Vol. 64 No. 4 Jul-Aug (2018): Revista Mexicana de Física

This review article has the antecedents of Jaskolski’s 1996 Physics Report Confined Many-electron Systems , the fifteen chapters on the Theory of Confined Quantum Systems in Vols. 57 and 58 of 2009 Advances in Quantum Chemistry, and the nine chapters of the 2014 Monograph “Electronic Structure of Confined Quantum Atoms and Molecules”. In this contribution the last two sets of reviews are taken as the points of reference to illustrate some advances in several lines of research in the elapsed periods. The recent progress is illustrated on the basis of a selection of references from the literature taking into account the confined quantum systems, the confining environments and their modelings; their properties and processes, emphasizing the changes due to the confinement; the methods of analysis and solutions, their results including confiability and accuracy; as well as applications in other areas. The updated and current works of the Reviewer are also presented. The complementary words in the title apply to the simplest atom in its free configuration and to the harmonic oscillator quantum dot because they admit more exact solutions than the number of their degrees of freedom; and to their many-electron and confined counterparts, due to their additional interactions and changes in boundary conditions.

Transparent films based on Ti, Sn and Zn oxides are of great importance in electronic devices such as sensors, solar cells and conductive films, then the characterization techniques are highly relevant. The aim of this work is to identify the advantages and disadvantages of direct methods, such as profilometry, and indirect methods such as ellipsometry and spectrophotometry used to quantify film thickness. In this work, films were deposited by spray-pyrolysis on glass substrates at 425±C. Thicknesses varied between 150 and 300 nm. Thicknesses calculated by means of spectrophotometry and ellipsometry, led to differences below 10% and 20 %, respectively, with respect to the value measured
by profilometry.

Corrosion causes great losses and catastrophic damages in industrial plants and infrastructure, among the methods to reduce it are the coatings. The use of metal-ceramic multilayer coatings to reduce corrosion in steels is a viable option, since they offer several advantages over single-layer coatings, among which, they can be deposited with relatively high thicknesses and are able to dissipate the residual stresses that form during the growth of the thin films, which maintains its adhesion to the substrate. The coatings were deposited by magnetron Sputtering, using Ti and W targets. Two multilayer architectures were designed and deposited, including tungsten nitride (WN) and titanium tungsten nitride (WTiN) coatings with alternated bilayers of Ti/TiN and W/WN, those two deposition sequences of layer were identified as A with more Ti and B layers with higher W content; both consist of a nine-layer deposit process. The structure was studied by X-ray diffraction and the morphology and composition by SEM and EDS respectively. The surface was studied with profilometry and atomic force microscopy. The electrochemical behavior was analyzed in a sodium chloride solution by means of potentiodynamic polarizations and electrochemical impedance spectroscopy (EIS). X-ray diffraction results show the presence of two phases of WN. The grain size of coating A is similar to that obtained in coating B. The morphology of the multilayers showed a mostly smooth surface but with the presence of spherical domes, as well as cracks in both coatings, being more abundant in the coating B. In its cross section, the sequence of multilayers composed of layers of Ti, W, TiN, WTiN and WN is observed, however in some cases the change between the individual layers is not observed and two layers remain as one in the images of MEB. The electrochemical results obtained by potentiodynamic polarization curves showed a shift of the corrosion potential towards more noble values. The corrosion current in coating A with more layers of Ti is lower than coating B and both improve the corrosion resistance of the substrate. This behavior was confirmed in the Nyquist diagram obtained by EIS.

A method is presented to obtain the orientation curve in the Eulerian space, of crystallites which diffract in one point of a Debye-Scherer ring in a second diffraction process. The incident beam is therefore the reflected beam of a previous diffraction process, and the sample has a general orientation for a pole figure measurement, given as usual by two angles, χ  around the sample Y axis, and φ around the sample normal. Two solutions are found for all secondary reflections. The method proposed here was outlined somewhere else for the measurement of pole figures by neutron diffraction [1], and here important improvements are made, especially regarding the mathematical methods.

Rare earth nano sized pollycrystalline orthoferrites and orthocromites ReT mO3 (Re = La, Nd, Gd, Dy, Y and T m = Fe, Cr) have been synthesized by sol-gel auto combustion citrate method. The samples have been characterized by means of X-ray diffraction (XRD), scanning electron microscope (SEM), energy dispersive X-ray spectroscopy (EDX), and UV-visible spectroscopy. The samples are single phase as confirmed by XRD analysis and correspond to the orthorhombic crystal symmetry with space group pbnm. Debye Scherer formula and Williamson Hall analysis have been used to calculate the average grain size which is consistent with that of determined from SEM analysis and varied between 25-75 nm. The elemental compositions of all samples have been checked by EDX analysis. Different crystallographic parameters are calculated with strong structural correlation among Re and Tm sites. The optical energy band gap has been calculated by using Tauc relation estimated to be in the range of 1.77 - 1.87 eV and 2.77 - 3.14 eV, for ReFeO3 and ReCrO3, respectively.

