation (t)</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">Acidolysis temperature (&#xb0;C)</td>
<td align="left"/>
<td align="left"/>
</tr>
<tr>
<td align="center">100</td>
<td align="center">0.01749</td>
<td align="center">1 &#x2b; 2(1 &#x2013; r) &#x2013; 3(1 &#x2013; <italic>r</italic>)<sup>2/3</sup> &#x3d; 0.00661</td>
</tr>
<tr>
<td align="center">110</td>
<td align="center">0.02064</td>
<td align="center">1 &#x2b; 2(1 &#x2013; r) &#x2013; 3(1 &#x2013; <italic>r</italic>)<sup>2/3</sup> &#x3d; 0.00914</td>
</tr>
<tr>
<td align="center">120</td>
<td align="center">0.02568</td>
<td align="center">1 &#x2b; 2(1 &#x2013; r) &#x2013; 3(1 &#x2013; <italic>r</italic>)<sup>2/3</sup> &#x3d; 0.02568</td>
</tr>
<tr>
<td align="center">130</td>
<td align="center">0.02697</td>
<td align="center">1 &#x2b; 2(1 &#x2013; r) &#x2013; 3(1 &#x2013; <italic>r</italic>)<sup>2/3</sup> &#x3d; 0.02985</td>
</tr>
<tr>
<td align="center">Acid-slag ratio (g&#xb7;g<sup>&#x2013;1</sup>)</td>
<td align="left"/>
<td align="left"/>
</tr>
<tr>
<td align="center">1.0</td>
<td align="center">0.00611</td>
<td align="center">1 &#x2b; 2(1 &#x2013; r) &#x2013; 3(1 &#x2013; <italic>r</italic>)<sup>2/3</sup> &#x3d; 0.00611</td>
</tr>
<tr>
<td align="center">1.2</td>
<td align="center">0.00822</td>
<td align="center">1 &#x2b; 2(1 &#x2013; r) &#x2013; 3(1 &#x2013; <italic>r</italic>)<sup>2/3</sup> &#x3d; 0.00822</td>
</tr>
<tr>
<td align="center">1.4</td>
<td align="center">0.02697</td>
<td align="center">1 &#x2b; 2(1 &#x2013; r) &#x2013; 3(1 &#x2013; <italic>r</italic>)<sup>2/3</sup> &#x3d; 0.02697</td>
</tr>
<tr>
<td align="center">1.6</td>
<td align="center">0.03067</td>
<td align="center">1 &#x2b; 2(1 &#x2013; r) &#x2013; 3(1 &#x2013; <italic>r</italic>)<sup>2/3</sup> &#x3d; 0.03067</td>
</tr>
<tr>
<td align="center">TBFS particle size (&#x3bc;m)</td>
<td align="left"/>
<td align="left"/>
</tr>
<tr>
<td align="center">300</td>
<td align="center">0.00854</td>
<td align="center">1 &#x2b; 2(1 &#x2013; r) &#x2013; 3(1 &#x2013; <italic>r</italic>)<sup>2/3</sup> &#x3d; 0.00854</td>
</tr>
<tr>
<td align="center">200</td>
<td align="center">0.00916</td>
<td align="center">1 &#x2b; 2(1 &#x2013; r) &#x2013; 3(1 &#x2013; <italic>r</italic>)<sup>2/3</sup> &#x3d; 0.00916</td>
</tr>
<tr>
<td align="center">150</td>
<td align="center">0.01163</td>
<td align="center">1 &#x2b; 2(1 &#x2013; r) &#x2013; 3(1 &#x2013; <italic>r</italic>)<sup>2/3</sup> &#x3d; 0.02098</td>
</tr>
<tr>
<td align="center">74</td>
<td align="center">0.01461</td>
<td align="center">1 &#x2b; 2(1 &#x2013; r) &#x2013; 3(1 &#x2013; <italic>r</italic>)<sup>2/3</sup> &#x3d; 0.01461</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>The apparent rate constant kr is influenced by the acidolysis temperature, the concentration of acidolysis solution in the reaction system and the feedstock radius, as shown in empirical Eq. <xref ref-type="disp-formula" rid="e2">2</xref> (<xref ref-type="bibr" rid="B32">Wang et al., 2013</xref>). Combined with the acidolysis conditions in this paper, this is translated into Eq. <xref ref-type="disp-formula" rid="e3">3</xref> to include the acid-slag ratio and TBFS particle size (<xref ref-type="bibr" rid="B14">Li et al., 2023b</xref>; <xref ref-type="bibr" rid="B17">Liang et al., 2023b</xref>).<disp-formula id="e2">
<mml:math id="m2">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>r</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>k</mml:mi>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c1;</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:msub>
<mml:mi>r</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(2)</label>
</disp-formula>
<disp-formula id="e3">
<mml:math id="m3">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>r</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>1.62</mml:mn>
<mml:mi>x</mml:mi>
<mml:mi>k</mml:mi>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:msub>
<mml:mi>&#x3c1;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>r</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1.62</mml:mn>
<mml:mi>x</mml:mi>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:msub>
<mml:mi>&#x3c1;</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:msub>
<mml:mi>&#x3c1;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(3)</label>
</disp-formula>
</p>
<p>Here, kr is the apparent rate constant, x is the acid-slag ratio, k is the temperature-dependent reaction rate constant, C2 is the concentration of concentrated sulphuric acid in the reaction system (the ratio of the molar concentration of sulphuric acid), M1 is the molar mass of TBFS,&#x3c1;2 is the density of the concentrated sulphuric acid, r1 is the radius of TBFS particles (mm); M2 is the molar mass of the concentrated sulphuric acid and&#x3c1;1 is the density of TBFS.</p>
<p>The relationship between kr and the acidolysis temperature follows the Arrhenius Eq. <xref ref-type="disp-formula" rid="e4">4</xref>. The logarithm of both sides of the equation is taken to obtain Eq. <xref ref-type="disp-formula" rid="e5">5</xref> (<xref ref-type="bibr" rid="B24">Shangguan et al., 2022b</xref>; <xref ref-type="bibr" rid="B28">Wang et al., 2022c</xref>).<disp-formula id="e4">
<mml:math id="m4">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>r</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>A</mml:mi>
<mml:msup>
<mml:mi>e</mml:mi>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mi>a</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:mi>R</mml:mi>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
<label>(4)</label>
</disp-formula>
<disp-formula id="e5">
<mml:math id="m5">
<mml:mrow>
<mml:mi>ln</mml:mi>
<mml:mo>&#x2061;</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>r</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mo>&#x2212;</mml:mo>
<mml:mfrac>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mi>a</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>l</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>A</mml:mi>
</mml:mrow>
</mml:math>
<label>(5)</label>
</disp-formula>
</p>
<p>Here, kr is the apparent rate constant, A is the frequency factor, Ea is the apparent activation energy (J&#xb7;mol&#x2013;1), R is the molar gas constant (8.314&#xa0;J&#xa0;mol&#x2013;1) and T is the acidolysis temperature.</p>
