Weak Convergence and Banach Space-Valued Functions: Improving the Stability Theory of Feynman’s Operational Calculi

In this paper we investigate the relation between weak convergence of a sequence \(\left\{ \mu_{n}\right\} \) of probability measures on a Polish space S converging weakly to the probability measure μ and continuous, norm-bounded functions into a Banach space X. We show that, given a norm-bounded continuous function f:S→X, it follows that \(\lim_{n\to\infty}\int_{S}f\, d\mu_{n}=\int_{S}f\, d\mu\)—the limit one has for bounded and continuous real (or complex)—valued functions on S. This result is then applied to the stability theory of Feynman’s operational calculus where it is shown that the theory can be significantly improved over previous results.     

Improvement of <Emphasis Type="Italic">n</Emphasis>-ZnO/<Emphasis Type="Italic">p</Emphasis>-Si photodiodes by embedding of silver nanoparticles

The photo-current of n-ZnO/p-Si heterojunction photodiodes was improved by embedding Ag nanoparticles in the interface (ZnO/nano-P_Ag/p-Si), and the ratio between photo- and dark-current increased by about three orders more than that of a n-ZnO/p-Si specimen. The improvement in the photo-current resulted from the light scattering of embedded Ag nanoparticles. The I–V curve of n-ZnO/p-Si degraded after thermal treatment (A-ZnO/p-Si) because the silicon robbed the oxygen from ZnO to form amorphous silicon dioxide and left an oxygen vacancy. Notably, the properties of ZnO/nano-P_Ag/p-Si were better in the time-dependent photoresponse under 10 V bias. Ag nanoparticles (15–20 nm) scattered the UV light randomly and increased the probability for the absorption of ZnO to enhance the properties of the photodiode.     

Pulsed spark-discharge assisted synthesis of colloidal gold nanoparticles in ethanol

A green method, using pulsed spark-discharge (PSD) to synthesize gold nanoparticles (AuNPs) in ethanol, is studied in this article. Unlike conventional methods for metal nanoparticles synthesis, the PSD method does not require the addition of chemical surfactants and stabilizers. The size of PSD–AuNPs is examined by transmission electron microscopy, with a range 5–50 nm. The chemical compounds, crystal structure, and surface plasmon resonance of PSD–AuNPs are studied using energy dispersive X-ray spectroscopy, X-ray diffraction, and UV–Visible spectroscopy, respectively. Zeta potential analysis shows that a negative charge (−40 mV) on the surface of the PSD–AuNPs may be contributing to the stability of the suspension. During the gold electrodes discharge in the ethanol, under an intensive electric field and thermal energy, bulk metallic gold and ethanol may produce AuNPs and varieties of chemical derivatives, which are also studied by GC/MS and FTIR to investigate the suspension mechanism. The analysis results show that there is an oxidation reaction of ethanol occurring during the PSD process to produce ethanol derivatives, such as acetaldehyde, acetic acid, and ethyl acetate, which may modify the surface of AuNPs by coordination of oxygen atoms. However, only acetic acid can form a negative charge by the deprotonation of the carboxylic group of surface in ethanol, resulting in the creation of a repulsion force between the particles to form the stable colloid system. The experimental results indicate that PSD is an alternative green process to synthesize gold nanoparticles suspension in ethanol. Moreover, with a gold rod consumption rate of 15 mg/L, concentrations of gold nanoparticles ~9 ppm have been observed; therefore, the net production rate is around 60%.     

Visible photoluminescence of nanometer-sized SiGe/Si heterostructure fabricated by ion implantation

An innovative fabrication technique for the nanometer-sized SiGe/Si heterostructure was developed in this study. Ge was induced in Si substrate by two-step ion implantation. The spherical SiGe nanoclusters are self-assembled in the Si substrate by subsequent rapid thermal annealing at 1,100 °C. The diameter of the spherical SiGe nanoclusters is 5–7 nm. Visible photoluminescence from this nanometer-sized SiGe/Si heterostructure at room temperature was investigated. We found three peak energies of visible luminescence spectra at 1.97, 2.13, and 2.16 eV, respectively. The luminescence intensity depends on the number of the nanoclusters and will be decreased because of the micro-defects around the heterostructure, which is discussed in detail.     

New concept of failure of thin organic films

A critical (steady state) value of the thermal expansion coefficients of different coatings was determined by a nondestructive technique (NDT) known as laser shearography. The behavior of organic coatings, i.e., ACE premium-grey enamel, a yellow acrylic lacquer, and a gold nail polish on a metallic alloy, i.e., a carbon steel, was investigated over a temperature range of 20–60 °C. The value of the thermal expansion coefficients of coatings was derived from the slope of the plot of the thermal deformation (strain) versus the applied temperature. The integrity of the coatings with respect to time was assessed by comparison the measured coefficients of thermal expansion (CTE) to the critical (steady state) or asymptotic value of CTE. By shearography, measurement of coating properties could be performed independent of parameters such as UV exposure, humidity, presence of chemical species, and other parameters which may normally interfere with conventional methods of the assessing of the integrity of coatings. Therefore, one may measure CTE of coatings, regardless of the history of the coating, in order to assess the integrity of coatings. Also, the obtained shearography data were found to be in a reasonable trend with the data of electrochemical impedance spectroscopy (EIS) in 3%NaCl solution.     

