{"id":884,"date":"2021-01-13T19:31:29","date_gmt":"2021-01-14T00:31:29","guid":{"rendered":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/?p=884"},"modified":"2021-01-21T13:56:56","modified_gmt":"2021-01-21T18:56:56","slug":"o-a-torres-matheus-r-e-garcia-and-c-m-bishop-microstructural-phase-coexistence-kinetics-near-the-polymorphic-phase-boundary-acta-materialia-p-116579-2020","status":"publish","type":"post","link":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/2021\/01\/13\/o-a-torres-matheus-r-e-garcia-and-c-m-bishop-microstructural-phase-coexistence-kinetics-near-the-polymorphic-phase-boundary-acta-materialia-p-116579-2020\/","title":{"rendered":"O. A. Torres-Matheus, R. E. Garc\u00eda, and C. M. Bishop &#8220;Microstructural phase coexistence kinetics near the polymorphic phase boundary.&#8221; Acta Materialia, vol. 206, p. 116579, 2021."},"content":{"rendered":"<p>O. A. Torres-Matheus, R. E. Garc\u00eda, and C. M. Bishop &#8220;<em>Microstructural phase coexistence kinetics near the polymorphic phase boundary.<\/em>&#8221; <strong>Acta Materialia<\/strong>, vol. 206, p. 116579, 2021.\u00a0<a href=\"https:\/\/doi.org\/10.1016\/j.actamat.2020.116579\">https:\/\/doi.org\/10.1016\/j.actamat.2020.116579<\/a><\/p>\n<h3>Abstract<\/h3>\n<p>By implementing a novel multiphase field model for ferroelectric systems, the phase coexistence of the tetragonal (T) and rhombohedral (R) phases in Pb-free BZT-40BCT was analyzed. Metastable coexistence of the T and R phases is predicted between a thermodynamic upper limit at<span class=\"Apple-converted-space\">\u00a0<\/span><span class=\"math\"><span id=\"MathJax-Element-1-Frame\" class=\"MathJax_SVG\" style=\"box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; font-style: normal; font-weight: normal; line-height: normal; font-size: 16.200000762939453px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mrow is=&quot;true&quot;&gt;&lt;msub is=&quot;true&quot;&gt;&lt;mi is=&quot;true&quot;&gt;T&lt;\/mi&gt;&lt;mrow is=&quot;true&quot;&gt;&lt;mi is=&quot;true&quot;&gt;C&lt;\/mi&gt;&lt;mo is=&quot;true&quot;&gt;,&lt;\/mo&gt;&lt;mrow is=&quot;true&quot;&gt;&lt;mi mathvariant=&quot;normal&quot; is=&quot;true&quot;&gt;R&lt;\/mi&gt;&lt;\/mrow&gt;&lt;\/mrow&gt;&lt;\/msub&gt;&lt;mo linebreak=&quot;goodbreak&quot; is=&quot;true&quot;&gt;=&lt;\/mo&gt;&lt;msup is=&quot;true&quot;&gt;&lt;mrow is=&quot;true&quot;&gt;&lt;mn is=&quot;true&quot;&gt;49.90&lt;\/mn&gt;&lt;\/mrow&gt;&lt;mo is=&quot;true&quot;&gt;&amp;#x2218;&lt;\/mo&gt;&lt;\/msup&gt;&lt;mi mathvariant=&quot;normal&quot; is=&quot;true&quot;&gt;C&lt;\/mi&gt;&lt;\/mrow&gt;&lt;\/math&gt;\"><\/span>\u00a0T=49.9C and a kinetic lower limit determined by the time-temperature-transformation behaviour. Predicted domain microstructures exhibit faceted domain walls and curved T-R phase interfaces that are consistent with recent TEM studies in the vicinity of the polymorphic phase boundary (PPB). Further, miniaturization of the domain structure near the PPB is a result of the relatively low interfacial energies and a pinning effect caused by the large metastable phase fraction that originates from the vanishing macroscopic driving force for phase transformation. Particularly, the vanishing of rhombohedral domain wall energies as <span id=\"MathJax-Element-2-Frame\" class=\"MathJax_SVG\" style=\"box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; font-style: normal; font-weight: normal; line-height: normal; font-size: 16.200000762939453px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mrow is=&quot;true&quot;&gt;&lt;mi is=&quot;true&quot;&gt;T&lt;\/mi&gt;&lt;mo is=&quot;true&quot;&gt;&amp;#x2192;&lt;\/mo&gt;&lt;msub is=&quot;true&quot;&gt;&lt;mi is=&quot;true&quot;&gt;T&lt;\/mi&gt;&lt;mrow is=&quot;true&quot;&gt;&lt;mi is=&quot;true&quot;&gt;C&lt;\/mi&gt;&lt;mo is=&quot;true&quot;&gt;,&lt;\/mo&gt;&lt;mrow is=&quot;true&quot;&gt;&lt;mi mathvariant=&quot;normal&quot; is=&quot;true&quot;&gt;R&lt;\/mi&gt;&lt;\/mrow&gt;&lt;\/mrow&gt;&lt;\/msub&gt;&lt;\/mrow&gt;&lt;\/math&gt;\"><\/span>\u00a0T reaches the critical transition temperature enables a phase transformation-induced polarization rotation mechanism and predicts a hierarchical domain morphology for the R phase. These results are in agreement with the higher piezoelectric response reported near the maximum temperature for R+T coexistence and the observations of a miniaturized nanodomains structure within micron-sized, wedge-shaped domains in the R phase for the BZT-<em>x<\/em><span id=\"MathJax-Element-3-Frame\" class=\"MathJax_SVG\" style=\"box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; font-style: normal; font-weight: normal; line-height: normal; font-size: 16.200000762939453px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi is=&quot;true&quot;&gt;x&lt;\/mi&gt;&lt;\/math&gt;\"><\/span>BCT system.