<p>According to the data in<xref ref-type="table" rid="T4">Table 4</xref>, the relationship between lnkr and 1/T is plotted. As shown in <xref ref-type="fig" rid="F6">Figure 6A</xref>, the apparent activation energy of the acidolysis reaction is estimated to be 19.05&#xa0;kJ&#xa0;mol&#x2013;1 based on the slope of the straight line in Eqs<xref ref-type="disp-formula" rid="e4">s 4, and A</xref> was estimated as 8.23 based on the intercept. It is generally accepted that higher activation energies (&#x3e;40&#xa0;kJ&#xa0;mol<sup>&#x2013;1</sup>) indicate chemical control, while activation energies of &#x3c;20&#xa0;kJ&#xa0;mol<sup>&#x2013;1</sup> indicate diffusion-controlled processes (<xref ref-type="bibr" rid="B2">Habashi, 1980</xref>; <xref ref-type="bibr" rid="B23">Santos et al., 2010</xref>). Thus, these results further indicated that the acidolysis process is consistent with internal diffusion control. The relationship between k r and the acidolysis temperature T could be expressed as Eq. <xref ref-type="disp-formula" rid="e6">6</xref>.<disp-formula id="e6">
<mml:math id="m6">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>r</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>8.23</mml:mn>
<mml:msup>
<mml:mi>e</mml:mi>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>19050</mml:mn>
<mml:mo>/</mml:mo>
<mml:mi>R</mml:mi>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
<label>(6)</label>
</disp-formula>
</p>
<p>When <inline-formula id="inf1">
<mml:math id="m7">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>r</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mi>k</mml:mi>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
</inline-formula> is replaced by constant A1, Eq. <xref ref-type="disp-formula" rid="e3">3</xref> is transformed into an equation relating kr to the acid-slag ratio x by taking the reciprocal and then the logarithm of both sides, as shown in <xref ref-type="disp-formula" rid="e7">Eq. 7</xref>
<sup>.</sup>
<disp-formula id="e7">
<mml:math id="m8">
<mml:mrow>
<mml:mi mathvariant="italic">ln</mml:mi>
<mml:mo>&#x2061;</mml:mo>
<mml:msubsup>
<mml:mi>k</mml:mi>
<mml:mi>r</mml:mi>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msubsup>
<mml:mo>&#x3d;</mml:mo>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>ln</mml:mi>
<mml:mo>&#x2061;</mml:mo>
<mml:msub>
<mml:mi>A</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mo>&#x2061;</mml:mo>
<mml:mi mathvariant="italic">ln</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c1;</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c1;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mn>1</mml:mn>
<mml:mrow>
<mml:mn>1.62</mml:mn>
<mml:mi>x</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(7)</label>
</disp-formula>
</p>
<p>The relationship between lnk<sub>r</sub> and <inline-formula id="inf2">
<mml:math id="m9">
<mml:mrow>
<mml:mi mathvariant="italic">ln</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c1;</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c1;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mn>1</mml:mn>
<mml:mrow>
<mml:mn>1.62</mml:mn>
<mml:mi>x</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> is shown in <xref ref-type="fig" rid="F6">Figure 6B</xref>. The slope of the fitted line is 9.80201, so the relationship between k<sub>r</sub> and x can be expressed as Eq. <xref ref-type="disp-formula" rid="e8">8</xref>.<disp-formula id="e8">
<mml:math id="m10">
<mml:mrow>
<mml:msubsup>
<mml:mi>k</mml:mi>
<mml:mi>r</mml:mi>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msubsup>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>A</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c1;</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c1;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mn>1</mml:mn>
<mml:mrow>
<mml:mn>1.62</mml:mn>
<mml:mi>x</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mn>9.80201</mml:mn>
</mml:msup>
</mml:mrow>
</mml:math>
<label>(8)</label>
</disp-formula>
</p>
<p>When <inline-formula id="inf3">
<mml:math id="m11">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mn>1.62</mml:mn>
<mml:mi>x</mml:mi>
<mml:mi>k</mml:mi>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:msub>
<mml:mi>&#x3c1;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1.62</mml:mn>
<mml:mi>x</mml:mi>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:msub>
<mml:mi>&#x3c1;</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:msub>
<mml:mi>&#x3c1;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
</inline-formula> is replaced by the constant A<sub>2</sub>, Eq. <xref ref-type="disp-formula" rid="e3">3</xref> can be converted into Eq. <xref ref-type="disp-formula" rid="e9">9</xref>.<disp-formula id="e9">
<mml:math id="m12">
<mml:mrow>
<mml:mi mathvariant="italic">ln</mml:mi>
<mml:mo>&#x2061;</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>r</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>ln</mml:mi>
<mml:mo>&#x2061;</mml:mo>
<mml:msub>
<mml:mi>A</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:mo>&#x2061;</mml:mo>
<mml:mi mathvariant="italic">ln</mml:mi>
<mml:mo>&#x2061;</mml:mo>
<mml:msub>
<mml:mi>r</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
<label>(9)</label>
</disp-formula>
</p>
<p>
<xref ref-type="fig" rid="F7">Figure 7C</xref> shows the relationship between lnk<sub>r</sub> and lnr<sub>1</sub>. The slope of the fitted line is &#x2212;0.40437, so the relationship between k<sub>r</sub> and r<sub>1</sub> can be expressed as Eq. <xref ref-type="disp-formula" rid="e10">10</xref>.<disp-formula id="e10">
<mml:math id="m13">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>r</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>A</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msubsup>
<mml:mi>r</mml:mi>
<mml:mn>1</mml:mn>
<mml:mn>0.40437</mml:mn>
</mml:msubsup>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(10)</label>
</disp-formula>
</p>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>Plot of k<sub>r</sub> <italic>versus</italic> different process parameters: <bold>(A)</bold> acidolysis temperature; <bold>(B)</bold> acid-slag ratio; <bold>(C)</bold> TBFS particle radius.</p>
</caption>
<graphic xlink:href="fchem-12-1369937-g007.tif"/>
</fig>
<p>Combining Eqs <xref ref-type="disp-formula" rid="e6">6</xref>, <xref ref-type="disp-formula" rid="e8">8</xref>, <xref ref-type="disp-formula" rid="e10">10</xref>, the semi-empirical kinetic equations related to the acid-slag ratio, acidolysis temperature, TBFS particle radius and k<sub>r</sub> are established as follows.<disp-formula id="equ1">
<mml:math id="m14">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>r</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>k</mml:mi>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>r</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c1;</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c1;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mn>1</mml:mn>
<mml:mrow>
<mml:mn>1.62</mml:mn>
