Topological criterion for metallic glass formation

Abstract

A topological model is proposed for metallic glass formation through destabilization of the host crystalline lattice by substitutional and/or interstitial solute elements. A solute element may partition between substitutional and interstitial sites and the model calculates relative site frequency as a function of the strain energy associated with each site. The strain energy, in turn, depends upon solute and solvent elastic properties and relative sizes, and upon temperature. The crystalline lattice is destabilized leading to amorphization when solute elements produce a critical internal strain required to change local coordination numbers. Fractions of solute atoms in interstitial and substitutional sites and the internal strain introduced by these atoms are calculated as functions of atomic radii and elastic moduli of solvent and solute elements and the absolute temperature. The critical concentration of a solute element required to destabilize the crystalline lattice of a binary alloy is also calculated as a function of the radius ratio R= R B/ R A of the solute and solvent elements. In the range of 0.5< R<1, the critical concentration decreases, reaches a minimum at R∼0.8 and then increases as the size of the solute element decreases relative to the solvent.