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class="vector-toc-numb">2</span> <span>Operation</span> </div> </a> <button aria-controls="toc-Operation-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Operation subsection</span> </button> <ul id="toc-Operation-sublist" class="vector-toc-list"> <li id="toc-Balance_of_plant" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Balance_of_plant"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Balance of plant</span> </div> </a> <ul id="toc-Balance_of_plant-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Anode" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Anode"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Anode</span> </div> </a> <ul id="toc-Anode-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Electrolyte" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Electrolyte"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Electrolyte</span> </div> </a> <ul id="toc-Electrolyte-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cathode" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Cathode"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Cathode</span> </div> </a> <ul id="toc-Cathode-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Interconnect" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Interconnect"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>Interconnect</span> </div> </a> <ul id="toc-Interconnect-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Polarizations" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Polarizations"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Polarizations</span> </div> </a> <button aria-controls="toc-Polarizations-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Polarizations subsection</span> </button> <ul id="toc-Polarizations-sublist" class="vector-toc-list"> <li id="toc-Ohmic_polarization" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ohmic_polarization"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Ohmic polarization</span> </div> </a> <ul id="toc-Ohmic_polarization-sublist" class="vector-toc-list"> <li id="toc-Ionic_conductivity" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Ionic_conductivity"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.1</span> <span>Ionic conductivity</span> </div> </a> <ul id="toc-Ionic_conductivity-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Concentration_polarization" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Concentration_polarization"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Concentration polarization</span> </div> </a> <ul id="toc-Concentration_polarization-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Activation_polarization" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Activation_polarization"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Activation polarization</span> </div> </a> <ul id="toc-Activation_polarization-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Mechanical_Properties" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Mechanical_Properties"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Mechanical Properties</span> </div> </a> <ul id="toc-Mechanical_Properties-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Target" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Target"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Target</span> </div> </a> <ul id="toc-Target-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Research" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Research"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Research</span> </div> </a> <button aria-controls="toc-Research-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Research subsection</span> </button> <ul id="toc-Research-sublist" class="vector-toc-list"> <li id="toc-SOEC" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#SOEC"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>SOEC</span> </div> </a> <ul id="toc-SOEC-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-ITSOFC" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#ITSOFC"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>ITSOFC</span> </div> </a> <ul id="toc-ITSOFC-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-LT-SOFC" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#LT-SOFC"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.3</span> <span>LT-SOFC</span> </div> </a> <ul id="toc-LT-SOFC-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-SOFC-GT" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#SOFC-GT"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.4</span> <span>SOFC-GT</span> </div> </a> <ul id="toc-SOFC-GT-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-DCFC" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#DCFC"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.5</span> <span>DCFC</span> </div> </a> <ul id="toc-DCFC-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " 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Available in 23 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-23" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">23 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AE%D9%84%D9%8A%D8%A9_%D9%88%D9%82%D9%88%D8%AF_%D8%A7%D9%84%D8%A3%D9%83%D8%B3%D9%8A%D8%AF_%D8%A7%D9%84%D8%B5%D9%84%D8%A8" title="خلية وقود الأكسيد الصلب – Arabic" lang="ar" hreflang="ar" data-title="خلية وقود الأكسيد الصلب" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Pila_de_combustible_d%27%C3%B2xid_s%C3%B2lid" title="Pila de combustible d'òxid sòlid – Catalan" lang="ca" hreflang="ca" data-title="Pila de combustible d'òxid sòlid" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Festoxidbrennstoffzelle" title="Festoxidbrennstoffzelle – German" lang="de" hreflang="de" data-title="Festoxidbrennstoffzelle" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Tahkeoksiidne_k%C3%BCtuseelement" title="Tahkeoksiidne kütuseelement – Estonian" lang="et" hreflang="et" data-title="Tahkeoksiidne kütuseelement" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Pila_de_combustible_de_%C3%B3xido_s%C3%B3lido" title="Pila de combustible de óxido sólido – Spanish" lang="es" hreflang="es" data-title="Pila de combustible de óxido sólido" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%BE%DB%8C%D9%84_%D8%B3%D9%88%D8%AE%D8%AA%DB%8C_%D8%A7%DA%A9%D8%B3%DB%8C%D8%AF_%D8%AC%D8%A7%D9%85%D8%AF" title="پیل سوختی اکسید جامد – Persian" lang="fa" hreflang="fa" data-title="پیل سوختی اکسید جامد" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Pile_%C3%A0_combustible_%C3%A0_oxyde_solide" title="Pile à combustible à oxyde solide – French" lang="fr" hreflang="fr" data-title="Pile à combustible à oxyde solide" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%97%B0%EB%A3%8C%EC%A0%84%EC%A7%80#고체산화물_연료전지_(Solid_Oxide_Fuel_Cell,_SOFC)" title="연료전지 – Korean" lang="ko" hreflang="ko" data-title="연료전지" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Gorivi_%C4%8Dlanak_s_%C4%8Dvrstim_oksidima_kao_elektrolitom" title="Gorivi članak s čvrstim oksidima kao elektrolitom – Croatian" lang="hr" hreflang="hr" data-title="Gorivi članak s čvrstim oksidima kao elektrolitom" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Pile_ad_ossido_solido" title="Pile ad ossido solido – Italian" lang="it" hreflang="it" data-title="Pile ad ossido solido" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Solid_oxide_fuel_cell" title="Solid oxide fuel cell – Dutch" lang="nl" hreflang="nl" data-title="Solid oxide fuel cell" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%87%83%E6%96%99%E9%9B%BB%E6%B1%A0#固体酸化物形燃料電池_(SOFC)" title="燃料電池 – Japanese" lang="ja" hreflang="ja" data-title="燃料電池" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Fast_oksid_brenselcelle" title="Fast oksid brenselcelle – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Fast oksid brenselcelle" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Qattiq_oksidli_yonilg%27i_xujayrasi" title="Qattiq oksidli yonilg'i xujayrasi – Uzbek" lang="uz" hreflang="uz" data-title="Qattiq oksidli yonilg'i xujayrasi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Ogniwo_paliwowe_ze_sta%C5%82ym_tlenkiem" title="Ogniwo paliwowe ze stałym tlenkiem – Polish" lang="pl" hreflang="pl" data-title="Ogniwo paliwowe ze stałym tlenkiem" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/C%C3%A9lula_de_combust%C3%ADvel_de_%C3%B3xido_s%C3%B3lido" title="Célula de combustível de óxido sólido – Portuguese" lang="pt" hreflang="pt" data-title="Célula de combustível de óxido sólido" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Pil%C4%83_de_combustie_cu_oxizi_solizi" title="Pilă de combustie cu oxizi solizi – Romanian" lang="ro" hreflang="ro" data-title="Pilă de combustie cu oxizi solizi" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A2%D0%B2%D0%B5%D1%80%D0%B4%D0%BE%D0%BE%D0%BA%D1%81%D0%B8%D0%B4%D0%BD%D1%8B%D0%B9_%D1%82%D0%BE%D0%BF%D0%BB%D0%B8%D0%B2%D0%BD%D1%8B%D0%B9_%D1%8D%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82" title="Твердооксидный топливный элемент – Russian" lang="ru" hreflang="ru" data-title="Твердооксидный топливный элемент" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Goriva_%C4%87elija_s_%C4%8Dvrstim_oksidima_kao_elektrolitom" title="Goriva ćelija s čvrstim oksidima kao elektrolitom – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Goriva ćelija s čvrstim oksidima kao elektrolitom" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Kiinte%C3%A4oksidipolttokenno" title="Kiinteäoksidipolttokenno – Finnish" lang="fi" hreflang="fi" data-title="Kiinteäoksidipolttokenno" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Kat%C4%B1_oksit_yak%C4%B1t_h%C3%BCcresi" title="Katı oksit yakıt hücresi – Turkish" lang="tr" hreflang="tr" data-title="Katı oksit yakıt hücresi" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A2%D0%B2%D0%B5%D1%80%D0%B4%D0%BE%D0%BE%D0%BA%D1%81%D0%B8%D0%B4%D0%BD%D0%B8%D0%B9_%D0%BF%D0%B0%D0%BB%D0%B8%D0%B2%D0%BD%D0%B8%D0%B9_%D0%B5%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82" title="Твердооксидний паливний елемент – Ukrainian" lang="uk" hreflang="uk" data-title="Твердооксидний паливний елемент" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%9B%BA%E6%85%8B%E6%B0%A7%E5%8C%96%E7%89%A9%E7%87%83%E6%96%99%E9%9B%BB%E6%B1%A0" title="固態氧化物燃料電池 – Chinese" lang="zh" hreflang="zh" data-title="固態氧化物燃料電池" data-language-autonym="中文" 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href="/wiki/Wikipedia:Manual_of_Style/Lead_section#Provide_an_accessible_overview" title="Wikipedia:Manual of Style/Lead section">provide an accessible overview</a> of all important aspects of the article.</span> <span class="date-container"><i>(<span class="date">February 2022</span>)</i></span></div></td></tr></tbody></table> </div> </div><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p class="mw-empty-elt"> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Solid_oxide_fuel_cell.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/42/Solid_oxide_fuel_cell.svg/330px-Solid_oxide_fuel_cell.svg.png" decoding="async" width="330" height="370" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/42/Solid_oxide_fuel_cell.svg/495px-Solid_oxide_fuel_cell.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/42/Solid_oxide_fuel_cell.svg/660px-Solid_oxide_fuel_cell.svg.png 2x" data-file-width="508" data-file-height="570" /></a><figcaption>Scheme of a solid-oxide fuel cell</figcaption></figure> <p>A <b>solid oxide fuel cell</b> (or <b>SOFC</b>) is an <a href="/wiki/Electrochemistry" title="Electrochemistry">electrochemical</a> conversion device that produces electricity directly from <a href="/wiki/Oxidizing" class="mw-redirect" title="Oxidizing">oxidizing</a> a <a href="/wiki/Fuel" title="Fuel">fuel</a>. <a href="/wiki/Fuel_cell" title="Fuel cell">Fuel cells</a> are characterized by their electrolyte material; the SOFC has a solid oxide or <a href="/wiki/Ceramic" title="Ceramic">ceramic</a> electrolyte. </p><p>Advantages of this class of fuel cells include high combined heat and power efficiency, long-term stability, fuel flexibility, low emissions, and relatively low cost. The largest disadvantage is the high <a href="/wiki/Operating_temperature" title="Operating temperature">operating temperature</a> which results in longer start-up times and mechanical and chemical compatibility issues.