[5] Carter studied material science and engineering and received his bachelor's, Masters and Doctoral degree from University of California, Berkeley in 1983, 1987, and 1989, respectively.

[9] Along with James A Warren and Ryo Kobayashi, Carter developed a phase-field model that incorporates crystallographic orientation as a microstructural parameter.

In the mid-2000s with Rowland Cannon and Ming Tang, he introduced a new concept of interface Complexion as a descriptor for the structure and local chemistry of a grain boundary.

[11] Complexion transitions occur when a grain boundary's chemistry and/or structure change at a critical temperature, pressure, or a chemical potential.

He studied olivine compounds[14] as enablers of positive electrode materials for high-power in lithium rechargeable batteries and discussed the miscibility gap in undoped Li1-xFePO4.

He collaborated with Neri Oxman of the MIT Media Lab on projects incorporating material science, mythology and natural designs.