RIGIDITY, CONNECTIVITY, AND GLASS-FORMING ABILITY

Following the ideas of Zachariasen and of Cooper, it is argued that the glass-forming ability of a system can be rationalized in terms of the degrees of freedom available to form an infinitely large topologically disordered network composed of rigid structural units connected at vertices, edges, or faces. Expressions are derived for the degrees of freedom for regular and irregular networks composed of regular or distorted polytopes sharing vertices, edges, or faces. The condition that degrees of freedom must be non-negative for such a disordered network to exist is in agreement with the empirical results on glass-forming abilities of a variety of covalent, ionic, and metallic systems. The present approach can be used to screen the proposed models of structure of a glass and to predict the boundaries of glass-forming regions in composition spaces.