{"id":3057,"date":"2020-04-14T15:05:32","date_gmt":"2020-04-14T14:05:32","guid":{"rendered":"https:\/\/www.nickzom.org\/blog\/?p=3057"},"modified":"2024-03-30T10:50:18","modified_gmt":"2024-03-30T09:50:18","slug":"how-to-calculate-and-solve-for-frenkel-defect-ceramics","status":"publish","type":"post","link":"https:\/\/www.nickzom.org\/blog\/2020\/04\/14\/how-to-calculate-and-solve-for-frenkel-defect-ceramics\/","title":{"rendered":"How to Calculate and Solve for Frenkel Defect | Ceramics"},"content":{"rendered":"<p><img decoding=\"async\" class=\"alignnone size-full wp-image-3058\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2020\/04\/frenkel-defect.jpeg\" alt=\"\" width=\"268\" height=\"188\" \/><\/p>\n<p>The image above represents frenkel defect. To calculate the frenkel defect, four essential parameters are needed and these parameters are <strong>N, activation energy (Q<sub>fr<\/sub>), Boltzmann&#8217;s Constant (K)<\/strong> and<strong> temperature (T).<\/strong><\/p>\n<p>The formula for calculating the frenkel defect:<\/p>\n<p>N<sub>fr<\/sub>\u00a0= N exp (<sup>-Q<sub>fr <\/sub><\/sup>\/ <sub>2KT<\/sub>)<\/p>\n<p>Where:<\/p>\n<p>N<sub>fr<\/sub> = Frenkel Defect<br \/>\nQ<sub>fr<\/sub>\u00a0= Activation Energy<br \/>\nK = Boltzmann&#8217;s Constant<br \/>\nT = Temperature<\/p>\n<p>Let&#8217;s solve an example;<br \/>\nFind the frenkel defect when the activation energy is 34, N is 22, Temperature is 12 and the boltzmann&#8217;s constant is 1.38064852e-23.<\/p>\n<p>This implies that;<\/p>\n<p>Q<sub>fr<\/sub>\u00a0= Activation Energy<br \/>\nK = Boltzmann&#8217;s Constant<br \/>\nT = Temperature<\/p>\n<p>N<sub>fr<\/sub>\u00a0= N exp (<sup>-Q<sub>fr <\/sub><\/sup>\/ <sub>2KT<\/sub>)<br \/>\nSo, N<sub>fr<\/sub>\u00a0= (22)exp(<sup>-(34) <\/sup>\/ <sub>2(1.38064852e-23)(14)<\/sub>)<br \/>\nN<sub>fr<\/sub>\u00a0= (22)exp(<sup>(-34) <\/sup>\/ <sub>(3.865815856e-22)<\/sub>)<br \/>\nN<sub>fr<\/sub> = (22)exp(-8.795038684325786e+22)<br \/>\nThat is, N<sub>fr<\/sub> = (22)(0)<br \/>\nN<sub>fr<\/sub>\u00a0= 0<\/p>\n<p>Therefore, the\u00a0<strong>frenkel defect\u00a0<\/strong>is\u00a0<strong>0.<\/strong><\/p>\n<h3><strong>Calculating the Activation Energy when the Frenkel Defect, the Boltzmann&#8217;s Constant and the Temperature are Given<\/strong><\/h3>\n<p>Q<sub>fr<\/sub> = &#8211; (In (<sup>N<sub>fr<\/sub><\/sup> \/ <sub>N<\/sub>) x 2KT)<\/p>\n<p>Where;<\/p>\n<p>Q<sub>fr<\/sub>\u00a0= Activation Energy<br \/>\nN<sub>fr<\/sub> = Frenkel Defect<br \/>\nK = Boltzmann&#8217;s Constant<br \/>\nT = Temperature<\/p>\n<p>Let&#8217;s solve an example;<br \/>\nGiven that the frenkel defect is 20, the boltzmann&#8217;s constant is 5, the temperature is 2 and N is 10. Find the activation energy?<\/p>\n<p>This implies that;<\/p>\n<p>N<sub>fr<\/sub> = Frenkel Defect = 20<br \/>\nK = Boltzmann&#8217;s Constant = 5<br \/>\nT = Temperature = 2<br \/>\nN = 10<\/p>\n<p>Q<sub>fr<\/sub> = &#8211; (In (<sup>N<sub>fr<\/sub><\/sup> \/ <sub>N<\/sub>) x 2KT)<br \/>\nQ<sub>fr<\/sub> = &#8211; (In (<sup>20<\/sup> \/ <sub>10<\/sub>) x 2 x 5 x 2)<br \/>\nThen, Q<sub>fr<\/sub> = &#8211; (In 2 x 20)<br \/>\nQ<sub>fr<\/sub> = &#8211; (In 40)<br \/>\nQ<sub>fr<\/sub> = &#8211; 3.688<\/p>\n<p>Therefore, the\u00a0<strong>activation energy\u00a0<\/strong>is <strong>&#8211; 3.688.