Exotic behavior and crystal structures of calcium under pressure

Emerging d-d orbital coupling between non-d-block main-group elements Mg and I at high pressure

d-d orbital coupling, which increases anisotropic and directional bonding, commonly occurs between d-block transition metals. Here, we report an unexpected d-d orbital coupling in the non-d-block main-group element compound Mg₂I based on first-principles calculations. The unfilled d orbitals of Mg and I atoms under ambient conditions become part of the valence orbitals and couple with each other under high pressures, resulting in the formation of highly symmetric I-Mg-I covalent bonding in Mg₂I, which forces the valence electrons of Mg atoms into the lattice voids to form interstitial quasi-atoms (ISQs). In turn, the ISQs highly interact with the crystal lattice, contributing to lattice stability. This study greatly enriches the fundamental understanding of chemical bonding between non-d-block main-group elements at high pressures.

Extreme structural stability of Ti0.5Sn0.5O2 nanoparticles: synergistic effect in the cationic sublattice

Ti_0.5Sn_0.5O₂ nanoparticles (∼5 nm and ∼10 nm) have been studied under high pressure by Raman spectroscopy. For particles with diameter ∼10 nm, a transformation has been observed at 20-25 GPa while for particles with ∼5 nm diameter no phase transition has been observed up to ∼30 GPa. The Ti_0.5Sn_0.5O₂ solid solution shows an extended stability at the nanoscale, both of its cationic and anionic sublattices. This ultrastability originates from the contribution of Ti and Sn mixing: Sn stabilizes the cationic network at high pressure and Ti ensures a coupling between the cationic and anionic sublattices. This result questions a "traditional" crystallographic description based on polyhedra packing and this synergistic effect reported in this work is similar to the case of metamaterials but at the nanoscale.

Pressure tuned incommensurability and guest structure transition in compressed scandium from machine learning atomic simulation

Scandium (Sc) is the lightest non-main-group element and transforms to a host-guest (H-G) incommensurate structure under gigapascal (GPa) pressures. While the host structure is stable over a wide pressure range, the guest structure may exist in multiple forms, featuring different incommensurate ratios, and mixing up to generate long-range "disordered" guest structures. Here, we employed the recently developed global neural network (g-NN) potential and the stochastic surface walking (SSW) global optimization algorithm to explore the global potential energy surface of Sc under various pressures. We probe the global minima structure in a system made of hundreds of atoms and revealed that the solid-phase transition between Sc-I and H-G Sc-II phases is fully reconstructive in nature. Above 62.5 GPa, the pressure will further destabilize the face-centered tetragonal (fct, Sc-IIa) guest structure to a body-centered tetragonal phase (bct, Sc-IIb), while sustaining the host structure. The structural transition mechanism of this work will shed light on the nature of the complex H-G structural modifications in compressed metals.

Crystal Structure Prediction and Lattice Dynamical Calculations for the Rare Platinum-Group Mineral Zaccariniite (RhNiAs)

The crystal structures of newly found minerals are routinely determined using single-crystal techniques. However, many rare minerals usually form micrometer-sized aggregates that are difficult to study with conventional structural methods. This is the case for numerous platinum-group minerals (PGMs) such as, for instance, zaccariniite (RhNiAs), the crystal structure of which was first obtained by studying synthetic samples. The aim of the present work is to explore the usefulness of USPEX, a powerful crystal structure prediction method, as an alternative means of determining the crystal structure of minerals such as zaccariniite, with a relatively simple crystal structure and chemical formula. We show that fixed composition USPEX searches with a variable number of formula units, using the ideal formula of the mineral as the only starting point, successfully predict the tetragonal structure of a mineral. Density functional theory (DFT) calculations can then be performed in order to more tightly relax the structure of the mineral and calculate different fundamental properties, such as the frequency of zone-center Raman-active phonons, or even their pressure behavior. These theoretical data can be subsequently compared to experimental results, which, in the case of newly found minerals, would allow one to confirm the correctness of the crystal structure predicted by the USPEX code.

