Electron anions and the glass transition temperatureLewis E. Johnsona, Peter V. Sushkoa,1, Yudai Tomotab, and Hideo Hosonob,1

aPhysical Sciences Division, Physical & Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, WA 99354; and bMaterialsResearch Center of Element Strategy, Tokyo Institute of Technology, Midori-ku, Yokohama 226-8503, Japan

Edited by James L. Dye, Michigan State University, East Lansing, MI, and approved July 20, 2016 (received for review April 29, 2016)

Properties of glasses are typically controlled by judicious selectionof the glass-forming and glass-modifying constituents. Through anexperimental and computational study of the crystalline, molten,and amorphous [Ca12Al14O32]

2+ · (e–)2, we demonstrate that elec-tron anions in this system behave as glass modifiers that stronglyaffect solidification dynamics, the glass transition temperature,and spectroscopic properties of the resultant amorphous material.The concentration of such electron anions is a consequential con-trol parameter: It invokes materials evolution pathways and prop-erties not available in conventional glasses, which opens a uniqueavenue in rational materials design.

amorphous materials | glass transition | electrides | molecular dynamics |density functional theory

One of the key challenges in materials design is identificationof degrees of freedom that ensure robust control of the

properties of interest. Small changes in composition of crystallinematerials can lead to large changes in their electronic properties,such as optical absorption and electrical conductivity (1). Similarly,a small concentration of (co)dopants in amorphous materials can beused to control their optical properties (2, 3). Glass properties aretypically controlled by varying composition or processing condi-tions (4). However, delicate control of viscosity and glass tran-sition temperature in multicomponent materials (Tg) has remainedelusive due to the collective origin of these properties. Substitutionof atomic anions with electron anions in materials to form electrides(5, 6) introduces an additional degree of freedom. Here wedemonstrate that electron anions dramatically change dynamicsof atoms in an inorganic amorphous material, which stronglyaffects its Tg. Extending the concept of electron anions to otheramorphous materials would provide a powerful instrument forthe design of glasses with finely tuned characteristics.Calcium aluminates (CA), composed of CaO and Al2O3,

represent a common family of oxide glasses. Whereas pureAl2O3 is a poor glass former, blending it with CaO leads to theformation of stable glasses composed of AlO4 tetrahedra withstrong and directional covalent bonds instead of nondirectionalionic bonds in bulk Al2O3 (7). In contrast, Ca-O bonds retaintheir ionic character; they are weaker than Al-O bonds and lack apreferred orientation, which enables motion of the AlO4 tetra-hedra relative to each other. Hence, the Tg of stoichiometric CAsystems decreases by ∼50 K as the CaO content increases from57 mol% to 70 mol% (Fig. 1). This relatively narrow interval ofTg variation with composition is typical of multicomponentglasses (8, 9). The Tg for stoichiometric [Ca12Al14O32]

2+ · (O2–)(C12A7:O2–) is in line with the general trend for CA systems(∼830 °C). Conceptually, Tg of a glass network can be furthermodified by introducing weak links. For example, Tg of CAsystems can be modified by addition of CaF2, which reduces thenumber of Al-O-Al bridges between the tetrahedral structuralelements and decreases their viscosity. As a result, Tg decreasesby ∼75 K at a mole fraction of 20% CaF2 (10). Similar effectscan also be achieved by replacing lattice oxygens with otheranions such as H− and OH− (11). Processing C12A7 in a re-ducing environment leads to replacement of clathrated oxygenswith electrons (12, 13), forming [Ca12Al14O32]

2+ · (O2–)1–x(e–)2x,

referred to as C12A7 electride (C12A7:e–) due to electrons

functioning as anions (5, 14, 15). In crystalline C12A7:e–, theelectrons occupy the cage conduction band (CCB) states asso-ciated with the lattice cages (16, 17), leading to polaron-typeconduction at x < ∼0.5 and metallic conduction at x > 0.5 (13,16). The exceptionally low work function of crystalline C12A7:e–