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Introduction">Introduction</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Solid_oxide_fuel_cell&action=edit&section=1" title="Edit section: Introduction"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Solid oxide fuel cells are a class of fuel cells characterized by the use of a solid <a href="/wiki/Oxide" title="Oxide">oxide</a> material as the <a href="/wiki/Electrolyte" title="Electrolyte">electrolyte</a>. SOFCs use a solid oxide electrolyte to conduct negative oxygen ions from the <a href="/wiki/Cathode" title="Cathode">cathode</a> to the <a href="/wiki/Anode" title="Anode">anode</a>. The electrochemical oxidation of the <a href="/wiki/Hydrogen" title="Hydrogen">hydrogen</a>, carbon monoxide or other organic intermediates by oxygen ions thus occurs on the anode side.<sup id="cite_ref-singh2021_2-0" class="reference"><a href="#cite_note-singh2021-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Boldrin2019_3-0" class="reference"><a href="#cite_note-Boldrin2019-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> More recently, proton-conducting SOFCs (PC-SOFC) are being developed which transport protons instead of oxygen ions through the electrolyte with the advantage of being able to be run at lower temperatures than traditional SOFCs.<sup id="cite_ref-gao2023_4-0" class="reference"><a href="#cite_note-gao2023-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-vignesh2023_5-0" class="reference"><a href="#cite_note-vignesh2023-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>They operate at very high temperatures, typically between 600 and 1,000 °C.<sup id="cite_ref-singh2021_2-1" class="reference"><a href="#cite_note-singh2021-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Boldrin2019_3-1" class="reference"><a href="#cite_note-Boldrin2019-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> At these temperatures, SOFCs do not require expensive <a href="/wiki/Platinum_group_metals" class="mw-redirect" title="Platinum group metals">platinum group metals</a> <a href="/wiki/Catalyst" class="mw-redirect" title="Catalyst">catalyst</a>,<sup id="cite_ref-Boldrin2019_3-2" class="reference"><a href="#cite_note-Boldrin2019-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-wang2022_6-0" class="reference"><a href="#cite_note-wang2022-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> as is currently necessary for lower temperature fuel cells such as <a href="/wiki/Proton-exchange_membrane_fuel_cell" title="Proton-exchange membrane fuel cell">PEMFCs</a>, and are not vulnerable to carbon monoxide catalyst poisoning. However, vulnerability to <a href="/wiki/Sulfur" title="Sulfur">sulfur</a> poisoning <sup id="cite_ref-hagen2011_7-0" class="reference"><a href="#cite_note-hagen2011-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Boldrin2019_3-3" class="reference"><a href="#cite_note-Boldrin2019-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-kim2021_8-0" class="reference"><a href="#cite_note-kim2021-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> has been widely observed and the sulfur must be removed before entering the cell. For fuels that are of lower quality, such as gasified biomass, coal, or <a href="/wiki/Biogas" title="Biogas">biogas</a>, the fuel processing becomes increasingly complex and, consequently, more expensive. The gasification process, which transforms the raw material into a gaseous state suitable for fuel cells, can generate significant quantities of aromatic compounds. These compounds include smaller molecules like methane and toluene, as well as larger polyaromatic and short-chain hydrocarbon compounds. These substances can lead to carbon buildup in SOFCs. Moreover, the expenses associated with reforming and desulfurization are comparable in magnitude to the cost of the fuel cell itself. These factors become especially critical for systems with lower power output or greater portability requirements.<sup id="cite_ref-Boldrin2016_9-0" class="reference"><a href="#cite_note-Boldrin2016-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>Solid oxide fuel cells have a wide variety of applications, from use as auxiliary power units in vehicles to stationary power generation with outputs from 100 W to 2 MW. In 2009, Australian company, <a href="/wiki/Ceramic_Fuel_Cells" title="Ceramic Fuel Cells">Ceramic Fuel Cells</a> successfully achieved an efficiency of an SOFC device up to the previously theoretical mark of 60%.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-e-collection.ethbib.ethz.ch_11-0" class="reference"><a href="#cite_note-e-collection.ethbib.ethz.ch-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> The higher operating temperature make SOFCs suitable candidates for application with <a href="/wiki/Heat_engine" title="Heat engine">heat engine</a> <a href="/wiki/Energy_recovery" title="Energy recovery">energy recovery</a> devices or <a href="/wiki/Combined_heat_and_power" class="mw-redirect" title="Combined heat and power">combined heat and power</a>, which further increases overall <a href="/wiki/Fuel_efficiency" title="Fuel efficiency">fuel efficiency</a>.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p><p>Because of these high temperatures, light hydrocarbon fuels, such as methane, propane, and butane can be internally reformed within the anode.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> SOFCs can also be fueled by externally <a href="/wiki/Fossil_fuel_reforming" class="mw-redirect" title="Fossil fuel reforming">reforming</a> heavier hydrocarbons, such as gasoline, diesel, jet fuel (JP-8) or biofuels. Such reformates are mixtures of hydrogen, carbon monoxide, carbon dioxide, steam and methane, formed by reacting the hydrocarbon fuels with air or steam in a device upstream of the SOFC anode. SOFC power systems can increase efficiency by using the heat given off by the exothermic electrochemical oxidation within the fuel cell for endothermic <a href="/wiki/Steam_reforming" title="Steam reforming">steam reforming</a> process. Additionally, solid fuels such as <a href="/wiki/Coal" title="Coal">coal</a> and <a href="/wiki/Biomass" title="Biomass">biomass</a> may be <a href="/wiki/Gasification" title="Gasification">gasified</a> to form <a href="/wiki/Syngas" title="Syngas">syngas</a> which is suitable for fueling SOFCs in <a href="/wiki/Integrated_Gasification_Fuel_Cell_Cycle" class="mw-redirect" title="Integrated Gasification Fuel Cell Cycle">integrated gasification fuel cell power cycles</a>. </p><p><a href="/wiki/Volumetric_thermal_expansion_coefficient" class="mw-redirect" title="Volumetric thermal expansion coefficient">Thermal expansion</a> demands a uniform and well-regulated heating process at startup. SOFC stacks with planar geometry require on the order of an hour to be heated to operating temperature. <a href="/w/index.php?title=Micro-tubular_fuel_cell_design&action=edit&redlink=1" class="new" title="Micro-tubular fuel cell design (page does not exist)">Micro-tubular fuel cell design</a><sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> geometries promise much faster start up times, typically in the order of minutes. </p><p>Unlike most other types of <a href="/wiki/Fuel_cell" title="Fuel cell">fuel cells</a>, SOFCs can have multiple geometries. The <a href="/w/index.php?title=Planar_fuel_cell_design&action=edit&redlink=1" class="new" title="Planar fuel cell design (page does not exist)">planar fuel cell design</a> geometry is the typical sandwich type geometry employed by most types of fuel cells, where the electrolyte is sandwiched in between the electrodes. SOFCs can also be made in tubular geometries where either air or fuel is passed through the inside of the tube and the other gas is passed along the outside of the tube. The tubular design is advantageous because it is much easier to seal air from the fuel. The performance of the planar design is currently better than the performance of the tubular design, however, because the planar design has a lower resistance comparatively. Other geometries of SOFCs include <a href="/w/index.php?title=Modified_planar_fuel_cell_design&action=edit&redlink=1" class="new" title="Modified planar fuel cell design (page does not exist)">modified planar fuel cell designs</a> (MPC or MPSOFC), where a wave-like structure replaces the traditional flat configuration of the planar cell. Such designs are highly promising because they share the advantages of both planar cells (low resistance) and tubular cells.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="Need citation for this modified planar design (May 2023)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading2"><h2 id="Operation">Operation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Solid_oxide_fuel_cell&action=edit&section=2" title="Edit section: Operation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:SOFC-en.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/81/SOFC-en.svg/330px-SOFC-en.svg.png" decoding="async" width="330" height="330" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/81/SOFC-en.svg/495px-SOFC-en.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/81/SOFC-en.svg/660px-SOFC-en.svg.png 2x" data-file-width="512" data-file-height="512" /></a><figcaption>Cross section of three ceramic layers of a tubular SOFC. From inner to outer: porous cathode, dense electrolyte, porous anode</figcaption></figure> <p>A solid oxide fuel cell is made up of four layers, three of which are <a href="/wiki/Ceramic" title="Ceramic">ceramics</a> (hence the name). A single cell consisting of these four layers stacked together is typically only a few millimeters thick. Hundreds of these cells are then connected in series to form what most people refer to as an "SOFC stack". The ceramics used in SOFCs do not become electrically and <a href="/wiki/Ion" title="Ion">ionically</a> active until they reach very high temperature and as a consequence, the stacks have to run at temperatures ranging from 500 to 1,000 °C. Reduction of oxygen into oxygen ions occurs at the cathode. These ions can then diffuse through the solid oxide electrolyte to the anode where they can electrochemically oxidize the fuel. In this reaction, a water byproduct is given off as well as two electrons. These electrons then flow through an external circuit where they can do work. The cycle then repeats as those electrons enter the cathode material again. </p> <div class="mw-heading mw-heading3"><h3 id="Balance_of_plant">Balance of plant</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Solid_oxide_fuel_cell&action=edit&section=3" title="Edit section: Balance of plant"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Most of the downtime of a SOFC stems from the <a href="/w/index.php?title=Mechanical_balance_of_plant&action=edit&redlink=1" class="new" title="Mechanical balance of plant (page does not exist)">mechanical balance of plant</a>, the <a href="/wiki/Air_preheater" title="Air preheater">air preheater</a>, <a href="/w/index.php?title=Prereformer&action=edit&redlink=1" class="new" title="Prereformer (page does not exist)">prereformer</a>, <a href="/wiki/Afterburner" title="Afterburner">afterburner</a>, <a href="/wiki/Water_heat_exchanger" class="mw-redirect" title="Water heat exchanger">water heat exchanger</a>, <a href="/w/index.php?title=Anode_tail_gas_oxidizer&action=edit&redlink=1" class="new" title="Anode tail gas oxidizer (page does not exist)">anode tail gas oxidizer</a>, and <a href="/w/index.php?title=Electrical_balance_of_plant&action=edit&redlink=1" class="new" title="Electrical balance of plant (page does not exist)">electrical balance of plant</a>, <a href="/wiki/Power_electronics" title="Power electronics">power electronics</a>, <a href="/wiki/Hydrogen_sulfide_sensor" title="Hydrogen sulfide sensor">hydrogen sulfide sensor</a> and fans. Internal reforming leads to a large decrease in the <a href="/wiki/Balance_of_plant" title="Balance of plant">balance of plant</a> costs in designing a full system.<sup id="cite_ref-e-collection.ethbib.ethz.ch_11-1" class="reference"><a href="#cite_note-e-collection.ethbib.ethz.ch-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Anode">Anode</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Solid_oxide_fuel_cell&action=edit&section=4" title="Edit section: Anode"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The ceramic <a href="/wiki/Anode" title="Anode">anode</a> layer must be very porous to allow the fuel to flow towards the electrolyte. Consequently, granular matter is often selected for anode fabrication procedures.