Edge Length using Interplanar Distance of Cubic Crystal Calculator

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Inter-planar distance and inter-planar angle

✖Interplanar Spacing is the distance between adjacent and parallel planes of the crystal.ⓘ Interplanar Spacing [d]			+10% -10%
✖The Miller Index along x-axis form a notation system in crystallography for planes in crystal (Bravais) lattices along the x-direction.ⓘ Miller Index along x-axis [h]			+10% -10%
✖The Miller Index along y-axis form a notation system in crystallography for planes in crystal (Bravais) lattices along the y-direction.ⓘ Miller Index along y-axis [k]			+10% -10%
✖The Miller Index along z-axis form a notation system in crystallography for planes in crystal (Bravais) lattices along the z-direction.ⓘ Miller Index along z-axis [l]			+10% -10%

✖The Edge length is the length of the edge of the unit cell.ⓘ Edge Length using Interplanar Distance of Cubic Crystal [a]

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Formula

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Edge Length using Interplanar Distance of Cubic Crystal

Formula

`"a" = "d"*sqrt(("h"^2)+("k"^2)+("l"^2))`

Example

`"103.3538A"="0.7nm"*sqrt((("9")^2)+(("4")^2)+(("11")^2))`

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Edge Length using Interplanar Distance of Cubic Crystal Solution

STEP 0: Pre-Calculation Summary

Formula Used

Edge Length = Interplanar Spacing*sqrt((Miller Index along x-axis^2)+(Miller Index along y-axis^2)+(Miller Index along z-axis^2))
a = d*sqrt((h^2)+(k^2)+(l^2))
This formula uses 1 Functions, 5 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.
Interplanar Spacing - (Measured in Meter) - Interplanar Spacing is the distance between adjacent and parallel planes of the crystal.
Miller Index along x-axis - The Miller Index along x-axis form a notation system in crystallography for planes in crystal (Bravais) lattices along the x-direction.
Miller Index along y-axis - The Miller Index along y-axis form a notation system in crystallography for planes in crystal (Bravais) lattices along the y-direction.
Miller Index along z-axis - The Miller Index along z-axis form a notation system in crystallography for planes in crystal (Bravais) lattices along the z-direction.

STEP 1: Convert Input(s) to Base Unit

Interplanar Spacing: 0.7 Nanometer --> 7E-10 Meter (Check conversion here)
Miller Index along x-axis: 9 --> No Conversion Required
Miller Index along y-axis: 4 --> No Conversion Required
Miller Index along z-axis: 11 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

a = d*sqrt((h^2)+(k^2)+(l^2)) --> 7E-10*sqrt((9^2)+(4^2)+(11^2))

Evaluating ... ...

a = 1.03353761421634E-08

STEP 3: Convert Result to Output's Unit

1.03353761421634E-08 Meter -->103.353761421634 Angstrom (Check conversion here)

FINAL ANSWER

103.353761421634 ≈ 103.3538 Angstrom <-- Edge Length

(Calculation completed in 00.004 seconds)

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University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA

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< 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 using Interplanar Distance of Cubic Crystal Formula

Edge Length = Interplanar Spacing*sqrt((Miller Index along x-axis^2)+(Miller Index along y-axis^2)+(Miller Index along z-axis^2))
a = d*sqrt((h^2)+(k^2)+(l^2))

What are Bravais Lattices?

Bravais Lattice refers to the 14 different 3-dimensional configurations into which atoms can be arranged in crystals. The smallest group of symmetrically aligned atoms which can be repeated in an array to make up the entire crystal is called a unit cell.
There are several ways to describe a lattice. The most fundamental description is known as the Bravais lattice. In words, a Bravais lattice is an array of discrete points with an arrangement and orientation that look exactly the same from any of the discrete points, that is the lattice points are indistinguishable from one another.
Out of 14 types of Bravais lattices some 7 types of Bravais lattices in three-dimensional space are listed in this subsection. Note that the letters a, b, and c have been used to denote the dimensions of the unit cells whereas the letters 𝛂, 𝞫, and 𝝲 denote the corresponding angles in the unit cells.

How to Calculate Edge Length using Interplanar Distance of Cubic Crystal?

Edge Length using Interplanar Distance of Cubic Crystal calculator uses Edge Length = Interplanar Spacing*sqrt((Miller Index along x-axis^2)+(Miller Index along y-axis^2)+(Miller Index along z-axis^2)) to calculate the Edge Length, The Edge Length using Interplanar Distance of Cubic Crystal is a line where two faces of a crystal lattice meet. Edge Length is denoted by a symbol.

How to calculate Edge Length using Interplanar Distance of Cubic Crystal using this online calculator? To use this online calculator for Edge Length using Interplanar Distance of Cubic Crystal, enter Interplanar Spacing (d), Miller Index along x-axis (h), Miller Index along y-axis (k) & Miller Index along z-axis (l) and hit the calculate button. Here is how the Edge Length using Interplanar Distance of Cubic Crystal calculation can be explained with given input values -> 1E+12 = 7E-10*sqrt((9^2)+(4^2)+(11^2)).

FAQ

What is Edge Length using Interplanar Distance of Cubic Crystal?

The Edge Length using Interplanar Distance of Cubic Crystal is a line where two faces of a crystal lattice meet and is represented as a = d*sqrt((h^2)+(k^2)+(l^2)) or Edge Length = Interplanar Spacing*sqrt((Miller Index along x-axis^2)+(Miller Index along y-axis^2)+(Miller Index along z-axis^2)). Interplanar Spacing is the distance between adjacent and parallel planes of the crystal, The Miller Index along x-axis form a notation system in crystallography for planes in crystal (Bravais) lattices along the x-direction, The Miller Index along y-axis form a notation system in crystallography for planes in crystal (Bravais) lattices along the y-direction & The Miller Index along z-axis form a notation system in crystallography for planes in crystal (Bravais) lattices along the z-direction.

How to calculate Edge Length using Interplanar Distance of Cubic Crystal?

The Edge Length using Interplanar Distance of Cubic Crystal is a line where two faces of a crystal lattice meet is calculated using Edge Length = Interplanar Spacing*sqrt((Miller Index along x-axis^2)+(Miller Index along y-axis^2)+(Miller Index along z-axis^2)). To calculate Edge Length using Interplanar Distance of Cubic Crystal, you need Interplanar Spacing (d), Miller Index along x-axis (h), Miller Index along y-axis (k) & Miller Index along z-axis (l). With our tool, you need to enter the respective value for Interplanar Spacing, Miller Index along x-axis, Miller Index along y-axis & Miller Index along z-axis 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 Interplanar Spacing, Miller Index along x-axis, Miller Index along y-axis & Miller Index along z-axis. 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 = 2*sqrt(2)*Radius of Constituent Particle

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