Edge Length of Face Centered Unit Cell Calculator

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Inter-planar distance and inter-planar angle

✖The Radius of Constituent Particle is the radius of the atom present in the unit cell.ⓘ Radius of Constituent Particle [R]

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✖The Edge length is the length of the edge of the unit cell.ⓘ Edge Length of Face Centered Unit Cell [a]

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Formula

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Edge Length of Face Centered Unit Cell

Formula

`"a" = 2*sqrt(2)*"R"`

Example

`"169.7056A"=2*sqrt(2)*"60A"`

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Edge Length of Face Centered Unit Cell Solution

STEP 0: Pre-Calculation Summary

Formula Used

Edge Length = 2*sqrt(2)*Radius of Constituent Particle
a = 2*sqrt(2)*R
This formula uses 1 Functions, 2 Variables

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

Edge Length - (Measured in Meter) - The Edge length is the length of the edge of the unit cell.
Radius of Constituent Particle - (Measured in Meter) - The Radius of Constituent Particle is the radius of the atom present in the unit cell.

STEP 1: Convert Input(s) to Base Unit

Radius of Constituent Particle: 60 Angstrom --> 6E-09 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

a = 2*sqrt(2)*R --> 2*sqrt(2)*6E-09

Evaluating ... ...

a = 1.69705627484771E-08

STEP 3: Convert Result to Output's Unit

1.69705627484771E-08 Meter -->169.705627484771 Angstrom (Check conversion here)

FINAL ANSWER

169.705627484771 ≈ 169.7056 Angstrom <-- Edge Length

(Calculation completed in 00.004 seconds)

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Home » Chemistry » Solid State Chemistry » Lattice » Edge Length of Face Centered Unit Cell

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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

Edge Length of Face Centered Unit Cell Formula

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

What is Face Centered Unit Cell?

The face-centered cubic unit cell also starts with identical particles on the eight corners of the cube. But this structure also contains the same particles in the centers of the six faces of the unit cell, for a total of 14 identical lattice points.

The face-centered cubic unit cell is the simplest repeating unit in a cubic closest-packed structure. In fact, the presence of face-centered cubic unit cells in this structure explains why the structure is known as cubic closest-packed.

How to Calculate Edge Length of Face Centered Unit Cell?

Edge Length of Face Centered Unit Cell calculator uses Edge Length = 2*sqrt(2)*Radius of Constituent Particle to calculate the Edge Length, The Edge Length of Face Centered Unit Cell formula is defined as 2* 2^(1/2) times the radius of constituent particle. Edge Length is denoted by a symbol.

How to calculate Edge Length of Face Centered Unit Cell using this online calculator? To use this online calculator for Edge Length of Face Centered Unit Cell, enter Radius of Constituent Particle (R) and hit the calculate button. Here is how the Edge Length of Face Centered Unit Cell calculation can be explained with given input values -> 1.7E+12 = 2*sqrt(2)*6E-09.

FAQ

What is Edge Length of Face Centered Unit Cell?

The Edge Length of Face Centered Unit Cell formula is defined as 2* 2^(1/2) times the radius of constituent particle and is represented as a = 2*sqrt(2)*R or Edge Length = 2*sqrt(2)*Radius of Constituent Particle. The Radius of Constituent Particle is the radius of the atom present in the unit cell.

How to calculate Edge Length of Face Centered Unit Cell?

The Edge Length of Face Centered Unit Cell formula is defined as 2* 2^(1/2) times the radius of constituent particle is calculated using Edge Length = 2*sqrt(2)*Radius of Constituent Particle. To calculate Edge Length of Face Centered Unit Cell, you need Radius of Constituent Particle (R). With our tool, you need to enter the respective value for Radius of Constituent 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 Edge Length?

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

Edge Length = 2*Radius of Constituent Particle
Edge Length = 4*Radius of Constituent Particle/sqrt(3)
Edge Length = Interplanar Spacing*sqrt((Miller Index along x-axis^2)+(Miller Index along y-axis^2)+(Miller Index along z-axis^2))

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