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Interplanar Distance in Tetragonal Crystal Lattice Formula

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GoInterplanar Distance in Cubic Crystal Lattice Formula

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

d - Interplanar Spacing?h - Miller Index along x-axis?k - Miller Index along y-axis?a_lattice - Lattice Constant a?l - Miller Index along z-axis?c - Lattice Constant c?

Interplanar Distance in Tetragonal Crystal Lattice Example

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

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

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

0.0984 = \sqrt{\frac{1}{(\frac{(9^{2}) + (4^{2})}{14^{2}}) + (\frac{11^{2}}{15^{2}})}}

0.0984nm = \sqrt{\frac{1}{(\frac{(9^{2}) + (4^{2})}{{14A}^{2}}) + (\frac{11^{2}}{{15A}^{2}})}}

0.0984 = \sqrt{\frac{1}{(\frac{(9^{2}) + (4^{2})}{14^{2}}) + (\frac{11^{2}}{15^{2}})}}

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Inter Planar Distance and Inter Planar Angle » fx Interplanar Distance in Tetragonal Crystal Lattice

Interplanar Distance in Tetragonal Crystal Lattice Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

d = \sqrt{\frac{1}{(\frac{(9^{2}) + (4^{2})}{{14A}^{2}}) + (\frac{11^{2}}{{15A}^{2}})}}

Next Step Convert Units

∴

d = \sqrt{\frac{1}{(\frac{(9^{2}) + (4^{2})}{{1.4E-9m}^{2}}) + (\frac{11^{2}}{{1.5E-9m}^{2}})}}

Next Step Prepare to Evaluate

∴

d = \sqrt{\frac{1}{(\frac{(9^{2}) + (4^{2})}{{1.4E-9}^{2}}) + (\frac{11^{2}}{{1.5E-9}^{2}})}}

Next Step Evaluate

∴

d = 9.84051920752373E-11m

Next Step Convert to Output's Unit

∴

d = 0.0984051920752373nm

LAST Step Rounding Answer

∴

d = 0.0984nm

Interplanar Distance in Tetragonal 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

Open Variable

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

Open Variable

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

Open Variable

Lattice Constant a

The Lattice Constant a refers to the physical dimension of unit cells in a crystal lattice along x-axis.

Symbol: a_lattice

Measurement: LengthUnit: A

Note: Value can be positive or negative.

Formulas to find Lattice Constant a

Open Variable

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

Open Variable

Lattice Constant c

The Lattice Constant c refers to the physical dimension of unit cells in a crystal lattice along z-axis.

Symbol: c

Measurement: LengthUnit: A

Note: Value can be positive or negative.

Formulas to find Lattice Constant c

Open Variable

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 Cubic Crystal Lattice

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

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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 Tetragonal Crystal Lattice?

Interplanar Distance in Tetragonal Crystal Lattice evaluator uses 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)))) to evaluate the Interplanar Spacing, The Interplanar Distance in Tetragonal 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 Tetragonal Crystal Lattice using this online evaluator? To use this online evaluator for Interplanar Distance in Tetragonal Crystal Lattice, enter Miller Index along x-axis (h), Miller Index along y-axis (k), Lattice Constant a (a_lattice), Miller Index along z-axis (l) & Lattice Constant c (c) and hit the calculate button.

FAQs on Interplanar Distance in Tetragonal Crystal Lattice

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

The formula of Interplanar Distance in Tetragonal Crystal Lattice is expressed as 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)))). Here is an example- 9.8E+7 = sqrt(1/((((9^2)+(4^2))/(1.4E-09^2))+((11^2)/(1.5E-09^2)))).

How to calculate Interplanar Distance in Tetragonal Crystal Lattice?

With Miller Index along x-axis (h), Miller Index along y-axis (k), Lattice Constant a (a_lattice), Miller Index along z-axis (l) & Lattice Constant c (c) we can find Interplanar Distance in Tetragonal Crystal Lattice using the formula - 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)))). 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=Edge Length/sqrt((Miller Index along x-axis^2)+(Miller Index along y-axis^2)+(Miller Index along z-axis^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 Tetragonal Crystal Lattice be negative?

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

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

Interplanar Distance in Tetragonal 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 Tetragonal Crystal Lattice can be measured.

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