Density functional modeling and total scattering analysis of the atomic structure of a quaternary $\mathrm{CaO}\text{−}\mathrm{MgO}\text{−}{\mathrm{Al}}_2{\mathrm{O}}_3\text{−}{\mathrm{SiO}}_2$ (CMAS) glass: Uncovering the local environment of calcium and magnesium

Quaternary $\mathrm{CaO}\text{−}\mathrm{MgO}\text{−}{\mathrm{Al}}_2{\mathrm{O}}_3\text{−}{\mathrm{SiO}}_2$ (CMAS) glasses are important constituents of the Earth's lower crust and mantle, and they also have important industrial applications such as in metallurgical processes, concrete production, and emerging low-${\mathrm{CO}}_2$ cement technologies. In particular, these applications rely heavily on the composition-structure-reactivity relationships for CMAS glasses, which are not yet well established. In this study, we combined force-field molecular dynamics (MD) simulations and density functional theory (DFT) calculations to generate detailed structural representations for a CMAS glass. The generated structures are not only thermodynamically favorable (according to DFT calculations) but also agree with experiments (including our x-ray and neutron total scattering data as well as literature data). Detailed analysis of the final structure (including partial pair distribution functions, coordination number, and oxygen environment) enabled existing discrepancies in the literature to be reconciled and has revealed important structural information on the CMAS glass, specifically (i) the unambiguous assignment of medium-range atomic ordering, (ii) the preferential role of Ca atoms as charge compensators and Mg atoms as network modifiers, (iii) the proximity of Mg atoms to free oxygen sites, and (iv) clustering of Mg atoms. Electronic property calculations suggest higher reactivity for Ca atoms as compared with Mg atoms, and that the reactivity of oxygen atoms varies considerably depending on their local bonding environment. Overall, this information may enhance our mechanistic understanding on CMAS glass dissolution behavior in the future, including dissolution-related mechanisms occurring during the formation of low-${\mathrm{CO}}_2$ cements.

Figure 1

(a) Stacked plot of the x-ray and neutron total scattering functions, (b) x-ray PDF, and (c) neutron PDF of the CMAS glass. Insets in (b) and (c) show a zoom of the PDF over an $r$ range of 1–4 Å.

Figure 2

Calculated (a) x-ray and (b) neutron PDFs from a force-field MD-generated CMAS glass structure and the subsequent DFT geometry-optimized structure, as compared with the experimental PDF data. Comparisons based on the average of all the ten structural representations are given in Figs. S4a and S4b in the Supplemental Material.

Figure 3

Impact of DFT optimization on the partial x-ray PDF for (a) Ca-Si and (b) Ca-Ca pairs in the same structural representation used to produce the results in Fig. 2. Partial PDFs for a complete list of different atom-atom pairs in the same structural representations are shown in Fig. S6 in the Supplemental Material. Comparisons of the Ca-Si and Ca-Ca partial PDFs based on the average of all the ten structural representations are given in Figs. S7a and S7b in the Supplemental Material.

Figure 4

(a) A representative final structure of the CMAS glass obtained after DFT geometry optimization. (b) The aluminosilicate network of the CMAS glass structure in (a).

Figure 5

Evolution of coordination number as a function of cutoff distance for (a) Si/Al/Mg/Ca-O (i.e., number of oxygen atoms surrounding Si, Al, Mg, Ca), (b) Si-Ca, Si-Mg, Al-Ca, and Al-Mg (i.e., number of Ca, Mg atoms surrounding Si, Al), and (c) Ca/Mg CN ratio around Si, Al, and fivefold Al atoms. The $y$-axis Ca/Mg ratio in (c) is calculated using the data in (b), for example, the Ca/Mg ratio around Si is determined by (Ca CN around Si)/(Mg CN around Si) at each given Ca/Mg-Si cutoff distance. Also given in (c) is the overall composition ratio of the system. The results are averages based on the ten structural representations optimized using DFT calculations.

Figure 6

Proportions of the different types of oxygen species. The total percentages of tricluster oxygen (TO), bridging oxygen (BO), nonbridging oxygen (NBO), and free oxygen (FO) are averages based on the ten DFT-optimized structural representations, with the red error bar indicating one standard deviation.

Figure 7

Average number of Ca or Mg around each type of oxygen species, where TO, BO, NBO, and FO denote tricluster oxygen, bridging oxygen, nonbridging oxygen and free oxygen, respectively. The cutoff distances for Ca-O and Mg-O are fixed at 3.2 and 2.9 Å, respectively.

Figure 8

(a) Small clusters of Mg atoms in a typical CMAS structural representation (several Mg atoms from adjecent cell are also shown), and (b) Mg-Mg partial x-ray PDF calculated using the ten final structural representations. For clarity, only Mg atoms are shown in (a) and Mg-Mg pairs with distance smaller than 3.5 Å are highlighted using red dashed circles.

Figure 9

Simulated partial x-ray PDFs based on the ten structural representations of the CMAS glass that have been geometry-optimized using DFT calculations.

Figure 10

(a),(b) 3D view of electron cloud density plots (denoted by the color yellow) around the different atoms with a threshold of $0.1\mathrm{eV}/{\AA }^3$ (a density lower than this value is not shown in the plots). Panels (c)–(e) show electron charge density contour plots on the plane passing through the selected atoms (as labeled in the plots). NBO-Si refers to nonbridging oxygen connected with a Si atom, whereas Si-BO-Si, Si-BO-Al, and Al-BO-Al refer to the three types of bridging oxygen.

Figure 11

Total electronic density of states (DOS) in states/eV for the DFT-optimized CMAS structure, along with the projected DOS contributions from each type of atom in the structure. All the energies are relative to the Fermi level set at the energy of 0 eV as shown by the dashed line.

Figure 12

Partial electronic density of states (DOS) in states/eV per atom for (a) each type of atom, and (b)–(d) different types of oxygen species. Panel (c) shows the two types of NBO bonded with either a Si or an Al atom, and (d) shows the three types of BO species.