Packing Efficiency Calculator

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Inter-planar distance and inter-planar angle

✖The Volume Occupied by Spheres in Unit Cell is the total volume occupied by all the atoms present in the unit cell.ⓘ Volume Occupied by Spheres in Unit Cell [v]			+10% -10%
✖The Total Volume of Unit Cell is geometrical volume of unit cell.ⓘ Total Volume of Unit Cell [V]			+10% -10%

✖The Packing Efficiency is the ratio of volume occupied by all the spheres in unit cell to the total volume of unit cell.ⓘ Packing Efficiency [P]

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Formula

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Packing Efficiency

Formula

`"P" = ("v"/"V")*100`

Example

`"77.77778"=("70m³"/"90m³")*100`

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Packing Efficiency Solution

STEP 0: Pre-Calculation Summary

Formula Used

Packing Efficiency = (Volume Occupied by Spheres in Unit Cell/Total Volume of Unit Cell)*100
P = (v/V)*100
This formula uses 3 Variables

Variables Used

Packing Efficiency - The Packing Efficiency is the ratio of volume occupied by all the spheres in unit cell to the total volume of unit cell.
Volume Occupied by Spheres in Unit Cell - (Measured in Cubic Meter) - The Volume Occupied by Spheres in Unit Cell is the total volume occupied by all the atoms present in the unit cell.
Total Volume of Unit Cell - (Measured in Cubic Meter) - The Total Volume of Unit Cell is geometrical volume of unit cell.

STEP 1: Convert Input(s) to Base Unit

Volume Occupied by Spheres in Unit Cell: 70 Cubic Meter --> 70 Cubic Meter No Conversion Required
Total Volume of Unit Cell: 90 Cubic Meter --> 90 Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P = (v/V)*100 --> (70/90)*100

Evaluating ... ...

P = 77.7777777777778

STEP 3: Convert Result to Output's Unit

77.7777777777778 --> No Conversion Required

FINAL ANSWER

77.7777777777778 ≈ 77.77778 <-- Packing Efficiency

(Calculation completed in 00.004 seconds)

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Credits

Created by Pragati Jaju

College Of Engineering (COEP), Pune

Pragati Jaju has created this Calculator and 50+ more calculators!

Verified by Akshada Kulkarni

National Institute of Information Technology (NIIT), Neemrana

Akshada Kulkarni has verified this Calculator and 900+ more calculators!

< 24 Lattice Calculators

Miller index along X-axis using Weiss Indices

Go Miller Index along x-axis = lcm(Weiss Index along x-axis,Weiss Index along y-axis,Weiss Index Along z-axis)/Weiss Index along x-axis

Miller index along Y-axis using Weiss Indices

Go Miller Index along y-axis = lcm(Weiss Index along x-axis,Weiss Index along y-axis,Weiss Index Along z-axis)/Weiss Index along y-axis

Miller index along Z-axis using Weiss Indices

Go Miller Index along z-axis = lcm(Weiss Index along x-axis,Weiss Index along y-axis,Weiss Index Along z-axis)/Weiss Index Along z-axis

Edge Length using Interplanar Distance of Cubic Crystal

Go Edge Length = Interplanar Spacing*sqrt((Miller Index along x-axis^2)+(Miller Index along y-axis^2)+(Miller Index along z-axis^2))

Fraction of impurity in lattice terms of Energy

Go Fraction of Impurities = exp(-Energy required per impurity/([R]*Temperature))

Energy per impurity

Go Energy required per impurity = -ln(Fraction of Impurities)*[R]*Temperature

Fraction of Vacancy in lattice terms of Energy

Go Fraction of Vacancy = exp(-Energy Required per Vacancy/([R]*Temperature))

Energy per vacancy

Go Energy Required per Vacancy = -ln(Fraction of Vacancy)*[R]*Temperature

Packing Efficiency

Go Packing Efficiency = (Volume Occupied by Spheres in Unit Cell/Total Volume of Unit Cell)*100

Number of lattice containing impurities

Go No. of Lattice Occupied by Impurities = Fraction of Impurities*Total no. of lattice points

