A lower bound for the hitting set size for combinatorial rectangles and an application

We prove a lower bound of Omega(1/epsilon (m + log(d - a)) where a = [log(m) (1/4epsilon)] for the hitting set size for combinatorial rectangles of volume at least epsilon in [m](d) space, for epsilon is an element of [m(-(d-2)), 2/9] and d > 2. (C) 2002 Elsevier Science B.V. All rights reserved.

The influence of grain size on deformation of copper

It is well know that grain boundaries enhance strength at low temperatures by acting as obstacles to dislocation motion, and they retard strength at higher temperatures by processes involving grain boundary sliding. The available data on the influence of grain boundaries on deformation in copper is summarized. Equi-channel angular extrusion offers a convenient means for imposing severe plastic deformation to refine the grain size in bulk materials. Experimental data on fine grained copper produced by equi-channel angular extrusion will be described, and the implications of the data for diffusion creep and superplasticity will be discussed.

Fe–Cr/Al2O3 metal-ceramic composites: Nature and size of the metal particles formed during hydrogen reduction

Fe-Cr/Al2O3 metal-ceramic composites prepared by hydrogen reduction at different temperatures and for different periods have been investigated by a combined use of Mössbauer spectroscopy, x-ray diffraction, transmission electron microscopy, and energy-dispersive x-ray spectroscopy in order to obtain information on the nature of the metallic species formed. Total reduction of Fe3+ does not occur by increasing the reduction time at 1320 K from 1 to 30 h, and the amount of superparamagnetic metallic species is essentially constant (about 10%). Temperatures higher than 1470 K are needed to achieve nearly total reduction of substitutional Fe3+. Interestingly, iron favors the reduction of chromium. The composition of the Fe-Cr particles is strongly dependent on their size, the Cr content being higher in particles smaller than 10 nm.

Size-dependent cohesive energy and melting of non-spherical nanoparticles

All most all theoretical models assume spherical nanoparticles. However, thermodynamic properties of non-spherical nanoparticles are the subject of recent interests. In this article, we have discussed the size-dependent cohesive energy and melting of non-spherical nanoparticles based on liquid-drop model. The surface to volume ratio is different for different shapes of nanoparticles and as a consequence, the variation of cohesive energy and melting of non-spherical nanoparticles is different from that of spherical case. By analyzing the reported experimental results, it has been observed that liquid-drop model can be used to understand the size-dependent cohesive energy and melting of non-spherical nanoparticles.

Size-dependent and strain rate effects in quantum dot nanostructures with molecular dynamic simulations

Size and strain rate effects are among several factors which play an important role in determining the response of nanostructures, such as their deformations, to the mechanical loadings. The mechanical deformations in nanostructure systems at finite temperatures are intrinsically dynamic processes. Most of the recent works in this context have been focused on nanowires [1, 2], but very little attention has been paid to such low dimensional nanostructures as quantum dots (QDs). In this contribution, molecular dynamics (MD) simulations with an embedded atom potential method(EAM) are carried out to analyse the size and strain rate effects in the silicon (Si) QDs, as an example. We consider various geometries of QDs such as spherical, cylindrical and cubic. We choose Si QDs as an example due to their major applications in solar cells and biosensing. The analysis has also been focused on the variation in the deformation mechanisms with the size and strain rate for Si QD embedded in a matrix of SiO2 [3] (other cases include SiN and SiC matrices).It is observed that the mechanical properties are the functions of the QD size, shape and strain rate as it is in the case for nanowires [2]. We also present the comparative study resulted from the application of different EAM potentials in particular, the Stillinger-Weber (SW) potential, the Tersoff potentials and the environment-dependent interatomic potential (EDIP) [1]. Finally, based on the stabilized structural properties we compute electronic bandstructures of our nanostructures using an envelope function approach and its finite element implementation.

Size dependent microstructure for Ag-Ni nanoparticles

The Ag-Ni system is characterized by large differences in atomic sizes (14%) and a positive heat of mixing (+23 kJ mol(-1)). The binary equilibrium diagram for this system therefore exhibits a large miscibility gap in both solid and liquid state. This paper explores the size-dependent changes in microstructure and the suppression of the miscibility gap which occurs when free alloy particles of nanometer size are synthesized by co-reduction of Ag and Ni metal precursors. The paper reports that complete mixing between Ag and Ni atoms could be achieved for smaller nanoparticles (<7 nm). These particles exhibit a single-phase solid solution with face-centered cubic (fcc) structure. With increase in size, the nanoparticles revealed two distinct regions. One of the regions is composed of pure Ag. This region partially surrounds a region of fcc solid solution at an early stage of decomposition. Experimental observations were compared with the results obtained from the thermodynamic calculations, which compared the free energies corresponding to a physical mixture of pure Ag and Ni phases and a fcc Ag-Ni solid solution for different particle sizes. Results from the theoretical calculations revealed that, for the Ag-Ni system, solid solution was energetically preferred over the physical mixture configuration for particle sizes of 7 nm and below. The experimentally observed two-phase microstructure for larger particles was thus primarily due to the growth of Ag-rich regions epitaxially on initially formed small fcc Ag-Ni nanoparticles. (C) 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.