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Interplanar Spacing is the distance between adjacent and parallel planes of the crystal. Check FAQs
d=1(h2alattice2)+((k2)⋅(sin(β)2)b2)+(l2c2)-(2⋅h⋅l⋅cos(β)alattice⋅c)(sin(β))2
d - Interplanar Spacing?h - Miller Index along x-axis?alattice - Lattice Constant a?k - Miller Index along y-axis?β - Lattice Parameter Beta?b - Lattice Constant b?l - Miller Index along z-axis?c - Lattice Constant c?

Interplanar Distance in Monoclinic Crystal Lattice Example

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

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

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

0.1236Edit=1(9Edit214Edit2)+((4Edit2)⋅(sin(35Edit)2)12Edit2)+(11Edit215Edit2)-(2⋅9Edit⋅11Edit⋅cos(35Edit)14Edit⋅15Edit)(sin(35Edit))2
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HomeIcon Home » Category Chemistry » Category Solid State Chemistry » Category Inter Planar Distance and Inter Planar Angle » fx Interplanar Distance in Monoclinic Crystal Lattice

Interplanar Distance in Monoclinic Crystal Lattice Solution

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

FIRST Step Consider the formula
d=1(h2alattice2)+((k2)⋅(sin(β)2)b2)+(l2c2)-(2⋅h⋅l⋅cos(β)alattice⋅c)(sin(β))2
Next Step Substitute values of Variables
∴ d=1(9214A2)+((42)⋅(sin(35°)2)12A2)+(11215A2)-(2⋅9⋅11⋅cos(35°)14A⋅15A)(sin(35°))2
Next Step Convert Units
∴ d=1(921.4E-9m2)+((42)⋅(sin(0.6109rad)2)1.2E-9m2)+(1121.5E-9m2)-(2⋅9⋅11⋅cos(0.6109rad)1.4E-9m⋅1.5E-9m)(sin(0.6109rad))2
Next Step Prepare to Evaluate
∴ d=1(921.4E-92)+((42)⋅(sin(0.6109)2)1.2E-92)+(1121.5E-92)-(2⋅9⋅11⋅cos(0.6109)1.4E-9⋅1.5E-9)(sin(0.6109))2
Next Step Evaluate
∴d=1.23627623337386E-10m
Next Step Convert to Output's Unit
∴d=0.123627623337386nm
LAST Step Rounding Answer
∴d=0.1236nm

Interplanar Distance in Monoclinic 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 SpacingOpen 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-axisOpen Variable
Lattice Constant a
The Lattice Constant a refers to the physical dimension of unit cells in a crystal lattice along x-axis.
Symbol: alattice
Measurement: LengthUnit: A
Note: Value can be positive or negative.
Formulas to find Lattice Constant aOpen 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-axisOpen Variable
Lattice Parameter Beta
The Lattice Parameter Beta is the angle between lattice constants a and c.
Symbol: β
Measurement: AngleUnit: °
Note: Value can be positive or negative.
Formulas to find Lattice Parameter BetaOpen Variable
Lattice Constant b
The Lattice Constant b refers to the physical dimension of unit cells in a crystal lattice along y-axis.
Symbol: b
Measurement: LengthUnit: A
Note: Value can be positive or negative.
Formulas to find Lattice Constant bOpen 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-axisOpen 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 cOpen Variable
sin
Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.
Syntax: sin(Angle)
cos
Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.
Syntax: cos(Angle)
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=a(h2)+(k2)+(l2)
​Go Interplanar Distance in Tetragonal Crystal Lattice
d=1((h2)+(k2)alattice2)+(l2c2)

Other formulas in Inter Planar Distance and Inter Planar Angle category

​Go Interplanar Angle for Simple Cubic System
θ=acos((h1⋅h2)+(k1⋅k2)+(l1⋅l2)(h12)+(k12)+(l12)⋅(h22)+(k22)+(l22))
​Go Interplanar Angle for Orthorhombic System
θ=acos((h1⋅h2alattice2)+(l1⋅l2c2)+(k1⋅k2b2)((h12alattice2)+(k12b2)⋅(l12c2))⋅((h22alattice2)+(k12b2)+(l12c2)))

How to Evaluate Interplanar Distance in Monoclinic Crystal Lattice?