<\/strong><\/p>\n<p>Read more:\u00a0<a href=\"https:\/\/www.nickzom.org\/blog\/2020\/04\/14\/how-to-calculate-and-solve-for-theoretical-density-of-ceramics-ceramics\/\">How to Calculate and Solve for Theoretical Density of Ceramics | Ceramics<\/a><\/p>\n<h3><strong>Calculating the Boltzmann&#8217;s Constant when the Frenkel Defect, the Activation Energy and the Temperature are Given<\/strong><\/h3>\n<p>K = <sup>&#8211; Q<sub>fr<\/sub><\/sup> \/ <sub>In (<sup>Nfr<\/sup> \/ N)<\/sub> x <sup>1<\/sup> \/ <sub>2T<\/sub><\/p>\n<p>Where;<\/p>\n<p>K = Boltzmann&#8217;s Constant<br \/>\nT = Temperature<br \/>\nQ<sub>fr<\/sub>\u00a0= Activation Energy<br \/>\nN<sub>fr<\/sub> = Frenkel Defect<\/p>\n<p>Let&#8217;s solve an example;<br \/>\nFind the boltzmann&#8217;s constant when the temperature is 20, the frenkel defect is 30, the activation energy is 12 and N is 6.<\/p>\n<p>This implies that;<\/p>\n<p>T = Temperature = 20<br \/>\nQ<sub>fr<\/sub> = Activation Energy = 12<br \/>\nN<sub>fr<\/sub> = Frenkel Defect = 30<br \/>\nN = 6<\/p>\n<p>K = <sup>&#8211; Q<sub>fr<\/sub><\/sup> \/ <sub>In (<sup>Nfr<\/sup> \/ <sub>N<\/sub>)<\/sub> x <sup>1<\/sup> \/ <sub>2T<\/sub><br \/>\nSo, K = <sup>&#8211; 12<\/sup> \/ <sub>In (<sup>30<\/sup> \/ <sub>6<\/sub>)<\/sub> x <sup>1<\/sup> \/ <sub>2 x 20<\/sub><br \/>\nK = <sup>&#8211; 12<\/sup> \/ <sub>In 5<\/sub> x <sup>1<\/sup> \/ <sub>40<\/sub><br \/>\nK = <sup>&#8211; 12<\/sup> \/ <sub>1.609<\/sub> x 0.025<br \/>\nThat is, K = &#8211; 7.458 x 0.025<br \/>\nK = &#8211; 0.1864<\/p>\n<p>Therefore, the\u00a0<strong>boltzmann&#8217;s constant\u00a0<\/strong>is\u00a0<strong>&#8211; 0.1864<\/strong><\/p>\n<h3><strong>Calculating the Temperature when the Frenkel Defect, the Activation Energy and the Boltzmann&#8217;s Constant are Given<\/strong><\/h3>\n<p>T = <sup>&#8211; Q<sub>fr<\/sub><\/sup> \/ <sub>In (<sup>Nfr<\/sup> \/ N)<\/sub> x <sup>1<\/sup> \/ <sub>2K<\/sub><\/p>\n<p>Where;<\/p>\n<p>T = Temperature<br \/>\nQ<sub>fr<\/sub>\u00a0= Activation Energy<br \/>\nN<sub>fr<\/sub> = Frenkel Defect<br \/>\nK = Boltzmann&#8217;s Constant<\/p>\n<p>Let&#8217;s solve an example;<br \/>\nFind the temperature when the activation energy is 40, the frenkel defect is 60, the boltzmann&#8217;s constant is 20, N is 30.<\/p>\n<p>This implies that;<\/p>\n<p>Q<sub>fr<\/sub> = Activation Energy = 40<br \/>\nN<sub>fr<\/sub> = Frenkel Defect = 60<br \/>\nK = Boltzmann&#8217;s Constant = 20<br \/>\nN = 30<\/p>\n<p>T = <sup>&#8211; Q<sub>fr<\/sub><\/sup> \/ <sub>In (<sup>Nfr<\/sup> \/ <sub>N<\/sub>)<\/sub> x <sup>1<\/sup> \/ <sub>2K<\/sub><br \/>\nSo, T = <sup>&#8211; 40<\/sup> \/ <sub>In (<sup>60<\/sup> \/ <sub>30<\/sub>)<\/sub> x <sup>1<\/sup> \/ <sub>2 x 20<\/sub><br \/>\nT = <sup>&#8211; 40<\/sup> \/ <sub>In 30<\/sub> x <sup>1<\/sup> \/ <sub>40<\/sub><br \/>\nT = <sup>&#8211; 40<\/sup> \/ <sub>3.401<\/sub> x 0.025<br \/>\nThat is, T = &#8211; 11.761 x 0.025<br \/>\nT = &#8211; 0.294<\/p>\n<p>Therefore, the\u00a0<strong>temperature\u00a0<\/strong>is\u00a0<strong>&#8211; 0.294.<\/strong><\/p>\n<h3><strong>How to Calculate and Solve for Frenkel Defect Using Nickzom Calculator<\/strong><\/h3>\n<p>Nickzom Calculator \u2013\u00a0<strong>The Calculator Encyclopedia<\/strong> is capable of calculating the frenkel defect.