Exotic behavior and crystal structures of calcium under pressure

Abstract

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 (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.evolutionary algorithms | high pressure | structure prediction | density functional theory | superconductivity C alcium exhibits a nontrivial and somewhat mysterious behavior under pressure. At 19.5 GPa it transforms from the fcc to the body-centered cubic (bcc) structure, and then, at 32 GPa, to the simple cubic (sc) structure (1, 2). Such a sequence of transitions is exactly opposite to normal intuition, as it is accompanied by a decrease of coordination numbers (12 → 8 → 6) and sphere packing efficiency (0.74 → 0.68 → 0.52). Good metal at ambient conditions, fcc-Ca shows increasing electrical resistivity under pressure (3-5). Even more intriguingly, the resistivity of the fcc phase at and just below this maximum has negative temperature derivative, characteristic of the nonmetallic (semiconducting) state, consistent with a small band gap found in ab initio calculations (6) in the same pressure range. Such demetallization under pressure is counterintuitive, because at sufficiently high pressure all materials must become free-electron metals, the expected behavior is an increasing tendency to the free-electron limit under pressure (see ref. 7 for a discussion). Contrary to these expectations, strong departure from the free-electron state under pressure has also been found for sodium (8, 9) and lithium (10-12) at megabar pressures.Ab initio calculations (13) confirmed the fcc → bcc → sc structure sequence and yielded reasonably accurate values for the transition pressures. However, the sc phase encounters problems: It cannot be explained within the Hume-Rothery approach (Fermi surface-Brillouin zone interaction) unless one assumes 4 valence electrons per atom (14), and, even more seriously, lattice dynamics calculations (15, 16) showed that it is dynamically unstable, and although this dynamical instability may be lifted by anharmonic effects (16), other structures (see below) have much lower enthalpies. This seeming contradiction with experiments that initially showed a perfect sc structure (1, 2, 17) is largely resolved by re...

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

“…To overcome this discrepancy, Teweldeberhan et al (16) used diffusion quantum Monte Carlo calculations, Errea et al (18) used ab initio methods including anharmonic effects to stabilize the sc phase at room temperature, and Yao et al (17) provided a detailed analysis of ab initio molecular dynamics simulations that could account for the stability of the sc structure at room temperature. The remaining major discrepancy is that Yao et al (14) and Oganov et al (13) predicted that Ca with I4 1 ∕amd symmetry (β-tin structure) has a much lower zero-temperature enthalpy than sc, but in spite of many experimental efforts, the presumably more stable β-tin structured Ca has never been discovered. Here we report the search and discovery of the β-tin structured Ca and establish its stability range.…”

“…Very recently, Tse et al (22) also conducted low-temperature experiments to study the Ca sc phase; their results showed a large and anisotropic vibrations in sc Ca unit cell over a large pressure range at low temperatures. However, although the enthalpy of predicted β-tin structure Ca at 40 GPa is about 50 meV more favorable than sc structure (13,16,23), there have been no experimental observations of the predicted I4 1 ∕amd phase until now. To further investigate the stability of the Ca sc phase and to search for the possible I4 1 ∕amd tetragonal phase, we performed synchrotron X-ray diffraction (XRD) experiments on Ca through various low-temperature, high-pressure paths.…”

“…The structures of the Cmmm (orthorhombic) and I4 1 ∕amd (tetragonal) phases can both be viewed as a distortion of the sc structure (9,13,14), and they were all observed by exploring the low-temperature areas. Our results indicate that the I4 1 ∕amd and Cmmm structures of Ca only exist in a very small pressure range just above the transition pressure from bcc to sc phase at room temperature.…”

“…The pressure-induced electronic transition from a normal metal to a superconductor occurs in the Ca-III phase region above 44 GPa (10,11), and the T c increases with pressure from 2 K to 10 K within the Ca-III region (6). Ca-III is also a very active test case of modern theories and experiments, where a number of paradoxes arise (12)(13)(14)(15)(16)(17)(18). Based on density-functional theory (DFT) calculations, Ca-III with sc structure has imaginary phonon frequencies, indicating dynamic instability (19)(20)(21).…”

Existence of the β-tin structure in Sr: First evidence from computational approach

“…In brief, sX-LDA functional treats d electron differently compared to other functionals, 22,36,[42][43][44][45] PBE and LDA, see Fig. 4.…”