<mml:mi>x</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>k</mml:mi>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msubsup>
<mml:mi>r</mml:mi>
<mml:mn>1</mml:mn>
<mml:mn>0.40437</mml:mn>
</mml:msubsup>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c1;</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c1;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mn>1</mml:mn>
<mml:mrow>
<mml:mn>1.62</mml:mn>
<mml:mi>x</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>9.80201</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</disp-formula>
<disp-formula id="equ2">
<mml:math id="m15">
<mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mrow>
<mml:msubsup>
<mml:mi>r</mml:mi>
<mml:mn>1</mml:mn>
<mml:mn>0.40437</mml:mn>
</mml:msubsup>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c1;</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c1;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mn>1</mml:mn>
<mml:mrow>
<mml:mn>1.62</mml:mn>
<mml:mi>x</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>9.80201</mml:mn>
</mml:mrow>
</mml:msup>
<mml:msub>
<mml:mi>A</mml:mi>
<mml:mn>3</mml:mn>
</mml:msub>
<mml:msup>
<mml:mi>e</mml:mi>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mi>a</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:mi>R</mml:mi>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</disp-formula>
<disp-formula id="equ3">
<mml:math id="m16">
<mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mrow>
<mml:msubsup>
<mml:mi>r</mml:mi>
<mml:mn>1</mml:mn>
<mml:mn>0.40437</mml:mn>
</mml:msubsup>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c1;</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c1;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mn>1</mml:mn>
<mml:mrow>
<mml:mn>1.62</mml:mn>
<mml:mi>x</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>9.80201</mml:mn>
</mml:mrow>
</mml:msup>
<mml:msub>
<mml:mi>A</mml:mi>
<mml:mn>3</mml:mn>
</mml:msub>
<mml:msup>
<mml:mi>e</mml:mi>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>19050</mml:mn>
<mml:mo>/</mml:mo>
<mml:mi>R</mml:mi>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</disp-formula>
<disp-formula id="equ4">
<mml:math id="m17">
<mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c1;</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c1;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mn>1</mml:mn>
<mml:mrow>
<mml:mn>1.62</mml:mn>
<mml:mi>x</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>9.80201</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
<mml:mrow>
<mml:msubsup>
<mml:mi>r</mml:mi>
<mml:mn>1</mml:mn>
<mml:mn>0.40437</mml:mn>
</mml:msubsup>
</mml:mrow>
</mml:mfrac>
<mml:msup>
<mml:mi>A</mml:mi>
<mml:mo>&#x2032;</mml:mo>
</mml:msup>
<mml:msup>
<mml:mi>e</mml:mi>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>19050</mml:mn>
<mml:mo>/</mml:mo>
<mml:mi>R</mml:mi>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</disp-formula>
</p>
<p>Here, A<sub>3</sub> is the frequency factor and <inline-formula id="inf4">
<mml:math id="m18">
<mml:mrow>
<mml:msup>
<mml:mi>A</mml:mi>
<mml:mo>&#x2032;</mml:mo>
</mml:msup>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:msub>
<mml:mi>A</mml:mi>
<mml:mn>3</mml:mn>
</mml:msub>
</mml:mrow>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mfrac>
</mml:mrow>
</mml:math>
</inline-formula> .</p>
<p>Since <inline-formula id="inf5">
<mml:math id="m19">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>r</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>8.23</mml:mn>
<mml:msup>
<mml:mi>e</mml:mi>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>19050</mml:mn>
<mml:mo>/</mml:mo>
<mml:mi>R</mml:mi>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula>, so <inline-formula id="inf6">
<mml:math id="m20">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c1;</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c1;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mn>1</mml:mn>
<mml:mrow>
<mml:mn>1.62</mml:mn>
<mml:mi>x</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>9.80201</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
<mml:mrow>
<mml:msubsup>
<mml:mi>r</mml:mi>
<mml:mn>1</mml:mn>
<mml:mn>0.40437</mml:mn>
</mml:msubsup>
</mml:mrow>
</mml:mfrac>
<mml:msup>
<mml:mi>A</mml:mi>
<mml:mo>&#x2032;</mml:mo>
</mml:msup>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>8.2</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>. Substituting &#x3c1;<sub>1</sub> &#x3d; 1.429, &#x3c1;<sub>2</sub> &#x3d; 1.84 and the process parameters with the best fit to the internal diffusion control equation; that is, x &#x3d; 1.6 and r<sub>1</sub> &#x3d; 75 &#xd7; 10<sup>&#x2212;6</sup>&#xa0;m, it is calculated that <inline-formula id="inf7">
<mml:math id="m21">
<mml:mrow>
<mml:msup>
<mml:mi>A</mml:mi>
<mml:mo>&#x2032;</mml:mo>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 77.29 &#xd7; 10<sup>&#x2212;2</sup>. Therefore, the kinetic equation could be shown as Eq. <xref ref-type="disp-formula" rid="e11">11</xref>.<disp-formula id="e11">
<mml:math id="m22">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>2</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mi mathvariant="normal">r</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>3</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mi mathvariant="normal">r</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:mfrac>
</mml:msup>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mn>1.02</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>0.78</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mn>1</mml:mn>
<mml:mrow>
<mml:mn>1.62</mml:mn>
<mml:mi>x</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>9.80201</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
<mml:mrow>
<mml:msubsup>
<mml:mi>d</mml:mi>
<mml:mn>1</mml:mn>
<mml:mn>0.40437</mml:mn>
</mml:msubsup>
</mml:mrow>
</mml:mfrac>
<mml:msup>
<mml:mi>e</mml:mi>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>19050</mml:mn>
<mml:mo>/</mml:mo>
<mml:mi>R</mml:mi>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:msup>
<mml:mo>&#xd7;</mml:mo>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:math>
<label>(11)</label>
</disp-formula>
</p>
<p>Here, x is the acid-slag ratio, d<sub>1</sub> is the TBFS particle size (m), R is the molar gas constant (R &#x3d; 8.314&#xa0;J&#xa0;mol<sup>&#x2013;1</sup>) and T is the acidolysis temperature (K).</p>
