a) DERIVE the equation for the change in the free energy of aCYLINDRICAL nucleus heterogeneously forming from an existing phase.The nucleus grows with its circular base on
the mold wall and the axis of the cylinder normal to the wall.ASSUME that the height of the cylinder can be written as h = a * r,where a is a constant, and r is the cylinder radius.
b) Find the critical radius and the energy barrier to nucleationfor this shape of precipitate.
c) We can vary the shape of the nucleating phase by changing theconstant a. Make a log- log plot of the size of the energy barrierversus the parameter a over a range from a
= 0.01 (disk shaped) to a = 100 (needle shaped). Explain yourresults.
