entropy Article Ion Hopping and Constrained Li Diffusion Pathways in the Superionic State of Antifluorite Li2O Ajay Annamareddy and Jacob Eapen * Department of Nuclear Engineering, North Carolina State University, Raleigh, NC 27695, USA; [email protected] * Correspondence: [email protected]; Tel.: +1-919-515-5952 Academic Editors: Giovanni Ciccotti, Mauro Ferrario and Christof Schuette Received: 21 March 2017; Accepted: 15 May 2017; Published: 18 May 2017 Abstract: Li2O belongs to the family of antifluorites that show superionic behavior at high temperatures. While some of the superionic characteristics of Li2O are well-known, the mechanistic details of ionic conduction processes are somewhat nebulous. In this work, we first establish an onset of superionic conduction that is emblematic of a gradual disordering process among the Li ions at a characteristic temperature Ta (~1000 K) using reported neutron diffraction data and atomistic simulations. In the superionic state, the Li ions are observed to portray dynamic disorder by hopping between the tetrahedral lattice sites. We then show that string-like ionic diffusion pathways are established among the Li ions in the superionic state. The diffusivity of these dynamical string-like structures, which have a finite lifetime, shows a remarkable correlation to the bulk diffusivity of the system. Keywords: Li2O; atomistic simulations; antifluorites; superionics; string-like; ionic conduction; diffusion 1. Introduction Lithium oxide (Li2O) has long been of interest because of its potential application as a tritium-breeding material in fusion reactors [1]. Li2O is also a superionic (or fast-ion) conductor, attaining liquid-like ionic conductivities within the solid state [2]. It is one of the simplest Li-based superionic conductors having just two species [3–7]. The structural and dynamic characteristics of Li2O thus have implications for important technologies ranging from future fusion reactors to solid state batteries [8]. The focus of this paper is to study the collective dynamics of Li ions in the highly conducting superionic state of Li2O using atomistic simulations and statistical mechanics. Li2O has an antifluorite structure (space group: Fm3m) with oxygen ions positioned on a face-centered cubic (FCC) lattice and the lithium ions occupying all the eight tetrahedral sites of the FCC lattice [9,10]. The crystal structure can be viewed alternatively as cations (Li) arranged on a simple cubic lattice, with anions occupying alternate cube centers. Both depictions are illustrated in Figure1, with cations and anions represented by smaller and larger spheres, respectively. The empty cube centers are the octahedral sites of the FCC lattice and are possible locations for interstitials. The lithium ions diffuse at temperatures lower than the melting point of the material; this leads to the superionic character of Li2O with the lithium ions contributing to the bulk of the ionic conductivity, while the less mobile oxygen ions play the important role of maintaining the crystalline structure. A transposition of cations to the FCC lattice and anions to the tetragonal sites gives rise to a popular variant—the fluorite structure. In Figure1, the anion and cation positions in antifluorites can simply be interchanged to obtain this structure. Fluorite materials such as PbF2, SrCl2, and CaF2 are also superionic conductors with anions making a dominant contribution to the ionic conductivity [9,11,12]. Entropy 2017, 19, 227; doi:10.3390/e19050227 www.mdpi.com/journal/entropy Entropy 2017, 19, 227 2 of 11 Entropy 2017, 19, 227 2 of 11 FigureFigure 1. (1.Left (Left) Lattice) Lattice structure structure of of an an antifluorite antifluorite crystal.crystal. The larger spheres spheres (shown (shown in in red) red) depict depict anionsanions that that form form an an FCC FCC structure structure while while the the smaller smaller spheresspheres (in green) represent represent cations cations occupying occupying allall the the available available tetrahedral tetrahedral sites sites of of the the FCC FCClattice; lattice. ((RightRight)) InIn an alternate illustration, illustration, the the cations cations formform a simple a simple cubic cubic lattice lattice while while the the anions anions occupy occupy alternativealternative cube centers. centers. A A fluorite fluorite structure structure is is realized when the cations and anions are interchanged. Neutron scattering/diffraction experiments realized when the cations and anions are interchanged. Neutron scattering/diffraction experiments and atomistic simulations indicate that the empty cube centers or the octahedral sites of the FCC and atomistic simulations indicate that the empty cube centers or the octahedral sites of the FCC lattice, lattice, which