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> Like the cathode, it must conduct electrons, with ionic conductivity a definite asset. The anode is commonly the thickest and strongest layer in each individual cell, because it has the smallest polarization losses, and is often the layer that provides the mechanical support. <a href="/wiki/Electrochemistry" title="Electrochemistry">Electrochemically</a> speaking, the anode's job is to use the oxygen ions that diffuse through the electrolyte to oxidize the hydrogen <a href="/wiki/Fuel" title="Fuel">fuel</a>. The <a href="/wiki/Redox" title="Redox">oxidation reaction</a> between the oxygen ions and the hydrogen produces heat as well as water and electricity. If the fuel is a light hydrocarbon, for example, methane, another function of the anode is to act as a catalyst for steam reforming the fuel into hydrogen. This provides another operational benefit to the fuel cell stack because the reforming reaction is endothermic, which cools the stack internally. The most common material used is a <a href="/wiki/Cermet" title="Cermet">cermet</a> made up of <a href="/wiki/Nickel" title="Nickel">nickel</a> mixed with the ceramic material that is used for the electrolyte in that particular cell, typically YSZ (yttria stabilized zirconia). These <a href="/wiki/Nanomaterial-based_catalyst" title="Nanomaterial-based catalyst">nanomaterial-based catalysts</a>, help stop the grain growth of nickel. Larger grains of nickel would reduce the contact area that ions can be conducted through, which would lower the cells efficiency. <a href="/wiki/Perovskite_(structure)" title="Perovskite (structure)">Perovskite materials</a> (mixed ionic/electronic conducting ceramics) have been shown to produce a power density of 0.6 W/cm2 at 0.7 V at 800 °C which is possible because they have the ability to overcome a larger <a href="/wiki/Activation_energy" title="Activation energy">activation energy</a>.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p><p><b>Chemical Reaction:</b> </p><p>H<sub>2</sub> +O<sup>2-</sup> ——> H<sub>2</sub>O+2e </p><p>However, there are a few disadvantages associated with YSZ as anode material. Ni coarsening, carbon deposition, reduction-oxidation instability, and sulfur poisoning are the main obstacles limiting the long-term stability of Ni-YSZ. Ni coarsening refers to the evolution of Ni particles in doped in YSZ grows larger in grain size, which decreases the surface area for the catalytic reaction. Carbon deposition occurs when carbon atoms, formed by hydrocarbon pyrolysis or CO disproportionation, deposit on the Ni catalytic surface.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> Carbon deposition becomes important especially when hydrocarbon fuels are used, i.e. methane, syngas. The high operating temperature of SOFC and the oxidizing environment facilitate the oxidation of Ni catalyst through reaction Ni + <style data-mw-deduplicate="TemplateStyles:r1154941027">.mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="frac"><span class="num">1</span>⁄<span class="den">2</span></span> O<sub>2</sub> = NiO. The oxidation reaction of Ni reduces the electrocatalytic activity and conductivity. Moreover, the density difference between Ni and NiO causes volume change on the anode surface, which could potentially lead to mechanical failure. Sulfur poisoning arises when fuel such as natural gas, gasoline, or diesel is used. Again, due to the high affinity between sulfur compounds (H<sub>2</sub>S, (CH<sub>3</sub>)<sub>2</sub>S) and the metal catalyst, even the smallest impurities of sulfur compounds in the feed stream could deactivate the Ni catalyst on the YSZ surface.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p><p>Current research is focused on reducing or replacing Ni content in the anode to improve long-term performance. The modified Ni-YSZ containing other materials including CeO<sub>2</sub>, Y<sub>2</sub>O<sub>3</sub>, La<sub>2</sub>O<sub>3</sub>, MgO, TiO<sub>2</sub>, Ru, Co, etc. are invented to resist sulfur poisoning, but the improvement is limited due to the rapid initial degradation.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> Copper-based cerement anode is considered as a solution to carbon deposition because it is inert to carbon and stable under typical SOFC oxygen partial pressures (pO<sub>2</sub>). Cu-Co bimetallic anodes in particular show a great resistivity of carbon deposition after the exposure to pure CH<sub>4</sub> at 800C.<sup id="cite_ref-:0_21-0" class="reference"><a href="#cite_note-:0-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> And Cu-CeO<sub>2</sub>-YSZ exhibits a higher electrochemical oxidation rate over Ni-YSZ when running on CO and syngas, and can achieve even higher performance using CO than H<sub>2</sub>, after adding a cobalt co-catalyst.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> Oxide anodes including zirconia-based fluorite and perovskites are also used to replace Ni-ceramic anodes for carbon resistance. Chromite i.e. La<sub>0.8</sub>Sr<sub>0.2</sub>Cr<sub>0.5</sub>Mn<sub>0.5</sub>O<sub>3</sub> (LSCM) is used as anodes and exhibited comparable performance against Ni–YSZ cermet anodes. LSCM is further improved by impregnating Cu and sputtering Pt as the current collector.<sup id="cite_ref-:0_21-1" class="reference"><a href="#cite_note-:0-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Electrolyte">Electrolyte</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Solid_oxide_fuel_cell&action=edit&section=5" title="Edit section: Electrolyte"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The electrolyte is a dense layer of ceramic that conducts oxygen ions. Its electronic conductivity must be kept as low as possible to prevent losses from leakage currents. The high operating temperatures of SOFCs allow the kinetics of oxygen ion transport to be sufficient for good performance. However, as the operating temperature approaches the lower limit for SOFCs at around <span class="nowrap">600 °C,</span> the electrolyte begins to have large ionic transport resistances and affect the performance. Popular electrolyte materials include <a href="/wiki/Yttria-stabilized_zirconia" title="Yttria-stabilized zirconia">yttria-stabilized zirconia</a> (YSZ) (often the 8% form 8YSZ), scandia stabilized zirconia (<a href="/w/index.php?title=ScSZ&action=edit&redlink=1" class="new" title="ScSZ (page does not exist)">ScSZ</a>) (usually 9 mol% Sc<sub>2</sub>O<sub>3</sub> – 9ScSZ) and <a href="/wiki/Gadolinium_doped_ceria" class="mw-redirect" title="Gadolinium doped ceria">gadolinium doped ceria</a> (GDC).<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> The electrolyte material has crucial influence on the cell performances.<sup id="cite_ref-elmater_24-0" class="reference"><a href="#cite_note-elmater-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> Detrimental reactions between YSZ electrolytes and modern cathodes such as <a href="/wiki/Lanthanum_strontium_cobalt_ferrite" title="Lanthanum strontium cobalt ferrite">lanthanum strontium cobalt ferrite</a> (LSCF) have been found, and can be prevented by thin (<100 nm) <a href="/wiki/Ceria" class="mw-redirect" title="Ceria">ceria</a> diffusion barriers.<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> </p><p>If the conductivity for oxygen ions in SOFC can remain high even at lower temperatures (current target in research ~500 °C), material choices for SOFC will broaden and many existing problems can potentially be solved. Certain processing techniques such as thin film deposition<sup id="cite_ref-Charpentier2000_26-0" class="reference"><a href="#cite_note-Charpentier2000-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> can help solve this problem with existing materials by: </p> <ul><li>reducing the traveling distance of oxygen ions and electrolyte resistance as resistance is proportional to conductor length;</li> <li>producing grain structures that are less resistive such as columnar grain structure;</li> <li>controlling the microstructural nano-crystalline fine grains to achieve "fine-tuning" of electrical properties;</li> <li>building composite possessing large interfacial areas as interfaces have been shown to have extraordinary electrical properties.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Cathode">Cathode</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Solid_oxide_fuel_cell&action=edit&section=6" title="Edit section: Cathode"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Cathode" title="Cathode">cathode</a>, or air <a href="/wiki/Electrode" title="Electrode">electrode</a>, is a thin porous layer on the electrolyte where oxygen reduction takes place. The overall reaction is written in <a href="/wiki/Kr%C3%B6ger-Vink_Notation" class="mw-redirect" title="Kröger-Vink Notation">Kröger-Vink Notation</a> as follows: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{2}}\mathrm {O_{2}(g)} +2\mathrm {e'} +{V}_{o}^{\bullet \bullet }\longrightarrow {O}_{o}^{\times }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">g</mi> <mo stretchy="false">)</mo> </mrow> <mo>+</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi mathvariant="normal">e</mi> <mo>′</mo> </msup> </mrow> <mo>+</mo> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∙</mo> <mo>∙</mo> </mrow> </msubsup> <mo stretchy="false">⟶</mo> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi>O</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>×</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{2}}\mathrm {O_{2}(g)} +2\mathrm {e'} +{V}_{o}^{\bullet \bullet }\longrightarrow {O}_{o}^{\times }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0c161c5516d00731f8d1f7a940d2682df47f3612" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:28.566ex; height:5.176ex;" alt="{\displaystyle {\frac {1}{2}}\mathrm {O_{2}(g)} +2\mathrm {e'} +{V}_{o}^{\bullet \bullet }\longrightarrow {O}_{o}^{\times }}"></span></dd></dl> <p>Cathode materials must be, at a minimum, electrically conductive. Currently, <a href="/wiki/Lanthanum_strontium_manganite" title="Lanthanum strontium manganite">lanthanum strontium manganite</a> (LSM) is the cathode material of choice for commercial use because of its compatibility with doped zirconia electrolytes. Mechanically, it has a similar coefficient of thermal expansion to YSZ and thus limits stress buildup because of CTE mismatch. Also, LSM has low levels of chemical reactivity with YSZ which extends the lifetime of the materials. Unfortunately, LSM is a poor ionic conductor, and so the electrochemically active reaction is limited to the <a href="/wiki/Triple_phase_boundary" title="Triple phase boundary">triple phase boundary</a> (TPB) where the electrolyte, air and electrode meet. LSM works well as a cathode at high temperatures, but its performance quickly falls as the operating temperature is lowered below 800 °C. In order to increase the reaction zone beyond the TPB, a potential cathode material must be able to conduct both electrons and oxygen ions. Composite cathodes consisting of LSM YSZ have been used to increase this triple phase boundary length. Mixed ionic/electronic conducting (MIEC) ceramics, such as perovskite <a href="/wiki/LSCF" class="mw-redirect" title="LSCF">LSCF</a>, are also being researched for use in intermediate temperature SOFCs as they are more active and can make up for the increase in the activation energy of the reaction.