Critical Chords of Convex Bodies of Constant Width

In this paper, we show that when Minkowski measure of asymmetry of convex body K of constant width is bigger than α (n-1), K has at least n+1 critical chords, where \(\alpha (n) = \frac{{n + \sqrt {2n(n + 1)} }}{{n + 2}}\).     

Wiener Indices in Random Cyclooctane Chains

The Wiener index of a connected graph (molecule graph) G is the sum of the distances between all pairs of vertices of G. In this paper, simple exact formula are established for the expected value of Wiener index in random cyclooctane chain. Moreover, we obtain the average value of the Wiener indices with respect to the set of all cyclooctane chains with n octagons.     

Shear-thickening behavior of Fe-ZSM5 zeolite slurry and its removal with alumina/boehmites

A cryogenic scanning electron microscopy (cryo-SEM) technique was used to explore the shear-thickening behavior of Fe-ZSM5 zeolite pastes and to discover its underlying mechanism. Bare Fe-ZSM5 zeolite samples were found to contain agglomerations, which may break the flow of the pastes and cause shear-thickening behaviors. However, the shear-thickening behaviors can be eliminated by the addition of halloysite and various boehmites because of improved particle packing. Furthermore, compared with pure Fe-ZSM5 zeolite samples and its composite samples with halloysite, the samples with boehmite (Pural SB or Disperal) additions exhibited network structures in their cryo-SEM images; these structures could facilitate the storage and release of flow water, smooth paste flow, and avoid shear-thickening. By contrast, another boehmite (Versal 250) formed agglomerations rather than network structures after being added to the Fe-ZSM5 zeolite paste and resulted in shear-thickening behavior. Consequently, the results suggest that these network structures play key roles in eliminating the shear-thickening behavior.     

Fabrication of homogeneously dispersed graphene/Al composites by solution mixing and powder metallurgy

Graphene-reinforced aluminum (Al) matrix composites were successfully prepared via solution mixing and powder metallurgy in this study. The mechanical properties of the composites were studied using microhardness and tensile tests. Compared to the pure Al alloy, the graphene/Al composites showed increased strength and hardness. A tensile strength of 255 MPa was achieved for the graphene/Al composite with only 0.3wt% graphene, which has a 25% increase over the tensile strength of the pure Al matrix. Raman spectroscopy, Fourier transform infrared spectroscopy, scanning electron microscopy, and transmission electron microscopy were used to investigate the morphologies, chemical compositions, and microstructures of the graphene and the graphene/Al composites. On the basis of fractographic evidence, a relevant fracture mechanism is proposed.     

Microstructure and mechanical properties of SiC-particle-strengthening tri-metal Al/Cu/Ni composite produced by accumulative roll bonding process

In this study, a multilayer Al/Ni/Cu composite reinforced with SiC particles was produced using an accumulative roll bonding (ARB) process with different cycles. The microstructure and mechanical properties of this composite were investigated using optical and scanning microscopy and hardness and tensile testing. The results show that by increasing the applied strain, the Al/Ni/Cu multilayer composite converted from layer features to near a particle-strengthening characteristic. After the fifth ARB cycle, a composite with a uniform distribution of reinforcements (Cu, Ni, and SiC) was fabricated. The tensile strength of the composite increased from the initial sandwich structure to the first ARB cycle and then decreased from the first to the third ARB cycle. Upon reaching five ARB cycles, the tensile strength of the composite increased again. The variation in the elongation of the composite exhibited a tendency similar to that of its tensile strength. It is observed that with increasing strain, the microhardness values of the Al, Cu, and Ni layers increased, and that the dominant fracture mechanisms of Al and Cu were dimple formation and ductile fracture. In contrast, brittle fracture in specific plains was the main characteristic of Ni fractures.     

Crystallographic texture and earing behavior analysis for different second cold reductions of double-reduction tinplate

Since the production of tinplate with non-earing properties is difficult, especially when it is produced via the double-reduction process, the optimal degree of second cold reduction is particularly important for achieving desirable drawing properties. The evolution of texture and the earing propensity of double-reduction tinplate with different extents of second reduction were investigated in this study. Optical microscopy and scanning electron microscopy were used to observe the changes in the microstructure at various extents of reduction. Two common testing methods, X-ray diffraction (XRD) and electron backscatter diffraction, were used to investigate the texture of the specimens, which revealed the effects of deformation percentage on the final texture development and the change in the grain boundary. The earing rate was determined via earing tests involving measurement of the height of any ear. The results obtained from both XRD analyses and earing tests revealed the same ideal value for the second cold reduction on the basis of the relationship between crystallographic texture and the degree of earing.     

