Efficient topology optimization using compatibility projection in micromechanical homogenization

The adjoint method allows efficient calculation of the gradient with respect to the design variables of a topology optimization problem. This method is almost exclusively used in combination with traditional Finite-Element-Analysis, whereas Fourier-based solvers have recently shown large efficiency gains for homogenization problems. In this paper, we derive the discrete adjoint method for Fourier-based solvers that employ compatibility projection. We demonstrate the method on the optimization of composite materials and auxetic metamaterials, where void regions are modelled with zero stiffness.Comment: 17 pages, 5 figure

The emergence of small-scale self-affine surface roughness from deformation

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 biaxial compression of single-crystal Au, the high-entropy alloy Ni36.67Co30Fe16.67Ti16.67, and amorphous Cu50Zr50 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. These results open routes toward interpreting and engineering roughness profiles

GaN-Nanostreifen für LED- und Laseranwendungen

In dieser Arbeit werden GaN-basierte Nanostreifen mit semipolaren InGaN-Quantenfilmen überwachsen und in polare LED- sowie Laserstrukturen eingebettet. Dafür werden nanolithografische Verfahren eingesetzt und sowohl Strukturierung als auch selektive Epitaxie im Submikrometer-Maßstab entwickelt und optimiert. Das emittierte Licht der so hergestellten Proben konnte in einem weiten Wellenlängenbereich von violett bis echt-grün (400 nm - 535 nm) eingestellt werden. Durch den semipolaren Charakter der Proben ist die Emission aus der Oberfläche polarisiert. Zudem wirken die Nanostrukturen als 1D-Photonischer Kristall, so dass eine gerichtete Emission mit hohem Q-Faktor nachgewiesen werden konnte. Bei Einbettung in eine Wellenleiterstruktur wurde eine Laserschwelle bestimmt. Zudem wurde die Qualität und die Optimierung der Nanostrukturen durch eine Vielzahl mikroskopischer und spektroskopischer Methoden untersucht

The emergence of small-scale self-affine surface roughness from deformation

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 biaxial compression of single-crystal Au, the high-entropy alloy Ni36.67Co30Fe16.67Ti16.67, and amorphous Cu50Zr50 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. These results open routes toward interpreting and engineering roughness profiles

An optimal preconditioned FFT-accelerated finite element solver for homogenization

We generalize and provide a linear algebra-based perspective on a finite element (FE) ho-mogenization scheme, pioneered by Schneider et al. (2017)[1] and Leuschner and Fritzen (2018)[2]. The efficiency of the scheme is based on a preconditioned, well-scaled refor-mulation allowing for the use of the conjugate gradient or similar iterative solvers. The geometrically-optimal preconditioner-a discretized Green's function of a periodic homo-geneous reference problem-has a block-diagonal structure in the Fourier space which per-mits its efficient inversion using fast Fourier transform (FFT) techniques for generic regular meshes. This implies that the scheme scales as O(n log(n)), like FFT, rendering it equiva-lent to spectral solvers in terms of computational efficiency. However, in contrast to clas-sical spectral solvers, the proposed scheme works with FE shape functions with local sup-ports and does not exhibit the Fourier ringing phenomenon. We show that the scheme achieves a number of iterations that are almost independent of spatial discretization. The scheme also scales mildly with phase contrast. We also discuss the equivalence between our displacement-based scheme and the recently proposed strain-based homogenization technique with finite-element projection. (c) 2023 Published by Elsevier Inc.LAMM

Elimination of ringing artifacts by finite-element projection in FFT-based homogenization

Micromechanical homogenization is often carried out with Fourier-accelerated methods that are prone to ringing artifacts. We here generalize the compatibility projection introduced by Vond.rejc et al. (2014) [24] beyond the Fourier basis. In particular, we formulate the compatibility projection for linear finite elements while maintaining Fourier-acceleration and the fast convergence properties of the original method. We demonstrate that this eliminates ringing artifacts and yields an efficient computational homogenization scheme that is equivalent to canonical finite-element formulations on fully structured grids. (C) 2021 The Author(s). Published by Elsevier Inc.LAMM

El Correo gallego : diario político de la mañana: Ano L Número 17779 - 1928 outubro 6

Anatase TiO₂ is among the most studied photocatalytic materials for solar energy conversion and environmental cleanup. However, its poor visible light absorption and high facet-dependent performance limits its utilization. In this study chemical substitution (doping) of TiO₂ 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 codoped TiO₂ nanoparticles were successfully synthesized by a microwave-assisted nonaqueous 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 codoped samples showed improved absorption in the visible range and in comparison to the undoped TiO₂ 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 TiO₂ 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 TiO₂ 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

LEDs on HVPE grown GaN substrates: influence of macroscopic surface features

We demonstrate the strong influence of GaN substrate surface morphology on optical properties and performance of light emitting devices grown on freestanding GaN. As-grown freestanding HVPE GaN substrates show excellent AFM RMS and XRD FWHM values over the whole area, but distinctive features were observed on the surface, such as macro-pits, hillocks and facets extending over several millimeters. Electroluminescence measurements reveal a strong correlation of the performance and peak emission wavelength of LEDs with each of these observed surface features. This results in multiple peaks and non-uniform optical output power for LEDs on as-grown freestanding GaN substrates. Removal of these surface features by chemical mechanical polishing results in highly uniform peak wavelength and improved output power over the whole wafer area