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  <front>
    <journal-meta>
      <journal-id journal-id-type="nlm-ta">Microstructures</journal-id>
      <journal-id journal-id-type="publisher-id">MICROSTRUCTURES</journal-id>
      <journal-title-group>
        <journal-title>Microstructures</journal-title>
      </journal-title-group>
      <issn pub-type="epub">2770-2995</issn>
      <publisher>
        <publisher-name>OAE Publishing Inc.</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
	 <article-id pub-id-type="doi">10.20517/microstructures.2026.08</article-id>
      <article-categories>
        <subj-group>
          <subject>Research Article</subject>
        </subj-group>
      </article-categories>
      <title-group>
        <article-title>Exploring the oxygen vacancies and electrical properties in pyrochlore-type Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub></article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name>
            <surname>Yao</surname>
            <given-names>Yuan</given-names>
          </name>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Liu</surname>
            <given-names>Shuhang</given-names>
          </name>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Sun</surname>
            <given-names>Heyuan</given-names>
          </name>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Yao</surname>
            <given-names>Jiajia</given-names>
          </name>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Li</surname>
            <given-names>Wen-Cui</given-names>
          </name>
        </contrib>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Zhang</surname>
            <given-names>Wenrui</given-names>
          </name>
          <xref ref-type="corresp" rid="cor1" />
          <contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-1590-534X</contrib-id>
        </contrib>
      </contrib-group>
      <aff id="I">State Key Laboratory of Fine Chemicals, School of Chemical Engineering, Dalian University of Technology, Dalian 116024, Liaoning, China.</aff>
      <author-notes>
        <corresp id="cor1">Correspondence to: Prof. Wenrui Zhang, State Key Laboratory of Fine Chemicals, School of Chemical Engineering, Dalian University of Technology, Dalian 116024, Liaoning, China. E-mail: <email>zhangwr@dlut.edu.cn</email></corresp>
     
	  <fn fn-type="other">
          <p>
            <bold>Received:</bold> 14 Jan 2026 | <bold>First Decision:</bold> 3 Mar 2026 | <bold>Revised:</bold> 17 Mar 2026 | <bold>Accepted:</bold> 26 Mar 2026 | <bold>Published:</bold> 17 Jun 2026</p>
        </fn>
        <fn fn-type="other">
          <p>
            <bold>Academic Editor:</bold> Zhanxi Fan | <bold>Copy Editor:</bold> Fangling Lan |  <bold>Production Editor:</bold> Fangling Lan</p>
        </fn>
      </author-notes>
	  <pub-date pub-type="ppub">
        <year>2026</year>
      </pub-date>
      <pub-date pub-type="epub">
        <day>17</day>
        <month>6</month>
        <year>2026</year>
      </pub-date>
         <volume>6</volume>
	  <issue>4</issue>
      <elocation-id>2026085</elocation-id>
	 
	 
	 
	 
	 
