Unit cell estimation of volumetrically-varying permittivity in additively-manufactured ceramic lattices with X-ray computed tomography

Abstract

Abstract Additive manufacturing of ceramics is transforming electromagnetics by providing density-varying lattices and stochastic foams within arbitrary envelopes. Periodic structures can now be fabricated with zirconia which offers the highest permittivity of any 3D printable material possible to be printed with nearly-full-density. By arranging a lattice with variation in the strut and node sizings as well as unit cell dimensions, the effective density of a structure can be spatially-modulated gracefully and with unprecedented freedom. These variations in density directly translate into variations in the effective permittivity of the bulk lattice (estimated locally and globally with a combination of mixing formulas, curve fits, and capacitance models). A lattice had previously been fabricated with a rectangular envelope for evaluation of effective global permittivity of the overall structure using a network analyzer. For this work, the structure was scanned with X-ray computed tomography (CT) to capture the three dimensional density of the structure including both the solid ceramic elements as well as the interstitial space. Software was developed that reads CT scan data and provides a 3D data structure with a pointwise unit cell estimation of the effective permittivity throughout the volume - a model well suited for electromagnetic simulations to optimize advanced microwave devices. The proposed technique serves as a foundation for the non-destructive estimation of space-varying permittivity within 3D printed lattices and foams.