Predicted Stable Electrides in Mg-Al System under High Pressure

Magnesium and aluminum, as the adjacent light metal elements, are difficult to form the stable stoichiometries compounds under ambient conditions. In this work, using evolutionary ab initio structural prediction approaches,...

Melting line of calcium characterized by in situ LH-DAC XRD and first-principles calculations

In this work, the melting line of calcium has been characterized both experimentally, using synchrotron X-ray diffraction in laser-heated diamond-anvil cells, and theoretically, using first-principles calculations. In the investigated pressure and temperature range (pressure between 10 and 40 GPa and temperature between 300 and 3000 K) it was possible to observe the face-centred phase of calcium and to confirm (and characterize for the first time at these conditions) the presence of the body-centred cubic and the simple cubic phase of calcium. The melting points obtained with the two techniques are in excellent agreement. Furthermore, the present results agree with the only existing melting line of calcium obtained in laser-heated diamond anvil cells, using the speckle method as melting detection technique. They also confirm a flat slope of the melting line in the pressure range between 10 and 30 GPa. The flat melting curve is associated with the presence of the solid high-temperature body-centered cubic phase of calcium and to a small volume change between this phase and the liquid at melting. Reasons for the stabilization of the body-centered face at high-temperature conditions will be discussed.

Pressure-induced electrides and metallic phases in the Y-Cl system

Pressure can profoundly change the electronic structure, leading to the formation of new phases and materials with exotic properties. Herein, using evolutionary algorithms and density functional theory, we systematically investigate the behaviour of materials in the yttrium-chlorine binary system under pressure. Electrons are found to be spatially confined at low pressures in yttrium chlorides and tend to form new electrides. In particular, a novel yttrium chloride, Y₃Cl₂, is predicted to be thermodynamically and lattice dynamically stable at approximately 10 GPa. Further analyses of the electron localization function and partial charge density identify trigonal Y₃Cl₂as a new 2D high-pressure electride with partially localized electrons contributing to the conduction. By further increasing the pressure, electrons in the yttrium-chlorine binary system tend to delocalize with the electrides decomposing into two new compounds (Y₂Cl and YCl₂) and a new YCl phase (space groupP6₃/mmc) above 20 GPa. These newly discovered phases are all metallic in their stable pressure range according to band structure simulations without interstitial electron localization. The discovery of these unconventional yttrium chlorides may inspire strategies to search for low-pressure electrides in other rare-earth halogenide systems.

Weak Coulomb correlations stabilize the electride high-pressure phase of elemental calcium

Theoretical studies using the state-of-the-art density functional theory and dynamicalmean-field theory (DFT + DMFT) method show that weak electronic correlation effects are crucial for reproducing the experimentally observed pressure-induced phase transitions of calcium from β-tin toCmmmand then to the simple cubic structure. The formation of an electride state in calcium leads to the emergence of partially filled and localized electronic states under compression. The electride state was described using a basis containing molecular orbitals centered on the interstitial site and Ca-d states. We investigate the influence of Coulomb correlations on the structural properties of elemental Ca, noting that approaches based on the Hartree-Fock method (DFT +Uor hybrid functional schemes) are poorly suited for describing correlated metals. We find that only the DFT + DMFT method reproduces the correct sequence of high-pressure phase transitions of Ca at low temperatures.

Anharmonic and Anomalous Trends in the High-Pressure Phase Diagram of Silicon

A multifaceted first-principles approach utilizing density functional theory, evolutionary algorithms, and lattice dynamics was used to construct the phase diagram of silicon up to 4 TPa and 26 000  K. These calculations predicted that (i) an anomalous sequence of face-centered cubic to body-centered cubic to simple cubic crystalline phase transitions occur at pressures of 2.87 and 3.89 TPa, respectively, along the cold curve, (ii) the orthorhombic phases of Imma and Cmce-16 appear on the phase diagram only when the anharmonic contribution to the Gibbs free energy is taken into account, and (iii) a substantial change in the slope of the principal Hugoniot is observed if the anharmonic free energy of the cubic diamond phase is considered.