	 
      <permissions>
        <copyright-statement>© The Author(s) 2026.</copyright-statement>
        <license xlink:href="https://creativecommons.org/licenses/by/4.0/">
          <license-p>© The Author(s) 2026. <bold>Open Access</bold> This article is licensed under a Creative Commons Attribution 4.0 International License (<uri xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</uri>), which permits unrestricted use, sharing, adaptation, distribution and reproduction in any medium or format, for any purpose, even commercially, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.</license-p>
        </license>
      </permissions>
      <abstract>
        <p>Pyrochlore-type oxides are considered potential oxide-ion conductors due to their high concentration of oxygen vacancies in the unit cell. In this work, the pyrochlore-type Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> was synthesized and its crystal structure was characterized by Rietveld refinement. A high oxygen vacancy concentration in the material was confirmed by thermogravimetry (TG) and X-ray photoelectron spectroscopy (XPS). TG, XPS, and electron paramagnetic resonance collectively demonstrated the change in oxygen vacancy concentration of the material following atmosphere switching. The electrical properties of Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> under different atmospheres were characterized by electrochemical impedance spectroscopy. The conductivity of Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> was <InlineParagraph>4.20 × 10<sup>-2</sup> S cm<sup>-1</sup></InlineParagraph> in 5% H<sub>2</sub>/Ar, 9.22 × 10<sup>-3</sup> S cm<sup>-1</sup> in Ar and 2.92 × 10<sup>-5</sup> S cm<sup>-1</sup> in air at 900 °C. Bond valence site energy calculations indicated that oxide ions diffuse three-dimensionally in Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub>. Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> is a promising solid electrolyte for oxygen sensors. This work investigates the structure-property relationship between oxygen vacancies and conductivity in pyrochlore-type oxides.</p>
      </abstract>
      <kwd-group>
        <kwd>Ionic conductor</kwd>
        <kwd>conductivity</kwd>
        <kwd>solid electrolyte</kwd>
        <kwd>solid oxide fuel cells</kwd>
        <kwd>ion migration</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec1">
      <title>INTRODUCTION</title>
      <p>Since Nernst's discovery of oxide-ion conduction in Y<sub>2</sub>O<sub>3</sub>-ZrO<sub>2</sub>, the field has advanced significantly, and oxide-ion conductors now play a vital role in daily life and industrial applications<sup>[<xref ref-type="bibr" rid="B1">1</xref>-<xref ref-type="bibr" rid="B4">4</xref>]</sup>. Oxide-ion conductors have found extensive applications as catalytic, sensing, and conductive materials under various atmospheres, including oxidizing, reducing, inert, and mixed environments. High-performance oxide-ion conductors are key materials for enabling efficient operation in solid-state electrochemical devices, such as solid oxide fuel cells and oxygen sensors<sup>[<xref ref-type="bibr" rid="B5">5</xref>]</sup>.</p>
      <p>In addition to the charge carrier (e.g. oxygen vacancies or interstitial oxygen ions) concentration, the local crystalline structure around the charge carrier is a crucial factor for oxide-ion conduction<sup>[<xref ref-type="bibr" rid="B6">6</xref>]</sup>. Most of the conventional oxide-ion conductors are fluorite-type materials, such as yttria-stabilized zirconia (YSZ) and Gd- or Sm-doped CeO<sub>2</sub> (GDC or SDC), the structure of which can provide large tolerances for disordered oxygen vacancies<sup>[<xref ref-type="bibr" rid="B7">7</xref>-<xref ref-type="bibr" rid="B10">10</xref>]</sup>. The pyrochlore structure is an intricate superstructure derived from the fluorite structure and inherently contains more oxygen vacancies<sup>[<xref ref-type="bibr" rid="B11">11</xref>]</sup>. Pyrochlore-type oxides have attracted high attention for a long time due to their potential applications such as thermal barrier coating materials, solid electrolytes, oxygen pumps, oxygen sensors, catalysts, and so on<sup>[<xref ref-type="bibr" rid="B12">12</xref>,<xref ref-type="bibr" rid="B13">13</xref>]</sup>.</p>
      <p>The typical pyrochlore structure consists of two types of cations, <italic>A</italic> and <italic>B</italic>, occupying different lattice sites, where <italic>A</italic>-site cations are larger and usually have a lower oxidation state, while <italic>B</italic>-site cations are smaller and have a higher oxidation state<sup>[<xref ref-type="bibr" rid="B14">14</xref>]</sup>. The <italic>A</italic>-site cations occupy the centers of oxygen octahedra, whereas the <italic>B</italic>-site cations, typically transition metals, reside within them<sup>[<xref ref-type="bibr" rid="B14">14</xref>]</sup>. Partial substitution of <italic>A</italic>-site or <italic>B</italic>-site ions with other metal ions not only disrupts the structural ordering of the pyrochlore lattice but also alters the unit cell size, thereby potentially decreasing the oxide-ion migration distance<sup>[<xref ref-type="bibr" rid="B15">15</xref>]</sup>. The presence of numerous oxygen vacancies in pyrochlore-type oxides is beneficial for oxide-ion conduction, as it provides pathways for ion migration<sup>[<xref ref-type="bibr" rid="B16">16</xref>]</sup>. The pyrochlore structure's coordination environment allows for diverse cationic configurations, supporting multiple oxidation states<sup>[<xref ref-type="bibr" rid="B17">17</xref>-<xref ref-type="bibr" rid="B19">19</xref>]</sup>. This structural arrangement, combined with its capability to incorporate a wide range of ions, significantly enhances the physical and chemical stability, making pyrochlore-type oxides suitable for use as oxide-ion conductors<sup>[<xref ref-type="bibr" rid="B20">20</xref>-<xref ref-type="bibr" rid="B26">26</xref>]</sup>.</p>
      <p>Roth <italic>et al</italic>.<sup>[<xref ref-type="bibr" rid="B27">27</xref>]</sup> reported the pyrochlore-type Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> and investigated its dielectric properties. Bond valence site energy (BVSE) calculations performed with the softBV software<sup>[<xref ref-type="bibr" rid="B28">28</xref>-<xref ref-type="bibr" rid="B30">30</xref>]</sup> indicate that the material exhibits a relatively low oxide-ion migration barrier (1.14 eV), suggesting its potential as an oxide-ion conductor. This work aims to investigate the conductive properties of Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> and elucidate its oxide-ion conduction mechanism. In particular, it seeks to clarify the structure-property relationship between oxygen vacancies and conductivity, as well as the formation mechanism of oxygen vacancies. The findings are expected to provide insights for future research on pyrochlore-type oxides.</p>
    </sec>
    <sec id="sec2">
      <title>EXPERIMENTAL PROCEDURE</title>
      <sec id="sec2-1">
        <title>Material synthesis</title>
        <p>Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> was synthesized using a solid-state reaction method. High-purity CaCO<sub>3</sub>, TiO<sub>2</sub> and Nb<sub>2</sub>O<sub>5</sub> powders (≥ 99.9%, Aladdin Biochemical Technology Co., Ltd., China) were used as starting materials, which were dried in an oven (DHG-9075A, Yiheng Scientific Instrument Co., Ltd., China) to remove adsorbed water prior to weighing. The starting materials were ground in anhydrous ethanol (AR, ≥ 99.7%, Sinopharm Chemical Reagent Co., Ltd., China) for approximately 30 min. The mixtures were pressed into pellets and pre-sintered at 1,000 °C for 12 h, and then sintered at 1,350 °C for 8 h. The sintered sample was ground, pressed into pellets, and finally sintered at 1,350 °C for 8 h for densification. All sintering processes were carried out in Ar gas (≥ 99.999%, Dalian Special Gases Co., Ltd., China) using a horizontal tube furnace (GYS-1700C, Hefei Weiyuans Laboratory Equipment Co., Ltd., China).</p>
