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*Tm^2/(3*ΔHf^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*Tm^2/(3*ΔHf^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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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 free energy for nucleation Formula

​LaTeX ​Go
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*Tm^2/(3*ΔHf^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 (Tm), Latent Heat of Fusion (ΔHf) & 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*Tm^2/(3*ΔHf^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 (Tm), Latent Heat of Fusion (ΔHf) & 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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