{"id":8151,"date":"2022-12-12T11:26:25","date_gmt":"2022-12-12T10:26:25","guid":{"rendered":"https:\/\/www.nickzom.org\/blog\/?p=8151"},"modified":"2024-06-04T13:29:48","modified_gmt":"2024-06-04T12:29:48","slug":"how-to-calculate-and-solve-for-critical-radius-for-heterogeneous-nucleation-phase-transformation","status":"publish","type":"post","link":"https:\/\/www.nickzom.org\/blog\/2022\/12\/12\/how-to-calculate-and-solve-for-critical-radius-for-heterogeneous-nucleation-phase-transformation\/","title":{"rendered":"How to Calculate and Solve for Critical Radius for Heterogeneous Nucleation | Phase Transformation"},"content":{"rendered":"

The image of critical radius for heterogenous nucleation. To calculate critical radius for heterogeneous nucleation, two essential parameters are needed and these parameters are Solid – Liquid Interface (\u03b3SL<\/sub>)\u00a0<\/strong>and\u00a0Volume Free Energy (\u0394Gv<\/sub>).<\/strong><\/p>\n

\"\"<\/p>\n

The formula for calculating critical radius for heterogeneous nucleation:<\/strong><\/h3>\n

r* =\u00a02\u03b3SL<\/sub><\/sup>\/\u0394Gv<\/sub><\/p>\n

Where:<\/p>\n

r* = Critical Radius for Heterogeneous Nucleation
\n\u03b3SL<\/sub>\u00a0= Solid – Liquid Interface
\n\u0394Gv<\/sub>\u00a0= Volume Free Energy<\/p>\n

Let’s solve an example;
\nFind the critical radius for heterogenous nucleation when the solid – liquid interface is 24 and the volume free energy is 3.<\/p>\n

This implies that;<\/p>\n

\u03b3SL<\/sub> = Solid – Liquid Interface = 24
\n\u0394Gv<\/sub> = Volume Free Energy = 3<\/p>\n

r* =\u00a02\u03b3SL<\/sub><\/sup>\/\u0394Gv<\/sub>
\nSo, r* = 2(24)<\/sup>\/3<\/sub>
\nr* =\u00a048<\/sup>\/3<\/sub>
\nr* = 16<\/p>\n

Therefore, the\u00a0critical radius for heterogenous nucleation\u00a0<\/strong>is\u00a016 mm.<\/strong><\/p>\n

Calculating the Solid-Liquid Interface when the Critical Radius for Heterogenous Nucleation and the Volume Free Energy are Given<\/strong><\/h3>\n

\u03b3SL<\/sub> = r*\u0394Gv<\/sub><\/sup> \/ 2<\/sub><\/p>\n

Where:<\/p>\n

\u03b3SL<\/sub>\u00a0= Solid – Liquid Interface
\nr* = Critical Radius for Heterogeneous Nucleation
\n\u0394Gv<\/sub>\u00a0= Volume Free Energy<\/p>\n

Let’s solve an example;
\nFind the solid – liquid interface when the critical radius for heterogenous nucleation is 15 and the volume free energy is 4.<\/p>\n

This implies that;<\/p>\n

r* = Critical Radius for Heterogeneous Nucleation = 15
\n\u0394Gv<\/sub> = Volume Free Energy = 4<\/p>\n

\u03b3SL<\/sub> = r*\u0394Gv<\/sub><\/sup> \/ 2<\/sub>
\nThen, \u03b3SL<\/sub> = (15)(4)<\/sup> \/ 2<\/sub>
\n\u03b3SL<\/sub> = 60<\/sup> \/ 2<\/sub>
\n\u03b3SL<\/sub> = 30<\/p>\n

Therefore, the\u00a0solid-liquid interface <\/strong><\/a>is\u00a030.<\/strong><\/p>\n

Calculating the Volume Free Energy when the Critical Radius for Heterogenous Nucleation and the Solid – Liquid Interface are Given<\/strong><\/h3>\n

\u0394Gv<\/sub> = 2\u03b3SL<\/sub><\/sup> \/ r*<\/sub><\/p>\n

Where:<\/p>\n

\u0394Gv<\/sub>\u00a0= Volume Free Energy<\/a>
\nr* = Critical Radius for Heterogeneous Nucleation
\n\u03b3SL<\/sub> = Solid – Liquid Interface<\/p>\n

Given an example;
\nFind the volume free energy when the critical radius for heterogenous nucleation is 10 and the solid – liquid interface is 30.<\/p>\n