      </sec>
      <sec id="sec2-2">
        <title>Material characterization</title>
        <p>The X-ray diffraction (XRD) pattern was obtained using a powder diffractometer (X'Pert3 Powder, PANalytical, The Netherlands) with Cu <italic>Kα</italic> radiation. Rietveld refinement and Maximum Entropy Method (MEM) analysis were carried out using the Z-Rietveld software. BVSE calculations were performed using the softBV program to calculate the oxide-ion migration barriers. Visualization of the results was achieved using VESTA software. The elemental composition of the sample was determined by X-ray fluorescence spectrometry (XRF) using a wavelength-dispersive spectrometer (S8 Tiger, Bruker, Germany). Field emission scanning electron microscopy (SEM) (JSM-7900F, JEOL Ltd., Japan) equipped with energy-dispersive X-ray spectroscopy (EDS) was employed to investigate the morphology of the pellet samples and the elemental distribution of the powder samples. The particle size distribution of the sample was determined using a laser particle size analyzer (BT-9300H, Dandong Bettersize Instruments Co., Ltd., China). For electrochemical impedance spectroscopy measurements, pellets (approximately 10 mm in diameter and 2 mm in thickness) were used. Platinum paste electrodes (55H-1800, Shenzhen Saiya Electronic Paste Co., Ltd., China) were coated on its opposite faces. The sample was then heated at 1,000 °C for 2 h in a horizontal tube furnace (GYS-1700C, Hefei Weiyuans Laboratory Equipment Co., Ltd., China) to form dense platinum electrodes. Electrochemical measurements were performed on an electrochemical workstation (SP-300, Bio-Logic, France; or DH7002A, Donghua Analytical Instrument Co., Ltd., China) using the two-electrode method during the heating process. The sample was heated to temperatures between 500 and 900 °C in either a tubular furnace (JS-G5012-S, Tianjin Jiusuo Technology Development Co., Ltd., China) or a solid oxide fuel cell test station (HBSOC-5B, Zhejiang H<sub>2</sub>-Bank Energy Technology Co., Ltd., China), followed by electrochemical measurements at each temperature. The process consisted of purging the system with various gases, including pure Ar, pure air, an Ar-H<sub>2</sub> mixture, an H<sub>2</sub>-N<sub>2</sub> mixture, and an N<sub>2</sub>-O<sub>2</sub> mixture. All gases (including the component gases in the mixtures) were of high purity (≥ 99.999%) and supplied by Dalian Special Gases Co., Ltd., China. The impedance was measured over a frequency range of 7 MHz to <InlineParagraph>0.1 Hz</InlineParagraph> with an applied voltage of 100 mV. The obtained impedance data were fitted using Zview 3.1 software. The thermogravimetry (TG) curve was recorded on a thermogravimetric analyzer (STA 449 F3, NETZSCH-Gerätebau GmbH, Germany) over a temperature range of 80 to 1,000 °C. The gas flow rate was set at 20 mL/min, and the heating rate was set at 10 °C/min. High-purity Ar or air gas (≥ 99.999%, Dalian Special Gases Co., Ltd., China) was used during the measurement. X-Ray Photoelectron Spectroscopy (XPS) characterization was performed using an X-ray photoelectron spectrometer (Axis Supra+, Shimadzu, China) to analyze the chemical state of elements in the samples. The Al/Ag double anode X-ray source was used for excitation. The main peak of C1s at 284.8 eV was used as the reference for charge correction, and the spectra were analyzed using Avantage software. Electron paramagnetic resonance (EPR) spectra were recorded at room temperature using a spectrometer (E500, Bruker Corporation, Germany) operating in the X-band at a frequency of 9.42 GHz.</p>
      </sec>
    </sec>
    <sec id="sec3">
      <title>RESULTS AND DISCUSSION</title>
      <sec id="sec3-1">
        <title>Structural and morphological characterization</title>
        <p>After the first sintering at 1,350 °C, the room-temperature XRD pattern of Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> confirmed the formation of the target phase, along with a small amount of TiO<sub>2</sub> as an impurity. This suggests that sintering temperatures below 1,350 °C may result in higher impurity levels due to incomplete reaction. To eliminate the TiO<sub>2</sub> impurity and achieve densification, the material was subjected to a second sintering at 1,350 °C for <InlineParagraph>8 h.</InlineParagraph> <xref ref-type="fig" rid="fig1">Figure 1</xref> shows the refined XRD pattern obtained at 700 °C of Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> after the second sintering at 1,350 °C. All diffraction peaks can be indexed to the pyrochlore structure<bold>,</bold> indicating the formation of a pure phase. <xref ref-type="table" rid="t1">Table 1</xref> lists the refined structural parameters obtained from <italic>in situ</italic> XRD data. Because the data were collected at 700 °C, they provide a more realistic representation of the crystal structure at high temperatures, which is essential for accurately predicting the ionic conduction mechanism under operating conditions. Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> is a typical pyrochlore structure with a space group of <italic>Fd-3m</italic> (No. 227, origin choice 2). There are two different kinds of oxygen sites, O1 (48<italic>f</italic>) and O2 (32<italic>e</italic>). The O2 site contains a high concentration of oxygen vacancies, while the O1 site exhibits a relatively low vacancy concentration. These parameters were then used to predict the influence of structural changes on the material's properties. The occupancies of Ca, Ti, and Nb were determined based on the stoichiometry of starting materials. The <italic>R</italic><sub>F</sub> is below 7%, and <italic>R</italic><sub>wp</sub> and <italic>R</italic><sub>p</sub> are below 4%, indicating that the refined crystal structure is in excellent agreement with the experimental data<sup>[<xref ref-type="bibr" rid="B16">16</xref>]</sup>. XRF analysis was conducted to verify the elemental composition of the synthesized material. Quantification was performed using a standardless fundamental parameters (FP) method. The measured oxide contents are 24.5 wt% CaO, 32.3 wt% TiO<sub>2</sub>, and 43.2 wt% Nb<sub>2</sub>O<sub>5</sub>. Based on these values, the calculated molar ratios of Ca, Ti, Nb and O are 1.46:1.35:1.09:6.88, which are very close to the nominal stoichiometry. As shown in <xref ref-type="fig" rid="fig2">Figure 2</xref>, the EDS mapping diagrams of Ca, Ti, Nb, O confirm that the elements distribute homogeneously without any apparent clustering or segregation<sup>[<xref ref-type="bibr" rid="B31">31</xref>]</sup>. Combined with the XRD results, this confirms the formation of a single-phase Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub>. <xref ref-type="fig" rid="fig3">Figure 3A</xref> shows the cross-section SEM image of the Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> pellet. A relatively dense microstructure can be observed, with particle sizes visually estimated to be in the range of several hundred nm. The particles are needle-like in shape. The relative density of the sample reached 92.6% as measured by the Archimedes method, which is close to the upper limit typically achieved by conventional solid-state sintering (manual grinding, uniaxial pressing). This indicates that a sintering temperature of <InlineParagraph>1,350 °C</InlineParagraph> is sufficient for Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> and that higher temperatures are unnecessary. However, the particle size distribution appears inhomogeneous in the SEM image. This observation is consistent with the particle size distribution measured by the laser diffraction particle size analyzer, which gives an average particle size of approximately 412.8 nm with a PDI of 0.371 [<xref ref-type="fig" rid="fig3">Figure 3B</xref>], confirming a broad size distribution. The inhomogeneity in particle size can be attributed to non-uniform temperature distribution within the pellet during sintering.</p>
