How to Calculate and Solve for Atomic Packing Factor | Crystal Structures

January 15, 2023 Loveth Idoko

Last Updated on June 9, 2024

To calculate atomic packing factor, two essential parameters are needed and these parameters are Volume of Atoms in a Unit Cell (V) and Total Unit Cell Volume (T).

The formula for calculating atomic packing factor:

APF = ^V/_T

Where:

APF = Atomic Packing Factor
V = Volume of Atoms in a Unit Cell
T = Total Unit Cell Volume

Let’s solve an example;
Find the atomic packing factor when the volume of atoms in a unit cell is 6 and the total unit cell volume is 3.

This implies that;

V = Volume of Atoms in a Unit Cell = 6
T = Total Unit Cell Volume = 3

APF = ^V/_T
So, APF = ⁶/₃
APF = 2

Therefore, the atomic packing factor is 2.

Calculating for the Volume of Atoms in a Unit Cell when the Atomic Packing Factor and the Total Unit Cell Volume are Given

V = APF x T

Where:

V = Volume of Atoms in a Unit Cell
APF = Atomic Packing Factor
T = Total Unit Cell Volume

Let’s solve an example;
Find the volume of atoms in a unit cell when the atomic packing factor is 10 and the total unit cell volume is 8.

This implies that;

APF = Atomic Packing Factor = 10
T = Total Unit Cell Volume = 8

V = APF x T
That is, V = 10 x 8
V = 80

Therefore, the volume of atoms in a unit cell is 80.

Calculating the Total Unit Cell Volume when the Atomic Packing Factor and the Volume of Atoms in a Unit Cell are Given

T = ^V / _APF

Where:

T = Total Unit Cell Volume
APF = Atomic Packing Factor
V = Volume of Atoms in a Unit Cell

Let’s solve an example;
Given that, the atomic packing factor is 4 and the volume of atoms in a unit cell is 36. Find the total unit cell volume?

This implies that;

APF = Atomic Packing Factor = 4
V = Volume of Atoms in a Unit Cell = 36

T = ^V / _APF
So, T = ³⁶ / ₄
T = 9

Therefore, the total unit cell volume is 9.

How to Calculate Atomic Packing Factor Using Nickzom Calculator

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the atomic packing factor.

To get the answer and workings of the atomic packing factor 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 Crystal Structures under Materials and Metallurgical

Now, Click on Atomic Packing Factor under Crystal Structures

The screenshot below displays the page or activity to enter your values, to get the answer for the atomic packing factor according to the respective parameter which is the Volume of Atoms in a Unit Cell (V) and Total Unit Cell Volume (T).

Now, enter the values appropriately and accordingly for the parameters as required by the Volume of Atoms in a Unit Cell (V) is 6 and Total Unit Cell Volume (T) is 3.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the atomic packing factor and presents the formula, workings and steps too.