Interplanar Distance in Cubic Crystal Lattice Calculator

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Inter-planar distance and inter-planar angle

Atomic Packing Factor

Density of different Cubic Cell

Lattice

Lattice Direction

Volume of Different Cubic Cell

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

✖Interplanar Spacing is the distance between adjacent and parallel planes of the crystal.ⓘ Interplanar Distance in Cubic Crystal Lattice [d]

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Formula

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Interplanar Distance in Cubic Crystal Lattice

Formula

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

Example

`"0.677285nm"="100A"/sqrt((("9")^2)+(("4")^2)+(("11")^2))`

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Interplanar Distance in Cubic Crystal Lattice Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Interplanar Spacing - (Measured in Meter) - Interplanar Spacing is the distance between adjacent and parallel planes of the crystal.
Edge Length - (Measured in Meter) - The Edge length is the length of the edge of the unit cell.
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

Edge Length: 100 Angstrom --> 1E-08 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

d = a/sqrt((h^2)+(k^2)+(l^2)) --> 1E-08/sqrt((9^2)+(4^2)+(11^2))

Evaluating ... ...

d = 6.77285461478596E-10

STEP 3: Convert Result to Output's Unit

6.77285461478596E-10 Meter -->0.677285461478596 Nanometer (Check conversion here)

FINAL ANSWER

0.677285461478596 ≈ 0.677285 Nanometer <-- Interplanar Spacing

(Calculation completed in 00.004 seconds)

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< 10+ Inter-planar distance and inter-planar angle Calculators

Interplanar Distance in Triclinic Crystal Lattice

Go Interplanar Spacing = sqrt(1/((((Lattice Constant b^2)*(Lattice Constant c^2)*((sin(Lattice parameter alpha))^2)*(Miller Index along x-axis^2))+((Lattice Constant a^2)*(Lattice Constant c^2)*((sin(Lattice Parameter Beta))^2)*(Miller Index along y-axis^2))+((Lattice Constant a^2)*(Lattice Constant b^2)*((sin(Lattice Parameter gamma))^2)*(Miller Index along z-axis^2))+(2*Lattice Constant a*Lattice Constant b*(Lattice Constant c^2)*((cos(Lattice parameter alpha)*cos(Lattice Parameter Beta))-cos(Lattice Parameter gamma))*Miller Index along x-axis*Miller Index along y-axis)+(2*Lattice Constant b*Lattice Constant c*(Lattice Constant a^2)*((cos(Lattice Parameter gamma)*cos(Lattice Parameter Beta))-cos(Lattice parameter alpha))*Miller Index along z-axis*Miller Index along y-axis)+(2*Lattice Constant a*Lattice Constant c*(Lattice Constant b^2)*((cos(Lattice parameter alpha)*cos(Lattice Parameter gamma))-cos(Lattice Parameter Beta))*Miller Index along x-axis*Miller Index along z-axis))/(Volume of Unit Cell^2)))

Interplanar Angle for Hexagonal System

Go Interplanar Angle = acos(((Miller Index along plane 1*Miller Index h along plane 2)+(Miller Index k along Plane 1*Miller Index k along Plane 2)+(0.5*((Miller Index along plane 1*Miller Index k along Plane 2)+(Miller Index h along plane 2*Miller Index k along Plane 1)))+((3/4)*((Lattice Constant a^2)/(Lattice Constant c^2))*Miller Index l along plane 1*Miller Index l along plane 2))/(sqrt(((Miller Index along plane 1^2)+(Miller Index k along Plane 1^2)+(Miller Index along plane 1*Miller Index k along Plane 1)+((3/4)*((Lattice Constant a^2)/(Lattice Constant c^2))*(Miller Index l along plane 1^2)))*((Miller Index h along plane 2^2)+(Miller Index k along Plane 2^2)+(Miller Index h along plane 2*Miller Index k along Plane 2)+((3/4)*((Lattice Constant a^2)/(Lattice Constant c^2))*(Miller Index l along plane 2^2))))))

Interplanar Angle for Orthorhombic System

Go Interplanar Angle = acos((((Miller Index along plane 1*Miller Index h along plane 2)/(Lattice Constant a^2))+((Miller Index l along plane 1*Miller Index l along plane 2)/(Lattice Constant c^2))+((Miller Index k along Plane 1*Miller Index k along Plane 2)/(Lattice Constant b^2)))/sqrt((((Miller Index along plane 1^2)/(Lattice Constant a^2))+((Miller Index k along Plane 1^2)/(Lattice Constant b^2))*((Miller Index l along plane 1^2)/(Lattice Constant c^2)))*(((Miller Index h along plane 2^2)/(Lattice Constant a^2))+((Miller Index k along Plane 1^2)/(Lattice Constant b^2))+((Miller Index l along plane 1^2)/(Lattice Constant c^2)))))

