Radius of Constituent Particle in BCC lattice Calculator

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

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

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Formula

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Radius of Constituent Particle in BCC lattice

Formula

`"R" = 3*sqrt(3)*"a"/4`

Example

`"129.9038A"=3*sqrt(3)*"100A"/4`

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Radius of Constituent Particle in BCC lattice Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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

STEP 1: Convert Input(s) to Base Unit

Edge Length: 100 Angstrom --> 1E-08 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R = 3*sqrt(3)*a/4 --> 3*sqrt(3)*1E-08/4

Evaluating ... ...

R = 1.29903810567666E-08

STEP 3: Convert Result to Output's Unit

1.29903810567666E-08 Meter -->129.903810567666 Angstrom (Check conversion here)

FINAL ANSWER

129.903810567666 ≈ 129.9038 Angstrom <-- Radius of Constituent Particle

(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

Radius of Constituent Particle in BCC lattice Formula

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

What is BCC lattice?

The body-centered cubic system has one lattice point in the center of the unit cell in addition to the eight corner points. It has a net total of 2 lattice points per unit cell (1⁄8 × 8 + 1).

How to Calculate Radius of Constituent Particle in BCC lattice?

Radius of Constituent Particle in BCC lattice calculator uses Radius of Constituent Particle = 3*sqrt(3)*Edge Length/4 to calculate the Radius of Constituent Particle, The Radius of Constituent Particle in BCC lattice formula is defined as 1.3 times the edge length of the unit cell. Radius of Constituent Particle is denoted by R symbol.

How to calculate Radius of Constituent Particle in BCC lattice using this online calculator? To use this online calculator for Radius of Constituent Particle in BCC lattice, enter Edge Length (a) and hit the calculate button. Here is how the Radius of Constituent Particle in BCC lattice calculation can be explained with given input values -> 1.3E+12 = 3*sqrt(3)*1E-08/4.

FAQ

What is Radius of Constituent Particle in BCC lattice?

The Radius of Constituent Particle in BCC lattice formula is defined as 1.3 times the edge length of the unit cell and is represented as R = 3*sqrt(3)*a/4 or Radius of Constituent Particle = 3*sqrt(3)*Edge Length/4. The Edge length is the length of the edge of the unit cell.

How to calculate Radius of Constituent Particle in BCC lattice?

The Radius of Constituent Particle in BCC lattice formula is defined as 1.3 times the edge length of the unit cell is calculated using Radius of Constituent Particle = 3*sqrt(3)*Edge Length/4. To calculate Radius of Constituent Particle in BCC lattice, you need Edge Length (a). With our tool, you need to enter the respective value for Edge Length 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 Radius of Constituent Particle?

In this formula, Radius of Constituent Particle uses Edge Length. We can use 2 other way(s) to calculate the same, which is/are as follows -

Radius of Constituent Particle = Edge Length/2
Radius of Constituent Particle = Edge Length/2.83

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