Structure, Stresses and Local Dynamics in Glasses

The interrelations between short range structural and elastic aspects in glasses and glass forming liquids pose important and yet unresolved questions. In this paper these relations are analyzed for mono-atomic glasses and stressed liquids with a short range repulsive-attractive pair potentials. Strong variations of the local pressure are found even in a zero temperature glass, whereas the largest values of pressure are the same in both glasses and liquids. The coordination number z(J) and the effective first peak radius depend on the local pressures J's. A linear relation was found between components of site stress tensor and the local elastic constants. A linear relation was also found between the trace of the squares of the local frequencies and the local pressures. Those relations hold for glasses at zero temperature and for liquids. We explain this by a relation between the structure and the potential terms. A structural similarity between liquids and solids is manifested by similar dependencies of the coordination number on the pressures.Comment: 7 pages, 11 figure

Random walk on disordered networks

Random walks are studied on disordered cellular networks in 2-and 3-dimensional spaces with arbitrary curvature. The coefficients of the evolution equation are calculated in term of the structural properties of the cellular system. The effects of disorder and space-curvature on the diffusion phenomena are investigated. In disordered systems the mean square displacement displays an enhancement at short time and a lowering at long ones, with respect to the ordered case. The asymptotic expression for the diffusion equation on hyperbolic cellular systems relates random walk on curved lattices to hyperbolic Brownian motion.Comment: 10 Pages, 3 Postscript figure

DISTRIBUTION DES MOMENTS MAGNÉTIQUES DANS LES ALLIAGES MÉTALLIQUES AMORPHES

Nous proposons un modèle simple pour le magnétisme dans un alliage métallique amorphe à température nulle. Ce modèle permet de distinguer les alliages ferromagnétiques des alliages antiferromagnétiques. Nous avons estimé la distribution statistique de la projection des moments magnétiques sur une direction de référence.We propose a simple model for magnetism in amorphous metallic alloys at O K temperature. The difference between ferromagnetism and antiferromagnetism is observed. The statistical distribution of the moment projection on a direction may be estimated

Periodic networks of disclination lines : application to metal structures

Complex structures for some metals (Mn, W, U etc...) are described. It is shown how it is possible to define these structures as polytetrahedral structures reticulated by a periodic network of disclination lines.Nous décrivons des structures complexes pour quelques métaux (Mn, W, U etc...) et montrons comment elles peuvent être définies comme des structures polytétraédriques réticulées par des lignes de disinclinaisons périodiques

Helices and helix packings derived from the {3,3,5}\mathsf{\{3,3,5\}} polytope

The $\{3,3,5\}$-polytope is described and used as template for dense structures. Then larger structures are derived from this polytope, using disclinations. That needs a study of symmetries in this polytope. A discretised version of the Hopf fibration is presented and used in order to generate a family of new polytopes. It is possible to gathered vertices of these structures on several helices and then to consider geometrical relation between these helices. This study is govern by biological consideration of helix building molecules, but the final purpose is to have a geometrical tool to study geometrical relationship occurring between different helices or strands. This can occur for instance in protein folding studies

ORIENTATIONAL ORDER IN DISORDERED SYSTEMS

Les structures désordonnées ne sont pas des structures aléatoires. Il y a encore beaucoup d'ordre dans un amorphe ou un liquide. Le point important est l'absence de périodicité qui était la référence pour la définition de l'ordre. L'ordre cristallin suppose trois types d'ordre : - L'Ordre local - L'Ordre de position - L'Ordre d'orientation Ces trois types d'ordre interagissant l'un avec l'autre. Dans les structures liquides ou amorphes, on suppose habituellement que seul l'ordre local persiste. Mais l'observation récente de quasi-cristaux ayant un ordre d'orientation sans périodicité démontre l'existence d'état intermédiaire entre le cristal et le liquide. Le concept d'ordre d'orientation est présenté à partir de l'exemple des phases hexatiques. Les pavages non périodiques de Penrose sont aussi des structures qui repoussent les frontières de la cristallographie. Des exemples à 2 et 3 dimensions sont présentés avec le calcul de leur transformée de Fourier (Duneau et Katz, 2 paraître dans PRL). Une propriété importante de ces structures est l'auto-similarité qui conduit au concept de hiérarchie. Des modèles avec un environnement local icosahédrique et une structure hiérarchique de défauts sont aussi une approche efficace des structures ayant un ordre intermédiaire entre le cristal et le liquide.Disordered structures are not random structures. There is still order in an amorphous or a liquid material. The main point is the lack of periodicity which was the reference for the definition of the order. Crystalline order supposes three types of order : - The local order - The positional order - The orientational order. All these orders interact one with the other. In amorphous or liquid structures we suppose usually that only the local order remains. But the recent experimental observation of quasi-crystal with a clear orientational order but without any periodicity indicates that there are intermediate cases between the crystalline and simple liquid structure. The concept of bond-orientational order is presented on the simple example of hexatic phase. The Penrose non-periodic tiling are also important structures which extend the frontier of the crystallography. Examples in 2D and 3D are presented with the recent calculation of their Fourier transform (Duneau and Katz, to appear in P R L). One important property of these structures is the self-similarity which leads to the concept of hierarchy. Models with icosahedral local configuration and with a hierarchy of defects are also fruitful ways to approach structures which have an intermediate order between the crystal and the simple liquid order

Disclination density in atomic structures described in curved spaces

The curvature of a space and the density of disclinations are two related quantities. There is an exact relation in 2-D spaces. We show how an approximate solution can be used in 3-D space. Applications to the β-W structure and the Laves phase are presented The coordination number in dense random structures is explained in terms of disclination density.La courbure de l'espace et la densité de disinclinaisons sont deux grandeurs connectées. Il y a une relation exacte à 2 dimensions. Nous montrons comment utiliser une relation approchée à 3 dimensions. Les applications à la structure W-β et aux phases de Laves sont présentées. La coordinance, dans les structures denses aléatoires, est expliquée à partir de la notion de densité de disinclinaison