are the interstitial locations, are increasingly avoided in the superionic state for fluorites which are the interstitial locations, are increasingly avoided in the superionic state for fluorites and and antifluorites [9,11,13,14]. antifluorites [9,11,13,14]. Superionic conductors can be categorized into two types depending on the nature of their transitionSuperionic to the conductors conducting can state: be Type categorized I materials into typically two typesshow an depending abrupt transition, on the natureat a particular of their transitiontemperature, to the to conducting the conducting state: state Type through I materials a solid typically-solid phase show transition, an abrupt while transition, Type II at superionics a particular temperature,portray a more to the gradual conducting transition state over through a wide a range solid-solid of temperatures phase transition, [9]. Thewhile superionic Type state II superionics of Type portrayII materials a more is also gradual characterized transition by overa quasi-second-order a wide range ofthermodynamic temperatures transition [9]. The at superionica characteristic state of Typetemperature II materials Tλ, below is alsothe melting characterized point, where by a the quasi-second-order specific heat (cp) shows thermodynamic an anomalous transition peak [15]. at a characteristicSeveral fluorites temperature that fall inT lthe, below Type theII category melting portray point, wherethis anomalous the specific behavior heat ( c[16].p) shows Other an anomalousthermodynamic peak [ 15and]. mechanical Several fluorites properties that also fall exhibit in the a Typechange II in category behavior portray near Tλ: thisfor example, anomalous a behaviorsignificant [16]. decrease Other thermodynamic in the value of andelastic mechanical constant C properties11 is observed also near exhibit Tλ afor change fluorites in behavior[17,18]. Although Li2O is known to be a Type II conductor with a gradual increase in the ionic conductivity near Tl: for example, a significant decrease in the value of elastic constant C11 is observed [2], the divergent-like behavior of cp has not yet been observed experimentally. Instead, Tλ for Li2O near Tl for fluorites [17,18]. Although Li2O is known to be a Type II conductor with a gradual has been estimated approximately from neutron diffraction [10], diffusivity measurements [19], and increase in the ionic conductivity [2], the divergent-like behavior of cp has not yet been observed variations in properties such as lattice parameter [10] or elastic constants [20]. While these experimentally. Instead, T for Li O has been estimated approximately from neutron diffraction [10], measurements do not agreel on 2the numerical value, it is commonly accepted that λ transition takes diffusivity measurements [19], and variations in properties such as lattice parameter [10] or elastic place in the vicinity of 1200 K [10,19]. constants [20]. While these measurements do not agree on the numerical value, it is commonly accepted Recently, we have shown that many fluorites exhibit an onset of disorder or an onset of that l transition takes place in the vicinity of 1200 K [10,19]. superionicity at a characteristic temperature (denoted as Tα) that can be obtained from neutron Recently, we have shown that many fluorites exhibit an onset of disorder or an onset diffraction, ionic conductivity, and specific heat data [16], which is distinct from Tλ. Atomistic ofsimulations superionicity have at further a characteristic helped in elucidating temperature the structural (denoted and as dynamicalTa) that changes can be observed obtained across from neutronTα [13,21–23], diffraction, as well ionic as across conductivity, the λ transition. and specific We thus heatregard data a Type [16 ],II ionic which conductor is distinct to be from in theT l. Atomisticsuperionic simulations state at temperatures have further above helped T inα. In elucidating this work, the we structural first apply and our dynamical theoretical changes and observedexperimental across dataTa [analysis13,21–23 methodologies], as well as acrossto the antifluorite the l transition. Li2O to show We thusthat the regard onset a of Type superionic II ionic conductorconduction to beoccurs in the at superionicTα ≈ 1000 K. state We then at temperatures show that Li aboveions formTa. string-like In this work, dynamical we first structures apply our theoreticalwith a finite and experimentallifetime, and datathe string analysis diffusivity, methodologies which is to based the antifluorite on peak participation Li2O to show of that Li theions onset in of superionicstrings, depicts conduction a remarkable occurs correlation at Ta ≈ 1000 to the K. Webulk then diffusivity show that of the Li system. ions form string-like