<p>The data in <xref ref-type="fig" rid="F4">Figure 4</xref> are substituted into the left-hand side of Eq. <xref ref-type="disp-formula" rid="e11">11</xref> and the corresponding values of the relevant process parameters are substituted into the right-hand side of Eq. <xref ref-type="disp-formula" rid="e11">11</xref> for comparative analysis. <xref ref-type="fig" rid="F8">Figure 8</xref> shows the results of the comparison between experimental and fitted values, which are in good correlation with each other. This indicates that the derived kinetic equations are valuable in reflecting the actual situation.</p>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>Comparison of experimental results and fitted results.</p>
</caption>
<graphic xlink:href="fchem-12-1369937-g008.tif"/>
</fig>
<p>Under the conditions of average particle size of 150&#xa0;&#x3bc;m, acid/solid ratio of 1.4, acidolysis temperature of 300&#xb0;C, and acidolysisi time of 40 min, the extraction rates of Ti, Mg, and Al reached 82.85%, 93.16%, and 96.96%, respectively. The chemical analysis and XRD of the leached residue are shown in <xref ref-type="table" rid="T5">Table 5</xref> and <xref ref-type="fig" rid="F9">Figure 9</xref>. After acidolysis with sulfuric acid and leaching with deionized water, the main elements in residual are S, Si, and Ca, with Ca mainly present in the form of gypsum.</p>
<table-wrap id="T5" position="float">
<label>TABLE 5</label>
<caption>
<p>Chemical composition of the leaching resides with titanium leaching rate at 82.5%.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Compound</th>
<th align="center">wt%</th>
<th align="center">Compound</th>
<th align="center">wt%</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">SO<sub>3</sub>
</td>
<td align="center">36.84</td>
<td align="center">K<sub>2</sub>O</td>
<td align="center">0.12</td>
</tr>
<tr>
<td align="center">SiO<sub>2</sub>
</td>
<td align="center">31.09</td>
<td align="center">MnO</td>
<td align="center">0.09</td>
</tr>
<tr>
<td align="center">CaO</td>
<td align="center">24.38</td>
<td align="center">Na<sub>2</sub>O</td>
<td align="center">0.07</td>
</tr>
<tr>
<td align="center">TiO<sub>2</sub>
</td>
<td align="center">5.26</td>
<td align="center">BaO</td>
<td align="center">0.05</td>
</tr>
<tr>
<td align="center">Al<sub>2</sub>O<sub>3</sub>
</td>
<td align="center">1.24</td>
<td align="center">SrO</td>
<td align="center">0.03</td>
</tr>
<tr>
<td align="center">MgO</td>
<td align="center">0.58</td>
<td align="center">ZrO<sub>2</sub>
</td>
<td align="center">0.01</td>
</tr>
<tr>
<td align="center">Fe<sub>2</sub>O<sub>3</sub>
</td>
<td align="center">0.25</td>
<td align="left"/>
<td align="left"/>
</tr>
</tbody>
</table>
</table-wrap>
<fig id="F9" position="float">
<label>FIGURE 9</label>
<caption>
<p>XRD patterns of water leached residues.</p>
</caption>
<graphic xlink:href="fchem-12-1369937-g009.tif"/>
</fig>
</sec>
<sec sec-type="conclusion" id="s4">
<title>4 Conclusion</title>
<p>
<list list-type="simple">
<list-item>
<p>a. The chemical composition of TBFS is complex, with the main chemical componets are CaO, SiO<sub>2</sub>, TiO<sub>2</sub>, Al<sub>2</sub>O<sub>3</sub>, and MgO. There is a certain correlation and close connection between different elements in TBFS, and the main mineral phase of TBFS is perovskite, and there are also some amorphous structures.</p>
</list-item>
<list-item>
<p>b. The acidolysis temperature, acid-slag ratio and TBFS particle size are positively correlated with the extraction rate of TBFS, with the higher the value of these three variables, the higher the extraction rate.</p>
</list-item>
<list-item>
<p>c. The acidolysis process is consistent with the &#x2018;unreacted shrinking core model&#x2019; and the reaction rate is controlled by internal diffusion through the solid product layer.</p>
</list-item>
<list-item>
<p>d. The apparent activation energy of the acidolysis reaction is calculated by the Arrhenius equation as 19.05&#xa0;kJ&#xa0;mol<sup>&#x2013;1</sup> and the kinetic equation is:</p>
</list-item>
</list>
<disp-formula id="equ5">
<mml:math id="m23">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>2</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mi mathvariant="normal">r</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>3</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mi mathvariant="normal">r</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:mfrac>
</mml:msup>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mn>1.02</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>0.78</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mn>1</mml:mn>
<mml:mrow>
<mml:mn>1.62</mml:mn>
<mml:mi>x</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>9.80201</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
<mml:mrow>
<mml:msubsup>
<mml:mi>d</mml:mi>
<mml:mn>1</mml:mn>
<mml:mn>0.40437</mml:mn>
</mml:msubsup>
</mml:mrow>
</mml:mfrac>
<mml:msup>
<mml:mi>e</mml:mi>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>19050</mml:mn>
<mml:mo>/</mml:mo>
<mml:mi>R</mml:mi>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</disp-formula>
</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 authors.</p>
</sec>
<sec id="s6">
<title>Author contributions</title>
<p>YW: Conceptualization, Data curation, Writing&#x2013;original draft, Writing&#x2013;review and editing. SH: Conceptualization, Data curation, Formal Analysis, Writing&#x2013;review and editing. XG: Conceptualization, Data curation, Formal Analysis, Investigation, Software, Writing&#x2013;review and editing. JG: Conceptualization, Data curation, Writing&#x2013;review and editing.</p>
</sec>
<sec sec-type="funding-information" id="s7">
<title>Funding</title>
<p>The author(s) declare financial support was received for the research, authorship, and/or publication of this article. Financial support for this research was provided by the Sichuan Science Provinces Science and Technology Support Program (2022NSFSC1072) and the Research Foundation of Mianyang Normal University (QD 2021A06). National Natural Science Foundation of China (42272042).</p>
</sec>
<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>
<ref-list>
<title>References</title>
<ref id="B1">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Alkan</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Do&#x11f;an</surname>
<given-names>M.</given-names>
</name>
</person-group> (<year>2004</year>). <article-title>Dissolution kinetics of colemanite in oxalic acid solutions</article-title>. <source>Chem. Eng. Process. Process Intensif.</source> <volume>43</volume> (<issue>7</issue>), <fpage>867</fpage>&#x2013;<lpage>872</lpage>. <pub-id pub-id-type="doi">10.1016/s0255-2701(03)00108-9</pub-id>
</citation>
</ref>
<ref id="B2">
<citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname>Habashi</surname>
<given-names>F.</given-names>
</name>
