How to Calculate and Solve for Nucleation Rate | Phase Transformation
Last Updated on December 12, 2022
The image above represents nucleation rate.
To compute for nucleation rate, three essential parameters are needed and these parameters are Constant (k3), Number of Stable Nuclei (n*) and Diffusion Coefficient for Vacancy (Vd).
The formula for calculating nucleation rate:
N’ = k3n*Vd
Where:
N’ = Nucleation Rate
k3 = Constant
n* = Number of Stable Nuclei
Vd = Diffusion Coefficient for Vacancy
Given an example;
Find the nucleation rate when the constant is 22, the number of stable nuclei is 14 and the diffusion coefficient for vacancy is 6.
This implies that;
k3 = Constant = 22
n* = Number of Stable Nuclei = 14
Vd = Diffusion Coefficient for Vacancy = 6
N’ = k3n*Vd
N’ = (22)(14)(6)
N’ = 1848
Therefore, the nucleation rate is 1848.
Calculating the Constant when the Nucleation Rate, the Number of Stable Nuclei and the Diffusion Coefficient for Vacancy is Given.
k3 = N’ / n*Vd
Where:
k3 = Constant
N’ = Nucleation Rate
n* = Number of Stable Nuclei
Vd = Diffusion Coefficient for Vacancy
Let’s solve an example;
Find the constant when the nucleation rate is 44, the number of stable nuclei is 4 and the diffusion coefficient for vacancy is 5.
This implies that;
N’ = Nucleation Rate = 44
n* = Number of Stable Nuclei = 4
Vd = Diffusion Coefficient for Vacancy = 5
k3 = N’ / n*Vd
k3 = 44 / (4)(5)
k3 = 44 / 20
k3 = 2.2
Therefore, the constant is 2.2
Calculating the Number of Stable Nuclei when the Nucleation Rate, the Constant and the Diffusion Coefficient for Vacancy is Given.
n* = N’ / k3Vd
Where:
n* = Number of Stable Nuclei
N’ = Nucleation Rate
k3 = Constant
Vd = Diffusion Coefficient for Vacancy
Let’s solve an example;
Find the number of stable nuclei when the nucleation rate is 30, the constant is 6 and the diffusion coefficient for vacancy is 2.
This implies that;
N’ = Nucleation Rate = 30
k3 = Constant = 6
Vd = Diffusion Coefficient for Vacancy = 2
n* = N’ / k3Vd
n* = 30 / (6)(2)
n* = 30 / 12
n* = 2.5
Therefore, the number of stable nuclei is 2.5
Calculating the Diffusion Coefficient for Vacancy when the Nucleation Rate, the Constant and the Number of Stable Nuclei is Given.
Vd = N’ / k3n*
Where:
Vd = Diffusion Coefficient for Vacancy
N’ = Nucleation Rate
k3 = Constant
n* = Number of Stable Nuclei
Let’s solve an example;
Find the diffusion coefficient for vacancy when the nucleation rate is 60, the constant is 10 and the number of stable nuclei is 3.
This implies that;
N’ = Nucleation Rate = 60
k3 = Constant = 10
n* = Number of Stable Nuclei = 3
Vd = N’ / k3n*
Vd = 60 / (10)(3)
Vd = 60 / 30
Vd = 2
Therefore, the diffusion coefficient for vacancy is 2.
Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the nucleation rate.
To get the answer and workings of the nucleation rate using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.
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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 Nucleation Rate under Phase Transformation
The screenshot below displays the page or activity to enter your values, to get the answer for the nucleation rate according to the respective parameter which is the Constant (k3), Number of Stable Nuclei (n*) and Diffusion Coefficient for Vacancy (Vd).
Now, enter the values appropriately and accordingly for the parameters as required by the Constant (k3) is 22, Number of Stable Nuclei (n*) is 14 and Diffusion Coefficient for Vacancy (Vd) is 6.
Finally, Click on Calculate
As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the nucleation rate and presents the formula, workings and steps too.