Structure of liquid tricalcium aluminate

The atomic-scale structure of aerodynamically levitated and laser-heated liquid tricalcium aluminate (${\mathrm{Ca}}_3{\mathrm{Al}}_2{\mathrm{O}}_6$) was measured at 2073(30) K by using the method of neutron diffraction with Ca isotope substitution (NDIS). The results enable the detailed resolution of the local coordination environment around calcium and aluminum atoms, including the direct determination of the liquid partial structure factor, $S_{\mathrm{CaCa}}\left(Q\right)$, and partial pair distribution function, $g_{\mathrm{CaCa}}\left(r\right)$. Molecular dynamics (MD) simulation and reverse Monte Carlo (RMC) refinement methods were employed to obtain a detailed atomistic model of the liquid structure. The composition ${\mathrm{Ca}}_3{\mathrm{Al}}_2{\mathrm{O}}_6$ lies at the CaO-rich limit of the CaO:${\mathrm{Al}}_2{\mathrm{O}}_3$ glass-forming system. Our results show that, although significantly depolymerized, liquid ${\mathrm{Ca}}_3{\mathrm{Al}}_2{\mathrm{O}}_6$ is largely composed of ${\mathrm{AlO}}_4$ tetrahedra forming an infinite network with a slightly higher fraction of bridging oxygen atoms than expected for the composition. Calcium-centered polyhedra exhibit a wide distribution of four- to sevenfold coordinated sites, with higher coordinated calcium preferentially bonding to bridging oxygens. Analysis of the MD configuration reveals the presence of $\sim 10\%$ unconnected ${\mathrm{AlO}}_4$ monomers and ${\mathrm{Al}}_2{\mathrm{O}}_7$ dimers in the liquid. As the CaO concentration increases, the number of these isolated units increases, such that the upper value for the glass-forming composition of CaO:${\mathrm{Al}}_2{\mathrm{O}}_3$ liquids could be described in terms of a percolation threshold at which the glass can no longer support the formation of an infinitely connected ${\mathrm{AlO}}_4$ network.

Figure 1

Total structure factors ${}^{44}F\left(Q\right)$, ${}^{\mathrm{mix}}F\left(Q\right)$, and ${}^{\mathrm{nat}}F\left(Q\right)$ measured by neutron diffraction for the aerodynamically levitated ${\mathrm{Ca}}_3{\mathrm{Al}}_2{\mathrm{O}}_6$ liquids at 2073(30) K. The vertical bars show the statistical errors and the solid dark-black curves are the Fourier back-transforms of the corresponding total pair distribution $G\left(r\right)$ functions shown in Fig. 3 after the region below the first interatomic distance was set to the theoretical $r=0$ limit. The chained blue curves show the functions generated from the MD simulations and the solid light-red curves show the results of the RMC structural refinement. For clarity, the results are displaced vertically.

Figure 2

The measured high-energy x-ray (a) structure factor $S_{\mathrm{X}}\left(Q\right)$ and (b) pair distribution function $G_{\mathrm{X}}\left(r\right)$ for liquid ${\mathrm{Ca}}_3{\mathrm{Al}}_2{\mathrm{O}}_6$ at 2273(30) K (solid dark-black curves) together with the corresponding functions obtained from the MD simulations (chained blue curve) and the results of the RMC structural refinement (solid light-red curve).

Figure 3

The total pair distribution functions ${}^{44}G\left(r\right)$, ${}^{\mathrm{mix}}G\left(r\right)$, and ${}^{\mathrm{nat}}G\left(r\right)$ for liquid ${\mathrm{Ca}}_3{\mathrm{Al}}_2{\mathrm{O}}_6$ at 2073(30) K (solid dark black curves), as obtained by Fourier transforming the corresponding total structure factors given in Fig. 1 after making a spline fit to the data and applying a cosine window function [32] between $20\le Q\left(\AA {}^{-1}\right)\le 23.55$. The broken black curves show the extent of the unphysical low-$r$ features, the chained blue curves are the functions generated directly from the MD simulations, and the solid light-red curves show the results of the RMC structural refinement. For clarity, the results are displaced vertically.

