Equation of state and properties of lithium

Prediction of Stable Ground-State Binary Sodium-Potassium Interalkalis under High Pressures

The complex structures and electronic properties of alkali metals and their alloys provide a natural laboratory for studying the interelectronic interactions of metals under compression. A recent theoretical study (J. Phys. Chem. Lett. 2019, 10, 3006) predicted an interesting pressure-induced decomposition-recombination behavior of the Na₂K compound over a pressure range of 10-500 GPa. However, a subsequent experiment (Phys. Rev. B 2020, 101, 224108) reported the formation of NaK rather than Na₂K at pressures above 5.9 GPa. To address this discordance, we study the chemical stability of different stoichiometries of Na_xK (x = 1/4, 1/3, 1/2, 2/3, 3/4, 4/3, 3/2, and 1-4) by an effective structure searching method combined with first-principles calculations. Na₂K is calculated to be unstable at 5-35 GPa due to the decomposition reaction Na₂K → NaK + Na, coinciding well with the experiment. NaK undergoes a combination-decomposition-recombination process accompanied by an opposite charge-transfer behavior between Na and K with pressure. Besides NaK, two hitherto unknown compounds NaK₃ and Na₃K₂ are uncovered. NaK₃ is a typical metallic alloy, while Na₃K₂ is an electride with strong interstitial electron localization.

Squeezing All Elements in the Periodic Table: Electron Configuration and Electronegativity of the Atoms under Compression

We present a quantum mechanical model capable of describing isotropic compression of single atoms in a non-reactive neon-like environment. Studies of 93 atoms predict drastic changes to ground-state electronic configurations and electronegativity in the pressure range of 0-300 GPa. This extension of atomic reference data assists in the working of chemical intuition at extreme pressure and can act as a guide to both experiments and computational efforts. For example, we can speculate on the existence of pressure-induced polarity (red-ox) inversions in various alloys. Our study confirms that the filling of energy levels in compressed atoms more closely follows the hydrogenic aufbau principle, where the ordering is determined by the principal quantum number. In contrast, the Madelung energy ordering rule is not predictive for atoms under compression. Magnetism may increase or decrease with pressure, depending on which atom is considered. However, Hund's rule is never violated for single atoms in the considered pressure range. Important (and understandable) electron shifts, s→p, s→d, s→f, and d→f are essential chemical and physical consequences of compression. Among the specific intriguing changes predicted are an increase in the range between the most and least electronegative elements with compression; a rearrangement of electronegativities of the alkali metals with pressure, with Na becoming the most electropositive s¹ element (while Li becomes a p group element and K and heavier become transition metals); phase transitions in Ca, Sr, and Ba correlating well with s→d transitions; spin-reduction in all d-block atoms for which the valence d-shell occupation is d ⁿ (4 ≤ n ≤ 8); d→f transitions in Ce, Dy, and Cm causing Ce to become the most electropositive element of the f-block; f→d transitions in Ho, Dy, and Tb and a s→f transition in Pu. At high pressure Sc and Ti become the most electropositive elements, while Ne, He, and F remain the most electronegative ones.

Emergence of topological electronic phases in elemental lithium under pressure

Lithium, a prototypical simple metal under ambient conditions, has a surprisingly rich phase diagram under pressure, taking up several structures with reduced symmetry, low coordination numbers, and even semiconducting character with increasing density. Using first-principles calculations, we demonstrate that some predicted high-pressure phases of elemental Li also host topological electronic structures. Beginning at 80 GPa and coincident with a transition to the previously predicted Pbca phase, we find Li to be a Dirac nodal line semimetal. We further calculate that Li retains linearly dispersing energy bands near the Fermi energy in subsequent predicted higher-pressure phases and that it exhibits a Lifshitz transition between two Cmca phases at 220 GPa. The Fd[Formula: see text]m phase at 500 GPa forms buckled honeycomb layers that give rise to a Dirac crossing 1 eV below the Fermi energy. The well-isolated topological nodes near the Fermi level in these phases result from increasing p-orbital character with density at the Fermi level, itself a consequence of rising 1s core wavefunction overlap, and a preference for nonsymmorphic symmetries in the crystal structures favored at these pressures. Our results provide evidence that under pressure, bulk 3D materials with light elements, or even pure elemental systems, can undergo phase transitions hosting nontrivial topological phase transitions hosting nontrivial topological properties near the Fermi level with measurable consequences and that, through pressure, we can access these phases in elemental lithium.