Fraction of impurity in lattice

Go Fraction of Impurities = No. of Lattice Occupied by Impurities/Total no. of lattice points

Fraction of Vacancy in lattice

Go Fraction of Vacancy = Number of Vacant Lattice/Total no. of lattice points

Number of vacant lattice

Go Number of Vacant Lattice = Fraction of Vacancy*Total no. of lattice points

Weiss Index along X-axis using Miller Indices

Go Weiss Index along x-axis = LCM of Weiss Indices/Miller Index along x-axis

Weiss Index along Y-axis using Miller Indices

Go Weiss Index along y-axis = LCM of Weiss Indices/Miller Index along y-axis

Weiss Index along Z-axis using Miller Indices

Go Weiss Index Along z-axis = LCM of Weiss Indices/Miller Index along z-axis

Radius of Constituent Particle in BCC lattice

Go Radius of Constituent Particle = 3*sqrt(3)*Edge Length/4

Edge length of Body Centered Unit Cell

Go Edge Length = 4*Radius of Constituent Particle/sqrt(3)

Edge Length of Face Centered Unit Cell

Go Edge Length = 2*sqrt(2)*Radius of Constituent Particle

Radius Ratio

Go Radius Ratio = Radius of Cation/Radius of Anion

Number of Tetrahedral Voids

Go Number of Tetrahedral Voids = 2*Number of Closed Packed Spheres

Radius of Constituent Particle in FCC lattice

Go Radius of Constituent Particle = Edge Length/2.83

Radius of Constituent particle in Simple Cubic Unit Cell

Go Radius of Constituent Particle = Edge Length/2

Edge length of Simple cubic unit cell

Go Edge Length = 2*Radius of Constituent Particle

Packing Efficiency Formula

Packing Efficiency = (Volume Occupied by Spheres in Unit Cell/Total Volume of Unit Cell)*100
P = (v/V)*100

What is Unit Cell?

The smallest repeating unit of the crystal lattice is the unit cell, the building block of a crystal.

The unit cells which are all identical are defined in such a way that they fill space without overlapping. The 3D arrangement of atoms, molecules or ions inside a crystal is called a crystal lattice. It is made up of numerous unit cells. One of the three constituent particles takes up every lattice point.

A unit cell can either be primitive cubic, body-centred cubic (BCC) or face-centred cubic (FCC). In this section, we will discuss the three types of unit cell in detail.

How to Calculate Packing Efficiency?

Packing Efficiency calculator uses Packing Efficiency = (Volume Occupied by Spheres in Unit Cell/Total Volume of Unit Cell)*100 to calculate the Packing Efficiency, The Packing Efficiency formula is defined as the ratio of volume occupied by all spheres in the unit cell to the total volume of the unit cell. Packing Efficiency is denoted by P symbol.

How to calculate Packing Efficiency using this online calculator? To use this online calculator for Packing Efficiency, enter Volume Occupied by Spheres in Unit Cell (v) & Total Volume of Unit Cell (V) and hit the calculate button. Here is how the Packing Efficiency calculation can be explained with given input values -> 77.77778 = (70/90)*100.

FAQ

What is Packing Efficiency?

The Packing Efficiency formula is defined as the ratio of volume occupied by all spheres in the unit cell to the total volume of the unit cell and is represented as P = (v/V)*100 or Packing Efficiency = (Volume Occupied by Spheres in Unit Cell/Total Volume of Unit Cell)*100. The Volume Occupied by Spheres in Unit Cell is the total volume occupied by all the atoms present in the unit cell & The Total Volume of Unit Cell is geometrical volume of unit cell.

How to calculate Packing Efficiency?

The Packing Efficiency formula is defined as the ratio of volume occupied by all spheres in the unit cell to the total volume of the unit cell is calculated using Packing Efficiency = (Volume Occupied by Spheres in Unit Cell/Total Volume of Unit Cell)*100. To calculate Packing Efficiency, you need Volume Occupied by Spheres in Unit Cell (v) & Total Volume of Unit Cell (V). With our tool, you need to enter the respective value for Volume Occupied by Spheres in Unit Cell & Total Volume of Unit Cell and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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