Predicted Pressure-Induced Superconducting Transition in Electride Li_{6}P

Electrides are unique compounds where most of the electrons reside at interstitial regions of the crystal behaving as anions, which strongly determines its physical properties. Interestingly, the magnitude and distribution of interstitial electrons can be effectively modified either by modulating its chemical composition or external conditions (e.g., pressure). Most of the electrides under high pressure are nonmetallic, and superconducting electrides are very rare. Here we report that a pressure-induced stable Li_{6}P electride, identified by first-principles swarm structure calculations, becomes a superconductor with a predicted superconducting transition temperature T_{c} of 39.3 K, which is the highest among the already known electrides. The interstitial electrons in Li_{6}P, with dumbbell-like connected electride states, play a dominant role in the superconducting transition. Other Li-rich phosphides, Li_{5}P, Li_{11}P_{2}, Li_{15}P_{2}, and Li_{8}P, are also predicted to be superconducting electrides, but with a lower T_{c}. Superconductivity in all these compounds can be attributed to a combination of a weak electronegativity of phosphorus (P) with a strong electropositivity of lithium (Li), and opens up the interest to explore high-temperature superconductivity in similar binary compounds.

Distortions in the cubic primitive high-pressure phases of calcium

The superconductivity in highly compressed calcium involves the occurrence of closely related low-symmetry structural patterns with an exceptionally low coordination number. Earlier theoretical and experimental results are controversial and some findings are inconsistent with our later observations in the pressure range up to 60 GPa. This situation motivated the present concerted computational and experimental re-investigation of the structural arrangement of calcium slightly above the high-pressure limit of the bcc arrangement at low-temperatures. We report here reproducible experimental evidence for a monoclinic distortion (mC4, space group C2/c) of the calcium polymorph previously assigned to the tetragonal β-Sn structure type. In accordance, the enthalpies calculated by electronic band structure calculations show the mC4 phase to be more stable than the undistorted β-Sn type by about 100 meV in the entire phase space. The other low-temperature phase of calcium adopts space group Cmcm (oC4) rather than the earlier assigned Cmmm symmetry. These structural alterations substantially effect the density of states at the Fermi level and, thus, the electronic properties.

Structural search for stable Mg–Ca alloys accelerated with a neural network interatomic model

We have combined a neural network formalism with metaheuristic structural global search algorithms to systematically screen the Mg–Ca binary system for new (meta)stable alloys.

New phases of 3d-transition metal–cerium binary compounds: an extensive structural search

The phase stabilities, structural features, electronic and mechanical properties of 3d transitional metal–cerium binary compounds were systematically studied.

Pressure-Induced Structural and Electronic Transition in Sr2ZnWO6 Double Perovskite

High-pressure structural and electrical properties of Sr2ZnWO6 double perovskite were investigated using in situ angle-dispersive synchrotron X-ray diffraction (XRD), Raman, and alternating current (AC) impedance spectroscopy. A structural transition from monoclinic (P21/n) to triclinic (P1̅) phase around 9 GPa was observed due to the pressure-induced distortion of (W, Zn)O6 octahedron. In situ high-pressure Raman spectroscopy showed the increasing interaction among O-W-O in WO6 octahedron with pressure and a transition pressure consistent with the XRD results. From the AC impedance spectroscopy measurements, the resistivity increased steeply by ∼1 order of magnitude around 11 GPa, indicating an electronic transition accompanying the symmetry change. The increase in the interaction among O-W-O enhances the attraction of O(2-) electrons toward W(6+), thus increasing the covalence, which in turn lowers the charge transfer energy between O(2-) and W(6+) and induces the resistivity increase under high pressure.

