Electron anions and the glass transition temperature

Abstract

Properties of glasses are typically controlled by judicious selection of the glass-forming and glass-modifying constituents. Through an experimental and computational study of the crystalline, molten, and amorphous [Ca12Al14O32](2+) ⋅ (e(-))2, we demonstrate that electron anions in this system behave as glass modifiers that strongly affect solidification dynamics, the glass transition temperature, and spectroscopic properties of the resultant amorphous material. The concentration of such electron anions is a consequential control parameter: It invokes materials evolution pathways and properties not available in conventional glasses, which opens a unique avenue in rational materials design.

Keywords: amorphous materials; density functional theory; electrides; glass transition; molecular dynamics.

Fig. 1.

Glass transition temperature (T_g) in CaO-Al₂O₃ glasses as a function of CaO content and electron anion concentrations. Inset shows T_g values of a-C12A7:e^– for several electron concentrations determined by differential thermal analysis. Data of conventional glasses in this system (blue) are taken from the literature (Table S1).

Fig. S1.

Apparatus used for fabrication of C12A7:e^– glass. Infrared lamp heating furnace for the floating zone is connected to the twin rollers. The atmosphere in the furnace was kept at pO₂ ∼ 10⁻²³ atm, using a hollow SiC rod; pO₂ in the vicinity of the twin roller was kept at ∼10⁻¹⁶ atm to prevent oxidization of the melt and the formation of glass flakes.

Fig. S2.

One-electron energies for heat–compress–quench molecular dynamics trajectories on C12A7:e^– for T_max = 1,910 K (Top) and 2,650 K (Bottom). The initial kinetic energy was added in a single pulse at the first time step. Energies for the spin-up electrons are shown as solid lines and spin-down electrons are shown as dotted lines (Top only); energy differences between spin states were negligible. Excess electrons occupy the states between the VBM and CBM and form bipolarons, Al(2e^–)Al and Al(2e^–)Ca defect states (Fig. 2 of the main text).

Fig. S3.

Solid-to-melt transition in C12A7:e^–. (A) Radial distribution function g_Al–Al(r) after equilibration and lattice compression to the a-C12A7:e^– mass density. (B) Negative internal pressure indicates spontaneous lattice compression at elevated temperatures, becoming more favorable above 2,000 K for the electride. (C) Localization of the excess electrons near Al atoms is quantified using the number of Al species with the ionic charge of less than +3.0 |e|. Such charge localization is a rare/transient event at T_max below 2,310 K and a frequent/persistent event at T_max of 2,310 K and above, indicating the formation of stable or metastable electron centers.

Fig. S4.

Quenched structures in C12A7:e^–. (A) Radial distribution functions g_Al–Al(r) for several C12A7:e^– structures at the end of the quenching stage (T ∼ 100 K). Radial distribution functions for systems in which melting occurred are indicated by dotted lines. (B) Dependence of the internal pressure on temperature during isochoric quenching for several values of T_max.

Fig. 2.

Macroscopic and microscopic properties of quenched C12A7:e^–. (A) Thermodynamic stability (left axis), mass density (right axis), and the distribution of 6-membered rings (Inset) show the clear distinction (at T_max+ ∼ 2,450 K) between a-C12A7:e^– and thermally distorted crystalline C12A7:e^–. (B) One-electron energies: top of the O 2p band (black lines), bottom of the conduction band (red lines), and electron anion states. (C) Charge density distributions in the electron defect centers: bipolaron formed by two spin-coupled electrons localized in two neighboring cages, Al(2e^–)Ca and Al(2e^–)Al centers where the two spin-coupled electrons are confined between undercoordinated Al³⁺ and Ca²⁺ ions.

Fig. S5.

Distribution of 4- and 6-membered rings in the nearly crystalline C12A7:e^– (T_max = 1,910 K) and a-C12A7:e^– (T_max = 2,650 K) after quenching. Separation into calcium-rich and aluminum-rich structures in a-C12A7:e^– is less distinct than for 6-membered ring structures but is still evident. Ring stoichiometries present in the amorphous material but not in the crystal are indicated by black markers.

