FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Interplanar Angle for Simple Cubic System Formula

GoInterplanar Angle for Orthorhombic System Formula

GoInterplanar Angle for Hexagonal System Formula

Fx Copy

LaTeX Copy

The Interplanar Angle is the angle, f between two planes, (h1, k1, l1) and (h2, k2, l2). Check FAQs

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})}})

θ - Interplanar Angle?h₁ - Miller Index along plane 1?h₂ - Miller Index h along plane 2?k₁ - Miller Index k along Plane 1?k₂ - Miller Index k along Plane 2?l₁ - Miller Index l along plane 1?l₂ - Miller Index l along plane 2?

Interplanar Angle for Simple Cubic System Example

With values

With units

Only example

Here is how the Interplanar Angle for Simple Cubic System equation looks like with Values.

Here is how the Interplanar Angle for Simple Cubic System equation looks like with Units.

Here is how the Interplanar Angle for Simple Cubic System equation looks like.

2.7558 = a \cos (\frac{(5 \cdot 8) + (3 \cdot 6) + (16 \cdot 25)}{\sqrt{(5^{2}) + (3^{2}) + (16^{2})} \cdot \sqrt{(8^{2}) + (6^{2}) + (25^{2})}})

2.7558° = a \cos (\frac{(5 \cdot 8) + (3 \cdot 6) + (16 \cdot 25)}{\sqrt{(5^{2}) + (3^{2}) + (16^{2})} \cdot \sqrt{(8^{2}) + (6^{2}) + (25^{2})}})

2.7558 = a \cos (\frac{(5 \cdot 8) + (3 \cdot 6) + (16 \cdot 25)}{\sqrt{(5^{2}) + (3^{2}) + (16^{2})} \cdot \sqrt{(8^{2}) + (6^{2}) + (25^{2})}})

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Chemistry » Category

Solid State Chemistry » Category

Inter Planar Distance and Inter Planar Angle » fx Interplanar Angle for Simple Cubic System

Interplanar Angle for Simple Cubic System Solution

Follow our step by step solution on how to calculate Interplanar Angle for Simple Cubic System?

FIRST Step Consider the formula

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})}})

Next Step Substitute values of Variables

∴

θ = a \cos (\frac{(5 \cdot 8) + (3 \cdot 6) + (16 \cdot 25)}{\sqrt{(5^{2}) + (3^{2}) + (16^{2})} \cdot \sqrt{(8^{2}) + (6^{2}) + (25^{2})}})

Next Step Prepare to Evaluate

∴

θ = a \cos (\frac{(5 \cdot 8) + (3 \cdot 6) + (16 \cdot 25)}{\sqrt{(5^{2}) + (3^{2}) + (16^{2})} \cdot \sqrt{(8^{2}) + (6^{2}) + (25^{2})}})

Next Step Evaluate

∴

θ = 0.0480969557269001rad

Next Step Convert to Output's Unit

∴

θ = 2.75575257057947°

LAST Step Rounding Answer

∴

θ = 2.7558°

Interplanar Angle for Simple Cubic System Formula Elements

Variables

Functions

Interplanar Angle

The Interplanar Angle is the angle, f between two planes, (h1, k1, l1) and (h2, k2, l2).

Symbol: θ

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Interplanar Angle

Miller Index along plane 1

The Miller Index along plane 1 form a notation system in crystallography for planes in crystal (Bravais) lattices along the x-direction in plane 1.

Symbol: h₁

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Miller Index along plane 1

Miller Index h along plane 2

The Miller Index h along plane 2 form a notation system in crystallography for planes in crystal (Bravais) lattices along the x-direction in plane 2.

Symbol: h₂

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Miller Index h along plane 2

Miller Index k along Plane 1

The Miller Index k along plane 1 form a notation system in crystallography for planes in crystal (Bravais) lattices along the y-direction in plane 1.

Symbol: k₁

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Miller Index k along Plane 1

Miller Index k along Plane 2

The Miller Index k along plane 2 form a notation system in crystallography for planes in crystal (Bravais) lattices along the y-direction in plane 2.

Symbol: k₂

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Miller Index k along Plane 2

Miller Index l along plane 1

The Miller Index l along plane 1 form a notation system in crystallography for planes in crystal (Bravais) lattices along the z-direction in plane 1.

Symbol: l₁

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Miller Index l along plane 1

Miller Index l along plane 2

The Miller Index l along plane 2 form a notation system in crystallography for planes in crystal (Bravais) lattices along the z-direction in plane 2.

Symbol: l₂

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Miller Index l along plane 2

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

acos

The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio.

Syntax: acos(Number)

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 Angle

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})))}})

Other formulas in Inter Planar Distance and Inter Planar Angle category

Go Interplanar Distance in Cubic Crystal Lattice

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

Go Interplanar Distance in Tetragonal Crystal Lattice

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

How to Evaluate Interplanar Angle for Simple Cubic System?

Interplanar Angle for Simple Cubic System evaluator uses Interplanar Angle = acos(((Miller Index along plane 1*Miller Index h along plane 2)+(Miller Index k along Plane 1*Miller Index k along Plane 2)+(Miller Index l along plane 1*Miller Index l along plane 2))/(sqrt((Miller Index along plane 1^2)+(Miller Index k along Plane 1^2)+(Miller Index l along plane 1^2))*sqrt((Miller Index h along plane 2^2)+(Miller Index k along Plane 2^2)+(Miller Index l along plane 2^2)))) to evaluate the Interplanar Angle, The Interplanar angle for Simple Cubic system is the angle between two planes, (h1, k1, l1) and (h2, k2, l2) in a Simple Cubic system. Interplanar Angle is denoted by θ symbol.