Computational analysis of stable hard structures in the Ti-B system

The lowest energy crystalline structures of various stoichiometric titanium boride (Ti-B) intermetallic compounds are sought based on density functional theory combined with the particle-swarm optimization (PSO) technique. Besides three established experimental structures, i.e., FeB-type TiB, AlB2-type, and Ta3B4-type Ti3B4, we predict additional six metastable phases at these stoichiometric ratios, namely, α- and β-phases for TiB, TiB2, and Ti3B4, respectively. Moreover, we predict the most stable crystalline structures of four new titanium boride compounds with different stoichiometric ratios: Ti2B-PSA, Ti2B3-PSB, TiB3-PSC, and TiB4-PSD. Notably, Ti2B-PSA is shown to have lower formation energy (thus higher stability) than the previously proposed Al2Cu-type Ti2B. The computed convex-hull and phonon dispersion relations confirm that all the newly predicted Ti-B intermetallic crystals are thermodynamically and dynamically stable. Remarkably, the predicted α-TiB2 and β-TiB2 show semi-metal-like electronic properties and possess high Vickers hardnesses (39.4 and 39.6 GPa), very close to the lower limit of superhard materials (40 GPa). Analyses of band structure, density of states, electronic localization function, and various elastic moduli provide further understanding of the electronic and mechanical properties of the intermetallic titanium borides. We hope the newly predicted hard intermetallic titanium borides coupled with desirable electronic properties and high elastic modulus will motivate future experimental synthesis for applications such as high-temperature structural materials.

Investigation of exotic stable calcium carbides using theory and experiment

It is well known that pressure causes profound changes in the properties of atoms and chemical bonding, leading to the formation of many unusual materials. Here we systematically explore all stable calcium carbides at pressures from ambient to 100 GPa using variable-composition evolutionary structure predictions using the USPEX code. We find that Ca₅C₂, Ca₂C, Ca₃C₂, CaC, Ca₂C₃ and CaC₂ have stability fields on the phase diagram. Among these, Ca₂C and Ca₂C₃ are successfully synthesized for the first time via high-pressure experiments with excellent structural correspondence to theoretical predictions. Of particular significance is the base-centred monoclinic phase (space group C2/m) of Ca₂C, a quasi-two-dimensional metal with layers of negatively charged calcium atoms, and the primitive monoclinic phase (space group P2₁/c) of CaC with zigzag C₄ groups. Interestingly, strong interstitial charge localization is found in the structure of R-3m-Ca₅C₂ with semi-metallic behaviour.

Pressure causes profound changes in the properties of atoms and chemical bonding leading to unusual materials. Here, the authors investigate the Ca-C system and find that it becomes increasingly complex and develops a multitude of phases with various compositions and new structures at higher pressures.

Metallic icosahedron phase of sodium at terapascal pressures

Alkali metals exhibit unexpected structures and electronic behavior at high pressures. Compression of metallic sodium (Na) to 200 GPa leads to the stability of a wide-band-gap insulator with the double hexagonal hP4 structure. Post-hP4 structures remain unexplored, but they are important for addressing the question of the pressure at which Na reverts to a metal. Here, we report the reentrant metallicity of Na at the very high pressure of 15.5 terapascal (TPa), predicted using first-principles structure searching simulations. Na is therefore insulating over the large pressure range of 0.2-15.5 TPa. Unusually, Na adopts an oP8 structure at pressures of 117-125 GPa and the same oP8 structure at 1.75-15.5 TPa. The metallization of Na occurs on the formation of a stable and striking body-centered cubic cI24 electride structure consisting of Na_{12} icosahedra, each housing at its center about one electron that is not associated with any Na ions.

Stable compositions and structures in the Na–Bi system

Predicted phase diversity and interesting properties of the Na–Bi system in the range of 0–320 GPa from first-principles calculations.

The search for the most stable structures of silicon-carbon monolayer compounds

The most stable structures of two-dimensional (2D) silicon-carbon monolayer compounds with different stoichiometric compositions (i.e., Si : C ratio = 2 : 3, 1 : 3 and 1 : 4) are predicted for the first time based on the particle-swarm optimization (PSO) technique combined with density functional theory optimization. Although the 2D Si-C monolayer compounds considered here are rich in carbon, many of the low-energy metastable and the lowest-energy silicon-carbon structures are not graphene (carbon monolayer) like. Phonon-spectrum calculations and ab initio molecular dynamics simulations were also performed to confirm the dynamical stability of the predicted most stable 2D silicon-carbon structures as well their thermal stability at elevated temperature. The computed electronic band structures show that all three predicted silicon-carbon compounds are semiconductors with direct or indirect bandgaps. Importantly, their bandgaps are predicted to be close to those of bulk silicon or bulk germanium. If confirmed in the laboratory, these 2D silicon-carbon compounds with different stoichiometric compositions may be exploited for future applications in nanoelectronic devices.

