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Interplanar 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{(\frac{4}{3}) \cdot ((h^{2}) + (h \cdot k) + (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 Hexagonal Crystal Lattice Example

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

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

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

0.0833 = \sqrt{\frac{1}{(\frac{(\frac{4}{3}) \cdot ((9^{2}) + (9 \cdot 4) + (4^{2}))}{14^{2}}) + (\frac{11^{2}}{15^{2}})}}

0.0833nm = \sqrt{\frac{1}{(\frac{(\frac{4}{3}) \cdot ((9^{2}) + (9 \cdot 4) + (4^{2}))}{{14A}^{2}}) + (\frac{11^{2}}{{15A}^{2}})}}

0.0833 = \sqrt{\frac{1}{(\frac{(\frac{4}{3}) \cdot ((9^{2}) + (9 \cdot 4) + (4^{2}))}{14^{2}}) + (\frac{11^{2}}{15^{2}})}}

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

Interplanar Distance in Hexagonal Crystal Lattice Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

d = \sqrt{\frac{1}{(\frac{(\frac{4}{3}) \cdot ((9^{2}) + (9 \cdot 4) + (4^{2}))}{{14A}^{2}}) + (\frac{11^{2}}{{15A}^{2}})}}

Next Step Convert Units

∴

d = \sqrt{\frac{1}{(\frac{(\frac{4}{3}) \cdot ((9^{2}) + (9 \cdot 4) + (4^{2}))}{{1.4E-9m}^{2}}) + (\frac{11^{2}}{{1.5E-9m}^{2}})}}

Next Step Prepare to Evaluate

∴

d = \sqrt{\frac{1}{(\frac{(\frac{4}{3}) \cdot ((9^{2}) + (9 \cdot 4) + (4^{2}))}{{1.4E-9}^{2}}) + (\frac{11^{2}}{{1.5E-9}^{2}})}}

Next Step Evaluate

∴

d = 8.32599442100411E-11m

Next Step Convert to Output's Unit

∴

d = 0.0832599442100411nm

LAST Step Rounding Answer

∴

d = 0.0833nm

Interplanar Distance in Hexagonal 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

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