Hello.
In generally if we talk so metallurgy is a subject of mechanical engineering , it is not a core branch but now you study it  like a core branch because many companies require student who have complete metallurgy based knowledge that's why it is considered as a core branch,
For more detail about metallurgy you can go with the below link.
https://engineering.careers360.com/articles/metallurgical-and-materials-engineering-0
Best of luck.