Novel superconducting skutterudite-type phosphorus nitride at high pressure from first-principles calculations

State of the art variable composition structure prediction based on density functional theory demonstrates that two new stoichiometries of PN, PN3 and PN2, become viable at high pressure. PN3 has a skutterudite-like Immm structure and is metastable with positive phonon frequencies at pressures between 10 and 100 GPa. PN3 is metallic and is the first reported nitrogen-based skutterudite. Its metallicity arises from nitrogen p-states which delocalise across N4 rings characteristic of skutterudites, and it becomes a good electron-phonon superconductor at 10 GPa, with a Tc of around 18 K. The superconductivity arises from strongly enhanced electron-phonon coupling at lower pressures, originating primarily from soft collective P-N phonon modes. The PN2 phase is an insulator with P2/m symmetry and is stable at pressures in excess of 200 GPa.

Structures of the elements - crystallography and art

Since simple data tables on phase transitions and structural systematics of the elements over a wide range of pressure and temperature are difficult to comprehend, this paper illustrates these systematics with some artwork together with an artist's view of the equations of states for the elements.

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.

Pressure-induced pseudoatom bonding collapse and isosymmetric phase transition in Zr2Cu: first-principles predictions

The structural evolution of tetragonal Zr2Cu has been investigated under high pressures up to 70 GPa by means of density functional theory. Our calculations predict a pressure-induced isosymmetric transition where the tetragonal symmetry (I4/mmm) is retained during the entire compression as well as decompression process while its axial ratio (c/a) undergoes a transition from ~3.5 to ~4.2 at around 35 GPa with a hysteresis width of about 4 GPa accompanied by an obvious volume collapse of 1.8% and anomalous elastic properties such as weak mechanical stability, dramatically high elastic anisotropy, and low Young's modulus. Crystallographically, the tetragonal axial ratio shift renders this transition analogous to a simple bcc-to-fcc structural transition, which implies it might be densification-driven. Electronically, the ambient Zr2Cu is uncovered with an intriguing pseudo BaFe2As2-type structure, which upon the phase transition undergoes an electron density topological change and collapses to an atomic-sandwich-like structure. The pseudo BaFe2As2-type structure is demonstrated to be shaped by hybridized dxz + yz electronic states below Fermi level, while the high pressure straight Zr-Zr bonding is accommodated by electronic states near Fermi level with dx(2) - y(2) dominant features.

Formation of Nanofoam carbon and re-emergence of Superconductivity in compressed CaC6

Pressure can tune material's electronic properties and control its quantum state, making some systems present disconnected superconducting region as observed in iron chalcogenides and heavy fermion CeCu2Si2. For CaC6 superconductor (Tc of 11.5 K), applying pressure first Tc increases and then suppresses and the superconductivity of this compound is eventually disappeared at about 18 GPa. Here, we report a theoretical finding of the re-emergence of superconductivity in heavily compressed CaC6. The predicted phase III (space group Pmmn) with formation of carbon nanofoam is found to be stable at wide pressure range with a Tc up to 14.7 K at 78 GPa. Diamond-like carbon structure is adhered to the phase IV (Cmcm) for compressed CaC6 after 126 GPa, which has bad metallic behavior, indicating again departure from superconductivity. Re-emerged superconductivity in compressed CaC6 paves a new way to design new-type superconductor by inserting metal into nanoporous host lattice.

Role of dynamical instability in the ab initio phase diagram of calcium

In the 32-119 GPa pressure range and at room temperature, a simple cubic phase was reported for calcium in many different experiments. Standard linear response theory, both within density functional perturbation theory and frozen phonon calculations, presents dynamical instabilities for the simple cubic structure in the whole pressure range. Many other possible candidate phases, as well as several possible stabilization mechanisms for the simple cubic phase, have been proposed as the result of ab initio predictions but the role of temperature on the relative stability of the different phases has not been systematically investigated. We revisit the stability of the three most important candidate phases of calcium for the intermediate pressure range and for various temperatures, taking explicitly into account thermal corrections relative to electronic as well as phononic entropy and anharmonic contributions. This corrects the discrepancies among previous theoretical results and experiments and presents a different picture of the temperature driven phase transition, which results from dynamical anharmonic stabilization of simple cubic and destabilization of the tetragonal phase.

