Broader Impact in Science and Technology: Materials with low thermal conductivity at high temperature are crucial to the development of higher energy efficiency engines for power generation and transport. New results indicate that there is the prospect of discovering materials with much lower thermal conductivities than existing ceramics and that the mechanisms of thermal conductivity may be radically different from the conventional phonon scattering picture in simple crystalline materials. This project addresses the challenge of identifying compounds having even lower thermal conductivity with an emphasis on layered crystal structures with strongly anisotropic thermal conductivity. We believe that the project will have broad impact on technology through improved heat management materials and impact the science of materials through fundamental advances in understanding thermal conductivity in complex crystal structures.Intellectual Merit: Apart from the important discovery aspects, we believe the merit of our proposal lies in our integrated, collaborative approach to the identifying candidate materials from an enormous number of oxide compounds and an understanding how anisotropic thermal conductivity is related to crystal structure anisotropy. The aim of our integrated experimental and simulation program is to go beyond an intuition-based Edisonian approach to a more systematic approach to the discovery of materials. The basis of the approach is to combine state-of-the art simulations with both traditional synthesis and processing of ceramics together with combinatorial approaches exploring compositional variations to provide a more rapid discovery path. The initial emphasis is on complex, fluorite-derived structures and perovskite-related layered structures that have very low and/or strongly anisotropic thermal conductivities. Layered crystal structures, such as the perovskites, provide the opportunity to investigate whether the layers can impede perpendicular thermal transport at the atomic level as well as facilitating both the thermal-transport properties and other important performance criteria.