Phase stabilities in the Li-Ar system are established at various pressures by judging the formation enthalpy of stoichiometric LimArn ((m, n )= (1,5)–(5,1); (2,3); and (3,2)) compounds. In such calculations, the formation enthalpy of per atom in LimArn is defined as follows:
There, hf is the formation enthalpy per atom, and H is the calculated enthalpy of each compound. Here, we restrict ourselves to ground state calculations, i.e 
If the formation enthalpy of a compound is negative, this compound is considered stable with respect to decomposition into the elements. For H (Li), we used the relevant structures across the entire pressure range43; for H (Ar), the hexagonal close packed (hcp) structure of solid Ar is adopted46(The enthalpies of hcp and fcc-Ar are almost equal, which does not affect the stability of the binary compounds, see Fig. S1). It is important to recognize that going beyond the ground state in light-element systems, ion dynamics can significantly change the total energies due to large zero point energy (ZPE) contributions47,48. Here, the ZPEs for the P4/mmm phase of LiAr, the hexagonal phase of Ar, and the Cmca-24 structure of Li at 100 GPa are calculated to be as 86, 8, and 86 meV/atom, respectively. The contribution of ZPE to hf is thus quite small in the case of LiAr, and it is valid to neglect the contribution of ZPE when discussing the relative stability of Li−Ar systems. However, to account for all possible "escape routes", we construct the "convex hull" or "global stability line" of all considered binary phases. In such a phase diagram, where 
is plotted versus the lithium content 
, all points on the convex hull (solid line) are stable against all decomposition reactions. The convex hull for LimArn phases is displayed in Fig. 1 at 100, 200 and 300 GPa. At 100 GPa, all enthalpies of formation are positive; no Li-Ar compounds are found that are stable with respect to the elements. At 200 GPa, we see that various formation enthalpies are negative except for LiArn (n = 3, 4, 5), which indicates that other unexpected compounds LimArn are perhaps synthesizable experimentally under high-pressure conditions. Specifically, from inspecting the convex hull it is found that LiAr and Li3Ar are enthalpically the most stable in under high pressures. The enthalpies of other phases are only slightly higher (about 0.1 eV/atom) than those of the stable compounds. In particular, Li4Ar (Fig. S2, Table S1) and Li5Ar under high pressure, but also Li2Ar, Li3Ar2, LiAr2 and Li2Ar3 (Fig. S2, Table S1) are metastable and possibly synthesizable. More Ar-rich phases were not found to be stable at any pressure.
Dashed lines connect data points, and solid lines denote the convex hull.
Full size imageAs shown in Fig. 2, LiAr, Li3Ar, and Li5Ar become stable above 112 GPa, 119 GPa, and 109 GPa, respectively. Note that Li5Ar is the first Li-Ar compound stabilized by pressure, followed in quick succession by LiAr and Li3Ar. While Li5Ar is stable between about 109 GPa and 140 GPa only, both LiAr and Li3Ar are found to be stable up to the highest pressures included in this study (Fig. S3). In order to judge the dynamic stability of LiAr, Li3Ar, and Li5Ar, we have calculated the phonon dispersion curves (Fig. S4). No dynamic instabilities were observed throughout the whole Brillouin zone, indicating that LiAr, Li3Ar and Li5Ar are dynamically stable above 100 GPa. This means that, once formed at pressures, these phases can be decompressed down to at least 100 GPa (no dynamic instabilities were found for LiAr down to 43 GPa).
Figure 2
(a) Enthalpy of formation as a function of pressure for various LimAr compounds, respectively, where ΔH(LimAr) = H(LimAr)-m*H(oC24-Li)-H(hcp-Ar); (b) Predicted pressure ranges of stability for Li-Ar compounds.
Full size imageLiAr, Li3Ar and Li5Ar adopt relatively simple layered structures that can be interpreted as stackings of square lattices comprised of the elements (Fig. 3). Crystallographic information of the stable phases of LiAr, Li3Ar and Li5Ar are summarized in Table S2. From Fig. 2(a), it is seen that LiAr takes up a tetragonal P4/mmm phase below 175 GPa. This phase (shown in Fig. 2(a)) comprises alternately stacked square lattices of Ar and Li in [ArArArLiLiLi] periodicity along its crystallographic c axis. At pressures P > 175 GPa, the most stable structure for LiAr is the CsCl structure type, which can also be considered as alternate stackings of Li and Ar (see Fig. 3(b)). This CsCl structure of LiAr has also been found in HgXe at 75 GPa6. While the high-pressure phase of LiAr is one of the two most common structure type of ionic compounds (see below on a thorough examination of its electronic structure), the P4/mmm structure is not known amongst binary compounds. In fact, it can be related to the much more complex structure of the high-Tc superconductor HgBa2CuO449, with lithium atoms occupying the sites of Cu and Ba cations, and some of the argon atoms occupying the sites of Hg. This comparison is not perfect, but it hints at a more complex electronic structure that stabilizes this structure for LiAr. Note that the layered nature of this structure is not an approximant to segregation. For one, P4/mmm-LiAr is more stable than the elements above 112 GPa. We also constructed larger unit cells of LiAr with [(Ar)5(Li)5] and [(Ar)6(Li)6] stacking orders; at 100 GPa, these are 0.019 eV/atom and 0.036 eV/atom higher in enthalpy than P4/mmm-LiAr (Fig. S5).
