According the stable Fe$-$C phase diagram, graphite should form instead of carbide in

cast irons. However, in reality, iron carbide forms unless we inoculate our gray and

ductile irons. Why is graphite hard to nucleate out of the melt? What is commonly used

as an inoculant in cast iron and why? Explain three ways inoculants encourage the

formation of graphite formation in cast iron. How does good inoculation affect the

mechanical properties of cast irons? $(10$pts$)$