NUCLEATION AND CRYSTAL GROWTH IN SOFT-SPHERE SYSTEMS

Partant d'une configuration amorphe modélisée, de 4000 "sphères-molles", une méthode de dynamique moléculaire permet d'illustrer la germination spontanée. L'analyse du processus de cristallisation, à trois étapes de la simulation, à l'aide des indices des polyèdres de Voronoï montre que des germes bcc et fcc continuent à croître. Des ambiguïtés dans la structure, apparaissant pour certains types d'indice, peuvent être levées en utilisant des méthodes graphiques numériques. Certaines de ces figures donnent l'impression d'un changement de phase localisé d'une structure bcc en fcc, ceci demandant à être confirmé expérimentalement.Spontaneous homogeneous nucleation can be demonstrated in a model of 4000 soft-spheres annealed from an amorphous starting configuration via a molecular dynamics method. Analysis of the crystallisation process at three stages of the simulation using Voronoi polyhedra indices shows that both bcc and fcc nuclei continue to grow. Methods of delineating the nuclei and the effects on their resulting shape and size are discussed, and it is shown how ambiguities in structure which arise both for particular index types and local arrangements can be resolved using computer graphics techniques. Some of the drawings displayed give the impression of localised phase change from bcc to fcc structure though these events have yet to be confirmed

A novel facility using a Laue focusing monochromator for high-pressure diffraction at the SRS, Daresbury, UK

In this paper, we present some generalizations of Gowers’s result about product-free subsets of groups. For any group G of order n, a subset A of G is said to be product-free if there is no solution of the equation ab = c with a, b, c Epsilon A. Previous results showed that the size of any product-free subset of G is at most n/delta1/3, where delta is the smallest dimension of a nontrivial representation of G. However, this upper bound does not match the best lower bound. We will generalize the upper bound to the case of product-poor subsets A, in which the equation ab = c is allowed to have a few solutions with a, b, c Epsilon A. We prove that the upper bound for the size of product-poor subsets is asymptotically the same as the size of product-free subsets. We will also generalize the concept of product-free to the case in which we have many subsets of a group, and different constraints about products of the elements in the subsets.National Science Foundation (U.S.) (CAREER grant DMS-0545904)Alfred P. Sloan Foundation (Sloan Fellowship)Massachusetts Institute of Technology. Undergraduate Research Opportunities Program (Paul E. Gray (1954) Endowed Fund

The structural characterization of amorphous thin films and coatings in their as-deposited state using x-rays at shallow angles of incidence

We demonstrate the method of x-ray diffraction at shallow angles of incidence, using the intrinsically highly collimated x-ray beam generated by a synchrotron source, to study the atomic-scale structure of amorphous thin films and coatings in their as-deposited (i.e., on-substrate) state. As the incident angle is decreased, scattering from the film/coating can be isolated as contributions from the substrate are reduced. Systems studied include chemical vapor deposition (CVD) diamond films deposited onto both silicon and steel substrates, where evidence of an interfacial region between the film and silicon wafer has been observed, but we focus on a range of amorphous films/coatings (mixed TiO2:SiO2 sol-gel spun films, hydrogenated carbon films and ''glassy'' carbon coatings, silicon: germanium semiconducting films and alumina coatings). The data are used both to comment upon the systems studied and to elucidate the potential, and the limitations, of the experimental method