Most natural and man-made surfaces appear to be rough on many length scales. There is presently no unifying theory of the origin of roughness or the self-affine nature of surface topography.One likely contributor to the formation of roughness is deformation, which underlies many processes that shape surfaces such as machining, fracture, and wear. Using molecular dynamics, we simulate the bi-axial compression of single-crystal Au, the high-entropy alloy Ni 36.67 Co 30 Fe 16.67 Ti 16.67 , and amorphous Cu 50 Zr 50 , and show that even surfaces of homogeneous materials develop a self-affine structure. By characterizing subsurface deformation, we connect the self-affinity of the surface to the spatial correlation of deformation events occurring within the bulk and present scaling relations for the evolution of roughness with strain.

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Anatase TiO 2 is among the most studied photocatalytic materials for solar energy conversion and environmental clean-up. However, its poor visible light absorption and high facet-dependent performance limits its utilization. In this study chemical substitution (doping) of TiO 2 nanoparticles with metal ions (Sb, Cr or Sb/Nb and Cr/Nb) is presented as an alternative strategy to address both issues simultaneously. Highly crystalline doped and co-doped TiO 2 nanoparticles were successfully synthesized by a microwave-assisted non-aqueous sol-gel synthesis. The structural and compositional analysis done by X-ray diffraction (XRD), high resolution transmission electron microscopy (HRTEM) and X-ray photoelectron spectroscopy (XPS) showed that depending on the doping applied, variations in particles size and morphology were observed. Doped and co-doped samples showed improved absorption in the visible range, and in comparison to the undoped TiO 2 displayed improved photocatalytic (PC) activity. The variations of the PC activity, observed among different samples, are attributed to the effect of doping on (i) particles size/morphology, (ii) optical activity and (iii) on the surface potential differences for the various crystal facets. We found that Sb-doping in TiO 2 diminishes the surface potential difference for {101} reductive and {001} oxidative sites, which makes all crystal surfaces equally attractive to both electrons and holes. Accordingly, in Sb-doped TiO 2 nanoparticles the photocatalytic activity is independent of the exposed crystal facets, and thus on the particle morphology. This observation also explains the superior PC performance of this material.

We propose a specialized preconditioned FE homogenization scheme that is significantly more efficient than generic FE implementations.• Our formulation offers computational efficiency equivalent to spectral homogenization solvers.• Our formulation is devoid of ringing phenomena intrinsic to spectral methods.• All results are reproducible in an open-source project µSpectre available at https: //muspectre.gitlab.io/muspectre.

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