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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Earth Sci.</journal-id>
<journal-title>Frontiers in Earth Science</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Earth Sci.</abbrev-journal-title>
<issn pub-type="epub">2296-6463</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">740685</article-id>
<article-id pub-id-type="doi">10.3389/feart.2021.740685</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Earth Science</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>High Pressure Behaviors and a Novel High-Pressure Phase of Cuprous Oxide Cu<sub>2</sub>O</article-title>
<alt-title alt-title-type="left-running-head">Qin et&#x20;al.</alt-title>
<alt-title alt-title-type="right-running-head">High-Pressure Novel Phase of Cu2O</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Qin</surname>
<given-names>Fei</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1392881/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Zhang</surname>
<given-names>Dongzhou</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Qin</surname>
<given-names>Shan</given-names>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
</contrib>
</contrib-group>
<aff id="aff1">
<label>
<sup>1</sup>
</label>School of Earth Sciences and Resources, China University of Geosciences (Beijing), <addr-line>Beijing</addr-line>, <country>China</country>
</aff>
<aff id="aff2">
<label>
<sup>2</sup>
</label>School of Ocean and Earth Science and Technology, Hawai&#x2019;i Institute of Geophysics and Planetology, University of Hawaii at Manoa, <addr-line>Honolulu</addr-line>, <addr-line>HI</addr-line>, <country>United&#x20;States</country>
</aff>
<aff id="aff3">
<label>
<sup>3</sup>
</label>School of Earth and Space Sciences, Peking University, <addr-line>Beijing</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/1234578/overview">Lidong Dai</ext-link>, Institute of Geochemistry (CAS), 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/1412709/overview">Fang Xu</ext-link>, University College London, United&#x20;Kingdom</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1414792/overview">Xiang Wu</ext-link>, China University of Geosciences, China</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Fei Qin, <email>fei.qin@cugb.edu.cn</email>
</corresp>
<fn fn-type="other">
<p>This article was submitted to Earth and Planetary Materials, a section of the journal Frontiers in Earth Science</p>
</fn>
</author-notes>
<pub-date pub-type="epub">
<day>20</day>
<month>08</month>
<year>2021</year>
</pub-date>
<pub-date pub-type="collection">
<year>2021</year>
</pub-date>
<volume>9</volume>
<elocation-id>740685</elocation-id>
<history>
<date date-type="received">
<day>13</day>
<month>07</month>
<year>2021</year>
</date>
<date date-type="accepted">
<day>11</day>
<month>08</month>
<year>2021</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2021 Qin, Zhang and Qin.</copyright-statement>
<copyright-year>2021</copyright-year>
<copyright-holder>Qin, Zhang and Qin</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&#x20;terms.</p>
</license>
</permissions>
<abstract>
<p>In the present study, we extensively explored the phase stabilities and elastic behaviors of Cu<sub>2</sub>O with elevated pressures up to 29.3&#xa0;GPa based on single-crystal X-ray diffraction measurements. The structural sequence of Cu<sub>2</sub>O is different than previously determined. Specifically, we have established that Cu<sub>2</sub>O under pressure, displays a cubic-tetragonal-monoclinic phase transition sequence, and a novel monoclinic high-pressure phase assigned to the <italic>P</italic>1<italic>a</italic>1 or <italic>P</italic>12/<italic>a</italic>1 space group was firstly observed. The monoclinic phase Cu<sub>2</sub>O exhibits anisotropic compression with axial compressibility <italic>&#x3b2;</italic>
<sub>
<italic>b</italic>
</sub> &#x3e; <italic>&#x3b2;</italic>
<sub>
<italic>c</italic>
</sub> &#x3e; <italic>&#x3b2;</italic>
<sub>
<italic>a</italic>
</sub> in a ratio of 1.00:1.64:1.45. The obtained isothermal bulk modulus of cubic and monoclinic phase Cu<sub>2</sub>O are 125(2) and 41(6) GPa, respectively, and the <italic>K</italic>
<sub>
<italic>T</italic>0</sub>&#x2019; is fixed at 4. Our results provide new insights into the phase stability and elastic properties of copper oxides and chalcogenides at extreme conditions.</p>
</abstract>
<kwd-group>
<kwd>Cu<sub>2</sub>O</kwd>
<kwd>phase transitions</kwd>
<kwd>synchrotron single-crystal X-ray diffraction</kwd>
<kwd>copper compounds</kwd>
<kwd>high pressure</kwd>
</kwd-group>
<contract-sponsor id="cn001">Foundation for Innovative Research Groups of the National Natural Science Foundation of China<named-content content-type="fundref-id">10.13039/501100012659</named-content>
</contract-sponsor>
</article-meta>
</front>
<body>
<sec id="s1">
<title>Introduction</title>