        <fig id="fig1" position="float" pdfpage="4" width="480">
          <label>Figure 1</label>
          <caption>
            <p>Refined XRD pattern of Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> obtained at 700 °C .</p>
          </caption>
          <graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="microstructures6008.fig.1.jpg" />
        </fig>
        <fig id="fig2" position="float">
          <label>Figure 2</label>
          <caption>
            <p>SEM image and corresponding elemental distribution maps of Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> powder.</p>
          </caption>
          <graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="microstructures6008.fig.2.jpg" />
        </fig>
        <fig id="fig3" position="float">
          <label>Figure 3</label>
          <caption>
            <p>(A) Cross-sectional SEM image of the Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> pellet; (B) Particle size distribution of Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> measured by laser diffraction.</p>
          </caption>
          <graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="microstructures6008.fig.3.jpg" />
        </fig>
        <table-wrap id="t1">
          <label>Table 1</label>
          <caption>
            <p>The final refined structural parameters for the sample Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> from XRD data at 700 °C: <italic>a</italic> = <italic>b</italic> = <italic>c</italic> = 10.302 Å</p>
          </caption>
          <table frame="hsides" rules="groups" displaytype="1">
            <thead>
              <tr>
                <td style="border-bottom:1;">
                  <bold>Atoms</bold>
                </td>
                <td style="border-bottom:1;">
                  <bold>Site</bold>
                </td>
                <td style="border-bottom:1;">
                  <bold>
                    <italic>x</italic>
                  </bold>
                </td>
                <td style="border-bottom:1;">
                  <bold>
                    <italic>y</italic>
                  </bold>
                </td>
                <td style="border-bottom:1;">
                  <bold>
                    <italic>z</italic>
                  </bold>
                </td>
                <td style="border-bottom:1;">
                  <bold>Occupancy</bold>
                </td>
                <td style="border-bottom:1;">
                  <bold>
                    <italic>U</italic> (Å<sup>2</sup>)</bold>
                </td>
                <td style="border-bottom:1;" />
                <td style="border-bottom:1;" />
                <td style="border-bottom:1;" />
                <td style="border-bottom:1;" />
                <td style="border-bottom:1;" />
              </tr>
            </thead>
            <tbody>
              <tr>
                <td>Nb</td>
                <td>16<italic>c</italic></td>
                <td>0.0000</td>
                <td>0.0000 </td>
                <td>0.0000 </td>
                <td>0.5550</td>
                <td>0.0124 </td>
                <td />
                <td />
                <td />
                <td />
                <td />
              </tr>
              <tr>
                <td>Ti1</td>
                <td>16<italic>c</italic></td>
                <td>0.0000 </td>
                <td>0.0000 </td>
                <td>0.0000 </td>
                <td>0.4450</td>
                <td>0.0129</td>
                <td />
                <td />
                <td />
                <td />
                <td />
              </tr>
              <tr>
                <td>Ca</td>
                <td>16<italic>d</italic></td>
                <td>0.5000</td>
                <td>0.5000 </td>
                <td>0.5000 </td>
                <td>0.7300</td>
                <td>0.0160 </td>
                <td />
                <td />
                <td />
                <td />
                <td />
              </tr>
              <tr>
                <td>Ti2</td>
                <td>96<italic>g</italic></td>
                <td>0.4681 </td>
                <td>0.4681 </td>
                <td>0.5595 </td>
                <td>0.0408 </td>
                <td>0.0059 </td>
                <td />
                <td />
                <td />
                <td />
                <td />
              </tr>
              <tr>
                <td />
                <td />
                <td />
                <td />
                <td />
                <td />
                <td>
                  <bold>
                    <italic>U</italic>
                    <sub>11</sub> (Å<sup>2</sup>)</bold>
                </td>
                <td>
                  <bold>
                    <italic>U</italic>
                    <sub>22</sub> (Å<sup>2</sup>)</bold>
                </td>
                <td>
                  <bold>
                    <italic>U</italic>
                    <sub>33</sub> (Å<sup>2</sup>)</bold>
                </td>
                <td>
                  <bold>
                    <italic>U</italic>
                    <sub>12</sub> (Å<sup>2</sup>)</bold>
                </td>
                <td>
                  <bold>
                    <italic>U</italic>
                    <sub>13</sub> (Å<sup>2</sup>)</bold>
                </td>
                <td>
                  <bold>
                    <italic>U</italic>
                    <sub>23</sub> (Å<sup>2</sup>)</bold>
                </td>
              </tr>
              <tr>
                <td>O1</td>
                <td>48<italic>f</italic></td>
                <td>0.3229 </td>
                <td>0.1250 </td>
                <td>0.1250 </td>
                <td>0.9774 </td>
                <td>0.0720</td>
                <td>0.0020</td>
                <td>0.0020</td>
                <td>0.0000</td>
                <td>0.0000</td>
                <td>0.0010</td>
              </tr>
              <tr>
                <td>O2</td>
                <td>32<italic>e</italic></td>
                <td>0.4013 </td>
                <td>0.4013</td>
                <td>0.4013 </td>
                <td>0.2254 </td>
                <td>0.0250</td>
                <td>0.0250</td>
                <td>0.0250</td>
                <td>0.0097</td>
                <td>0.0097</td>
                <td>0.0097</td>
              </tr>
            </tbody>
          </table>
        </table-wrap>
      </sec>
      <sec id="sec3-2">
        <title>Electrical properties</title>
        <p>Conductivity measurements were first performed in Ar to both prevent oxidation of the material and to assess its electrical response following sintering in Ar. Electrochemical impedance spectroscopy was used to characterize the electrical properties of Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub>. The resistance in the high frequency range represents the grain resistance, the resistance in the mid-frequency range corresponds to the grain-boundary resistance, and the resistance in the low-frequency range can be due to the polarization effect of the electrodes. The impedance plots [<xref ref-type="fig" rid="fig4">Figure 4A</xref>-<xref ref-type="fig" rid="fig4">C</xref>] exhibit a single, nearly symmetric semicircular arc, which arises from overlapping grain and grain-boundary responses and can be modeled using an equivalent circuit with a single RC (resistance-capacitance) element. The total conductivity (σ<sub>b+gb</sub>, representing the sum of bulk and grain-boundary contributions) of Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> is presented in the Arrhenius plot in <xref ref-type="fig" rid="fig4">Figure 4D</xref>. These values were derived from the impedance spectra measured in Ar, 5% H<sub>2</sub>/Ar, and air atmospheres over the temperature range of 500-900 °C. The conductivity (σ) was calculated from the resistance using Equation (1)<sup>[<xref ref-type="bibr" rid="B32">32</xref>]</sup>,</p>
       
