Theories in Spin Dynamics of Solid-State Nuclear Magnetic Resonance Spectroscopy

This short review article presents theories used in solid-state nuclear magnetic resonance spectroscopy. Main theories used in NMR include the average Hamiltonian theory, the Floquet theory and the developing theories are the Fer expansion or the Floquet-Magnus expansion. These approaches provide solutions to the time-dependent Schrodinger equation which is a central problem in quantum physics in general and solid-state nuclear magnetic resonance in particular. Methods of these expansion schemes used as numerical integrators for solving the time dependent Schrodinger equation are presented. The action of their propagator operators is also presented. We highlight potential future theoretical and numerical directions such as the time propagation calculated by Chebychev expansion of the time evolution operators and an interesting transformation called the Cayley method

Potential relativistic dispersion in material medium

Lorentz space-time transformation has been applied to the phase factor of a plane electromagnetic wave in linear material medium. The derivation shows in the limiting case for v = c, the phase velocity converges to its monochromatic value implying no such dispersion effect can exist in free space. However in linear material medium, wave speed may exceed the monochromatic phase velocity by a factor purely due to the relativistic consideration of the phase factor invariant under Lorentz transformation. The equation suggests such speed dispersion factor will be higher in the denser medium to its monochromatic material phase velocity. A critical cut-off number for the refractive index may exist to excite such mode in the material. The results can be interesting particularly for materials with high refractive index as well as for anisotropic space-time metric formulations in Transformation Optics. Keywords: Lorentz transformation, Phase factor, Refractive index, Dispersion facto

A study of PbS nanoparticle synthesis via sulfur powder

PbS nanoparticles (NPs) were synthesized by the hot-injection solution-phase method using sulfur powder as precursor. Pb-precursor (446 mg PbO) was dissolved with 1.5 ml oleic acid in 15 ml 1-octadecene (ODE) solvent inside a four-neck flask under N2 atmosphere and nucleated at 120 °C for half an hour. S-precursor (S powder), dissolved in a mixture of 3 ml ODE and 1 ml Oleylamine, was then injected swiftly by a syringe into the flask with well-dissolved Pb-precursor. The growth time varied from 10 minutes to a few hours and growth temperature was maintained at from 90 to 120 °C after injection, which would result in nanoparticles of different sizes from 5 to 10 nm. The synthesized PbS NPs were characterized by TEM, XRD, and UV-Vis-NIR spectrometer. The morphology as well as absorption spectra were found to be highly sensitive to the synthesis conditions. The XRD spectra showed that the structures were less sensitive to synthesis conditions