(2.4 eV) (18) is used in electron field emitters (19, 20), field-effect transistors (21), resistive memory (22), and enhancement ofcatalytic activity for ammonia synthesis (23). Amorphous C12A7:e–

(a-C12A7:e–) also has a low work function (24), providing a host ofnew applications and technologies at the industrial scale. Whereasthe structure and electronic properties of the crystalline C12A7have been extensively investigated, there is a handful of experi-mental and computational studies of a-C12A7:O2– (25, 26) anda-C12A7:e– (27, 28), focused on the structural properties of a-C12A7.However, the effects of nonstoichiometry have remained elusive.Electron anions, even at low concentrations (Ne), lead to

dramatic changes in the Tg values (Fig. 1): for x = 0.095 (Ne =2.2 × 1020 cm–3) the Tg drops by 50 °C to ∼770 °C and for x = 0.475(Ne = 1.1 × 1021 cm–3) it decreases by over 40 °C more, to∼725 °C, for a total change of over 90 °C. These data support arecent report where only one Tg value for an electron-richC12A7 was reported (29). The change in Tg in this CaO-Al2O3system induced per mole of electron anions is a factor of6 greater than that induced per mole of F−. Such a dramaticTg effect is remarkable and, if understood and controlled,promises the development of a fundamental class of multicompo-nent amorphous materials in which Tg is responsive to smallcompositional changes.The experimental results raise two questions: (i) Why does the

effect of oxygen deficiency outweigh the effect of CaO/Al2O3ratio? And (ii) can it be realized and harnessed in other systems?Here we reveal atomic-scale mechanisms of how electron anionsin C12A7 alter the lattice dynamics in the crystalline and moltenphases, ultimately affecting the Tg, structure, and electronicproperties of this material. To reveal the distinctive role of the

Significance

Electrides are ionic materials in which electrons act as anions.Solvated electrons in ammonia are one of the early knownexamples of such anions in liquids. Electron anions in crystal-line materials have previously been shown to dramatically altertheir electronic properties, for example, to turn an insulatorinto a superconductor with minimal changes in the structureand stoichiometry. We show that electron anions modify thedisordered glass network by creating highly mobile weak links,thus fundamentally altering the thermodynamic and electronicproperties of the network and enabling a new design para-digm for amorphous materials.

Author contributions: P.V.S. and H.H. designed research; L.E.J., P.V.S., Y.T., and H.H. per-formed research; L.E.J. and P.V.S. analyzed data; L.E.J., P.V.S., and H.H. wrote the paper;and H.H. directed the project.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.1To whom correspondence may be addressed. Email: peter.sushko@pnnl.gov or hosono@msl.titech.ac.jp.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1606891113/-/DCSupplemental.

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electron anions in the glass formation process and the resultingproperties, we conducted ab initio (density functional theory)spin-polarized molecular dynamics (AIMD) simulations, inwhich crystalline [Ca24Al28O64]

4+ · (O2–)2(1–x)(e–)4x (for x = 0 and

x = 1) was subjected to heat–compress–quench treatments mim-icking the experimental procedure. Analysis of the electronicproperties and structure evolution with T and Ne reveals charac-teristic structural and spectroscopic signatures associated with theelectron anions and allows us to (i) explain the strong dependenceof the Tg on Ne and (ii) propose the formation mechanism that mayhold for other materials containing electron anions.