	  
<p><disp-formula> <label>(1)</label> <tex-math id="E1"> $$ \begin{equation}  \begin{aligned} \sigma=\frac{1}{R} \times \frac{l}{A} \end{aligned} \end{equation} $$ </tex-math>
</disp-formula></p>

		<p>where <italic>R</italic>, <italic>l</italic>, and <italic>A</italic> represent the resistance, the spacing between the probes, and the cross-sectional area of the sample, respectively.</p>
		
		 <fig id="fig4" position="float">
          <label>Figure 4</label>
          <caption>
            <p>(A) The complex impedance plot obtained at <InlineParagraph>600 °C</InlineParagraph> in Ar of Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub>; (B) The complex impedance plot obtained at <InlineParagraph>600 °C</InlineParagraph> in air of Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub>; (C) The complex impedance plot obtained at 600 °C in 5% H<sub>2</sub>/Ar of Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub>; (D) The total conductivity σ<sub>b+gb</sub> of Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> in the range of 500-900 °C in 5% H<sub>2</sub>/Ar, Ar, and air (data from impedance curve fitting).</p>
          </caption>
          <graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="microstructures6008.fig.4.jpg" />
        </fig>
		
		
        <p>σ<sub>b+gb</sub> of Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> increases gradually with increasing temperature from 500 to 900 °C, indicating a thermally activated ionic diffusion process. The conductivity of the sample varies approximately linearly with temperature in air. The temperature dependence of the conductivity in air can be described by Equation (2)<sup>[<xref ref-type="bibr" rid="B33">33</xref>]</sup>,</p>
		
		<p><disp-formula> <label>(2)</label> <tex-math id="E1"> $$ \begin{equation}  \begin{aligned} \sigma T=\sigma_{0} e^{-\frac{E}{k_{B}T}}\end{aligned} \end{equation} $$ </tex-math>
</disp-formula></p>
		
        
		
