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 **Volume Free Energy (Î”G _{v})** and

**Surface Free Energy (Î³).**

**The formula for calculating critical radius for homogenous nucleation:**

r* =Â ^{-2Î³}/_{Î”Gv}

Where:

r* = Critical Radius for Homogeneous Nucleation

Î³ = Surface Free Energy

Î”G_{v}Â = 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;

Î³ = Surface Free Energy = 8

Î”G_{v} = Volume Free Energy = 40

r* =Â ^{-2Î³}/_{Î”Gv}

That is, r* = ^{-2(8)}/_{(40)}

r* =Â ^{(-16)}/_{(40)}

r* = -0.4

Therefore, theÂ **critical radius for homogenous nucleationÂ **isÂ **-0.4.**

**Calculating the Volume Free Energy when the Critical Radius for Homogenous Nucleation and the Surface Free Energy are Given**

Î”G_{v} = ^{-2Î³} / _{r*}

Where:

Î”G_{v}Â = Volume Free Energy

r* = Critical Radius for Homogeneous Nucleation

Î³ = 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;

### Master Every Calculation Instantly

Unlock solutions for every math, physics, engineering, and chemistry problem with step-by-step clarity. No internet required. Just knowledge at your fingertips, anytime, anywhere.

r* = Critical Radius for Homogeneous Nucleation = 12

Î³ = Surface Free Energy = 5

Î”G_{v} = ^{-2Î³} / _{r*}

Then, Î”G_{v} = ^{-2(5)} / _{12}

Î”G_{v} = ^{-10} / _{12}

Î”G_{v} = 0.83

Therefore, theÂ **volume free energyÂ **isÂ **0.83.**

Read more:Â How to Calculate and Solve for Homogeneous; Heterogeneous Relationship | Phase Transformation

**Calculating the Surface Free Energy when the Critical Radius for Homogenous Nucleation and the Volume Free Energy are Given**

Î³ = ^{r* x Î”Gv} / _{-2}

Where:

Î³ = Surface Free Energy

r* = Critical Radius for Homogeneous Nucleation

Î”G_{v}Â = 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

Î”G_{v} = Volume Free Energy = 4

Î³ = ^{r* x Î”Gv} / _{-2}

Î³ = ^{10 x 4} / _{-2}

So, Î³ = ^{40} / _{-2}

Î³ = -20

Therefore, theÂ **surface free energyÂ **isÂ **-20.**

Read more:Â How to Calculate and Solve for Critical Radius for Heterogeneous Nucleation | Phase Transformation

**How to Calculate the Critical Radius for Homogeneous Nucleation With Nickzom Calculator**

Nickzom Calculator â€“Â **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 â€“ The Calculator Encyclopedia.Â **First, you need to obtain the app.

You can get this app via any of these means:

**Web**Â â€“Â https://www.nickzom.org/calculator-plus

To get access to theÂ **professionalÂ **version via web, you need toÂ **register**Â andÂ **subscribeÂ **to have utter access to all functionalities.

You can also try theÂ **demoÂ **version viaÂ https://www.nickzom.org/calculator

**Android (Paid)**Â â€“Â https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator

**Android (Free)**Â â€“Â https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator

**Apple (Paid)**Â â€“Â https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8

Once, you have obtained the calculator encyclopedia app, proceed to theÂ **Calculator Map,Â **then click onÂ **Materials and MetallurgicalÂ **underÂ **Engineering****.**

Now, Click onÂ **Phase Transformation****Â **underÂ **Materials and Metallurgical**

Now, Click on **Critical Radius for Homogenous Nucleation****Â **underÂ **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 (Î”G _{v})** and

**Surface Free Energy (Î³).**

Now, enter the values appropriately and accordingly for the parameters as required by the **Volume Free Energy (Î”G _{v})Â **isÂ

**40**and

**Surface Free Energy (Î³)**is

**8**.

Finally, Click on Calculate

As you can see fromÂ the screenshot above,Â **Nickzom Calculator**â€“ The Calculator Encyclopedia can calculate the critical radius for homogenous nucleation and presents the formula, workings and steps too.