# 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 (ΔG _{v})** 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

ΔG_{v} = 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

ΔG_{v} = 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.**

ΔG_{v} = ^{-2γ} / _{r*}

Where:

ΔG_{v} = 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

ΔG_{v} = ^{-2γ} / _{r*}

ΔG_{v} = ^{-2(5)} / _{12}

ΔG_{v} = ^{-10} / _{12}

ΔG_{v} = 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

ΔG_{v} = 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

ΔG_{v} = 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 (ΔG _{v})** and

**Surface Free Energy (γ).**

Now, enter the values appropriately and accordingly for the parameters as required by the **Volume Free Energy (ΔG _{v}) **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.