<p>The behaviors of transition metals and their oxides under high-temperature and high-pressure conditions have been studied extensively over a few decades, and knowledge about such material has important applications in physics, materials science, and engineering (<xref ref-type="bibr" rid="B2">Austin and Mott, 1970</xref>; <xref ref-type="bibr" rid="B7">Errandonea, 2006</xref>). Copper and its oxides are among the most investigated transition-metal materials. Cuprous oxide is a high-temperature semiconductor and one promising candidate materials for photo-electrochemical applications (<xref ref-type="bibr" rid="B17">Maksimov, 2000</xref>; <xref ref-type="bibr" rid="B13">Laskowski et&#x20;al., 2003</xref>; <xref ref-type="bibr" rid="B12">Khanna et&#x20;al., 2007</xref>). However, variations in physical properties and structural change of cuprous oxide Cu<sub>2</sub>O at extreme conditions have not been fully investigated.</p>
<p>Cu<sub>2</sub>O crystalizes in a simple cubic Bravais lattice with space group <italic>Pn</italic>-3<italic>m</italic> under normal thermodynamic conditions, while it has numerous structure forms at extreme conditions (<xref ref-type="bibr" rid="B16">Machon et&#x20;al., 2003</xref>; <xref ref-type="bibr" rid="B4">Cortona and Mebarki, 2011</xref>; <xref ref-type="bibr" rid="B9">Feng et&#x20;al., 2017</xref>). Most of previous studies have focused on the structural variations under high <italic>P-T</italic> conditions based on first-principles calculations. <xref ref-type="bibr" rid="B4">Cortona and Mebarki (2011)</xref> described the transition from cubic Cu<sub>2</sub>O to the CdI<sub>2</sub>-type structure (hexagonal, <italic>R</italic>-3<italic>m</italic>) at 10&#xa0;GPa, while <xref ref-type="bibr" rid="B9">Feng et&#x20;al. (2017)</xref> suggested two phase transitions, one at 5&#xa0;GPa (<italic>Pn</italic>-3<italic>m</italic>&#x2192;<italic>R</italic>-3<italic>m</italic>) and the other at 12&#xa0;GPa (<italic>R</italic>-3<italic>m</italic>&#x2192;<italic>R</italic>-3<italic>m</italic>1). However, this is hard to reconcile with some experimental results on the pressure-induced structural transformations of Cu<sub>2</sub>O. A tetragonal phase was demonstrated by <xref ref-type="bibr" rid="B16">Machon et&#x20;al. (2003)</xref> at pressures between 0.7 and 2.2&#xa0;GPa using angle-dispersive powder X-ray diffraction (XRD), and another pseudocubic phase was detected at &#x223c;8.5&#xa0;GPa. What is more, <xref ref-type="bibr" rid="B23">Sinitsyn et&#x20;al. (2004)</xref> found a new hexagonal phase with lattice parameters of <italic>a</italic>&#x20;&#x3d; 5.86&#xa0;&#xc5; and <italic>c</italic>&#x20;&#x3d; 18.78&#xa0;&#xc5;&#xa0;at 21&#xa0;GPa which was significantly different from those reported earlier by <xref ref-type="bibr" rid="B26">Werner and Hochheimer (1982)</xref>, who studied a hexagonal phase with CdCl<sub>2</sub>-type structure with <italic>a</italic>&#x20;&#x3d; 2.82&#xa0;&#xc5; and <italic>c</italic>&#x20;&#x3d; 12.7&#xa0;&#xc5; measured at 18&#xa0;GPa. Therefore, phase relations of Cu<sub>2</sub>O at higher pressures are more sparse and show less mutual agreement. Further investigation is needed to study the exact high temperature and high pressures phases of&#x20;Cu<sub>2</sub>O.</p>
<p>There are limited studies on the behavior of cuprous oxides and copper chalcogenides under high pressure and high temperature conditions. In this present work, we report the phase transformations and elastic properties of Cu<sub>2</sub>O up to &#x223c;30&#xa0;GPa at room temperature, by using synchrotron-based single-crystal XRD with diamond anvil cell (DAC). We confirmed the tetragonal phase Cu<sub>2</sub>O observed between 10.4 and 13.8&#xa0;GPa, and a novel monoclinic phase at higher pressures is also reported. As is well-known, physical properties of materials can be modified by tailoring either chemical composition or microstructure. These results can improve our knowledge of how pressure affect their elastic and physical properties. In this report we also present the measured compressibilities and equations of states of these high pressure phases of&#x20;Cu<sub>2</sub>O.</p>
</sec>
<sec sec-type="materials|methods" id="s2">
<title>Materials and Methods</title>
<p>The cuprite measured in this study was originated from the Tonglushan Copper Miners in Daye, Hubei province. Single-crystal samples of natural, brick-red cuprite were selected as the starting material of our study. We screened several chips and polished them to &#x223c;10&#xa0;&#x3bc;m in thickness. At ambient conditions, the Cu<sub>2</sub>O was characterized in an empty diamond anvil cell (DAC) by single crystal X-ray diffraction, at the GSECARS beamline 13-BM-C of the Advanced Photon Source (APS), Argonne National Laboratory (<xref ref-type="bibr" rid="B28">Zhang et&#x20;al., 2017</xref>). Diffraction collected at ambient conditions showed that the cuprite crystal had a <italic>Pn</italic>-3<italic>m</italic> space group with <italic>a</italic>&#x20;&#x3d; 4.2733(7) &#xc5;, and the Cu<sub>2</sub>O samples with a purity of 99.99% were used for the current&#x20;study.</p>
