Miller index along Y-axis using Weiss Indices Calculator

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Density of different Cubic Cell

Inter-planar distance and inter-planar angle

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Volume of Different Cubic Cell

✖The Weiss Index along x-axis give an approximate indication of a face orientation with respect to the crystallographic x-axis.ⓘ Weiss Index along x-axis [a_x-axis]			+10% -10%
✖The Weiss Index along y-axis give an approximate indication of a face orientation with respect to the crystallographic y-axis.ⓘ Weiss Index along y-axis [b]			+10% -10%
✖The Weiss Index along z-axis give an approximate indication of a face orientation with respect to the crystallographic z-axis.ⓘ Weiss Index Along z-axis [c]			+10% -10%

✖The Miller Index along y-axis form a notation system in crystallography for planes in crystal (Bravais) lattices along the y-direction.ⓘ Miller index along Y-axis using Weiss Indices [k]

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Formula

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Miller index along Y-axis using Weiss Indices

Formula

`"k" = lcm("a"_{"x-axis"},"b","c")/"b"`

Example

`"5"=lcm("3","9","5")/"9"`

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Miller index along Y-axis using Weiss Indices Solution

STEP 0: Pre-Calculation Summary

Formula Used

Miller Index along y-axis = lcm(Weiss Index along x-axis,Weiss Index along y-axis,Weiss Index Along z-axis)/Weiss Index along y-axis
k = lcm(a_x-axis,b,c)/b
This formula uses 1 Functions, 4 Variables

Functions Used

lcm - LCM of any two is the value that is evenly divisible by the two given numbers., lcm(a1, …, an)

Variables Used

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.
Weiss Index along x-axis - The Weiss Index along x-axis give an approximate indication of a face orientation with respect to the crystallographic x-axis.
Weiss Index along y-axis - The Weiss Index along y-axis give an approximate indication of a face orientation with respect to the crystallographic y-axis.
Weiss Index Along z-axis - The Weiss Index along z-axis give an approximate indication of a face orientation with respect to the crystallographic z-axis.

STEP 1: Convert Input(s) to Base Unit

Weiss Index along x-axis: 3 --> No Conversion Required
Weiss Index along y-axis: 9 --> No Conversion Required
Weiss Index Along z-axis: 5 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

k = lcm(a_x-axis,b,c)/b --> lcm(3,9,5)/9

Evaluating ... ...

k = 5

STEP 3: Convert Result to Output's Unit

5 --> No Conversion Required

FINAL ANSWER

5 <-- Miller Index along y-axis

(Calculation completed in 00.004 seconds)

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Created by Prerana Bakli

University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA

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National Institute of Information Technology (NIIT), Neemrana

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< 24 Lattice Calculators

Miller index along X-axis using Weiss Indices

Go Miller Index along x-axis = lcm(Weiss Index along x-axis,Weiss Index along y-axis,Weiss Index Along z-axis)/Weiss Index along x-axis

Miller index along Y-axis using Weiss Indices

Go Miller Index along y-axis = lcm(Weiss Index along x-axis,Weiss Index along y-axis,Weiss Index Along z-axis)/Weiss Index along y-axis

Miller index along Z-axis using Weiss Indices

Go Miller Index along z-axis = lcm(Weiss Index along x-axis,Weiss Index along y-axis,Weiss Index Along z-axis)/Weiss Index Along z-axis

Edge Length using Interplanar Distance of Cubic Crystal

Go Edge Length = Interplanar Spacing*sqrt((Miller Index along x-axis^2)+(Miller Index along y-axis^2)+(Miller Index along z-axis^2))

Fraction of impurity in lattice terms of Energy

Go Fraction of Impurities = exp(-Energy required per impurity/([R]*Temperature))

Energy per impurity

Go Energy required per impurity = -ln(Fraction of Impurities)*[R]*Temperature

Fraction of Vacancy in lattice terms of Energy

Go Fraction of Vacancy = exp(-Energy Required per Vacancy/([R]*Temperature))

Energy per vacancy

Go Energy Required per Vacancy = -ln(Fraction of Vacancy)*[R]*Temperature

Packing Efficiency

Go Packing Efficiency = (Volume Occupied by Spheres in Unit Cell/Total Volume of Unit Cell)*100

Number of lattice containing impurities

Go No. of Lattice Occupied by Impurities = Fraction of Impurities*Total no. of lattice points

Fraction of impurity in lattice

Go Fraction of Impurities = No. of Lattice Occupied by Impurities/Total no. of lattice points

