Andriy O. Lyakhov

Transparent dense sodium

Under pressure, metals exhibit increasingly shorter interatomic distances. Intuitively, this response is expected to be accompanied by an increase in the widths of the valence and conduction bands and hence a more pronounced free-electron-like behaviour. But at the densities that can now be achieved experimentally, compression can be so substantial that core electrons overlap. This effect dramatically alters electronic properties from those typically associated with simple free-electron metals such as lithium (Li; refs 1–3) and sodium (Na; refs 4, 5), leading in turn to structurally complex phases and superconductivity with a high critical temperature. But the most intriguing prediction—that the seemingly simple metals Li (ref. 1) and Na (ref. 4) will transform under pressure into insulating states, owing to pairing of alkali atoms—has yet to be experimentally confirmed. Here we report experimental observations of a pressure-induced transformation of Na into an optically transparent phase at ∼200 GPa (corresponding to ∼5.0-fold compression). Experimental and computational data identify the new phase as a wide bandgap dielectric with a six-coordinated, highly distorted double-hexagonal close-packed structure. We attribute the emergence of this dense insulating state not to atom pairing, but to p–d hybridizations of valence electrons and their repulsion by core electrons into the lattice interstices. We expect that such insulating states may also form in other elements and compounds when compression is sufficiently strong that atomic cores start to overlap strongly.

Unexpected Stable Stoichiometries of Sodium Chlorides

Salt to Squeeze Simple table salt, NaCl, is the only known stable phase of Na and Cl at ambient conditions. Previous attempts to understand its structure and chemical properties under pressure and at high temperatures revealed phase and bonding transitions, while keeping the balance of one Na to one Cl. Using crystal structure prediction algorithms, Zhang et al. (p. 1502; see the Perspective by Ibáñez Insa) show that other compounds—including Na3Cl, Na2Cl, Na3Cl2, NaCl3, and NaCl7 are as stable as NaCl across a range of pressures. Several phases in the Na-Cl system are stable at high pressures and temperatures. [Also see Perspective by Ibáñez Insa] Sodium chloride (NaCl), or rocksalt, is well characterized at ambient pressure. As a result of the large electronegativity difference between Na and Cl atoms, it has highly ionic chemical bonding (with 1:1 stoichiometry dictated by charge balance) and B1-type crystal structure. By combining theoretical predictions and diamond anvil cell experiments, we found that new materials with different stoichiometries emerge at high pressures. Compounds such as Na3Cl, Na2Cl, Na3Cl2, NaCl3, and NaCl7 are theoretically stable and have unusual bonding and electronic properties. To test this prediction, we synthesized cubic and orthorhombic NaCl3 and two-dimensional metallic tetragonal Na3Cl. These experiments establish that compounds violating chemical intuition can be thermodynamically stable even in simple systems at nonambient conditions.

A little bit of lithium does a lot for hydrogen

From detailed assessments of electronic structure, we find that a combination of significantly quantal elements, six of seven atoms being hydrogen, becomes a stable metal at a pressure approximately 1/4 of that required to metalize pure hydrogen itself. The system, LiH6 (and other LiHn), may well have extensions beyond the constituent lithium. These hypothetical materials demonstrate that nontraditional stoichiometries can considerably expand the view of chemical combination under moderate pressure.

Evolutionary search for superhard materials: Methodology and applications to forms of carbon and TiO2

We have developed a method for prediction of the hardest crystal structures in a given chemical system. It is based on the evolutionary algorithm USPEX (Universal Structure Prediction: Evolutionary Xtallography) and electronegativity-based hardness model that we have augmented with bond-valence model and graph theory. These extensions enable correct description of the hardness of layered, molecular, and low-symmetry crystal structures. Applying this method to C and TiO2, we have (i) obtained a number of low-energy carbon structures with hardness slightly lower than diamond and (ii) proved that TiO2 in any of its possible polymorphs cannot be the hardest oxide, its hardness being below 17 GPa. DOI: 10.1103/PhysRevB.84.092103