<p>High-pressure compression measurements were performed, using short symmetric DACs fitted with Boehler-Almax diamond anvils with 300&#xa0;&#x3bc;m flat culets and mounted into seats with 60&#xb0; opening. Rhenium gaskets were preindented to &#x223c;40&#xa0;&#x3bc;m thickness, and holes were drilled to &#x223c;170&#xa0;&#x3bc;m diameter for the samples. On compression, the gasket thickness and sample chamber diameter both decrease to &#x223c;20&#xa0;&#x3bc;m&#xa0;at the highest pressures reached. The polished Cu<sub>2</sub>O sample was loaded together into the sample chamber along with Pt foil for pressure calibration (<xref ref-type="bibr" rid="B8">Fei et&#x20;al., 2007</xref>). To achieve quasi-hydrostatic conditions and maintain similar pressure environments everywhere in the sample chamber, we loaded the cell with neon as the pressure-transmitting medium using the COMPRES/GSECARS gas-loading system (<xref ref-type="bibr" rid="B21">Rivers et&#x20;al., 2008</xref>).</p>
<p>
<italic>In situ</italic> high-pressure single-crystal X-ray diffraction experiments on Beamline 13-BM-C used a monochromatic X-ray beam with a wavelength of 0.4340&#xa0;&#xc5; and focused to a 15&#x20;&#xd7; 15&#xa0;&#x3bc;m<sup>2</sup> spot. The experimental details were also described previously (<xref ref-type="bibr" rid="B19">Qin et&#x20;al., 2017</xref>; <xref ref-type="bibr" rid="B28">Zhang et&#x20;al., 2017</xref>). To obtain adequate number of diffraction peaks of samples and increase the coverage of the reciprocal space, we collected data at four different detector positions. The diffraction images were analyzed using the ATREX/RSV software package (<xref ref-type="bibr" rid="B6">Dera et&#x20;al., 2013</xref>). Integrated diffraction data were analyzing using the DIOPTAS software (<xref ref-type="bibr" rid="B18">Prescher and Prakapenka, 2015</xref>), the high-pressure synchrotron XRD patterns were indexed by Dicvol06 (<xref ref-type="bibr" rid="B15">Lou&#xeb;r and Boultif, 2007</xref>). Lattice parameters were calculated by the program UnitCell and the Le Bail refinement by GSAS (<xref ref-type="bibr" rid="B11">Holland and Redfern, 1997</xref>; <xref ref-type="bibr" rid="B25">Toby, 2001</xref>).</p>
</sec>
<sec sec-type="results" id="s3">
<title>Results</title>
<sec id="s3-1">
<title>Tetragonal Phase</title>
<p>
<italic>In situ</italic> X-ray diffraction patterns of Cu<sub>2</sub>O were measured up to 29.3&#xa0;GPa under hydrostatic pressure which presented in <xref ref-type="fig" rid="F1">Figure&#x20;1A</xref>. At ambient conditions, all peaks can be indexed as the <italic>Pn</italic>-3<italic>m</italic> cubic structure (<xref ref-type="bibr" rid="B10">Hahn et&#x20;al., 1983</xref>). When pressure increased to 16.1&#xa0;GPa, an abrupt change in the integrated diffraction pattern was observed. As can be seen in the diffraction patterns in <xref ref-type="fig" rid="F1">Figure&#x20;1B</xref>, reflections from the crystal show diffuse scattering and appear as short streaks at pressures above 16.1&#xa0;GPa. Some diffraction peaks become fainter at higher angle, making it more difficult to determine the peak positions exactly (<xref ref-type="fig" rid="F1">Figure&#x20;1B</xref>). We compared our integrated data of the high-pressure phase with previous studies but did not find any compatible structures (<xref ref-type="bibr" rid="B26">Werner and Hochheimer, 1982</xref>; <xref ref-type="bibr" rid="B4">Cortona and Mebarki, 2011</xref>; <xref ref-type="bibr" rid="B9">Feng et&#x20;al., 2017</xref>).</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>
<bold>(A)</bold> Integrated XRD patterns of Cu<sub>2</sub>O at elevated pressures. Backgrounds were subtracted from the origin data. Asterisk (&#x2a;) represents the scattering peaks of neon. <bold>(B)</bold> Diffraction patterns of Cu<sub>2</sub>O at 1.2 and 13.8 GPa, respectively. The very intense diffraction spots are from the diamond anvils. Diamond peaks and diffraction lines attributed to the neon are not marked.</p>
</caption>
<graphic xlink:href="feart-09-740685-g001.tif"/>
</fig>
<p>A suspected phase transition from cubic to tetragonal between 0.7 and 2.2&#xa0;GPa was reported previously (<xref ref-type="bibr" rid="B16">Machon et&#x20;al., 2003</xref>), and our diffraction measurements confirmed this transition but at a different pressure (between 8.4 and 10.4&#xa0;GPa, <xref ref-type="fig" rid="F2">Figure&#x20;2A</xref>). We noticed that all the diffraction peaks deviated from a cubic lattice at pressures above 10.4&#xa0;GPa, and can be well indexed as tetragonal lattice Cu<sub>2</sub>O with space group <italic>P</italic>4<sub>2</sub>/<italic>nnm</italic>. The high-pressure tetragonal phase Cu<sub>2</sub>O at 10.4&#xa0;GPa, was refined by Rietveld method in GSAS program shown in <xref ref-type="fig" rid="F2">Figure&#x20;2B</xref>. The quality of the refinement is illustrated by the small <italic>R</italic>-factors and reduced <italic>&#x3a7;</italic>
<sup>2</sup>; <italic>R</italic>
<sub>p</sub> &#x3d; 0.18%, <italic>R</italic>
<sub>wp</sub> &#x3d; 0.25%, and <italic>&#x3a7;</italic>