Interplanar Distance in Rhombohedral Crystal Lattice

Go Interplanar Spacing = sqrt(1/(((((Miller Index along x-axis^2)+(Miller Index along y-axis^2)+(Miller Index along z-axis^2))*(sin(Lattice parameter alpha)^2))+(((Miller Index along x-axis*Miller Index along y-axis)+(Miller Index along y-axis*Miller Index along z-axis)+(Miller Index along x-axis*Miller Index along z-axis))*2*(cos(Lattice parameter alpha)^2))-cos(Lattice parameter alpha))/(Lattice Constant a^2*(1-(3*(cos(Lattice parameter alpha)^2))+(2*(cos(Lattice parameter alpha)^3))))))

Interplanar Distance in Monoclinic Crystal Lattice

Go Interplanar Spacing = sqrt(1/((((Miller Index along x-axis^2)/(Lattice Constant a^2))+(((Miller Index along y-axis^2)*(sin(Lattice Parameter Beta)^2))/(Lattice Constant b^2))+((Miller Index along z-axis^2)/(Lattice Constant c^2))-(2*Miller Index along x-axis*Miller Index along z-axis*cos(Lattice Parameter Beta)/(Lattice Constant a*Lattice Constant c)))/((sin(Lattice Parameter Beta))^2)))

Interplanar Angle for Simple Cubic System

Go Interplanar Angle = acos(((Miller Index along plane 1*Miller Index h along plane 2)+(Miller Index k along Plane 1*Miller Index k along Plane 2)+(Miller Index l along plane 1*Miller Index l along plane 2))/(sqrt((Miller Index along plane 1^2)+(Miller Index k along Plane 1^2)+(Miller Index l along plane 1^2))*sqrt((Miller Index h along plane 2^2)+(Miller Index k along Plane 2^2)+(Miller Index l along plane 2^2))))

Interplanar Distance in Hexagonal Crystal Lattice

Go Interplanar Spacing = sqrt(1/((((4/3)*((Miller Index along x-axis^2)+(Miller Index along x-axis*Miller Index along y-axis)+(Miller Index along y-axis^2)))/(Lattice Constant a^2))+((Miller Index along z-axis^2)/(Lattice Constant c^2))))

Interplanar Distance in Orthorhombic Crystal Lattice

Go Interplanar Spacing = sqrt(1/(((Miller Index along x-axis^2)/(Lattice Constant a^2))+((Miller Index along y-axis^2)/(Lattice Constant b^2))+((Miller Index along z-axis^2)/(Lattice Constant c^2))))

Interplanar Distance in Tetragonal Crystal Lattice

Go Interplanar Spacing = sqrt(1/((((Miller Index along x-axis^2)+(Miller Index along y-axis^2))/(Lattice Constant a^2))+((Miller Index along z-axis^2)/(Lattice Constant c^2))))

Interplanar Distance in Cubic Crystal Lattice

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

Interplanar Distance in Cubic Crystal Lattice Formula

Interplanar Spacing = Edge Length/sqrt((Miller Index along x-axis^2)+(Miller Index along y-axis^2)+(Miller Index along z-axis^2))
d = a/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 Interplanar Distance in Cubic Crystal Lattice?

Interplanar Distance in Cubic Crystal Lattice calculator uses Interplanar Spacing = Edge Length/sqrt((Miller Index along x-axis^2)+(Miller Index along y-axis^2)+(Miller Index along z-axis^2)) to calculate the Interplanar Spacing, The Interplanar Distance in Cubic Crystal Lattice, also called Interplanar Spacing is the perpendicular distance between two successive planes on a family (hkl). Interplanar Spacing is denoted by d symbol.

How to calculate Interplanar Distance in Cubic Crystal Lattice using this online calculator? To use this online calculator for Interplanar Distance in Cubic Crystal Lattice, enter Edge Length (a), 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 Interplanar Distance in Cubic Crystal Lattice calculation can be explained with given input values -> 6.8E+8 = 1E-08/sqrt((9^2)+(4^2)+(11^2)).

FAQ

What is Interplanar Distance in Cubic Crystal Lattice?

