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Interplanar Spacing of Crystal Calculator

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✖Order of reflection which must be an integer.ⓘ Order of reflection [n]			+10% -10%
✖The Wavelength of X-ray can be defined as the distance between two successive crests or troughs of X-Ray.ⓘ Wavelength of X-ray [λ_X-ray]			+10% -10%
✖The angle of incidence is the angle between a ray incident on a surface and the line perpendicular to the surface at the point of incidence, called the normal.ⓘ Angle of Incidence [θ]			+10% -10%

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

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Interplanar Spacing of Crystal Solution

STEP 0: Pre-Calculation Summary

Formula Used

Interplanar Spacing = Order of reflection*Wavelength of X-ray/(2*sin(Angle of Incidence))
d = n*λ_X-ray/(2*sin(θ))
This formula uses 1 Functions, 4 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)

Variables Used

Interplanar Spacing - (Measured in Meter) - Interplanar Spacing is the distance between adjacent and parallel planes of the crystal.
Order of reflection - Order of reflection which must be an integer.
Wavelength of X-ray - (Measured in Meter) - The Wavelength of X-ray can be defined as the distance between two successive crests or troughs of X-Ray.
Angle of Incidence - (Measured in Radian) - The angle of incidence is the angle between a ray incident on a surface and the line perpendicular to the surface at the point of incidence, called the normal.

STEP 1: Convert Input(s) to Base Unit

Order of reflection: 3 --> No Conversion Required
Wavelength of X-ray: 0.45 Nanometer --> 4.5E-10 Meter (Check conversion here)
Angle of Incidence: 30 Degree --> 0.5235987755982 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d = n*λ_X-ray/(2*sin(θ)) --> 3*4.5E-10/(2*sin(0.5235987755982))

Evaluating ... ...

d = 1.35E-09

STEP 3: Convert Result to Output's Unit

1.35E-09 Meter -->1.35 Nanometer (Check conversion here)

FINAL ANSWER

1.35 Nanometer <-- Interplanar Spacing

(Calculation completed in 00.004 seconds)

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Indian Institute of Technology (IIT), Chennai

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< Crystal Lattice Calculators

Interplanar Spacing of Crystal given Lattice Parameter

LaTeX Go Interplanar Spacing = Lattice Parameter/sqrt(Miller Index h^2+Miller Index k^2+Miller Index l^2)

Interplanar Spacing of Crystal

LaTeX Go Interplanar Spacing = Order of reflection*Wavelength of X-ray/(2*sin(Angle of Incidence))

Lattice Parameter of FCC

LaTeX Go Lattice Parameter of FCC = 2*Atomic Radius*sqrt(2)

Lattice Parameter of BCC

LaTeX Go Lattice Parameter of BCC = 4*Atomic Radius/sqrt(3)

Interplanar Spacing of Crystal Formula

LaTeX Go

Interplanar Spacing = Order of reflection*Wavelength of X-ray/(2*sin(Angle of Incidence))
d = n*λ_X-ray/(2*sin(θ))

Bragg's Law

Bragg's law gives the relation between the spacing of atomic planes (interplanar spacing) in crystals and the angle of incidence at which these planes produce the most intense reflections of electromagnetic radiations (X rays).

How to Calculate Interplanar Spacing of Crystal?

Interplanar Spacing of Crystal calculator uses Interplanar Spacing = Order of reflection*Wavelength of X-ray/(2*sin(Angle of Incidence)) to calculate the Interplanar Spacing, Interplanar spacing of crystal is the distance between adjacent and parallel atomic planes of the crystal. Interplanar Spacing is denoted by d symbol.

How to calculate Interplanar Spacing of Crystal using this online calculator? To use this online calculator for Interplanar Spacing of Crystal, enter Order of reflection (n), Wavelength of X-ray (λ_X-ray) & Angle of Incidence (θ) and hit the calculate button. Here is how the Interplanar Spacing of Crystal calculation can be explained with given input values -> 1.4E+9 = 3*4.5E-10/(2*sin(0.5235987755982)).

FAQ

What is Interplanar Spacing of Crystal?

Interplanar spacing of crystal is the distance between adjacent and parallel atomic planes of the crystal and is represented as d = n*λ_X-ray/(2*sin(θ)) or Interplanar Spacing = Order of reflection*Wavelength of X-ray/(2*sin(Angle of Incidence)). Order of reflection which must be an integer, The Wavelength of X-ray can be defined as the distance between two successive crests or troughs of X-Ray & The angle of incidence is the angle between a ray incident on a surface and the line perpendicular to the surface at the point of incidence, called the normal.

How to calculate Interplanar Spacing of Crystal?

Interplanar spacing of crystal is the distance between adjacent and parallel atomic planes of the crystal is calculated using Interplanar Spacing = Order of reflection*Wavelength of X-ray/(2*sin(Angle of Incidence)). To calculate Interplanar Spacing of Crystal, you need Order of reflection (n), Wavelength of X-ray (λ_X-ray) & Angle of Incidence (θ). With our tool, you need to enter the respective value for Order of reflection, Wavelength of X-ray & Angle of Incidence 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 Order of reflection, Wavelength of X-ray & Angle of Incidence. We can use 1 other way(s) to calculate the same, which is/are as follows -

Interplanar Spacing = Lattice Parameter/sqrt(Miller Index h^2+Miller Index k^2+Miller Index l^2)

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