Crystal Structures of CaB₃N₃ at High Pressures

Liu H., Naumov I.I., Hemley R.J.

The structure, bonding, and other properties of phases in the carbon-hydrogen system over a range of conditions are of considerable importance to a broad range of scientific problems. However, the phase diagram of the C-H system at high pressures and temperatures is still not known. To search for new low-energy hydrocarbon structures, we carried out systematic structure prediction calculations for the C-H system from 100 to 300 GPa. We confirmed several previously predicted structures but found additional compositions that adopt more stable structures. In particular, a C2H4 structure is found that has an indirect band gap, and phonon calculations confirm that it is dynamically stable over a broad pressure range. We also identify more carbon-rich structures that are energetically favorable. The results are important for understanding carbon-hydrogen interactions in high-pressure experiments, dense astrophysical environments and the deep carbon cycle in planetary interiors.

Yong X., Liu H., Wu M., Yao Y., Tse J.S., Dias R., Yoo C.

Significance Using multiple theoretical techniques, the temperature and pressure dependence of the structures and dynamics of dense CO 2 were investigated. Near the transition to the extended structure, CO 2 molecules were found to exhibit large-amplitude bending vibrations. A 4-coordinated Pna 2 1 structure (CO 2 -V′) with a diffraction pattern similar to CO 2 -V ( P2 1 2 1 2 1 ) was found. Both CO 2 -V and -V′ are predicted to be metastable at ambient pressure. This result is in agreement with the experimental recovery of CO 2 -V below 200 K at ambient pressure. This 4-coordinated structure formed from main group molecules was recovered from high pressure. Both recovered fully extended CO 2 solids possess high- energy density and hardness.

Shi J., Cui W., Flores-Livas J.A., San-Miguel A., Botti S., Marques M.A.

Barium silicides are versatile materials that have attracted attention for a variety of applications in electronics and optoelectronics.

Li Y., Hao J., Liu H., Lu S., Tse J.S.

The pressure-induced transformation of diatomic nitrogen into nonmolecular polymeric phases may produce potentially useful high-energy-density materials. We combine first-principles calculations with structure searching to predict a new class of nitrogen-rich boron nitrides with a stoichiometry of B(3)N(5) that are stable or metastable relative to solid N(2) and h-BN at ambient pressure. The most stable phase at ambient pressure has a layered structure (h-B(3)N(5)) containing hexagonal B(3)N(3) layers sandwiched with intercalated freely rotating N(2) molecules. At 15 GPa, a three-dimensional C222(1) structure with single N-N bonds becomes the most stable. This pressure is much lower than that required for triple-to-single bond transformation in pure solid nitrogen (110 GPa). More importantly, C222(1)-B(3)N(5) is metastable, and can be recovered under ambient conditions. Its energy density of ∼3.44 kJ/g makes it a potential high-energy-density material. In addition, stress-strain calculations estimate a Vicker's hardness of ∼44 GPa. Structure searching reveals a new clathrate sodalitelike BN structure that is metastable under ambient conditions.

Miao M., Hoffmann R.

Building on our previous chemical and physical model of high-pressure electrides (HPEs), we explore the effects of interaction of electrons confined in crystals but off the atoms, under conditions of extreme pressure. Electrons in the quantized energy levels of voids or vacancies, interstitial quasiatoms (ISQs), effectively interact with each or with other atoms, in ways that are quite chemical. With the well-characterized Na HPE as an example, we explore the ionic limit, ISQs behaving as anions. A detailed comparison with known ionic compounds points to high ISQ charge density. ISQs may also form what appear to be covalent bonds with neighboring ISQs or real atoms, similarly confined. Our study looks specifically at quasimolecular model systems (two ISQs, a Li atom and a one-electron ISQ, a Mg atom and two ISQs), in a compression chamber made of He atoms. The electronic density due to the formation of bonding and antibonding molecular orbitals of the compressed entities is recognizable, and a bonding stabilization, which increases with pressure, is estimated. Finally, we use the computed Mg electride to understand metallic bonding in one class of electrides. In general, the space confined between atoms in a high pressure environment offers up quantized states to electrons. These ISQs, even as they lack centering nuclei, in their interactions with each other and neighboring atoms may show anionic, covalent, or metallic bonding, all the chemical features of an atom.

Liu H., Yao Y., Klug D.D.