How to predict very large and complex crystal structures

Abstract Evolutionary crystal structure prediction proved to be a powerful approach in discovering new materials. Certain limitations are encountered for systems with a large number of degrees of freedom (“large systems”) and complex energy landscapes (“complex systems”). We explore the nature of these limitations and address them with a number of newly developed tools. For large systems a major problem is the lack of diversity: any randomly produced population consists predominantly of high-energy disordered structures, offering virtually no routes toward the ordered ground state. We offer two solutions: first, modified variation operators that favor atoms with higher local order (a function we introduce here), and, second, construction of the first generation non-randomly, using pseudo-subcells with, in general, fractional atomic occupancies. This enhances order and diversity and improves energies of the structures. We introduce an additional variation operator, coordinate mutation, which applies preferentially to low-order (“badly placed”) atoms. Biasing other variation operators by local order is also found to produce improved results. One promising version of coordinate mutation, explored here, displaces atoms along the eigenvector of the lowest-frequency vibrational mode. For complex energy landscapes, the key problem is the possible existence of several energy funnels – in this situation it is possible to get trapped in one funnel (not necessarily containing the ground state). To address this problem, we develop an algorithm incorporating the ideas of abstract “distance” between structures. These new ingredients improve the performance of the evolutionary algorithm USPEX, in terms of efficiency and reliability, for large and complex systems.

High-pressure crystal structures and superconductivity of Stannane (SnH4)

There is great interest in the exploration of hydrogen-rich compounds upon strong compression where they can become superconductors. Stannane (SnH4) has been proposed to be a potential high-temperature superconductor under pressure, but its high-pressure crystal structures, fundamental for the understanding of superconductivity, remain unsolved. Using an ab initio evolutionary algorithm for crystal structure prediction, we propose the existence of two unique high-pressure metallic phases having space groups Ama2 and P63/mmc, which both contain hexagonal layers of Sn atoms and semimolecular (perhydride) H2 units. Enthalpy calculations reveal that the Ama2 and P63/mmc structures are stable at 96–180 GPa and above 180 GPa, respectively, while below 96 GPa SnH4 is unstable with respect to elemental decomposition. The application of the Allen-Dynes modified McMillan equation reveals high superconducting temperatures of 15–22 K for the Ama2 phase at 120 GPa and 52–62 K for the P63/mmc phase at 200 GPa.

Graphane sheets and crystals under pressure

Eight isomeric two-dimensional graphane sheets are found in a theoretical study. Four of these nets—two built on chair cyclohexanes, two on boat—are more stable thermodynamically than the isomeric benzene, or polyacetylene. Three-dimensional crystals are built up from the two-dimensional sheets, and their hypothetical behavior under pressure (up to 300 GPa) is explored. While the three-dimensional graphanes remain, as expected, insulating or semiconducting in this pressure range, there is a remarkable inversion in stability of the five crystals studied. Two stacking polytypes that are not the most stable at ambient pressure (one based on an unusual chair cyclohexane net, the other on a boat) are significantly stabilized with increasing pressure relative to stackings of simple chair sheets. The explanation may lie in the balance on intra and intersheet contacts in the extended arrays.

Exotic behavior and crystal structures of calcium under pressure

Experimental studies established that calcium undergoes several counterintuitive transitions under pressure: fcc → bcc → simple cubic → Ca-IV → Ca-V, and becomes a good superconductor in the simple cubic and higher-pressure phases. Here, using ab initio evolutionary simulations, we explore the behavior of Ca under pressure and find a number of new phases. Our structural sequence differs from the traditional picture for Ca, but is similar to that for Sr. The β-tin (I41/amd) structure, rather than simple cubic, is predicted to be the theoretical ground state at 0 K and 33–71 GPa. This structure can be represented as a large distortion of the simple cubic structure, just as the higher-pressure phases stable between 71 and 134 GPa. The structure of Ca-V, stable above 134 GPa, is a complex host-guest structure. According to our calculations, the predicted phases are superconductors with Tc increasing under pressure and reaching approximately 20 K at 120 GPa, in good agreement with experiment.

Towards the Theory of Hardness of Materials

Recent studies have shown that hardness, a complex property, can be calculated using very simple approaches or even analytical formulae. These form the basis for evaluating controversial experimental results (as we illustrate for TiO2-cotunnite) and enable a systematic search for novel hard materials, for instance, using global optimization algorithms (as we show on the example of SiO2 polymorphs).

Evolutionary metadynamics: a novel method to predict crystal structures

A novel method for crystal structure prediction, based on metadynamics and evolutionary algorithms, is presented here. This technique can be used to produce efficiently both the ground state and metastable states easily reachable from a reasonable initial structure. We use the cell shape as collective variable and evolutionary variation operators developed in the context of the USPEX method [Oganov, Glass, J. Chem. Phys., 2006, 124, 244704; Lyakhov et al., Comp. Phys. Comm., 2010, 181, 1623; Oganov et al., Acc. Chem. Res., 2011, 44, 227] to equilibrate the system as a function of the collective variables. We illustrate how this concept helps one to find stable and metastable states for Al2SiO5, SiO2, MgSiO3, and carbon. Apart from predicting crystal structures, the new method can also provide insight into the mechanisms of phase transitions.