How to evaluate Interplanar Angle for Simple Cubic System using this online evaluator? To use this online evaluator for Interplanar Angle for Simple Cubic System, enter Miller Index along plane 1 (h₁), Miller Index h along plane 2 (h₂), Miller Index k along Plane 1 (k₁), Miller Index k along Plane 2 (k₂), Miller Index l along plane 1 (l₁) & Miller Index l along plane 2 (l₂) and hit the calculate button.

FAQs on Interplanar Angle for Simple Cubic System

What is the formula to find Interplanar Angle for Simple Cubic System?

The formula of Interplanar Angle for Simple Cubic System is expressed as Interplanar Angle = acos(((Miller Index along plane 1*Miller Index h along plane 2)+(Miller Index k along Plane 1*Miller Index k along Plane 2)+(Miller Index l along plane 1*Miller Index l along plane 2))/(sqrt((Miller Index along plane 1^2)+(Miller Index k along Plane 1^2)+(Miller Index l along plane 1^2))*sqrt((Miller Index h along plane 2^2)+(Miller Index k along Plane 2^2)+(Miller Index l along plane 2^2)))). Here is an example- 157.893 = acos(((5*8)+(3*6)+(16*25))/(sqrt((5^2)+(3^2)+(16^2))*sqrt((8^2)+(6^2)+(25^2)))).

How to calculate Interplanar Angle for Simple Cubic System?

With Miller Index along plane 1 (h₁), Miller Index h along plane 2 (h₂), Miller Index k along Plane 1 (k₁), Miller Index k along Plane 2 (k₂), Miller Index l along plane 1 (l₁) & Miller Index l along plane 2 (l₂) we can find Interplanar Angle for Simple Cubic System using the formula - Interplanar Angle = acos(((Miller Index along plane 1*Miller Index h along plane 2)+(Miller Index k along Plane 1*Miller Index k along Plane 2)+(Miller Index l along plane 1*Miller Index l along plane 2))/(sqrt((Miller Index along plane 1^2)+(Miller Index k along Plane 1^2)+(Miller Index l along plane 1^2))*sqrt((Miller Index h along plane 2^2)+(Miller Index k along Plane 2^2)+(Miller Index l along plane 2^2)))). This formula also uses Cosine (cos)Inverse Cosine (acos), Square Root (sqrt) function(s).

What are the other ways to Calculate Interplanar Angle?

Here are the different ways to Calculate Interplanar Angle-

Interplanar Angle=acos((((Miller Index along plane 1*Miller Index h along plane 2)/(Lattice Constant a^2))+((Miller Index l along plane 1*Miller Index l along plane 2)/(Lattice Constant c^2))+((Miller Index k along Plane 1*Miller Index k along Plane 2)/(Lattice Constant b^2)))/sqrt((((Miller Index along plane 1^2)/(Lattice Constant a^2))+((Miller Index k along Plane 1^2)/(Lattice Constant b^2))*((Miller Index l along plane 1^2)/(Lattice Constant c^2)))*(((Miller Index h along plane 2^2)/(Lattice Constant a^2))+((Miller Index k along Plane 1^2)/(Lattice Constant b^2))+((Miller Index l along plane 1^2)/(Lattice Constant c^2)))))
Interplanar Angle=acos(((Miller Index along plane 1*Miller Index h along plane 2)+(Miller Index k along Plane 1*Miller Index k along Plane 2)+(0.5*((Miller Index along plane 1*Miller Index k along Plane 2)+(Miller Index h along plane 2*Miller Index k along Plane 1)))+((3/4)*((Lattice Constant a^2)/(Lattice Constant c^2))*Miller Index l along plane 1*Miller Index l along plane 2))/(sqrt(((Miller Index along plane 1^2)+(Miller Index k along Plane 1^2)+(Miller Index along plane 1*Miller Index k along Plane 1)+((3/4)*((Lattice Constant a^2)/(Lattice Constant c^2))*(Miller Index l along plane 1^2)))*((Miller Index h along plane 2^2)+(Miller Index k along Plane 2^2)+(Miller Index h along plane 2*Miller Index k along Plane 2)+((3/4)*((Lattice Constant a^2)/(Lattice Constant c^2))*(Miller Index l along plane 2^2))))))

Can the Interplanar Angle for Simple Cubic System be negative?

Yes, the Interplanar Angle for Simple Cubic System, measured in Angle can be negative.

Which unit is used to measure Interplanar Angle for Simple Cubic System?

Interplanar Angle for Simple Cubic System is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Interplanar Angle for Simple Cubic System can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!

Interplanar Angle for Simple Cubic System Formula

​GoInterplanar Angle for Orthorhombic System Formula

​GoInterplanar Angle for Hexagonal System Formula

Interplanar Angle for Simple Cubic System Example

Interplanar Angle for Simple Cubic System Solution

Interplanar Angle for Simple Cubic System Formula Elements

Other Formulas to find Interplanar Angle

Other formulas in Inter Planar Distance and Inter Planar Angle category

How to Evaluate Interplanar Angle for Simple Cubic System?

FAQs on Interplanar Angle for Simple Cubic System

Variable Name

GoInterplanar Angle for Orthorhombic System Formula

GoInterplanar Angle for Hexagonal System Formula