Evidence from Fermi surface analysis for the low-temperature structure of lithium

The low-temperature crystal structure of elemental lithium, the prototypical simple metal, is a several-decades-old problem. At 1 atm pressure and 298 K, Li forms a body-centered cubic lattice, which is common to all alkali metals. However, a low-temperature phase transition was experimentally detected to a structure initially identified as having the 9R stacking. This structure, proposed by Overhauser in 1984, has been questioned repeatedly but has not been confirmed. Here we present a theoretical analysis of the Fermi surface of lithium in several relevant structures. We demonstrate that experimental measurements of the Fermi surface based on the de Haas-van Alphen effect can be used as a diagnostic method to investigate the low-temperature phase diagram of lithium. This approach may overcome the limitations of X-ray and neutron diffraction techniques and makes possible, in principle, the determination of the lithium low-temperature structure (and that of other metals) at both ambient and high pressure. The theoretical results are compared with existing low-temperature ambient pressure experimental data, which are shown to be inconsistent with a 9R phase for the low-temperature structure of lithium.

Chemical bonding in hydrogen and lithium under pressure

Though hydrogen and lithium have been assigned a common column of the periodic table, their crystalline states under common conditions are drastically different: the former at temperatures where it is crystalline is a molecular insulator, whereas the latter is a metal that takes on simple structures. On compression, however, the two come to share some structural and other similarities associated with the insulator-to-metal and metal-to-insulator transitions, respectively. To gain a deeper understanding of differences and parallels in the behaviors of compressed hydrogen and lithium, we performed an ab initio comparative study of these systems in selected identical structures. Both elements undergo a continuous pressure-induced s-p electronic transition, though this is at a much earlier stage of development for H. The valence charge density accumulates in interstitial regions in Li but not in H in structures examined over the same range of compression. Moreover, the valence charge density distributions or electron localization functions for the same arrangement of atoms mirror each other as one proceeds from one element to the other. Application of the virial theorem shows that the kinetic and potential energies jump across the first-order phase transitions in H and Li are opposite in sign because of non-local effects in the Li pseudopotential. Finally, the common tendency of compressed H and Li to adopt three-fold coordinated structures as found is explained by the fact that such structures are capable of yielding a profound pseudogap in the electronic densities of states at the Fermi level, thereby reducing the kinetic energy. These results have implications for the phase diagrams of these elements and also for the search for new structures with novel properties.

Origin of Transitions between Metallic and Insulating States in Simple Metals

Unifying principles that underlie recently discovered transitions between metallic and insulating states in elemental solids under pressure are developed. Using group theory arguments and first-principles calculations, we show that the electronic properties of the phases involved in these transitions are controlled by symmetry principles. The valence bands in these systems are described by simple and composite band representations constructed from localized Wannier functions centered on points unoccupied by atoms, and which are not necessarily all symmetrical. The character of the Wannier functions is closely related to the degree of s-p(-d) hybridization and reflects multicenter chemical bonding in these insulating states. The conditions under which an insulating state is allowed for structures having an integer number of atoms per primitive unit cell as well as reentrant (i.e., metal-insulator-metal) transition sequences are detailed, resulting in predictions of behavior such as phases having band-contact lines. The general principles developed are tested and applied to the alkali and alkaline earth metals, including elements where high-pressure insulating phases have been reported (e.g., Li, Na, and Ca).

