Molecular dynamics calculation of mean square displacement in alkali metals and rare gas solids and comparison with lattice dynamics

Molec ul ar dynamics calculations of the mean sq ua re displacement have been carried out for the alkali metals Na, K and Cs and for an fcc nearest neighbour Lennard-Jones model applicable to rare gas solids. The computations for the alkalis were done for several temperatures for temperature vol ume a swell as for the the ze r 0 pressure ze ro zero pressure volume corresponding to each temperature. In the fcc case, results were obtained for a wide range of both the temperature and density. Lattice dynamics calculations of the harmonic and the lowe s t order anharmonic (cubic and quartic) contributions to the mean square displacement were performed for the same potential models as in the molecular dynamics calculations. The Brillouin zone sums arising in the harmonic and the quartic terms were computed for very large numbers of points in q-space, and were extrapolated to obtain results ful converged with respect to the number of points in the Brillouin zone.An excellent agreement between the lattice dynamics results was observed molecular dynamics and in the case of all the alkali metals, e~ept for the zero pressure case of CSt where the difference is about 15 % near the melting temperature. It was concluded that for the alkalis, the lowest order perturbation theory works well even at temperat ures close to the melting temperat ure. For the fcc nearest neighbour model it was found that the number of particles (256) used for the molecular dynamics calculations, produces a result which is somewhere between 10 and 20 % smaller than the value converged with respect to the number of particles. However, the general temperature dependence of the mean square displacement is the same in molecular dynamics and lattice dynamics for all temperatures at the highest densities examined, while at higher volumes and high temperatures the results diverge. This indicates the importance of the higher order (eg. ~* ) perturbation theory contributions in these cases.

A29 NMR spin-lattice relaxation study of paramagnetics -doped orthosilictes

A ~si MAS NMR study of spin-lattice relaxation behaviour in paramagnetic-doped crystalline silicates was undertaken, using synthetic magnesium orthosilicate (forsterite) and synthetic zinc orthosilicate (willemite) doped with 0.1% to 20% of Co(II), Ni(II), or CU(II), as experimental systems. All of the samples studied exhibited a longitudinal magnetization return to the Boltzmann distribution of nuclear spin states which followed a stretched-exponential function of time: Y=exp [- (tjTn) n], Olattice relaxation time and paramagnetic dopant ion concentration, with Tni[M2+]i=Tnj[M2+]j for a given dopant and mineral. There are many cases where this correlation is not apparent, however, and this is attributed to the structural, phase, and ion distribution complexities inherent in many of these systems.

Investigating a dynamic modular framework for subjective well-being

According to Diener (1984), the three primary components of subjective well-being (SWB) are high life satisfaction (LS), frequent positive affect (P A), and infrequent negative affect (NA). The present dissertation extends previous research and theorizing on SWB by testing an innovative framework developed by Shmotkin (2005) in which SWB is conceptualized as an agentic process that promotes and maintains positive functioning. Two key components ofShmotkin's framework were explored in a longitudinal study of university students. In Part 1, SWB was examined as an integrated system of components organized within individuals. Using cluster analysis, five distinct configurations of LS, P A, and NA were identified at each wave. Individuals' SWB configurations were moderately stable over time, with the highest and lowest stabilities observed among participants characterized by "high SWB" and "low SWB" configurations, respectively. Changes in SWB configurations in the direction of a high SWB pattern, and stability among participants already characterized by high SWB, coincided with better than expected mental, physical, and interpersonal functioning over time. More positive levels of functioning and improvements in functioning over time discriminated among SWB configurations. However, prospective effects of SWB configurations on subsequent functioning were not observed. In Part 2, subjective temporal perspective "trajectories" were examined based on individuals' ratings of their past, present, and anticipated future LS. Upward subjective LS trajectories were normative at each wave. Cross-sectional analyses revealed consistent associations between upward subjective trajectories and lower levels of LS, as well as less positive mental, physical, and interpersonal functioning. Upward subjective LS trajectories were biased both with respect to underestimation of past LS and overestimation of future LS, demonstrating their illusional nature. Further, whereas more negative retrospective bias was associated with greater current distress and dysfunction, more positive prospective bias was associated with less positive functioning in the future. Prospective relations, however, were not consistently observed. Thus, steep upward subjective LS trajectory appeared to be a form of wishful-thinking, rather than an adaptive form of selfenhancement. Major limitations and important directions for future research are considered. Implications for Shmotkin's (2005) framework, and for research on SWB more generally, also are discussed

Tintype of Girl Peering through Lattice [n.d.]

A young African American girl peers through a lattice window in an unknown photographer's studio in this small black and white tintype. The girl in the photo is unidentified. There are slight scratches on the surface of the tintype, which is cut in a hexagonal shape. This tintype was in the possession of Iris Sloman Bell, of St. Catharines, Ontario. The Sloman - Bell families have relatives who are descended from Black slaves from the United States."Tintypes were the invention of Prof. Hamilton Smith of Ohio. They begin as thin sheets of iron, covered with a layer of black paint. This serves as the base for the same iodized collodion coating and silver nitrate bath used in the ambrotype process. First made in 1856, millions were produced well into the twentieth century. When tintypes were finished in the same sorts of mats and cases used for ambrotypes, it can be almost impossible to distinguish which process was used without removing the image to examine the substrate." Source: American Museum of Photography http://www.photographymuseum.com/primer.html