First-principles calculations of structural changes in ${\text{B}}_2{\text{O}}_3$ glass under pressure

Using first-principles calculations, we study pressure effects in ${\text{B}}_2{\text{O}}_3$ glass up to 600 GPa and perform a detailed analysis of the densified structure. Below approximately 10 GPa, the glass structure deforms without the appearance of increased coordination numbers. At the same time, some of the ${\text{BO}}_3$ units lose planarity. At higher pressure, we find a gradual increase in fourfold coordinated B atoms. Above approximately 150 GPa, ${\text{BO}}_5$ and ${\text{BO}}_6$ polyhedra appear in the structure, and their proportion increases up to the highest studied pressure of 600 GPa. We propose that our analysis stimulate the search for high-density phases of ${\text{B}}_2{\text{O}}_3$.

Figure 1

(Color online) Glass structure at (a) zero pressure, (b) 20 GPa, (c) 200 GPa, and (d) 600 GPa. (e) is a distorted ${\text{BO}}_3$ unit at 20 GPa. The following elements of glass at $P>150\text{GPa}$ are also shown: (f) five-coordinated ${\text{BO}}_5$ pyramid with a nearly flat base; (g) same as (f) with a different orientation; (h) ${\text{BO}}_5$ polyhedron; (i) ${\text{BO}}_6$ polyhedron; (j) fourfold coordinated O atom. Images generated using CrystalMaker® by CrystalMaker Software Ltd. (www.crystalmaker.com).

Figure 2

Experimental (circles) and simulated (solid line) density as a function of pressure. The inset magnifies the low-pressure region, and includes previous MD results with empirical potentials: △,[8] ▽.[7] Crosses $\times$, joined by the dotted line, show simulated density obtained by sequential decompression from 20 GPa.

Figure 3

Average coordination number of B, $N_{\text{B}}$, (top) and O, $N_{\text{O}}$, (bottom) atoms as a function of pressure. The inset magnifies the low-pressure region and compares the current ab initio results (◇) with our recent x-ray diffraction experiments[6] (○), previous inelastic x-ray scattering experiments[5] (△), and previous MD simulations with empirical potentials from Refs. 7 (dashed line) and 8 (long-dashed line). Crosses $\times$, joined by the dotted line, show simulated $N_{\text{B}}$ obtained by sequential decompression from 20 GPa.

Figure 4

Distribution of O-O-O angles in ${\text{BO}}_4$ tetrahedra at 20 (solid line) and 100 GPa (dashed line).

Figure 5

Distribution of distance $d$ from B atom to the O3 plane in the three-coordinated ${\text{BO}}_3$ states. Solid and dashed lines correspond to 20 and 6 GPa, respectively.

Figure 6

(a) Total radial distribution function in glass at zero pressure (solid line) and 20 GPa (dashed line); (b) distribution of B-O distances in ${\text{BO}}_3$ triangles at zero pressure (solid line), in ${\text{BO}}_3$ triangles (dashed line), and ${\text{BO}}_4$ tetrahedra (long-dashed line) at 20 GPa; (c) distribution of O-O distances in ${\text{BO}}_3$ triangles at zero pressure (solid line), in ${\text{BO}}_3$ triangles (dashed line), and ${\text{BO}}_4$ tetrahedra (long-dashed line) at 20 GPa. Distributions in (b) and (c) have the area of unity.