Figure 3: The structures of LiAr and Li3Ar.
(a) P4/mmm-LiAr; (b) LiAr in CsCl structure type; (c) P4/mmm-Li3Ar; (d) Cmmm-Li3Ar; (e) P21-Li5Ar; (f) Cmcm-Li5Ar. The large green balls and the smaller golden balls represent Ar atom and Li atom, respectively. Red squares indicate layers in the Li5Ar structures.
Full size imageFor Li3Ar, the stable structure above 119 GPa also has space group P4/mmm (stacking order [LiLiLiAr] (Fig. 3(c)). At about 305 GPa, an orthorhombic structure (space group Cmmm), which is also a layered structure, becomes the most stable phase of Li3Ar. Its conventional cell is shown in Fig. 3(d). Li5Ar crystallizes in the pressure range of 109 GPa to 130 GPa in a monoclinic P21 phase, which is also a stacking variant, and shown in Fig. 3(e). Above 130 GPa, Li5Ar is most stable in an orthorhombic Cmcm phase (see Fig. 3(f)). The structures found in the stable Li-Ar phases are very similar (but not identical) to predicted Mg-Xe and Mg-Kr compounds38.
To further investigate the nature of the stabilization of these Li-Ar compounds, we analyzed their electronic structure. Due to their predicted stability over a wide pressure range, we will focus on the LiAr and Li3Ar phases here. For LiAr, Fig. 4 (a) shows the electronic band structure and projected density of states (PDOS) of the P4/mmm structure at 150 GPa and the CsCl structure type at 200 GPa, respectively. Both structures are metallic, as several bands cross the respective Fermi level. The states around the Fermi level indicate a partial occupation of Ar-3d states in both phases, which is more pronounced in the CsCl structure at higher pressure. The same is true for the stable phases of Li3Ar (see Fig. S6). Moreover, we find that the density of states at the Fermi level in both Li-Ar compounds (at 150 and 200 GPa) is larger than in elemental Li at the same pressures (Fig. S7). Note that P4/mmm-LiAr has a very flat band at 2 eV below the Fermi energy. We plot the charge density of this band in Fig. 4(b), and find the electron density to be partially localized in the interstitial region in the Li layer. Li itself undergoes a structural phase transition at about 70 GPa and becomes a semiconducting 'electride'50,51, a phenomenon that is caused by localization of valence electrons in the interstitial region of a densely packed Li lattice42. In contrast, tetragonal LiAr remains metallic under high pressure throughout its stability range. This is caused by partial charge transfer from Li-2s to Ar-3d states. A topological analysis of the electron density based on Bader's atoms-in-molecules approach52 helps us to quantify this effect: the net atomic charges in P4/mmm-LiAr at P = 160 GPa are + 0.71e for Li1, + 0.59e for Li2, −0.12e for Ar1 and −0.40e for Ar2. Note that these charges do not add up to zero: Bader's analysis finds two pockets of electronic charge in the interstitial region, at the 2e (1/2, 0, 1/2) position in the unit cell, with −0.54e in each pocket. These interstitial electrons are at the same position as oxygen anions in the CuO2 layers of HgBa2CuO4. Because the lithium atoms' valence electrons are not completely localized, but also partially populate the Ar-3d states, the structure remains metallic, in contrast to the pure lithium "electride" phase. The localized nature of the interstitial electron is confirmed by the Electron Localization Function (ELF), which carries information about the bonding character and valence electron configurations of atoms in a compound53. Larger ELF values usually correspond to inner shell or lone pair electrons and covalent bonds, whereas ionic and metallic bonds correspond to small ELF values. In Fig. 5(a), ELF is shown for a cut through the z = 1/2 plane of tetragonal LiAr at 150 GPa: besides the 1 s2 shell of lithium, there is significant interstitial electron localization visible between adjacent lithium cations (with a maximum value of ELF = 0.87).
