Theoretical confirmation of the high pressure simple cubic phase in calcium

Compressed Sr superconducting transition temperature up to 17.65 K

Due to the simplicity of their composition, the study of the superconducting properties of elemental substances holds significant importance for understanding the mechanisms of high-temperature superconductivity. This work involves simulated calculations to investigate the phase transition sequence and superconducting properties of Sr under pressure. The stability range of the Sr-IV phase C2/c was redefined, determining that it can extend up to 150 GPa, and the phase transition sequence of Sr under high pressure was studied. It was discovered that the d-electrons in the Sr-IV phase significantly contribute to the Fermi surface, a phenomenon closely related to the Van Hove singularity (VHS) near the saddle points. The increase in Tc of Sr under pressure is attributed to phonon softening and strong coupling resulting from the gradual overlap of VHS with the Fermi level, which is associated with the incomplete saturation of s-d electron transfer. Ultimately, the Tc of Sr reaches 17.65 K at 150 GPa, with a λ value of 1.26. This strong EPC is contributed by the interaction between d-electrons and medium-high-frequency phonons. This study extends new pathways for investigating the superconductivity of high-pressure phases of Sr and provides new insights for the theoretical study of elemental superconductors.

Structural Transformation and Melting in Gold Shock Compressed to 355 GPa

Gold is believed to retain its ambient crystal structure at very high pressures under static and shock compression, enabling its wide use as a pressure marker. Our in situ x-ray diffraction measurements on shock-compressed gold show that it transforms to the body-centered-cubic (bcc) phase, with an onset pressure between 150 and 176 GPa. A liquid-bcc coexistence was observed between 220 and 302 GPa and complete melting occurs by 355 GPa. Our observation of the lower coordination bcc structure in shocked gold is in marked contrast to theoretical predictions and the reported observation of the hexagonal-close-packed structure under static compression.

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.

A high pressure Ca-VI phase between 158 and 180 GPa: stability, electronic structure and superconductivity

We have performed ab initio calculations for a new high pressure phase of Ca-VI between 158 and 180 GPa. The study includes elastic parameters of monocrystalline and polycrystalline aggregates, electronic band structure, lattice dynamics and superconductivity. The calculations show that the orthorhombic Pnma structure is mechanically and dynamically stable in the pressure range studied. The structure is superconducting over the entire pressure range and the calculated T(c) (24.7 K with μ* = 0.1) is maximum at 172 GPa, which is close to the experimentally observed value of 25 K at 161 GPa.

Distortions and stabilization of simple-cubic calcium at high pressure and low temperature

Ca-III, the first superconducting calcium phase under pressure, was identified as simple-cubic (sc) by previous X-ray diffraction (XRD) experiments. In contrast, all previous theoretical calculations showed that sc had a higher enthalpy than many proposed structures and had an imaginary (unstable) phonon branch. By using our newly developed submicrometer high-pressure single-crystal XRD, cryogenic high-pressure XRD, and theoretical calculations, we demonstrate that Ca-III is neither exactly sc nor any of the lower-enthalpy phases, but sustains the sc-like, primitive unit by a rhombohedral distortion at 300 K and a monoclinic distortion below 30 K. This surprising discovery reveals a scenario that the high-pressure structure of calcium does not go to the zero-temperature global enthalpy minimum but is dictated by high-temperature anharmonicity and low-temperature metastability fine-tuned with phonon stability at the local minimum.

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 beta-tin (I4(1)/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.

Phases of Ca from first principles

Structures and properties of many of the phases of Ca under pressure are calculated from first principles by a systematic procedure that minimizes total energy E with respect to structure under the constraint of constant volume V. The minima of E are followed on successive sweeps of lattice parameters for 11 of 14 Bravais symmetries for one-atom-per-cell structures. The structures include the four orthorhombic phases. Also included are the hexagonal close-packed and cubic diamond phases with two atoms per primitive cell. No uniquely orthorhombic phases are found; all one-atom orthorhombic phases over a mega-bar pressure range are identical to higher-symmetry phases. The simple cubic phase is shown to be stable where it is the ground state. The number of distinct one-atom phases reduces to five plus the two two-atom phases. For each of these phases the Gibbs free energy at pressure p, G(p), is calculated for a non-vibrating lattice; the functions G(p) give the ground state at each p, the relative stabilities of all phases and the thermodynamic phase transition pressures for all phase transitions over a several-megabar range.

