Structure and Ionic Conductivity in the Mixed-Network Former Chalcogenide Glass System [Na2S](2/3)[(B2S3)(x)(P2S5)(1-x)](1/3)

Glasses in the system [Na2S](2/3)[(B2S3)(x)(P2S5)(1-x)](1/3) (0.0 <= x <= 1.0) were prepared by the melt quenching technique, and their properties were characterized by thermal analysis and impedance spectroscopy. Their atomic-level structures were comprehensively characterized by Raman spectroscopy and B-11, P-31, and Na-23 high resolution solid state magic-angle spinning (MAS) NMR techniques. P-31 MAS NMR peak assignments were made by the presence or absence of homonuclear indirect P-31-P-31 spin-spin interactions as detected using homonuclear J-resolved and refocused INADEQUATE techniques. The extent of B-S-P connectivity in the glassy network was quantified by P-31{B-11} and B-11{P-31} rotational echo double resonance spectroscopy. The results clearly illustrate that the network modifier alkali sulfide, Na2S, is not proportionally shared between the two network former components, B and P. Rather, the thiophosphate (P) component tends to attract a larger concentration of network modifier species than predicted by the bulk composition, and this results in the conversion of P2S74-, pyrothiophosphate, Na/P = 2:1, units into PS43-, orthothiophosphate, Na/P = 3:1, groups. Charge balance is maintained by increasing the net degree of polymerization of the thioborate (B) units through the formation of covalent bridging sulfur (BS) units, B S B. Detailed inspection of the B-11 MAS NMR spectra reveals that multiple thioborate units are formed, ranging from neutral BS3/2 groups all the way to the fully depolymerized orthothioborate (BS33-) species. On the basis of these results, a comprehensive and quantitative structural model is developed for these glasses, on the basis of which the compositional trends in the glass transition temperatures (T-g) and ionic conductivities can be rationalized. Up to x = 0.4, the dominant process can be described in a simplified way by the net reaction equation P-1 + B-1 reversible arrow P-0 + B-4, where the superscripts denote the number of BS atoms for the respective network former species. Above x = 0.4, all of the thiophosphate units are of the P-0 type and both pyro-(B-1) and orthothioborate (B-0) species make increasing contributions to the network structure with increasing x. In sharp contrast to the situation in sodium borophosphate glasses, four-coordinated thioborate species are generally less abundant and heteroatomic B-S-P linkages appear to not exist. On the basis of this structural information, compositional trends in the ionic conductivities are discussed in relation to the nature of the charge-compensating anionic species and the spatial distribution of the charge carriers.

STRUCTURE AND BIFURCATION OF PULLBACK ATTRACTORS IN A NON-AUTONOMOUS CHAFEE-INFANTE EQUATION

The Chafee-Infante equation is one of the canonical infinite-dimensional dynamical systems for which a complete description of the global attractor is available. In this paper we study the structure of the pullback attractor for a non-autonomous version of this equation, u(t) = u(xx) + lambda(xx) - lambda u beta(t)u(3), and investigate the bifurcations that this attractor undergoes as A is varied. We are able to describe these in some detail, despite the fact that our model is truly non-autonomous; i.e., we do not restrict to 'small perturbations' of the autonomous case.

Hard Thermal Loops in the n-Dimensional phi(3) Theory

We derive a closed-form result for the leading thermal contributions which appear in the n-dimensional I center dot (3) theory at high temperature. These contributions become local only in the long wavelength and in the static limits, being given by different expressions in these two limits.