Theory of the formation of metallic glasses

Abstract

The structure and stability of metallic glasses and the relationship between the constitution diagram and glass formation in binary alloy systems is discussed on a quantum-mechanical basis. An ab initio pseudopotential method is used to calculate the interatomic forces in transition-metal-free glass-forming alloys. The knowledge of the interatomic forces allows a microscopic calculation of the structure and of the thermodynamic properties of the crystalline, liquid, and amorphous intermetallic phases. The liquid and amorphous structures are calculated using cluster-relaxation and thermodynamic variational techniques. We show that the bonding in all stable phases arises from an optimal embedding of the neighboring atoms into the attractive minima of the interatomic pair potentials---for disordered phases this is visualized by the close matching between the minima in the pair potentials and the maxima in the partial pair-distribution functions. The role of the traditional alloy-chemical factors [(i) size ratio, (ii) strong chemical bonding (charge transfer and screening), and (iii) valence-electron concentration] in establishing this "constructive interference" is elucidated. It is argued that the geometrical basis of all these structures---crystalline as well as disordered---is tetrahedral close packing. For a majority concentration of the smaller atoms this leads to Frank-Kasper phases; for a majority concentration of the larger atoms this leads to a random tetrahedral packing based on icosahedral microunits. Thus the interrelation between the formation of topologically close-packed intermetallic compounds, the formation of eutectic phase diagrams, and the formation of metallic glasses is readily, and quantitatively, understood. The use of the pseudopotential technique restricts the application of our method to simple-metal glasses, but we argue that many of our results apply to all metalloid-free metallic glasses.