Gold,silver, and palladium nanoparticle/nano-agglomerate generation,collection, and characterization

Generation, collection, and characterization of gold, silver, and palladium nanoparticles and nano-agglomerates (collectively “nanoparticles”) have been explored. The nanoparticles were generated with a spark aerosol generator (Palas GFG-1000). They were collected using a deposition cell under diffusion and thermophoresis. The shapes and sizes of the deposited particles were measured using transmission electron microscopy (TEM). TEM images showed that the particles were in the range of 8–100 nm in diameter, and their shapes varied from nearly spherical to highly non-spherical. Thermophoresis enhanced the deposition of nanoparticles (over the diffusive or the isothermal deposition) in all cases. Further, the size distributions of the nanoparticles generated in the gas phase (aerosol) were measured using a scanning mobility particle sizer (SMPS 3080, TSI) spectrometer. The SMPS results show that an increase in the spark frequency of the generator shifted the size distributions of the nanoparticles to larger diameters, and the total particle mass production rate increased linearly with increase in the spark frequency. The computational fluid dynamics code Fluent (Ansys) was used to model the flow in the deposition cell, and the computed results conform to the observations.     

Modelling of optical absorption of silver NP’s produced by UV radiation embedded in mesostructured silica films

Hexagonal mesostructured films containing silver ions were obtained by sol–gel method. Brij 58 was used to produce channels into the film, which house these ions. The films were exposure to UV radiation to produced silver metallic nanoparticles. The presence of the metallic nanoparticles was determined by infrared spectroscopy and optical absorption. Besides, these nanoparticles and core–shell structures of silver–silver oxide nanoparticles were identified by high-resolution transmission electronic microscopy. From these measurements, the obtained size range for silver nanoparticles was 6.1 nm. The absorption spectrum located at 440 nm was modelled and well fitted with the Gans theory considering refractive index higher than the one coming from host matrix. This index is explained because the silver oxide shell modifies the local surrounding medium of the metallic nanoparticles.     

A carbon–LiFePO<Subscript>4</Subscript> nanocomposite as high-performance cathode material for lithium-ion batteries

A cathode material of an electrically conducting carbon–LiFePO₄ nanocomposite is synthesized by wet ball milling and spray drying of precursor powders prior to a solid-state reaction. The structural characterization shows that the composite is composed of LiFePO₄ crystals and 4.8 wt.% amorphous carbon. Galvanostatic charge/discharge measurements indicate that the composite exhibits a superior high energy and high cycling stability. This composite delivers a discharge capacity of 159.1 mAh g⁻¹ at 0.1 C, 150.8 mAh g⁻¹ at 1 C, and 140.1 mAh g⁻¹ at 2 C rate. The capacity retention of 99% is achieved after 200 cycles at 2 C. The 18,650 cylindrical batteries are assembled using the composite as cathode materials and demonstrate the capacity of 1,400 mAh and the capacity retention of 97% after 100 cycles at 1 C. These results reveal that the as-prepared LiFePO₄–carbon composite is one of the promising cathode materials for high-performance, advanced lithium-ion batteries directed to the hybrid electric vehicle and pure electric vehicle markets.     

Dielectric properties of thin-film ZrO<Subscript>2</Subscript> up to 50 GHz for RF MEMS switches

The dielectric properties of zirconium dioxide (ZrO₂) ceramic thin films were characterized up to 50 GHz using coplanar waveguides (CPWs) and metal–insulator–metal (MIM) capacitors with top circular electrodes. The ZrO₂ films were deposited using a chemical solution onto high-resistivity Si wafers and metal layers. The real part of the dielectric constant of approximately 22 and 26 was extracted at 50 GHz for CPW and MIM structures, respectively, and the loss tangent was approximately 0.09 at 50 GHz. C–V and I–V measurements were carried out to determine low-frequency and DC dielectric properties. The measurement results indicate that ZrO₂ is a promising material to be used as a dielectric layer for radio-frequency (RF) microelectromechanical systems (MEMS) capacitive switches.     

Magneto-electric response functions for simple atomic systems

We consider a simple atomic two-body bound state system that is overall charge neutral and placed in a static electric and magnetic field, and calculate the magneto-electric response function as a function of frequency. This is done from first principles using a two-particle Hamiltonian for both an harmonic oscillator and Coulomb binding potential. In the high frequency limit, the response function falls off as 1/ω ² whilst at low frequencies it tends to a constant value.