Interplanar Distance in Monoclinic Crystal Lattice evaluator uses Interplanar Spacing = sqrt(1/((((Miller Index along x-axis^2)/(Lattice Constant a^2))+(((Miller Index along y-axis^2)*(sin(Lattice Parameter Beta)^2))/(Lattice Constant b^2))+((Miller Index along z-axis^2)/(Lattice Constant c^2))-(2*Miller Index along x-axis*Miller Index along z-axis*cos(Lattice Parameter Beta)/(Lattice Constant a*Lattice Constant c)))/((sin(Lattice Parameter Beta))^2))) to evaluate the Interplanar Spacing, The Interplanar Distance in Monoclinic 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 Monoclinic Crystal Lattice using this online evaluator? To use this online evaluator for Interplanar Distance in Monoclinic Crystal Lattice, enter Miller Index along x-axis (h), Lattice Constant a (alattice), Miller Index along y-axis (k), Lattice Parameter Beta (β), Lattice Constant b (b), Miller Index along z-axis (l) & Lattice Constant c (c) and hit the calculate button.

FAQs on Interplanar Distance in Monoclinic Crystal Lattice

What is the formula to find Interplanar Distance in Monoclinic Crystal Lattice?
The formula of Interplanar Distance in Monoclinic Crystal Lattice is expressed as Interplanar Spacing = sqrt(1/((((Miller Index along x-axis^2)/(Lattice Constant a^2))+(((Miller Index along y-axis^2)*(sin(Lattice Parameter Beta)^2))/(Lattice Constant b^2))+((Miller Index along z-axis^2)/(Lattice Constant c^2))-(2*Miller Index along x-axis*Miller Index along z-axis*cos(Lattice Parameter Beta)/(Lattice Constant a*Lattice Constant c)))/((sin(Lattice Parameter Beta))^2))). Here is an example- 1.2E+8 = sqrt(1/((((9^2)/(1.4E-09^2))+(((4^2)*(sin(0.610865238197901)^2))/(1.2E-09^2))+((11^2)/(1.5E-09^2))-(2*9*11*cos(0.610865238197901)/(1.4E-09*1.5E-09)))/((sin(0.610865238197901))^2))).
How to calculate Interplanar Distance in Monoclinic Crystal Lattice?
With Miller Index along x-axis (h), Lattice Constant a (alattice), Miller Index along y-axis (k), Lattice Parameter Beta (β), Lattice Constant b (b), Miller Index along z-axis (l) & Lattice Constant c (c) we can find Interplanar Distance in Monoclinic Crystal Lattice using the formula - Interplanar Spacing = sqrt(1/((((Miller Index along x-axis^2)/(Lattice Constant a^2))+(((Miller Index along y-axis^2)*(sin(Lattice Parameter Beta)^2))/(Lattice Constant b^2))+((Miller Index along z-axis^2)/(Lattice Constant c^2))-(2*Miller Index along x-axis*Miller Index along z-axis*cos(Lattice Parameter Beta)/(Lattice Constant a*Lattice Constant c)))/((sin(Lattice Parameter Beta))^2))). This formula also uses SineCosine, Square Root Function 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))OpenImg
  • 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))))OpenImg
  • 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))))OpenImg
Can the Interplanar Distance in Monoclinic Crystal Lattice be negative?
No, the Interplanar Distance in Monoclinic Crystal Lattice, measured in Wavelength cannot be negative.
Which unit is used to measure Interplanar Distance in Monoclinic Crystal Lattice?
Interplanar Distance in Monoclinic 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 Monoclinic Crystal Lattice can be measured.
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