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p class=\"post-excerpt\" class=\"post-excerpt\">O. A. Torres-Matheus, R. E. Garc\u00eda, and C. M. Bishop &#8220;Microstructural phase&hellip;<\/p>\n<div class=\"link-more\"><a href=\"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/2021\/01\/13\/o-a-torres-matheus-r-e-garcia-and-c-m-bishop-microstructural-phase-coexistence-kinetics-near-the-polymorphic-phase-boundary-acta-materialia-p-116579-2020\/\">Continue reading<span class=\"screen-reader-text\"> &#8220;O. A. Torres-Matheus, R. E. Garc\u00eda, and C. M. Bishop &#8220;Microstructural phase coexistence kinetics near the polymorphic phase boundary.&#8221; Acta Materialia, vol. 206, p. 116579, 2021.&#8221;<\/span>&hellip;<\/a><\/div>\n<div class=\"link-more\"><a href=\"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/2021\/01\/13\/o-a-torres-matheus-r-e-garcia-and-c-m-bishop-microstructural-phase-coexistence-kinetics-near-the-polymorphic-phase-boundary-acta-materialia-p-116579-2020\/\">Continue reading<span class=\"screen-reader-text\"> \"O. A. Torres-Matheus, R. E. Garc\u00eda, and C. M. Bishop &#8220;Microstructural phase coexistence kinetics near the polymorphic phase boundary.&#8221; Acta Materialia, vol. 206, p. 116579, 2021.\"<\/span>&hellip;<\/a><\/div>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"advanced_seo_description":"","jetpack_publicize_message":"","jetpack_is_tweetstorm":false,"jetpack_publicize_feature_enabled":true},"categories":[45],"tags":[11,48,15,7],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/peeeSR-eg","jetpack_likes_enabled":true,"jetpack-related-posts":[{"id":781,"url":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/2018\/10\/26\/oat-matheus-re-garcia-cm-bishop-phase-field-theory-and-coexistence-of-ferroelectric-phases-near-the-morphotropic-phase-boundary-acta-materialia-in-press-oct-2018\/","url_meta":{"origin":884,"position":0},"title":"OA Torres-Matheus, RE Garc\u00eda, CM Bishop. \u201cPhase Coexistence Near the Morphotropic Phase Boundary.\u201d Acta Materialia. 164:577-585, 2019.","date":"10\/26\/2018","format":false,"excerpt":"OA Torres-Matheus, RE Garc\u00eda, CM Bishop. \u201cPhase \u00a0Coexistence Near the Morphotropic Phase Boundary.\u201d Acta Materialia. 164:577-585, 2019.\u00a0https:\/\/doi.org\/10.1016\/j.actamat.2018.10.041 Abstract A novel multiphase field theory for ferroelectric systems in the vicinity of a polymorphic phase boundary (PPB) is developed by coupling the Landau-Devonshire thermodynamic potentials of the individual phases. The model naturally\u2026","rel":"","context":"In &quot;Papers&quot;","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":901,"url":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/2021\/08\/07\/o-a-torres-matheus-r-e-garcia-and-c-m-bishop-physics-based-optimization-of-landau-parameters-for-ferroelectrics-application-to-bzt-50bct-modelling-and-simulation-in-materials-science-and\/","url_meta":{"origin":884,"position":1},"title":"O. A. Torres-Matheus, R.E. Garc\u00eda, and C. M. Bishop &#8220;Physics-based optimization of Landau parameters for ferroelectrics: application to BZT-50BCT.&#8221; Modelling and Simulation in Materials Science and Engineering. 29 075001, 2021.","date":"08\/07\/2021","format":false,"excerpt":"O. A. Torres-Matheus, R.E. Garc\u00eda and C. M. Bishop \"Physics-based optimization of Landau parameters for ferroelectrics: application to BZT-50BCT.\" Modelling and Simulation in Materials Science and Engineering. 29, 075001,. 2021. https:\/\/doi.org\/10.1088\/1361-651X\/ac1a60 Abstract In analogy to thermochemical parameter optimization in the CALculation of PHAse Diagrams (CALPHAD) approach that relies on a\u2026","rel":"","context":"In &quot;Papers&quot;","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":877,"url":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/2020\/12\/10\/j-lund-k-s-n-vikrant-c-m-bishop-w-rheinheimer-r-e-garcia-thermodynamically-consistent-variational-principles-for-charged-interfaces-acta-materialia-205116525-2021\/","url_meta":{"origin":884,"position":2},"title":"J. Lund, K. S. N. Vikrant, C. M. Bishop, W. Rheinheimer, R. E. Garc\u00eda &#8220;Thermodynamically Consistent Variational Principles for Charged Interfaces.&#8221; Acta Materialia, 205:116525,  (2021).","date":"12\/10\/2020","format":false,"excerpt":"J. Lund, K. S. N. Vikrant, C. M. Bishop, W. Rheinheimer, R. E. Garc\u00eda \"Thermodynamically Consistent Variational Principles for Charged Interfaces.