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Interplanar Distance in Cubic Crystal Lattice Formula

GoInterplanar Distance in Tetragonal Crystal Lattice Formula

GoInterplanar Distance in Hexagonal Crystal Lattice 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 - Edge Length?h - Miller Index along x-axis?k - Miller Index along y-axis?l - Miller Index along z-axis?

Interplanar Distance in Cubic Crystal Lattice Example

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Here is how the Interplanar Distance in Cubic Crystal Lattice equation looks like with Values.

Here is how the Interplanar Distance in Cubic Crystal Lattice equation looks like with Units.

Here is how the Interplanar Distance in Cubic Crystal Lattice equation looks like.

0.6773 = \frac{100}{\sqrt{(9^{2}) + (4^{2}) + (11^{2})}}

0.6773nm = \frac{100A}{\sqrt{(9^{2}) + (4^{2}) + (11^{2})}}

0.6773 = \frac{100}{\sqrt{(9^{2}) + (4^{2}) + (11^{2})}}

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Interplanar Distance in Cubic Crystal Lattice Solution

Follow our step by step solution on how to calculate Interplanar Distance in Cubic Crystal Lattice?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

d = \frac{100A}{\sqrt{(9^{2}) + (4^{2}) + (11^{2})}}

Next Step Convert Units

∴

d = \frac{1E-8m}{\sqrt{(9^{2}) + (4^{2}) + (11^{2})}}

Next Step Prepare to Evaluate

∴

d = \frac{1E-8}{\sqrt{(9^{2}) + (4^{2}) + (11^{2})}}

Next Step Evaluate

∴

d = 6.77285461478596E-10m

Next Step Convert to Output's Unit

∴

d = 0.677285461478596nm

LAST Step Rounding Answer

∴

d = 0.6773nm

Interplanar Distance in Cubic Crystal Lattice 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

Edge Length

The Edge length is the length of the edge of the unit cell.

Symbol: a

Measurement: LengthUnit: A

Note: Value can be positive or negative.

Formulas to find Edge Length

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.

Symbol: h

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Miller Index along x-axis

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.

Symbol: k

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Miller Index along y-axis

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.

Symbol: l

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Miller Index along z-axis

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 Distance in Tetragonal Crystal Lattice

d = \sqrt{\frac{1}{(\frac{(h^{2}) + (k^{2})}{{a lattice}^{2}}) + (\frac{l^{2}}{c^{2}})}}

Go Interplanar Distance in Hexagonal Crystal Lattice

d = \sqrt{\frac{1}{(\frac{(\frac{4}{3}) \cdot ((h^{2}) + (h \cdot k) + (k^{2}))}{{a lattice}^{2}}) + (\frac{l^{2}}{c^{2}})}}

Go Interplanar Distance in Rhombohedral Crystal Lattice

d = \sqrt{\frac{1}{\frac{(((h^{2}) + (k^{2}) + (l^{2})) \cdot ({\sin (α)}^{2})) + (((h \cdot k) + (k \cdot l) + (h \cdot l)) \cdot 2 \cdot ({\cos (α)}^{2})) - \cos (α)}{{a lattice}^{2} \cdot (1 - (3 \cdot ({\cos (α)}^{2})) + (2 \cdot ({\cos (α)}^{3})))}}}

Go Interplanar Distance in Orthorhombic Crystal Lattice

d = \sqrt{\frac{1}{(\frac{h^{2}}{{a lattice}^{2}}) + (\frac{k^{2}}{b^{2}}) + (\frac{l^{2}}{c^{2}})}}

Other formulas in Inter Planar Distance and Inter Planar Angle category

Go Interplanar Angle for Simple Cubic System

θ = a \cos (\frac{(h 1 \cdot h 2) + (k 1 \cdot k 2) + (l 1 \cdot l 2)}{\sqrt{({h 1}^{2}) + ({k 1}^{2}) + ({l 1}^{2})} \cdot \sqrt{({h 2}^{2}) + ({k 2}^{2}) + ({l 2}^{2})}})