MethodsExperimental Details. Stoichiometric C12A7 can be readily converted to a glassform by a conventional melt-and-quench method. Whereas the chemicalcomposition of C12A7 electride (C12A7:e–) differs from that of stoichiometricC12A7 by only 3% of the oxygen content, C12A7:e– glass could not beobtained by the same method due to very fast crystallization of the melt. Toovercome this problem, we designed a process that ensures C12A7:e– cool-ing at a shorter timescale than crystallization. This result was achieved withthe help of the twin-roller apparatus shown in Fig. S1 and described in detailelsewhere (29). The sintered powder of the polycrystalline C12A7:e– wasmelted in the controlled O2 atmosphere with the gas pressure (pO2) of ∼10−23

atm, using a floating zone furnace with lamp heaters. The melt was droppedinto the space between the rotating twin rollers. The low pO2 (10–23 atm) at-mosphere was kept around the twin roller apparatus to prevent the oxidation ofmelt and the formation of glass flakes. The amorphous nature of the resultingsamples was confirmed by X-ray diffraction experiments and by electron dif-fraction experiments carried out for a selected part of the material in thetransmission electron microscopy mode. The electron concentrations and thechemical compositions of the resulting glasses were determined by iodo-metric titration and X-ray fluorescence, respectively. The Ca:Al atomic ratioin the samples was 47 ± 1:53 ± 1, which is almost the same as the Ca:Al ratioin crystalline C12A7. The glass-transition temperature (Tg) was determinedby differential thermal analysis (DTA). Before conducting the DTA mea-surements, the sealed glass was annealed at ∼650 °C (heating rate was 20 K/min)in the ambient atmosphere to alleviate quenching-induced stress. Theresulting glass flakes were sealed into a thin wall SiO2 glass tube to suppressthe oxidation during heating.

Computational Details. Models of the amorphous stoichiometric (a-C12A7:O2–)and electride (a-C12A7:e–) C12A7 were obtained from the correspondingcrystalline forms, using the melt-and-quench approach. The initial crystallinephases were represented using a cubic unit cell [Ca24Al28O64]

4+ · (e–)4 forthe electride and [Ca24Al28O64]

4+ · (O2–)2 for the stoichiometric C12A7,

respectively, and the lattice constant a0 = 12.0 Å. Their geometrical pa-rameters and electronic properties were in good agreement with the ex-perimental data (16, 30, 31). To separate the effect of the electrons aspseudoanionic species from the effect of the stoichiometry (i.e., the relativecontent of Al2O3 and CaO components), we conducted simulations on theC12A7 “pseudo-electride,” in which the excess electrons are replaced by ahomogeneous electron gas with the density ρ corresponding to the totalcharge of 4e– per cell: [Ca24Al28O64]

4+ · ρ(4–).Atomic trajectories were simulated in the microcanonical (constant par-

ticle number, volume, and energy) ensemble, using the Vienna Ab InitioSimulation Package (VASP) 5.2.12 (32), the exchange-correlation functionalby Perdew–Burke–Ernzerhof (PBE) (33), projector augmented wave (PAW)pseudopotentials (34, 35), and a time step of 0.5 fs. Each molecular dynamics(MD) simulation begins with 4.0 ps of isochoric heating to a target tempera-ture Tmax. After equilibration, the supercell was isotropically compressed infour equal decrements over 16.0 ps until the target density was reached (2.95g/cm3 and 2.79 g/cm3 for C12A7:e– and C12A7:O2–, respectively). Then, thesystems were quenched by uniformly scaling atomic velocities so kinetic en-ergy was decreased by 5.0 eV every 2.0 ps until a temperature of ∼100 K wasreached. Finally, the total energies of quenched systems were minimized withrespect to the fractional coordinates of all atoms and the cell parameters.Dielectric functions were calculated for selected prerelaxed systems, usingVASP 5.4.1 and the HSE06 hybrid functional (36).

Trajectories were visualized using the VMD program (37), and extractedcoordinates and band-projected charge densities were visualized using theVESTA program (38). Cyclic structures were identified using R.I.N.G.S 1.2.5 (39),and partial charges were calculated using the Bader method (40). Ramanspectra, including resonance effects, were calculated for simplified models oflocalized electron anions, using NWChem 6.5 (41). Further details of simulationparameters and data analysis are included as Supporting Information.

