Critical free energy for nucleation Calculator

✖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 free energy for the formation of stable nuclei.ⓘ Critical free energy for nucleation [ΔG_*]

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Formula

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Critical free energy for nucleation

Formula

`"ΔG"_{"*"} = 16*pi*"𝛾"^3*"T"_{"m"}^2/(3*"ΔH"_{"f"}^2*"ΔT"^2)`

Example

`"9.3E^-18J"=16*pi*("0.2J/m²")^3*("1000")^2/(3*("1.2E9J/m³")^2*("100")^2)`

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Critical free energy for nucleation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Critical free energy = 16*pi*Surface free energy^3*Melting temperature^2/(3*Latent Heat of Fusion^2*Undercooling value^2)
ΔG_* = 16*pi*𝛾^3*T_m^2/(3*ΔH_f^2*ΔT^2)
This formula uses 1 Constants, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Critical free energy - (Measured in Joule) - Critical free energy for the formation of stable nuclei.
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

ΔG_* = 16*pi*𝛾^3*T_m^2/(3*ΔH_f^2*ΔT^2) --> 16*pi*0.2^3*1000^2/(3*1200000000^2*100^2)

Evaluating ... ...

ΔG_* = 9.30842267730309E-18

STEP 3: Convert Result to Output's Unit

9.30842267730309E-18 Joule --> No Conversion Required

FINAL ANSWER

9.30842267730309E-18 ≈ 9.3E-18 Joule <-- Critical free energy

(Calculation completed in 00.004 seconds)

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Home » Engineering » Materials Science » Phase Diagrams and Phase Transformations » Kinetics of Phase Transformation » Critical free energy for nucleation

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Created by Hariharan V S

Indian Institute of Technology (IIT), Chennai

Hariharan V S has created this Calculator and 25+ more calculators!

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< 11 Kinetics of Phase Transformation Calculators

Total free energy change during solidification

Go Total free energy change = ((4/3)*pi*Radius of nucleus^3*Volume free energy)+(4*pi*Radius of nucleus^2*Surface free energy)

Critical free energy for nucleation

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

Avrami equation

Go Fraction transformed = 1-exp(-Time independent coefficient in Avrami equation*Transformation time^Time independent constant in Avrami equation)

Time taken for X percent reaction to complete

Go Reaction Time = ln(Initial Concentration/(Initial Concentration-Amount reacted in time t))/Rate Constant

Rate constant of first order reaction

Go Rate Constant = ln(Initial Concentration/(Initial Concentration-Amount reacted in time t))/Reaction Time

Critical radius of nucleus

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

Volume free energy

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

Critical free energy for nucleation( from volume free energy)

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

Energy of photon

Go Energy of photon = [hP]*[c]/Wavelength of photon

Critical radius of nucleus (from volume free energy)

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

Half Life period of first order reaction

Go Half Life Period = ln(2)/Rate Constant

Critical free energy for nucleation Formula

Critical free energy = 16*pi*Surface free energy^3*Melting temperature^2/(3*Latent Heat of Fusion^2*Undercooling value^2)
ΔG_* = 16*pi*𝛾^3*T_m^2/(3*ΔH_f^2*ΔT^2)

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 free energy for nucleation?

Critical free energy for nucleation calculator uses Critical free energy = 16*pi*Surface free energy^3*Melting temperature^2/(3*Latent Heat of Fusion^2*Undercooling value^2) to calculate 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 calculate Critical free energy for nucleation using this online calculator? To use this online calculator 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. Here is how the Critical free energy for nucleation calculation can be explained with given input values -> 9.3E-18 = 16*pi*0.2^3*1000^2/(3*1200000000^2*100^2).

FAQ

What is Critical free energy for nucleation?

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 and is represented as ΔG_* = 16*pi*𝛾^3*T_m^2/(3*ΔH_f^2*ΔT^2) or Critical free energy = 16*pi*Surface free energy^3*Melting temperature^2/(3*Latent Heat of Fusion^2*Undercooling value^2). 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 free energy for nucleation?

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 is calculated using Critical free energy = 16*pi*Surface free energy^3*Melting temperature^2/(3*Latent Heat of Fusion^2*Undercooling value^2). To calculate Critical free energy for nucleation, 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 free energy?

In this formula, Critical free energy 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 free energy = 16*pi*Surface free energy^3/(3*Volume free energy^2)

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