        <p>where <italic>σ</italic>, <italic>T</italic>, <italic>σ</italic><sub>0</sub>, <italic>E</italic>, and <italic>k<sub>B</sub></italic> are the conductivity, absolute temperature, pre-exponential factor, activation energy, and Boltzmann constant, respectively.</p>
        <p>Across the entire temperature range, the conductivity follows the order: 5% H<sub>2</sub>/Ar &gt; Ar &gt; air, indicating that the material exhibits n-type conduction. The conductivity of Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> was 4.20 × 10<sup>-2</sup> S cm<sup>-1</sup> in 5% H<sub>2</sub>/Ar, 9.22 × 10<sup>-3</sup> S cm<sup>-1</sup> in Ar and 2.92 × 10<sup>-5</sup> S cm<sup>-1</sup> in air at 900 °C. <xref ref-type="fig" rid="fig5">Figure 5</xref> demonstrates that the change in conductivity upon gas switching is reversible. This sensitive and reversible conductivity response to different atmospheres suggests that the material is a promising candidate for gas sensor applications. The DC conductivity σ<sub>DC</sub> of Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> as a function of oxygen partial pressure (<italic>p</italic>O<sub>2</sub>) is shown in <xref ref-type="fig" rid="fig6">Figure 6A</xref>. At 900 °C, σ<sub>DC</sub> decreases with increasing <italic>p</italic>O<sub>2</sub>, which is consistent with n-type conduction. σ<sub>DC</sub> changes little with the oxygen partial pressure in the range of 1.0 × 10<sup>-5</sup> to 1.0 atm at 500 °C, indicating that the conductivity is primarily ionic at this temperature. Negligible proton conduction is observed because there is little difference in σ<sub>DC</sub> of Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> under wet and dry air flows [<xref ref-type="fig" rid="fig6">Figure 6B</xref>]. Electromotive force (EMF) measurements were conducted to determine the ion transport number (t<sub>ion</sub>) of the material under different atmospheres [<xref ref-type="fig" rid="fig7">Figure 7</xref>]. Using an air|N<sub>2</sub> gas concentration cell, the t<sub>ion</sub> value is 0.995 at 500 °C, indicating that the material is an almost pure oxide-ion conductor at this temperature. The t<sub>ion</sub> values in the entire temperature range are above 0.8, suggesting that oxide-ion conduction is dominant in oxidizing (air, O<sub>2</sub>) and inert (Ar, N<sub>2</sub>) atmospheres. In contrast, EMF measurements using an air|5% H<sub>2</sub>/N<sub>2</sub> gas concentration cell revealed a drastically different behavior. The t<sub>ion</sub> values are below 0.25 in the whole temperature range, indicating that the material exhibits predominantly electronic conduction under a reducing atmosphere (e.g., 5% H<sub>2</sub>/N<sub>2,</sub> 5% H<sub>2</sub>/Ar). <xref ref-type="fig" rid="fig8">Figure 8</xref> presents a comparison of the conductivity of Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> with that of recently reported pyrochlores. Compared with these pyrochlores, the conductivity of Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> is lower in air, comparable in Ar, and significantly higher in 5% H<sub>2</sub>/Ar. σ<sub>DC</sub> remains stable over 27 h <InlineParagraph>[<xref ref-type="fig" rid="fig9">Figure 9A</xref>],</InlineParagraph> demonstrating the excellent long-term stability of the material. No significant degradation in σ<sub>b+gb</sub> is observed over 7 thermal cycles between 100 and 900 °C [<xref ref-type="fig" rid="fig9">Figure 9B</xref>], demonstrating the high structural stability of the material under repeated thermal cycling. These results indicate that Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> is suitable for high-temperature applications.</p>
        <fig id="fig5" position="float" width="480">
          <label>Figure 5</label>
          <caption>
            <p>Reversibility of the conductivity of Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> upon switching between 5% H<sub>2</sub>/Ar, air and Ar at 900 °C.</p>
          </caption>
          <graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="microstructures6008.fig.5.jpg" />
        </fig>
        <fig id="fig6" position="float">
          <label>Figure 6</label>
          <caption>
            <p>(A) Oxygen partial pressure <italic>p</italic>O<sub>2</sub> dependence of the DC conductivity σ<sub>DC</sub> of Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> at 500 and 900 °C; (B) Arrhenius plots of σ<sub>DC</sub> of Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> in wet (water vapor pressure of 0.042 atm) and dry air.</p>
          </caption>
          <graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="microstructures6008.fig.6.jpg" />
        </fig>
        <fig id="fig7" position="float" width="480">
          <label>Figure 7</label>
          <caption>
            <p>Ion transport number t<sub>ion</sub> of Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> from EMF measurements using air|N<sub>2</sub> and air|5% H<sub>2</sub>/N<sub>2</sub> gas concentration cells.</p>
          </caption>
          <graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="microstructures6008.fig.7.jpg" />
        </fig>
        <fig id="fig8" position="float">
          <label>Figure 8</label>
          <caption>
            <p>Comparison of the conductivity of Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> with that of recently reported pyrochlores<sup>[<xref ref-type="bibr" rid="B11">11</xref>,<xref ref-type="bibr" rid="B14">14</xref>,<xref ref-type="bibr" rid="B16">16</xref>,<xref ref-type="bibr" rid="B34">34</xref>,<xref ref-type="bibr" rid="B35">35</xref>]</sup>.</p>
          </caption>
          <graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="microstructures6008.fig.8.jpg" />
        </fig>
        <fig id="fig9" position="float">
          <label>Figure 9</label>
          <caption>
            <p>(A) Time dependence of the DC conductivity σ<sub>DC</sub> of Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> at 800 °C in air; (B) The total conductivity σ<sub>b+gb</sub> in air of Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> from 600 to 900 °C during the thermal cycling process between 100 and 900 °C.</p>
          </caption>
          <graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="microstructures6008.fig.9.jpg" />
        </fig>
      </sec>
      <sec id="sec3-3">
        <title>Conduction mechanism</title>
        <sec id="sec3-3-1">
          <title>Thermogravimetry</title>
          <p>The TG curve of Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> in air [<xref ref-type="fig" rid="fig10">Figure 10</xref>] showed an overall mass gain with increasing temperature, reaching 101.13% of the initial mass up to 1,000 °C. The mass gain is attributed to the addition of oxygen atoms in the air into the lattice. The incorporation of oxygen atoms decreases the oxygen vacancy concentration, thereby reducing the conductivity. Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> exhibited negligible mass change upon heating in Ar [<xref ref-type="fig" rid="fig10">Figure 10</xref>], owing to the extremely low oxygen partial pressure. It can be inferred from the TG curve in Ar that no significant change in oxygen vacancy concentration occurred during the conductivity measurements from 500 to 900 °C in Ar. Therefore, the oxygen vacancy concentration in the material is significantly higher during conductivity measurement in Ar than in air, leading to a notably higher conductivity in Ar.</p>
          <fig id="fig10" position="float" width="480">
            <label>Figure 10</label>
            <caption>
              <p>The TG curve of Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> in air and Ar.</p>
            </caption>
            <graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="microstructures6008.fig.10.jpg" />
          </fig>
        </sec>
        <sec id="sec3-3-2">
          <title>X-ray photoelectron spectroscopy</title>
          <p>To directly compare the oxygen vacancy concentrations in Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> under different atmospheres, the Ar-synthesized sample was subjected to annealing under contrasting atmospheres (in air and H<sub>2</sub>). The samples before and after annealing treatment were then characterized by XPS for comparison. The wide-survey XPS spectra [<xref ref-type="fig" rid="fig11">Figure 11</xref>] show all characteristic peaks of Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub>. The core-level peaks observed at 530.0, 458.1, 346.9, and 207.1 eV correspond to O 1s, Ti 2p, Ca 2p, and Nb 3d, respectively, confirming the presence of these elements. No other elements were observed in the wide-survey spectra, indicating that no impurities were incorporated during the preparation process. The Ca 2p spectra <InlineParagraph>[<xref ref-type="fig" rid="fig12">Figure 12A</xref>]</InlineParagraph> show prominent peaks at 346.7 and 350.2 eV, corresponding to the Ca 2p3/2 and <InlineParagraph>Ca 2p1/2</InlineParagraph> peaks, respectively<sup>[<xref ref-type="bibr" rid="B36">36</xref>]</sup>. The spin-orbit splitting is 3.5 eV, and the chemical valence is +2. The Ti 2p spectra of both the pristine and the air-annealed samples [<xref ref-type="fig" rid="fig12">Figure 12B</xref>] exhibited prominent peaks at 458.4 and <InlineParagraph>464.3 eV,</InlineParagraph> corresponding to the Ti 2p3/2 and Ti 2p1/2 peaks, respectively<sup>[<xref ref-type="bibr" rid="B37">37</xref>]</sup>. A spin-orbit splitting of 5.9 eV was observed, common to both samples, corresponding to Ti<sup>4+</sup>. In the Ti 2p spectrum of the H<sub>2</sub>-annealed sample [<xref ref-type="fig" rid="fig12">Figure 12B</xref>], the peaks observed at 456.6 and 462.8 eV are assigned to the Ti<sup>3+</sup> 2p3/2 and <InlineParagraph>Ti<sup>3+</sup> 2p1/2,</InlineParagraph> respectively<sup>[<xref ref-type="bibr" rid="B38">38</xref>-<xref ref-type="bibr" rid="B40">40</xref>]</sup>. During H<sub>2</sub>-annealing of Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub>, electron injection into the conduction band results in the partial reduction of Ti<sup>4+</sup> to Ti<sup>3+</sup>, which contributes to the material's high conductivity in 5% H<sub>2</sub>/Ar<sup>[<xref ref-type="bibr" rid="B41">41</xref>]</sup>. This is consistent with EMF measurements under an air|5% H<sub>2</sub>/N<sub>2</sub> gas concentration cell, which revealed that the t<sub>ion</sub> values are below 0.25 across the entire temperature range, confirming predominantly electronic conduction under a reducing atmosphere [<xref ref-type="fig" rid="fig7">Figure 7</xref>]. The Nb 3d spectra [<xref ref-type="fig" rid="fig12">Figure 12C</xref>] show prominent peaks at 206.8 and 209.7 eV, corresponding to the Nb 3d5/2 and Nb 3d3/2 peaks, respectively<sup>[<xref ref-type="bibr" rid="B42">42</xref>]</sup>. The spin-orbit splitting is 2.9 eV, and the chemical valence is +5. In the O 1s spectra [<xref ref-type="fig" rid="fig12">Figure 12D</xref>], the peaks near 529.7 eV represent metal-oxygen bonds (Ca-O, Ti-O, Nb-O), while the peaks near 531.6 eV represent oxygen vacancies<sup>[<xref ref-type="bibr" rid="B43">43</xref>-<xref ref-type="bibr" rid="B48">48</xref>]</sup>. The spectral asymmetry suggests variations in metal-oxygen bonding and the presence of oxygen vacancies in the lattice. The corresponding computed percentage of oxygen vacancies is 45.2% before air-annealing and 31.7% after air-annealing<sup>[<xref ref-type="bibr" rid="B11">11</xref>]</sup>. The higher percentage of oxygen vacancies leads to the higher conductivity, while oxygen vacancies provide better channels for oxide-ion conduction<sup>[<xref ref-type="bibr" rid="B49">49</xref>]</sup>. After the Ar-synthesized sample was air-annealed, it exhibited a reduction in oxygen vacancy concentration and corresponding low conductivity. Following H<sub>2</sub>-annealing, the lattice oxygen content in Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> was further reduced to 34.48%, as H<sub>2</sub> removed lattice oxygen in the form of water vapor. This led to the formation of oxygen vacancies, which are largely occupied by adsorbed oxygen species. The reduction process was facilitated by electron injection into the conduction band, weakening metal-oxygen bonds and promoting oxygen loss<sup>[<xref ref-type="bibr" rid="B41">41</xref>]</sup>. The reversibility of the conductivity change upon atmosphere switching suggests that the changes of oxygen vacancies are also reversible [<xref ref-type="fig" rid="fig5">Figure 5</xref>].</p>
          <fig id="fig11" position="float" width="480">
            <label>Figure 11</label>
            <caption>
              <p>Wide XPS survey spectra of Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub>.</p>
            </caption>
            <graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="microstructures6008.fig.11.jpg" />
          </fig>
          <fig id="fig12" position="float">
            <label>Figure 12</label>
            <caption>
              <p>XPS spectra of Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub>. (A) Ca 2p spectra; (B) Ti 2p spectra; (C) Nb 3d spectra; (D) O 1s spectra.</p>
            </caption>
            <graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="microstructures6008.fig.12.jpg" />
          </fig>
        </sec>
        <sec id="sec3-3-3">
          <title>Electron paramagnetic resonance</title>
          <p>Although sintering in Ar generated a large number of oxygen vacancies in Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub>, the valence states of the metal elements remained unchanged. This phenomenon, where oxygen vacancies form without reduction of the metal cations, was also observed in R-WO₃ by Zhang <italic>et al.</italic><sup>[<xref ref-type="bibr" rid="B43">43</xref>]</sup>. While the charge-compensating electrons from oxygen vacancies can be either trapped by metal ions or localized at the vacancy sites, Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> is an example of the latter<sup>[<xref ref-type="bibr" rid="B41">41</xref>]</sup>. The EPR spectrum [<xref ref-type="fig" rid="fig13">Figure 13</xref>] shows a symmetric signal at g = 2.0014, which is consistent with electrons being trapped at oxygen vacancies<sup>[<xref ref-type="bibr" rid="B43">43</xref>,<xref ref-type="bibr" rid="B50">50</xref>-<xref ref-type="bibr" rid="B56">56</xref>]</sup>. The weak intensity of the EPR signal indicates a very small number of unpaired electrons, suggesting a relatively minor contribution of electronic conduction in Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub>. This is supported by preceding EMF measurements under an air|N<sub>2</sub> gas concentration cell, which revealed that the t<sub>ion</sub> values are above 0.8 across the entire temperature range [<xref ref-type="fig" rid="fig7">Figure 7</xref>]. When heating Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> in Ar, the generation of oxygen vacancies can be described by Equation (3)<sup>[<xref ref-type="bibr" rid="B41">41</xref>]</sup>,</p>
         