In this work, it is shown the feasibility for obtaining silver nanoparticles by ultrasonic spray pyrolysis and their simultaneous incorporation during deposition of thin layers of aluminum oxide to get a Cermet coating of Al₂O₃-Ag. The synthesis of these Cermets was achieved on the basis of both the simultaneous pyrolysis of silver nitrate and aluminum acetylacetonate on different substrates: Quartz, glass, crystalline silicon (c-Si), and titanium at temperatures of 500, 550 and 600 °C. The optical and structural properties of the Cermets were studied by Scanning Electron Microscopy, Atomic Force Microscopy, X-ray diffraction, UV-vis, UV-vis-IR and FT-IR spectroscopies. UV-Vis spectroscopy showed that the intensity of the absorption peak (plasmon) was limited to the concentration of silver nitrate, and it shifted toward shorter wavelengths with the decrease in the size of the Ag nanoparticles inside the Cermets. The plasmon position of Ag nanoparticles in the different samples was found to be centered at 504 nm, 506 nm, 497 nm and 475 nm for samples deposited with 0.1 mol, 0.05 mol, 0.02 mol, and 0.01 mol of Ag(NO₃), respectively. The shape of the Ag nanoparticles was approximately spherical, ranging from 4 nm to 35 nm, and their concentration was proportional to the concentration of Ag(NO₃) included in the spray solution. By means of the UV-Vis Spectroscopy-IR and FT-IR, in the best of cases, a solar absorptance of 0.83 and an infrared thermal emittance of 0.14, for a sample of Al₂O₃-Ag prepared with 0.1 mol of Ag(NO₃) in the precursor solution, were obtained.

We computed accurate values for the ground state energy of a hydrogen atom by a finite spherical barrier of height V₀ as a function of the confinement radius . We consider the nucleus as a sphere with a uniform charge distribution instead of as a point particle. The contribution to the ground state energy due to the finite nuclear size is computed as a function of the confinement radius,  and the height of the barrier, V₀, using time-independent perturbation theory. For an impenetrable cavity with .5 au, we found that this energy correction is fifty times higher than the corresponding value for the free hydrogen atom. For a finite value of V₀,we found that the maximum of the energy correction is reached at a value  which very is close to the position at which the electron density is most compact around to the nucleus. This is confirmed though the Shannon entropy in configuration space.

Inspired in a recent theoretical work for the determination of the Mueller matrix, using as incidence a single classically entangled polarization state (F. Töppel et al., New J. Phys. 16 (2014) 073019), an experimental setup is proposed and tested.  The open space and two wave plate retarders are used as the transparent, nondepolarizing samples under study. Results show some experimental improvements are necessary in order to implement accurately the theoretical proposal in which this work is based.

We realized a study of the shortest path fractal dimension  in three dimensions for randomly crumpled paper balls. We took measurements between all possible combinations of pairs of points in crumpled and flat configurations, we found that a correlation between these distances exist, even more, such mean experimental value is dmin=1.2953±0.02 that coincides almost numerically with the very known 3D shortest path fractal dimension for percolation systems reported in computational simulations.

Non-linear thermal radiation effects on non-aligned stagnation point flow of Maxwell fluid have been carried out in the present investigation. It is observed that the non-linear radiation augments the temperature and heat transfer rate. This physical phenomenon is translated into a system of partial differential equations (PDEs). After useful transformation, these non-linear constitutive equations are transformed into a system of ordinary differential equations (ODEs) and interpreted numerically by means of parallel shooting technique. Effects of pertinent parameters on flow and heat transfer are elaborated through tables and graphs. It is observed that radiation and surface heating enhance the rate of heat transfer, however Prandtl number has inverse relation with thermal boundary layer thickness. It has been observed that for increasing Prandtl number, heat transfer rate enhances. The detailed discussion of heat transfer rate is also presented in this study. Flow pattern is judged through streamlines graphs. It is also observed that oblique stagnation point flow behaves like orthogonal stagnation point flow, when free stream velocity is very large as compared to stretching velocity.

The b-boundary is a mathematical tool used to attach a topological boundary to incomplete Lorentzian manifolds using a Riemaniann metric called the Schmidt metric on the frame bundle. In this paper we give the general form of the Schmidt metric in the case of Lorentzian surfaces. Furthermore, we write the Ricci scalar of the Schmidt metric in terms of the Ricci scalar of the Lorentzian manifold and give some examples. Finally, we discuss some applications to general relativity.