Simulated structural and thermal properties of glassy and liquid germania

Structural, dynamical, and thermal properties of germanium dioxide are investigated with classical molecular dynamics simulations from the amorphous to the liquid state. Pair correlation functions and coordination numbers are computed under pressure change and show the progressive conversion of the tetrahedral network into an octahedral network, in agreement with experiments. The thermodynamical behavior of the liquid is investigated by means of an equation of state that allows a precise estimation of the compressibility. At low temperature, the diffusion constant $D$ shows an Arrhenius law that progressively deviates when the temperature is increased. The overall comparison with simulated silica permits finally to outline not only the differences in the physical behavior of these two similar systems but also to stress the limitation of the employed germania potential.

Figure 1

Evolution of the liquid potential energy with temperature for two different densities ${\rho }_g=3.66\mathrm{g}{\mathrm{cm}}^{-3}$ and $\rho =4.10\mathrm{g}{\mathrm{cm}}^{-3}$. Both are represented after subtraction of $9RT∕2$ to account for the harmonic motions in the glassy state upon cooling (solid line) and heating (broken line). The dotted curves correspond to a heating after relaxation of the glass during $1\mathrm{ns}$ at $800\mathrm{K}$. For clarity, the upper curves have been shifted upwards by $25\mathrm{kJ}{\mathrm{mol}}^{-1}$. The inset shows the high- and low-temperature linear extrapolation that serve to roughly estimate $T_g$ (here $\rho =4.1\mathrm{g}∕{\mathrm{cm}}^3)$

Figure 2

Liquid potential energy (solid line) with temperature from a different cooling scheme (see below) together with a fit (broken line) that permits to extract the heat capacity (inset). The filled box corresponds to the inflexion point of $C_p$.

Figure 3

Computed enthalpy of the liquid and glass phase $H\left(T\right)-H\left(273\right)$ (solid line) compared to calorimetric data from Richet [46] and a polynomial expansion (broken line) of $H\left(T\right)$ from Richet and Bottinga [47].

Figure 4

Time dependence of the mean-squared displacement of oxygen for different temperatures ranging from $2500\text{to}920\mathrm{K}$.

Figure 5

Arrhenius plot of the germanium and oxygen diffusion constants. Solid and broken lines: Arrhenius fits to the data at low temperatures with the displayed activation energies.

Figure 6

Diffusion constants of germania (same symbols as Fig. 5) and silica (Si filled triangles, O open triangles, [51]) compared with “Eyring” diffusion constants [Eq. (3) using $\lambda =2.8\mathrm{\AA }$ and the experimental viscosities for $\mathrm{Si}{\mathrm{O}}_2$ and $\mathrm{Ge}{\mathrm{O}}_2$]. Also shown are the experimental measurements of the silicon (filled boxes) and oxygen (open boxes) diffusion in silica [56, 57] and the oxygen diffusion in germania (∗, Ref. 52). The vertical broken line points out the approximate diffusivity cross-over at $T_g∕T=0.9$ between silica and germania (see text for details).

Figure 7

Pair distribution functions $g_{ij}\left(r\right)$ for amorphous germania, together with the total neutron distribution function $g^N\left(r\right)$. The arrows indicate the approximate position $r=r^{\prime }$ of the minimum and the inserts represent the corresponding running coordination numbers for the partials.

Figure 8

Simulated total neutron $T\left(r\right)$ (solid line) of vitreous germania, compared with results from neutron diffraction (points [63]).

Figure 9

Simulated neutron structure factor $S^N\left(Q\right)$ (solid line) of vitreous germania, compared with results from neutron diffraction from Price et al. (open circles [61]) and Hannon et al. (filled circles [63]).

Figure 10

Partial static structure factors $S_{ij}\left(Q\right)$ for vitreous germania at $300\mathrm{K}$ (solid lines). Same partials for a $\mathrm{Ge}{\mathrm{O}}_2$ glass under $16\mathrm{GPa}$ pressure (broken lines).

Figure 11

Upper panel: Density change with applied pressure (filled circles) and decompression from $16.6\mathrm{GPa}$ (open circles), $8.9\mathrm{GPa}$ (open boxes) and $5.8\mathrm{GPa}$ (open triangles). Lower panel: Ge-O coordination number variation with pressure under compression and decompression. The broken line shows the corresponding compression behavior in amorphous silica using the Tsuneyucki potential [59].

Figure 12

Neutron structure factor evolution with applied pressure in amorphous $\mathrm{Ge}{\mathrm{O}}_2$. The lower curve corresponds to the glass at zero pressure (density ${\rho }_g$). The vertical broken lines indicate the positions of the peaks of interest (see text for details).

Figure 13

Upper panel: Computed neutron pair correlation function $T\left(r\right)$ in the glass at $300\mathrm{K}$ (solid line, same as in Fig. 8) and in the melt at $T=1373\mathrm{K}$ (broken line). Lower panel: experimental radial distribution function obtained from x-ray scattering [38] at the same temperatures.

Figure 14

Isotherms for liquid germania from the low-temperature to the critical region $(1500\mathrm{K}⩽T⩽5000\mathrm{K})$. The curves are separated by $500\pm 40\mathrm{K}$ each. The inset shows the corresponding data in $(\rho ,P)$ together with the BM fits (solid lines).

Figure 15

Isothermal compressibility ${\kappa }_T$ with respect to density in liquid $\mathrm{Ge}{\mathrm{O}}_2$ for various temperatures ranging from $3500\text{to}1500\mathrm{K}$ separated by $500\mathrm{K}$ each (solid lines). The curves are computed using our BMEOS. The dashed line is extracted from a polynomial volume-pressure relationship obtained by Dingwell et al. [78] (see text for details) for $T\simeq 1700\mathrm{K}$. The inset shows along the liquid-vapor coexistence curve the computed density change with temperature (filled boxes), compared with experimental data from [38] (open box) and [78] (open circles). The broken line is a fit performed by Dingwell and co-workers [78].