Effect of concentration in Ge-Te liquids: A combined density functional and neutron scattering study

The structural properties of three compositions of Ge-Te liquids (${\mathrm{Ge}}_{10}{\mathrm{Te}}_{90}$, ${\mathrm{Ge}}_{15}{\mathrm{Te}}_{85}$, ${\mathrm{Ge}}_{20}{\mathrm{Te}}_{80}$) are studied from a combination of density functional based molecular dynamics simulations and neutron scattering experiments. We investigate structural properties including structure factors, pair distribution functions, angular distributions, coordination numbers, neighbor distributions and compare our results with experimental findings. Most noticeable is the good agreement found in the reproduction of the structure in real and reciprocal space, resulting from the incorporation of dispersion forces in the simulation. This leads to Ge and Te coordination numbers which are lower than in previous studies and which can now be followed with temperature, while also strongly depending on the chosen cutoff distance. Results show a gradual conversion of higher coordinated species (Te${}^{\text{IV}}$, Ge${}^{\text{V}}$) into lower coordinated ones at lower temperature, while leaving anticipated coordinations from the octet rule (Te${}^{\text{II}}$ and Ge${}^{\text{IV}}$) nearly unchanged. Structural correlations are characterized as a function of temperature and composition. The vibrational density of states is also measured from inelastic neutron scattering for different compositions and temperatures, and compared to the simulated counterpart which exhibits a reasonable agreement at low frequency.

Figure 1

A snapshot of the 200-atoms liquid Ge${}_{20}$Te${}_{80}$ at 923 K.

Figure 2

Experimental total structure factor $S$${}_{\mathrm{expt}}$($k$) for three compositions Ge${}_{10}$Te${}_{90}$ (a), Ge${}_{15}$Te${}_{85}$ (b), and Ge${}_{20}$Te${}_{80}$ (c) measured at three temperatures. The corresponding total pair correlation function $g_{\mathrm{expt}}\left(r\right)$ are presented as insets. In panel (c), the decomposition from simulation in the partials $S_{\text{GeGe}}\left(k\right)$ (solid curves) and $S_{\text{GeTe}}\left(k\right)$ (broken curves) is shown for 700 K (green) and 923 K (black). The arrow indicates the tiny shoulder observed experimentally [also seen in panel (b) at the lowest temperature, green curve].

Figure 3

Calculated total neutron structure factor $S_T\left(k\right)$ (a), (b) and interference function $k[S_T\left(k\right)-1]$ (c) in Ge-Te liquids for three compositions Ge${}_{10}$Te${}_{90}$, Ge${}_{15}$Te${}_{85}$, and Ge${}_{20}$Te${}_{80}$ and three temperatures (700, 823, and 923 K, red curves) compared to results from neutron diffraction (black curves, same as Fig. 2). The green curves correspond to similar simulation conditions but without taking into account the dispersion forces of Eq. (1) (see text for details).

Figure 4

Calculated total pair distribution functions $g\left(r\right)$ for three compositions Ge${}_{10}$Te${}_{90}$, Ge${}_{15}$Te${}_{85}$, and Ge${}_{20}$Te${}_{80}$ and three temperatures (700, 823, and 923 K, red curves) compared to results from neutron diffraction (solid black curves, same as Fig. 2, and broken curve [31]). In panels (a) and (b), a decomposition into partials (blue curves) is shown for the Ge${}_{20}$Te${}_{80}$ alloy: Ge-Ge (solid curve), Ge-Te (broken curve), Te-Te (dotted curve). In panel (c), green curves correspond to simulations without the dispersion forces [Eq. (1)]. The arrows indicate the position $r$${}_{min}$ of respective minima in Ge${}_{20}$Te${}_{80}$ (see text for details).

