Chapter 6 Electrides and Their High-Pressure Chemistry

Chapter 6 Electrides and Their High-Pressure Chemistry Xiao Dong and Artem R. Oganov Abstract Recently, electrides were discovered in many systems (especially those containing alkali and alkali earth metals) at high pressures. An electride can be defined as an ionic compound where the role of an anion is played by a strongly localized electron density. High-pressure emergence of electrides is due to the Pauli expulsion of valence electrons from the core, while some electrides are better described as originating from multicenter covalent bonds. Not being bound directly to a nucleus, these localized electrons are chemically active, making electrides the strongest reducing agents known, able to interact even with such an extremely inert element as helium. The Discovery of Electrides In classical chemical systems, electron density is peaked on nuclei. However, in the 1970–1980s, a new type of compounds was established, in which bare electrons, not bound to any particular nucleus, are concentrated in the interstitial space and behave as anions. Such compounds were named electrides. X. Dong (B) Center for High Pressure Science and Technology Advanced Research, Beijing 100193, China e-mail: [email protected] A.R. Oganov Skolkovo Innovation Center, Skolkovo Institute of Science and Technology, 3 Nobel Street, Moscow 143026, Russia e-mail: [email protected] A.R. Oganov State University of New York, Stony Brook, NY 11794-2100, USA A.R. Oganov Moscow Institute of Physics and Technology, 9 Institutskiy Lane, Dolgoprudny, Moscow Region 141700, Russia A.R. Oganov International Center for Materials Design, Northwestern Polytechnical University, Xi’an 710072, China © Springer International Publishing AG 2017 69 G.G.N. Angilella and A. La Magna (eds.), Correlations in Condensed Matter under Extreme Conditions, DOI 10.1007/978-3-319-53664-4_6 [email protected] 70 X. Dong and A.R. Oganov Fig. 6.1 Structure of the organic electride Cs+(15-crown-5)2e−. Electron-trapping cavities and channels are shown in pink, 15-crown-5 molecules in blue, and cesium cations in yellow.Inset shows the ball-and-stick representation of the Cs+(15-crown-5)2 “sandwich,” with the Cs+ ion drawn to scale [1] (color figure online) The first clear report of an electride we could find dates back to 1981 [2], followed by many other discoveries of chemically complex compounds (at first, only organic, but then also inorganic [3]). In 1990, Dye [1, 4, 5] discovered that an organic crown ether or cryptand can trap electrons as counterions, in alkali metal complexes, such as Cs+(18-crown-6)2e− or Cs+(15-crown-5)2e−. In such electrides as shown in Fig. 6.1, the localized electrons are usually single electrons occupying the cavities, and there is a weak spin–spin interaction between electrons occupying neighboring cavities. So, electrides known at normal pressure are paramagnetic or antiferromagnetic. Since high pressure favors spin pairing, such spin-polarized electrides will obvi- ously give way to spin-paired electrides under compression. Another insight into the nature of high-pressure electrides comes from a quantum-mechanical consideration of the interaction between valence and core electrons. In 2008, Rousseau and Ashcroft [6] modeled the effects of core electrons as a hard potential v(r) V0θ(rc r), where rc is the ionic radius, θ is the Heaviside = − step function and V0 a hard screening potential. Using this potential, they wrote the Hamiltonian and the Schrödinger equation: 2 H(r) 2 v(r R), (6.1a) =−2m ∇ + − R Hϕ Eϕ, (6.1b) = where R is the position of nucleus. To consider the effect of compression, they also 3 employed an average radius of ions, rs √3Ω/4π N, where N is the number of = atoms and Ω the volume. In this way, the parameter rc/rs can describe the compression ratio. [email protected] 6 Electrides and Their High-Pressure Chemistry 71 Fig. 6.2 Electronic properties calculated from Eq.(6.1b)withrc/rs 0.7. a Electron density in the z 0plane.b Band structure (eigenvalue spectrum) for excluding= spheres. The Fermi energy (green= line) and the free electron Fermi energy (black line) are indicated [6] (color figure online) Solving numerically the Schrödinger’s equation for the face-center cubic (fcc) structure, they found that when rc/rs > 0.5, the wave function will deviate sig- nificantly from the nearly free electron gas behavior and localize in the interstitial regions (Fig. 6.2a). In the band structure, the band width decreases with compression, which means the electrons are more localized (Fig. 6.2b). Already this oversimplified model gives an enlightening idea that electropositive atoms at strong compression may experience band narrowing, interstitial localization of valence electrons, and metal–insulator transition. The first anticipation of demetallization of alkali metals under pressure came from Professor Pucci’s