Ca-VII: a chain ordered host-guest structure of calcium above 210 GPa

The recently discovered high pressure phase VII of calcium [M. Sakata et al., Phys. Rev. B 83, 220512(R) (2011)] has the highest superconducting transition temperature (T(c)) of 29 K among all the elements. Understanding the cause for such a high T(c) state is necessary to clarify its crystal structure. The structure of this phase was determined by an x-ray powder diffraction experiment and a density functional theory calculation and was not found to be the usual host-guest type but consisted of a 2×2 supercell in the tetragonal ab plane with a commensurate host-guest ratio of 4/3 along the c axis containing 128 atoms.

Predicted suppression of the superconducting transition of new high-pressure yttrium phases with increasing pressure from first-principles calculations

Structure searches for new high-pressure phases of Y metal have been performed by using evolutionary algorithms in conjunction with a first-principles, pseudopotential plane-wave method based on density functional theory. The oF16-Fddd and hP3-P3(1)21 phases are predicted to be energetically favorable at pressures over 97 GPa. These two phases are shown to be dynamically stable by computing their phonon dispersions. We thus propose that oF16-Fddd and hP3-P3(1)21 are the most probable crystal structures Y may take in the 97-206 GPa range. The superconducting critical temperatures (T(c)) of the new phases are estimated using the Allen-Dynes formula. The T(c) is predicted to decrease with increasing pressure over about 100 GPa, in sharp contrast to its observed monotonic increase under lower pressure. The electronic origins of the stabilities of the proposed high-pressure phases have also been investigated.

Calcium with the β-tin structure at high pressure and low temperature

Using synchrotron high-pressure X-ray diffraction at cryogenic temperatures, we have established the phase diagram for calcium up to 110 GPa and 5-300 K. We discovered the long-sought for theoretically predicted β-tin structured calcium with I4(1)/amd symmetry at 35 GPa in a s mall low-temperature range below 10 K, thus resolving the enigma of absence of this lowest enthalpy phase. The stability and relations among various distorted simple-cubic phases in the Ca-III region have also been examined and clarified over a wide range of high pressures and low temperatures.

Pressure-induced amorphous-to-amorphous configuration change in Ca-Al metallic glasses

Pressure-induced amorphous-to-amorphous configuration changes in Ca-Al metallic glasses (MGs) were studied by performing in-situ room-temperature high-pressure x-ray diffraction up to about 40 GPa. Changes in compressibility at about 18 GPa, 15.5 GPa and 7.5 GPa during compression are detected in Ca₈₀Al₂₀, Ca_72.7Al_27.3, and Ca_66.4Al_33.6 MGs, respectively, whereas no clear change has been detected in the Ca₅₀Al₅₀ MG. The transfer of s electrons into d orbitals under pressure, reported for the pressure-induced phase transformations in pure polycrystalline Ca, is suggested to explain the observation of an amorphous-to-amorphous configuration change in this Ca-Al MG system. Results presented here show that the pressure induced amorphous-to-amorphous configuration is not limited to f electron-containing MGs.

Large amplitude fluxional behaviour of elemental calcium under high pressure

Experimental evidences are presented showing unusually large and highly anisotropic vibrations in the “simple cubic” (SC) unit cell adopted by calcium over a broad pressure ranging from 30–90 GPa and at temperature as low as 40 K. X-ray diffraction patterns show a preferential broadening of the (110) Bragg reflection indicating that the atomic displacements are not isotropic but restricted to the [110] plane. The unusual observation can be rationalized invoking a simple chemical perspective. As the result of pressure-induced s → d transition, Ca atoms situated in the octahedral environment of the simple cubic structure are subjected to Jahn-Teller distortions. First-principles molecular dynamics calculations confirm this suggestion and show that the distortion is of dynamical nature as the cubic unit cell undergoes large amplitude tetragonal fluctuations. The present results show that, even under extreme compression, the atomic configuration is highly fluxional as it constantly changes.