The knowledge of the structures that can exist in compounds containing helium is of interest for understanding the conditions where and if this inert element can form structures where closed shell electrons of helium can participate in bonding that is not describable exclusively by van der Waals interactions alone. In this study we examine stable mixtures of He and ${\mathrm{H}}_{2}\mathrm{O}$ at high pressures using a first-principles structure searching method. We find a thermodynamically stable structure that can be characterized by interactions comparable in strength to that of conventional hydrogen bonds. An orthorhombic structure with space group Ibam is identified that has progressively lower enthalpy with increasing pressure above 296 GPa than a mixture of He and ${\mathrm{H}}_{2}\mathrm{O}$. This mechanically and dynamically stable structure is found at pressures that are now becoming accessible to high-pressure techniques.

Zhang M., Liu H., Li Q., Gao B., Wang Y., Li H., Chen C., Ma Y.

We solve the crystal structure of recently synthesized cubic BC(3) using an unbiased swarm structure search, which identifies a highly symmetric BC(3) phase in the cubic diamond structure (d-BC(3)) that contains a distinct B-B bonding network along the body diagonals of a large 64-atom unit cell. Simulated x-ray diffraction and Raman peaks of d-BC(3) are in excellent agreement with experimental data. Calculated stress-strain relations of d-BC(3) demonstrate its intrinsic superhard nature and reveal intriguing sequential bond-breaking modes that produce superior ductility and extended elasticity, which are unique among superhard solids. The present results establish the first boron carbide in the cubic diamond structure with remarkable properties, and these new findings also provide insights for exploring other covalent solids with complex bonding configurations.

Zhang M., Lu M., Du Y., Gao L., Lu C., Liu H.

A recent experimental study reported the successful synthesis of an orthorhombic FeB4 with a high hardness of 62(5) GPa [H. Gou et al., Phys. Rev. Lett. 111, 157002 (2013)], which has reignited extensive interests on whether transition-metal borides compounds will become superhard materials. However, it is contradicted with some theoretical studies suggesting transition-metal boron compounds are unlikely to become superhard materials. Here, we examined structural and electronic properties of FeB4 using density functional theory. The electronic calculations show the good metallicity and covalent Fe–B bonding. Meanwhile, we extensively investigated stress-strain relations of FeB4 under various tensile and shear loading directions. The calculated weakest tensile and shear stresses are 40 GPa and 25 GPa, respectively. Further simulations (e.g., electron localization function and bond length along the weakest loading direction) on FeB4 show the weak Fe–B bonding is responsible for this low hardness. Moreover, these results are consistent with the value of Vickers hardness (11.7–32.3 GPa) by employing different empirical hardness models and below the superhardness threshold of 40 GPa. Our current results suggest FeB4 is a hard material and unlikely to become superhard (>40 GPa).

Zhu L., Liu H., Pickard C.J., Zou G., Ma Y.

Studies of the Earth's atmosphere have shown that more than 90% of xenon (Xe) is depleted compared with its abundance in chondritic meteorites. This long-standing missing Xe paradox has become the subject of considerable interest and several models for a Xe reservoir have been proposed. Whether the missing Xe is hiding in the Earth's core has remained a long unanswered question. The key to address this issue lies in the reactivity of Xe with iron (Fe, the main constituent of the Earth's core), which has been denied by earlier studies. Here we report on the first evidence of the chemical reaction of Xe and Fe at the conditions of the Earth's core, predicted through first-principles calculations and unbiased structure searching techniques. We find that Xe and Fe form a stable, inter-metallic compound of XeFe3, adopting a Cu3Au-type face-centered cubic structure above 183 GPa and at 4470 K. As the result of a Xe ->Fe charge transfer, Xe loses its chemical inertness by opening up the filled 5p electron shell and functioning as a 5p-like element, whilst Fe is unusually negatively charged, acting as an oxidant rather than a reductant as usual. Our work establishes that the Earth's core is a natural reservoir for Xe storage, and possibly provides the key to unlocking the missing Xe paradox.

Miao M., Hoffmann R.

