6850
J. Phys. Chem. B 2004, 108, 6850-6855
Organization of Coordination Polyhedra in an Amorphous Binary Alloy† Julia´ n R. Ferna´ ndez‡ and Peter Harrowell*,§ School of Chemistry, UniVersity of Sydney, New South Wales 2006, Australia, and Comisio´ n Nacional de Energı´a Ato´ mica, AV. Libertador 8250, Capital Federal, Buenos Aires, Argentina ReceiVed: December 1, 2003
The local and intermediate structure of a simulated metal-metalloid glass-forming alloy is reported. The model, due to Kob and Andersen, has been the subject of considerable study in the context of the glass transition. In the A75B25 mixture the low-temperature coordination polyhedra about the B (“metalloid”) particles are dominated by geometries based on either the capped trigonal prism or the square antiprism. As the concentration of B particles increases from 0.25 to 0.5, the B coordination changes from regular 8- and 9-fold polyhedra to distorted and irregular 6- and 7-fold geometries.
1. Introduction science,1
In a recently published history of material Robert Cahn identified three preconditions for the emergence of material science: understanding the atomic structure; identifying the phase equilibria; establishing the microsctructure. It could be argued that amorphous materials struggle to meet all three of these preconditions. The difficulty in describing the structure of glasses has particularly serious consequences. Open any text on materials or the solid state and one finds atomic structure consistently invoked to rationalize properties as diverse as thermal expansivity, electronic conductivity, particle diffusion, and plastic deformation. Without a description of structure, the account of these properties in amorphous materials is condemned to the phenomenological. In this paper we examine the structure of a simulated amorphous alloy consisting of a binary mixture whose interactions have been chosen to resemble those between a transition metal and a metalloid. “Structure”, here, refers to (i) the arrangement of nearest neighbor atoms into coordination polyhedra (the local order) and (ii) the links between these polyhedra (the intermediate order). Any useful description of structure must entail a significant reduction of information from that represented by the positions of all atoms in a given stable configuration. Why should we believe that such a reduction exists in the case of amorphous solids? Here is one reason for hope. The number of local minima in the configurational potential energy of an amorphous material is found to decrease rapidly with the decreasing energy of the minima. The increasing rarity of low-energy minima implies the increase of the implicit structural constraints that these arrangements of atoms must satisfy. Identify these constraints and we might have found our “useful” structural description of amorphous order. 2. Background In 1960 Duwez2 produced the first metallic glass by rapidly quenching a Au4Si alloy. This work coincided with the development by Bernal3 and Finney4 of the idea that random close packing of hard spheres offered a reasonable model of †
Part of the special issue “Hans C. Andersen Festschrift”. Comisio´n Nacional de Energı´a Ato´mica. § University of Sydney. ‡
liquid and glass structure. While random close packing is now most frequently invoked in a thermodynamic context as the end point of compression of the hard sphere liquid, it is worth noting in the context of this paper that Bernal looked upon it as a state with structure. Specifically, Bernal noted that one could classify the stable voids by considering the possible polyhedra within which a particle could not fit. In 1972 Polk5 suggested that the metal-metalloid glasses consisted of a random close-packed arrangement of metal atoms with the smaller metalloid occupying the appropriate subset of Bernal’s voids. This proposal was criticized6 because its prediction that the metal-metal structure factor would be essentially independent of the choice of metalloid did not agree with experiment. Gaskell,7 in response, argued that the metal-metalloid glasses exhibited specific chemical ordering in which the metalloid organized the surrounding metals into a preferred coordination polyhedron. In the case of the Ni80P20 glass, Gaskell suggested that this coordination geometry would be the tricapped trigonal prism (TTP), the same coordination as found in the crystal Ni3P. He went on to propose that the intermediate structure could be generated by the packing of TTP’s in a random combination of Fe3C-like and Fe3P-like arrangements. The partial radial distribution functions, generated along these lines and followed energy relaxation, are in good agreement with scattering data. The presence of local structure in metal-metalloid glasses based on the trigonal prism is now generally accepted.8 The nature of the intermediate structure, however, remains largely unresolved. Packing arguments developed by Egami9 and Miracle10 form the basis of much of the theoretical discussion of the preferred local structure in amorphous solids. These theories have used the minimization of strain within the shell of first neighbors about a solute atom as a criterion for identifying the suitable size ratios for good glass-forming alloys. In this approach, the stability of the TTP coordination is associated with atomic size ratios
