Miller index along X-axis using Weiss Indices Solution

STEP 0: Pre-Calculation Summary
Formula Used
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
h = lcm(ax-axis,b,c)/ax-axis
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 x-axis - The Miller Index along x-axis form a notation system in crystallography for planes in crystal (Bravais) lattices along the x-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
h = lcm(ax-axis,b,c)/ax-axis --> lcm(3,9,5)/3
Evaluating ... ...
h = 15
STEP 3: Convert Result to Output's Unit
15 --> No Conversion Required
FINAL ANSWER
15 <-- Miller Index along x-axis
(Calculation completed in 00.020 seconds)

Credits

Created by Prerana Bakli
University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA
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Verified by Akshada Kulkarni
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 X-axis using Weiss Indices Formula

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
h = lcm(ax-axis,b,c)/ax-axis

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 X-axis using Weiss Indices?

Miller index along X-axis using Weiss Indices calculator uses 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 to calculate the Miller Index along x-axis, The Miller index along X-axis using Weiss Indices form a notation system in crystallography for planes in crystal (Bravais) lattices along the x-direction. Miller Index along x-axis is denoted by h symbol.

How to calculate Miller index along X-axis using Weiss Indices using this online calculator? To use this online calculator for Miller index along X-axis using Weiss Indices, enter Weiss Index along x-axis (ax-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 X-axis using Weiss Indices calculation can be explained with given input values -> 15 = lcm(3,9,5)/3.

FAQ

What is Miller index along X-axis using Weiss Indices?
The Miller index along X-axis using Weiss Indices form a notation system in crystallography for planes in crystal (Bravais) lattices along the x-direction and is represented as h = lcm(ax-axis,b,c)/ax-axis or 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. 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 X-axis using Weiss Indices?
The Miller index along X-axis using Weiss Indices form a notation system in crystallography for planes in crystal (Bravais) lattices along the x-direction is calculated using 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. To calculate Miller index along X-axis using Weiss Indices, you need Weiss Index along x-axis (ax-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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