Weiss Index along X-axis using Miller Indices Solution

STEP 0: Pre-Calculation Summary
Formula Used
Weiss Index along x-axis = LCM of Weiss Indices/Miller Index along x-axis
ax-axis = LCMw/h
This formula uses 3 Variables
Variables Used
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.
LCM of Weiss Indices - The LCM of Weiss Indices is the least common multiple of Weiss indices a, b, c ,i.e, along x, y, z axes respectively.
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.
STEP 1: Convert Input(s) to Base Unit
LCM of Weiss Indices: 6 --> No Conversion Required
Miller Index along x-axis: 9 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ax-axis = LCMw/h --> 6/9
Evaluating ... ...
ax-axis = 0.666666666666667
STEP 3: Convert Result to Output's Unit
0.666666666666667 --> No Conversion Required
FINAL ANSWER
0.666666666666667 0.666667 <-- Weiss Index along x-axis
(Calculation completed in 00.004 seconds)

Credits

Created by Prerana Bakli
University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA
Prerana Bakli has created this Calculator and 800+ more calculators!
Verified by Akshada Kulkarni
National Institute of Information Technology (NIIT), Neemrana
Akshada Kulkarni has verified this Calculator and 900+ more calculators!

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

Weiss Index along X-axis using Miller Indices Formula

Weiss Index along x-axis = LCM of Weiss Indices/Miller Index along x-axis
ax-axis = LCMw/h

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 Weiss Index along X-axis using Miller Indices?

Weiss Index along X-axis using Miller Indices calculator uses Weiss Index along x-axis = LCM of Weiss Indices/Miller Index along x-axis to calculate the Weiss Index along x-axis, The Weiss Index along X-axis using Miller Indices gives an approximate indication of a face orientation with respect to the crystallographic x-axis. Weiss Index along x-axis is denoted by ax-axis symbol.

How to calculate Weiss Index along X-axis using Miller Indices using this online calculator? To use this online calculator for Weiss Index along X-axis using Miller Indices, enter LCM of Weiss Indices (LCMw) & Miller Index along x-axis (h) and hit the calculate button. Here is how the Weiss Index along X-axis using Miller Indices calculation can be explained with given input values -> 0.666667 = 6/9.

FAQ

What is Weiss Index along X-axis using Miller Indices?
The Weiss Index along X-axis using Miller Indices gives an approximate indication of a face orientation with respect to the crystallographic x-axis and is represented as ax-axis = LCMw/h or Weiss Index along x-axis = LCM of Weiss Indices/Miller Index along x-axis. The LCM of Weiss Indices is the least common multiple of Weiss indices a, b, c ,i.e, along x, y, z axes respectively & The Miller Index along x-axis form a notation system in crystallography for planes in crystal (Bravais) lattices along the x-direction.
How to calculate Weiss Index along X-axis using Miller Indices?
The Weiss Index along X-axis using Miller Indices gives an approximate indication of a face orientation with respect to the crystallographic x-axis is calculated using Weiss Index along x-axis = LCM of Weiss Indices/Miller Index along x-axis. To calculate Weiss Index along X-axis using Miller Indices, you need LCM of Weiss Indices (LCMw) & Miller Index along x-axis (h). With our tool, you need to enter the respective value for LCM of Weiss Indices & Miller Index along x-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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