Growth and Melting of Metallic Nanoclusters in Glass: A Review of Recent Investigations

The mechanisms of nucleation and growth and the solid-to-liquid transition of metallic nanoclusters embedded in sodium borate glass were recently studied in situ via small-angle X-ray scattering (SAXS) and wide-an-le X-ray scattering (WAXS). SAXS results indicate that, under isothermal annealing conditions, the formation and growth of Bi or Ag nanoclusters embedded in sodium borate glass occurs through two successive stages after a short incubation period. The first stage is characterized by the nucleation and growth of spherical metal clusters promoted by the diffusion of Bi or Ag atoms through the initially supersaturated glass phase. The second stage is named the coarsening stage and occurs when the (Bi- or Ag-) doping level of the vitreous matrix is close to the equilibrium value. The experimental results demonstrated that, at advanced stages of the growth process, the time dependence of the average radius and density number of the clusters is in agreement with the classical Lifshitz-Slyozov-Waoner (LSW) theory. However, the radius distribution function is better described by a lognormal function than by the function derived from the theoretical LSW model. From the results of SAXS measurements at different temperatures, the activation energies for the diffusion of Ag and Bi through sodium borate glass were determined. In addition, via combination of the results of simultaneous WAXS and SAXS measurements at different temperatures, the crystallographic structure and the dependence of melting temperature T(m) on crystal radius R of Bi nanocrystals were established. The experimental results indicate that T(m) is a linear and decreasing function of nanocrystal reciprocal radius 1/R, in agreement with the Couchman and Jesser theoretical model. Finally, a weak contraction in the lattice parameters of Bi nanocrystals with respect to bulk crystals was established.

TAUT REPRESENTATIONS OF COMPACT SIMPLE LIE GROUPS

The concept of taut submanifold of Euclidean space is due to Carter and West, and can be traced back to the work of Chern and Lashof on immersions with minimal total absolute curvature and the subsequent reformulation of that work by Kuiper in terms of critical point theory. In this paper, we classify the reducible representations of compact simple Lie groups, all of whose orbits are tautly embedded in Euclidean space, with respect to Z(2)-coefficients.