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Atomic Packing Factor of BCC in Terms of Particle Radius Calculator

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✖Radius of Particle is defined as half of the diameter of that particle.ⓘ Radius of Particle [r]

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✖Atomic Packing Factor is the fraction of volume in a crystal structure that is occupied by constituent particles.ⓘ Atomic Packing Factor of BCC in Terms of Particle Radius [APF]

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Atomic Packing Factor of BCC in Terms of Particle Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Atomic Packing Factor = (2*(4/3)*pi*(Radius of Particle^3))/(((4*Radius of Particle)/sqrt(3))^3)
APF = (2*(4/3)*pi*(r^3))/(((4*r)/sqrt(3))^3)
This formula uses 1 Constants, 1 Functions, 2 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Atomic Packing Factor - Atomic Packing Factor is the fraction of volume in a crystal structure that is occupied by constituent particles.
Radius of Particle - (Measured in Meter) - Radius of Particle is defined as half of the diameter of that particle.

STEP 1: Convert Input(s) to Base Unit

Radius of Particle: 2 Meter --> 2 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

APF = (2*(4/3)*pi*(r^3))/(((4*r)/sqrt(3))^3) --> (2*(4/3)*pi*(2^3))/(((4*2)/sqrt(3))^3)

Evaluating ... ...

APF = 0.680174761587831

STEP 3: Convert Result to Output's Unit

0.680174761587831 --> No Conversion Required

FINAL ANSWER

0.680174761587831 ≈ 0.680175 <-- Atomic Packing Factor

(Calculation completed in 00.004 seconds)

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Atomic Packing Factor of BCC in Terms of Particle Radius Formula

LaTeX Go

Atomic Packing Factor = (2*(4/3)*pi*(Radius of Particle^3))/(((4*Radius of Particle)/sqrt(3))^3)
APF = (2*(4/3)*pi*(r^3))/(((4*r)/sqrt(3))^3)

What is the physical significance of Atomic Packing Factor?

Packing factor indicates how closely atoms are packed in a unit cell and is given by the ratio of volume of atoms in the unit cell and volume of the unit cell. In atomic systems, by convention, the packing factor is determined by assuming that atoms are rigid spheres. The radius of the spheres is taken to be the maximal value such that the atoms do not overlap.
A slip plane with the highest atomic density is preferred for deformation because the distance between atoms are so small that dislocation movement due to lower applied stress is easier and higher atomic packing factor is an indication of ease of deformation.

How to Calculate Atomic Packing Factor of BCC in Terms of Particle Radius?

Atomic Packing Factor of BCC in Terms of Particle Radius calculator uses Atomic Packing Factor = (2*(4/3)*pi*(Radius of Particle^3))/(((4*Radius of Particle)/sqrt(3))^3) to calculate the Atomic Packing Factor, The Atomic Packing Factor of BCC in terms of particle radius is the fraction of volume in a body centered cubic crystal that is occupied by constituent particles. It is a dimensionless quantity and always less than unity. For a simple cubic packing, the number of atoms per unit cell is two. Atomic Packing Factor is denoted by APF symbol.

How to calculate Atomic Packing Factor of BCC in Terms of Particle Radius using this online calculator? To use this online calculator for Atomic Packing Factor of BCC in Terms of Particle Radius, enter Radius of Particle (r) and hit the calculate button. Here is how the Atomic Packing Factor of BCC in Terms of Particle Radius calculation can be explained with given input values -> 0.680175 = (2*(4/3)*pi*(2^3))/(((4*2)/sqrt(3))^3).

FAQ

What is Atomic Packing Factor of BCC in Terms of Particle Radius?

The Atomic Packing Factor of BCC in terms of particle radius is the fraction of volume in a body centered cubic crystal that is occupied by constituent particles. It is a dimensionless quantity and always less than unity. For a simple cubic packing, the number of atoms per unit cell is two and is represented as APF = (2*(4/3)*pi*(r^3))/(((4*r)/sqrt(3))^3) or Atomic Packing Factor = (2*(4/3)*pi*(Radius of Particle^3))/(((4*Radius of Particle)/sqrt(3))^3). Radius of Particle is defined as half of the diameter of that particle.

How to calculate Atomic Packing Factor of BCC in Terms of Particle Radius?

The Atomic Packing Factor of BCC in terms of particle radius is the fraction of volume in a body centered cubic crystal that is occupied by constituent particles. It is a dimensionless quantity and always less than unity. For a simple cubic packing, the number of atoms per unit cell is two is calculated using Atomic Packing Factor = (2*(4/3)*pi*(Radius of Particle^3))/(((4*Radius of Particle)/sqrt(3))^3). To calculate Atomic Packing Factor of BCC in Terms of Particle Radius, you need Radius of Particle (r). With our tool, you need to enter the respective value for Radius of Particle and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Atomic Packing Factor?

In this formula, Atomic Packing Factor uses Radius of Particle. We can use 3 other way(s) to calculate the same, which is/are as follows -

Atomic Packing Factor = (Number of Atoms*Volume of Each Particle)/(Volume of Unit Cell)
Atomic Packing Factor = Volume of Each Particle/Volume of Unit Cell
Atomic Packing Factor = (4*Volume of Each Particle)/(Volume of Unit Cell)

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