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Interconnect">Interconnect</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Solid_oxide_fuel_cell&action=edit&section=7" title="Edit section: Interconnect"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The interconnect can be either a metallic or ceramic layer that sits between each individual cell. Its purpose is to connect each cell in series, so that the electricity each cell generates can be combined. Because the interconnect is exposed to both the oxidizing and reducing side of the cell at high temperatures, it must be extremely stable. For this reason, ceramics have been more successful in the long term than metals as interconnect materials. However, these ceramic interconnect materials are very expensive when compared to metals. Nickel- and steel-based alloys are becoming more promising as lower temperature (600–800 °C) SOFCs are developed. The material of choice for an interconnect in contact with Y8SZ is a metallic 95Cr-5Fe alloy. Ceramic-metal composites called "cermet" are also under consideration, as they have demonstrated thermal stability at high temperatures and excellent electrical conductivity. </p> <div class="mw-heading mw-heading2"><h2 id="Polarizations">Polarizations</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Solid_oxide_fuel_cell&action=edit&section=8" title="Edit section: Polarizations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Polarizations, or overpotentials, are losses in voltage due to imperfections in materials, microstructure, and design of the fuel cell. Polarizations result from ohmic resistance of oxygen ions conducting through the electrolyte (iRΩ), electrochemical activation barriers at the anode and cathode, and finally concentration polarizations due to inability of gases to diffuse at high rates through the porous anode and cathode (shown as ηA for the anode and ηC for cathode).<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> The cell voltage can be calculated using the following equation: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {V}={E}_{0}-{iR}_{\omega }-{\eta }_{cathode}-{\eta }_{anode}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> </msub> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi>η</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mi>a</mi> <mi>t</mi> <mi>h</mi> <mi>o</mi> <mi>d</mi> <mi>e</mi> </mrow> </msub> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi>η</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> <mi>n</mi> <mi>o</mi> <mi>d</mi> <mi>e</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {V}={E}_{0}-{iR}_{\omega }-{\eta }_{cathode}-{\eta }_{anode}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ca50267fab42c16a578b86e48f3e639e4afa6e07" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:32.597ex; height:2.676ex;" alt="{\displaystyle {V}={E}_{0}-{iR}_{\omega }-{\eta }_{cathode}-{\eta }_{anode}}"></span></dd></dl> <p>where: </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {E}_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {E}_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7e46475a2182268f6a2e3a3661940cea0d02a3de" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.769ex; height:2.509ex;" alt="{\displaystyle {E}_{0}}"></span> = <a href="/wiki/Nernst_potential" class="mw-redirect" title="Nernst potential">Nernst potential</a> of the reactants</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}"></span> = <a href="/wiki/Th%C3%A9venin%27s_theorem" title="Thévenin's theorem">Thévenin equivalent</a> resistance value of the electrically conducting portions of the cell</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\eta }_{cathode}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi>η</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mi>a</mi> <mi>t</mi> <mi>h</mi> <mi>o</mi> <mi>d</mi> <mi>e</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\eta }_{cathode}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c73f6f3b52dc5c0ec2d4a96d8ea670742d55ad77" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.933ex; height:2.176ex;" alt="{\displaystyle {\eta }_{cathode}}"></span> = polarization losses in the cathode</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\eta }_{anode}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi>η</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> <mi>n</mi> <mi>o</mi> <mi>d</mi> <mi>e</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\eta }_{anode}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1774d32c3798d5dcbd05b77474b85fd16c50d579" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.667ex; height:2.176ex;" alt="{\displaystyle {\eta }_{anode}}"></span> = polarization losses in the anode</li></ul> <p>In SOFCs, it is often important to focus on the ohmic and concentration polarizations since high operating temperatures experience little activation polarization. However, as the lower limit of SOFC operating temperature is approached (~600 °C), these polarizations do become important.<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> </p><p>Above mentioned equation is used for determining the SOFC voltage (in fact for fuel cell voltage in general). This approach results in good agreement with particular experimental data (for which adequate factors were obtained) and poor agreement for other than original experimental working parameters. Moreover, most of the equations used require the addition of numerous factors which are difficult or impossible to determine. It makes very difficult any optimizing process of the SOFC working parameters as well as design architecture configuration selection. Because of those circumstances a few other equations were proposed:<sup id="cite_ref-Milewski_J,_Miller_A._2006_396-402_30-0" class="reference"><a href="#cite_note-Milewski_J,_Miller_A._2006_396-402-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{SOFC}={\frac {E_{max}-i_{max}\cdot \eta _{f}\cdot r_{1}}{{\frac {r_{1}}{r_{2}}}\cdot \left(1-\eta _{f}\right)+1}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> <mi>O</mi> <mi>F</mi> <mi>C</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>⋅</mo> <msub> <mi>η</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <mo>⋅</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> <mo>⋅</mo> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <msub> <mi>η</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{SOFC}={\frac {E_{max}-i_{max}\cdot \eta _{f}\cdot r_{1}}{{\frac {r_{1}}{r_{2}}}\cdot \left(1-\eta _{f}\right)+1}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5ee785dd253bf3d05197d2bf7cba0e9d2cfdb992" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.505ex; width:30.757ex; height:7.176ex;" alt="{\displaystyle E_{SOFC}={\frac {E_{max}-i_{max}\cdot \eta _{f}\cdot r_{1}}{{\frac {r_{1}}{r_{2}}}\cdot \left(1-\eta _{f}\right)+1}}}"></span></dd></dl> <p>where: </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{SOFC}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> <mi>O</mi> <mi>F</mi> <mi>C</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{SOFC}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e949193d9ad15051609ff57d0b8de290f2ce83e5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.741ex; height:2.509ex;" alt="{\displaystyle E_{SOFC}}"></span> = cell voltage</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{max}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{max}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b49a8d426494f4ac0141e3d2d93467e218bb85b3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.2ex; height:2.509ex;" alt="{\displaystyle E_{max}}"></span> = maximum voltage given by the Nernst equation</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i_{max}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i_{max}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b534a71dc2f3845fd58617e13da355b8fe30116e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.287ex; height:2.509ex;" alt="{\displaystyle i_{max}}"></span> = maximum current density (for given fuel flow)</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \eta _{f}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>η</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \eta _{f}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/54e653b37247430f898d57b6c9021ea7827de668" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.292ex; height:2.343ex;" alt="{\displaystyle \eta _{f}}"></span> = fuel utilization factor<sup id="cite_ref-Milewski_J,_Miller_A._2006_396-402_30-1" class="reference"><a href="#cite_note-Milewski_J,_Miller_A._2006_396-402-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup></li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ea214f2b31fb3869344bb9311da41c5cc38a99e1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.103ex; height:2.009ex;" alt="{\displaystyle r_{1}}"></span> = ionic specific resistance of the electrolyte</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4cbe9b0b294fdd6fadbf9a7249813f016dcbc44f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.103ex; height:2.009ex;" alt="{\displaystyle r_{2}}"></span> = electric specific resistance of the electrolyte.</li></ul> <p>This method was validated and found to be suitable for optimization and sensitivity studies in plant-level modelling of various systems with solid oxide fuel cells.<sup id="cite_ref-Kupecki_J,_Milewski_J,_Jewulski_J_32-0" class="reference"><a href="#cite_note-Kupecki_J,_Milewski_J,_Jewulski_J-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> With this mathematical description it is possible to account for different properties of the SOFC. There are many parameters which impact cell working conditions, e.g. electrolyte material, electrolyte thickness, cell temperature, inlet and outlet gas compositions at anode and cathode, and electrode porosity, just to name some. The flow in these systems is often calculated using the <a href="/wiki/Navier%E2%80%93Stokes_equations" title="Navier–Stokes equations">Navier–Stokes equations</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Ohmic_polarization">Ohmic polarization</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Solid_oxide_fuel_cell&action=edit&section=9" title="Edit section: Ohmic polarization"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ohmic losses in an SOFC result from ionic conductivity through the electrolyte and electrical resistance offered to the flow of electrons in the external electrical circuit. This is inherently a materials property of the crystal structure and atoms involved. However, to maximize the ionic conductivity, several methods can be done. Firstly, operating at higher temperatures can significantly decrease these ohmic losses. Substitutional doping methods to further refine the crystal structure and control defect concentrations can also play a significant role in increasing the conductivity. Another way to decrease ohmic resistance is to decrease the thickness of the electrolyte layer. </p> <div class="mw-heading mw-heading4"><h4 id="Ionic_conductivity">Ionic conductivity</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Solid_oxide_fuel_cell&action=edit&section=10" title="Edit section: Ionic conductivity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>An ionic specific resistance of the electrolyte as a function of temperature can be described by the following relationship:<sup id="cite_ref-Milewski_J,_Miller_A._2006_396-402_30-2" class="reference"><a href="#cite_note-Milewski_J,_Miller_A._2006_396-402-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r_{1}={\frac {\delta }{\sigma }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>δ</mi> <mi>σ</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r_{1}={\frac {\delta }{\sigma }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7efaffa9a62ad048238afccef69cf123906ee892" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.367ex; height:5.343ex;" alt="{\displaystyle r_{1}={\frac {\delta }{\sigma }}}"></span></dd></dl> <p>where: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5321cfa797202b3e1f8620663ff43c4660ea03a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:2.343ex;" alt="{\displaystyle \delta }"></span> – electrolyte thickness, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>σ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59f59b7c3e6fdb1d0365a494b81fb9a696138c36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle \sigma }"></span> – ionic conductivity. </p><p>The ionic conductivity of the solid oxide is defined as follows:<sup id="cite_ref-Milewski_J,_Miller_A._2006_396-402_30-3" class="reference"><a href="#cite_note-Milewski_J,_Miller_A._2006_396-402-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma =\sigma _{0}\cdot e^{\frac {-E}{R\cdot T}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>σ</mi> <mo>=</mo> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>⋅</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>−</mo> <mi>E</mi> </mrow> <mrow> <mi>R</mi> <mo>⋅</mo> <mi>T</mi> </mrow> </mfrac> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma =\sigma _{0}\cdot e^{\frac {-E}{R\cdot