Raúl W. Gómez

Synthesis by molten salt method of the AFeO3 system (A=La, Gd) and its structural, vibrational and internal hyperfine magnetic field characterization

Abstract Polycrystalline samples of LaFeO3 and GdFeO3 were synthesized by the molten salt method. Some properties and the quality of the resulting compounds were investigated. The crystal structure and purity of the samples were determined through X-ray diffraction and Rietveld analysis. The vibrational properties were characterized by Raman and IR spectroscopy. Mossbauer spectroscopy was used to determine the ionic state of the Fe ions and the internal hyperfine magnetic fields. Considerable reduction of the heat treatment (temperature and time) for the reaction to take place was achieved without detriment of the quality of the compounds.

On the performance of Usain Bolt in the 100?m sprint

Many university texts on mechanics consider the effect of air drag force, using the slowing down of a parachute as an example. Very few discuss what happens when the drag force is proportional to both u and u 2 . In this paper we deal with a real problem to illustrate the effect of both terms on the speed of a runner: a theoretical model of the world-record 100 m sprint of Usain Bolt during the 2009 World Championships in Berlin is developed, assuming a drag force proportional to u and to u 2 . The resulting equation of motion is solved and fitted to the experimental data obtained from the International Association of Athletics Federations, which recorded Bolt’s position with a laser velocity guard device. It is worth noting that our model works only for short sprints. (Some figures may appear in colour only in the online journal)

A jumping cylinder on an inclined plane

The problem of a cylinder of mass m and radius r, with its centre of mass out of the cylinder’s axis, rolling on an inclined plane that makes an angle α with respect to the horizontal, is analysed. The equation of motion is partially solved to obtain the site where the cylinder loses contact with the inclined plane (jumps). Several simplifications are made: the analysed system consists of an homogeneous disc with a one-dimensional straight line mass parallel to the disc axis at a distance y < r of the centre of the cylinder. To compare our results with experimental data, we use a styrofoam cylinder to which a long brass rod is embedded parallel to the disc axis at a distance y < r from it, so the centre of mass lies at a distance d from the centre of the cylinder. Then the disc rolls without slipping on a long wooden ramp inclined at 15 ◦ ,3 0 ◦ and 45 ◦ with respect to the horizontal. To determine the jumping site, the movements are recorded with a high-speed video camera (Casio EX ZR100) at 240 and 480 frames per second. The experimental results agree well with the theoretical predictions.

Interactions of calcium with the external surfaces of fullerenes and endofullerenes doped with radioactive sodium iodide

AbstractWe report first-principles calculations carried out to analyze the adsorption of calcium on the outer surface of the fullerene C60, yielding [C60 + mCa]. Geometric optimization (GO) and molecular dynamics (MD) simulation were performed using the plane-wave pseudopotential method within the framework of density functional theory (DFT) and time-dependent DFT (TD-DFT) to investigate the configurations, the associated energies in the ground state, and the stabilities of fullerenes and endofullerenes doped with radioactive sodium iodide when they interact with calcium atoms on the outer fullerene surface (i.e., [nNa131I@C60 + mCa]). The reason for investigating these calcium-functionalized (endo)fullerene systems was to gauge their potential stability when used as vectors to deliver radioiodine to cancerous tissue in the human body. In the simulations, we found that the geometric limit on the number of calcium atoms that can be physisorbed on the outer surface of an empty fullerene while maintaining its structural stability is 28 calcium atoms, which also takes into account the proportional expansion of the fullerene as the number of absorbed calcium atoms increases. However, the stability of a fullerene system during calcium adsorption also strongly depends on whether any atoms or molecules are being encapsulated by the fullerene, as these encapsulated atoms/molecules can also interact with the fullerene and influence its stability. A Mulliken electronegativity analysis revealed that, when atoms inside and/or outside the fullerene donate charge (electrons) to the fullerene, the fullerene expands. The excess charge on the carbon atoms of the fullerene weakens some of the carbon–carbon bonds, potentially causing them to break, in which case the fullerene loses its ability to encapsulate molecules and releases them. Graphical AbstractDFT simulation of a endo fullerene doped with radioactive sodium iodide interacting with 28 calcium atoms in a geometric arrangement