<sup>2</sup> &#x3d; 0.93. As the tetragonal phase is the subgroup of the cubic phase (<italic>Pn</italic>-3<italic>m</italic>) and the two phases have very similar lattice parameters, i.e.,&#x20;for cubic phase, <italic>a</italic>&#x20;&#x3d; 4.267&#xa0;&#xc5; and for tetragonal phase, <italic>a</italic>&#x20;&#x3d; 4.193, <italic>a</italic>/<italic>c</italic>&#x20;&#x3d; 0.988 (<xref ref-type="bibr" rid="B10">Hahn et&#x20;al., 1983</xref>; <xref ref-type="bibr" rid="B20">Restori and Schwarzenbach, 1986</xref>; <xref ref-type="bibr" rid="B16">Machon et&#x20;al., 2003</xref>). This tetragonal structure is also indicated by the asymmetry of the peaks centered at &#x223c;8.5&#xb0;, 14.6&#xb0;, 17&#xb0; and 20&#xb0;, resulting from the overlap of the (110)(011), (211)(112), (220)(202) and (131)(113) pairs of the tetragonal structure, respectively (<xref ref-type="fig" rid="F2">Figure&#x20;2A</xref>). The tetragonal structure can be regarded as the distorted cubic structure under the uniaxial stress in the&#x20;DAC.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>
<bold>(A)</bold> Selected XRD patterns of Cu<sub>2</sub>O in the tetragonal phase. Asterisk (&#x2a;) represents the scattering peaks of neon. <bold>(B)</bold> The Rietveld refinement of Cu<sub>2</sub>O (<italic>P</italic>4<sub>2</sub>/<italic>nnm</italic>). Observed and the calculated profiles are shown using black crosses and red solid line, respectively. The residual between them is shown by the blue line at the bottom. Bragg peak positions are indicated by the small&#x20;ticks.</p>
</caption>
<graphic xlink:href="feart-09-740685-g002.tif"/>
</fig>
</sec>
<sec id="s3-2">
<title>Novel Monoclinic Phase</title>
<p>During the compression of Cu<sub>2</sub>O, all the diffraction peaks move to larger 2<italic>&#x3b8;</italic> values, as expected for pressure-induced bond shortening, and their intensities weaken gradually. When the pressure exceeds 16.1&#xa0;GPa, some new peaks appeared (<italic>d</italic> spacings at &#x223c;2.83. 2.74, 2.42, 2.30, 2.03, 1.97, 1.76&#xa0;&#xc5; and so on) and the <italic>d</italic> values of these peaks are totally different from those previous patterns, suggesting that the Cu<sub>2</sub>O undergoes a reconstructive phase transition, and with further compression to the highest pressure, the structure can persist and no other transition was observed (<xref ref-type="fig" rid="F1">Figure&#x20;1A</xref>). We have compared our patterns with some predicted hexagonal high-pressure phases of Cu<sub>2</sub>O based on previous <italic>ab initio</italic> calculation and measurement results, but none of the predicted structures matches our measured diffraction pattern (<xref ref-type="bibr" rid="B26">Werner and Hochheimer, 1982</xref>; <xref ref-type="bibr" rid="B4">Cortona and Mebarki, 2011</xref>; <xref ref-type="bibr" rid="B14">Liu et&#x20;al., 2014</xref>; <xref ref-type="bibr" rid="B9">Feng et&#x20;al., 2017</xref>). In this case, the high quality data allow us to determine the crystal structure of the new high-pressure phase of Cu<sub>2</sub>O. We chose several recognizable Debye rings, except for the neon rings, to index the crystal lattice using Dicvol06 software (<xref ref-type="bibr" rid="B15">Lou&#xeb;r and Boultif, 2007</xref>). According to our results, the 16 chosen peaks of high-pressure phase Cu<sub>2</sub>O, obtained at 16.1&#xa0;GPa, can be successfully indexed as a monoclinic structure with the lattice parameters: <italic>a</italic>&#x20;&#x3d; 5.665(3) &#xc5;, <italic>b</italic>&#x20;&#x3d; 2.741(2) &#xc5;, <italic>c</italic>&#x20;&#x3d; 4.255(2) &#xc5;, <italic>&#x3b2;</italic> &#x3d; 93.54(8)&#xb0; and <italic>V</italic>&#x20;&#x3d; 65.94(2) &#xc5;<sup>3</sup> (<xref ref-type="table" rid="T1">Table&#x20;1</xref>).</p>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Calculated and Observed <italic>d</italic> spacings of a new monoclinic polymorph Cu<sub>2</sub>O, as well as the normalized intensity <italic>I</italic>
<sub>obs</sub> for the <italic>h k l</italic> reflections.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">
<italic>h k l</italic>
</th>
<th align="center">
<italic>d</italic>
<sub>obs</sub>
</th>
<th align="center">
<italic>d</italic>
<sub>cal</sub>
</th>
<th align="center">
<italic>d</italic>
<sub>obs</sub>-<italic>d</italic>
<sub>cal</sub>
</th>
<th align="center">2<italic>&#x3b8;</italic>
<sub>obs</sub>
</th>
<th align="center">2<italic>&#x3b8;</italic>
<sub>cal</sub>
</th>
<th align="center">2<italic>&#x3b8;</italic>
<sub>obs</sub>-2<italic>&#x3b8;</italic>
<sub>cal</sub>
</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">200</td>
<td align="char" char=".">2.8301</td>
<td align="char" char=".">2.8274</td>
<td align="char" char=".">0.0027</td>
<td align="char" char=".">8.795</td>
<td align="char" char=".">8.804</td>
<td align="char" char=".">&#x2212;0.008</td>
</tr>
<tr>
<td align="left">010</td>
<td align="char" char=".">2.741</td>
<td align="char" char=".">2.7407</td>
<td align="char" char=".">0.0003</td>
<td align="char" char=".">9.082</td>
<td align="char" char=".">9.082</td>
<td align="char" char=".">&#x2212;0.001</td>
</tr>
<tr>
<td align="left">20-1</td>
<td align="char" char=".">2.419</td>
<td align="char" char=".">2.4234</td>
