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Critical radius of nucleus Calculator

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✖Surface free energy is the energy to create solid–liquid phase boundary during the solidification.ⓘ Surface free energy [𝛾]			+10% -10%
✖Melting temperature of the metal or alloy in kelvin.ⓘ Melting temperature [T_m]			+10% -10%
✖Latent heat of fusion or enthalpy of solidification is the heat liberated during solidification. Enter the magnitude only. It is taken negative by default.ⓘ Latent Heat of Fusion [ΔH_f]			+10% -10%
✖Undercooling value is the difference between the melting temperature and temperature under consideration (below melting temperature). It is also known as supercooling.ⓘ Undercooling value [ΔT]			+10% -10%

✖Critical radius of nucleus is the minimum size of a stable nucleus formed during solidification.ⓘ Critical radius of nucleus [r_*]

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Critical radius of nucleus Solution

STEP 0: Pre-Calculation Summary

Formula Used

Critical radius of nucleus = 2*Surface free energy*Melting temperature/(Latent Heat of Fusion*Undercooling value)
r_* = 2*𝛾*T_m/(ΔH_f*ΔT)
This formula uses 5 Variables

Variables Used

Critical radius of nucleus - (Measured in Meter) - Critical radius of nucleus is the minimum size of a stable nucleus formed during solidification.
Surface free energy - (Measured in Joule per Square Meter) - Surface free energy is the energy to create solid–liquid phase boundary during the solidification.
Melting temperature - Melting temperature of the metal or alloy in kelvin.
Latent Heat of Fusion - (Measured in Joule per Cubic Meter) - Latent heat of fusion or enthalpy of solidification is the heat liberated during solidification. Enter the magnitude only. It is taken negative by default.
Undercooling value - Undercooling value is the difference between the melting temperature and temperature under consideration (below melting temperature). It is also known as supercooling.

STEP 1: Convert Input(s) to Base Unit

Surface free energy: 0.2 Joule per Square Meter --> 0.2 Joule per Square Meter No Conversion Required
Melting temperature: 1000 --> No Conversion Required
Latent Heat of Fusion: 1200000000 Joule per Cubic Meter --> 1200000000 Joule per Cubic Meter No Conversion Required
Undercooling value: 100 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_* = 2*𝛾*T_m/(ΔH_f*ΔT) --> 2*0.2*1000/(1200000000*100)

Evaluating ... ...

r_* = 3.33333333333333E-09

STEP 3: Convert Result to Output's Unit

3.33333333333333E-09 Meter -->3.33333333333333 Nanometer (Check conversion here)

FINAL ANSWER

3.33333333333333 ≈ 3.333333 Nanometer <-- Critical radius of nucleus

(Calculation completed in 00.004 seconds)

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Indian Institute of Technology (IIT), Chennai

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< Kinetics of Phase Transformation Calculators

Critical free energy for nucleation

LaTeX Go Critical free energy = 16*pi*Surface free energy^3*Melting temperature^2/(3*Latent Heat of Fusion^2*Undercooling value^2)

Critical radius of nucleus

LaTeX Go Critical radius of nucleus = 2*Surface free energy*Melting temperature/(Latent Heat of Fusion*Undercooling value)

Volume free energy

LaTeX Go Volume free energy = Latent Heat of Fusion*Undercooling value/Melting temperature

Critical radius of nucleus (from volume free energy)

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

Critical radius of nucleus Formula

LaTeX Go

Critical radius of nucleus = 2*Surface free energy*Melting temperature/(Latent Heat of Fusion*Undercooling value)
r_* = 2*𝛾*T_m/(ΔH_f*ΔT)

Nucleation and growth

The progress of solidification involves two distinct stages: nucleation and growth. Nucleation involves the appearance of very small particles, or nuclei of the solid (often consisting of only a few hundred atoms), which are capable of growing. During the growth stage these nuclei increase in size, which results in the disappearance of some (or all) of the parent phase. The transformation reaches completion if the growth of these new phase particles is allowed to proceed until the equilibrium fraction is reached.

How to Calculate Critical radius of nucleus?

Critical radius of nucleus calculator uses Critical radius of nucleus = 2*Surface free energy*Melting temperature/(Latent Heat of Fusion*Undercooling value) to calculate 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 calculate Critical radius of nucleus using this online calculator? To use this online calculator 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. Here is how the Critical radius of nucleus calculation can be explained with given input values -> 3.3E+9 = 2*0.2*1000/(1200000000*100).

FAQ

What is Critical radius of nucleus?

Critical radius of nucleus is the minimum radius of a stable nucleus formed during solidification, assuming homogeneous nucleation conditions and is represented as r_* = 2*𝛾*T_m/(ΔH_f*ΔT) or Critical radius of nucleus = 2*Surface free energy*Melting temperature/(Latent Heat of Fusion*Undercooling value). Surface free energy is the energy to create solid–liquid phase boundary during the solidification, Melting temperature of the metal or alloy in kelvin, Latent heat of fusion or enthalpy of solidification is the heat liberated during solidification. Enter the magnitude only. It is taken negative by default & Undercooling value is the difference between the melting temperature and temperature under consideration (below melting temperature). It is also known as supercooling.

How to calculate Critical radius of nucleus?

Critical radius of nucleus is the minimum radius of a stable nucleus formed during solidification, assuming homogeneous nucleation conditions is calculated using Critical radius of nucleus = 2*Surface free energy*Melting temperature/(Latent Heat of Fusion*Undercooling value). To calculate Critical radius of nucleus, you need Surface free energy (𝛾), Melting temperature (T_m), Latent Heat of Fusion (ΔH_f) & Undercooling value (ΔT). With our tool, you need to enter the respective value for Surface free energy, Melting temperature, Latent Heat of Fusion & Undercooling value 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 Critical radius of nucleus?

In this formula, Critical radius of nucleus uses Surface free energy, Melting temperature, Latent Heat of Fusion & Undercooling value. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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