Fraction of impurity in lattice terms of Energy Calculator

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Density of different Cubic Cell

Inter-planar distance and inter-planar angle

Lattice Direction

Volume of Different Cubic Cell

✖The Energy required per impurity is E is the energy required for occupancy of one impurity in the crystal lattice.ⓘ Energy required per impurity [ΔE]			+10% -10%
✖Temperature is the degree or intensity of heat present in a substance or object.ⓘ Temperature [T]			+10% -10%

✖The Fraction of Impurities is the ratio of crystal lattice occupied by impurity to total no. of crystal lattice.ⓘ Fraction of impurity in lattice terms of Energy [f]

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Formula

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Fraction of impurity in lattice terms of Energy

Formula

`"f" = exp(-"ΔE"/("[R]"*"T"))`

Example

`"0.492883"=exp(-"500J"/("[R]"*"85K"))`

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Fraction of impurity in lattice terms of Energy Solution

STEP 0: Pre-Calculation Summary

Formula Used

Fraction of Impurities = exp(-Energy required per impurity/([R]*Temperature))
f = exp(-ΔE/([R]*T))
This formula uses 1 Constants, 1 Functions, 3 Variables

Constants Used

[R] - Universal gas constant Value Taken As 8.31446261815324

Functions Used

exp - n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable., exp(Number)

Variables Used

Fraction of Impurities - The Fraction of Impurities is the ratio of crystal lattice occupied by impurity to total no. of crystal lattice.
Energy required per impurity - (Measured in Joule) - The Energy required per impurity is E is the energy required for occupancy of one impurity in the crystal lattice.
Temperature - (Measured in Kelvin) - Temperature is the degree or intensity of heat present in a substance or object.

STEP 1: Convert Input(s) to Base Unit

Energy required per impurity: 500 Joule --> 500 Joule No Conversion Required
Temperature: 85 Kelvin --> 85 Kelvin No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f = exp(-ΔE/([R]*T)) --> exp(-500/([R]*85))

Evaluating ... ...

f = 0.492882514112385

STEP 3: Convert Result to Output's Unit

0.492882514112385 --> No Conversion Required

FINAL ANSWER

0.492882514112385 ≈ 0.492883 <-- Fraction of Impurities

(Calculation completed in 00.007 seconds)

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Home » Chemistry » Solid State Chemistry » Lattice » Fraction of impurity in lattice terms of Energy

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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

Fraction of impurity in lattice terms of Energy Formula

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

What are defects in crystal?

The arrangement of the atoms in all materials contains imperfections which have profound effect on the behavior of the materials.
Lattice defects can be sorted into three
1. Point defects (vacancies, interstitial defects, substitution defects)
2. Line defect (screw dislocation, edge dislocation)
3. surface defects (material surface, grain boundaries)

Why defect are important?

There are a lot of properties that are controlled or affected by
defects, for example:
1. Electric and thermal conductivity in metals (strongly reduced by
point defects).
2. Electronic conductivity in semi-conductors (controlled by substitution
defects).
3. Diffusion (controlled by vacancies).
4. Ionic conductivity (controlled by vacancies).
5. Plastic deformation in crystalline materials (controlled by
dislocation).
6. Colors (affected by defects).
7. Mechanical strength (strongly depended on defects).

How to Calculate Fraction of impurity in lattice terms of Energy?

Fraction of impurity in lattice terms of Energy calculator uses Fraction of Impurities = exp(-Energy required per impurity/([R]*Temperature)) to calculate the Fraction of Impurities, The Fraction of impurity in lattice terms of Energy is the ratio of crystal lattice occupied by impurities to total number of crystal lattice. Fraction of Impurities is denoted by f symbol.

How to calculate Fraction of impurity in lattice terms of Energy using this online calculator? To use this online calculator for Fraction of impurity in lattice terms of Energy, enter Energy required per impurity (ΔE) & Temperature (T) and hit the calculate button. Here is how the Fraction of impurity in lattice terms of Energy calculation can be explained with given input values -> 0.492883 = exp(-500/([R]*85)).

FAQ

What is Fraction of impurity in lattice terms of Energy?

The Fraction of impurity in lattice terms of Energy is the ratio of crystal lattice occupied by impurities to total number of crystal lattice and is represented as f = exp(-ΔE/([R]*T)) or Fraction of Impurities = exp(-Energy required per impurity/([R]*Temperature)). The Energy required per impurity is E is the energy required for occupancy of one impurity in the crystal lattice & Temperature is the degree or intensity of heat present in a substance or object.

How to calculate Fraction of impurity in lattice terms of Energy?

The Fraction of impurity in lattice terms of Energy is the ratio of crystal lattice occupied by impurities to total number of crystal lattice is calculated using Fraction of Impurities = exp(-Energy required per impurity/([R]*Temperature)). To calculate Fraction of impurity in lattice terms of Energy, you need Energy required per impurity (ΔE) & Temperature (T). With our tool, you need to enter the respective value for Energy required per impurity & Temperature and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Fraction of Impurities?

In this formula, Fraction of Impurities uses Energy required per impurity & Temperature. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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