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Atomic Packing Factor in Terms of Particle Radius Calculator

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✖The Number of Atoms is the the total number of constituent atoms in the unit cell.ⓘ Number of Atoms [z]			+10% -10%
✖Radius of Particle is defined as half of the diameter of that particle.ⓘ Radius of Particle [r]			+10% -10%
✖Edge Length in APF is the length of the edge of the unit cell in Atomic packing factor.ⓘ Edge Length in APF [a]			+10% -10%

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

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Atomic Packing Factor in Terms of Particle Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Atomic Packing Factor = (Number of Atoms*(4/3)*pi*(Radius of Particle^3))/(Edge Length in APF^3)
APF = (z*(4/3)*pi*(r^3))/(a^3)
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Atomic Packing Factor - Atomic Packing Factor is the fraction of volume in a crystal structure that is occupied by constituent particles.
Number of Atoms - The Number of Atoms is the the total number of constituent atoms in the unit cell.
Radius of Particle - (Measured in Meter) - Radius of Particle is defined as half of the diameter of that particle.
Edge Length in APF - (Measured in Meter) - Edge Length in APF is the length of the edge of the unit cell in Atomic packing factor.

STEP 1: Convert Input(s) to Base Unit

Number of Atoms: 35 --> No Conversion Required
Radius of Particle: 2 Meter --> 2 Meter No Conversion Required
Edge Length in APF: 55 Meter --> 55 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

APF = (z*(4/3)*pi*(r^3))/(a^3) --> (35*(4/3)*pi*(2^3))/(55^3)

Evaluating ... ...

APF = 0.00704950417634975

STEP 3: Convert Result to Output's Unit

0.00704950417634975 --> No Conversion Required

FINAL ANSWER

0.00704950417634975 ≈ 0.00705 <-- Atomic Packing Factor

(Calculation completed in 00.004 seconds)

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Atomic Packing Factor in Terms of Volume of Particle and Unit Cell

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

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LaTeX Go Atomic Packing Factor = (4*Volume of Each Particle)/(Volume of Unit Cell)

Atomic Packing Factor of BCC

LaTeX Go Atomic Packing Factor = (2*Volume of Each Particle)/(Volume of Unit Cell)

Atomic Packing Factor of SCC

LaTeX Go Atomic Packing Factor = Volume of Each Particle/Volume of Unit Cell

Atomic Packing Factor in Terms of Particle Radius Formula

LaTeX Go

Atomic Packing Factor = (Number of Atoms*(4/3)*pi*(Radius of Particle^3))/(Edge Length in APF^3)
APF = (z*(4/3)*pi*(r^3))/(a^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 in Terms of Particle Radius?

Atomic Packing Factor in Terms of Particle Radius calculator uses Atomic Packing Factor = (Number of Atoms*(4/3)*pi*(Radius of Particle^3))/(Edge Length in APF^3) to calculate the Atomic Packing Factor, The Atomic Packing Factor in terms of particle radius is the fraction of volume in a crystal structure that is occupied by constituent particles. It is a dimensionless quantity and always less than unity. Atomic Packing Factor is denoted by APF symbol.

How to calculate Atomic Packing Factor in Terms of Particle Radius using this online calculator? To use this online calculator for Atomic Packing Factor in Terms of Particle Radius, enter Number of Atoms (z), Radius of Particle (r) & Edge Length in APF (a) and hit the calculate button. Here is how the Atomic Packing Factor in Terms of Particle Radius calculation can be explained with given input values -> 0.00705 = (35*(4/3)*pi*(2^3))/(55^3).

FAQ

What is Atomic Packing Factor in Terms of Particle Radius?

The Atomic Packing Factor in terms of particle radius is the fraction of volume in a crystal structure that is occupied by constituent particles. It is a dimensionless quantity and always less than unity and is represented as APF = (z*(4/3)*pi*(r^3))/(a^3) or Atomic Packing Factor = (Number of Atoms*(4/3)*pi*(Radius of Particle^3))/(Edge Length in APF^3). The Number of Atoms is the the total number of constituent atoms in the unit cell, Radius of Particle is defined as half of the diameter of that particle & Edge Length in APF is the length of the edge of the unit cell in Atomic packing factor.

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

The Atomic Packing Factor in terms of particle radius is the fraction of volume in a crystal structure that is occupied by constituent particles. It is a dimensionless quantity and always less than unity is calculated using Atomic Packing Factor = (Number of Atoms*(4/3)*pi*(Radius of Particle^3))/(Edge Length in APF^3). To calculate Atomic Packing Factor in Terms of Particle Radius, you need Number of Atoms (z), Radius of Particle (r) & Edge Length in APF (a). With our tool, you need to enter the respective value for Number of Atoms, Radius of Particle & Edge Length in APF 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 Number of Atoms, Radius of Particle & Edge Length in APF. 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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