T}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c369f67876f82eeff647a4534f980b440e074f02" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.964ex; height:4.009ex;" alt="{\displaystyle \sigma =\sigma _{0}\cdot e^{\frac {-E}{R\cdot T}}}"></span></dd></dl> <p>where: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma _{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b2f330c7d4a4ee92e5d43dfe3e23f0de3406ec78" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.382ex; height:2.009ex;" alt="{\displaystyle \sigma _{0}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}"></span> – factors depended on electrolyte materials, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span> – electrolyte temperature, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}"></span> – ideal gas constant. </p> <div class="mw-heading mw-heading3"><h3 id="Concentration_polarization">Concentration polarization</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Solid_oxide_fuel_cell&action=edit&section=11" title="Edit section: Concentration polarization"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The concentration polarization is the result of practical limitations on mass transport within the cell and represents the voltage loss due to spatial variations in reactant concentration at the chemically active sites. This situation can be caused when the reactants are consumed by the electrochemical reaction faster than they can diffuse into the porous electrode, and can also be caused by variation in bulk flow composition. The latter is due to the fact that the consumption of reacting species in the reactant flows causes a drop in reactant concentration as it travels along the cell, which causes a drop in the local potential near the tail end of the cell. </p><p>The concentration polarization occurs in both the anode and cathode. The anode can be particularly problematic, as the oxidation of the hydrogen produces steam, which further dilutes the fuel stream as it travels along the length of the cell. This polarization can be mitigated by reducing the reactant utilization fraction or increasing the electrode porosity, but these approaches each have significant design trade-offs. </p> <div class="mw-heading mw-heading3"><h3 id="Activation_polarization">Activation polarization</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Solid_oxide_fuel_cell&action=edit&section=12" title="Edit section: Activation polarization"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The activation polarization is the result of the kinetics involved with the electrochemical reactions. Each reaction has a certain activation barrier that must be overcome in order to proceed and this barrier leads to the polarization. The activation barrier is the result of many complex electrochemical reaction steps where typically the rate limiting step is responsible for the polarization. The polarization equation shown below is found by solving the <a href="/wiki/Butler%E2%80%93Volmer_equation" title="Butler–Volmer equation">Butler–Volmer equation</a> in the high current density regime (where the cell typically operates), and can be used to estimate the activation polarization: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\eta }_{act}={\frac {RT}{{\beta }zF}}\times ln\left({\frac {i}{{i}_{0}}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi>η</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> <mi>c</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>R</mi> <mi>T</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> </mrow> <mi>z</mi> <mi>F</mi> </mrow> </mfrac> </mrow> <mo>×</mo> <mi>l</mi> <mi>n</mi> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>i</mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\eta }_{act}={\frac {RT}{{\beta }zF}}\times ln\left({\frac {i}{{i}_{0}}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1e06a20aa123fc029d887542b8bfb2f4daff8c8f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:23.088ex; height:6.176ex;" alt="{\displaystyle {\eta }_{act}={\frac {RT}{{\beta }zF}}\times ln\left({\frac {i}{{i}_{0}}}\right)}"></span></dd></dl> <p>where: </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}"></span> = gas constant</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {T}_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {T}_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a1847baf662ea7b9aeaaf96c0ed48d918137ae8e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.412ex; height:2.509ex;" alt="{\displaystyle {T}_{0}}"></span> = operating temperature</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\beta }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\beta }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4f08e5bb6adcac8ac464df79e6a2e43779898ab7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.332ex; height:2.509ex;" alt="{\displaystyle {\beta }}"></span> = electron transfer coefficient</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf368e72c009decd9b6686ee84a375632e11de98" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.088ex; height:1.676ex;" alt="{\displaystyle z}"></span> = electrons associated with the electrochemical reaction</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/545fd099af8541605f7ee55f08225526be88ce57" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.741ex; height:2.176ex;" alt="{\displaystyle F}"></span> = Faraday's constant</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span> = operating current</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/91677c698b4d3f062d76d9e43ad3e914d243e758" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.857ex; height:2.509ex;" alt="{\displaystyle i_{0}}"></span> = exchange current density</li></ul> <p>The polarization can be modified by microstructural optimization. The Triple Phase Boundary (TPB) length, which is the length where porous, ionic and electronically conducting pathways all meet, directly relates to the electrochemically active length in the cell. The larger the length, the more reactions can occur and thus the less the activation polarization. Optimization of TPB length can be done by processing conditions to affect microstructure or by materials selection to use a mixed ionic/electronic conductor to further increase TPB length. </p> <div class="mw-heading mw-heading2"><h2 id="Mechanical_Properties">Mechanical Properties</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Solid_oxide_fuel_cell&action=edit&section=13" title="Edit section: Mechanical Properties"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Current SOFC research focuses heavily on optimizing cell performance while maintaining acceptable mechanical properties because optimized performance often compromises mechanical properties. Nevertheless, mechanical failure represents a significant problem to SOFC operation. The presence of various kinds of load and <a href="/wiki/Thermal_stress" title="Thermal stress">Thermal stress</a> during operation requires high mechanical strength. Additional stresses associated with changes in gas atmosphere, leading to reduction or oxidation also cannot be avoided in prolonged operation.<sup id="cite_ref-Progress_in_Material_Selection_33-0" class="reference"><a href="#cite_note-Progress_in_Material_Selection-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> When electrode layers delaminate or crack, conduction pathways are lost, leading to a redistribution of current density and local changes in temperature. These local temperature deviations, in turn, lead to increased thermal strains, which propagate cracks and <a href="/wiki/Delamination" title="Delamination">Delamination</a>. Additionally, when electrolytes crack, separation of fuel and air is no longer guaranteed, which further endangers the continuous operation of the cell.<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> </p><p>Since SOFCs require materials with high oxygen conductivity, thermal stresses provide a significant problem. The <a href="/wiki/Coefficient_of_thermal_expansion" class="mw-redirect" title="Coefficient of thermal expansion">Coefficient of thermal expansion</a> in mixed ionic-electronic perovskites can be directly related to oxygen vacancy concentration, which is also related to ionic conductivity.<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> Thus, thermal stresses increase in direct correlation with improved cell performance. Additionally, however, the temperature dependence of oxygen vacancy concentration means that the CTE is not a linear property, which further complicates measurements and predictions. </p><p>Just as thermal stresses increase as cell performance improves through improved ionic conductivity, the fracture toughness of the material also decreases as cell performance increases. This is because, to increase reaction sites, porous ceramics are preferable. However, as shown in the equation below, fracture toughness decreases as porosity increases.<sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K_{IC}=K_{IC,0}\exp {(-b_{k}p')}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>I</mi> <mi>C</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>I</mi> <mi>C</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> <mi>exp</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mo>−</mo> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <msup> <mi>p</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K_{IC}=K_{IC,0}\exp {(-b_{k}p')}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e04c713f4fad0c23a66bbb33da2bf4656ebc81f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:24.828ex; height:3.176ex;" alt="{\displaystyle K_{IC}=K_{IC,0}\exp {(-b_{k}p')}}"></span> </p><p>Where: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K_{IC}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>I</mi> <mi>C</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K_{IC}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fbe013a706bc20c6ba9bca0ce3273867604cbb88" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.283ex; height:2.509ex;" alt="{\displaystyle K_{IC}}"></span> = fracture toughness </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K_{IC,0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>I</mi> <mi>C</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K_{IC,0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f41cfd3170b2862a128af6fb64786e28b85ace5f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:5.562ex; height:2.843ex;" alt="{\displaystyle K_{IC,0}}"></span> = fracture toughness of the non-porous structure </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b_{k}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b_{k}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9ca33a19a52bbe58090767bcfb0aae551c925dcb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.086ex; height:2.509ex;" alt="{\displaystyle b_{k}}"></span> = experimentally determined constant </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>p</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/40e623e3163571a220ed60ecb31aa78c24104b85" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.944ex; height:2.843ex;" alt="{\displaystyle p'}"></span> = porosity </p><p>Thus, porosity must be carefully engineered to maximize reaction kinetics while maintaining an acceptable fracture toughness. Since fracture toughness represents the ability of pre-existing cracks or pores to propagate, a potentially more useful metric is the failure stress of a material, as this depends on sample dimensions instead of crack diameter. Failure stresses in SOFCs can also be evaluated using a ring-on ring biaxial stress test. This type of test is generally preferred, as sample edge quality does not significantly impact measurements. The determination of the sample's failure stress is shown in the equation below.<sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma _{cr}={\frac {3F_{cr}}{2\pi h_{s}^{2}}}+{\Biggl (}(1-\nu ){\frac {D_{sup}^{2}-D_{load}^{2}}{2D_{s}^{2}}}+(1+\nu )\ln \left({\frac {D_{sup}}{D_{load}}}\right){\Biggr )}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mi>r</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>3</mn> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mi>r</mi> </mrow> </msub> </mrow> <mrow> <mn>2</mn> <mi>π</mi> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="2.470em" minsize="2.470em">(</mo> </mrow> </mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>ν</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msubsup> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mi>u</mi> <mi>p</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>−</mo> <msubsup> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>o</mi> <mi>a</mi> <mi>d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> <mrow> <mn>2</mn> <msubsup> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> </mfrac> </mrow> <mo>+</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mi>ν</mi> <mo stretchy="false">)</mo> <mi>ln</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mi>u</mi> <mi>p</mi> </mrow> </msub> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>o</mi> <mi>a</mi> <mi>d</mi> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="2.470em" minsize="2.470em">)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma _{cr}={\frac {3F_{cr}}{2\pi h_{s}^{2}}}+{\Biggl (}(1-\nu ){\frac {D_{sup}^{2}-D_{load}^{2}}{2D_{s}^{2}}}+(1+\nu )\ln \left({\frac {D_{sup}}{D_{load}}}\right){\Biggr )}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/881a39bc08a88aa497314b7efdabdede060db57e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:60.588ex; height:7.509ex;" alt="{\displaystyle \sigma _{cr}={\frac {3F_{cr}}{2\pi h_{s}^{2}}}+{\Biggl (}(1-\nu ){\frac {D_{sup}^{2}-D_{load}^{2}}{2D_{s}^{2}}}+(1+\nu )\ln \left({\frac {D_{sup}}{D_{load}}}\right){\Biggr )}}"></span> </p><p>Where: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma _{cr}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mi>r</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma _{cr}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cdf6b61e66bd5097ce33d3539f5e2c7dd9c0babe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.013ex; height:2.009ex;" alt="{\displaystyle \sigma _{cr}}"></span> = failure stress of the small deformation </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{cr}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mi>r</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{cr}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/612fe85bfd550aef998a99a524af2ed5c6722814" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.18ex; height:2.509ex;" alt="{\displaystyle F_{cr}}"></span> = critical applied force </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h_{s}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h_{s}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b6d75beabd0038674f5545e00f8fa5c4f38fb63b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.342ex; height:2.509ex;" alt="{\displaystyle h_{s}}"></span> = height of the sample </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ν</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c15bbbb971240cf328aba572178f091684585468" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.232ex; height:1.676ex;" alt="{\displaystyle \nu }"></span> = Poisson's ratio </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f34a0c600395e5d4345287e21fb26efd386990e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}"></span> = diameter (sup = support ring, load = loading ring, s = sample) </p><p>However, this equation is not valid for deflections exceeding 1/2h,<sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> making it less applicable for thin samples, which are of great interest in SOFCs. Therefore, while this method does not require knowledge of crack or pore size, it must be used with great caution and is more applicable to support layers in SOFCs than active layers. In addition to failure stresses and fracture toughness, modern fuel cell designs that favor mixed ionic electronic conductors (MIECs), <a href="/wiki/Creep_(deformation)" title="Creep (deformation)">Creep (deformation)</a> pose another great problem, as MIEC electrodes often operate at temperatures exceeding half of the melting temperature. As a result, diffusion creep must also be considered.<sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dot {\epsilon }}_{eq}^{creep}={\frac {{\tilde {k}}_{0}D}{T}}{\frac {\sigma _{eq}^{m}}{d_{grain}^{n}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ϵ</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> <mi>q</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mi>r</mi> <mi>e</mi> <mi>e</mi> <mi>p</mi> </mrow> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>k</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi>D</mi> </mrow> <mi>T</mi> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msubsup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> <mi>q</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msubsup> <msubsup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>g</mi> <mi>r</mi> <mi>a</mi> <mi>i</mi> <mi>n</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msubsup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {\epsilon }}_{eq}^{creep}={\frac {{\tilde {k}}_{0}D}{T}}{\frac {\sigma _{eq}^{m}}{d_{grain}^{n}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f843d8a2c60056468a9e038367206e7bffe9ad8b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:19.692ex; height:7.009ex;" alt="{\displaystyle {\dot {\epsilon }}_{eq}^{creep}={\frac {{\tilde {k}}_{0}D}{T}}{\frac {\sigma _{eq}^{m}}{d_{grain}^{n}}}}"></span> </p><p>Where: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dot {\epsilon }}_{eq}^{creep}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ϵ</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> <mi>q</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mi>r</mi> <mi>e</mi> <mi>e</mi> <mi>p</mi> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {\epsilon }}_{eq}^{creep}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/08d069a6a1996319cf7a95bce7b7f31659c67dac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:5.336ex; height:3.009ex;" alt="{\displaystyle {\dot {\epsilon }}_{eq}^{creep}}"></span> = equivalent creep strain </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f34a0c600395e5d4345287e21fb26efd386990e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}"></span> = <a href="/wiki/Diffusion" title="Diffusion">Diffusion</a> coefficient </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span> = temperature </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {k}}_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>k</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {k}}_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/42e96ffde28ee5deff22bc134fd70870f5941455" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.265ex; height:3.009ex;" alt="{\displaystyle {\tilde {k}}_{0}}"></span> = kinetic constant </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma _{eq}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> <mi>q</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma _{eq}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2bf5a830e2d98d52d4413c0b05fb93ab3e416c0a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.082ex; height:2.343ex;" alt="{\displaystyle \sigma _{eq}}"></span> = equivalent stress (e.g. von Mises) </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}"></span> = creep stress exponential factor </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> = particle size exponent (2 for <a href="/wiki/Nabarro%E2%80%93Herring_creep" title="Nabarro–Herring creep">Nabarro–Herring creep</a>, 3 for <a href="/wiki/Coble_creep" title="Coble creep">Coble creep</a>) </p><p>To properly model creep strain rates, knowledge of <a href="/wiki/Microstructure" title="Microstructure">Microstructure</a> is therefore of significant importance. Due to the difficulty in mechanically testing SOFCs at high temperatures, and due to the microstructural evolution of SOFCs over the lifetime of operation resulting from <a href="/wiki/Grain_growth" title="Grain growth">Grain growth</a> and coarsening, the actual creep behavior of SOFCs is currently not completely understood </p> <div class="mw-heading mw-heading2"><h2 id="Target">Target</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Solid_oxide_fuel_cell&action=edit&section=14" title="Edit section: Target"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/United_States_Department_of_Energy" title="United States Department of Energy">DOE</a> target requirements are 40,000 hours of service for <a href="/wiki/Stationary_fuel_cell_applications" class="mw-redirect" title="Stationary fuel cell applications">stationary fuel cell applications</a> and greater than 5,000 hours for transportation systems (<a href="/wiki/Fuel_cell_vehicle" title="Fuel cell vehicle">fuel cell vehicles</a>) at a factory cost of $40/kW for a 10 kW <a href="/wiki/Coal" title="Coal">coal</a>-based system<sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> without additional requirements. Lifetime effects (phase stability, thermal expansion compatibility, element migration, conductivity and aging) must be addressed. The <a href="/w/index.php?title=Solid_State_Energy_Conversion_Alliance&action=edit&redlink=1" class="new" title="Solid State Energy Conversion Alliance (page does not exist)">Solid State Energy Conversion Alliance</a> 2008 (interim) target for overall degradation per 1,000 hours is 4.0%.<sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Research">Research</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Solid_oxide_fuel_cell&action=edit&section=15" title="Edit section: Research"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Research is going now in the direction of lower-temperature SOFCs (600 °C). Low temperature systems can reduce costs by reducing insulation, materials, start-up and degradation-related costs. With higher operating temperatures, the temperature gradient increases the severity of thermal stresses, which affects materials cost and life of the system.<sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> An intermediate temperature system (650-800 °C) would enable the use of cheaper metallic materials with better mechanical properties and <a href="/wiki/Thermal_conductivity" class="mw-redirect" title="Thermal conductivity">thermal conductivity</a>. New developments in nano-scale electrolyte structures have been shown to bring down operating temperatures to around 350 °C, which would enable the use of even cheaper steel and <a href="/wiki/Elastomer" title="Elastomer">elastomeric</a>/<a href="/wiki/Polymer" title="Polymer">polymeric</a> components.<sup id="cite_ref-ReferenceA_43-0" class="reference"><a href="#cite_note-ReferenceA-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> </p><p>Lowering operating temperatures has the added benefit of increased efficiency. Theoretical fuel cell efficiency increases with decreasing temperature. For example, the efficiency of a SOFC using CO as fuel increases from 63% to 81% when decreasing the system temperature from 900 °C to 350 °C.<sup id="cite_ref-ReferenceA_43-1" class="reference"><a href="#cite_note-ReferenceA-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> </p><p>Research is also under way to improve the fuel flexibility of SOFCs. While stable operation has been achieved on a variety of hydrocarbon fuels, these cells typically rely on external fuel processing. In the case of <a href="/wiki/Natural_gas" title="Natural gas">natural gas</a>, the fuel is either externally or internally reformed and the <a href="/wiki/Sulfur" title="Sulfur">sulfur</a> compounds are removed. These processes add to the cost and complexity of SOFC systems. Work is under way at a number of institutions to improve the stability of anode materials for hydrocarbon oxidation and, therefore, relax the requirements for fuel processing and decrease SOFC balance of plant costs. </p><p>Research is also going on in reducing start-up time to be able to implement SOFCs in mobile applications.<sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> This can be partially achieved by lowering operating temperatures, which is the case for <a href="/wiki/Proton-exchange_membrane_fuel_cell" title="Proton-exchange membrane fuel cell">proton-exchange membrane fuel cell</a> (PEMFCs).