Electrides, in which electrons occupy interstitial regions in the crystal and behave as anions, appear as new phases for many elements (and compounds) under high pressure. We propose a unified theory of high pressure electrides (HPEs) by treating electrons in the interstitial sites as filling the quantized orbitals of the interstitial space enclosed by the surrounding atom cores, generating what we call an interstitial quasi-atom, ISQ. With increasing pressure, the energies of the valence orbitals of atoms increase more significantly than the ISQ levels, due to repulsion, exclusion by the atom cores, effectively giving the valence electrons less room in which to move. At a high enough pressure, which depends on the element and its orbitals, the frontier atomic electron may become higher in energy than the ISQ, resulting in electron transfer to the interstitial space and the formation of an HPE. By using a He lattice model to compress (with minimal orbital interaction at moderate pressures between the surrounding He and the contained atoms or molecules) atoms and an interstitial space, we are able to semiquantitatively explain and predict the propensity of various elements to form HPEs. The slopes in energy of various orbitals with pressure (s > p > d) are essential for identifying trends across the entire Periodic Table. We predict that the elements forming HPEs under 500 GPa will be Li, Na (both already known to do so), Al, and, near the high end of this pressure range, Mg, Si, Tl, In, and Pb. Ferromagnetic electrides for the heavier alkali metals, suggested by Pickard and Needs, potentially compete with transformation to d-group metals.

Miao M.

The periodicity of the elements and the non-reactivity of the inner-shell electrons are two related principles of chemistry, rooted in the atomic shell structure. Within compounds, Group I elements, for example, invariably assume the +1 oxidation state, and their chemical properties differ completely from those of the p-block elements. These general rules govern our understanding of chemical structures and reactions. Here, first-principles calculations show that, under pressure, caesium atoms can share their 5p electrons to become formally oxidized beyond the +1 state. In the presence of fluorine and under pressure, the formation of CsFn (n > 1) compounds containing neutral or ionic molecules is predicted. Their geometry and bonding resemble that of isoelectronic XeFn molecules, showing a caesium atom that behaves chemically like a p-block element under these conditions. The calculated stability of the CsFn compounds shows that the inner-shell electrons can become the main components of chemical bonds. Caesium has so far not been found in oxidation states higher than +1, but quantum chemical calculations have now shown that, under high pressures, 5p inner shell electrons of caesium can participate in — and become the main components of — bonds. Caesium is predicted to form stable CsFn molecules that resemble isoelectronic XeFn.

Wang Y., Lv J., Zhu L., Ma Y.

We have developed a software package CALYPSO (Crystal structure AnaLYsis by Particle Swarm Optimization) to predict the energetically stable/metastable crystal structures of materials at given chemical compositions and external conditions (e.g., pressure). The CALYPSO method is based on several major techniques (e.g. particle-swarm optimization algorithm, symmetry constraints on structural generation, bond characterization matrix on elimination of similar structures, partial random structures per generation on enhancing structural diversity, and penalty function, etc.) for global structural minimization from scratch. All of these techniques have been demonstrated to be critical to the prediction of global stable structure. We have implemented these techniques into the CALYPSO code. Testing of the code on many known and unknown systems shows high efficiency and the highly successful rate of this CALYPSO method [Y. Wang, J. Lv, L. Zhu, Y. Ma, Phys. Rev. B 82 (2010) 094116] [29]. In this paper, we focus on descriptions of the implementation of CALYPSO code and why it works.

Ruiz-Fuertes J., López-Moreno S., López-Solano J., Errandonea D., Segura A., Lacomba-Perales R., Muñoz A., Radescu S., Rodríguez-Hernández P., Gospodinov M., Nagornaya L.L., Tu C.Y.

The electronic band-structure and band-gap dependence on the $d$ character of ${A}^{2+}$ cation in $A$WO${}_{4}$ wolframite-type oxides is investigated for different compounds ($A$ $=$ Mg, Zn, Cd, and Mn) by means of optical-absorption spectroscopy and first-principles density-functional calculations. High pressure is used to tune their properties up to 10 GPa by changing the bonding distances establishing electronic to structural correlations. The effect of unfilled $d$ levels is found to produce changes in the nature of the band gap as well as its pressure dependence without structural changes. Thus, whereas Mg, Zn, and Cd, with empty or filled $d$ electron shells, give rise to direct and wide band gaps, Mn, with a half-filled $d$ shell, is found to have an indirect band gap that is more than 1.6 eV smaller than for the other wolframites. In addition, the band gaps of MgWO${}_{4}$, ZnWO${}_{4}$, and CdWO${}_{4}$ blue-shift linearly with pressure, with a pressure coefficient of approximately 13 eV/GPa. However, the band gap of multiferroic MnWO${}_{4}$ red-shifts at \ensuremath{-}22 meV/GPa. Finally, in MnWO${}_{4}$, absorption bands are observed at lower energy than the band gap and followed with pressure based on the Tanabe-Sugano diagram. This study allows us to estimate the crystal-field variation with pressure for the MnO${}_{6}$ complexes and how it affects their band-gap closure.