Figure 4

The reciprocal-space difference functions ${\delta }_{\mu \mu }\left(Q\right)$, ${\mathrm{\Delta }}_{\mu \mu }\left(Q\right)$, ${\mathrm{\Delta }}_{\mathrm{Ca}}\left(Q\right)$, and ${\delta }_{\mathrm{Ca}\mu }\left(Q\right)$ for liquid ${\mathrm{Ca}}_3{\mathrm{Al}}_2{\mathrm{O}}_6$. The vertical bars show the statistical errors arising from the experimental measurements, the solid dark black curves are the Fourier back-transforms of the corresponding real-space functions shown in Fig. 4 after the region below the first interatomic distance was set to the theoretical $r=0$ limit, the chained blue curves show the difference functions calculated from the partial structure factors generated from the MD simulations, and the solid light-red curves are the results of the RMC structural refinement. For clarity, the results are displaced vertically.

Figure 5

The real-space difference functions $\delta G_{\mu \mu }\left(r\right)$, $\mathrm{\Delta }{G}_{\mu \mu }\left(r\right)$, $\mathrm{\Delta }{G}_{\mathrm{Ca}}\left(r\right)$, and $\delta G_{\mathrm{Ca}\mu }\left(r\right)$ for liquid ${\mathrm{Ca}}_3{\mathrm{Al}}_2{\mathrm{O}}_6$ (solid dark-black curves), as obtained by Fourier transforming the corresponding reciprocal-space functions given in Fig. 4. The broken black curves show the extent of the unphysical low-$r$ features, the chained blue curves show the functions calculated from the partial pair distribution functions generated directly from the MD simulations, and the solid light-red curves are the results of the RMC structural refinement. For clarity, the results are displaced vertically.

Figure 6

Running coordination numbers (a) ${\overline{n}}_{\mathrm{Al}}^{\mathrm{O}}$ and (b) ${\overline{n}}_{\mathrm{Ca}}^{\mathrm{O}}$ determined from the measured difference functions and MD and RMC partial pair distribution functions indicated in the legend. The deviation at higher-$r$ values is due to the contributions from correlations of other atomic pairs in the measured difference functions.

Figure 7

(a) The partial structure factor $S_{\mathrm{CaCa}}\left(Q\right)$ for liquid ${\mathrm{Ca}}_3{\mathrm{Al}}_2{\mathrm{O}}_6$ as determined from the NDIS measurements (vertical error bars). The solid dark-black curve shows the Fourier back-transform of the experimental $g_{\mathrm{CaCa}}\left(r\right)$ after the region below the first interatomic distance was set to the theoretical $g_{\mathrm{CaCa}}(r=0)=0$ limit. (b) The partial pair distribution function $g_{\mathrm{CaCa}}\left(r\right)$ as obtained by Fourier transforming the measured $S_{\mathrm{CaCa}}\left(Q\right)$ shown in panel (a) after making a spline fit to the data and truncation at $8.0\AA {}^{-1}$ using a Lorch window function [37] (solid dark-black curve). The chained blue curves show the results generated directly from the MD simulations and the solid light-red curves show the RMC structural refinement.

Figure 8

The comparison of the partial pair radial distribution functions, $g_{\alpha \beta }\left(r\right)$, obtained from the MD simulation (chained blue curves) and after the RMC refinement of the MD configuration (solid black curves). For clarity, the results are displaced vertically.

Figure 9

The ${\mathrm{AlO}}_4$ network structure in liquid ${\mathrm{Ca}}_3{\mathrm{Al}}_2{\mathrm{O}}_6$ from the MD simulation at 2500 K. The blue tetrahedra represent the infinitely connected major cluster, with the red polyhedra showing two clusters with 11 and 12 connected tetrahedra and yellow polyhedra denoting the ${\mathrm{AlO}}_4$ monomers and ${\mathrm{Al}}_2{\mathrm{O}}_7$ dimers.

Figure 10

Representative snapshot showing two (strongly distorted) calcium-centered polyhedra with coordination numbers of 5 and 6 (orange units). The blue units denote ${\mathrm{AlO}}_4$ tetrahedra and the sticks represent oxygen-cation bonds.