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

S. Kraposhin, A. L. Talis

ABSTRACT:

High atomic packing densities of metallic melts and glasses are in the apparent contradiction with the concept of a random atomic packing. To remove this contradiction it is proposed a description for the structure of metallic melts and glasses based on: 1) the set of three spiral packing of tetrahedra having a special non-crystallographic symmetry; 2) combinatorial permutations of vertices which are belonging to the limited set of coordination polyhedra. The permutations  said above were proposed before as  a mechanism for polymorphic transformations in metals. The projective linear groups PSL(2, p) with the Galois field of order p = 3, 7, 11 serve as symmetry foundations for the proposed model. These groups are uniquely determining a tetrahedron, 7-vertex tetra-block as joining of four tetrahedra in a face-to-face mode, 11-vertex joining of two tetra-blocks into a spiral chain, and also throwing over diagonals in the rhombus consisting of two triangular faces in the neighboring tetrahedra. The throwing over of rhombus diagonals were considered as the unit action of any structure transformation, and it ensure the fulfillment of transitions as following: melt-crystal, melt-glass, glass-crystal, and a set of relaxation phenomena during annealing of metallic glasses. In the frameworks of the proposed model high atomic packing densities of melts and glasses could be explained by tetrahedral packing (up to 78%), The polymer model could also explain the collective phenomena (string oscillations) which was observed during shear modulus relaxations of metallic glasses.

KEYWORDS:

structure, melts, glasses, symmetry, combinatorics, tetrahedral chains, structure transformations