Due to essential need of Al-Cu alloys in different applications such as aerospace and automotive industries, and the mechanical characteristics of Al-Cu alloys being weak; the effect of vanadium addition at a rate of 0.1% on the mechanical behavior, microhardness, and microstructure have been investigated. The effect of upsetting process -cold work- on the microstructure, microhardness has been also investigated. Three set of alloys namely; Al, Al-9%Cu, and Al-9%Cu-0.1%Vwere prepared. Thespecimens for microstructure, microhardness and compression tests were machined. The mechanical tests were performed to investigate the effect of vanadium addition and the effect of upsetting process.It was found that the 0.1% vanadium addition resulted in grain refinement of Al-9% Cu alloys of about 32.3 %, furthermore, and extra refining resulted after upsetting process by 44.2 %. On the other hand, the microhardness of Al-9%Cu enhanced by 54.1 %, and the valuable result was a 422.8 % enhancement in the microhardness of Al-9%Cu-0.1%V alloy after upsetting process compared to pure Al.
An experimental method for determining the equilibrium charge state of fast helium ions backscattered by solid Al-foils has been conducted using single Silicon Surface Barrier Detector (SBD) in a post acceleration system (PAS). The charge state measurements have been conducted to cover a wide energy range of the incident singly charged helium ion He + . The detected charge states increases from 0 to +Z with the incident ion's velocity. The method consists of measuring the charge states of ions after backscattering from the Al-foil as a function of projectile velocity and also finding the charge state distributions as a function of Al-foil thickness. The measurements are conducted for two types of Al-foil, one of which is thinner (2.5, 4.0, 5.4 μg/cm 2 ) and the other of which is of the order of an equilibrium foil thickness, where thicknesses of 6.8, 8.1, 9.5, and 10.8 were used. Ratios of equilibrium charge state yields for singly to doubly ionized He ions; He +1 and He
+2, were also measured. The kinematics behavior of the measured He 0 , He + and He +2 fractions is understood by the well-known Rutherford Backscattering Spectrometry technique (RBS). It has been shown that the dominant processes occurring to a fast He + ions traversing Al-foil are the capture of the electron from the Al-atom to vacant state in the ion and the stripping of the bound electron from the He + ion. The charge composition of the ion beams changes when it backscatters Al-foil, which thick enough for multiple atomic collisions, leading eventually to an equilibrium charge state distribution (ECSD). It was found that the theoretical calculations for electron-capture and loss ratios, based of semi-classical approach of Bianconi, are successful in describing the measured He ions. The satisfactory fits of the measured equilibrium charge state fractions (ECSF's) are mainly accounted to the contribution of both free valance electrons of the target and screened target nucleus in the calculation of total electron-loss cross sections. Bianconi approach is also applied to describe the measured mean equilibrium charges (MEC). The agreement between experiment and theory in this investigation is accounted to the reliability of the used post-acceleration system where all the backscattering charge-states, at certain incident ion's velocity, are separated and collected in one measurement.
In this paper, time-independent Schr"{o}dinger equation for a charged particle, in the presence of electric potential and vector potential, has been solved using He's Homotopy Perturbation Method (HPM). HPM is one of the newest analytical methods to solve linear and nonlinear differential equations. In contrast to the traditional perturbation methods, the Homotopy method does not require a small parameter in the equation. In this method, according to the homotopy technique, a Homotopy with an embedding parameter $delta in lbrack 0,1]$ is constructed, and the embedding parameter is considered as a small parameter. Using cylindrical coordinates, it has been found that the z-equation of the charged particle is a one-dimensional harmonic oscillator and the r equation is actually a two-dimensional harmonic oscillator. The obtained results show the evidence of simplicity, usefulness, and effectiveness of the HPM for obtaining approximate analytical solutions for the time-independent Schr"{o}dinger equation for a charged particle in parallel electric and magnetic fields
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