Results and DiscussionThe electronic structure changes in C12A7 after heating andquenching were characterized using the one-electron energiesassociated with the top of the O 2p valence band (VB) andseveral lowest states of the CCB. Two representative cases forC12A7:e– (x = 1) are shown in Fig. S2. For the maximum tem-perature (Tmax) of 1,910 K, the crystalline C12A7:e– did not meltwithin the simulation time. No significant fluctuations occurredin the energy levels with one notable exception at ∼7 ps into theMD run where the energy of one of the occupied states de-creased by over 1 eV due to the formation of a defect center inwhich two electrons were trapped between two Al species—anAl(2e–)Al center. In contrast, at Tmax = 2,650 K, energies fluc-tuate until well into the quenching stage of the simulation.Charge distributions and pairwise correlation functions (Figs. S3and S4) indicate that the system melted and then solidifiedduring this MD run, whereas the four electrons became localizedin two defects centers: Al(2e–)Al and Al(2e–)Ca. The solid-to-melt phase transition and quenching are discussed further inSupporting Information.Similar simulations were conducted for seven values of Tmax.

The resulting total energies and mass densities are compared inFig. 2A. For Tmax > 2,400 K the calculated density of the materialwas ∼15% higher than that for Tmax < 2,400 K. Although atypicalfor a glass, which is typically less dense than the correspondingcrystalline material (4, 42), it is consistent with the density dif-ference between the amorphous and crystalline C12A7:e– ob-served experimentally (29), which we attribute to the collapse ofthe lattice framework and loss of the framework cage space. Thetopology change is evidenced by the loss of the six-membered Al-O-Al-O-Ca-O rings (Fig. 2A, Inset) connecting the neighboringcages in the crystal and the appearance of other types of six-membered rings; the corresponding changes of the four-mem-bered ring distribution are shown in Fig. S5. The density corre-lates with the internal energy of the material: More compactstructures correspond to larger deviations from the crystallineC12A7:e– and are less thermodynamically stable (Fig. 2A).The electron anions in quenched C12A7:e– localize in three

types of defects; the corresponding one-electron energies relativeto the band edges are shown in Fig. 2B and the local structure of

Fig. 1. Glass transition temperature (Tg) in CaO-Al2O3 glasses as a functionof CaO content and electron anion concentrations. Inset shows Tg values ofa-C12A7:e– for several electron concentrations determined by differentialthermal analysis. Data of conventional glasses in this system (blue) are takenfrom the literature (Table S1).

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electron centers in Fig. 2C. Bipolarons, i.e., pairs of spin-coupledelectrons localized in two neighboring distorted cages, closelyresemble pairs of electron polarons in crystalline C12A7:e– (16,27). The spin-up and spin-down electrons have similar chargedensity distributions and indistinguishable one-electron energies,located within several 10ths of an electronvolt from the con-duction band (CB) minimum. The formation of bipolarons issuppressed if the lattice cages deform or collapse. Deformationresults in Al(2e–)Ca centers: cage-like structures with two elec-trons localized between a 3-coordinated Al3+ ion and one ormore Ca2+ ions. The corresponding one-electron energies areapproximately in the middle of the quenched C12A7:e– band gap.Alternatively, Al(2e–)Al centers (Fig. 2C) are formed either due tothe lattice collapse at high Tmax or, at low Tmax, via local de-formation of an Al–O–Al angle from ∼140° to ∼70°. The lattermechanism does not necessitate melting of the lattice frame-work; furthermore, it may provide an opportunity for manipu-lating glass formation by varying pressure (43). In both cases twoAl3+ ions are brought to 2.6–2.8 Å from each other, which cre-ates a deep potential well that traps two electrons. The post-AIMD electronic structure calculations using a hybrid densityfunctional resulted in the same ordering of the defect energylevels and similar electron density distributions. Details of theelectronic structure are shown in Fig. S6.These two-electron defects are fully consistent with the ob-

servation that less than 1% of electron anions give rise to un-paired spins, as detected by electron spin resonance spectroscopy(29). Indeed, in Al(2e–)Al and Al(2e–)Ca the spatial distributionsof the spin-up and spin-down electrons coincide. In contrast,spin-up and spin-down electrons in bipolarons occupy differentregions of space and can become further separated from eachother in the process of thermal treatment. Because (bi)polaronsare a minority defect (Fig. 2B), the concentration of unpairedspins is low.According to our statistics, bipolarons are formed if Tmax is

below or near the melting temperature (Tm), whereas Al(2e–)Cacenters appear if Tmax is close to Tm or above it. In contrast, the