</person-group> (<year>1980</year>). <source>Principles of extractive metallurgy. General Principles</source>, <volume>1</volume>. <publisher-loc>New York</publisher-loc>: <publisher-name>Gordon and Breach</publisher-name>.</citation>
</ref>
<ref id="B3">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>He</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Peng</surname>
<given-names>T.</given-names>
</name>
<name>
<surname>Sun</surname>
<given-names>H.</given-names>
</name>
</person-group> (<year>2019</year>). <article-title>Titanium recovery from Ti-bearing blast furnace slag by alkali calcination and acidolysis</article-title>. <source>Jom</source> <volume>71</volume> (<issue>9</issue>), <fpage>3196</fpage>&#x2013;<lpage>3201</lpage>. <pub-id pub-id-type="doi">10.1007/s11837-019-03575-9</pub-id>
</citation>
</ref>
<ref id="B4">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>He</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>Y.</given-names>
</name>
</person-group> (<year>2023</year>). <article-title>Extraction of valuable components from Ti-bearing blast furnace slag using sulfuric acid calcination process</article-title>. <source>JOM</source> <volume>75</volume> (<issue>2</issue>), <fpage>392</fpage>&#x2013;<lpage>399</lpage>. <pub-id pub-id-type="doi">10.1007/s11837-022-05557-w</pub-id>
</citation>
</ref>
<ref id="B5">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Hongjuan</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Guobiao</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Tongjiang</surname>
<given-names>P.</given-names>
</name>
<name>
<surname>Xiao</surname>
<given-names>W.</given-names>
</name>
<name>
<surname>Siqi</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Fan</surname>
<given-names>Z.</given-names>
</name>
</person-group> (<year>2015</year>). <article-title>Recovery of titanium from titanium-rich product prepared from high ti-bearing blast furnace slag by sulfuric acid leaching</article-title>. <source>Min. metallurgy</source> <volume>24</volume> (<issue>3</issue>), <fpage>54</fpage>&#x2013;<lpage>58</lpage>.</citation>
</ref>
<ref id="B6">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Huang</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>R.</given-names>
</name>
</person-group> (<year>1994</year>). <article-title>Pilot test of carbonization of the molten blast furnace TiO2 slag at PanZhiHua iron and steel company</article-title>. <source>Iron Steel Vanadium Titan.</source> <volume>15</volume> (<issue>2</issue>), <fpage>17</fpage>&#x2013;<lpage>21</lpage>.</citation>
</ref>
<ref id="B7">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Huang</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Liu</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Hu</surname>
<given-names>W.</given-names>
</name>
<name>
<surname>Ni</surname>
<given-names>W.</given-names>
</name>
</person-group> (<year>2016</year>). <article-title>On the use of blast furnace slag and steel slag in the preparation of green artificial reef concrete</article-title>. <source>Constr. Build. Mater.</source> <volume>112</volume>, <fpage>241</fpage>&#x2013;<lpage>246</lpage>. <pub-id pub-id-type="doi">10.1016/j.conbuildmat.2016.02.088</pub-id>
</citation>
</ref>
<ref id="B8">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Jiang</surname>
<given-names>T.</given-names>
</name>
<name>
<surname>Dong</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Guo</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>G.</given-names>
</name>
<name>
<surname>Yang</surname>
<given-names>Y.</given-names>
</name>
</person-group> (<year>2010</year>). <article-title>Study on leaching Ti from Ti bearing blast furnace slag by sulphuric acid</article-title>. <source>Mineral Process. Extr. Metallurgy</source> <volume>119</volume> (<issue>1</issue>), <fpage>33</fpage>&#x2013;<lpage>38</lpage>. <pub-id pub-id-type="doi">10.1179/037195509x12585446038807</pub-id>
</citation>
</ref>
<ref id="B9">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Ju</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Feng</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Wu</surname>
<given-names>R.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>B.</given-names>
</name>
</person-group> (<year>2022</year>). <article-title>An approach towards utilization of water-quenched blast furnace slag for recovery of titanium, magnesium, and aluminum</article-title>. <source>J. Environ. Chem. Eng.</source> <volume>10</volume> (<issue>4</issue>), <fpage>108153</fpage>. <pub-id pub-id-type="doi">10.1016/j.jece.2022.108153</pub-id>
</citation>
</ref>
<ref id="B10">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Kuwahara</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Ohmichi</surname>
<given-names>T.</given-names>
</name>
<name>
<surname>Kamegawa</surname>
<given-names>T.</given-names>
</name>
<name>
<surname>Mori</surname>
<given-names>K.</given-names>
</name>
<name>
<surname>Yamashita</surname>
<given-names>H.</given-names>
</name>
</person-group> (<year>2010</year>). <article-title>A novel conversion process for waste slag: synthesis of a hydrotalcite-like compound and zeolite from blast furnace slag and evaluation of adsorption capacities</article-title>. <source>J. Mater. Chem.</source> <volume>20</volume> (<issue>24</issue>), <fpage>5052</fpage>&#x2013;<lpage>5062</lpage>. <pub-id pub-id-type="doi">10.1039/c0jm00518e</pub-id>
</citation>
</ref>
<ref id="B11">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Li</surname>
<given-names>W. X.</given-names>
</name>
<name>
<surname>Liu</surname>
<given-names>M. S.</given-names>
</name>
<name>
<surname>Cheng</surname>
<given-names>S. B.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>H. F.</given-names>
</name>
<name>
<surname>Yang</surname>
<given-names>W. X.</given-names>
</name>
<name>
<surname>Yi</surname>
<given-names>Z.</given-names>
</name>
<etal/>
</person-group> (<year>2024a</year>). <article-title>Polarization independent tunable bandwidth absorber based on single-layer graphene</article-title>. <source>Diam. Relat. Mater.</source> <volume>142</volume>, <fpage>110793</fpage>. <pub-id pub-id-type="doi">10.1016/j.diamond.2024.110793</pub-id>
</citation>
</ref>
<ref id="B12">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Li</surname>
<given-names>W. X.</given-names>
</name>
<name>
<surname>Ma</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>H. F.</given-names>
</name>
<name>
<surname>Cheng</surname>
<given-names>S. B.</given-names>
</name>
<name>
<surname>Yang</surname>
<given-names>W. X.</given-names>
</name>
<name>
<surname>Yi</surname>
<given-names>Z.</given-names>
</name>
<etal/>