<\/p>\n<p>To get the answer and workings of the frenkel defect 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>for<strong>\u00a0NGN 1,500\u00a0<\/strong>per<strong>\u00a0annum<\/strong>\u00a0to 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><br \/>\n<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 <strong>Materials &amp; Metallurgical<\/strong><b>\u00a0<\/b>under\u00a0<strong>Engineering<\/strong><strong>.<\/strong><\/p>\n<p><img decoding=\"async\" class=\"alignnone wp-image-3065 size-full\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2020\/04\/Screenshot-1095-1.png\" alt=\"\" width=\"1366\" height=\"768\" srcset=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2020\/04\/Screenshot-1095-1.png 1366w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2020\/04\/Screenshot-1095-1-300x169.png 300w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2020\/04\/Screenshot-1095-1-1024x576.png 1024w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2020\/04\/Screenshot-1095-1-768x432.png 768w\" sizes=\"(max-width: 1366px) 100vw, 1366px\" \/><\/p>\n<p>Now, Click on <strong>Ceramics<\/strong><strong>\u00a0<\/strong>under\u00a0<strong>Material &amp; Metallurgical<\/strong><\/p>\n<p><img decoding=\"async\" class=\"alignnone wp-image-3064 size-full\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2020\/04\/Screenshot-1098-1.png\" alt=\"\" width=\"1366\" height=\"768\" srcset=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2020\/04\/Screenshot-1098-1.png 1366w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2020\/04\/Screenshot-1098-1-300x169.png 300w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2020\/04\/Screenshot-1098-1-1024x576.png 1024w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2020\/04\/Screenshot-1098-1-768x432.png 768w\" sizes=\"(max-width: 1366px) 100vw, 1366px\" \/><\/p>\n<p>Now, Click on <strong>Frenkel Defect<\/strong><strong>\u00a0<\/strong>under\u00a0<strong>Ceramics<\/strong><\/p>\n<p><img decoding=\"async\" class=\"alignnone wp-image-3066 size-full\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2020\/04\/Screenshot-1109.png\" alt=\"How to Calculate and Solve for Frenkel Defect | Ceramics\" width=\"1366\" height=\"768\" srcset=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2020\/04\/Screenshot-1109.png 1366w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2020\/04\/Screenshot-1109-300x169.png 300w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2020\/04\/Screenshot-1109-1024x576.png 1024w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2020\/04\/Screenshot-1109-768x432.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 frenkel defect according to the respective parameters which are the <strong>N, activation energy (Q<sub>fr<\/sub>), Boltzmann&#8217;s Constant (K)<\/strong> and<strong> temperature (T).