Al(2e–)Al centers form at both low (1,900–2,200 K) and high(>2,550 K) values of Tmax. Their formation at Tmax ∼ Tm appearsto be suppressed in favor of bipolarons and Al(2e–)Ca centers.Given that Al(2e–)Al is the most stable defect type, as quantifiedby one-electron energies, we attribute this effect to the activationof multiple competing kinetic pathways near Tm.Cross-correlated analysis of the thermodynamic properties of

quenched C12A7:e–, atomic trajectories, and electron chargetrapping reveals the microscopic origin of the effect of electronanions on Tg. Fig. 3A shows the atomic speed of individual atomsin C12A7:e– and C12A7:O2– averaged over 2-ps intervals, as afunction of temperature during the quenching stage. At hightemperatures all ions are mobile, with stronger-bonded AlOxunits forming near 1,900 K, indicated by the rapid slowing of Aland O species. Glass formation temperature is determined byweaker bonds involving Ca, O, and electron anion species. At1,100–1,300 K atomic diffusion continues in C12A7:e–, whereasit is negligible in C12A7:O2–. This is consistent with the tem-perature dependence of the heat capacity (Cv): The electrideundergoes a phase transition at ∼1,150 K, whereas the sametransition in C12A7:O2– occurs at higher temperatures, peakingnear 1,250 K (Fig. 3B). We adopt these temperatures as theTg values for the C12A7:e– and C12A7:O2–, respectively, and notethat (i) these Cv peaks occur at the same temperature as the ces-sation of Ca and O diffusion and (ii) the difference between them(∼100 K) is very close to the observed difference. The relationshipbetween Tg and electron anions was further tested by replacing themwith a homogeneous static charge distribution (ρ−); no correspond-ing decrease in Tg was observed (Fig. 3B and Fig. S7).The atomic scale events occurring in quenched C12A7:e– are

illustrated in Fig. 3 C and D. Dynamics of the electron anions areillustrated in Fig. 3C (Tmax = 2,650 K), where black circles markAl atoms that trap electrons and Qe(Al) is the amount of theelectron charge summed over all Al species. As the temperatureof the system decreases to below 1,500 K, only three Al ions areassociated with these electrons. Similarly, variations in Qe(Al)become small at T < 1,200 K, indicating that electron transfer

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

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between Al and Ca species as well as between Al and remnantsof the lattice cages ceases at this temperature.Although diffusive motion of Al ceases at ∼1,900 K in both

C12A7:e– and C12A7:O2–, Al3+ ions contribute to the latticedynamics until the system temperature approaches Tg. Fig. 3Dshows the interatomic distance between a selected pair of Al3+ ionsduring the quench stage (Tmax = 2,650 K). At high temperature thedistance between these atoms oscillates in the vicinity of 3.5 Å.However, at ∼9 ps into the simulation run (T ∼ 1,500 K), the dis-tance between these atoms rapidly increases to over 4.0 Å and thenrapidly decreases to 2.7 Å. This structural rearrangement results inthe formation of an Al(2e–)Al center; the signature of this pro-cess is also visible in Fig. 3C: The amount of electron charge

trapped by Al ions increases sharply at the same time as theAl–Al distance decreases. Furthermore, at ∼12 ps the Al–Aldistance increases to ∼4 Å for about 2 ps before decreasingagain. This event is accompanied by a simultaneous decreaseand then, 2 ps later, an increase of the electron charge trapped byAl species.Analysis of the AIMD atomic trajectories and charge density

distributions reveals that the formation of Al(2e–)Al and Al(2e–)Cacenters is controlled by the correlated motion of the O2– andAl3+ ions, whereby the defect formation step is triggered bythermally driven diffusion of an O2– ion from the first (tetrahe-dral) coordination shell of an aluminum (Fig. 3D and Fig. S8).As O2– ions diffuse through the melt, the coordination number