</person-group> (<year>2023c</year>). <article-title>Tunable broadband absorber based on a layered resonant structure with a Dirac semimetal</article-title>. <source>Phys. Chem. Chem. Phys.</source> <volume>25</volume>, <fpage>8489</fpage>&#x2013;<lpage>8496</lpage>. <pub-id pub-id-type="doi">10.1039/d2cp05562g</pub-id>
</citation>
</ref>
<ref id="B13">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Li</surname>
<given-names>W. X.</given-names>
</name>
<name>
<surname>Xu</surname>
<given-names>F.</given-names>
</name>
<name>
<surname>Cheng</surname>
<given-names>S. B.</given-names>
</name>
<name>
<surname>Yang</surname>
<given-names>W. X.</given-names>
</name>
<name>
<surname>Liu</surname>
<given-names>B.</given-names>
</name>
<name>
<surname>Liu</surname>
<given-names>M. S.</given-names>
</name>
<etal/>
</person-group> (<year>2024b</year>). <article-title>Six-band rotationally symmetric tunable absorption film based on AlCuFe quasicrystals</article-title>. <source>Opt. Laser Technol.</source> <volume>169</volume>, <fpage>110186</fpage>. <pub-id pub-id-type="doi">10.1016/j.optlastec.2023.110186</pub-id>
</citation>
</ref>
<ref id="B14">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Li</surname>
<given-names>W. X.</given-names>
</name>
<name>
<surname>Yi</surname>
<given-names>Y. T.</given-names>
</name>
<name>
<surname>Yang</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Cheng</surname>
<given-names>S. B.</given-names>
</name>
<name>
<surname>Yang</surname>
<given-names>W. X.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>H. F.</given-names>
</name>
<etal/>
</person-group> (<year>2023b</year>). <article-title>Active tunable terahertz bandwidth absorber based on single layer graphene</article-title>. <source>Commun. Theor. Phys.</source> <volume>75</volume>, <fpage>045503</fpage>. <pub-id pub-id-type="doi">10.1088/1572-9494/acbe2d</pub-id>
</citation>
</ref>
<ref id="B15">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Li</surname>
<given-names>W. X.</given-names>
</name>
<name>
<surname>Zhao</surname>
<given-names>W. C.</given-names>
</name>
<name>
<surname>Cheng</surname>
<given-names>S. B.</given-names>
</name>
<name>
<surname>Yang</surname>
<given-names>W. X.</given-names>
</name>
<name>
<surname>Yi</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>G. F.</given-names>
</name>
<etal/>
</person-group> (<year>2023a</year>). <article-title>Terahertz selective active electromagnetic absorption film based on single-layer graphene</article-title>. <source>Surfaces Interfaces</source> <volume>40</volume>, <fpage>103042</fpage>. <pub-id pub-id-type="doi">10.1016/j.surfin.2023.103042</pub-id>
</citation>
</ref>
<ref id="B16">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Liang</surname>
<given-names>S. R.</given-names>
</name>
<name>
<surname>Xu</surname>
<given-names>F.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>W. X.</given-names>
</name>
<name>
<surname>Yang</surname>
<given-names>W. X.</given-names>
</name>
<name>
<surname>Cheng</surname>
<given-names>S. B.</given-names>
</name>
<name>
<surname>Yang</surname>
<given-names>H.</given-names>
</name>
<etal/>
</person-group> (<year>2023a</year>). <article-title>Tunable smart mid infrared thermal control emitter based on phase change material VO2 thin film</article-title>. <source>Appl. Therm. Eng.</source> <volume>232</volume>, <fpage>121074</fpage>. <pub-id pub-id-type="doi">10.1016/j.applthermaleng.2023.121074</pub-id>
</citation>
</ref>
<ref id="B17">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Liang</surname>
<given-names>S. R.</given-names>
</name>
<name>
<surname>Xu</surname>
<given-names>F.</given-names>
</name>
<name>
<surname>Yang</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Cheng</surname>
<given-names>S. B.</given-names>
</name>
<name>
<surname>Yang</surname>
<given-names>W. X.</given-names>
</name>
<name>
<surname>Yi</surname>
<given-names>Z.</given-names>
</name>
<etal/>
</person-group> (<year>2023b</year>). <article-title>Ultra long infrared metamaterial absorber with high absorption and broad band based on nano cross surrounding</article-title>. <source>Opt. Laser Technol.</source> <volume>158</volume>, <fpage>108789</fpage>. <pub-id pub-id-type="doi">10.1016/j.optlastec.2022.108789</pub-id>
</citation>
</ref>
<ref id="B18">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Ma</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Wu</surname>
<given-names>P. H.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>W. X.</given-names>
</name>
<name>
<surname>Liang</surname>
<given-names>S. R.</given-names>
</name>
<name>
<surname>Shangguan</surname>
<given-names>Q. Y.</given-names>
</name>
<name>
<surname>Cheng</surname>
<given-names>S. B.</given-names>
</name>
<etal/>
</person-group> (<year>2023</year>). <article-title>A five-peaks graphene absorber with multiple adjustable and high sensitivity in the far infrared band</article-title>. <source>Diam. Relat. Mater.</source> <volume>136</volume>, <fpage>109960</fpage>. <pub-id pub-id-type="doi">10.1016/j.diamond.2023.109960</pub-id>
</citation>
</ref>
<ref id="B19">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Nie</surname>
<given-names>W.</given-names>
</name>
<name>
<surname>Wen</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Feng</surname>
<given-names>Q.</given-names>
</name>
<name>
<surname>Liu</surname>
<given-names>D.</given-names>
</name>
<name>
<surname>Zhou</surname>
<given-names>Y.</given-names>
</name>
</person-group> (<year>2020</year>). <article-title>Mechanism and kinetics study of sulfuric acid leaching of titanium from titanium-bearing electric furnace slag</article-title>. <source>J. Mater. Res. Technol.</source> <volume>9</volume> (<issue>2</issue>), <fpage>1750</fpage>&#x2013;<lpage>1758</lpage>. <pub-id pub-id-type="doi">10.1016/j.jmrt.2019.12.006</pub-id>
</citation>
</ref>
<ref id="B20">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Nie</surname>
<given-names>W.</given-names>
</name>
<name>
<surname>Wen</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Liu</surname>
<given-names>D.</given-names>
</name>
<name>
<surname>Hu</surname>
<given-names>T.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>L.</given-names>
</name>
</person-group> (<year>2023a</year>). <article-title>Innovative application of two-stage sulfuric acid leaching for efficient recovery of Ti from titanium-bearing electric furnace slag</article-title>. <source>J. Environ. Chem. Eng.</source> <volume>11</volume> (<issue>1</issue>), <fpage>109174</fpage>. <pub-id pub-id-type="doi">10.1016/j.jece.2022.109174</pub-id>
</citation>
</ref>
<ref id="B21">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Nie</surname>
<given-names>W.</given-names>
</name>