Analysis of the formation conditions and characteristics of interphase and random vanadium precipitation in a low-carbon steel during isothermal heat treatment

The characteristics of nanosized precipitates in steels depend on the heat-treatment parameters. The effects of characteristics of vanadium precipitates formed during isothermal heat treatment on the hardness of the ferrite matrix in low-carbon vanadium-alloyed steel were investigated through analysis of transmission electron microscopy images and microhardness measurements. The results show that, during isothermal holding in the temperature range from 675 to 750℃, only interphase precipitation occurs, whereas only random precipitation occurs in the ferrite matrix during holding at 600℃. Furthermore, during isothermal heat treatment between 600 and 675℃, both random and interphase precipitates occurred in the ferrite. Nanoscale vanadium carbides with different atomic ratios of vanadium (V) and carbon (C) were the dominant precipitates in the random and interphase precipitates. The sizes of random precipitation carbides were smaller than those of interphase ones. Also, the sample isothermally heat treated at 650℃ for 900 s exhibited a higher hardness with a narrower hardness distribution.     

Solid-phase synthesis of Cu<Subscript>2</Subscript>MoS<Subscript>4</Subscript> nanoparticles for degradation of methyl blue under a halogen-tungsten lamp

The Cu₂MoS₄ nanoparticles were prepared using a relatively simple and convenient solid-phase process, which was applied for the first time. The crystalline structure, morphology, and optical properties of Cu₂MoS₄ nanoparticles were characterized using X-ray diffraction, X-ray photoelectron spectroscopy, field emission scanning electron microscopy, and UV-vis spectrophotometry. Cu₂MoS₄ nanoparticles having a band gap of 1.66 eV exhibits good photocatalytic activity in the degradation of methylene blue, which indicates that this simple process may be critical to facilitate the cheap production of photocatalysts.     

Isothermal reduction kinetics and mineral phase of chromium-bearing vanadium-titanium sinter reduced with CO gas at 873-1273 K

Reduction of chromium-bearing vanadium-titanium sinter (CVTS) was studied under simulated conditions of a blast furnace, and thermodynamics and kinetics were theoretically analyzed. Reduction kinetics of CVTS at different temperatures was evaluated using a shrinking unreacted core model. The microstructure, mineral phase, and variation of the sinter during reduction were observed by X-ray diffraction, scanning electron microscopy, and metallographic microscopy. Results indicate that porosity of CVTS increased with temperature. Meanwhile, the reduction degree of the sinter improved with the reduction rate. Reduction of the sinter was controlled by a chemical reaction at the initial stage and inner diffusion at the final stage. Activation energies measured 29.22-99.69 kJ/mol. Phase transformations in CVTS reduction are as follows:Fe₂O₃→Fe₃O₄→FeO→Fe; Fe₂TiO₅→Fe₂TiO₄→FeTiO₃; FeO·V₂O₃→V₂O₃; FeO·Cr₂O₃→Cr₂O₃.     

Effects of Zn content on the microstructure and the mechanical and corrosion properties of as-cast low-alloyed Mg–Zn–Ca alloys

The effects of Zn content on the microstructure and the mechanical and corrosion properties of as-cast low-alloyed Mg–xZn–0.2Ca alloys (x=0.6wt%, 2.0wt%, 2.5wt%, hereafter denoted as 0.6Zn, 2.0Zn, and 2.5Zn alloys, respectively) are investigated. The results show that the Zn content not only influences grain refinement but also induces different phase precipitation behaviors. The as-cast microstructure of the 0.6Zn alloy is composed of α-Mg, Mg₂Ca, and Ca₂Mg₆Zn₃ phases, whereas 2.0Zn and 2.5Zn alloys only contain α-Mg and Ca₂Mg₆Zn₃ phases, as revealed by X-ray diffraction (XRD) and transmission electron microscopy (TEM) analyses. Moreover, with increasing Zn content, both the ultimate tensile strength (UTS) and the elongation to fracture first increase and then decrease. Among the three investigated alloys, the largest UTS (178 MPa) and the highest elongation to fracture (6.5%) are obtained for the 2.0Zn alloy. In addition, the corrosion rate increases with increasing Zn content. This paper provides an updated investigation of the alloy composition–microstructure–property relationships of different Zn-containing Mg–Zn–Ca alloys.