Nature of the Structural Transformations in ${\mathrm{B}}_2{\mathrm{O}}_3$ Glass under High Pressure

We study high-pressure polyamorphism of ${\mathrm{B}}_2{\mathrm{O}}_3$ glass using x-ray diffraction up to 10 GPa in the 300–700 K temperature range, in situ volumetric measurements up to 9 GPa, and first-principles simulations. Under pressure, glass undergoes two-stage transformations including a gradual increase of the first B-O (O-B) coordination numbers above 5 GPa. The fraction of boron atoms in the fourfold-coordinated state at $P<10\mathrm{GPa}$ is smaller than was assumed from inelastic x-ray scattering spectroscopy data, but is considerably larger than was previously suggested by the classical molecular dynamics simulations. The observed transformations under both compression and decompression are broad in hydrostatic conditions. On the basis of ab initio results, we also predict one more transformation to a superdense phase, in which B atoms are sixfold coordinated.

Figure 1

Examples of the energy-dispersive x-ray diffraction (EDXD) data for the glassy ${\mathrm{B}}_2{\mathrm{O}}_3$ (a), measured at different pressures at the two angles of the detector; calculated from the experimental EDXD data structure factor (b) and total correlation function $T(r)$ (c), and comparison of the experimental and computer simulated structural correlation functions $g(r)$ for different pressures (d). All experimental curves for $P=9.5\mathrm{GPa}$ correspond to the sample obtained after heating to 650 K. The line type notations in (c) and in the inset of (c) are the same as in (b). The inset in (c) shows enlarged fragments of selected $T(r)$ curves for the first B-O and O-B coordination spheres. Thicker lines in (b) and (c) correspond to the second stage of the glass transformation.

Figure 2

Polyhedron representation of the simulated ${\mathrm{B}}_2{\mathrm{O}}_3$ glass structure at zero pressure (a), $P=20\mathrm{GPa}$ (b), and $P=200\mathrm{GPa}$ (c). The plot (d) shows the distribution of distances from the B atom to the ${\mathrm{O}}_3$ plane in the ${\mathrm{BO}}_3$ units for 2 different pressures.

Figure 3

Results of the in situ volumetric measurements of the glassy ${\mathrm{B}}_2{\mathrm{O}}_3$ under pressure (a) in the two different runs of compression (solid symbols) and decompression (open symbols), and pressure dependences of the bulk modulus (b) obtained by the direct numerical differentiation of the curves from the plot (a) (relaxed modulus). The significant jumps of the bulk modulus between the final of compression and onset of decompression for both runs correspond to the jumps between relaxed and unrelaxed values (see the text).

Figure 4

Comparison of pressure dependences of the experimental Fig. 3, compression in the run I) and simulated density (a), and simulated pressure dependences of the averaged 1st coordination numbers for B and O (b). The inset in (b) shows pressure dependences of the 1st coordination number for B from the current experiment (x-ray diffraction) and simulation and according to the data from Refs. 12, 13, 14. Point A in the experimental dependence corresponds to the sample state after heating to 650 K under pressure, whereas the open circle (point B) corresponds to the similar state as point A (estimation) which should be observed under room-temperature compression.