		 <p><disp-formula> <label>(3)</label> <tex-math id="E1"> $$ \begin{equation}  \begin{aligned}  O_{O}^{x} \rightleftharpoons V_{\ddot{O} }+2 e^{-}+\frac{1}{2} O_{2}  \end{aligned} \end{equation} $$ </tex-math>
</disp-formula></p>
		 
		 <p>where <inline-formula><tex-math id="M4">$$O_{O}^{x}$$</tex-math></inline-formula> represents a neutral lattice oxygen atom, <inline-formula><tex-math id="M4">$$V_{\ddot{O} }$$</tex-math></inline-formula> represents an oxygen vacancy in the +2 charge state, and e<sup>-</sup> represents electrons.</p>
		 
		  <fig id="fig13" position="float" width="480">
            <label>Figure 13</label>
            <caption>
              <p>EPR spectrum at room-temperature of Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub>.</p>
            </caption>
            <graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="microstructures6008.fig.13.jpg" />
          </fig>
		 
		 
          <p>Accordingly, the equilibrium <inline-formula><tex-math id="M4">$$V_{\ddot{O} }$$</tex-math></inline-formula> concentration, [<inline-formula><tex-math id="M4">$$V_{\ddot{O} }$$</tex-math></inline-formula>], can be described by Equation (4)<sup>[<xref ref-type="bibr" rid="B41">41</xref>]</sup>,</p>
         
		 
		  <p><disp-formula> <label>(4)</label> <tex-math id="E1"> $$ \begin{equation}  \begin{aligned} K=\left[V_{\ddot{O} }\right] \cdot {pO}_{2}^{1 / 2} /\left[O_{o}^{x}\right]=\exp \left(\frac{-\Delta G_{f}}{k_{B}T}\right) \end{aligned} \end{equation} $$ </tex-math>
</disp-formula></p>
		 
		 
		 
