We employ Molecular Dynamics simulations to study the structure of vitreous boron oxide. Although six-membered boroxol rings have been observed at fractions over 60% by various experimental techniques, simulation methods have not produced similar results. We adapt the polarization model, which includes many body polarization effects thought to stablize such structures, for boron-oxygen interactions. This model is then used in MD simulations of boron oxide glass at various temperatures. We find a variation in the fraction of rings depending on the temperature of the system during network formation. The maximum ring fraction [>40%] occurs when the sample is prepared at low temperatures. At these temperatures, the energy level of boron atoms in rings is approximately 6% lower than the energies of boron atoms outside of rings. When higher equlibration temperatures are used, the fraction drops to 11%. Thus, in order to observe boroxol ring formation in simulations of boron oxide, a model which incorporates polarization effects must be used and network formation must occur at temperatures where ring formation is favored.

I. Introduction

Boron oxide [chemical formula B₂O₃] is a network glass-former. The short-range structure of B₂O₃ is the planar BO₃ triangle, where each boron atom is bonded to three oxygen atoms with O-B-O angles of 120°. The intermediate-range structure, or the arrangement of these triangles, has been established by various experimental techniques as the planar boroxol ring, illustrated in Figure 1. Boroxol rings at fractions ranging from f = 0.50 to f = 0.85 have been observed by inelastic neutron scattering (1,2), nuclear magnetic resonance (3-6), nuclear quadrupole resonance (7-9), Raman scattering (10-20), electron paramagnetic resonance (21,22) and diffraction techniques (23,24). Despite the abundant experimental evidence for boroxol rings, the majority of molecular simulation studies do not reveal such structures. A reverse Monte Carlo study () has shown that a high percentage of boroxol rings cannot reproduce both structural data and density. In one simulation study, a small percentage [approx. 12%] of boroxol rings were observed (35) by including polarization of oxygen atoms. The other studies have employed various two-body, three-body and in one case (33) four-body potentials. In the four-body case, a ring fraction of 3% was observed. One study using a three-body potential (36) cites a ring fraction of less than 20%.

No simulation study thus far has found a significant found fraction of boroxol rings, and the reason for this is uncertain. One suggestion comes from the work of Teter (35). This work used ab initio calculations to calibrate a model for boron oxide. These calculations revealed that polarization of the oxygen atoms is crucial in models of this type. Polarization is built into the Teter model by constructing an oxygen ion as a central charge surrounded by four auxiliary charges in tetrahedral symmetry. Within this simple representation of oxygen polarizability, the fraction of boroxol rings increased from less than 1% to a final value of 12% as the magnitude of the auxiliary charges was increased from zero. Thus for a simple ionic model, negligible ring formation was observed, but as polarization effects are introduced, the ring concentration rises.

One of us (37,38) has developed a more realistic model of polarizability. This model incorporates a many body, non-additive interaction describing the dipole moments induced by vibrational distortion. Polarization of oxygen ions thus arises from the other ions present and is dependent upon their locations in the sample and thus its configuration. Potentials for this model have been developed for Si⁴⁺, O^2-, H⁺, and F^- (39). The MD program for this polarization model implements an alternative to periodic boundary conditions that allows for simulation of chemical reactions. Conservative external forces are used to provide what can be viewed as a "chemical reactor containment vessel". These forces act as semipermeable membranes the selectively pass or block individual atomic species. This allows for a study of reactive processes with automatic removal of reaction byproducts. The polarization model has been used to study reactions and charge transfer processes in water (40-43) and recently has been applied to silica glass (39). A description of the model is given in Section II.

The current paper describes the application of the polarization model to the simulation of vitreous boron oxide. We develop the necessary boron-oxygen and boron-boron potentials by matching structural and energetic data of isolated boron-oxygen and boron-oxygen-hydrogen molecules. This development is presented in Section III. We describe in Section IV the application of this model to investigate the structure of boron oxide. As with experimental preparation, we begin with an initial system of boric acid [H₃BO₃] molecules, from which dehydration reactions occur, eventually ending with boron oxide. The sample is then cooled, and a network structure develops. As expected, the developing structure consists of BO₃ triangles. Whether this network incorporates boroxol rings is sensitive to the temperature at which the system is held during network formation. In the temperature range where boroxol rings are energetically favored, we find an experimentally relevant fraction of boroxol rings, f = 0.45.

Last updated 1-5-01