<td align="char" char=".">&#x2212;0.0044</td>
<td align="char" char=".">10.293</td>
<td align="char" char=".">10.275</td>
<td align="char" char=".">0.019</td>
</tr>
<tr>
<td align="left">011</td>
<td align="char" char=".">2.3014</td>
<td align="char" char=".">2.3028</td>
<td align="char" char=".">&#x2212;0.0016</td>
<td align="char" char=".">10.823</td>
<td align="char" char=".">10.815</td>
<td align="char" char=".">0.008</td>
</tr>
<tr>
<td align="left">002</td>
<td align="char" char=".">2.124</td>
<td align="char" char=".">2.1233</td>
<td align="char" char=".">0.0007</td>
<td align="char" char=".">11.728</td>
<td align="char" char=".">11.732</td>
<td align="char" char=".">&#x2212;0.004</td>
</tr>
<tr>
<td align="left">10-2</td>
<td align="char" char=".">2.0315</td>
<td align="char" char=".">2.0294</td>
<td align="char" char=".">0.0021</td>
<td align="char" char=".">12.267</td>
<td align="char" char=".">12.277</td>
<td align="char" char=".">0.01</td>
</tr>
<tr>
<td align="left">210</td>
<td align="char" char=".">1.971</td>
<td align="char" char=".">1.9679</td>
<td align="char" char=".">0.0031</td>
<td align="char" char=".">12.642</td>
<td align="char" char=".">12.662</td>
<td align="char" char=".">&#x2212;0.02</td>
</tr>
<tr>
<td align="left">211</td>
<td align="char" char=".">1.7613</td>
<td align="char" char=".">1.7569</td>
<td align="char" char=".">0.0044</td>
<td align="char" char=".">14.157</td>
<td align="char" char=".">14.189</td>
<td align="char" char=".">&#x2212;0.033</td>
</tr>
<tr>
<td align="left">30-1</td>
<td align="center">&#x2014;</td>
<td align="char" char=".">1.7636</td>
<td align="char" char=".">&#x2212;0.0026</td>
<td align="center">&#x2014;</td>
<td align="char" char=".">14.135</td>
<td align="char" char=".">0.021</td>
</tr>
<tr>
<td align="left">21-2</td>
<td align="char" char=".">1.4741</td>
<td align="char" char=".">1.4753</td>
<td align="char" char=".">&#x2212;0.0012</td>
<td align="char" char=".">16.932</td>
<td align="char" char=".">16.917</td>
<td align="char" char=".">0.015</td>
</tr>
<tr>
<td align="left">003</td>
<td align="char" char=".">1.4138</td>
<td align="char" char=".">1.4155</td>
<td align="char" char=".">&#x2212;0.0017</td>
<td align="char" char=".">17.656</td>
<td align="char" char=".">17.637</td>
<td align="char" char=".">0.019</td>
</tr>
<tr>
<td align="left">212</td>
<td align="center">&#x2014;</td>
<td align="char" char=".">1.4134</td>
<td align="char" char=".">0.0007</td>
<td align="center">&#x2014;</td>
<td align="char" char=".">17.664</td>
<td align="char" char=".">&#x2212;0.008</td>
</tr>
<tr>
<td align="left">400</td>
<td align="center">&#x2014;</td>
<td align="char" char=".">1.4137</td>
<td align="char" char=".">&#x2212;0.0003</td>
<td align="center">&#x2014;</td>
<td align="char" char=".">17.66</td>
<td align="char" char=".">&#x2212;0.004</td>
</tr>
<tr>
<td align="left">013</td>
<td align="char" char=".">1.257</td>
<td align="char" char=".">1.2577</td>
<td align="char" char=".">&#x2212;0.0007</td>
<td align="char" char=".">19.882</td>
<td align="char" char=".">19.871</td>
<td align="char" char=".">0.011</td>
</tr>
<tr>
<td align="left">11-3</td>
<td align="char" char=".">1.2441</td>
<td align="char" char=".">1.2422</td>
<td align="char" char=".">&#x2212;0.0019</td>
<td align="char" char=".">20.092</td>
<td align="char" char=".">20.121</td>
<td align="char" char=".">&#x2212;0.03</td>
</tr>
<tr>
<td align="left">312</td>
<td align="char" char=".">1.2243</td>
<td align="char" char=".">1.2242</td>
<td align="char" char=".">0.0001</td>
<td align="char" char=".">20.424</td>
<td align="char" char=".">20.42</td>
<td align="char" char=".">0.004</td>
</tr>
<tr>
<td align="left">41-1</td>
<td align="center">&#x2014;</td>
<td align="char" char=".">1.2232</td>
<td align="char" char=".">0.0009</td>
<td align="center">&#x2014;</td>
<td align="char" char=".">20.438</td>
<td align="char" char=".">&#x2212;0.014</td>
</tr>
<tr>
<td align="left">022</td>
<td align="char" char=".">1.1511</td>
<td align="char" char=".">1.1514</td>
<td align="char" char=".">&#x2212;0.0003</td>
<td align="char" char=".">21.734</td>
<td align="char" char=".">21.727</td>
<td align="char" char=".">0.007</td>
</tr>
<tr>
<td align="left">004</td>
<td align="char" char=".">1.061</td>
<td align="char" char=".">1.0616</td>
<td align="char" char=".">&#x2212;0.0006</td>
<td align="char" char=".">23.603</td>
<td align="char" char=".">23.589</td>
<td align="char" char=".">0.014</td>
</tr>
<tr>
<td align="left">023</td>
<td align="char" char=".">0.984</td>
<td align="char" char=".">0.9846</td>
<td align="char" char=".">&#x2212;0.0006</td>
<td align="char" char=".">25.48</td>
<td align="char" char=".">25.465</td>