Fig. 3. (A) Atomic speed (Å/fs) distributions of individual atoms for C12A7:e– (Top) and C12A7:O2– (Bottom) during quenching. The mobility of Al atomsceases 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 changein heat capacity, with the lower-temperature transition corresponding to Tg. The presence of electron anions decreases Tg, and no such decrease is observedwhen they are replaced with a uniform negative charge distribution ρ−. (C) Al ions trapping electron charge (black circles) and the total amount of electronanions 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 thechanges of Qe(Al) in C.

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 fre-

quency and intensity of the Raman response are strongly dependent on the metal–metal distance. The resonant (solid triangles) and nonresonant (opensquares) responses are detailed in Insets. (C) Comparison of experimental and simulated UV/visible absorption in C12A7. The Al(2e−)Ca and Al(2e−)Al centerscontribute 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).

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of Al3+ typically varies between 3 and 5 (Fig. S9). In a-C12A7:O2–, the Al3+ tetrahedral coordination is restored when eitheranother O2– ions diffuses into and occupies the vacant oxygensite or the local structure rearranges from corner-sharingneighboring AlO4 tetrahedra to edge-sharing ones. In contrast,in a-C12A7:e–, electron anions preferentially and rapidly localizeat the site of the missing O2– to neutralize the exposed chargeand restore the tetrahedral environment, leading to the forma-tion of Al(2e–)Al and Al(2e–)Ca centers. Oxygen ions displacedby electron anions coordinate with adjacent metal atoms to formhypercoordinated species such as 5-coordinated Al3+ (Fig. S9).We note that the metal–metal bonding in the M1(2e

–)M2centers (where M1 and M2 are either Al or Ca) is considerablyweaker than that in the M1(O

2–)M2 lattice, forming weak linksthat disrupt polymeric Al-O structures and increase local mo-bility in the system, analogous to fluoride or hydroxide anions inconventional glasses. However, in addition to being far weakerthan metal–oxygen bonds, electron anions are far more mobilethan conventional anions and can be easily displaced. O2– ionsdiffusing through the lattice react with the M1(2e

–)M2 centersand displace the trapped electrons either to the remnants of theC12A7 lattice cages or to other undercoordinated metal sites.Because the electron transfer occurs at a much faster time-scale than atomic displacements, such electron transfer and(re)trapping events change the local potential energy surface,i.e., induce forces that accelerate atoms in the vicinity of thedefects. Thus, we propose that electron anion transfer events inC12A7:e– elevate the local temperature above the global aver-age, thus maintaining the molten phase to lower global tem-peratures than in a-C12A7:O2–.Amorphous C12A7:e– and C12A7:O2– have virtually indistin-

guishable X-ray scattering, neutron diffraction, and infraredspectra. However, the Raman spectra of C12A7:e– show a nar-row resonantly enhanced band peaking at ∼186 cm−1 andstrongly increasing in intensity as a function of Ne (29). Thesedata provide us with a reference point for the experimentalvalidation of the proposed electronic defects and mechanisms.To test whether the Raman band is associated with electronanions, we represent the Al(2e–)Al and Al(2e–)Ca defects usinglinear clusters OAl–AlO (Fig. 4A) and FCa–AlO (Fig. 4B), re-spectively, denoted for brevity as LM–ML, where M are metals(M = Al, Ca) and L are ligands (L = O, F). These clusters re-produce critical elements of the electron defects in C12A7:e–:electrostatic neutrality, coordination of the metal atoms by ligands

