Symmetry foundations of a polymer model for close-packed metallic liquids and glasses

Abstract

The atomic packing density of metallic melts and glasses is too high for their structures to be considered as chaotic. To remove this contradiction, we propose to describe the structures of metallic liquids and the glasses that form from them using (i) a base set of three spirals made of regular tetrahedra with specific noncrystallographic symmetry and (ii) combinatorial permutations of the vertices of a set of the coordination polyhedra that describe the polymorphic transformations in metals. The symmetry base of the proposed model of the structures of liquids and glasses is represented by projective linear groups PSL(2, p), where the order of the Galois field is p = 3, 7, and 11. These groups uniquely determine a tetrahedron, the 7-vertex joining of four tetrahedra along their faces (tetrablock), the 11-vertex joining of two tetrablocks into a spiral, and the throwing over of the diagonals in a rhombus from two triangular faces of neighboring tetrahedra. The throwing over of the diagonals in a rhombus is considered as a unit act of any structural transformation and ensures the melt–crystal, melt–glass, and glass-crystal transitions and the structural relaxation of metallic glasses. In terms of the proposed scheme, the high density of melts and glasses is caused by tetrahedral packing (up to 78%), and the absence of a diffraction pattern of melts and glasses is explained by the absence of translation along the spiral axis. The suggested polymer model also explains the collective effects (string vibrations) that were detected upon measuring the shear modulus relaxation of a metallic glass.