How to Calculate and Solve for Equilibrium Number of Vacancies | Imperfection in Solids
Last Updated on January 13, 2023
The image above represents equilibrium number of vacancies.
To compute for equilibrium number of vacancies, four essential parameters are needed and these parameters are Total Number of Atomic Sites (N), Energy for Forming Vacancy (-Qv), Boltzmann’s Constant (K) and Temperature (T).
The formula for calculating equilibrium number of vacancies:
Nv = Nexp(-Qv/KT)
Where:
Nv = Equilibrium Number of Vacancies
N = Total Number of Atomic Sites
-Qv = Energy for Forming Vacancy
K = Boltzmann’s Constant
T = Temperature (in Kelvin)
Let’s solve an example;
Find the equilibrum number of vacancies when the total number of atomic sites is 12, the energy for forming vacancy is 10 and the boltzmann’s constant is 1.38064852E-23 and the temperature is 5.
This implies that;
N = Total Number of Atomic Sites = 12
-Qv = Energy for Forming Vacancy = 10
K = Boltzmann’s Constant = 1.38064852E-23
T = Temperature (in Kelvin) = 5
Nv = Nexp(-Qv/KT)
Nv = 12exp(10/(1.38064852e-23)(5))
Nv = 12exp(10/(6.903242599999999e-23))
Nv = 12exp(1.4485946068301296e+23)
Nv = 12(Infinity)
Nv = Infinity
Therefore, the equilibrum number of vacanies is infinity.
Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the equilibrium number of vacancies.
To get the answer and workings of the equilibrium number of vacancies 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
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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 Imperfection in Solids under Materials and Metallurgical
Now, Click on Equilibrium Number of Vacancies under Imperfection in Solids
The screenshot below displays the page or activity to enter your values, to get the answer for the Equilibrium number of vacancies according to the respective parameter which is the Total Number of Atomic Sites (N), Energy for Forming Vacancy (-Qv), Boltzmann’s Constant (K) and Temperature (T).
Now, enter the values appropriately and accordingly for the parameters as required by the Total Number of Atomic Sites (N) is 12, Energy for Forming Vacancy (-Qv) is 10, Boltzmann’s Constant (K) is 1.38064852E-23 and Temperature (T) is 5.
Finally, Click on Calculate
As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the equilibrium number of vacancies and presents the formula, workings and steps too.