<td align="char" char=".">0.015</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>Crystal lattice parameters, characteristic X-ray extinctions and diffracted intensities unambiguously documented that the crystal structure of the monoclinic phase Cu<sub>2</sub>O belongs to the primitive lattice with no exception. 0<italic>k</italic>0 manage the requirement of <italic>k</italic>&#x20;&#x3d; 2n &#x2b; 1, and <italic>h</italic>00, 00<italic>l</italic> are also fulfilled the rules <italic>h</italic>&#x20;&#x3d; 2n and <italic>l</italic>&#x20;&#x3d; 2n. Consequently, space groups fulfilling these conditions are <italic>P</italic>1<italic>a</italic>1 (No. 7) and <italic>P</italic>12/<italic>a</italic>1 (No. 13) (<xref ref-type="bibr" rid="B10">Hahn et&#x20;al., 1983</xref>). However, the quality of our diffraction pattern is not enough to differentiate the two space groups, as the space group <italic>Pa</italic> is a subgroup of <italic>P</italic>2/<italic>a</italic>, and both have very similar diffraction peak distributions.</p>
</sec>
<sec id="s3-3">
<title>Compressibility of Cu<sub>2</sub>O</title>
<p>The <italic>P-V</italic> data of both Cu<sub>2</sub>O phases were fitted using the third-order Birch-Murnaghan equation of state (BM3-EoS) with the data all equally weighted, since the errors in volume and pressure were similar for all measurements (<xref ref-type="bibr" rid="B1">Angle et&#x20;al., 2014</xref>) (<xref ref-type="fig" rid="F3">Figure&#x20;3</xref>). The refined lattice parameters of Cu<sub>2</sub>O at various pressures are listed in <xref ref-type="table" rid="T2">Table&#x20;2</xref>. As the tetragonal structure could be regarded as the distorted cubic phase and the volumes of two phases only have marginal difference, thus we used cubic structure model to calculate the equation of state between 10.4 and 13.8&#xa0;GPa to get higher accuracy. The resulting fitted parameters of volume, bulk modulus and its pressure derivative of cubic Cu<sub>2</sub>O are as follows: <italic>V</italic>
<sub>0</sub> &#x3d; 78.05(3) &#xc5;<sup>3</sup>, <italic>K</italic>
<sub>
<italic>T</italic>0</sub> &#x3d; 137(5) GPa and <italic>K</italic>
<sub>
<italic>T</italic>0</sub>&#x2019; &#x3d; 1.8(7), respectively, which are 4.6% higher compared with the corresponding values from the experimental data from <xref ref-type="bibr" rid="B26">Werner and Hochheimer (1982)</xref>, who reported 131&#xa0;GPa when <italic>K</italic>&#x2032; is 5.7. In this present study, we also calculated the equation of state by fixing <italic>K</italic>
<sub>
<italic>T</italic>0</sub>&#x2019; at 4, resulting in <italic>K</italic>
<sub>
<italic>T</italic>0</sub> &#x3d; 125(2)&#x20;GPa.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>The volume of Cu<sub>2</sub>O as a function of pressure. A volume collapse of 7.7% at about 10.4&#x2013;13.8&#xa0;GPa, which is the location where the phase transition occurs between the tetragonal and monoclinic phases.</p>
</caption>
<graphic xlink:href="feart-09-740685-g003.tif"/>
</fig>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>Lattice parameters of Cu<sub>2</sub>O (cubic, tetragonal and monoclinic phases) at various pressures.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Pressure (GPa)</th>
<th align="center">a (&#xc5;)</th>
<th align="center">b (&#xc5;)</th>
<th align="center">c (&#xc5;)</th>
<th align="center">&#x392;</th>
<th align="center">V (&#xc5;<sup>3</sup>)</th>
<th align="center">Symmetry</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">0.00001</td>
<td align="center">4.2733(7)</td>
<td align="center">&#x2014;</td>
<td align="center">&#x2014;</td>
<td align="center">&#x2014;</td>
<td align="center">78.04(2)</td>
<td align="left">Cubic</td>
</tr>
<tr>
<td align="left">1.2<xref ref-type="table-fn" rid="Tfn1">
<sup>a</sup>
</xref>
</td>
<td align="center">4.2630(6)</td>
<td align="center">&#x2014;</td>
<td align="center">&#x2014;</td>
<td align="center">&#x2014;</td>
<td align="center">77.47(9)</td>
<td align="left">&#x2014;</td>
</tr>
<tr>
<td align="left">3.4</td>
<td align="center">4.2405(6)</td>
<td align="center">&#x2014;</td>
<td align="center">&#x2014;</td>
<td align="center">&#x2014;</td>
<td align="center">76.25(9)</td>
<td align="left">&#x2014;</td>
</tr>
<tr>
<td align="left">7.1</td>
<td align="center">4.2036(6)</td>
<td align="center">&#x2014;</td>
<td align="center">&#x2014;</td>
<td align="center">&#x2014;</td>
<td align="center">74.28(9)</td>
<td align="left">&#x2014;</td>
</tr>
<tr>
<td align="left">8.4</td>
<td align="center">4.1909(5)</td>
<td align="center">&#x2014;</td>
<td align="center">&#x2014;</td>
<td align="center">&#x2014;</td>
<td align="center">73.61(7)</td>
<td align="left">&#x2014;</td>
</tr>
<tr>
<td align="left">10.4</td>
<td align="center">4.174(2)</td>
<td align="center">4.174(2)</td>
<td align="center">4.171(3)</td>
<td align="center">&#x2014;</td>
<td align="center">72.67(7)</td>
<td align="left">Tetragonal</td>
</tr>
<tr>
<td align="left">12.2</td>
<td align="center">4.157(2)</td>
<td align="center">4.157(2)</td>
<td align="center">4.152(3)</td>
<td align="center">&#x2014;</td>
<td align="center">71.75(7)</td>
<td align="left">&#x2014;</td>
</tr>
<tr>
<td align="left">13.8</td>
<td align="center">4.147(3)</td>
<td align="center">4.147(3)</td>
<td align="center">4.149(4)</td>
<td align="center">&#x2014;</td>
<td align="center">71.36(10)</td>
<td align="left">&#x2014;</td>
</tr>
<tr>
<td align="left">16.1</td>
<td align="center">5.696(2)</td>
<td align="center">2.737(1)</td>
