Materials Science Graduate Program...?

http://tmi.utexas.edu/prospective-students/admissions-faq/ says:

http://tmi.utexas.edu/current-students/coursework-requirements/ says that upper division courses in quantum mechanics and thermodynamics are expected of entering students.

You can also look at graduate admissions pages for other schools’ materials engineering departments for their preferred qualifications. You can also look at the core graduate materials engineering courses for each program and then check what undergraduate courses are listed as prerequisites for them.

From the above, you can figure out what courses you need to include in your undergraduate course selection to prepare for graduate study in materials engineering (these courses may be part of your major or taken as electives outside your major).