High pressure electrides: a predictive chemical and physical theory

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.

Comparison of density functional approximations and the finite-temperature Hartree-Fock approximation in warm dense lithium

We compare the behavior of the finite-temperature Hartree-Fock model with that of thermal density functional theory using both ground-state and temperature-dependent approximate exchange functionals. The test system is bcc Li in the temperature-density regime of warm dense matter (WDM). In this exchange-only case, there are significant qualitative differences in results from the three approaches. Those differences may be important for Born-Oppenheimer molecular dynamics studies of WDM with ground-state approximate density functionals and thermal occupancies. Such calculations require reliable regularized potentials over a demanding range of temperatures and densities. By comparison of pseudopotential and all-electron results at T=0 K for small Li clusters of local bcc symmetry and bond lengths equivalent to high density bulk Li, we determine the density ranges for which standard projector augmented wave (PAW) and norm-conserving pseudopotentials are reliable. Then, we construct and use all-electron PAW data sets with a small cutoff radius that are valid for lithium densities up to at least 80 g/cm{3}.

An embedded-atom-method model for alkali-metal vibrations

We present an embedded-atom-method (EAM) model that accurately describes the vibrational dynamics in the alkali metals Li, Na, K, Rb and Cs. The bulk dispersion curves, frequency-moment Debye temperatures and temperature-dependent entropy Debye temperatures are all in excellent agreement with experimental results. The model is also well suited for studying surface vibrational dynamics in these materials, as illustrated by calculations for the Na(110) surface.

Optimization and Application of Lithium Parameters for the Reactive Force Field, ReaxFF

To make a practical molecular dynamics (MD) simulation of the large-scale reactive chemical systems of Li-H and Li-C, we have optimized parameters of the reactive force field (ReaxFF) for these systems. The parameters for this force field were obtained from fitting to the results of density functional theory (DFT) calculations on the structures and energy barriers for a number of Li-H and Li-C molecules, including Li(2), LiH, Li(2)H(2), H(3)C-Li, H(3)C-H(2)C-Li, H(2)C=C-LiH, HCCLi, H(6)C(5)-Li, and Li(2)C(2), and to the equations of state and lattice parameters for condensed phases of Li. The accuracy of the developed ReaxFF was also tested by comparison to the dissociation energies of lithium-benzene sandwich compounds and the collision behavior of lithium atoms with a C(60) buckyball.

On the constitution of sodium at higher densities

Using density functional theory the atomic and electronic structures of sodium are predicted to depart substantially from those expected of simple metals for r(s)<2.48 ( p>130 GPa). Newly predicted phases include those with low structural symmetry and semimetallic electronic properties (including zero-gap semiconducting limiting behavior), and even those that raise the possibility of superconductivity, all at currently achievable pressures. Important differences emerge between sodium and lithium at high densities, and these are attributable to corresponding differences in their respective cores.

New high-pressure phases of lithium

Lithium is considered a 'simple' metal because, under ordinary conditions of pressure and temperature, the motion of conduction electrons is only weakly perturbed by interactions with the cubic lattice of atomic cores. It was recently predicted that at pressures below 100 GPa, dense Li may undergo several structural transitions, possibly leading to a 'paired-atom' phase with low symmetry and near-insulating properties. Here we report synchrotron X-ray diffraction measurements that confirm that Li undergoes pronounced structural changes under pressure. Near 39 GPa, the element transforms from a high-pressure face-centred-cubic phase, through an intermediate rhombohedral modification, to a cubic polymorph with 16 atoms per unit cell. This cubic phase has not been observed previously in any element; unusually, its calculated electronic density of states exhibits a pronounced semimetal-like minimum near the Fermi energy. We present total-energy calculations that provide theoretical support for the observed phase transition sequence. Our calculations indicate a large stability range of the 16-atom cubic phase relative to various other crystal structures tested here.