<td align="center">4.2568(8)</td>
<td align="center">93.17(3)</td>
<td align="center">66.26(2)</td>
<td align="left">Monoclinic</td>
</tr>
<tr>
<td align="left">18.6</td>
<td align="center">5.639(3)</td>
<td align="center">2.704(1)</td>
<td align="center">4.2237(8)</td>
<td align="center">92.98(3)</td>
<td align="center">64.33(2)</td>
<td align="left">&#x2014;</td>
</tr>
<tr>
<td align="left">20.7</td>
<td align="center">5.615(2)</td>
<td align="center">2.675(1)</td>
<td align="center">4.1913(7)</td>
<td align="center">93.08(3)</td>
<td align="center">62.85(2)</td>
<td align="left">&#x2014;</td>
</tr>
<tr>
<td align="left">23.0</td>
<td align="center">5.577(2)</td>
<td align="center">2.661(1)</td>
<td align="center">4.1645(7)</td>
<td align="center">93.24(3)</td>
<td align="center">61.71(2)</td>
<td align="left">&#x2014;</td>
</tr>
<tr>
<td align="left">25.7</td>
<td align="center">5.533(2)</td>
<td align="center">2.647(1)</td>
<td align="center">4.1307(7)</td>
<td align="center">93.47(3)</td>
<td align="center">60.40(2)</td>
<td align="left">&#x2014;</td>
</tr>
<tr>
<td align="left">29.3</td>
<td align="center">5.520(2)</td>
<td align="center">2.630(1)</td>
<td align="center">4.0997(7)</td>
<td align="center">93.60(3)</td>
<td align="center">59.38(2)</td>
<td align="left">&#x2014;</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn id="Tfn1">
<label>a</label>
<p>Nominal uncertainty in pressure in &#xb1;0.1&#xa0;GPa.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<p>Here, we also firstly determined the elastic properties of the monoclinic phase Cu<sub>2</sub>O using the EoSFit7c software (<xref ref-type="bibr" rid="B1">Angle et&#x20;al., 2014</xref>). The measured lattice parameters are also provided in <xref ref-type="table" rid="T2">Table&#x20;2</xref>. The derived BM2-EoS (<italic>K</italic>
<sub>
<italic>T</italic>0</sub>&#x2019; &#x3d; 4 implied) parameters yield the following bulk modulus <italic>K</italic>
<sub>
<italic>T</italic>0</sub> &#x3d; 41(6) GPa, and it is three times softer than the low-pressure phase. Axial compression behaviors are also presented in <xref ref-type="fig" rid="F4">Figure&#x20;4</xref>. It is noteworthy that the <italic>b</italic>-axis possesses a larger axial compressibility compared with <italic>a</italic>- and <italic>c</italic>-axes, and therefore being the most compressible direction within the structure. The interaxial angle <italic>&#x3b2;</italic> has an increasing trend with compression.</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Pressure dependence of normalized cell lengths (a, b and c) of monoclinic phase Cu<sub>2</sub>O. EoS fits in the current study are shown by solid curves.</p>
</caption>
<graphic xlink:href="feart-09-740685-g004.tif"/>
</fig>
</sec>
</sec>
<sec sec-type="discussion" id="s4">
<title>Discussion</title>
<p>The high-pressure behavior of cuprous oxide Cu<sub>2</sub>O has attracted broad interests due to their various structures at different <italic>P-T</italic> conditions and its potential applications. Several previous studies have been published which focus on the phase transitions and decompositions of Cu<sub>2</sub>O and its thermodynamic properties as well (<xref ref-type="bibr" rid="B16">Machon et&#x20;al., 2003</xref>; <xref ref-type="bibr" rid="B23">Sinitsyn et&#x20;al., 2004</xref>; <xref ref-type="bibr" rid="B4">Cortona and Mebarki, 2011</xref>; <xref ref-type="bibr" rid="B14">Liu et&#x20;al., 2014</xref>; <xref ref-type="bibr" rid="B9">Feng et&#x20;al., 2017</xref>). However, these previous results were unclear about the high-pressure crystal structure of Cu<sub>2</sub>O (tetragonal or hexagonal phase) and it is obvious that a large discrepancy of transformation pressure between the cubic and high-pressure phases existed between literatures. In this study, we re-confirmed the phase transition sequence from cubic-to-tetragonal phase occurred between 8.4 and 10.4&#xa0;GPa using single-crystal XRD, which is significantly more higher than previously estimated (<xref ref-type="bibr" rid="B16">Machon et&#x20;al., 2003</xref>). A new high-pressure phase of Cu<sub>2</sub>O was also indexed using Dicvol06 software (<xref ref-type="bibr" rid="B15">Lou&#xeb;r and Boultif, 2007</xref>). A volume collapse of &#x223c;7.7% in the region of 13.8&#x2013;16.1&#xa0;GPa was observed during the structural transformation from cubic to monoclinic phase (<xref ref-type="fig" rid="F3">Figure&#x20;3</xref>). There is no indication of structural decomposition in this case. In addition, it is obvious that a considerable anisotropy in axial compressibility with <italic>&#x3b2;</italic>
<sub>
<italic>b</italic>
</sub> &#x3e; <italic>&#x3b2;</italic>
<sub>
<italic>c</italic>
</sub> &#x3e; <italic>&#x3b2;</italic>
<sub>
<italic>a</italic>
</sub> and we found the ratio of zero-pressure axial compressibility is 1.00:1.64:1.45 according to our data. Thus, it can be concluded that the largest anisotropy in compressibility is along the <italic>b</italic> axis, which behaves about twice as compressible than the <italic>a</italic>-axis in the structure (<xref ref-type="fig" rid="F4">Figure&#x20;4</xref>). Further investigation should be done to investigate the exact high temperature phases of&#x20;Cu<sub>2</sub>O.</p>