Go Interplanar Angle for Orthorhombic System

θ = a \cos (\frac{(\frac{h 1 \cdot h 2}{{a lattice}^{2}}) + (\frac{l 1 \cdot l 2}{c^{2}}) + (\frac{k 1 \cdot k 2}{b^{2}})}{\sqrt{((\frac{{h 1}^{2}}{{a lattice}^{2}}) + (\frac{{k 1}^{2}}{b^{2}}) \cdot (\frac{{l 1}^{2}}{c^{2}})) \cdot ((\frac{{h 2}^{2}}{{a lattice}^{2}}) + (\frac{{k 1}^{2}}{b^{2}}) + (\frac{{l 1}^{2}}{c^{2}}))}})

Go Interplanar Angle for Hexagonal System

θ = a \cos (\frac{(h 1 \cdot h 2) + (k 1 \cdot k 2) + (0.5 \cdot ((h 1 \cdot k 2) + (h 2 \cdot k 1))) + ((\frac{3}{4}) \cdot (\frac{{a lattice}^{2}}{c^{2}}) \cdot l 1 \cdot l 2)}{\sqrt{(({h 1}^{2}) + ({k 1}^{2}) + (h 1 \cdot k 1) + ((\frac{3}{4}) \cdot (\frac{{a lattice}^{2}}{c^{2}}) \cdot ({l 1}^{2}))) \cdot (({h 2}^{2}) + ({k 2}^{2}) + (h 2 \cdot k 2) + ((\frac{3}{4}) \cdot (\frac{{a lattice}^{2}}{c^{2}}) \cdot ({l 2}^{2})))}})

How to Evaluate Interplanar Distance in Cubic Crystal Lattice?

Interplanar Distance in Cubic Crystal Lattice evaluator 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 evaluate 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 evaluate Interplanar Distance in Cubic Crystal Lattice using this online evaluator? To use this online evaluator 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.

FAQs on Interplanar Distance in Cubic Crystal Lattice

What is the formula to find Interplanar Distance in Cubic Crystal Lattice?

The formula of Interplanar Distance in Cubic Crystal Lattice is expressed as Interplanar Spacing = Edge Length/sqrt((Miller Index along x-axis^2)+(Miller Index along y-axis^2)+(Miller Index along z-axis^2)). Here is an example- 6.8E+8 = 1E-08/sqrt((9^2)+(4^2)+(11^2)).

How to calculate Interplanar Distance in Cubic Crystal Lattice?

With Edge Length (a), Miller Index along x-axis (h), Miller Index along y-axis (k) & Miller Index along z-axis (l) we can find Interplanar Distance in Cubic Crystal Lattice using the formula - Interplanar Spacing = Edge Length/sqrt((Miller Index along x-axis^2)+(Miller Index along y-axis^2)+(Miller Index along z-axis^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=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))))))

Can the Interplanar Distance in Cubic Crystal Lattice be negative?

No, the Interplanar Distance in Cubic Crystal Lattice, measured in Wavelength cannot be negative.

Which unit is used to measure Interplanar Distance in Cubic Crystal Lattice?

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

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Interplanar Distance in Cubic Crystal Lattice Formula

​GoInterplanar Distance in Tetragonal Crystal Lattice Formula

​GoInterplanar Distance in Hexagonal Crystal Lattice Formula

Interplanar Distance in Cubic Crystal Lattice Example

Interplanar Distance in Cubic Crystal Lattice Solution

Interplanar Distance in Cubic Crystal Lattice Formula Elements

Other Formulas to find Interplanar Spacing

Other formulas in Inter Planar Distance and Inter Planar Angle category

How to Evaluate Interplanar Distance in Cubic Crystal Lattice?

FAQs on Interplanar Distance in Cubic Crystal Lattice

Variable Name

GoInterplanar Distance in Tetragonal Crystal Lattice Formula

GoInterplanar Distance in Hexagonal Crystal Lattice Formula