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Interplanar Spacing of Crystal given Lattice Parameter Calculator

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✖Lattice Parameter is defined as the length between two points on the corners of a unit cell.ⓘ Lattice Parameter [a]			+10% -10%
✖Miller Index h is the reciprocal of the x intercept of the atomic plane.ⓘ Miller Index h [h]			+10% -10%
✖Miller Index k is the reciprocal of the y intercept of the atomic plane.ⓘ Miller Index k [k]			+10% -10%
✖Miller Index l is the reciprocal of the z intercept of the atomic plane.ⓘ Miller Index l [l]			+10% -10%

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

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Interplanar Spacing of Crystal given Lattice Parameter Solution

STEP 0: Pre-Calculation Summary

Formula Used

Interplanar Spacing = Lattice Parameter/sqrt(Miller Index h^2+Miller Index k^2+Miller Index l^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.
Lattice Parameter - (Measured in Meter) - Lattice Parameter is defined as the length between two points on the corners of a unit cell.
Miller Index h - Miller Index h is the reciprocal of the x intercept of the atomic plane.
Miller Index k - Miller Index k is the reciprocal of the y intercept of the atomic plane.
Miller Index l - Miller Index l is the reciprocal of the z intercept of the atomic plane.

STEP 1: Convert Input(s) to Base Unit

Lattice Parameter: 2.5 Angstrom --> 2.5E-10 Meter (Check conversion here)
Miller Index h: 2 --> No Conversion Required
Miller Index k: 7 --> No Conversion Required
Miller Index l: 5 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d = a/sqrt(h^2+k^2+l^2) --> 2.5E-10/sqrt(2^2+7^2+5^2)

Evaluating ... ...

d = 2.83069258536149E-11

STEP 3: Convert Result to Output's Unit

2.83069258536149E-11 Meter -->0.0283069258536149 Nanometer (Check conversion here)

FINAL ANSWER

0.0283069258536149 ≈ 0.028307 Nanometer <-- Interplanar Spacing

(Calculation completed in 00.004 seconds)

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Indian Institute of Technology (IIT), Chennai

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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 given Lattice Parameter Formula

LaTeX Go

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

Relation between lattice parameter and interplanar spacing

The magnitude of the distance between two adjacent and parallel planes of
atoms (i.e., the interplanar spacing ) is a function of the Miller indices (h, k,
and l) as well as the lattice parameter(a). For non-cubic systems, the relation is much complex than shown above.

How to Calculate Interplanar Spacing of Crystal given Lattice Parameter?

Interplanar Spacing of Crystal given Lattice Parameter calculator uses Interplanar Spacing = Lattice Parameter/sqrt(Miller Index h^2+Miller Index k^2+Miller Index l^2) to calculate the Interplanar Spacing, Interplanar Spacing of Crystal given Lattice Parameter 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 given Lattice Parameter using this online calculator? To use this online calculator for Interplanar Spacing of Crystal given Lattice Parameter, enter Lattice Parameter (a), Miller Index h (h), Miller Index k (k) & Miller Index l (l) and hit the calculate button. Here is how the Interplanar Spacing of Crystal given Lattice Parameter calculation can be explained with given input values -> 2.8E+7 = 2.5E-10/sqrt(2^2+7^2+5^2).

FAQ

What is Interplanar Spacing of Crystal given Lattice Parameter?

Interplanar Spacing of Crystal given Lattice Parameter is the distance between adjacent and parallel atomic planes of the crystal and is represented as d = a/sqrt(h^2+k^2+l^2) or Interplanar Spacing = Lattice Parameter/sqrt(Miller Index h^2+Miller Index k^2+Miller Index l^2). Lattice Parameter is defined as the length between two points on the corners of a unit cell, Miller Index h is the reciprocal of the x intercept of the atomic plane, Miller Index k is the reciprocal of the y intercept of the atomic plane & Miller Index l is the reciprocal of the z intercept of the atomic plane.

How to calculate Interplanar Spacing of Crystal given Lattice Parameter?

Interplanar Spacing of Crystal given Lattice Parameter is the distance between adjacent and parallel atomic planes of the crystal is calculated using Interplanar Spacing = Lattice Parameter/sqrt(Miller Index h^2+Miller Index k^2+Miller Index l^2). To calculate Interplanar Spacing of Crystal given Lattice Parameter, you need Lattice Parameter (a), Miller Index h (h), Miller Index k (k) & Miller Index l (l). With our tool, you need to enter the respective value for Lattice Parameter, Miller Index h, Miller Index k & Miller Index l 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 Lattice Parameter, Miller Index h, Miller Index k & Miller Index l. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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