Boubaker Polynomials Expansion Scheme Research Articles

Study of ytterbium doping effects on structural, mechanical and opto-thermal properties of sprayed ZnO thin films using the Boubaker Polynomials Expansion Scheme (BPES)

In this work, ZnO thin films have been grown on glass substrates by using a solution of propanol (C 3H 8O), water (H 2O) and zinc acetate (Z n (CH 3CO 2) 2) in acidified medium (pH 5). The obtained films were n doped with ytterbium (Yb) at the rates of 100, 200 and 300 ppm. The structural features of the doped films were investigated using XRD, atomic force microscopy and scanning electronic microscopy techniques. XRD analysis shows a strong (0 0 2) X-ray diffraction line for increasing Yb-doping amounts. This c-axis preferential orientation of ZnO crystallites is naturally required to use this oxide as transparent conductor in optoelectronic applications. Atomic force microscopy (AFM) analysis shows an enhancement in the surface roughness of the doped ZnO:Yb thin films. Optical measurements were performed in 300–1800 nm domain via transmittance T( λ) and reflectance R( λ) spectra. Conjoint optical and thermal properties were deduced from the optical measurements in reference to the Amlouk–Boubaker opto-thermal expansivity ψ AB. Optically relevant ytterbium doping effects have been discussed. Finally, mechanical measurements have been carried out using Vickers standard disposal. The results confirmed the structural and functional changes that several recent studies attributed to ytterbium doping.

Mathematical model of the Bloch NMR flow equations for the analysis of fluid flow in restricted geometries using the Boubaker polynomials expansion scheme

In this study, the Bloch NMR flow equations are modelled into diffusion equation with constant transport coefficient in terms of the NMR transverse magnetization. Mathematical conditions are established for the diffusion coefficients to be constant or spatially varied with direction. When these conditions are met, the diffusion coefficients can then be easily evaluated in terms of Boubaker polynomials for the study of flow in restricted geometries.

Cut-off cooling velocity profiling inside a keyhole model using the Boubaker polynomials expansion scheme

The time dependent heating and cooling velocities are investigated in this paper. The temperature profile is found by using a keyhole approximation for the melted zone and solving the heat transfer equation. A polynomial expansion has been deployed to determine the cooling velocity during welding cut-off stage. The maximum cooling velocity has been estimated to be V max ≈ 83°C s−1.

A Boubaker polynomials expansion scheme (BPES)-related protocol for measuring sprayed thin films thermal characteristics

Measurements of In2S3 and ZnIn2S4 sprayed thin films thermal characteristics have been carried out using the photodetection technique. The thermal conductivity k and diffusivity D were obtained using a new protocol based on photothermal signal parameters analysis. Measured values of k and D were respectively, (15.2±0.85) Wm−1K−1 and (69.8±7.1)×10−6m2s−1 for In2S3, (7.2±0.7) Wm−1K−1 and (32.7±4.3)×10−6m2s−1 for ZnIn2S4. These values are extremely important since similar compounds are more and more proposed as Cd-free alternative materials for solar cells buffer layers.

A study of sulfur/selenium substitution effects on physical and mechanical properties of vacuum-grown ZnS 1− xSe x compounds using Boubaker polynomials expansion scheme (BPES)

In this study, the effects of the sulfur–selenium substitution inside sprayed ZnS compounds are discussed. First, the spray pyrolysis method has been used to grow the ZnS layers on glass substrates at relatively low temperatures. After an appropriate cooling phase, the substrate-layer set was introduced inside a sealed tube. Consecutively, selenium supply was introduced and vaporized under vacuum conditions inside the sealed tube containing the formerly ZnS prepared layers. The annealing time was varied from 1 to 48 h. Precisely, the tube arrangement was heated to about 350 °C in order to vaporize the selenium. On heating supply withdrawal, the selenium reacts with the existing layer. To prevent revaporization and minimize undesirable zinc oxides formation during crystal growth, a small amount of nitrogen was introduced into the tube. AFM technique and Vickers microhardness protocol subjected to the Boubaker polynomials expansion Scheme (BPES), have been carried out in order to evaluate the obtained ZnS 1− x Se x | 0≤ x<0.5 layers performance and properties.