This implies that;<\/p>\n

r* = Critical Radius for Heterogeneous Nucleation = 10
\n\u03b3SL<\/sub> = Solid – Liquid Interface = 30<\/p>\n

\u0394Gv<\/sub> = 2\u03b3SL<\/sub><\/sup> \/ r*<\/sub>
\nSo, \u0394Gv<\/sub> = 2(30)<\/sup> \/ 10<\/sub>
\n\u0394Gv<\/sub> = 60<\/sup> \/ 10<\/sub>
\n\u0394Gv<\/sub> = 6<\/p>\n

Therefore, the\u00a0volume free energy\u00a0<\/strong>is\u00a06.<\/strong><\/p>\n

How to Calculate\u00a0 Critical Radius for Heterogeneous Nucleation Using Nickzom Calculator<\/strong><\/h3>\n

Nickzom Calculator \u2013\u00a0The Calculator Encyclopedia<\/strong> is capable of calculating the critical radius of heterogenous nucleation.<\/p>\n

\n

To get the answer and workings of the critical radius of heterogenous nucleation using the Nickzom Calculator \u2013 The Calculator Encyclopedia.\u00a0<\/strong>First, you need to obtain the app.<\/p>\n

You can get this app via any of these means:<\/p>\n

Web<\/strong>\u00a0\u2013\u00a0https:\/\/www.nickzom.org\/calculator-plus<\/a><\/p>\n

To get access to the\u00a0professional\u00a0<\/strong>version via web, you need to\u00a0register<\/strong>\u00a0and\u00a0subscribe\u00a0<\/strong>to have utter access to all functionalities.
\nYou can also try the\u00a0demo\u00a0<\/strong>version via\u00a0https:\/\/www.nickzom.org\/calculator<\/a><\/p>\n

Android (Paid)<\/strong>\u00a0\u2013\u00a0https:\/\/play.google.com\/store\/apps\/details?id=org.nickzom.nickzomcalculator<\/a>
\nAndroid (Free)<\/strong>\u00a0\u2013\u00a0https:\/\/play.google.com\/store\/apps\/details?id=com.nickzom.nickzomcalculator<\/a><\/p>\n

Apple (Paid)<\/strong>\u00a0\u2013\u00a0https:\/\/itunes.apple.com\/us\/app\/nickzom-calculator\/id1331162702?mt=8<\/a>
\nOnce, you have obtained the calculator encyclopedia app, proceed to the\u00a0Calculator Map,\u00a0<\/strong>then click on\u00a0Materials and Metallurgical\u00a0<\/b>under\u00a0Engineering<\/strong>.<\/strong><\/p>\n<\/div>\n

<\/p>\n

Now, Click on\u00a0Phase Transformation<\/strong>\u00a0<\/b>under\u00a0Materials and Metallurgical<\/strong><\/p>\n

\"\"<\/p>\n

Now, Click on Critical Radius of Heterogenous Nucleation<\/strong>\u00a0<\/strong>under\u00a0Phase Transformation<\/strong><\/p>\n

\"\"<\/p>\n

The screenshot below displays the page or activity to enter your values, to get the answer for the critical radius of heterogenous nucleation according to the respective parameter which is the Solid – Liquid Interface (\u03b3SL<\/sub>)\u00a0<\/strong>and\u00a0Volume Free Energy (\u0394Gv<\/sub>).<\/strong><\/p>\n

\"How<\/p>\n

Now, enter the values appropriately and accordingly for the parameters as required by the Solid – Liquid Interface (\u03b3SL<\/sub>)<\/strong> is 24 <\/strong>and Volume Free Energy (\u0394Gv<\/sub>)<\/strong> is 3<\/strong>.<\/p>\n

\"How<\/p>\n

Finally, Click on Calculate<\/p>\n

\"How<\/p>\n

As you can see from\u00a0the screenshot above,\u00a0Nickzom Calculator<\/strong>\u2013 The Calculator Encyclopedia can calculate the critical radius of heterogenous nucleation and presents the formula, workings and steps too.<\/p>\n","protected":false},"excerpt":{"rendered":"The image of critical radius for heterogenous nucleation. To calculate critical radius for heterogeneous nucleation, two essential parameters…","protected":false},"author":5,"featured_media":16326,"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":[2289,60,543,2244,2284,2269],"class_list":["post-8151","post","type-post","status-publish","format-standard","has-post-thumbnail","category-engineering","tag-critical-radius-of-heterogeneous-nucleation","tag-engineering","tag-materials-and-metallurgical","tag-phase-transformation","tag-solid-liquid-interface","tag-volume-free-energy","cs-entry"],"yoast_head":"\nHow to Calculate and Solve for Critical 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