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The scientific community generally agrees on the theory, introduced by Riemann and furthered by Helmholtz and Schrodinger, that perceived color space is not Euclidean ¨ but rather, a three-dimensional Riemannian space. We show that the principle of diminishing returns applies to human color perception. This means that large color differences cannot be derived by adding a series of small steps, and therefore, perceptual color space cannot be described by a Riemannian geometry. This finding is inconsistent with the current approaches to modeling perceptual color space. Therefore, the assumed shape of color space requires a paradigm shift. Consequences of this apply to color metrics that are currently used in image and video processing, color mapping, and the paint and textile industries.These metrics are valid only for small differences. Rethinking them outside of a Riemannian setting could provide a path to extending them to large differences. This finding further hints at the existence of a second-order Weber–Fechner law describing perceived differences. [ABSTRACT FROM AUTHOR]

• UO 2 grain size was enlarged using Cr 2 O 3 dopant up to 7800 ppm (pre-sintering). • ∼48 % reduction in Cr content measured post-sintering. • Cr incorporation in the UO 2 lattice confirmed via XRD. • Thermal conductivity decreases at/above 2500 ppm in contrast to undoped UO 2. Chromium-doped UO 2 fuel has received significant interest due to the ability for chromium to produce pellets with large average grain size (>30 μm), which has shown to increase fission gas retention during operation. Sintering of chromium-doped UO 2 pellets was pursued with oxygen potential and sintering atmosphere controlled to tailor the final microstructure of the material. Chromium additions in this study ranged from 750 to 7800 ppm. Cr concentrations were studied pre and post sintering using Inductively Coupled Plasma Optical Emission Spectroscopy (ICP-OES). Effects of chromium content on lattice parameter and microstructure were examined with X-ray diffraction (XRD) and scanning electron microscopy (SEM). Contraction of the UO 2 lattice parameter was observed, as well as enlargement of grain size with increasing chromium content up to 4900 ppm Cr 2 O 3. SEM indicated Cr incorporation within the matrix and the formation of chromium oxide precipitates throughout the microstructure at high Cr concentrations. Evaluation of thermophysical properties of Cr-doped UO 2 pellets were conducted up to 1200 °C to illustrate their evolution with increased dopant concentration and microstructural changes. The results show that grain size is maximized at 52 μm with Cr 2 O 3 concentration equal to 4900 ppm; however, grain size decreases at higher Cr 2 O 3 concentrations. No significant changes were observed in specific heat capacity, linear thermal expansion, and coefficient of thermal expansion compared to undoped UO 2. The thermal conductivity also decreased through the incorporation of Cr 2 O 3 dopants above 750 ppm and is shown to be ∼15 % lower than reported UO 2 values. [ABSTRACT FROM AUTHOR]