{"id":8098,"date":"2022-12-11T12:14:38","date_gmt":"2022-12-11T11:14:38","guid":{"rendered":"https:\/\/www.nickzom.org\/blog\/?p=8098"},"modified":"2024-05-31T07:45:00","modified_gmt":"2024-05-31T06:45:00","slug":"how-to-calculate-and-solve-for-critical-radius-for-homogeneous-nucleation-phase-transformation","status":"publish","type":"post","link":"https:\/\/www.nickzom.org\/blog\/2022\/12\/11\/how-to-calculate-and-solve-for-critical-radius-for-homogeneous-nucleation-phase-transformation\/","title":{"rendered":"How to Calculate and Solve for Critical Radius for Homogeneous Nucleation | Phase Transformation"},"content":{"rendered":"<p><img decoding=\"async\" class=\"alignnone size-full wp-image-8102\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2022\/12\/critical-radius-for-homogenous-nucleation.jpg\" alt=\"\" width=\"215\" height=\"234\" \/><\/p>\n<p>The image above represents the critical radius for homogenous nucleation. To calculate the critical radius for homogeneous nucleation, two essential parameters are needed and these parameters are <strong>Volume Free Energy (\u0394G<sub>v<\/sub>)<\/strong> and<strong> Surface Free Energy (\u03b3).<\/strong><\/p>\n<h3><strong>The formula for calculating critical radius for homogenous nucleation:<\/strong><\/h3>\n<p>r* =\u00a0<sup>-2\u03b3<\/sup>\/<sub>\u0394Gv<\/sub><\/p>\n<p>Where:<\/p>\n<p>r* = Critical Radius for Homogeneous Nucleation<br \/>\n\u03b3 = Surface Free Energy<br \/>\n\u0394G<sub>v<\/sub>\u00a0= Volume Free Energy<\/p>\n<p>Given an example;<br \/>\nFind the critical radius for homogenous nucleation when the surface free energy is 8 and the volume free energy is 40.<\/p>\n<p>This implies that;<\/p>\n<p>\u03b3 = Surface Free Energy = 8<br \/>\n\u0394G<sub>v<\/sub> = Volume Free Energy = 40<\/p>\n<p>r* =\u00a0<sup>-2\u03b3<\/sup>\/<sub>\u0394Gv<\/sub><br \/>\nThat is, r* = <sup>-2(8)<\/sup>\/<sub>(40)<\/sub><br \/>\nr* =\u00a0<sup>(-16)<\/sup>\/<sub>(40)<\/sub><br \/>\nr* = -0.4<\/p>\n<p>Therefore, the\u00a0<strong>critical radius for homogenous nucleation\u00a0<\/strong>is\u00a0<strong>-0.4.<\/strong><\/p>\n<h3><strong>Calculating the Volume Free Energy when the Critical Radius for Homogenous Nucleation and the Surface Free Energy are Given<\/strong><\/h3>\n<p>\u0394G<sub>v<\/sub> = <sup>-2\u03b3<\/sup> \/ <sub>r*<\/sub><\/p>\n<p>Where:<\/p>\n<p>\u0394G<sub>v<\/sub>\u00a0= Volume Free Energy<br \/>\nr* = Critical Radius for Homogeneous Nucleation<br \/>\n\u03b3 = Surface Free Energy<\/p>\n<p>Let&#8217;s solve an example;<br \/>\nFind the volume free energy when the critical radius for homogenous nucleation is 12 and the surface free energy is 5.<\/p>\n<p>This implies that;<\/p>\n<p>r* = Critical Radius for Homogeneous Nucleation = 12<br \/>\n\u03b3 = Surface Free Energy = 5<\/p>\n<p>\u0394G<sub>v<\/sub> = <sup>-2\u03b3<\/sup> \/ <sub>r*<\/sub><br \/>\nThen, \u0394G<sub>v<\/sub> = <sup>-2(5)<\/sup> \/ <sub>12<\/sub><br \/>\n\u0394G<sub>v<\/sub> = <sup>-10<\/sup> \/ <sub>12<\/sub><br \/>\n\u0394G<sub>v<\/sub> = 0.83<\/p>\n<p>Therefore, the\u00a0<strong>volume free energy\u00a0<\/strong>is\u00a0<strong>0.83.<\/strong><\/p>\n<p>Read more:\u00a0<a href=\"https:\/\/www.nickzom.org\/blog\/2022\/12\/12\/how-to-calculate-and-solve-for-homogeneous-heterogeneous-relationship-phase-transformation\/\">How to Calculate and Solve for Homogeneous; Heterogeneous Relationship | Phase Transformation<\/a><\/p>\n<h3><strong>Calculating the Surface Free Energy when the Critical Radius for Homogenous Nucleation and the Volume Free Energy are Given<\/strong><\/h3>\n<p>\u03b3 = <sup>r* x \u0394G<sub>v<\/sub><\/sup> \/ <sub>-2<\/sub><\/p>\n<p>Where:<\/p>\n<p>\u03b3 = Surface Free Energy<br \/>\nr* = Critical Radius for Homogeneous Nucleation<br \/>\n\u0394G<sub>v<\/sub>\u00a0= Volume Free Energy<\/p>\n<p>Let&#8217;s solve an example;<br \/>\nFind the surface free energy when the critical radius for homogenous nucleation is 10 and the volume free energy is 4.<\/p>\n<p>This implies that;<\/p>\n<p>r* = Critical Radius for Homogeneous Nucleation = 10<br \/>\n\u0394G<sub>v<\/sub> = Volume Free Energy = 4<\/p>\n<p>\u03b3 = <sup>r* x \u0394G<sub>v<\/sub><\/sup> \/ <sub>-2<\/sub><br \/>\n\u03b3 = <sup>10 x 4<\/sup> \/ <sub>-2<\/sub><br \/>\nSo, \u03b3 = <sup>40<\/sup> \/ <sub>-2<\/sub><br \/>\n\u03b3 = -20<\/p>\n<p>Therefore, the\u00a0<strong>surface free energy\u00a0<\/strong>is\u00a0<strong>-20.