| Abstract Scope |
Additive manufacturing now enables continuous spatial control of composition and orientation, making functionally graded materials (FGMs) practical; but predicting the resulting electronic and electromagnetic behavior remains difficult, because graded, aperiodic structures violate the periodicity assumptions of Bloch's theorem underlying standard first-principles methods. We present an ab initio quantum framework that closes this gap, providing a physics-based link between spatial gradients and functional properties. Using a modulated Bloch-state formulation and effective field equations solved via a generalized WKB method, an effective-mass approximation, and Boltzmann transport, we show that effective observables—conductivity, permeability, and permittivity—generally lose their tensorial character in graded media, and that engineered orientational gradients enable precise control of Landau quantization. As a device example, we develop graded p-n junctions with enhanced electronic tunability. This framework establishes a quantum foundation for the predictive, AI-accelerated design of graded functional architectures, connecting AM process control directly to targeted electromagnetic performance. |