<sup id="cite_ref-45" class="reference"><a href="#cite_note-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> Due to their fuel flexibility, they may run on partially reformed <a href="/wiki/Diesel_fuel" title="Diesel fuel">diesel</a>, and this makes SOFCs interesting as auxiliary power units (APU) in refrigerated trucks. </p><p>Specifically, <a href="/wiki/Delphi_Corporation" class="mw-redirect" title="Delphi Corporation">Delphi Automotive Systems</a> are developing an SOFC that will power auxiliary units in automobiles and tractor-trailers, while <a href="/wiki/BMW" title="BMW">BMW</a> has recently stopped a similar project. A high-temperature SOFC will generate all of the needed electricity to allow the engine to be smaller and more efficient. The SOFC would run on the same <a href="/wiki/Gasoline" title="Gasoline">gasoline</a> or diesel as the engine and would keep the air conditioning unit and other necessary electrical systems running while the engine shuts off when not needed (e.g., at a stop light or truck stop).<sup id="cite_ref-46" class="reference"><a href="#cite_note-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Rolls-Royce_plc" class="mw-redirect" title="Rolls-Royce plc">Rolls-Royce</a> is developing solid-oxide fuel cells produced by <a href="/wiki/Screen_printing" title="Screen printing">screen printing</a> onto inexpensive ceramic materials.<sup id="cite_ref-47" class="reference"><a href="#cite_note-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> Rolls-Royce Fuel Cell Systems Ltd is developing an SOFC gas turbine hybrid system fueled by natural gas for power generation applications in the order of a megawatt (e.g. <a href="/wiki/Futuregen" class="mw-redirect" title="Futuregen">Futuregen</a>).<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (August 2016)">citation needed</span></a></i>]</sup> </p><p>3D printing is being explored as a possible manufacturing technique that could be used to make SOFC manufacturing easier by the Shah Lab at Northwestern University. This manufacturing technique would allow SOFC cell structure to be more flexible, which could lead to more efficient designs. This process could work in the production of any part of the cell. The 3D printing process works by combining about 80% ceramic particles with 20% binders and solvents, and then converting that slurry into an ink that can be fed into a 3D printer. Some of the solvent is very volatile, so the ceramic ink solidifies almost immediately. Not all of the solvent evaporates, so the ink maintains some flexibility before it is fired at high temperature to densify it. This flexibility allows the cells to be fired in a circular shape that would increase the surface area over which electrochemical reactions can occur, which increases the efficiency of the cell. Also, the 3D printing technique allows the cell layers to be printed on top of each other instead of having to go through separate manufacturing and stacking steps. The thickness is easy to control, and layers can be made in the exact size and shape that is needed, so waste is minimized.<sup id="cite_ref-48" class="reference"><a href="#cite_note-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Ceres_Power" title="Ceres Power">Ceres Power</a> Ltd. has developed a low cost and low temperature (500–600 degrees) SOFC stack using cerium gadolinium oxide (CGO) in place of current industry standard ceramic, <a href="/wiki/Yttria" class="mw-redirect" title="Yttria">yttria</a> stabilized <a href="/wiki/Zirconia" class="mw-redirect" title="Zirconia">zirconia</a> (<a href="/wiki/YSZ" class="mw-redirect" title="YSZ">YSZ</a>), which allows the use of <a href="/wiki/Stainless_steel" title="Stainless steel">stainless steel</a> to support the ceramic.<sup id="cite_ref-ceres_49-0" class="reference"><a href="#cite_note-ceres-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup> </p><p>Solid Cell Inc. has developed a unique, low-cost cell architecture that combines properties of planar and tubular designs, along with a Cr-free <a href="/wiki/Cermet" title="Cermet">cermet</a> interconnect.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (December 2023)">citation needed</span></a></i>]</sup> </p><p>The high temperature electrochemistry center (HITEC) at the University of Florida, Gainesville is focused on studying ionic transport, electrocatalytic phenomena and microstructural characterization of ion conducting materials.<sup id="cite_ref-50" class="reference"><a href="#cite_note-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> </p><p>SiEnergy Systems, a Harvard spin-off company, has demonstrated the first macro-scale thin-film solid-oxide fuel cell that can operate at 500 degrees.<sup id="cite_ref-51" class="reference"><a href="#cite_note-51"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="SOEC">SOEC</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Solid_oxide_fuel_cell&action=edit&section=16" title="Edit section: SOEC"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A <a href="/wiki/Solid_oxide_electrolyser_cell" class="mw-redirect" title="Solid oxide electrolyser cell">solid oxide electrolyser cell</a> (SOEC) is a solid oxide fuel cell set in <a href="/wiki/Regenerative_fuel_cell" title="Regenerative fuel cell">regenerative mode</a> for the <a href="/wiki/Electrolysis_of_water" title="Electrolysis of water">electrolysis of water</a> with a solid oxide, or <a href="/wiki/Ceramic" title="Ceramic">ceramic</a>, <a href="/wiki/Electrolyte" title="Electrolyte">electrolyte</a> to produce oxygen and <a href="/wiki/Hydrogen_gas" class="mw-redirect" title="Hydrogen gas">hydrogen gas</a>.<sup id="cite_ref-52" class="reference"><a href="#cite_note-52"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup> </p><p>SOECs can also be used to do electrolysis of CO<sub>2</sub> to produce CO and oxygen<sup id="cite_ref-53" class="reference"><a href="#cite_note-53"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup> or even co-electrolysis of water and CO<sub>2</sub> to produce syngas and oxygen. </p> <div class="mw-heading mw-heading3"><h3 id="ITSOFC">ITSOFC</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Solid_oxide_fuel_cell&action=edit&section=17" title="Edit section: ITSOFC"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>SOFCs that operate in an intermediate temperature (IT) range, meaning between 600 and 800 °C, are named ITSOFCs. Because of the high degradation rates and materials costs incurred at temperatures in excess of 900 °C, it is economically more favorable to operate SOFCs at lower temperatures. The push for high-performance ITSOFCs is currently the topic of much research and development. One area of focus is the cathode material. It is thought that the oxygen reduction reaction is responsible for much of the loss in performance so the catalytic activity of the cathode is being studied and enhanced through various techniques, including catalyst impregnation. The research on NdCrO<sub>3</sub> proves it to be a potential cathode material for the cathode of ITSOFC since it is thermochemically stable within the temperature range.<sup id="cite_ref-54" class="reference"><a href="#cite_note-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup> </p><p>Another area of focus is electrolyte materials. To make SOFCs competitive in the market, ITSOFCs are pushing towards lower operational temperature by use of alternative new materials. However, efficiency and stability of the materials limit their feasibility. One choice for the electrolyte new materials is the ceria-salt ceramic composites (CSCs). The two-phase CSC electrolytes GDC (gadolinium-doped ceria) and SDC (samaria-doped ceria)-MCO<sub>3</sub> (M=Li, Na, K, single or mixture of carbonates) can reach the power density of 300-800 mW*cm<sup>−2</sup>.<sup id="cite_ref-55" class="reference"><a href="#cite_note-55"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="LT-SOFC">LT-SOFC</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Solid_oxide_fuel_cell&action=edit&section=18" title="Edit section: LT-SOFC"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Low-temperature solid oxide fuel cells (LT-SOFCs), operating lower than 650 °C, are of great interest for future research because the high operating temperature is currently what restricts the development and deployment of SOFCs. A low-temperature SOFC is more reliable due to smaller thermal mismatch and easier sealing. Additionally, a lower temperature requires less insulation and therefore has a lower cost. Cost is further lowered due to wider material choices for interconnects and compressive nonglass/ceramic seals. Perhaps most importantly, at a lower temperature, SOFCs can be started more rapidly and with less energy, which lends itself to uses in portable and transportable applications.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (December 2023)">citation needed</span></a></i>]</sup> </p><p>As temperature decreases, the maximum theoretical fuel cell efficiency increases, in contrast to the Carnot cycle. For example, the maximum theoretical efficiency of an SOFC using CO as a fuel increases from 63% at 900 °C to 81% at 350 °C.<sup id="cite_ref-56" class="reference"><a href="#cite_note-56"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup> </p><p>This is a materials issue, particularly for the electrolyte in the SOFC. YSZ is the most commonly used electrolyte because of its superior stability, despite not having the highest conductivity. Currently, the thickness of YSZ electrolytes is a minimum of ~10 μm due to deposition methods, and this requires a temperature above 700 °C. Therefore, low-temperature SOFCs are only possible with higher conductivity electrolytes. Various alternatives that could be successful at low temperature include gadolinium-doped ceria (GDC) and erbia-cation-stabilized bismuth (ERB). They have superior ionic conductivity at lower temperatures, but this comes at the expense of lower thermodynamic stability. CeO2 electrolytes become electronically conductive and Bi2O3 electrolytes decompose to metallic Bi under the reducing fuel environment.<sup id="cite_ref-57" class="reference"><a href="#cite_note-57"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup> </p><p>To combat this, researchers created a functionally graded ceria/bismuth-oxide bilayered electrolyte where the GDC layer on the anode side protects the ESB layer from decomposing while the ESB on the cathode side blocks the leakage current through the GDC layer. This leads to near-theoretical open-circuit potential (OPC) with two highly conductive electrolytes, that by themselves would not have been sufficiently stable for the application. This bilayer proved to be stable for 1400 hours of testing at 500 °C and showed no indication of interfacial phase formation or thermal mismatch. While this makes strides towards lowering the operating temperature of SOFCs, it also opens doors for future research to try and understand this mechanism.<sup id="cite_ref-58" class="reference"><a href="#cite_note-58"><span class="cite-bracket">[</span>58<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Ion_Conductivity.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/6/60/Ion_Conductivity.png" decoding="async" width="281" height="282" class="mw-file-element" data-file-width="281" data-file-height="282" /></a><figcaption>Comparison of ionic conductivity of various solid oxide electrolytes</figcaption></figure> <p>Researchers at the Georgia Institute of Technology dealt with the instability of BaCeO<sub>3</sub> differently. They replaced a desired fraction of Ce in BaCeO<sub>3</sub> with Zr to form a solid solution that exhibits proton conductivity, but also chemical and thermal stability over the range of conditions relevant to fuel cell operation. A new specific composition, Ba(Zr0.1Ce0.7Y0.2)O3-δ (BZCY7) that displays the highest ionic conductivity of all known electrolyte materials for SOFC applications. This electrolyte was fabricated by dry-pressing powders, which allowed for the production of crack free films thinner than 15 μm. The implementation of this simple and cost-effective fabrication method may enable significant cost reductions in SOFC fabrication.