# How to Calculate and Solve for Schottky Defect | Ceramics

**Last Updated on March 30, 2024**

The image above represents schottky defect.

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

**Temperature (T).**

**The Formula for Calculating Schottky Defect**

N_{s} = N exp (^{-Qs}/_{2KT})

Where:

Q_{s} = Activation Energy

K = Boltzmann’s Constant

T = Temperature

Let’s solve an example;

Find the schottky defect when the activation energy is 44, N is 22, boltzmann’s constant is 1.38064852E-23 and the temperature is 30.

This implies that;

N = 22

Q_{s} = Activation Energy = 44

K = Boltzmann’s Constant = 1.38054852E-23

T = Temperature = 30

N_{s} = N exp (^{-Qs}/_{2KT})

So, N_{s} = (22)exp(^{-(44)}/_{2(1.38064852e-23)(30)})

N_{s} = (22)exp(^{(-44)}/_{(8.283891119e-22)})

N_{s} = (22)exp(-5.3115135583771414e+22)

That is, N_{s} = (22)(0)

N_{s} = 0

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

**Calculating the N when the Schottky Defect, the Activation Energy, the Boltzmann’s Constant and the Temperature are Given**

N = ^{Ns} / _{e (-Qs / 2KT)}

Where;

N_{s} = Schottky Defect

Q_{s} = Activation Energy

K = Boltzmann’s Constant

T = Temperature

Let’s solve an example;

Find the N when the schottky defect is 40, the activation energy is 24, the boltzmann’s constant is 1.38064852E-23 and the temperature is 10.

This implies that;

N_{s} = Schottky Defect = 40

Q_{s} = Activation Energy = 24

K = Boltzmann’s Constant = 1.38064852E-23

T = Temperature = 10

N = ^{Ns} / _{e (-Qs / 2KT)}

N = ^{40} / _{e (-24 / 2 x 1.38064852E-23 x 10)}

So, N = ^{40} / _{e (-24 / 2.76129704E+23)}

N = ^{40} / _{e (8.691567e-23)}

That is, N = ^{40} / _{8.691567e+23}

N = 4.602e-23

Therefore, the **N **is **4.602e-23.**

Read more: How to Calculate and Solve for Frenkel Defect | Ceramics

**Calculating the Activation Energy when the Schottky Defect, the Boltzmann’s Constant, the Temperature and N are Given**

Q_{s} = – (In (^{Ns} / _{N}) x 2KT)

Where;

Q_{s} = Activation Energy

N_{s} = Schottky Defect

K = Boltzmann’s Constant

T = Temperature

Let’s solve an example;

Find the activation energy when the schottky defect is 25, the boltzmann’s Constant is 1.38064852E-23, the temperature is 10 and N is 5.

This implies that;

N_{s} = Schottky Defect = 25

K = Boltzmann’s Constant = 1.38064852e-23

T = Temperature = 10

N = 5

Q_{s} = – (In (^{Ns} / _{N}) x 2KT)

Q_{s} = – (In (^{25} / _{5}) x 2 x 1.38064852e-23 x 10)

That is, Q_{s} = – (In (5) x 2.76129704e+23)

Q_{s} = – (In 1.38064852e+24)

Q_{s} = – 55.584

Therefore, the **activation energy **is **– 55.584.**

**Calculating the Temperature when the Schottky Defect, the Activation Energy, Boltzmann’s Constant and N are Given**

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

Where;

T = Temperature

Q_{s} = Activation Energy

N_{s} = Schottky Defect

K = Boltzmann’s Constant

Let’s solve an example;

Find the temperature when the activation energy is 44, the schottky defect is 32, the boltzmann’s constant is 1.38064852e-23 and N is 8.

This implies that;

Q_{s} = Activation Energy = 44

N_{s} = Schottky Defect = 32

K = Boltzmann’s Constant = 1.38064852e-23

N = 8

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

T = ^{– 44} / _{In (32 / 8)} x ^{1} / _{2 x 1.38064852e-23}

So, T = ^{– 44} / _{In (4)} x ^{1} / _{2.76129704e+23}

T = ^{– 44} / _{1.38629} x 3.6214e-24

Then, T = – 31.739 x 3.6214e-24

T = 1.14939e+23

Therefore, the **temperature **is **1.14939e+23.**

**How to Calculate and Solve for Schottky Defect in Ceramics Using Nickzom Calculator**

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

To get the answer and workings of the schottky 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 **Schottky**** Defect**** **under **Ceramics**

The screenshot below displays the page or activity to enter your values, to get the answer for the schottky defect according to the respective parameters which are the **N, activation energy (Q _{s}), 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 _{s})** is

**44**,

**Boltzmann’s Constant (K)**is

**1.38064852e-23**and

**temperature (T)**is

**30**.

Finally, Click on Calculate

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