J. Phys. I France
Volume 3, Numéro 5, May 1993
Page(s) 1119 - 1130
DOI: 10.1051/jp1:1993260
J. Phys. I France 3 (1993) 1119-1130

Vitreous B 2O 3 : a geometrical study

J. A. de Miranda-Neto and Fernando Moraes

Departamento de Fisica, UFPE, 50739 Recife, PE, Brazil

(Received 18 September 1992, revised 22 December 1992, accepted 15 January 1993)

Vitreous boron trioxide (B 2O 3) is an intrinsic noncrystalline material with planar equilateral triangles (BO 3 triangles) as structural units, presenting an overall two-dimensional character, a solid-like membrane structure. The local structural similarities between that glass and the negatively curved Bethe lattice motivated us to build an ideal model for vitreous B 2O 3, propagating its local order on a surface of constant negative Gaussian curvature (the hyperbolic plane $\mathbb{H} ^2$) and using non-Euclidean hierarchical lattices as structural substrates. Based on the metric and symmetry properties of such lattices, we make an analytical investigation of the structure of the ideal glass model. This way, we obtain the peaks of the geometrical radial distribution function for the ideal glass structure, which are in good agreement with experimental data and theoretical studies for vitreous B 2O 3. Those facts suggest the evidence of non-Euclidean local order for that amorphous solid, indicating the arrangement of planar triangular units on a negatively curved surface, forming few or no six-membered (boroxol) rings.

61.40D - 64.60C - 02.40

© Les Editions de Physique 1993

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