Energy per vacancy Calculator

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Inter-planar distance and inter-planar angle

✖The Fraction of Vacancy is the ratio of vacant crystal lattice to total no. of crystal lattice.ⓘ Fraction of Vacancy [f_vacancy]			+10% -10%
✖Temperature is the degree or intensity of heat present in a substance or object.ⓘ Temperature [T]			+10% -10%

✖The Energy Required per Vacancy is E is the energy required to create one vacancy in the crystal lattice.ⓘ Energy per vacancy [ΔE_vacancy]

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Formula

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Energy per vacancy

Formula

`"ΔE"_{"vacancy"} = -ln("f"_{"vacancy"})*"[R]"*"T"`

Example

`"361.0154J"=-ln("0.6")*"[R]"*"85K"`

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Energy per vacancy Solution

STEP 0: Pre-Calculation Summary

Formula Used

Energy Required per Vacancy = -ln(Fraction of Vacancy)*[R]*Temperature
ΔE_vacancy = -ln(f_vacancy)*[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 Vacancy - (Measured in Joule) - The Energy Required per Vacancy is E is the energy required to create one vacancy in the crystal lattice.
Fraction of Vacancy - The Fraction of Vacancy is the ratio of vacant crystal lattice 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 Vacancy: 0.6 --> No Conversion Required
Temperature: 85 Kelvin --> 85 Kelvin No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ΔE_vacancy = -ln(f_vacancy)*[R]*T --> -ln(0.6)*[R]*85

Evaluating ... ...

ΔE_vacancy = 361.015447021757

STEP 3: Convert Result to Output's Unit

361.015447021757 Joule --> No Conversion Required

FINAL ANSWER

361.015447021757 ≈ 361.0154 Joule <-- Energy Required per Vacancy

(Calculation completed in 00.004 seconds)

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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 Prashant Singh

K J Somaiya College of science (K J Somaiya), Mumbai

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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

Energy per vacancy Formula

Energy Required per Vacancy = -ln(Fraction of Vacancy)*[R]*Temperature
ΔE_vacancy = -ln(f_vacancy)*[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 vacancy?

Energy per vacancy calculator uses Energy Required per Vacancy = -ln(Fraction of Vacancy)*[R]*Temperature to calculate the Energy Required per Vacancy, The Energy per vacancy is the energy required to create one vacant lattice point in a crystal lattice. Energy Required per Vacancy is denoted by ΔE_vacancy symbol.

How to calculate Energy per vacancy using this online calculator? To use this online calculator for Energy per vacancy, enter Fraction of Vacancy (f_vacancy) & Temperature (T) and hit the calculate button. Here is how the Energy per vacancy calculation can be explained with given input values -> 361.0154 = -ln(0.6)*[R]*85.

FAQ

What is Energy per vacancy?

The Energy per vacancy is the energy required to create one vacant lattice point in a crystal lattice and is represented as ΔE_vacancy = -ln(f_vacancy)*[R]*T or Energy Required per Vacancy = -ln(Fraction of Vacancy)*[R]*Temperature. The Fraction of Vacancy is the ratio of vacant crystal lattice 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 vacancy?

The Energy per vacancy is the energy required to create one vacant lattice point in a crystal lattice is calculated using Energy Required per Vacancy = -ln(Fraction of Vacancy)*[R]*Temperature. To calculate Energy per vacancy, you need Fraction of Vacancy (f_vacancy) & Temperature (T). With our tool, you need to enter the respective value for Fraction of Vacancy & 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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