{"title":"Predicting Room-Temperature Conductivity of Na-Ion Super Ionic Conductors with the Minimal Number of Easily-Accessible Descriptors","authors":"Seong-Hoon Jang, Randy Jalem, Yoshitaka Tateyama","doi":"10.1002/aesr.202400158","DOIUrl":null,"url":null,"abstract":"<p>Given the vast compositional possibilities <span></span><math>\n <semantics>\n <mrow>\n <msub>\n <mrow>\n <mtext>Na</mtext>\n </mrow>\n <mi>n</mi>\n </msub>\n <msub>\n <mi>M</mi>\n <mi>m</mi>\n </msub>\n <msubsup>\n <mi>M</mi>\n <msup>\n <mi>m</mi>\n <mo>′</mo>\n </msup>\n <mo>′</mo>\n </msubsup>\n <msub>\n <mrow>\n <mtext>Si</mtext>\n </mrow>\n <mrow>\n <mn>3</mn>\n <mo>−</mo>\n <mi>p</mi>\n <mo>−</mo>\n <mi>a</mi>\n </mrow>\n </msub>\n <msub>\n <mi>P</mi>\n <mi>p</mi>\n </msub>\n <msub>\n <mrow>\n <mtext>As</mtext>\n </mrow>\n <mi>a</mi>\n </msub>\n <msub>\n <mi>O</mi>\n <mrow>\n <mn>12</mn>\n </mrow>\n </msub>\n </mrow>\n <annotation>$\\left(\\text{Na}\\right)_{n} \\left(\\text{M}\\right)_{\\text{m}} \\text{M}_{m^{&amp;#x00026;amp;amp;amp;amp;amp;aposx;}}^{&amp;#x00026;amp;amp;amp;amp;amp;aposx;} \\left(\\text{Si}\\right)_{3 - \\text{p} - \\text{a}} \\left(\\text{P}\\right)_{\\text{p}} \\left(\\text{As}\\right)_{\\text{a}} \\left(\\text{O}\\right)_{12}$</annotation>\n </semantics></math>, Na-ion superionic conductors are attractive but complicated for designing materials with enhanced room-temperature Na-ion conductivity <span></span><math>\n <semantics>\n <mrow>\n <msub>\n <mi>σ</mi>\n <mrow>\n <mtext>Na</mtext>\n <mo>,</mo>\n <mn>300</mn>\n <mo> </mo>\n <mi>K</mi>\n </mrow>\n </msub>\n </mrow>\n <annotation>$\\left(\\sigma\\right)_{\\text{Na} , 300 \\text{K}}$</annotation>\n </semantics></math>. An explicit regression model for <span></span><math>\n <semantics>\n <mrow>\n <msub>\n <mi>σ</mi>\n <mrow>\n <mtext>Na</mtext>\n <mo>,</mo>\n <mn>300</mn>\n <mo> </mo>\n <mi>K</mi>\n </mrow>\n </msub>\n </mrow>\n <annotation>$\\left(\\sigma\\right)_{\\text{Na} , 300 \\text{K}}$</annotation>\n </semantics></math> with easily-accessible descriptors is proposed by exploiting density functional theory molecular dynamics (DFT-MD). Initially, it is demonstrated that two primary descriptors, the bottleneck width along Na-ion diffusion paths <span></span><math>\n <semantics>\n <mrow>\n <msub>\n <mi>d</mi>\n <mn>1</mn>\n </msub>\n </mrow>\n <annotation>$d_{1}$</annotation>\n </semantics></math> and the average Na–Na distance <span></span><math>\n <semantics>\n <mrow>\n <mo>⟨</mo>\n <mrow>\n <msub>\n <mi>d</mi>\n <mrow>\n <mtext>Na</mtext>\n <mo>−</mo>\n <mtext>Na</mtext>\n </mrow>\n </msub>\n </mrow>\n <mo>⟩</mo>\n </mrow>\n <annotation>$$ &amp;#x00026;amp;amp;amp;amp;lt;{d}_{\\text{Na}-\\text{Na}}&amp;#x00026;amp;amp;amp;amp;gt;$$</annotation>\n </semantics></math>, modulate room-temperature Na-ion self-diffusion coefficient <span></span><math>\n <semantics>\n <mrow>\n <msub>\n <mi>D</mi>\n <mrow>\n <mtext>Na</mtext>\n <mo>,</mo>\n <mn>300</mn>\n <mo> </mo>\n <mi>K</mi>\n </mrow>\n </msub>\n </mrow>\n <annotation>$D_{\\text{Na} , 300 \\text{K}}$</annotation>\n </semantics></math>. Then, two secondary easily-accessible descriptors are introduced: Na-ion content <i>n</i>, which influences <span></span><math>\n <semantics>\n <mrow>\n <msub>\n <mi>d</mi>\n <mn>1</mn>\n </msub>\n </mrow>\n <annotation>$d_{1}$</annotation>\n </semantics></math>, <span></span><math>\n <semantics>\n <mrow>\n <mo>⟨</mo>\n <mrow>\n <msub>\n <mi>d</mi>\n <mrow>\n <mtext>Na</mtext>\n <mo>−</mo>\n <mtext>Na</mtext>\n </mrow>\n </msub>\n </mrow>\n <mo>⟩</mo>\n </mrow>\n <annotation>$$ &amp;#x00026;amp;amp;amp;amp;lt;{d}_{\\text{Na}-\\text{Na}}&amp;#x00026;amp;amp;amp;amp;gt;$$</annotation>\n </semantics></math>, and Na-ion density <span></span><math>\n <semantics>\n <mrow>\n <msub>\n <mi>ρ</mi>\n <mrow>\n <mtext>Na</mtext>\n </mrow>\n </msub>\n </mrow>\n <annotation>$\\left(\\rho\\right)_{\\text{Na}}$</annotation>\n </semantics></math>; and the average ionic radius <span></span><math>\n <semantics>\n <mrow>\n <mo>⟨</mo>\n <mrow>\n <msub>\n <mi>r</mi>\n <mi>M</mi>\n </msub>\n </mrow>\n <mo>⟩</mo>\n </mrow>\n <annotation>$$ &amp;#x00026;amp;amp;amp;amp;lt;{r}_{\\text{M}}&amp;#x00026;amp;amp;amp;amp;gt;$$</annotation>\n </semantics></math> of metal ions, which impacts <span></span><math>\n <semantics>\n <mrow>\n <msub>\n <mi>d</mi>\n <mn>1</mn>\n </msub>\n </mrow>\n <annotation>$d_{1}$</annotation>\n </semantics></math> and <span></span><math>\n <semantics>\n <mrow>\n <mo>⟨</mo>\n <mrow>\n <msub>\n <mi>d</mi>\n <mrow>\n <mtext>Na</mtext>\n <mo>−</mo>\n <mtext>Na</mtext>\n </mrow>\n </msub>\n </mrow>\n <mo>⟩</mo>\n </mrow>\n <annotation>$$ &amp;#x00026;amp;amp;amp;amp;lt;{d}_{\\text{Na}-\\text{Na}}&amp;#x00026;amp;amp;amp;amp;gt;$$</annotation>\n </semantics></math>. These secondary descriptors enable the development of a regression model for <span></span><math>\n <semantics>\n <mrow>\n <msub>\n <mi>σ</mi>\n <mrow>\n <mtext>Na</mtext>\n <mo>,</mo>\n <mn>300</mn>\n <mo> </mo>\n <mi>K</mi>\n </mrow>\n </msub>\n </mrow>\n <annotation>$\\left(\\sigma\\right)_{\\text{Na} , 300 \\text{K}}$</annotation>\n </semantics></math> with <i>n</i> and <span></span><math>\n <semantics>\n <mrow>\n <mo>⟨</mo>\n <mrow>\n <msub>\n <mi>r</mi>\n <mi>M</mi>\n </msub>\n </mrow>\n <mo>⟩</mo>\n </mrow>\n <annotation>$$ &amp;#x00026;amp;amp;amp;amp;lt;{r}_{\\text{M}}&amp;#x00026;amp;amp;amp;amp;gt;$$</annotation>\n </semantics></math> only. Subsequently, this model identifies a promising yet unexplored stable composition, <span></span><math>\n <semantics>\n <mrow>\n <msub>\n <mrow>\n <mtext>Na</mtext>\n </mrow>\n <mrow>\n <mn>2.75</mn>\n </mrow>\n </msub>\n <msub>\n <mrow>\n <mtext>Zr</mtext>\n </mrow>\n <mrow>\n <mn>1.75</mn>\n </mrow>\n </msub>\n <msub>\n <mrow>\n <mtext>Nb</mtext>\n </mrow>\n <mrow>\n <mn>0.25</mn>\n </mrow>\n </msub>\n <msub>\n <mrow>\n <mtext>Si</mtext>\n </mrow>\n <mn>2</mn>\n </msub>\n <msub>\n <mrow>\n <mtext>PO</mtext>\n </mrow>\n <mrow>\n <mn>12</mn>\n </mrow>\n </msub>\n </mrow>\n <annotation>$\\left(\\text{Na}\\right)_{2.75} \\left(\\text{Zr}\\right)_{1.75} \\left(\\text{Nb}\\right)_{0.25} \\left(\\text{Si}\\right)_{2} \\left(\\text{PO}\\right)_{12}$</annotation>\n </semantics></math>, which, upon DFT-MD calculations, indeed exhibits <span></span><math>\n <semantics>\n <mrow>\n <msub>\n <mi>σ</mi>\n <mrow>\n <mtext>Na</mtext>\n <mo>,</mo>\n <mn>300</mn>\n <mo> </mo>\n <mi>K</mi>\n </mrow>\n </msub>\n <mo>></mo>\n <msup>\n <mrow>\n <mn>10</mn>\n </mrow>\n <mrow>\n <mo>−</mo>\n <mn>3</mn>\n </mrow>\n </msup>\n </mrow>\n <annotation>$\\left(\\sigma\\right)_{\\text{Na} , 300 \\text{K}}&amp;#x00026;amp;amp;amp;amp;gt; \\left(10\\right)^{- 3}$</annotation>\n </semantics></math> S cm<sup>−1</sup>. Furthermore, the adjusted version effectively fits <span></span><math>\n <semantics>\n <mrow>\n <mn>140</mn>\n </mrow>\n <annotation>$140$</annotation>\n </semantics></math> experimental values with <span></span><math>\n <semantics>\n <mrow>\n <msup>\n <mi>R</mi>\n <mn>2</mn>\n </msup>\n <mo>=</mo>\n <mn>0.718</mn>\n </mrow>\n <annotation>$R^{2} = 0.718$</annotation>\n </semantics></math>.</p>","PeriodicalId":29794,"journal":{"name":"Advanced Energy and Sustainability Research","volume":"5 12","pages":""},"PeriodicalIF":6.2000,"publicationDate":"2024-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/aesr.202400158","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advanced Energy and Sustainability Research","FirstCategoryId":"1085","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/aesr.202400158","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENERGY & FUELS","Score":null,"Total":0}
引用次数: 0
Abstract
Given the vast compositional possibilities , Na-ion superionic conductors are attractive but complicated for designing materials with enhanced room-temperature Na-ion conductivity . An explicit regression model for with easily-accessible descriptors is proposed by exploiting density functional theory molecular dynamics (DFT-MD). Initially, it is demonstrated that two primary descriptors, the bottleneck width along Na-ion diffusion paths and the average Na–Na distance , modulate room-temperature Na-ion self-diffusion coefficient . Then, two secondary easily-accessible descriptors are introduced: Na-ion content n, which influences , , and Na-ion density ; and the average ionic radius of metal ions, which impacts and . These secondary descriptors enable the development of a regression model for with n and only. Subsequently, this model identifies a promising yet unexplored stable composition, , which, upon DFT-MD calculations, indeed exhibits S cm−1. Furthermore, the adjusted version effectively fits experimental values with .
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