<\/strong><\/p>\n<p>Read more:\u00a0<a href=\"https:\/\/www.nickzom.org\/blog\/2022\/12\/12\/how-to-calculate-and-solve-for-critical-radius-for-heterogeneous-nucleation-phase-transformation\/\">How to Calculate and Solve for Critical Radius for Heterogeneous Nucleation | Phase Transformation<\/a><\/p>\n<h3><strong>How to Calculate the Critical Radius for Homogeneous Nucleation With Nickzom Calculator<\/strong><\/h3>\n<p>Nickzom Calculator \u2013\u00a0<strong>The Calculator Encyclopedia<\/strong> is capable of calculating the critical radius for homogenous nucleation.<\/p>\n<div>\n<p>To get the answer and workings of the critical radius for homogenous nucleation using the <strong>Nickzom Calculator \u2013 The Calculator Encyclopedia.\u00a0<\/strong>First, you need to obtain the app.<\/p>\n<p>You can get this app via any of these means:<\/p>\n<p><strong>Web<\/strong>\u00a0\u2013\u00a0<a href=\"https:\/\/www.nickzom.org\/calculator-plus\">https:\/\/www.nickzom.org\/calculator-plus<\/a><\/p>\n<p>To get access to the\u00a0<strong>professional\u00a0<\/strong>version via web, you need to\u00a0<strong>register<\/strong>\u00a0and\u00a0<strong>subscribe\u00a0<\/strong>to have utter access to all functionalities.<br \/>\nYou can also try the\u00a0<strong>demo\u00a0<\/strong>version via\u00a0<a href=\"https:\/\/www.nickzom.org\/calculator\">https:\/\/www.nickzom.org\/calculator<\/a><\/p>\n<p><strong>Android (Paid)<\/strong>\u00a0\u2013\u00a0<a href=\"https:\/\/play.google.com\/store\/apps\/details?id=org.nickzom.nickzomcalculator\">https:\/\/play.google.com\/store\/apps\/details?id=org.nickzom.nickzomcalculator<\/a><br \/>\n<strong>Android (Free)<\/strong>\u00a0\u2013\u00a0<a href=\"https:\/\/play.google.com\/store\/apps\/details?id=com.nickzom.nickzomcalculator\">https:\/\/play.google.com\/store\/apps\/details?id=com.nickzom.nickzomcalculator<\/a><\/p>\n<p><strong>Apple (Paid)<\/strong>\u00a0\u2013\u00a0<a href=\"https:\/\/itunes.apple.com\/us\/app\/nickzom-calculator\/id1331162702?mt=8\">https:\/\/itunes.apple.com\/us\/app\/nickzom-calculator\/id1331162702?mt=8<\/a><br \/>\nOnce, you have obtained the calculator encyclopedia app, proceed to the\u00a0<strong>Calculator Map,\u00a0<\/strong>then click on\u00a0<b>Materials and Metallurgical\u00a0<\/b>under\u00a0<strong>Engineering<\/strong><strong>.<\/strong><\/p>\n<\/div>\n<p><img decoding=\"async\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2021\/07\/Screenshot-2.png\" \/><\/p>\n<p>Now, Click on\u00a0<strong>Phase Transformation<\/strong><b>\u00a0<\/b>under\u00a0<strong>Materials and Metallurgical<\/strong><\/p>\n<p><img decoding=\"async\" class=\"alignnone wp-image-8001 size-full\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2022\/12\/Screenshot-44.png\" alt=\"\" width=\"1366\" height=\"768\" srcset=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2022\/12\/Screenshot-44.png 1366w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2022\/12\/Screenshot-44-300x169.png 300w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2022\/12\/Screenshot-44-1024x576.png 1024w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2022\/12\/Screenshot-44-768x432.png 768w\" sizes=\"(max-width: 1366px) 100vw, 1366px\" \/><\/p>\n<p>Now, Click on <strong>Critical Radius for Homogenous Nucleation<\/strong><strong>\u00a0<\/strong>under\u00a0<strong>Phase Transformation<\/strong><\/p>\n<p><img decoding=\"async\" class=\"alignnone wp-image-8109 size-full\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2022\/12\/Screenshot-102.png\" alt=\"\" width=\"1366\" height=\"768\" srcset=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2022\/12\/Screenshot-102.png 1366w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2022\/12\/Screenshot-102-300x169.png 300w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2022\/12\/Screenshot-102-1024x576.png 1024w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2022\/12\/Screenshot-102-768x432.png 768w\" sizes=\"(max-width: 1366px) 100vw, 1366px\" \/><\/p>\n<p>The screenshot below displays the page or activity to enter your values, to get the answer for the critical radius for homogenous nucleation according to the respective parameter which is the <strong>Volume Free Energy (\u0394G<sub>v<\/sub>)<\/strong> and<strong> Surface Free Energy (\u03b3).