Fraction of Vacancy in lattice

Go Fraction of Vacancy = Number of Vacant Lattice/Total no. of lattice points

Number of vacant lattice

Go Number of Vacant Lattice = Fraction of Vacancy*Total no. of lattice points

Weiss Index along X-axis using Miller Indices

Go Weiss Index along x-axis = LCM of Weiss Indices/Miller Index along x-axis

Weiss Index along Y-axis using Miller Indices

Go Weiss Index along y-axis = LCM of Weiss Indices/Miller Index along y-axis

Weiss Index along Z-axis using Miller Indices

Go Weiss Index Along z-axis = LCM of Weiss Indices/Miller Index along z-axis

Radius of Constituent Particle in BCC lattice

Go Radius of Constituent Particle = 3*sqrt(3)*Edge Length/4

Edge length of Body Centered Unit Cell

Go Edge Length = 4*Radius of Constituent Particle/sqrt(3)

Edge Length of Face Centered Unit Cell

Go Edge Length = 2*sqrt(2)*Radius of Constituent Particle

Radius Ratio

Go Radius Ratio = Radius of Cation/Radius of Anion

Number of Tetrahedral Voids

Go Number of Tetrahedral Voids = 2*Number of Closed Packed Spheres

Radius of Constituent Particle in FCC lattice

Go Radius of Constituent Particle = Edge Length/2.83

Radius of Constituent particle in Simple Cubic Unit Cell

Go Radius of Constituent Particle = Edge Length/2

Edge length of Simple cubic unit cell

Go Edge Length = 2*Radius of Constituent Particle

Miller index along Y-axis using Weiss Indices Formula

Miller Index along y-axis = lcm(Weiss Index along x-axis,Weiss Index along y-axis,Weiss Index Along z-axis)/Weiss Index along y-axis
k = lcm(a_x-axis,b,c)/b

How to convert Weiss Indices into Miller Indices?

The Weiss parameters, introduced by Christian Samuel Weiss in 1817, are the ancestors of the Miller indices. They give an approximate indication of a face orientation with respect to the crystallographic axes, and were used as a symbol for the face.
Now that we know the equation of a plane in space, the rules for Miller Indices are a little more intelligible. They are:
- Determine the intercepts of the face along the crystallographic axes, in terms of unit cell dimensions.
- Take the reciprocals
- Clear fractions
- Reduce to lowest terms
If a plane is parallel to an axis, its intercept is at infinity and its Miller index is zero. A generic Miller index is denoted by (hkl).

How to Calculate Miller index along Y-axis using Weiss Indices?

Miller index along Y-axis using Weiss Indices calculator uses Miller Index along y-axis = lcm(Weiss Index along x-axis,Weiss Index along y-axis,Weiss Index Along z-axis)/Weiss Index along y-axis to calculate the Miller Index along y-axis, The Miller index along Y-axis using Weiss Indices form a notation system in crystallography for planes in crystal (Bravais) lattices along the y-direction. Miller Index along y-axis is denoted by k symbol.

How to calculate Miller index along Y-axis using Weiss Indices using this online calculator? To use this online calculator for Miller index along Y-axis using Weiss Indices, enter Weiss Index along x-axis (a_x-axis), Weiss Index along y-axis (b) & Weiss Index Along z-axis (c) and hit the calculate button. Here is how the Miller index along Y-axis using Weiss Indices calculation can be explained with given input values -> 5 = lcm(3,9,5)/9.

FAQ

What is Miller index along Y-axis using Weiss Indices?

The Miller index along Y-axis using Weiss Indices form a notation system in crystallography for planes in crystal (Bravais) lattices along the y-direction and is represented as k = lcm(a_x-axis,b,c)/b or Miller Index along y-axis = lcm(Weiss Index along x-axis,Weiss Index along y-axis,Weiss Index Along z-axis)/Weiss Index along y-axis. The Weiss Index along x-axis give an approximate indication of a face orientation with respect to the crystallographic x-axis, The Weiss Index along y-axis give an approximate indication of a face orientation with respect to the crystallographic y-axis & The Weiss Index along z-axis give an approximate indication of a face orientation with respect to the crystallographic z-axis.

How to calculate Miller index along Y-axis using Weiss Indices?

The Miller index along Y-axis using Weiss Indices form a notation system in crystallography for planes in crystal (Bravais) lattices along the y-direction is calculated using Miller Index along y-axis = lcm(Weiss Index along x-axis,Weiss Index along y-axis,Weiss Index Along z-axis)/Weiss Index along y-axis. To calculate Miller index along Y-axis using Weiss Indices, you need Weiss Index along x-axis (a_x-axis), Weiss Index along y-axis (b) & Weiss Index Along z-axis (c). With our tool, you need to enter the respective value for Weiss Index along x-axis, Weiss Index along y-axis & Weiss Index Along z-axis and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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