Figure 5

Calculated partial pair distribution functions $g_{\text{GeTe}}$$\left(r\right)$ and $g$${}_{\text{TeTe}}$$\left(r\right)$ for three compositions Ge${}_{10}$Te${}_{90}$, Ge${}_{15}$Te${}_{85}$, and Ge${}_{20}$Te${}_{80}$ and two temperatures: 923 K (black curve) and 700 K (green curve). The arrow indicates the position (3.31 Å) of the minimum at 700 K (see text for details).

Figure 6

Running Ge-Te coordination number as a function of interatomic distance, calculated from the integration of the function $r$${}^2$$g$${}_{\text{GeTe}}$$\left(r\right)$. (a) Effect of temperature (923, 823, and 700 K) on Ge${}_{20}$Te${}_{80}$. (b) Effect of composition on the 700-K liquid: Ge${}_{10}$Te${}_{90}$ (black), Ge${}_{15}$Te${}_{85}$ (red), and Ge${}_{20}$Te${}_{80}$ (green). The gray areas correspond to the zones where $g$${}_{\text{GeTe}}$ is minimum (see arrow in Fig. 5). Horizontal broken lines correspond to $n$${}_{\text{GeTe}}=4$ and serve as a guide. The broken curve in (a) represents results from a simulation without the dispersion forces, and the arrows indicate either the cutoff needed to obtain $n$${}_{\text{GeTe}}=4$ (3.20 Å), or the location of the minimum ($r$${}_{min}=3.53$ Å) of the corresponding partial pair distribution function $g$${}_{\text{GeTe}}$$\left(r\right)$.

Figure 7

Effect of the cutoff distance $r$${}_c$ on the species population (in %) at 823 K for Ge${}_{10}$Te${}_{90}$ (broken lines) and Ge${}_{20}$Te${}_{80}$ (solid lines). (a) Population Ge${}^{\text{III}}$, Ge${}^{\text{IV}}$, and Ge${}^{\text{V}}$. (b) Population Te${}^{\text{II}}$, Te${}^{\text{III}}$, and Te${}^{\text{IV}}$. The arrows indicate the cutoff distance used for the computation of the coordination distribution of Table 3, and which correspond to the minimum $r_{min}$ of Ge${}_{20}$Te${}_{80}$ and Ge${}_{10}$Te${}_{90}$ in the corresponding pair distribution function (Fig. 4).

Figure 8

Te-Ge-Te and Ge-Te-Ge bond angle distributions at 823 K for the three compositions Ge${}_{10}$Te${}_{90}$ (black), Ge${}_{15}$Te${}_{85}$ (red), and Ge${}_{20}$Te${}_{80}$ (green). Note that the Te-Te-Te and Te-Te-Ge bond angle distributions of Ge${}_{10}$Te${}_{90}$ and Ge${}_{15}$Te${}_{85}$ (not shown) have exactly the same shape as Ge${}_{20}$Te${}_{80}$ (see Fig. 9).

Figure 9

Te-Te-Te, Te-Te-Ge, Te-Ge-Te, and Ge-Te-Ge bond angle distributions and Ge${}_{20}$Te${}_{80}$ liquid at the three temperatures: 923 K (red), 823 K (blue), and 700 K (black). The broken line in the top panel (Te-Te-Te) is the computed bond angle distribution of a 970-K simulated liquid Te (see text for details).

Figure 10

Computed and experimental vibrational density of states (VDOS) in Ge-Te liquids. (a) Experimentally measured VDOS of Ge${}_{15}$Te${}_{85}$ at 723 K (black), 823 K (red), and 923 K (blue), compared to the computed VDOS at 700 K (green curve). (b) Measured VDOS of Ge${}_{20}$Te${}_{80}$ at 723 K (black) and 923 K (red), compared to the computed VDOS at 700 K (green curve). (c) Computed partial contribution (Ge, black and Te, red) to the VDOS at 700 K.

Figure 11

Computed electronic density of states of liquid (700 K, black and 923 K, red) Ge${}_{10}$Te${}_{90}$, Ge${}_{15}$Te${}_{85}$, and Ge${}_{20}$Te${}_{80}$ alloys. The green curve is a calculation without the dispersion correction of Eq. (1).