\" Acta Materialia, 205:116525, (2021).\u00a0https:\/\/doi.org\/10.1016\/j.actamat.2020.116525 Abstract A generalized framework that naturally incorporates the free energy contributions of thermochemical, structural, mechanical, and electrical fields is presented to describe the Space Charge\u2026","rel":"","context":"In &quot;Papers&quot;","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":921,"url":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/2022\/06\/08\/l-d-robinson-k-s-n-vikrant-j-e-blendell-c-a-handwerker-r-e-garcia-interfacial-and-volumetric-melting-regimes-of-sn-nanoparticles-acta-materialia-in-press-2022\/","url_meta":{"origin":884,"position":3},"title":"L.D. Robinson, K.S.N. Vikrant, J.E. Blendell, C.A. Handwerker, R.E. Garc\u00eda  &#8220;Interfacial and Volumetric Melting Regimes of Sn Nanoparticles.&#8221; Acta Materialia. In Press. 2022","date":"06\/08\/2022","format":false,"excerpt":"L.D. Robinson, K.S.N. Vikrant, J.E. Blendell, C.A. Handwerker, and R.E. Garc\u00eda \"Interfacial and Volumetric Melting Regimes of Sn Nanoparticles.\" Acta Materialia. In Press. 2022.\u00a0https:\/\/doi.org\/10.1016\/j.actamat.2022.118084 Abstract A thermodynamically consistent phase field formulation was developed to describe what has been historically known as the premelted surface layer in Sn nanoparticles. Two interfacial\u2026","rel":"","context":"In &quot;Papers&quot;","img":{"alt_text":"","src":"https:\/\/i0.wp.com\/engineering.purdue.edu\/ComputationalMaterials\/wp-content\/uploads\/2022\/06\/1-s2.0-S1359645422004657-ga1_lrg-1.jpg?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":318,"url":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/2017\/10\/29\/thermodynamically-consistent-variational-principles-with-applications-to-electrically-and-magnetically-active-systems\/","url_meta":{"origin":884,"position":4},"title":"RE Garc\u00eda, CM Bishop, WC Carter &#8220;Thermodynamically consistent variational principles with applications to electrically and magnetically active systems&#8221; Acta Materialia, 52(1):11-21, 2004.","date":"10\/29\/2017","format":false,"excerpt":"RE Garc\u00eda, CM Bishop, WC Carter \"Thermodynamically consistent variational principles with applications to electrically and magnetically active systems\" Acta Materialia, 52(1):11-21, 2004. Abstract We propose a theoretical framework to derive thermodynamically consistent equilibrium equations and kinetic driving forces to describe the time evolution for electrically and magnetically active materials. This\u2026","rel":"","context":"In &quot;Papers&quot;","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":851,"url":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/2020\/09\/27\/ksn-vikrant-w-rheinheimer-h-sternlicht-m-baurer-re-garcia-electrochemically-driven-abnormal-grain-growth-in-ionic-ceramics-acta-materialia-200-720-734-2020\/","url_meta":{"origin":884,"position":5},"title":"KSN Vikrant, W Rheinheimer, H Sternlicht, M B\u00e4urer, RE Garc\u00eda &#8220;Electrochemically-driven abnormal grain growth in ionic ceramics.&#8221;  Acta Materialia 200: 720-734, 2020.","date":"09\/27\/2020","format":false,"excerpt":"KSN Vikrant, W Rheinheimer, H Sternlicht, M B\u00e4urer, RE Garc\u00eda \"Electrochemically-driven abnormal grain growth in ionic ceramics.\" Acta Materialia 200: 720-734, 2020. \u00a0https:\/\/doi.org\/10.1016\/j.actamat.2020.08.027 \u00a0 Abstract A combined theoretical and experimental analysis was performed to understand the effects of extrinsic ionic species and point defects on the microstructural evolution of ionic\u2026","rel":"","context":"In &quot;Papers&quot;","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]}],"_links":{"self":[{"href":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/wp-json\/wp\/v2\/posts\/884"}],"collection":[{"href":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/wp-json\/wp\/v2\/comments?post=884"}],"version-history":[{"count":3,"href":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/wp-json\/wp\/v2\/posts\/884\/revisions"}],"predecessor-version":[{"id":889,"href":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/wp-json\/wp\/v2\/posts\/884\/revisions\/889"}],"wp:attachment":[{"href":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/wp-json\/wp\/v2\/media?parent=884"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/wp-json\/wp\/v2\/categories?post=884"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/wp-json\/wp\/v2\/tags?post=884"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}