How to Calculate and Solve for Critical Radius for Homogeneous Nucleation | Phase Transformation
Last Updated on December 11, 2022
The image above represents the critical radius for homogenous nucleation.
To compute for critical radius for homogenous nucleation, two essential parameters are needed and these parameters are Volume Free Energy (ΔGv) and Surface Free Energy (γ).
The formula for calculating critical radius for homogenous nucleation:
r* = -2γ/ΔGv
Where:
r* = Critical Radius for Homogeneous Nucleation
γ = Surface Free Energy
ΔGv = Volume Free Energy
Given an example;
Find the critical radius for homogenous nucleation when the surface free energy is 8 and the volume free energy is 40.
This implies that;
γ = Surface Free Energy = 8
ΔGv = Volume Free Energy = 40
r* = -2γ/ΔGv
r* = -2(8)/(40)
r* = (-16)/(40)
r* = -0.4
Therefore, the critical radius for homogenous nucleation is -0.4.
Calculating the Volume Free Energy when the Critical Radius for Homogenous Nucleation and the Surface Free Energy is Given.
ΔGv = -2γ / r*
Where:
ΔGv = Volume Free Energy
r* = Critical Radius for Homogeneous Nucleation
γ = Surface Free Energy
Let’s solve an example;
Find the volume free energy when the critical radius for homogenous nucleation is 12 and the surface free energy is 5.
This implies that;
r* = Critical Radius for Homogeneous Nucleation = 12
γ = Surface Free Energy = 5
ΔGv = -2γ / r*
ΔGv = -2(5) / 12
ΔGv = -10 / 12
ΔGv = 0.83
Therefore, the volume free energy is 0.83.
Calculating the Surface Free Energy when the Critical Radius for Homogenous Nucleation and the Volume Free Energy is Given.
γ = r* x ΔGv / -2
Where:
γ = Surface Free Energy
r* = Critical Radius for Homogeneous Nucleation
ΔGv = Volume Free Energy
Let’s solve an example;
Find the surface free energy when the critical radius for homogenous nucleation is 10 and the volume free energy is 4.
This implies that;
r* = Critical Radius for Homogeneous Nucleation = 10
ΔGv = Volume Free Energy = 4
γ = r* x ΔGv / -2
γ = 10 x 4 / -2
γ = 40 / -2
γ = -20
Therefore, the surface free energy is -20.
Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the critical radius for homogenous nucleation.
To get the answer and workings of the critical radius for homogenous nucleation using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.
You can get this app via any of these means:
Web – https://www.nickzom.org/calculator-plus
To get access to the professional version via web, you need to register and subscribe to have utter access to all functionalities.
You can also try the demo version via https://www.nickzom.org/calculator
Android (Paid) – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator
Android (Free) – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator
Apple (Paid) – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8
Once, you have obtained the calculator encyclopedia app, proceed to the Calculator Map, then click on Materials and Metallurgical under Engineering.
Now, Click on Phase Transformation under Materials and Metallurgical
Now, Click on Critical Radius for Homogenous Nucleation under Phase Transformation
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 Volume Free Energy (ΔGv) and Surface Free Energy (γ).
Now, enter the values appropriately and accordingly for the parameters as required by the Volume Free Energy (ΔGv) is 40 and Surface Free Energy (γ) is 8.
Finally, Click on Calculate
As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the critical radius for homogenous nucleation and presents the formula, workings and steps too.