Figure 4
(a) The electronic band structure and density of states of P4/mmm-LiAr at 150 GPa; (b) The charge density of the flat band around −2.5 eV; (c) The electronic band structure and PDOS of the CsCl structure of LiAr at 200GPa.
Full size image Figure 5: The calculated ELF of Li-Ar compounds.
(a) P4/mmm-LiAr along (001) plane at 150 GPa, (b) CsCl structure of LiAr along (110) plane at 200 GPa, (c) P4/mmm-Li3Ar along (001) plane at 200 GPa, and (d) Cmmm-Li3Ar along (001) plane at 310 GPa. Color scheme follows the rainbow colors from blue to red.
Full size imageThe CsCl phase of LiAr at 200 GPa is also found to be metallic and from Fig. 4(c), we can see that the value of DOS at the Fermi level is larger than that of tetragonal LiAr at 150 GPa. This indicates that the charge transfer is larger in this structure (and at the higher pressure), as Ar-3d states are lowered relative to Li-2s states. Bader's analysis gives partial charges of + 0.67e for Li and −0.67e for Ar at P = 200 GPa, which reduce to ± 0.62e at P = 300 GPa. As could be expected, no interstitial charge density forms in this structure – see the plot of the ELF in the [110] plane at P = 200 GPa in Fig. 5(b). Thus, at pressures above P = 175 GPa, LiAr is predicted to form a simple intermetallic compound – with anionic character of Ar. The Li core does not contain p-orbitals and is thus quite compact, due to the absence of orthogonality constraints, which contributes to the stability of LiAr with respect to elemental Li and Ar.
For Li3Ar, the electronic band structure and PDOS of the tetragonal P4/mmm phase at 200 GPa and the orthorhombic Cmmm phase at 310 GPa are compiled in Fig. S4. They indicate that Li3Ar under high pressure is metallic in either phase. As in LiAr, this is driven by partial occupation of the Ar-3d states. The ELF plots for Li3Ar at 200 GPa and 310 GPa (see Fig. 5(c,d)) show that, similar to tetragonal LiAr, there is electron localization in the interstitial region between Li atoms. A Bader analysis corroborates this picture: in tetragonal Li3Ar, the partial charge of Li1 is + 0.61e at 200 GPa (+0.57e at 300 GPa), + 0.55e (+0.49e) for Li2, and −1.03e (−1.02e) for Ar. The interstitial site at 2f (1/2, 0, 0) has a partial charge of −0.46e (−0.37e). In the orthorhombic structure of Li3Ar at 310 GPa, the charge transfer numbers agree qualitatively with all other Li-Ar phases discussed here.
Since all predicted stable phases are metallic, we estimated their potential for phonon-mediated superconductivity, with electron-phonon coupling calculated with the Quantum ESPRESSO package54. In our calculations we found that neither of the stable LiAr high-pressure phases exhibits significant electron-phonon coupling. However, for the tetragonal P4/mmm-Li3Ar, we find an electron-phonon coupling strength of λ = 0.721 and a superconducting temperature Tc = 17.6 K at 120 GPa, which reduce to λ = 0.454 and Tc = 6.5 K at 200 GPa. Superconductivity in an electride has been measured at ambient pressure: in 12CaO·7Al2O3, a superconducting phase was found below Tc = 0.4 K55.
In summary, by crystal structure searches based on CALYPSO methodology and density functional total energy calculations, potentially stable Li−Ar phases are systematically investigated at high pressure up to 300 GPa. Two unexpected LimAr compounds (LiAr and Li3Ar) might be experimentally synthesizable over a wide range of pressures. Our calculations indicate that LiAr and Li3Ar are enthalpically and dynamically stable above pressures of 112 GPa and 119 GPa, respectively, while Li5Ar is stable in a small pressure window of 109–140 GPa. We found that all stable phases are metallic.
High pressure can induce argon to become an electron acceptor, as evidenced here by its ability to form stable intermetallic compounds with Li. In this particular system, the formation of ionic compounds (involving charge transfer from Li-2 s to Ar-3d states) competes with lithium's propensity to shed its valence electron into interstitial space. The first stable Li-Ar compounds are thus predicted to feature both electride and metallic behavior. With higher pressure, the tendency of electron localization decreases in favor of increased ionic character. The absolute value of electronic charge transferred gradually decreased for all stable Li-Ar compounds. Amongst the stable Li-Ar compounds, Li3Ar exhibits reasonable electron-phonon coupling, with predicted superconducting temperatures of 17.6 K at 120 GPa and 6.5 K at 200 GPa, thus adding this compound to an intriguingly short list of candidates of superconducting electride phases.
Original source: https://www.nature.com/articles/srep16675
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