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Fraction of Vacancy in lattice terms of Energy Calculator

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✖The Energy Required per Vacancy is E is the energy required to create one vacancy in the crystal lattice.ⓘ Energy Required per Vacancy [ΔE_vacancy]			+10% -10%
✖Temperature is the degree or intensity of heat present in a substance or object.ⓘ Temperature [T]			+10% -10%

✖The Fraction of Vacancy is the ratio of vacant crystal lattice to total no. of crystal lattice.ⓘ Fraction of Vacancy in lattice terms of Energy [f_vacancy]

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Formula

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Fraction of Vacancy in lattice terms of Energy

Formula

f vacancy = \exp (- \frac{ΔE vacancy}{[R] \cdot T})

Example

0.459217 = \exp (- \frac{550 J}{[R] \cdot 85 K})

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Fraction of Vacancy in lattice terms of Energy Solution

STEP 0: Pre-Calculation Summary

Formula Used

Fraction of Vacancy = exp(-Energy Required per Vacancy/([R]*Temperature))
f_vacancy = exp(-ΔE_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

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 Vacancy - The Fraction of Vacancy is the ratio of vacant crystal lattice to total no. of crystal lattice.
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.
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 Vacancy: 550 Joule --> 550 Joule No Conversion Required
Temperature: 85 Kelvin --> 85 Kelvin No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f_vacancy = exp(-ΔE_vacancy/([R]*T)) --> exp(-550/([R]*85))

Evaluating ... ...

f_vacancy = 0.459216783334827

STEP 3: Convert Result to Output's Unit

0.459216783334827 --> No Conversion Required

FINAL ANSWER

0.459216783334827 ≈ 0.459217 <-- Fraction of Vacancy

(Calculation completed in 00.004 seconds)

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University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA

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< Lattice Calculators

Packing Efficiency

Go Packing Efficiency = (Volume Occupied by Spheres in Unit Cell/Total Volume of Unit Cell)*100

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

Edge length of Simple cubic unit cell

Go Edge Length = 2*Radius of Constituent Particle

Fraction of Vacancy in lattice terms of Energy Formula

Fraction of Vacancy = exp(-Energy Required per Vacancy/([R]*Temperature))
f_vacancy = exp(-ΔE_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 Fraction of Vacancy in lattice terms of Energy?

Fraction of Vacancy in lattice terms of Energy calculator uses Fraction of Vacancy = exp(-Energy Required per Vacancy/([R]*Temperature)) to calculate the Fraction of Vacancy, The Fraction of Vacancy in lattice terms of Energy is the ratio of vacant crystal lattice to total no. of crystal lattice. Fraction of Vacancy is denoted by f_vacancy symbol.

How to calculate Fraction of Vacancy in lattice terms of Energy using this online calculator? To use this online calculator for Fraction of Vacancy in lattice terms of Energy, enter Energy Required per Vacancy (ΔE_vacancy) & Temperature (T) and hit the calculate button. Here is how the Fraction of Vacancy in lattice terms of Energy calculation can be explained with given input values -> 0.459217 = exp(-550/([R]*85)).

FAQ

What is Fraction of Vacancy in lattice terms of Energy?

The Fraction of Vacancy in lattice terms of Energy is the ratio of vacant crystal lattice to total no. of crystal lattice and is represented as f_vacancy = exp(-ΔE_vacancy/([R]*T)) or Fraction of Vacancy = exp(-Energy Required per Vacancy/([R]*Temperature)). The Energy Required per Vacancy is E is the energy required to create one vacancy in the crystal lattice & Temperature is the degree or intensity of heat present in a substance or object.

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

The Fraction of Vacancy in lattice terms of Energy is the ratio of vacant crystal lattice to total no. of crystal lattice is calculated using Fraction of Vacancy = exp(-Energy Required per Vacancy/([R]*Temperature)). To calculate Fraction of Vacancy in lattice terms of Energy, you need Energy Required per Vacancy (ΔE_vacancy) & Temperature (T). With our tool, you need to enter the respective value for Energy Required per Vacancy & 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 Vacancy?

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

Fraction of Vacancy = Number of Vacant Lattice/Total no. of lattice points

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