Liu H., Wang H., Ma Y.

The high-pressure phases of solid hydrogen are of fundamental interest and relevant to the interior of giant planets; however, knowledge of these phases is far from complete. Particle swarm optimization (PSO) techniques were applied to a structural search, yielding hitherto unexpected high-pressure phases of solid hydrogen at pressures up to 5 TPa. An exotic quasi-molecular mC24 structure (space group C2/c, stable at 0.47-0.59 TPa) with two types of intramolecular bonds was predicted, providing a deeper understanding of molecular dissociation in solid hydrogen, which has been a mystery for decades. We further predicted the existence of two atomic phases: (i) the oC12 structure (space group Cmcm, stable at > 2.1 TPa), consisting of planar H3 clusters, and (ii) the cI16 structure, previously observed in lithium and sodium, stable above 3.5 TPa upon consideration of the zero-point energy. This work clearly revised the known zero-temperature and high-pressure (>0.47 TPa) phase diagram for solid hydrogen and has implications for the constituent structures of giant planets.

Wang Y., Liu H., Lv J., Zhu L., Wang H., Ma Y.

Water ice dissociates into a superionic solid at high temperature (>2,000 K) and pressure, where oxygen forms the lattice, but hydrogen diffuses completely. At low temperature, however, the dissociation into an ionic ice of hydronium (H(3)O)(+) hydroxide (OH)(-) is not expected because of the extremely high energy cost (~1.5 eV) of proton transfer between H(2)O molecules. Here we show the pressure-induced formation of a partially ionic phase (monoclinic P2(1) structure) consisting of coupled alternate layers of (OH)(δ-) and (H(3)O)(δ+) (δ=0.62) in water ice predicted by particle-swarm optimization structural search at zero temperature and pressures of >14 Mbar. The occurrence of this ionic phase follows the break-up of the typical O-H covalently bonded tetrahedrons in the hydrogen symmetric atomic phases and is originated from the volume reduction favourable for a denser structure packing.

Zhang D., Gao L., Tian Y., Zhang S., Du Y., Kou C., Zhang M., Peng F.

Zhong X., Xu M., Yang L., Qu X., Yang L., Zhang M., Liu H., Ma Y.

The search for new inorganic electrides has attracted significant attention due to their potential applications in transparent conductors, battery electrodes, electron emitters, as well as catalysts for chemical synthesis. However, only a few inorganic electrides have been successfully synthesized thus far, limiting the variety of electride examples. Here, we show the stabilization of inorganic electrides in the Ti-rich Ti–O system through first-principles calculations in conjunction with swarm-intelligence-based CALYPSO method for structure prediction. Besides the known Ti-rich stoichiometries of Ti2O, Ti3O, and Ti6O, two hitherto unknown Ti4O and Ti5O stoichiometries are predicted to be thermodynamically stable at certain pressure conditions. We found that these Ti-rich Ti–O compounds are primarily zero-dimensional electrides with excess electrons confined in the atom-sized lattice voids or between the cationic layers playing the role as anions. The underlying mechanism behind the stabilization of electrides has been rationalized in terms of the excess electrons provided by Ti atoms and their accommodation of excess electrons by multiple cavities and layered atomic packings. The present results provide a viable direction for searching for practical electrides in the technically important Ti–O system. Computer simulations predict that compounds made of oxygen and titanium atoms form cages that can host electrons in their interstices. A team led by Hanyu Liu and Yanming Ma from Jilin University, China, have investigated the possibility for materials belonging to the family of titanium dioxide, a pigment used in paints and sunscreens, to behave as electrides, materials in which electrons resemble larger negatively charged atoms in the way in which they localize and interact with the surrounding atomic structure. Their calculations show that this occurs if the amount of titanium atoms in the material exceeds that of oxygen atoms by at least a factor of 2, which allows the formation of larger cages in which electrons can be confined. The synthesis of these materials will allow to assess their significance for catalysis or other applications.