<\/strong><\/p>\n<p><img decoding=\"async\" class=\"alignnone wp-image-8110 size-full\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2022\/12\/Screenshot-103.png\" alt=\"How to Calculate and Solve for Critical Radius for Homogeneous Nucleation | Phase Transformation\" width=\"1366\" height=\"768\" srcset=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2022\/12\/Screenshot-103.png 1366w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2022\/12\/Screenshot-103-300x169.png 300w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2022\/12\/Screenshot-103-1024x576.png 1024w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2022\/12\/Screenshot-103-768x432.png 768w\" sizes=\"(max-width: 1366px) 100vw, 1366px\" \/><\/p>\n<p>Now, enter the values appropriately and accordingly for the parameters as required by the <strong>Volume Free Energy (\u0394G<sub>v<\/sub>)\u00a0<\/strong>is\u00a0<strong>40<\/strong> and<strong> Surface Free Energy (\u03b3)<\/strong> is <strong>8<\/strong>.<\/p>\n<p><img decoding=\"async\" class=\"alignnone wp-image-8111 size-full\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2022\/12\/Screenshot-104.png\" alt=\"How to Calculate and Solve for Critical Radius for Homogeneous Nucleation | Phase Transformation\" width=\"1366\" height=\"768\" srcset=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2022\/12\/Screenshot-104.png 1366w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2022\/12\/Screenshot-104-300x169.png 300w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2022\/12\/Screenshot-104-1024x576.png 1024w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2022\/12\/Screenshot-104-768x432.png 768w\" sizes=\"(max-width: 1366px) 100vw, 1366px\" \/><\/p>\n<p>Finally, Click on Calculate<\/p>\n<p><img decoding=\"async\" class=\"alignnone wp-image-8112 size-full\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2022\/12\/Screenshot-105.png\" alt=\"How to Calculate and Solve for Critical Radius for Homogeneous Nucleation | Phase Transformation\" width=\"1366\" height=\"768\" srcset=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2022\/12\/Screenshot-105.png 1366w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2022\/12\/Screenshot-105-300x169.png 300w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2022\/12\/Screenshot-105-1024x576.png 1024w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2022\/12\/Screenshot-105-768x432.png 768w\" sizes=\"(max-width: 1366px) 100vw, 1366px\" \/><\/p>\n<p>As you can see from\u00a0the screenshot above,\u00a0<strong>Nickzom Calculator<\/strong>\u2013 The Calculator Encyclopedia can calculate the critical radius for homogenous nucleation and presents the formula, workings and steps too.<\/p>\n","protected":false},"excerpt":{"rendered":"The image above represents the critical radius for homogenous nucleation. To calculate the critical radius for homogeneous nucleation,&hellip;","protected":false},"author":5,"featured_media":16152,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_opengraph-title":"","_yoast_wpseo_opengraph-description":"","_yoast_wpseo_twitter-title":"","_yoast_wpseo_twitter-description":"","_lmt_disableupdate":"","_lmt_disable":"","_sitemap_exclude":false,"_sitemap_priority":"","_sitemap_frequency":"","_yoast_wpseo_focuskw_text_input":"","csco_display_header_overlay":false,"csco_singular_sidebar":"","csco_page_header_type":"","footnotes":""},"categories":[47],"tags":[2273,60,543,2244,2270,2269],"class_list":["post-8098","post","type-post","status-publish","format-standard","has-post-thumbnail","category-engineering","tag-critical-radius-for-homogenous-nucleation","tag-engineering","tag-materials-and-metallurgical","tag-phase-transformation","tag-surface-free-energy","tag-volume-free-energy","cs-entry"],"yoast_head":"<!-- This site is optimized with the 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