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Interplanar Spacing of Crystal given Lattice Parameter Formula

GoInterplanar Spacing of Crystal Formula

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Interplanar Spacing is the distance between adjacent and parallel planes of the crystal. Check FAQs

d = \frac{a}{\sqrt{h^{2} + k^{2} + l^{2}}}

d - Interplanar Spacing?a - Lattice Parameter?h - Miller Index h?k - Miller Index k?l - Miller Index l?

Interplanar Spacing of Crystal given Lattice Parameter Example

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Here is how the Interplanar Spacing of Crystal given Lattice Parameter equation looks like with Values.

Here is how the Interplanar Spacing of Crystal given Lattice Parameter equation looks like with Units.

Here is how the Interplanar Spacing of Crystal given Lattice Parameter equation looks like.

0.0283 = \frac{2.5}{\sqrt{2^{2} + 7^{2} + 5^{2}}}

0.0283nm = \frac{2.5A}{\sqrt{2^{2} + 7^{2} + 5^{2}}}

0.0283 = \frac{2.5}{\sqrt{2^{2} + 7^{2} + 5^{2}}}

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Interplanar Spacing of Crystal given Lattice Parameter Solution

Follow our step by step solution on how to calculate Interplanar Spacing of Crystal given Lattice Parameter?

FIRST Step Consider the formula

d = \frac{a}{\sqrt{h^{2} + k^{2} + l^{2}}}

Next Step Substitute values of Variables

∴

d = \frac{2.5A}{\sqrt{2^{2} + 7^{2} + 5^{2}}}

Next Step Convert Units

∴

d = \frac{2.5E-10m}{\sqrt{2^{2} + 7^{2} + 5^{2}}}

Next Step Prepare to Evaluate

∴

d = \frac{2.5E-10}{\sqrt{2^{2} + 7^{2} + 5^{2}}}

Next Step Evaluate

∴

d = 2.83069258536149E-11m

Next Step Convert to Output's Unit

∴

d = 0.0283069258536149nm

LAST Step Rounding Answer

∴

d = 0.0283nm

Interplanar Spacing of Crystal given Lattice Parameter Formula Elements

Variables

Functions

Interplanar Spacing

Interplanar Spacing is the distance between adjacent and parallel planes of the crystal.

Symbol: d

Measurement: WavelengthUnit: nm

Note: Value should be greater than 0.

Formulas to find Interplanar Spacing

Lattice Parameter

Lattice Parameter is defined as the length between two points on the corners of a unit cell.

Symbol: a

Measurement: LengthUnit: A

Note: Value should be greater than 0.

Formulas to find Lattice Parameter

Miller Index h

Miller Index h is the reciprocal of the x intercept of the atomic plane.

Symbol: h

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Miller Index h

Miller Index k

Miller Index k is the reciprocal of the y intercept of the atomic plane.

Symbol: k

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Miller Index k

Miller Index l

Miller Index l is the reciprocal of the z intercept of the atomic plane.

Symbol: l

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Miller Index l

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.

Syntax: sqrt(Number)

Other Formulas to find Interplanar Spacing

Go Interplanar Spacing of Crystal

d = n \cdot \frac{λ X-ray}{2 \cdot \sin (θ)}

Other formulas in Crystal Lattice category

Go Lattice Parameter of FCC

a FCC = 2 \cdot r \cdot \sqrt{2}

Go Lattice Parameter of BCC

a BCC = 4 \cdot \frac{r}{\sqrt{3}}

Go Number of atomic sites

N = \frac{ρ}{A}

Go Density of cubic crystals

ρ = z \cdot \frac{A}{[Avaga-no] \cdot {(a)}^{3}}

How to Evaluate Interplanar Spacing of Crystal given Lattice Parameter?

Interplanar Spacing of Crystal given Lattice Parameter evaluator uses Interplanar Spacing = Lattice Parameter/sqrt(Miller Index h^2+Miller Index k^2+Miller Index l^2) to evaluate 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 evaluate Interplanar Spacing of Crystal given Lattice Parameter using this online evaluator? To use this online evaluator 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.

FAQs on Interplanar Spacing of Crystal given Lattice Parameter

What is the formula to find Interplanar Spacing of Crystal given Lattice Parameter?

The formula of Interplanar Spacing of Crystal given Lattice Parameter is expressed as Interplanar Spacing = Lattice Parameter/sqrt(Miller Index h^2+Miller Index k^2+Miller Index l^2). Here is an example- 2.8E+7 = 2.5E-10/sqrt(2^2+7^2+5^2).

How to calculate Interplanar Spacing of Crystal given Lattice Parameter?

With Lattice Parameter (a), Miller Index h (h), Miller Index k (k) & Miller Index l (l) we can find Interplanar Spacing of Crystal given Lattice Parameter using the formula - Interplanar Spacing = Lattice Parameter/sqrt(Miller Index h^2+Miller Index k^2+Miller Index l^2). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Interplanar Spacing?

Here are the different ways to Calculate Interplanar Spacing-

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

Can the Interplanar Spacing of Crystal given Lattice Parameter be negative?

No, the Interplanar Spacing of Crystal given Lattice Parameter, measured in Wavelength cannot be negative.

Which unit is used to measure Interplanar Spacing of Crystal given Lattice Parameter?

Interplanar Spacing of Crystal given Lattice Parameter is usually measured using the Nanometer[nm] for Wavelength. Meter[nm], Megameter[nm], Kilometer[nm] are the few other units in which Interplanar Spacing of Crystal given Lattice Parameter can be measured.

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Interplanar Spacing of Crystal given Lattice Parameter Formula

​GoInterplanar Spacing of Crystal Formula

Interplanar Spacing of Crystal given Lattice Parameter Example

Interplanar Spacing of Crystal given Lattice Parameter Solution

Interplanar Spacing of Crystal given Lattice Parameter Formula Elements

Other Formulas to find Interplanar Spacing

Other formulas in Crystal Lattice category

How to Evaluate Interplanar Spacing of Crystal given Lattice Parameter?

FAQs on Interplanar Spacing of Crystal given Lattice Parameter

Variable Name

GoInterplanar Spacing of Crystal Formula