Metallic high-pressure modifications of main group elements

The high-pressure structural chemistry of main group elements in the metallic state is reviewed under consideration of more recent determinations of atomic arrangements with to some extend unexpected complexity. Following the concept of the pressure-coordination rule, the number of nearest neighbours is employed as a guiding quantity to reveal systematic trends. Violations of the rule will be mainly discussed in the light of electronic ground state changes upon compression.

Structural prediction and phase transformation mechanisms in calcium at high pressure

High-pressure phase transformations of Ca are studied using the metadynamics method to explore the anharmonic free-energy surface, together with a genetic algorithm structural search method to identify lowest enthalpy structures. Disagreement between theory and experiment regarding the structure of Ca in the pressure range 32-119 GPa is partially resolved by the demonstration of different phase transition behavior at 300 K from that at low temperatures. A new lowest enthalpy I4(1)/amd structure is obtained with both methods with an estimated superconducting critical temperature in agreement with experiment.

Prediction of incommensurate crystal structure in Ca at high pressure

Ca shows an interesting high-pressure phase transformation sequence, but, despite similar physical properties at high pressure and affinity in the electronic structure with its neighbors in the periodic table, no complex phase has been identified for Ca so far. We predict an incommensurate high-pressure phase of Ca from first principle calculations and describe a procedure of estimating incommensurate structure parameters by means of electronic structure calculations for periodic crystals. Thus, by using the ab initio technique for periodic structures, one can get not only reliable information about the electronic structure and structural parameters of an incommensurate phase, but also identify and predict such phases in new elements.

Self-assembly of the simple cubic lattice with an isotropic potential

Conventional wisdom presumes that low-coordinated crystal ground states require directional interactions. Using our recently introduced optimization procedure to achieve self-assembly of targeted structures [M. C. Rechtsman, Phys. Rev. Lett. 95, 228301 (2005); Phys. Rev. E 73, 011406 (2006)], we present an isotropic pair potential V(r) for a three-dimensional many-particle system whose classical ground state is the low-coordinated simple cubic lattice. This result is part of an ongoing pursuit by the authors to develop analytical and computational tools to solve statistical-mechanical inverse problems for the purpose of achieving targeted self-assembly. The purpose of these methods is to design interparticle interactions that cause self-assembly of technologically important target structures for applications in photonics, catalysis, separation, sensors, and electronics. We also show that standard approximate integral-equation theories of the liquid state that utilize pair correlation function information cannot be used in the reverse mode to predict the correct simple cubic potential. We report in passing optimized isotropic potentials that yield the body-centered-cubic and simple hexagonal lattices, which provide other examples of non-close-packed structures that can be assembled using isotropic pair interactions.

Comparative study of the high-pressure behavior of As, Sb, and Bi

The high-pressure behavior of the heavier group 15 elements As, Sb, and Bi was investigated by means of ab initio density functional calculations employing pseudopotentials and a plane wave basis set. The high-pressure structural sequence of these elements is distinguished by the occurrence of the Bi-III structure, which is a complex, incommensurately modulated, host-guest structure. We approximated this structure by a supercell which reproduced the experimentally established pressure stability ranges of the host-guest structure for the different elements extremely well. With pressure we find an increasing admixture of d states (s-d hybridization) in the occupied levels of the electronic structure of As, Sb, and Bi. However, the s-d mixing remains at a low level. Thus, the emergence of a complex intermediate pressure structure cannot be explained by a pressure-induced altered valence state for these elements. Instead, it is argued that the Bi-III structure is a consequence of a delicate interplay between the electrostatic and the band energy contribution to the total energy. In the intermediate pressure range of heavier group 15 elements, both important parts of the total energy account equally for structural stability.

Gallium and indium under high pressure

Ga and In crystallize in unusual open ground-state crystal structures. Recent experiments have discovered that Ga under high pressure transforms into a close-packed structure, while this has so far not been observed for In. Results from first principles calculations explain in a simple way this difference in behavior. We predict a so far undiscovered transition of In to a close-packed structure at extreme pressures and show that the structure determining mechanism originates from the degree of s-p mixing of the valence orbitals. Group-III elements are shown to strongly disobey the standard corresponding-state rule.