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Equilibrium Vacancy Concentration Formula

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Number of vacancies per cubic metre. Check FAQs

N v = N \cdot \exp (- \frac{Q v}{[BoltZ] \cdot T})

N_v - Number of vacancies?N - Number of atomic sites?Q_v - Activation energy for vacancy formation?T - Temperature?[BoltZ] - Boltzmann constant?

Equilibrium Vacancy Concentration Example

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Here is how the Equilibrium Vacancy Concentration equation looks like with Values.

Here is how the Equilibrium Vacancy Concentration equation looks like with Units.

Here is how the Equilibrium Vacancy Concentration equation looks like.

3.5E-25 = 8E+28 \cdot \exp (- \frac{0.9}{1.4E-23 \cdot 85})

3.5E-25 = 8E+28 \cdot \exp (- \frac{0.9eV}{1.4E-23J/K \cdot 85K})

3.5E-25 = 8E+28 \cdot \exp (- \frac{0.9}{1.4E-23 \cdot 85})

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Equilibrium Vacancy Concentration Solution

Follow our step by step solution on how to calculate Equilibrium Vacancy Concentration?

FIRST Step Consider the formula

N v = N \cdot \exp (- \frac{Q v}{[BoltZ] \cdot T})

Next Step Substitute values of Variables

∴

N v = 8E+28 \cdot \exp (- \frac{0.9eV}{[BoltZ] \cdot 85K})

Next Step Substitute values of Constants

∴

N v = 8E+28 \cdot \exp (- \frac{0.9eV}{1.4E-23J/K \cdot 85K})

Next Step Convert Units

∴

N v = 8E+28 \cdot \exp (- \frac{1.4E-19J}{1.4E-23J/K \cdot 85K})

Next Step Prepare to Evaluate

∴

N v = 8E+28 \cdot \exp (- \frac{1.4E-19}{1.4E-23 \cdot 85})

Next Step Evaluate

∴

N v = 3.47288975669238E-25

LAST Step Rounding Answer

∴

N v = 3.5E-25

Equilibrium Vacancy Concentration Formula Elements

Variables

Constants

Functions

Number of vacancies

Number of vacancies per cubic metre.

Symbol: N_v

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of vacancies

Number of atomic sites

Number of atomic sites per cubic metre.

Symbol: N

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of atomic sites

Activation energy for vacancy formation

Activation energy for vacancy formation is the energy needed for formation of a vacancy.

Symbol: Q_v

Measurement: EnergyUnit: eV

Note: Value can be positive or negative.

Formulas to find Activation energy for vacancy formation

Temperature

Temperature is the degree or intensity of heat present in a substance or object.

Symbol: T

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Formulas to find Temperature

Boltzmann constant

Boltzmann constant relates the average kinetic energy of particles in a gas with the temperature of the gas and is a fundamental constant in statistical mechanics and thermodynamics.

Symbol: [BoltZ]

Value: 1.38064852E-23 J/K

exp

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

Syntax: exp(Number)

Other formulas in Composition and Diffusion category

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J = D \cdot (\frac{ΔC}{d})

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V 1 = M 1 \cdot ρ 2 \cdot \frac{100}{M 1 \cdot ρ 2 + (100 - M 1) \cdot 𝜌 1}

Go Atom percent to mass percent

m 1 = X 1 \cdot A 1 \cdot \frac{100}{X 1 \cdot A 1 + (100 - X 1) \cdot A 2}

Go Entropy of mixing

ΔS mix = 8.314 \cdot (X A \cdot \ln (X A) + (1 - X A) \cdot \ln (1 - X A))

How to Evaluate Equilibrium Vacancy Concentration?

Equilibrium Vacancy Concentration evaluator uses Number of vacancies = Number of atomic sites*exp(-Activation energy for vacancy formation/([BoltZ]*Temperature)) to evaluate the Number of vacancies, Equilibrium Vacancy Concentration is the number of vacancy per cubic metre at a given temperature. Number of vacancies is denoted by N_v symbol.

How to evaluate Equilibrium Vacancy Concentration using this online evaluator? To use this online evaluator for Equilibrium Vacancy Concentration, enter Number of atomic sites (N), Activation energy for vacancy formation (Q_v) & Temperature (T) and hit the calculate button.

FAQs on Equilibrium Vacancy Concentration

What is the formula to find Equilibrium Vacancy Concentration?

The formula of Equilibrium Vacancy Concentration is expressed as Number of vacancies = Number of atomic sites*exp(-Activation energy for vacancy formation/([BoltZ]*Temperature)). Here is an example- 3.5E-25 = 8E+28*exp(-1.44195959700001E-19/([BoltZ]*85)).

How to calculate Equilibrium Vacancy Concentration?

With Number of atomic sites (N), Activation energy for vacancy formation (Q_v) & Temperature (T) we can find Equilibrium Vacancy Concentration using the formula - Number of vacancies = Number of atomic sites*exp(-Activation energy for vacancy formation/([BoltZ]*Temperature)). This formula also uses Boltzmann constant and Exponential Growth (exp) function(s).

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