Anharmonic stabilization of the high-pressure simple cubic phase of calcium

The phonon spectrum of the high-pressure simple cubic phase of calcium, in the harmonic approximation, shows imaginary branches that make it mechanically unstable. In this Letter, the phonon spectrum is recalculated by using density-functional theory ab initio methods fully including anharmonic effects up to fourth order at 50 GPa. Considering that the perturbation theory cannot be employed with imaginary harmonic frequencies, a variational procedure based on the Gibbs-Bogoliubov inequality is used to estimate the renormalized phonon frequencies. The results show that strong quantum anharmonic effects make the imaginary phonons become positive even at zero temperature so that the simple cubic phase becomes mechanically stable, as experiments suggest. Moreover, our calculations find a superconducting T(c) in agreement with experiments and predict an anomalous behavior of the specific heat.

How evolutionary crystal structure prediction works--and why

Once the crystal structure of a chemical substance is known, many properties can be predicted reliably and routinely. Therefore if researchers could predict the crystal structure of a material before it is synthesized, they could significantly accelerate the discovery of new materials. In addition, the ability to predict crystal structures at arbitrary conditions of pressure and temperature is invaluable for the study of matter at extreme conditions, where experiments are difficult. Crystal structure prediction (CSP), the problem of finding the most stable arrangement of atoms given only the chemical composition, has long remained a major unsolved scientific problem. Two problems are entangled here: search, the efficient exploration of the multidimensional energy landscape, and ranking, the correct calculation of relative energies. For organic crystals, which contain a few molecules in the unit cell, search can be quite simple as long as a researcher does not need to include many possible isomers or conformations of the molecules; therefore ranking becomes the main challenge. For inorganic crystals, quantum mechanical methods often provide correct relative energies, making search the most critical problem. Recent developments provide useful practical methods for solving the search problem to a considerable extent. One can use simulated annealing, metadynamics, random sampling, basin hopping, minima hopping, and data mining. Genetic algorithms have been applied to crystals since 1995, but with limited success, which necessitated the development of a very different evolutionary algorithm. This Account reviews CSP using one of the major techniques, the hybrid evolutionary algorithm USPEX (Universal Structure Predictor: Evolutionary Xtallography). Using recent developments in the theory of energy landscapes, we unravel the reasons evolutionary techniques work for CSP and point out their limitations. We demonstrate that the energy landscapes of chemical systems have an overall shape and explore their intrinsic dimensionalities. Because of the inverse relationships between order and energy and between the dimensionality and diversity of an ensemble of crystal structures, the chances that a random search will find the ground state decrease exponentially with increasing system size. A well-designed evolutionary algorithm allows for much greater computational efficiency. We illustrate the power of evolutionary CSP through applications that examine matter at high pressure, where new, unexpected phenomena take place. Evolutionary CSP has allowed researchers to make unexpected discoveries such as a transparent phase of sodium, a partially ionic form of boron, complex superconducting forms of calcium, a novel superhard allotrope of carbon, polymeric modifications of nitrogen, and a new class of compounds, perhydrides. These methods have also led to the discovery of novel hydride superconductors including the "impossible" LiH(n) (n=2, 6, 8) compounds, and CaLi(2). We discuss extensions of the method to molecular crystals, systems of variable composition, and the targeted optimization of specific physical properties.

High-pressure phases of calcium: density-functional theory and diffusion quantum Monte Carlo approach

The phase diagram of Ca is examined using a combination of density-functional theory (DFT) and diffusion quantum Monte Carlo (DMC) calculations. Gibbs free energies of several competing structures are computed at pressures near 50 GPa. Existing disagreements for the stability of Ca both at low and room temperature are resolved with input from DMC. Furthermore, DMC calculations are performed on 0 K crystalline structures up to 150 GPa and it is demonstrated that the widely used generalized gradient approximation of DFT is insufficient to accurately account for the relative stability of the high-pressure phases of Ca. The results indicate that the theoretical phase diagram of Ca needs a revision.