VITREOUS B2O3 - A GEOMETRICAL STUDY

Vitreous boron trioxide (B2O3) is an intrinsic noncrystalline material with planar equilateral triangles (BO3 triangles) as structural units , presenting an overall two-dimensional character, a solid-like membra ne structure. The local structural similarities between that glass and the negatively curved Bethe lattice motivated us to build an ideal mo del for vitreous B2O3, propagating its local order on a surface of con stant negative Gaussian curvature (the hyperbolic plane H2) and using non-Euclidean hierarchical lattices as structural substrates. Based on the metric and symmetry properties of such lattices, we make an analy tical investigation of the structure of the ideal glass model. This wa y, we obtain the peaks of the geometrical radial distribution function for the ideal glass structure, which are in good agreement with exper imental data and theoretical studies for vitreous B2O3. Those facts su ggest the evidence of non-Euclidean local order for that amorphous sol id, indicating the arrangement of planar triangular units on a negativ ely curved surface, forming few or no six-membered (boroxol) rings.