Multilevel algorithms for finite difference discretizations on sparse grids

We propose some algorithms to solve the system of linear equations arising from the finite difference discretization on sparse grids. For this, we will use the multilevel structure of the sparse grid space or its full grid subspaces, respectively.     

Direct experimental determination of grain boundary excess volume in metals

The grain boundary excess volume, i.e., the grain boundary expansion, e{GB}, was experimentally determined for high-angle grain boundaries in nickel using the direct technique of high-precision difference dilatometry. Values of e{GB}=(0.35±0.04)×10{-10} m and e{GB}=(0.32±0.04)×10{-10} m were obtained by measuring the removal of grain boundary volume upon grain growth for two different types of ultrafine-grained samples. The results are discussed in comparison to values obtained so far from indirect techniques and from computer simulations. It demonstrates the strength of the presented novel, direct approach for grain boundary expansion measurements.     

Lifetime of Positrons in Nanostructured Nonstoichiometric Silver Sulfide Ag<Subscript>2–δ</Subscript>S

The lifetime of positrons in nanostructured nonstoichiometric silver sulfide Ag_2–δS samples with average nanoparticle sizes from 44 to 230 nm has been measured. It has been found that the lifetime spectra of Ag_2?δS nanoparticles include two components corresponding to the capture and annihilation of positrons in two types of defects: structural vacancies of the metallic sublattice and vacancy clusters at the interfaces between nanoparticles. The long surface component depends on the size of silver sulfide particles and indicates a difference in their defect structure.     

Formation of thermal vacancies on the Si sublattice of the intermetallic compound MoSi2

For a detailed understanding of high-temperature processes in complex solids the identification of the sublattice on which thermal defects are formed is of basic interest. Theoretical studies in intermetallic compounds favor a particular sublattice for thermal vacancy formation. In the present study we detect in ordered MoSi2 thermal vacancies with a low formation enthalpy of H(F)(V)=(1.6+/-0.1) eV, and we succeed in showing by experimental and theoretical efforts that they are preferentially formed on the Si sublattice. By these data self-diffusion in MoSi2 can be understood.     

Free volumes in bulk nanocrystalline metals studied by the complementary techniques of positron annihilation and dilatometry

Free-volume type defects, such as vacancies, vacancy-agglomerates, dislocations, and grain boundaries represent a key parameter in the properties of ultrafine-grained and nanocrystalline materials. Such free-volume type defects are introduced in high excess concentration during the processes of structural refinement by severe plastic deformation. The direct method of time-differential dilatometry is applied in the present work to determine the total amount and the kinetics of free volume by measuring the irreversible length change upon annealing of bulk nanocrystalline metals (Fe, Cu, Ni) prepared by high-pressure torsion (HPT). In the case of HPT-deformed Ni and Cu, distinct substages of the length change upon linear heating occur due to the loss of grain boundaries in the wake of crystallite growth. The data on dilatometric length change can be directly related to the fast annealing of free-volume type defects studied by in situ Doppler broadening measurements performed at the high-intensity positron beam of the FRM II (Garching, Munich, Germany).