Density functional and classical simulations of liquid and glassy selenium

Molecular dynamics simulations of liquid and glassy selenium have been carried out using density functional (400–773 K, 600 atoms) and classical force field (290–500 K, 5488 atoms) methods. Structural features (structure factors, pair distribution functions, bond lengths, bond and dihedral angles, cavities) and dynamical properties (diffusion coefficients, power spectra, sound velocity, collective excitations, bond lifetimes) agree well with experimental data where available. The structures are predominantly chainlike, with a small fraction of rings with a range of sizes, and large cavity volumes lead to flexible chains. It is striking that the density functional simulations show very few ${\mathrm{Se}}_8$ rings at 600 K and below.

Figure 1

Structure factors $S\left(q\right)$ calculated (DF) for 500 K (full blue curve) and 773 K (full red curve) compared with IXS measurements [52] at 523 K (blue triangles) and 773 K (red triangles) and IND measurements [51] at 503 K (dashed blue curve) and 773 K (dashed red curve) (after [52]).

Figure 2

Color maps of bond lengths ($d_2$) of twofold-coordinated atoms against the average of bonds to neighboring atoms ($d_1, d_3$) for (a) 500 K and (b) 773 K. The origins of the axes correspond to the interatomic separation in ${\mathrm{Se}}_2$ (2.17 Å).

Figure 3

Color maps of bond lengths $d_2$ of twofold-coordinated atoms against the dihedral angle $\gamma$ for 500 K (upper) and 773 K (lower). The origin of the $d_2$ axis corresponds to the interatomic separation in ${\mathrm{Se}}_2$ (2.17 Å).

Figure 4

Distribution of bond angles $\alpha$ for twofold- and threefold-coordinated atoms at 500 K (above) and 773 K (below).

Figure 5

Average number of rings with less than 30 atoms during 600-atom simulations at 500 K and 773 K. The bond cutoff is 2.8 Å.

Figure 6

Surface-based cavities (blue) in unit cell of Se (brown atoms) at 500 K using cutoff radius of 2.6 Å.

Figure 7

Long-time diffusion coefficients $D_{\infty }\left(T\right)$ of Se between 500 K and 270 K and the corresponding values of $\alpha \left(T\right)$ [Eq. (6)] in units of ${\mathrm{ns}}^{-1}$ [37] (FF simulations).

Figure 8

Vibrational components of power spectra of Se from DF simulations at 400 K (cyan), 450 K (green), 500 K (blue), 600 K (black), and 773 K (red).

Figure 9

Ratio of dynamical to static structure factors, $S(q,\omega )/S\left(q\right)$, for selected $q$ values at 500 K. Red: DF with 3 meV Gaussian broadening; black, circles: experimental IXS at 523 K [52], with corresponding $q$ values in ${\AA }^{-1}$.

Figure 10

Ratio of dynamical to static structure factors, $S(q,\omega )/S\left(q\right)$, for selected $q$ values at 773 K. Red: DF with 3 meV Gaussian broadening; black, circles: experimental IXS at 773 K [52], with corresponding $q$ values in ${\AA }^{-1}$.

Figure 11

Calculated longitudinal dispersion (open circles) at 500 K (blue) and 773 K (red) up to $q=5.0{\AA }^{-1}$. Experimental results of Inui et al. for 523 K and 773 K are shown as blue and red triangles, respectively [52]. Full circles: Calculated frequencies of transverse modes; dashed and dot-dashed curves: sound velocities of 1500 m/s and 750 m/s, respectively.

Figure 12

Time dependence of number of active bonds in DF simulations at 500 K (blue) and 773 K (red). Dashed curves: Bonds break at 2.8 Å; full curves: bonds initially shorter than 2.4 Å, break at 3.8 Å.