Energy per impurity Calculator

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Inter-planar distance and inter-planar angle

✖The Fraction of Impurities is the ratio of crystal lattice occupied by impurity to total no. of crystal lattice.ⓘ Fraction of Impurities [f]			+10% -10%
✖Temperature is the degree or intensity of heat present in a substance or object.ⓘ Temperature [T]			+10% -10%

✖The Energy required per impurity is E is the energy required for occupancy of one impurity in the crystal lattice.ⓘ Energy per impurity [ΔE]

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Formula

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Energy per impurity

Formula

`"ΔE" = -ln("f")*"[R]"*"T"`

Example

`"489.8674J"=-ln("0.5")*"[R]"*"85K"`

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Energy per impurity Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

[R] - Universal gas constant Value Taken As 8.31446261815324

Functions Used

ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)

Variables Used

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.
Fraction of Impurities - The Fraction of Impurities is the ratio of crystal lattice occupied by impurity to total no. of 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

Fraction of Impurities: 0.5 --> No Conversion Required
Temperature: 85 Kelvin --> 85 Kelvin No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ΔE = -ln(f)*[R]*T --> -ln(0.5)*[R]*85

Evaluating ... ...

ΔE = 489.867437339738

STEP 3: Convert Result to Output's Unit

489.867437339738 Joule --> No Conversion Required

FINAL ANSWER

489.867437339738 ≈ 489.8674 Joule <-- Energy required per impurity

(Calculation completed in 00.004 seconds)

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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

Energy per impurity Formula

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

Energy per impurity calculator uses Energy required per impurity = -ln(Fraction of Impurities)*[R]*Temperature to calculate the Energy required per impurity, The Energy per impurity is the energy required for an impurity to occupy one lattice point in a crystal lattice. Energy required per impurity is denoted by ΔE symbol.

How to calculate Energy per impurity using this online calculator? To use this online calculator for Energy per impurity, enter Fraction of Impurities (f) & Temperature (T) and hit the calculate button. Here is how the Energy per impurity calculation can be explained with given input values -> 489.8674 = -ln(0.5)*[R]*85.

FAQ

What is Energy per impurity?

The Energy per impurity is the energy required for an impurity to occupy one lattice point in a crystal lattice and is represented as ΔE = -ln(f)*[R]*T or Energy required per impurity = -ln(Fraction of Impurities)*[R]*Temperature. The Fraction of Impurities is the ratio of crystal lattice occupied by impurity to total no. of crystal lattice & Temperature is the degree or intensity of heat present in a substance or object.

How to calculate Energy per impurity?

The Energy per impurity is the energy required for an impurity to occupy one lattice point in a crystal lattice is calculated using Energy required per impurity = -ln(Fraction of Impurities)*[R]*Temperature. To calculate Energy per impurity, you need Fraction of Impurities (f) & Temperature (T). With our tool, you need to enter the respective value for Fraction of Impurities & Temperature 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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