Three dimensional accurate morphology measurements of polystyrene standard particles on silicon substrate by electron tomography

Polystyrene latex (PSL) nanoparticle (NP) sample is one of the most widely used standard materials. It is used for calibration of particle counters and particle size measurement tools. It has been reported that the measured NP sizes by various methods, such as Differential Mobility Analysis, dynamic light scattering (DLS), optical microscopy (OM), scanning electron microscopy (SEM) and atomic force microscopy (AFM), differ from each other. Deformation of PSL NPs on mica substrate has been reported in AFM measurements: the lateral width of PSL NPs is smaller than their vertical height. To provide a reliable calibration standard, the deformation must be measured by a method that can reliably visualize the entire three dimensional (3D) shape of the PSL NPs. Here we present a method for detailed measurement of PSL NP 3D shape by means of electron tomography in a transmission electron microscope. The observed shape of the PSL NPs with 100 nm and 50 nm diameter were not spherical, but squished in direction perpendicular to the support substrate by about 7.4% and 12.1%, respectively. The high difference in surface energy of the PSL NPs and that of substrate together with their low Young modulus appear to explain the squishing of the NPs without presence of water film.     

Asymptotically exact a posteriori local discontinuous Galerkin error estimates for the one‐dimensional second‐order wave equation

In this article, we analyze a residual‐based a posteriori error estimates of the spatial errors for the semidiscrete local discontinuous Galerkin (LDG) method applied to the one‐dimensional second‐order wave equation. These error estimates are computationally simple and are obtained by solving a local steady problem with no boundary condition on each element. We apply the optimal L² error estimates and the superconvergence results of Part I of this work [Baccouch, Numer Methods Partial Differential Equations 30 (2014), 862–901] to prove that, for smooth solutions, these a posteriori LDG error estimates for the solution and its spatial derivative, at a fixed time, converge to the true spatial errors in the L²‐norm under mesh refinement. The order of convergence is proved to be , when p‐degree piecewise polynomials with are used. As a consequence, we prove that the LDG method combined with the a posteriori error estimation procedure yields both accurate error estimates and superconvergent solutions. Our computational results show higher convergence rate. We further prove that the global effectivity indices, for both the solution and its derivative, in the L²‐norm converge to unity at rate while numerically they exhibit and rates, respectively. Numerical experiments are shown to validate the theoretical results. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1461–1491, 2015     

On the Nano/Micro-Mechanics of Metallic Glass

Metallic glass (MG) is amorphous and has some outstanding properties such as ultrahigh strength, superior elasticity, and excellent thermo-plasticity. However, as MG is relatively new to the metal family, the relationship between its physical properties and amorphous structure is still unclear. This article aims to provide an insightful discussion through a comprehensive review about the investigations in the past few decades on the scientific mechanisms of this class of material. The discussion of the paper will include the following key aspects: (1) the formation mechanism of an amorphous structure through glass transition, (2) the structural characterization and models, (3) the micromechanics of plastic event and shear band, and (4) the correlation between the amorphous structure and its mechanical properties.     

Nonlinear phase field theory for fracture and twinning with analysis of simple shear

A phase field theory for coupled twinning and fracture in single crystal domains is developed. Distinct order parameters denote twinned and fractured domains, finite strains are addressed and elastic nonlinearity is included via a neo-Hookean strain energy potential. The governing equations and boundary conditions are derived; an incremental energy minimization approach is advocated for prediction of equilibrium microstructural morphologies under quasi-static loading protocols. Aspects of the theory are analysed in detail for a material element undergoing simple shear deformation. Exact analytical and/or one-dimensional numerical solutions are obtained in dimensionless form for stress states, stability criteria and order parameter profiles at localized fractures or twinning zones. For sufficient applied strain, the relative likelihood of localized twinning vs. localized fracture is found to depend only on the ratio of twin boundary surface energy to fracture surface energy. Predicted criteria for shear stress-driven fracture or twinning are often found to be in closer agreement with test data for several types of real crystals than those based on the concept of theoretical strength.     

Deformation Temperature and Lamellar Thickness Dependency of FormⅠto Form Ⅲ Phase Transition in Syndiotactic Polypropylene during Tensile Stretching

Phase transition from form Ⅰto form Ⅲ in syndiotactic polypropylene crystallized at different conditions during tensile deformation at different temperatures was investigated by using in situ synchrotron wide angle X-ray diffraction technique. In all cases, the occurrence of this phase transition was observed. The onset strain of this transition was found to be crystalline thickness decided by crystallization temperature and drawing temperature dependent. The effect of drawing temperature on this phase transition is understood by the changes in mechanical properties with temperature. Moreover, crystalline thickness dependency of the phase transition reveals that this form I to from III phase transition occurs first in those lamellae with their normal along the stretching direction which have not experienced stress induced melting and recrystallization.     

Light-Driven Crawling of Molecular Crystals by Phase-Dependent Transient Elastic Lattice Deformation

The light-driven crawling of a molecular crystal that can form three phases, (α, β, and γ) is presented. Laser irradiation of the molecular crystal can generate phase-dependent transient elastic lattice deformation. The resulting elastic lattice deformation that follows scanning irradiation of a laser can actuate the different phases of molecular crystal to move with different velocity and direction. Because the γ phase has a large Young's modulus (ca. 26 GPa), a force of 0.1 μN can be generated under one laser spot. The generated force is sufficient to actuate the γ-formed molecular crystals in a wide dimensional range to move longitudinally at a velocity of about 60 μm min⁻¹, which is two orders of magnitude faster than the α and β phases.     

Performance of a parallel viscoelastic-viscoplastic model for a microcellular thermoplastic foam on wide temperature range

This paper is concerned with the experimental testing and the constitutive modelling of a thermoplastic microcellular polyethylene-terephthalate (MC-PET) foam on the temperature range of 21–210 °C in order to investigate the temperature-dependent performance of the applied parallel viscoelastic-viscoplastic material model. By means of carefully designed uniaxial mechanical tests in temperature chamber, the viscous, elastic and yielding behaviours of the investigated material are identified, which are then applied for selecting suitable viscoelastic-viscoplastic constitutive models. The material characterization process is conducted using finite-element-based fitting method, including also the analysis of the applied numerical optimization algorithm. The fitting results are used to analyse the parameter sensitivity and to propose closed-form analytical relations for the temperature dependency of the material parameters. Finally, the utilisation of the analytical temperature functions for speeding up the parameter-fitting process is also demonstrated.     

Resistivity and Thermal Expansion (4.2–820 K) of Skutterudites after Severe Plastic Deformation via HPT

Thermoelectric materials with a high figure of merit, ZT, are the essential basis to build thermoelectric generators, which can directly convert heat into electricity. Severe plastic deformation (SPD) via high-pressure torsion (HPT) was successfully applied to enhance ZT of ball-milled and hot-pressed skutterudites as well as to produce bulk nanostructured skutterudites directly from powders. SPD introduces many defects into the sample and in parallel the crystallite size is significantly reduced. During measurement-induced heating these defects anneal partially out, and the grains grow. In this work for the first time systematically the changes of the temperature-dependent electrical resistivity and of thermal expansion were compared. It could be shown that for p- and n-type skutterudites, being hot-pressed and HPT-processed as well as directly HPT-processed from compacted powder, these changes occur more or less simultaneously within the same temperature ranges. This evaluation gives a much deeper insight into the thermoelectric behavior of HPT samples under the influence of changing temperature.