<\/strong><\/p>\n<p><img decoding=\"async\" class=\"alignnone wp-image-3063 size-full\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2020\/04\/Screenshot-1105.png\" alt=\"How to Calculate and Solve for Frenkel Defect | Ceramics\" width=\"1366\" height=\"768\" srcset=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2020\/04\/Screenshot-1105.png 1366w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2020\/04\/Screenshot-1105-300x169.png 300w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2020\/04\/Screenshot-1105-1024x576.png 1024w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2020\/04\/Screenshot-1105-768x432.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>N<\/strong> is <strong>22<\/strong>,<strong> activation energy (Q<sub>fr<\/sub>)<\/strong> is <strong>34<\/strong>,<strong> Boltzmann&#8217;s Constant (K)<\/strong> is <strong>1.38064852e-23 <\/strong>and<strong> temperature (T)<\/strong> is <strong>12<\/strong>.<\/p>\n<p><img decoding=\"async\" class=\"alignnone wp-image-3062 size-full\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2020\/04\/Screenshot-1106.png\" alt=\"How to Calculate and Solve for Frenkel Defect | Ceramics\" width=\"1366\" height=\"768\" srcset=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2020\/04\/Screenshot-1106.png 1366w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2020\/04\/Screenshot-1106-300x169.png 300w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2020\/04\/Screenshot-1106-1024x576.png 1024w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2020\/04\/Screenshot-1106-768x432.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-3061 size-full\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2020\/04\/Screenshot-1107.png\" alt=\"How to Calculate and Solve for Frenkel Defect | Ceramics\" width=\"1366\" height=\"768\" srcset=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2020\/04\/Screenshot-1107.png 1366w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2020\/04\/Screenshot-1107-300x169.png 300w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2020\/04\/Screenshot-1107-1024x576.png 1024w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2020\/04\/Screenshot-1107-768x432.png 768w\" sizes=\"(max-width: 1366px) 100vw, 1366px\" \/><\/p>\n<p>As you can see from the screenshot above,\u00a0<strong>Nickzom Calculator<\/strong>\u2013 The Calculator Encyclopedia solves for the frenkel defect and presents the formula, workings and steps too.<\/p>\n","protected":false},"excerpt":{"rendered":"The image above represents frenkel defect. To calculate the frenkel defect, four essential parameters are needed and these&hellip;","protected":false},"author":5,"featured_media":13536,"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":"","_members_access_role":[],"_members_access_error":""},"categories":[47],"tags":[872,873,865,60,874,543,786,75],"class_list":["post-3057","post","type-post","status-publish","format-standard","has-post-thumbnail","category-engineering","tag-activation-energy","tag-boltzmanns-constant","tag-ceramics","tag-engineering","tag-frenkel-defect","tag-materials-and-metallurgical","tag-n","tag-temperature","cs-entry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.0 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>How to Calculate and Solve for Frenkel Defect | Ceramics<\/title>\n<meta name=\"description\" content=\"Master the steps and the formula on How to Calculate and Solve for Frenkel Defect | Ceramics. 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