<sup id="cite_ref-59" class="reference"><a href="#cite_note-59"><span class="cite-bracket">[</span>59<span class="cite-bracket">]</span></a></sup> However, this electrolyte operates at higher temperatures than the bilayered electrolyte model, closer to 600 °C rather than 500 °C. </p><p>Currently, given the state of the field for LT-SOFCs, progress in the electrolyte would reap the most benefits, but research into potential anode and cathode materials would also lead to useful results, and has started to be discussed more frequently in literature. </p> <div class="mw-heading mw-heading3"><h3 id="SOFC-GT">SOFC-GT</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Solid_oxide_fuel_cell&action=edit&section=19" title="Edit section: SOFC-GT"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>An <a href="/w/index.php?title=SOFC-GT&action=edit&redlink=1" class="new" title="SOFC-GT (page does not exist)">SOFC-GT</a> system is one which comprises a solid oxide fuel cell combined with a gas turbine. Such systems have been evaluated by <a href="/wiki/Siemens_Westinghouse" class="mw-redirect" title="Siemens Westinghouse">Siemens Westinghouse</a> and <a href="/wiki/Rolls-Royce_plc" class="mw-redirect" title="Rolls-Royce plc">Rolls-Royce</a> as a means to achieve higher operating efficiencies by running the SOFC under pressure. <a href="/w/index.php?title=SOFC-GT&action=edit&redlink=1" class="new" title="SOFC-GT (page does not exist)">SOFC-GT</a> systems typically include anodic and/or cathodic atmosphere recirculation, thus increasing <a href="/wiki/Efficiency" title="Efficiency">efficiency</a>.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (December 2023)">citation needed</span></a></i>]</sup> </p><p>Theoretically, the combination of the SOFC and gas turbine can give result in high overall (electrical and thermal) efficiency.<sup id="cite_ref-60" class="reference"><a href="#cite_note-60"><span class="cite-bracket">[</span>60<span class="cite-bracket">]</span></a></sup> Further combination of the SOFC-GT in a combined cooling, heat and power (or <a href="/wiki/Trigeneration" class="mw-redirect" title="Trigeneration">trigeneration</a>) configuration (via <a href="/wiki/HVAC" class="mw-redirect" title="HVAC">HVAC</a>) also has the potential to yield even higher thermal efficiencies in some cases.<sup id="cite_ref-61" class="reference"><a href="#cite_note-61"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup> </p><p>Another feature of the introduced hybrid system is on the gain of 100% CO<sub>2</sub> capturing at comparable high <a href="/wiki/Energy_efficiency_(physics)" class="mw-redirect" title="Energy efficiency (physics)">energy efficiency</a>. These features like zero CO<sub>2</sub> emission and high energy efficiency make the power plant performance noteworthy.<sup id="cite_ref-62" class="reference"><a href="#cite_note-62"><span class="cite-bracket">[</span>62<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="DCFC">DCFC</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Solid_oxide_fuel_cell&action=edit&section=20" title="Edit section: DCFC"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For the direct use of solid coal fuel without additional gasification and reforming processes, a <a href="/wiki/Direct_carbon_fuel_cell" title="Direct carbon fuel cell">direct carbon fuel cell</a> (<a rel="nofollow" class="external text" href="http://www.materialsviews.com/direct-carbon-fuel-cells-ultra-low-emission-technology-power-generation/">DCFC</a>) has been developed as a promising novel concept of a high-temperature energy conversion system. The underlying progress in the development of a coal-based DCFC has been categorized mainly according to the electrolyte materials used, such as solid oxide, molten carbonate, and molten hydroxide, as well as hybrid systems consisting of solid oxide and molten carbonate binary electrolyte or of liquid anode (Fe, Ag, In, Sn, Sb, Pb, Bi, and its alloying and its metal/metal oxide) solid oxide electrolyte.<sup id="cite_ref-63" class="reference"><a href="#cite_note-63"><span class="cite-bracket">[</span>63<span class="cite-bracket">]</span></a></sup> People's research on DCFC with GDC-Li/Na<sub>2</sub>CO<sub>3</sub> as the electrolyte, Sm<sub>0.5</sub>Sr<sub>0.5</sub>CoO<sub>3</sub> as cathode shows good performance. The highest power density of 48 mW*cm<sup>−2</sup> can be reached at 500 °C with O<sub>2</sub> and CO<sub>2</sub> as oxidant and the whole system is stable within the temperature range of 500 °C to 600 °C.<sup id="cite_ref-64" class="reference"><a href="#cite_note-64"><span class="cite-bracket">[</span>64<span class="cite-bracket">]</span></a></sup> </p><p><b>SOFC operated on <a href="/wiki/Landfill_gas" title="Landfill gas">landfill gas</a></b> </p><p>Every household produces waste/garbage on a daily basis. In 2009, Americans produced about 243 million tons of municipal solid waste, which is 4.3 pounds of waste per person per day. All that waste is sent to landfill sites. Landfill gas which is produced from the decomposition of waste that gets accumulated at the landfills has the potential to be a valuable source of energy since methane is a major constituent. Currently, the majority of the landfills either burn away their gas in flares or combust it in mechanical engines to produce electricity. The issue with mechanical engines is that incomplete combustion of gasses can lead to pollution of the atmosphere and is also highly inefficient.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (December 2023)">citation needed</span></a></i>]</sup> </p><p>The issue with using landfill gas to fuel an SOFC system is that landfill gas contains hydrogen sulfide. Any landfill accepting biological waste will contain about 50-60 ppm of hydrogen sulfide and around 1-2 ppm mercaptans. However, construction materials containing reducible sulfur species, principally sulfates found in gypsum-based wallboard, can cause considerably higher levels of sulfides in the hundreds of ppm. At operating temperatures of 750 °C hydrogen sulfide concentrations of around 0.05 ppm begin to affect the performance of the SOFCs.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (December 2023)">citation needed</span></a></i>]</sup> </p><p>Ni + H<sub>2</sub>S → NiS + H<sub>2</sub> </p><p>The above reaction controls the effect of sulfur on the anode. </p><p>This can be prevented by having background hydrogen which is calculated below. </p><p>At 453 K the equilibrium constant is 7.39 x 10<sup>−5</sup> </p><p>ΔG calculated at 453 K was 35.833 kJ/mol </p><p>Using the standard heat of formation and entropy ΔG at room temperature (298 K) came out to be 45.904 kJ/mol </p><p>On extrapolation to 1023 K, ΔG is -1.229 kJ/mol </p><p>On substitution, K<sub>eq</sub> at 1023 K is 1.44 x 10<sup>−4</sup>. Hence theoretically we need 3.4% hydrogen to prevent the formation of NiS at 5 ppm H<sub>2</sub>S.<sup id="cite_ref-65" class="reference"><a href="#cite_note-65"><span class="cite-bracket">[</span>65<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Solid_oxide_fuel_cell&action=edit&section=21" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239009302">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .portalbox-entry{display:table-row;font-size:85%;line-height:110%;height:1.9em;font-style:italic;font-weight:bold}.mw-parser-output .portalbox-image{display:table-cell;padding:0.2em;vertical-align:middle;text-align:center}.mw-parser-output .portalbox-link{display:table-cell;padding:0.2em 0.2em 0.2em 0.3em;vertical-align:middle}@media(min-width:720px){.mw-parser-output .portalleft{clear:left;float:left;margin:0.5em 1em 0.5em 0}.mw-parser-output .portalright{clear:right;float:right;margin:0.5em 0 0.5em 1em}}</style><ul role="navigation" aria-label="Portals" class="noprint portalbox portalborder portalright"> <li class="portalbox-entry"><span class="portalbox-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Nuvola_apps_ksim.png" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Nuvola_apps_ksim.png/28px-Nuvola_apps_ksim.png" decoding="async" width="28" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Nuvola_apps_ksim.png/42px-Nuvola_apps_ksim.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Nuvola_apps_ksim.png/56px-Nuvola_apps_ksim.png 2x" data-file-width="128" data-file-height="128" /></a></span></span><span class="portalbox-link"><a href="/wiki/Portal:Electronics" title="Portal:Electronics">Electronics portal</a></span></li><li class="portalbox-entry"><span class="portalbox-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Crystal_energy.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/14/Crystal_energy.svg/29px-Crystal_energy.svg.png" decoding="async" width="29" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/14/Crystal_energy.svg/44px-Crystal_energy.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/14/Crystal_energy.svg/59px-Crystal_energy.svg.png 2x" data-file-width="130" data-file-height="124" /></a></span></span><span class="portalbox-link"><a href="/wiki/Portal:Energy" title="Portal:Energy">Energy portal</a></span></li></ul> <ul><li><a href="/wiki/Auxiliary_power_unit" title="Auxiliary power unit">Auxiliary power unit</a></li> <li><a href="/wiki/Bloom_Energy_Server" title="Bloom Energy Server">Bloom Energy Server</a> – SOFC product from an American company</li> <li><a href="/wiki/Ceramic_Fuel_Cells" title="Ceramic Fuel Cells">Ceramic Fuel Cells</a> Ltd – Australian company producing solid oxide fuel cells</li> <li><a href="/wiki/Glossary_of_fuel_cell_terms" title="Glossary of fuel cell terms">Glossary of fuel cell terms</a></li> <li><a href="/wiki/Hydrogen_technologies" title="Hydrogen technologies">Hydrogen technologies</a></li> <li><a href="/wiki/Micro_combined_heat_and_power" title="Micro combined heat and power">Micro combined heat and power</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Solid_oxide_fuel_cell&action=edit&section=22" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 35em;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFBadwal" class="citation journal cs1">Badwal, SPS. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20141129041316/http://www.austceram.com/JAC-2014-1/ACS-Journal-2014-v1-23">"Review of Progress in High Temperature Solid Oxide Fuel 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Energy page on SOFCs</a></li> <li><a rel="nofollow" class="external text" href="http://www.netl.doe.gov/research/coal/energy-systems/fuel-cells/">National Energy Technology Laboratory website on SOFCs</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160415012053/http://www.netl.doe.gov/research/coal/energy-systems/fuel-cells/">Archived</a> 15 April 2016 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20090606191408/http://electrochem.cwru.edu/encycl/art-f02-sofc.htm">An article in Encyclopedia at YCES</a></li> <li><a rel="nofollow" class="external text" href="http://www.iit.edu/~smart/garrear/fuelcells.htm">Illinois Institute of Technology page on SOFCs</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20080218055544/http://www.iit.edu/~smart/garrear/fuelcells.htm">Archived</a> 18 February 2008 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20130124034344/http://www.ecw.org/prod/207-R.pdf">Assessment of Solid Oxide Fuel Cells in Building Applications Phase 1: Modeling and Preliminary Analyses</a></li> <li><a rel="nofollow" class="external text" href="http://www.csa.com/discoveryguides/fuecel/overview.php">CSA Overview of SOFCs</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20141105105225/http://www.csa.com/discoveryguides/fuecel/abstracts_s.php">Archived</a> 5 November 2014 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li> <li><a rel="nofollow" class="external text" href="http://glassproperties.com/sofc/">SOFC glass-ceramic sealing</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20090913090843/http://www.rsifibre.com/lightweightkiln.html">Refractory Specialties Inc.</a></li> <li><a rel="nofollow" class="external text" href="http://www.msrihome.com/FuelCell.html">Materials & Systems Research, Inc.'s (MSRI)</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20070216195533/http://www.msrihome.com/FuelCell.html">Archived</a> 16 February 2007 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li> <li><a rel="nofollow" class="external text" href="http://www.sofccanada.com/">Solid Oxide Fuel Cells Canada (SOFCC) Strategic Research Network</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210430142929/http://www.sofccanada.com/">Archived</a> 30 April 2021 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li> <li><a rel="nofollow" class="external text" href="http://apmonitor.com/wiki/index.php/Apps/FuelCell">SOFC Dynamics and Control Research</a></li> <li><a rel="nofollow" class="external text" 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