Linear Density for BCC 101 direction 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 Linear Density is the measure of a quantity of any characteristic value per unit of length.ⓘ Linear Density for BCC 101 direction [L.D]

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Formula

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Linear Density for BCC 101 direction

Formula

`"L.D" = sqrt(3)/(4*"R"*sqrt(2))`

Example

`"5.1E^7"=sqrt(3)/(4*"60A"*sqrt(2))`

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Linear Density for BCC 101 direction Solution

STEP 0: Pre-Calculation Summary

Formula Used

Linear Density = sqrt(3)/(4*Radius of Constituent Particle*sqrt(2))
L.D = sqrt(3)/(4*R*sqrt(2))
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

Linear Density - The Linear Density is the measure of a quantity of any characteristic value per unit of length.
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

L.D = sqrt(3)/(4*R*sqrt(2)) --> sqrt(3)/(4*6E-09*sqrt(2))

Evaluating ... ...

L.D = 51031036.3079829

STEP 3: Convert Result to Output's Unit

51031036.3079829 --> No Conversion Required

FINAL ANSWER

51031036.3079829 ≈ 5.1E+7 <-- Linear Density

(Calculation completed in 00.006 seconds)

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Created by Pragati Jaju

College Of Engineering (COEP), Pune

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National Institute of Information Technology (NIIT), Neemrana

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< 13 Density of different Cubic Cell Calculators

Density of Unit Cell

Go Density = Number of Atoms*Mass of Atom/((Edge Length^3)*[Avaga-no])

Linear Density for BCC 101 direction

Go Linear Density = sqrt(3)/(4*Radius of Constituent Particle*sqrt(2))

Density of BCC lattice

Go Density = 2*Mass of Atom/(Volume of Unit Cell*[Avaga-no])

Density of FCC Lattice

Go Density = 4*Mass of Atom/(Volume of Unit Cell*[Avaga-no])

Linear Density

Go Linear Density = Number of Atoms Centered on Direction Vector/Length of Direction Vector

Density of Simple Cubic Unit Cell

Go Density = Mass of Atom/(Volume of Unit Cell*[Avaga-no])

Planar Density

Go Planar Density = Number of Atoms Centered on Plane/Area of Plane

Planar Density for FCC 110 plane

Go Planar Density = 0.177/(Radius of Constituent Particle^2)

Planar Density for BCC 100 Plane

Go Planar Density = 0.19/(Radius of Constituent Particle^2)

Planar Density for FCC 100 Plane

Go Planar Density = 0.25/(Radius of Constituent Particle^2)

Planar Density for FCC 111 plane

Go Planar Density = 0.29/(Radius of Constituent Particle^2)

Linear Density for BCC 111 Direction

Go Linear Density = 1/(2*Radius of Constituent Particle)

Linear Density for BCC 110 direction

Go Linear Density = 0.306/Radius of Constituent Particle

Linear Density for BCC 101 direction Formula

Linear Density = sqrt(3)/(4*Radius of Constituent Particle*sqrt(2))
L.D = sqrt(3)/(4*R*sqrt(2))

What is Linear Density?

Linear density (LD ) is defined as the number of atoms per unit length whose centers lie on the direction vector for a specific crystallographic direction; that is,
𝐿𝐷 =number of atoms centered on direction vector/length of direction vector
The units of linear density are reciprocal length (e.g., nm^−1,m^−1).

How to Calculate Linear Density for BCC 101 direction?

Linear Density for BCC 101 direction calculator uses Linear Density = sqrt(3)/(4*Radius of Constituent Particle*sqrt(2)) to calculate the Linear Density, The Linear Density for BCC 101 direction formula is defined as the number of atoms lying on the direction vector per unit length of the direction vector. Linear Density is denoted by L.D symbol.

How to calculate Linear Density for BCC 101 direction using this online calculator? To use this online calculator for Linear Density for BCC 101 direction, enter Radius of Constituent Particle (R) and hit the calculate button. Here is how the Linear Density for BCC 101 direction calculation can be explained with given input values -> 5.1E+7 = sqrt(3)/(4*6E-09*sqrt(2)).

FAQ

What is Linear Density for BCC 101 direction?

The Linear Density for BCC 101 direction formula is defined as the number of atoms lying on the direction vector per unit length of the direction vector and is represented as L.D = sqrt(3)/(4*R*sqrt(2)) or Linear Density = sqrt(3)/(4*Radius of Constituent Particle*sqrt(2)). The Radius of Constituent Particle is the radius of the atom present in the unit cell.

How to calculate Linear Density for BCC 101 direction?

The Linear Density for BCC 101 direction formula is defined as the number of atoms lying on the direction vector per unit length of the direction vector is calculated using Linear Density = sqrt(3)/(4*Radius of Constituent Particle*sqrt(2)). To calculate Linear Density for BCC 101 direction, 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 Linear Density?

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

Linear Density = Number of Atoms Centered on Direction Vector/Length of Direction Vector
Linear Density = 1/(2*Radius of Constituent Particle)
Linear Density = 0.306/Radius of Constituent Particle

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