<p>In some recent studies, several members of copper chalcogenides, such as Cu<sub>2</sub>S and Cu<sub>2</sub>Se have been theoretically proposed and experimentally exhibited as the thermoelastic materials (<xref ref-type="bibr" rid="B5">Danilkin et&#x20;al., 2011</xref>; <xref ref-type="bibr" rid="B22">Santamaria-Perez et&#x20;al., 2014</xref>; <xref ref-type="bibr" rid="B29">Zhang et&#x20;al., 2018</xref>; <xref ref-type="bibr" rid="B30">Zimmer et&#x20;al., 2018</xref>; <xref ref-type="bibr" rid="B27">Xue et&#x20;al., 2019</xref>). The high-pressure phase Cu<sub>2</sub>O, Cu<sub>2</sub>Se and Cu<sub>2</sub>S may adopt the same monoclinic structure at different pressure conditions, which indicates that these copper compounds may have a similar crystal chemistry configuration (<xref ref-type="bibr" rid="B22">Santamaria-Perez et&#x20;al., 2014</xref>; <xref ref-type="bibr" rid="B29">Zhang et&#x20;al., 2018</xref>). The structural complexity of Cu<sub>2</sub>S have been studied previously, in which two phase transitions occurred at 3.2 and 7.4&#xa0;GPa from the <italic>P</italic>21/<italic>c</italic> phase to two different monoclinic structures (<xref ref-type="bibr" rid="B22">Santamaria-Perez et&#x20;al., 2014</xref>). Pressure-induced structural transition sequence is also identified in Cu<sub>2</sub>Se. The initial low-pressure phase (<italic>C</italic>2/<italic>c</italic>) transformed to phase II and semimetallic phase III at 3.2 GPa, and then followed by a reconstructive transformation to bulk metallic phase IV (<italic>Pca</italic>21) at 7.4&#xa0;GPa. These mentioned phases could be confidently associated with the electronic state transitions (<xref ref-type="bibr" rid="B29">Zhang et&#x20;al., 2018</xref>; <xref ref-type="bibr" rid="B3">Chuli&#xe1;-Jordan et&#x20;al., 2020</xref>). As for the copper sulfide, three phase-transitions occurred at 3.2, 7.4 and 26&#xa0;GPa, respectively, and there is a significant difference of the reported values of bulk modulus, ranging from 72 to 113&#xa0;GPa (<xref ref-type="bibr" rid="B22">Santamaria-Perez et&#x20;al., 2014</xref>). The determination of the phase stability of such stoichiometric copper oxides under compression will give more insight into possible systematic trends in group copper chalcogenides, and provide a direct comparison with such thermoelastic materials at extreme conditions where their phase behaviors could converge.</p>
</sec>
<sec sec-type="conclusion" id="s5">
<title>Conclusion</title>
<p>The high-pressure behaviors of cuprous oxide Cu<sub>2</sub>O have been studied by synchrotron-based single-crystal XRD at pressures up to &#x223c;30&#xa0;GPa at 300&#xa0;K conditions. The initial low-pressure cubic phase transforms to distorted <italic>P</italic>4<sub>2</sub>/<italic>nnm</italic> phase between 10.4 and 13.8&#xa0;GPa, and the tetragonal structure persisted at pressure up to &#x223c;16&#xa0;GPa. A new high-pressure phase of Cu<sub>2</sub>O (monoclinic phase, <italic>P</italic>1a or <italic>P</italic>12/<italic>a</italic>1) was obtained at 16.1&#xa0;GPa at room temperature and the high-pressure elastic properties was firstly measured in this study. It is expected that the three times more compressible high-pressure phase Cu<sub>2</sub>O may process some advantages properties than previously thought. The findings contribute to broadening our knowledge of the crystal chemistry of cuprite at high-pressure conditions, thus giving a better understand of thermoelastic materials in the copper chalcogenide system.</p>
</sec>
</body>
<back>
<sec id="s6">
<title>Data Availability Statement</title>
<p>The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.</p>
</sec>
<sec id="s7">
<title>Author Contributions</title>
<p>FQ and DZ carried out the experiments. FQ, DZ, and SQ performed the data analysis and interpretation. FQ wrote the manuscript. All authors contributed to the discussion of the results and revisions of the manuscript.</p>
</sec>
<sec id="s8">
<title>Funding</title>
<p>This research was supported by the Fundamental Research Funds for the Central Universities (grant no. 590421013) and the National Natural Science Foundation of China (grant no. 42072047). Work performed at GSECARS (Sector 13) of the Advanced photon Source (APS) is supported by the NSF EAR-1634415 and the Department of Energy (DOE) DE-FG02- 94ER1446. The APS at Argonne National Laboratory is supported by the DOE, Office of Science, under Contract No.DE-AC02-06CH11357. Experiments at Sector 13-BM-C of the APS used the PX&#x5e;2 facility, supported by GSECARS and COMPRES under NSF Cooperative Agreement EAR-1661511.</p>
</sec>
<sec sec-type="COI-statement" id="s9">
<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 id="s10" sec-type="disclaimer">
<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>
<ack>
<p>We also thank S.Tkachev for gas loading the diamond&#x20;cells.</p>
</ack>
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