<name>
<surname>Wen</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Liu</surname>
<given-names>D.</given-names>
</name>
<name>
<surname>Hu</surname>
<given-names>T.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>L.</given-names>
</name>
</person-group> (<year>2023b</year>). <article-title>Innovative application of two-stage sulfuric acid leaching for efficient recovery of Ti from titanium-bearing electric furnace slag</article-title>. <source>J. Environ. Chem. Eng.</source> <volume>11</volume> (<issue>1</issue>), <fpage>109174</fpage>. <pub-id pub-id-type="doi">10.1016/j.jece.2022.109174</pub-id>
</citation>
</ref>
<ref id="B22">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Peng</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Ao</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Xia</surname>
<given-names>Q.</given-names>
</name>
</person-group> (<year>2005</year>). <article-title>The causes and countermeasures for non-hydrated activity of residual slags from chlorination process of PanGang BF slags</article-title>. <source>Multipurp. Util. Mineral Resour.</source> <volume>6</volume>, <fpage>40</fpage>&#x2013;<lpage>46</lpage>.</citation>
</ref>
<ref id="B23">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Santos</surname>
<given-names>F. M.</given-names>
</name>
<name>
<surname>Pina</surname>
<given-names>P. S.</given-names>
</name>
<name>
<surname>Porcaro</surname>
<given-names>R.</given-names>
</name>
<name>
<surname>Oliveira</surname>
<given-names>V. A.</given-names>
</name>
<name>
<surname>Silva</surname>
<given-names>C. A.</given-names>
</name>
<name>
<surname>Le&#xe3;o</surname>
<given-names>V. A.</given-names>
</name>
</person-group> (<year>2010</year>). <article-title>The kinetics of zinc silicate leaching in sodium hydroxide</article-title>. <source>Hydrometallurgy</source> <volume>102</volume> (<issue>1-4</issue>), <fpage>43</fpage>&#x2013;<lpage>49</lpage>. <pub-id pub-id-type="doi">10.1016/j.hydromet.2010.01.010</pub-id>
</citation>
</ref>
<ref id="B24">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Shangguan</surname>
<given-names>Q. Y.</given-names>
</name>
<name>
<surname>Chen</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Yang</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Liang</surname>
<given-names>S. R.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>Y. J.</given-names>
</name>
<name>
<surname>Cheng</surname>
<given-names>S. B.</given-names>
</name>
<etal/>
</person-group> (<year>2022b</year>). <article-title>A &#x201c;belfry-typed&#x201d; narrow-band tunable perfect absorber based on graphene and the application potential research</article-title>. <source>Diam. Relat. Mater.</source> <volume>125</volume>, <fpage>108973</fpage>. <pub-id pub-id-type="doi">10.1016/j.diamond.2022.108973</pub-id>
</citation>
</ref>
<ref id="B25">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Shangguan</surname>
<given-names>Q. Y.</given-names>
</name>
<name>
<surname>Zhao</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Song</surname>
<given-names>Z. J.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Yang</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Chen</surname>
<given-names>J.</given-names>
</name>
<etal/>
</person-group> (<year>2022a</year>). <article-title>High sensitivity active adjustable graphene absorber for refractive index sensing applications</article-title>. <source>Diam. Relat. Mater.</source> <volume>128</volume>, <fpage>109273</fpage>. <pub-id pub-id-type="doi">10.1016/j.diamond.2022.109273</pub-id>
</citation>
</ref>
<ref id="B26">
<citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname>Sohn</surname>
<given-names>H. Y.</given-names>
</name>
<name>
<surname>Wadsworth</surname>
<given-names>M. E.</given-names>
</name>
</person-group> (<year>2013</year>). <source>Rate processes of extractive metallurgy</source>. <publisher-loc>Germany</publisher-loc>: <publisher-name>Springer Science and Business Media</publisher-name>.</citation>
</ref>
<ref id="B27">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Valighazvini</surname>
<given-names>F.</given-names>
</name>
<name>
<surname>Rashchi</surname>
<given-names>F.</given-names>
</name>
<name>
<surname>Nekouei</surname>
<given-names>R. K.</given-names>
</name>
</person-group> (<year>2013</year>). <article-title>Recovery of titanium from blast furnace slag</article-title>. <source>Industrial Eng. Chem. Res.</source> <volume>52</volume> (<issue>4</issue>), <fpage>1723</fpage>&#x2013;<lpage>1730</lpage>. <pub-id pub-id-type="doi">10.1021/ie301837m</pub-id>
</citation>
</ref>
<ref id="B28">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Wang</surname>
<given-names>D. Y.</given-names>
</name>
<name>
<surname>Yi</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Ma</surname>
<given-names>G. L.</given-names>
</name>
<name>
<surname>Dai</surname>
<given-names>B.</given-names>
</name>
<name>
<surname>Yang</surname>
<given-names>J. B.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>J. F.</given-names>
</name>
<etal/>
</person-group> (<year>2022c</year>). <article-title>Two-channel photonic crystal fiber based on surface plasmon resonance for magnetic field and temperature dual-parameter sensing</article-title>. <source>Phys. Chem. Chem. Phys.</source> <volume>24</volume>, <fpage>21233</fpage>&#x2013;<lpage>21241</lpage>. <pub-id pub-id-type="doi">10.1039/d2cp02778j</pub-id>
</citation>
</ref>
<ref id="B29">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Wang</surname>
<given-names>D. Y.</given-names>
</name>
<name>
<surname>Zhu</surname>
<given-names>W. L.</given-names>
</name>
<name>
<surname>Yi</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Ma</surname>
<given-names>G. L.</given-names>
</name>
<name>
<surname>Gao</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Dai</surname>
<given-names>B.</given-names>
</name>
<etal/>
</person-group> (<year>2022b</year>). <article-title>Highly sensitive sensing of a magnetic field and temperature based on two open ring channels SPR-PCF</article-title>. <source>Opt. Express</source> <volume>30</volume>, <fpage>39055</fpage>. <pub-id pub-id-type="doi">10.1364/oe.470386</pub-id>
</citation>
</ref>
<ref id="B30">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Wang</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Chen</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Liu</surname>
<given-names>W.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>G.</given-names>
</name>
<name>
<surname>Tang</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Yue</surname>
<given-names>H.</given-names>
</name>
<etal/>