The Interplanar Distance in Cubic Crystal Lattice, also called Interplanar Spacing is the perpendicular distance between two successive planes on a family (hkl) and is represented as d = a/sqrt((h^2)+(k^2)+(l^2)) or Interplanar Spacing = Edge Length/sqrt((Miller Index along x-axis^2)+(Miller Index along y-axis^2)+(Miller Index along z-axis^2)). The Edge length is the length of the edge of the unit cell, 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 Interplanar Distance in Cubic Crystal Lattice?

The Interplanar Distance in Cubic Crystal Lattice, also called Interplanar Spacing is the perpendicular distance between two successive planes on a family (hkl) is calculated using Interplanar Spacing = Edge Length/sqrt((Miller Index along x-axis^2)+(Miller Index along y-axis^2)+(Miller Index along z-axis^2)). To calculate Interplanar Distance in Cubic Crystal Lattice, you need Edge Length (a), 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 Edge Length, 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 Interplanar Spacing?

In this formula, Interplanar Spacing uses Edge Length, Miller Index along x-axis, Miller Index along y-axis & Miller Index along z-axis. We can use 6 other way(s) to calculate the same, which is/are as follows -

Interplanar Spacing = sqrt(1/((((Miller Index along x-axis^2)+(Miller Index along y-axis^2))/(Lattice Constant a^2))+((Miller Index along z-axis^2)/(Lattice Constant c^2))))
Interplanar Spacing = sqrt(1/((((4/3)*((Miller Index along x-axis^2)+(Miller Index along x-axis*Miller Index along y-axis)+(Miller Index along y-axis^2)))/(Lattice Constant a^2))+((Miller Index along z-axis^2)/(Lattice Constant c^2))))
Interplanar Spacing = sqrt(1/(((((Miller Index along x-axis^2)+(Miller Index along y-axis^2)+(Miller Index along z-axis^2))*(sin(Lattice parameter alpha)^2))+(((Miller Index along x-axis*Miller Index along y-axis)+(Miller Index along y-axis*Miller Index along z-axis)+(Miller Index along x-axis*Miller Index along z-axis))*2*(cos(Lattice parameter alpha)^2))-cos(Lattice parameter alpha))/(Lattice Constant a^2*(1-(3*(cos(Lattice parameter alpha)^2))+(2*(cos(Lattice parameter alpha)^3))))))
Interplanar Spacing = sqrt(1/(((Miller Index along x-axis^2)/(Lattice Constant a^2))+((Miller Index along y-axis^2)/(Lattice Constant b^2))+((Miller Index along z-axis^2)/(Lattice Constant c^2))))
Interplanar Spacing = sqrt(1/((((Miller Index along x-axis^2)/(Lattice Constant a^2))+(((Miller Index along y-axis^2)*(sin(Lattice Parameter Beta)^2))/(Lattice Constant b^2))+((Miller Index along z-axis^2)/(Lattice Constant c^2))-(2*Miller Index along x-axis*Miller Index along z-axis*cos(Lattice Parameter Beta)/(Lattice Constant a*Lattice Constant c)))/((sin(Lattice Parameter Beta))^2)))
Interplanar Spacing = sqrt(1/((((Lattice Constant b^2)*(Lattice Constant c^2)*((sin(Lattice parameter alpha))^2)*(Miller Index along x-axis^2))+((Lattice Constant a^2)*(Lattice Constant c^2)*((sin(Lattice Parameter Beta))^2)*(Miller Index along y-axis^2))+((Lattice Constant a^2)*(Lattice Constant b^2)*((sin(Lattice Parameter gamma))^2)*(Miller Index along z-axis^2))+(2*Lattice Constant a*Lattice Constant b*(Lattice Constant c^2)*((cos(Lattice parameter alpha)*cos(Lattice Parameter Beta))-cos(Lattice Parameter gamma))*Miller Index along x-axis*Miller Index along y-axis)+(2*Lattice Constant b*Lattice Constant c*(Lattice Constant a^2)*((cos(Lattice Parameter gamma)*cos(Lattice Parameter Beta))-cos(Lattice parameter alpha))*Miller Index along z-axis*Miller Index along y-axis)+(2*Lattice Constant a*Lattice Constant c*(Lattice Constant b^2)*((cos(Lattice parameter alpha)*cos(Lattice Parameter gamma))-cos(Lattice Parameter Beta))*Miller Index along x-axis*Miller Index along z-axis))/(Volume of Unit Cell^2)))

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