group in 1997 [7], although not through the electride mechanism. Then, Ma and Oganov [8] found a true high-pressure electride, transparent hP4 phase of sodium. In the high-pressure experiment, metallic sodium transformed under compression first to a poorly metallic incommensurate tI19 phase (black at 156 GPa, Fig. 6.3a) and then to the transparent phase hP4. In the hP4 structure, there are two kinds of Na atoms, Na1 and Na2, in total four atoms of Na and two interstitial sites with electron localization in the unit cell. Each interstitial site contains an electron pair, and the chemical formula can be written as Na2(2e). From structural geometry, one could imply pd and pd2 hybridizations for Na1 in the octahedral sites and Na2 in the triangular prismatic coordination, respectively (Fig.6.3b). It has a wide band gap—for example, GW calculations predict the band gap to be over 6eV at 600 GPa, which implies a colorless transparent insulator. Similar electrides were also found for Li [9–12]. However, lithium atom has two differences from sodium: (1) the core radius (i.e., the ionic Li+ radius, 0.76 Å) is much smaller than its covalent radius (1.28 Å) and van der Waals radius (1.82 Å). This means Li is quite compressible and easy to get into the electride state—compared with Na (which becomes an electride at pressures 200 GPa), Li only needs 60 GPa to get into the semiconducting phase C2cb–40 [∼10]. (2) Li is much smaller than Na, thus the interstitial electrons are localized in a smaller space and nearer to each other, which means that electrons can more easily tunnel from one interstitial site to [email protected] 72 X. Dong and A.R. Oganov Fig. 6.3 a Photographs of the Na sample taken under pressure in the diamond anvil cell (DAC), showing an optically transparent sample at 199GPa. b Crystal structure of hP4-Na (space group P63/mmc). c Band structure and partial densities of states (DOS) at 300GPa. From Ref. [8] another, and over the potential barrier formed by the repulsion from core electrons. As a result, the electride state is sensitive and easy to break: e.g., the band gap is quite small (0.8eV) and the external pressure causes a phase transition to the metallic Cmca-24 phase at 90GPa [10]. Besides elementary substances, electride states were reported for Al [13], Mg3O2 [14], Na3Cl [15], and Na2He [16], SiO [17]. Many of these compounds have chemical formulas very different from those known at zero pressure. The Effect of Core Electron and Anti-Wilson Phase Transition The free electron gas model is a convenient tool to show the expected effect of band broadening under pressure. Besides being convenient, this model becomes exact (if one neglects nuclear strong and weak interactions) for any chemical system at infinite 2 2 compression. In this model, the electronic dispersion relation is Ek k /2m. Here, the wave vector is in the momentum space, k ( π/a,π/a), where= a is the lattice 2 2 ∈ 2− parameter. So the band width ΔEk π /2ma . With pressure reducing the lattice parameter, the range of both k and Δ=E will increase, which is ruled by Heisenberg’s uncertainty principle. This means that in this simple theoretical model, Heisenberg’s uncertainty principle requires that the band width of solids increases with pressure. For a semiconductor or insulator at high pressure, the broadening band will occupy the energy space of forbidden band, thereby decreasing the band gap. If the pressure is sufficiently high, the conduction band and valence band will finally overlap, and the insulator–metal transition will occur, see Fig.6.4. This mechanism was discovered by Wilson, after whom it is named [18]. [email protected] 6 Electrides and Their High-Pressure Chemistry 73 Fig. 6.4 Evolution of the band structure under pressure in Wilson and anti-Wilson models The band overlap originating from the Wilson mechanism affects the electronic states near Fermi surface, and is normally accompanied with the strengthening of electron–phonon coupling to cause the Peierls distortion, or other more complex phonon and electron effects, often causing complex phase transitions. The related pressure-induced insulator–metal phase transition is usually called the Wilson transition. Wilson transition is indeed a common phenomenon at high pressure, but based on a crude theoretical model of free electron gas, which ignores the effect of atomic cores—i.e., strong Pauli and electrostatic repulsion of valence electrons from the core orbitals. In quantum mechanics, valence orbitals must be radially orthogonal with core electrons of the same angular momentum—and can be thought to be not “allowed” to get close to the core due to the Pauli exclusion principle. If pressure is sufficiently high, most of the free volume for such electrons will disappear and such “expelled” electrons will have to localize in the intersticial space.

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