The segregation of  Ce and/or  Mg  to the interface between graphite  flakes and the matrix  in grey cast  iron  increases the interfacial specific free energy,  which increases the capillary potential CP as such that  during further heat treatment,  the gradient  of CP  acts  as driving force to transfer chemical species (carbon)  from the sharp corners and edges to the smooth regions in order to lower the global surface free energy. The result  is the formation of nodular graphite out of flakes. This product is also  called spheroidal graphite.

Note: Capillary potential = local curvature x interfacial specific Helmholtz energy .

The segregation of  Ce and/or  Mg  to the interface between graphite  flakes and the matrix  in grey cast  iron  increases the interfacial specific free energy,  which increases the capillary potential CP as such that  during further heat treatment,  the gradient  of CP  acts  as driving force to transfer chemical species (carbon)  from the sharp corners and edges to the smooth regions in order to lower the global surface free energy. The result  is the formation of nodular graphite out of flakes. This product is also  called spheroidal graphite.

Note: Capillary potential = local curvature x interfacial specific Helmholtz energy .

Why should Ce ang Mg segregate at interface of graphite flakes and ferrite/pearlite? How does this segregation increase the interfacial free energy?

Ce and Mg actually enhances the growth of flakes in in all direction. This results in globular structure instead flakes. The reason behind is drastic reduction in inter-facial energy leads to grow in all direction by the addition of those elements.

Graphite Flakes have large surface area to volume ratio than spheroidal or nodular graphite. So by heating GCI at high temperature or prolonged period itself can yield us SG Iron. What does Ce and Mg do in this process whether it fastens this process or what?

The Ce and Mg can be add during melt the gray cast iron in  casting to convert the gray cast iron to spheroidal cast iron

The magnesium must be added when the material is in liquid state. This element modify the form taken by the precipitated graphite during solidification, forming nodules instead of sheets.

Mr.Daniel Martinez Krahmer i don't think that graphite flakes turn into nodules during solidification itself. Only after heat treatment it changes its morphology.

The Ce and Mg can be add during melt the gray cast iron in casting to convert the gray cast iron to spheroidal cast iron

I think there are a confusion between malleable iron and ductile iron. While malleable iron need a heat treatment to take malleability (there are two types:(white heart and black heart), ductile iron need magnesium adding during the material is in liquid state.