Lowering temperature below the equilibrium solidification temperature nucleation occurs more readily

[marcousc]

In the book science and engineering of William Callister in the pages 315 an 316 at the final paragraph the book says that the critical radius r* and the Gibbs free energy G* are decreasing functions of temperature, the higher the temperature the lower the critical radius r* and the Gibbs free energy G*. After that the book mention a plot that has two profiles of Gibbs free energy G* Vs critical radius r* corresponding of two different temperatures T1 & T2 in which T2>T1, the profile of temperature T1 looks displayed to the right because of r* and G* are greater for lower T1. After this the book says “ lowering the temperature at temperatures below the equilibrium solidifiaction temperature (Tm) nucleation occurs more readily” and I don’t understand and find the connection of this part with the other parts of this parragraph.

 

[arunmrao]

Read books by Flemings , and by Winegard. You will get a clear understanding of nucleation and growth phenomenon. You will also get to understand undercooling effect, about which you are asking.

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( read somewhere on the internet)

 

[steelmtllrgst]

I am not able to see your link to comment on the figures that you have noted. That said, the plot of G vs r is typically used just to show the inflection point noted as r* where the precipitate becomes energetically stable, and any increase in r will result in a lowering of the total free energy. Lowering the temperature drives the chemical free energy term. Chemical energy is a volumetric term and will vary with the cube of r while interfacial and strain energy are surface terms and vary with the square of r, so unless the surface terms are significantly effected a lower temperature will give finer and faster precipitation in general.

It sounds like possibly the figure you are referring to is mislabeled but I cannot see to verify.