</person-group> (<year>2022a</year>). <article-title>Recovery of titanium, aluminum, magnesium and separating silicon from titanium-bearing blast furnace slag by sulfuric acid curing&#x2014;leaching</article-title>. <source>Int. J. Minerals, Metallurgy Mater.</source> <volume>29</volume> (<issue>9</issue>), <fpage>1705</fpage>&#x2013;<lpage>1714</lpage>. <pub-id pub-id-type="doi">10.1007/s12613-021-2293-3</pub-id>
</citation>
</ref>
<ref id="B31">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Wang</surname>
<given-names>M. Z.</given-names>
</name>
<name>
<surname>Chen</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Jing</surname>
<given-names>B. Y.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>L. Y.</given-names>
</name>
<name>
<surname>Dong</surname>
<given-names>Y. Y.</given-names>
</name>
<name>
<surname>Yu</surname>
<given-names>X. Z.</given-names>
</name>
</person-group> (<year>2020</year>). <article-title>Analysis of reaction kinetics of edible oil oxidation at ambient temperature by FTIR spectroscopy</article-title>. <source>Eur. J. Lipid Sci. Technol.</source> <volume>122</volume>, <fpage>1900302</fpage>. <pub-id pub-id-type="doi">10.1002/ejlt.201900302</pub-id>
</citation>
</ref>
<ref id="B32">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Wang</surname>
<given-names>W.</given-names>
</name>
<name>
<surname>Zeng</surname>
<given-names>D.</given-names>
</name>
<name>
<surname>Chen</surname>
<given-names>Q.</given-names>
</name>
<name>
<surname>Yin</surname>
<given-names>X.</given-names>
</name>
</person-group> (<year>2013</year>). <article-title>Experimental determination and modeling of gypsum and insoluble anhydrite solubility in the system CaSO4&#x2013;H2SO4&#x2013;H2O</article-title>. <source>Chem. Eng. Sci.</source> <volume>101</volume>, <fpage>120</fpage>&#x2013;<lpage>129</lpage>. <pub-id pub-id-type="doi">10.1016/j.ces.2013.06.023</pub-id>
</citation>
</ref>
<ref id="B33">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Zhang</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Yi</surname>
<given-names>Y. T.</given-names>
</name>
<name>
<surname>Yang</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Yi</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Chen</surname>
<given-names>X. F.</given-names>
</name>
<name>
<surname>Zhou</surname>
<given-names>Z. G.</given-names>
</name>
<etal/>
</person-group> (<year>2022</year>). <article-title>Wide spectrum solar energy absorption based on germanium plated ZnO nanorod arrays: energy band regulation, Finite element simulation, Super hydrophilicity, Photothermal conversion</article-title>. <source>Appl. Mater. Today</source> <volume>28</volume>, <fpage>101531</fpage>. <pub-id pub-id-type="doi">10.1016/j.apmt.2022.101531</pub-id>
</citation>
</ref>
<ref id="B34">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Zhang</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>G.</given-names>
</name>
<name>
<surname>Sui</surname>
<given-names>Z.</given-names>
</name>
</person-group> (<year>2007</year>). <article-title>Recovery of titanium compounds from molten Ti-bearing blast furnace slag under the dynamic oxidation condition</article-title>. <source>Miner. Eng.</source> <volume>20</volume> (<issue>7</issue>), <fpage>684</fpage>&#x2013;<lpage>693</lpage>. <pub-id pub-id-type="doi">10.1016/j.mineng.2007.01.003</pub-id>
</citation>
</ref>
<ref id="B35">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Zhang</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Nicol</surname>
<given-names>M. J.</given-names>
</name>
</person-group> (<year>2010</year>). <article-title>Kinetics of the dissolution of ilmenite in sulfuric acid solutions under reducing conditions</article-title>. <source>Hydrometallurgy</source> <volume>103</volume> (<issue>1-4</issue>), <fpage>196</fpage>&#x2013;<lpage>204</lpage>. <pub-id pub-id-type="doi">10.1016/j.hydromet.2010.03.019</pub-id>
</citation>
</ref>
<ref id="B36">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Zhang</surname>
<given-names>Y. J.</given-names>
</name>
<name>
<surname>Yi</surname>
<given-names>Y. T.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>W. X.</given-names>
</name>
<name>
<surname>Liang</surname>
<given-names>S. R.</given-names>
</name>
<name>
<surname>Ma</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Cheng</surname>
<given-names>S. B.</given-names>
</name>
<etal/>
</person-group> (<year>2023</year>). <article-title>High absorptivity and ultra-wideband solar absorber based on Ti-Al2O3 cross elliptical disk arrays</article-title>. <source>Coatings</source> <volume>13</volume> (<issue>3</issue>), <fpage>531</fpage>. <pub-id pub-id-type="doi">10.3390/coatings13030531</pub-id>
</citation>
</ref>
<ref id="B37">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Zhou</surname>
<given-names>G.</given-names>
</name>
<name>
<surname>Peng</surname>
<given-names>T.</given-names>
</name>
<name>
<surname>Sun</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Liang</surname>
<given-names>Y.</given-names>
</name>
</person-group> (<year>2013</year>). <article-title>The products transformation and formation mechanism in the roasting process of high Ti-bearing blast furnace slag with ammonium sulfate</article-title>. <source>Acta Petrologica Mineralogica</source> <volume>32</volume> (<issue>6</issue>), <fpage>893</fpage>&#x2013;<lpage>898</lpage>.</citation>
</ref>
<ref id="B38">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Zhou</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>B.</given-names>
</name>
<name>
<surname>Zhu</surname>
<given-names>Z.</given-names>
</name>
</person-group> (<year>1999</year>). <article-title>A test of titania separation from high titania bearing blast furnace slag</article-title>. <source>Iron Steel Vanadium Titan.</source> <volume>20</volume> (<issue>4</issue>), <fpage>37</fpage>&#x2013;<lpage>40</lpage>.</citation>
</ref>
<ref id="B39">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Zhu</surname>
<given-names>W. L.</given-names>
</name>
<name>
<surname>Yi</surname>
<given-names>Y. T.</given-names>
</name>
<name>
<surname>Yi</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Bian</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Yang</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>J. G.</given-names>
</name>
<etal/>
</person-group> (<year>2023</year>). <article-title>High confidence plasmonic sensor based on photonic crystal fibers with a U-shaped detection channel</article-title>. <source>Phys. Chem. Chem. Phys.</source> <volume>25</volume>, <fpage>8583</fpage>&#x2013;<lpage>8591</lpage>. <pub-id pub-id-type="doi">10.1039/d2cp04605a</pub-id>
</citation>
</ref>
</ref-list>
</back>
</article>