Fig. S6.

(A) Density of states calculated at the PAW-PBE level of theory for Al(2e^–)Ca and Al(2e^–)Al centers in amorphous C12A7:e^– obtained by quenching from T_max = 2,650 K and projected on the atomic functions of the constituent Al and Ca atoms. The total density of states (DOS) for the system is overlaid as a black line; the difference is due to the contribution of oxygen ions surrounding the M(2e^–)M center. (B) Contributions of the Al and Ca atoms, decomposed over s-type and p-type functions. Most of the metal atom contribution comes from the Al 3s and 3p atomic orbitals, consistent with the σ-type bonding state of the two electrons in both Al(2e^–)Ca and Al(2e^–)Al centers.

Fig. 3.

(A) Atomic speed (Å/fs) distributions of individual atoms for C12A7:e^– (Top) and C12A7:O^2– (Bottom) during quenching. The mobility of Al atoms ceases by T ∼ 1,900 K; Ca and O atoms remain mobile until a substantially lower temperature. (B) Each of these transitions in mobility corresponds to a change in heat capacity, with the lower-temperature transition corresponding to T_g. The presence of electron anions decreases T_g, and no such decrease is observed when they are replaced with a uniform negative charge distribution ρ⁻. (C) Al ions trapping electron charge (black circles) and the total amount of electron anions trapped near these ions (red triangles). (D) Evolution of selected Al–O and Al–Al distances during the Al(2e^–)Al center formation, also manifested in the changes of Q_e(Al) in C.

Fig. S7.

Atomic speed distribution during quenching for the C12A7 pseudoelectride (T_max = 2,870 K). Because the pseudoelectride does not contain explicitly treated electron anions, the response of this system to thermally induced charge fluctuations takes place on the timescale of atomic motion, i.e., on the same timescale as in the stoichiometric C12A7. Hence, the apparent glass transition temperature of the pseudoelectride (1,300 K) is nearly equivalent to that of the stoichiometric material (1,250 K).

Fig. S8.

Evolution of distances between the aluminum ions involved in the Al(2e^–)Al (A) and Al(2e^–)Ca (B) centers and their oxygen neighbors during the quench procedure. Shown with different colors are Al-O distances for oxygen that remain in the first coordination shell of Al (black), were diffused out of the first coordination shell (dotted), were diffused into the first coordination shell (gray), were displaced from between the two metal atoms, and were replaced by an electron pair (blue).

Fig. S9.

(A) Aluminum coordination numbers, i.e., the number of oxygen neighbors per Al, for C12A7:e^– quenched from T_max = 2,650 K. Three aluminum ions were hypo-coordinated at the end of the quench. (B) Coordination numbers for specific aluminum ions involved in the formation of Al(2e^–)Al and Al(2e^–)Ca centers. Formation of these centers is indicated by the coordination number decreasing to 3 and remaining hypo-coordinated.

Fig. 4.

(A and B) Simulated Raman spectra for simplified models of M₁(2e^–)M₂ centers, O-Al-Al-O (A) and F-Ca-Al-O (B) under 457-nm excitation. The frequency and intensity of the Raman response are strongly dependent on the metal–metal distance. The resonant (solid triangles) and nonresonant (open squares) responses are detailed in Insets. (C) Comparison of experimental and simulated UV/visible absorption in C12A7. The Al(2e⁻)Ca and Al(2e⁻)Al centers contribute to the peaks in the imaginary dielectric function (absorption) of C12A7:e⁻ (solid line) at 3.3 eV and 4 eV, respectively, consistent with the experimental UV/visible spectrum of C12A7:e⁻ (right axis). The two low-energy peaks are absent in the dielectric function of the stoichiometric system (dashed line).

Fig. 5.

Continuous random networks of strongly bonded structural elements are modified by introducing weak links (network modifiers), including cations, such as Na⁺ and Ca²⁺, that induce the formation of ionic bonds (dashed lines) or monovalent anions, such as F⁻ and OH⁻, that terminate polymerization of network fragments. Electron anions introduce another category of network modifiers: highly mobile weak links.