The image above represents frenkel defect.

To compute for frenkel defect, four essential parameters are needed and these parameters are **N, activation energy (Q _{fr}), Boltzmann’s Constant (K)** and

**temperature (T).**

The formula for calculating the frenkel defect:

N_{fr} = N exp (^{-Qfr }/ _{2KT})

Where:

N_{fr} = Frenkel Defect

Q_{fr} = Activation Energy

K = Boltzmann’s Constant

T = Temperature

Let’s solve an example;

Find the frenkel defect when the activation energy is 34, N is 22, Temperature is 12 and the boltzmann’s constant is 1.38064852e-23.

This implies that;

Q_{fr} = Activation Energy

K = Boltzmann’s Constant

T = Temperature

N_{fr} = N exp (^{-Qfr }/ _{2KT})

N_{fr} = (22)exp(^{-(34) }/ _{2(1.38064852e-23)(14)})

N_{fr} = (22)exp(^{(-34) }/ _{(3.865815856e-22)})

N_{fr} = (22)exp(-8.795038684325786e+22)

N_{fr} = (22)(0)

N_{fr} = 0

Therefore, the **frenkel defect **is **0.**

**Calculating the Activation Energy when the Frenkel Defect, the Boltzmann’s Constant and the Temperature is Given.**

Q_{fr} = – (In (^{Nfr} / _{N}) x 2KT)

Where;

Q_{fr} = Activation Energy

N_{fr} = Frenkel Defect

K = Boltzmann’s Constant

T = Temperature

Let’s solve an example;

Given that the frenkel defect is 20, the boltzmann’s constant is 5, the temperature is 2 and N is 10. Find the activation energy?

This implies that;

N_{fr} = Frenkel Defect = 20

K = Boltzmann’s Constant = 5

T = Temperature = 2

N = 10

Q_{fr} = – (In (^{Nfr} / _{N}) x 2KT)

Q_{fr} = – (In (^{20} / _{10}) x 2 x 5 x 2)

Q_{fr} = – (In 2 x 20)

Q_{fr} = – (In 40)

Q_{fr} = – 3.688

Therefore, the **activation energy **is **– 3.688.**

**Calculating the Boltzmann’s Constant when the Frenkel Defect, the Activation Energy and the Temperature is Given.**

K = ^{– Qfr} / _{In (Nfr / N)} x ^{1} / _{2T}

Where;

K = Boltzmann’s Constant

T = Temperature

Q_{fr} = Activation Energy

N_{fr} = Frenkel Defect

Let’s solve an example;

Find the boltzmann’s constant when the temperature is 20, the frenkel defect is 30, the activation energy is 12 and N is 6.

This implies that;

T = Temperature = 20

Q_{fr} = Activation Energy = 12

N_{fr} = Frenkel Defect = 30

N = 6

K = ^{– Qfr} / _{In (Nfr / N)} x ^{1} / _{2T}

K = ^{– 12} / _{In (30 / 6)} x ^{1} / _{2 x 20}

K = ^{– 12} / _{In 5} x ^{1} / _{40}

K = ^{– 12} / _{1.609} x 0.025

K = – 7.458 x 0.025

K = – 0.1864

Therefore, the **boltzmann’s constant **is **– 0.1864**

**Calculating the Temperature when the Frenkel Defect, the Activation Energy and the Boltzmann’s Constant is Given.**

T = ^{– Qfr} / _{In (Nfr / N)} x ^{1} / _{2K}

Where;

T = Temperature

Q_{fr} = Activation Energy

N_{fr} = Frenkel Defect

K = Boltzmann’s Constant

Let’s solve an example;

Find the temperature when the activation energy is 40, the frenkel defect is 60, the boltzmann’s constant is 20, N is 30.

This implies that;

Q_{fr} = Activation Energy = 40

N_{fr} = Frenkel Defect = 60

K = Boltzmann’s Constant = 20

N = 30

T = ^{– Qfr} / _{In (Nfr / N)} x ^{1} / _{2K}

T = ^{– 40} / _{In (60 / 30)} x ^{1} / _{2 x 20}

T = ^{– 40} / _{In 30} x ^{1} / _{40}

T = ^{– 40} / _{3.401} x 0.025

T = – 11.761 x 0.025

T = – 0.294

Therefore, the **temperature **is **– 0.294.**

Nickzom Calculator – **The Calculator Encyclopedia** is capable of calculating the frenkel defect.

To get the answer and workings of the frenkel defect 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 **for** NGN 1,500 **per** annum** 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 & Metallurgical**** **under **Engineering****.**

Now, Click on **Ceramics**** **under **Material & Metallurgical**

Now, Click on **Frenkel Defect**** **under **Ceramics**

The screenshot below displays the page or activity to enter your values, to get the answer for the frenkel defect according to the respective parameters which are the **N, activation energy (Q _{fr}), Boltzmann’s Constant (K)** and

**temperature (T).**

Now, enter the values appropriately and accordingly for the parameters as required by the **N** is **22**,** activation energy (Q _{fr})** is

**34**,

**Boltzmann’s Constant (K)**is

**1.38064852e-23**and

**temperature (T)**is

**12**.

Finally, Click on Calculate

As you can see from the screenshot above, **Nickzom Calculator**– The Calculator Encyclopedia solves for the frenkel defect and presents the formula, workings and steps too.