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Critical radius of nucleus Formula

GoCritical radius of nucleus (from volume free energy) Formula

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Critical radius of nucleus is the minimum size of a stable nucleus formed during solidification. Check FAQs

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

r_* - Critical radius of nucleus?𝛾 - Surface free energy?T_m - Melting temperature?ΔH_f - Latent Heat of Fusion?ΔT - Undercooling value?

Critical radius of nucleus Example

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Here is how the Critical radius of nucleus equation looks like with Values.

Here is how the Critical radius of nucleus equation looks like with Units.

Here is how the Critical radius of nucleus equation looks like.

3.3333 = 2 \cdot 0.2 \cdot \frac{1000}{1.2E+9 \cdot 100}

3.3333nm = 2 \cdot 0.2J/m² \cdot \frac{1000}{1.2E+9J/m³ \cdot 100}

3.3333 = 2 \cdot 0.2 \cdot \frac{1000}{1.2E+9 \cdot 100}

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Critical radius of nucleus Solution

Follow our step by step solution on how to calculate Critical radius of nucleus?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r * = 2 \cdot 0.2J/m² \cdot \frac{1000}{1.2E+9J/m³ \cdot 100}

Next Step Prepare to Evaluate

∴

r * = 2 \cdot 0.2 \cdot \frac{1000}{1.2E+9 \cdot 100}

Next Step Evaluate

∴

r * = 3.33333333333333E-09m

Next Step Convert to Output's Unit

∴

r * = 3.33333333333333nm

LAST Step Rounding Answer

∴

r * = 3.3333nm

Critical radius of nucleus Formula Elements

Variables

Critical radius of nucleus

Critical radius of nucleus is the minimum size of a stable nucleus formed during solidification.

Symbol: r_*

Measurement: LengthUnit: nm

Note: Value should be greater than 0.

Formulas to find Critical radius of nucleus

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

Other Formulas to find Critical radius of nucleus

Go Critical radius of nucleus (from volume free energy)

r * = - 2 \cdot \frac{𝛾}{𝚫G v}

Other formulas in Kinetics of Phase Transformation category

Go Critical free energy for nucleation

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

Go Volume free energy

𝚫G v = ΔH f \cdot \frac{ΔT}{T m}

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

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

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 radius of nucleus?

Critical radius of nucleus evaluator uses Critical radius of nucleus = 2*Surface free energy*Melting temperature/(Latent Heat of Fusion*Undercooling value) to evaluate the Critical radius of nucleus, Critical radius of nucleus is the minimum radius of a stable nucleus formed during solidification, assuming homogeneous nucleation conditions. Critical radius of nucleus is denoted by r_* symbol.

How to evaluate Critical radius of nucleus using this online evaluator? To use this online evaluator for Critical radius of nucleus, 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 radius of nucleus

What is the formula to find Critical radius of nucleus?

The formula of Critical radius of nucleus is expressed as Critical radius of nucleus = 2*Surface free energy*Melting temperature/(Latent Heat of Fusion*Undercooling value). Here is an example- 3.3E+9 = 2*0.2*1000/(1200000000*100).

How to calculate Critical radius of nucleus?

With Surface free energy (𝛾), Melting temperature (T_m), Latent Heat of Fusion (ΔH_f) & Undercooling value (ΔT) we can find Critical radius of nucleus using the formula - Critical radius of nucleus = 2*Surface free energy*Melting temperature/(Latent Heat of Fusion*Undercooling value).

What are the other ways to Calculate Critical radius of nucleus?

Here are the different ways to Calculate Critical radius of nucleus-

Critical radius of nucleus=-2*Surface free energy/Volume free energy

Can the Critical radius of nucleus be negative?

No, the Critical radius of nucleus, measured in Length cannot be negative.

Which unit is used to measure Critical radius of nucleus?

Critical radius of nucleus is usually measured using the Nanometer[nm] for Length. Meter[nm], Millimeter[nm], Kilometer[nm] are the few other units in which Critical radius of nucleus can be measured.

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Critical radius of nucleus Formula

​GoCritical radius of nucleus (from volume free energy) Formula

Critical radius of nucleus Example

Critical radius of nucleus Solution

Critical radius of nucleus Formula Elements

Other Formulas to find Critical radius of nucleus

Other formulas in Kinetics of Phase Transformation category

How to Evaluate Critical radius of nucleus?

FAQs on Critical radius of nucleus

Variable Name

GoCritical radius of nucleus (from volume free energy) Formula