		 
          <p>where <italic>K</italic> is the equilibrium constant, <italic>k<sub>B</sub></italic> is the Boltzmann constant, <italic>pO</italic><sub>2</sub> is the <italic>O</italic><sub>2</sub> partial pressure, Δ<italic>G<sub>f</sub></italic> is the formation free energy of <inline-formula><tex-math id="M4">$$V_{\ddot{O} }$$</tex-math></inline-formula>, and [<inline-formula><tex-math id="M4">$$O_{O}^{x}$$</tex-math></inline-formula>] is the lattice oxygen concentration.</p>
          <p>Based on Equation (4), a decrease in <italic>pO</italic><sub>2</sub> leads to an increase in [<inline-formula><tex-math id="M4">$$V_{\ddot{O} }$$</tex-math></inline-formula>]. This provides a rationale for creating oxygen vacancies in a low-oxygen atmosphere or under vacuum.</p>
        </sec>
        <sec id="sec3-3-4">
          <title>Bond valence site energy calculations and maximum entropy method</title>
          <p>Studying the oxide-ion migration pathways is crucial for understanding the electrochemical behavior of the material. BVSE calculations, based on Pauling's principle of local charge neutrality, were performed by placing the mobile ion at all points of a three-dimensional grid that spans the unit cell<sup>[<xref ref-type="bibr" rid="B57">57</xref>]</sup>. This grid represents a fixed, rigid structural framework. The BVSE method has been extensively used to identify crystalline frameworks with infinite networks that facilitate the transport of ions. It also serves to rank materials based on the accessible volume within the crystal structure where the valence mismatch is low. The migration pathways are simulated through a two-step process: first, transition positions between equilibrium sites are identified by calculating the ion's valence state; then, the complete pathways are reconstructed by connecting these positions. The oxide-ion migration pathways in Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> were simulated by BVSE calculations. At an iso-surface value (oxide-ion migration barrier) of 0.55 eV, the O1-site atoms are interconnected [<xref ref-type="fig" rid="fig14">Figure 14A</xref>]. Simultaneously, O1 and O2 sites are connected. This indicates that oxide ion migration occurs through O1-O1 and O2-O1-O2 pathways within the lattice, confirming three-dimensional oxide-ion diffusion. The results highlight the importance of O1-site vacancies for oxide-ion migration, as O2-site atoms must pass through the O1 site during migration. Thus, creating oxygen vacancies at the O1 site will enhance the conductivity of O2-site atoms. The MEM electron density distribution of oxide ions along the migration pathway exhibits good agreement with the BVSE calculations [<xref ref-type="fig" rid="fig14">Figure 14B</xref>], thereby further confirming the reliability of the BVSE results. Notably, the oxide-ion migration barrier calculated in this work (0.55 eV) is lower than that derived from the crystal structure reported by Roth <italic>et al</italic>.<sup>[<xref ref-type="bibr" rid="B27">27</xref>]</sup> (1.14 eV). This difference can be attributed primarily to the different conditions under which the XRD data were obtained. The structure reported by Roth <italic>et al.</italic> was determined from room-temperature XRD data, whereas our calculations are based on crystal structure parameters refined from high-temperature XRD data. Oxide-ion conduction is a thermally activated process. Therefore, the high-temperature structure provides a more accurate representation of the conduction behavior. This structure more accurately captures the migration pathways and local coordination environments under operating conditions, thereby providing a more reliable basis for the calculated migration barrier. The reliability of our refined result is further supported by the high quality of the Rietveld refinement, with <italic>R</italic><sub>F</sub> &lt; 7% and both <italic>R</italic><sub>wp</sub> and <italic>R</italic><sub>p</sub> &lt; 4%. These low residual factors ensure the accuracy of the refined crystal structure and further guarantee the credibility of the subsequent BVSE calculations. Therefore, the calculation results in this work represent the high-temperature conduction behavior of Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> more realistically.</p>
          <fig id="fig14" position="float">
            <label>Figure 14</label>
            <caption>
              <p>BVSE and MEM calculations for Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub>. (A) The calculated BVSE map of oxide ions with an iso-surface at 0.55 eV, where the iso-surface is marked by yellow areas; (B) MEM electron density distribution for oxide ions, where the electron density is marked by pink areas.</p>
            </caption>
            <graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="microstructures6008.fig.14.jpg" />
          </fig>
        </sec>
      </sec>
    </sec>
    <sec id="sec4">
      <title>CONCLUSIONS</title>
      <p>This work aims to investigate the conductive properties and conduction mechanism of Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub>. The conductivity of Ca<sub>1.46</sub>Ti<sub>1.38</sub>Nb<sub>1.11</sub>O<sub>7</sub> is strongly dependent on the oxygen partial pressure, exhibiting significantly enhanced conductivity under a reducing atmosphere. The variations in conductivity across different atmospheres can be attributed to changes in the oxygen vacancy concentration and the valence states of the metal cations. These results confirm that creating oxygen vacancies through synthesis in a low-oxygen atmosphere is an effective strategy for enhancing ionic conductivity. Future research will focus on optimizing the defect chemistry by carefully controlling the synthesis atmosphere to further enhance the material's performance.</p>
    </sec>
  </body>
  <back>
    <sec>
      <title>DECLARATIONS</title>
	  <sec>
        <title>Authors’ contributions</title>
        <p>Methodology, data curation, investigation, writing - original draft: Yao, Y.</p>
        <p>Methodology, investigation: Liu, S.; Sun, H.; Yao, J.</p>
        <p>Funding acquisition, investigation, methodology, supervision: Li, W. C.</p>
        <p>Data curation, funding acquisition, investigation, methodology, supervision, writing - original draft, writing – review &amp; editing: Zhang, W.</p>
      </sec>
      <sec>
        <title>Availability of data and materials</title>
        <p>The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.</p>
      </sec>
      <sec>
        <title>AI and AI-assisted tools statement</title>
        <p>Not applicable.</p>
      </sec>
      <sec>
        <title>Financial support and sponsorship</title>
        <p>This work was financially supported by National Natural Science Foundation of China (NSFC) (Nos. 22478066) and Fundamental Research Funds for the Central Universities, DUT23RC(3)024.</p>
      </sec>
      <sec>
        <title>Conflicts of interest</title>
        <p>All authors declared that there are no conflicts of interest.</p>
      </sec>
      <sec>
        <title>Ethical approval and consent to participate</title>
        <p>Not applicable.</p>
      </sec>
      <sec>
        <title>Consent for publication</title>
        <p>Not applicable.</p>
      </sec>
	  
	    <sec>
        <title>Copyright</title>
        <p>© The Author(s) 2026.</p>
      </sec> 
	  
    </sec>
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