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Critical free energy for nucleation Formula

GoCritical free energy for nucleation( from volume free energy) Formula

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Critical free energy for the formation of stable nuclei. Check FAQs

ΔG * = 16 \cdot π \cdot 𝛾^{3} \cdot \frac{{T m}^{2}}{3 \cdot {ΔH f}^{2} \cdot {ΔT}^{2}}

ΔG_* - Critical free energy?𝛾 - Surface free energy?T_m - Melting temperature?ΔH_f - Latent Heat of Fusion?ΔT - Undercooling value?π - Archimedes' constant?

Critical free energy for nucleation Example

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Here is how the Critical free energy for nucleation equation looks like with Values.

Here is how the Critical free energy for nucleation equation looks like with Units.

Here is how the Critical free energy for nucleation equation looks like.

9.3E-18 = 16 \cdot 3.1416 \cdot {0.2}^{3} \cdot \frac{1000^{2}}{3 \cdot {1.2E+9}^{2} \cdot 100^{2}}

9.3E-18J = 16 \cdot 3.1416 \cdot {0.2J/m²}^{3} \cdot \frac{1000^{2}}{3 \cdot {1.2E+9J/m³}^{2} \cdot 100^{2}}

9.3E-18 = 16 \cdot 3.1416 \cdot {0.2}^{3} \cdot \frac{1000^{2}}{3 \cdot {1.2E+9}^{2} \cdot 100^{2}}

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Critical free energy for nucleation Solution

Follow our step by step solution on how to calculate Critical free energy for nucleation?

FIRST Step Consider the formula

ΔG * = 16 \cdot π \cdot 𝛾^{3} \cdot \frac{{T m}^{2}}{3 \cdot {ΔH f}^{2} \cdot {ΔT}^{2}}

Next Step Substitute values of Variables

∴

ΔG * = 16 \cdot π \cdot {0.2J/m²}^{3} \cdot \frac{1000^{2}}{3 \cdot {1.2E+9J/m³}^{2} \cdot 100^{2}}

Next Step Substitute values of Constants

∴

ΔG * = 16 \cdot 3.1416 \cdot {0.2J/m²}^{3} \cdot \frac{1000^{2}}{3 \cdot {1.2E+9J/m³}^{2} \cdot 100^{2}}

Next Step Prepare to Evaluate

∴

ΔG * = 16 \cdot 3.1416 \cdot {0.2}^{3} \cdot \frac{1000^{2}}{3 \cdot {1.2E+9}^{2} \cdot 100^{2}}

Next Step Evaluate

∴

ΔG * = 9.30842267730309E-18J

LAST Step Rounding Answer

∴

ΔG * = 9.3E-18J

Critical free energy for nucleation Formula Elements

Variables

Constants

Critical free energy

Critical free energy for the formation of stable nuclei.

Symbol: ΔG_*

Measurement: EnergyUnit: J

Note: Value can be positive or negative.

Formulas to find Critical free energy

Surface free energy

Surface free energy is the energy to create solid–liquid phase boundary during the solidification.

Symbol: 𝛾

Measurement: Heat DensityUnit: J/m²

Note: Value should be greater than 0.

Formulas to find Surface free energy

Melting temperature

Melting temperature of the metal or alloy in kelvin.

Symbol: T_m

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Melting temperature

Latent Heat of Fusion

Latent heat of fusion or enthalpy of solidification is the heat liberated during solidification. Enter the magnitude only. It is taken negative by default.

Symbol: ΔH_f

Measurement: Heat of Combustion (per Volume)Unit: J/m³

Note: Value should be greater than 0.

Formulas to find Latent Heat of Fusion

Undercooling value

Undercooling value is the difference between the melting temperature and temperature under consideration (below melting temperature). It is also known as supercooling.

Symbol: ΔT

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Undercooling value

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other Formulas to find Critical free energy

Go Critical free energy for nucleation( from volume free energy)

ΔG * = 16 \cdot π \cdot \frac{𝛾^{3}}{3 \cdot {𝚫G v}^{2}}

Other formulas in Kinetics of Phase Transformation category

Go Critical radius of nucleus

r * = 2 \cdot 𝛾 \cdot \frac{T m}{ΔH f \cdot ΔT}

Go Volume free energy

𝚫G v = ΔH f \cdot \frac{ΔT}{T m}

Go Critical radius of nucleus (from volume free energy)

r * = - 2 \cdot \frac{𝛾}{𝚫G v}

Go Total free energy change during solidification

𝚫G = ((\frac{4}{3}) \cdot π \cdot r^{3} \cdot 𝚫G v) + (4 \cdot π \cdot r^{2} \cdot 𝛾)

How to Evaluate Critical free energy for nucleation?

Critical free energy for nucleation evaluator uses Critical free energy = 16*pi*Surface free energy^3*Melting temperature^2/(3*Latent Heat of Fusion^2*Undercooling value^2) to evaluate the Critical free energy, Critical free energy for nucleation is the free energy required for the formation of a stable nucleus. Equivalently, it may be considered an energy barrier to the nucleation process. Critical free energy is denoted by ΔG_* symbol.

How to evaluate Critical free energy for nucleation using this online evaluator? To use this online evaluator for Critical free energy for nucleation, enter Surface free energy (𝛾), Melting temperature (T_m), Latent Heat of Fusion (ΔH_f) & Undercooling value (ΔT) and hit the calculate button.

FAQs on Critical free energy for nucleation

What is the formula to find Critical free energy for nucleation?

The formula of Critical free energy for nucleation is expressed as Critical free energy = 16*pi*Surface free energy^3*Melting temperature^2/(3*Latent Heat of Fusion^2*Undercooling value^2). Here is an example- 9.3E-18 = 16*pi*0.2^3*1000^2/(3*1200000000^2*100^2).

How to calculate Critical free energy for nucleation?

With Surface free energy (𝛾), Melting temperature (T_m), Latent Heat of Fusion (ΔH_f) & Undercooling value (ΔT) we can find Critical free energy for nucleation using the formula - Critical free energy = 16*pi*Surface free energy^3*Melting temperature^2/(3*Latent Heat of Fusion^2*Undercooling value^2). This formula also uses Archimedes' constant .

What are the other ways to Calculate Critical free energy?

Here are the different ways to Calculate Critical free energy-

Critical free energy=16*pi*Surface free energy^3/(3*Volume free energy^2)

Can the Critical free energy for nucleation be negative?

Yes, the Critical free energy for nucleation, measured in Energy can be negative.

Which unit is used to measure Critical free energy for nucleation?

Critical free energy for nucleation is usually measured using the Joule[J] for Energy. Kilojoule[J], Gigajoule[J], Megajoule[J] are the few other units in which Critical free energy for nucleation can be measured.

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Critical free energy for nucleation Formula

​GoCritical free energy for nucleation( from volume free energy) Formula

Critical free energy for nucleation Example

Critical free energy for nucleation Solution

Critical free energy for nucleation Formula Elements

Other Formulas to find Critical free energy

Other formulas in Kinetics of Phase Transformation category

How to Evaluate Critical free energy for nucleation?

FAQs on Critical free energy for nucleation

Variable Name

GoCritical free energy for nucleation( from volume free energy) Formula