L, and localization of two electrons between the metal atomssimilar to that in Al(2e–)Al and Al(2e–)Ca. Importantly, thesemodels allow us to isolate the motion of the metal atoms fromthat of the rest of the system and calculate resonant Ramanintensities as functions of M–M distances. Both LM–ML clustersexhibit a strong Raman peak due to in-phase stretching of theM–M bond. As the M–M distance increases, the intensities of thepeaks increase and their frequencies decrease. The Ramanspectra in Fig. 4 show that for the M–M distances close to thosein the Al(2e–)Al and Al(2e–)Ca centers, the frequencies of bothstretching modes are consistent with the observed 186-cm−1 peakand the resonant enhancement in LAl–CaL is approximately anorder of magnitude higher than that in LAl–AlL. We note thatbecause the excited states in the clusters are at higher energiesthan in the bulk C12A7:e– system, enhancement in the LAl–AlLcluster is underestimated.The computed imaginary part of the bulk dielectric function

Im(e) for a-C12A7:e– (Tmax = 2,650 K) is compared with theexperimentally measured optical absorption spectrum in Fig. 4C.The two intense peaks at 3.2 eV and 4.0 eV are assigned tothe transition between the bonding and antibonding orbitals ofthe Al(2e–)Ca and Al(2e–)Al centers, respectively, whereas the2.5-eV peak is attributed to the electron transfer from thesedefects to the gap states associated with the remaining distortedlattice cages. The calculated values are in good agreement withthe experimentally observed bands peaking at 3.3 eV and 4.6 eVand a low-energy tail and consistent with the optical absorptionof electron anions in crystalline C12A7:e– (30), which providesfurther validation of the proposed electron defect models. Fi-nally we note that the Im(e) for a-C12A7:O2– shows no opticalabsorption features up to ∼5 eV in complete agreement with theexperimental data (29).Properties of glasses are modified by weakening their contin-

uous polymeric networks with (Fig. 5) dopants that provide ionicnondirectional bonds (e.g., Na+, Ca2+) or break and terminatepolymeric chains (e.g., F–). Electron anions provide a method tointroduce weak links into a glass network, complementing con-ventional substitution of anions or cations. Furthermore, elec-tron anions are capable of inducing such modifications at lowerconcentrations than conventional glass modifiers due to theirexceptional mobility.The strong dependence of the Tg on the concentration of

electron anions in C12A7 opens up the possibility of fine-tuningthe glass formation and processing approaches with small com-position changes as long as the origin of this dependence is un-derstood and the underlying mechanisms are controlled. Themicroscopic model presented here reveals the mechanisms ofC12A7 transformation from the crystalline to the amorphousform and explains the dependence of Tg on the concentration ofelectron anions; it also gives insight into the multiple kineticallycontrolled processes near Tm. We propose that use of electronsas highly mobile anions offers a promising method for attenu-ating the thermal and electronic properties of amorphous ma-terials formed from oxides of nonreducible metals, facilitatingthe design of structural and functional glasses and building onthe recent discoveries of other stable solid electrides (44–47).Furthermore, the concept of altering network properties viahighly mobile weak links, such as electron anions, as opposed tostationary weak links, may have applications in a diverse varietyof networks, well beyond the science of noncrystalline materials.

ACKNOWLEDGMENTS. Calculations were performed using Pacific NorthwestNational Laboratory (PNNL) Institutional Computing resources. This workwas supported by the Accelerated Innovation Research Initiative TurningTop Science and Ideas into High-Impact Values program of the Japan Scienceand Technology Agency. P.V.S. was supported by the Laboratory DirectedResearch and Development program at PNNL, a multiprogram nationallaboratory operated by Battelle for the US Department of Energy underContract DE-AC05-76RLO1830.

Fig. 5. Continuous random networks of strongly bonded structural ele-ments are modified by introducing weak links (network modifiers), includingcations, such as Na+ and Ca2+, that induce the formation of ionic bonds(dashed lines) or monovalent anions, such as F− and OH−, that terminatepolymerization of network fragments. Electron anions introduce anothercategory of network modifiers: highly mobile weak links.

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