Theoretical study of the structure of calcium in phases IV and V via<i>ab initio</i>metadynamics simulation

Ishikawa, Takahiro; Ichikawa, Ayako; Nagara, Hitose; Geshi, Masaaki; Kusakabe, Kouichi; Suzuki, N.

doi:10.1103/physrevb.77.020101

Cited by 33 publications

(14 citation statements)

References 16 publications

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“…We reproduced also the results of Ishikawa et al (18). At the pressure of 77 GPa the cP1 structure undergoes a transition to Ca-IV with a volume collapse of 3.5%, which in turn transforms Ͼ115 GPa into Ca-V phase with a volume collapse of 1%.…”

Section: Resultssupporting

confidence: 85%

Prediction of incommensurate crystal structure in Ca at high pressure

Arapan

Mao

Ahuja

2008

Proc. Natl. Acad. Sci. U.S.A.

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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.ab initio calculations ͉ alkali metals T he continuous improvement of the high-pressure technique and the advances in the methods of characterization of materials under high pressure have opened new perspectives for materials physics community. The discovery of a series of phases for periodic table elements within the explored interval of pressures (1, 2) have stimulated an increased interest from both experimentalists and theoreticians to understand the unexpected behavior of simple elements under high pressure. Within the alkali and earth-alkaline metals, a series of complex structures at high pressure have been identified and, in particular, the complex phases of Ba-IV (3), Sr-V (4), Rb-IV (5), and K-III (6) have been determined as composite host-guest structures, which are incommensurate along the common axis of host and guest sub-lattices. The occurrence of such complex composite structures in a large number of elements and the robustness of these complex phases over a wide range of pressures and temperatures make the existence of composite incommensurate structures an intrinsic high-pressure phenomenon. Therefore, other elements may undergo similar high-pressure phase transitions. The nature of the transition to a composite structure is not completely understood yet, partly, because such an essential theoretical tool for describing the condensed matter as electronic structure calculations cannot be directly applied to study an incommensurate structure. However, one can perform first-principles calculations on commensurate analogues of an incommensurate phase and, indeed, such calculations can reproduce the phase transition sequence in close agreement with the experiment and provide reliable information about the electronic structure (7,8). Ab initio calculations of Ba-IV commensurate analogue (7) suggest that the transition from a closed, packed structure at low pressure to a more open, complex structure at high pressure might be because of the transfer of electrons from free-electron like s-bands to more directional d-bands. In the Ba-IV phase, the sd-hybridization occurs between the orbitals of two nonequivalent Ba atoms: guest atoms with a more d-like character and host atoms with a more s-like character. Therefore, from the electronic structure perspective, the composite s...

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Section: Resultssupporting

confidence: 85%

Prediction of incommensurate crystal structure in Ca at high pressure

Arapan

Mao

Ahuja

2008

Proc. Natl. Acad. Sci. U.S.A.

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“…In conclusion, whereas many structures, typically with larger unit cells of 4-8 atoms per cell, have been proposed (12)(13)(14)(15)17) to have lower zero-temperature enthalpies than sc, Ca remains in its simplest form with one atom per primitive unit cell. Given the rh to pm transition at low T, it is clear that at 300 K, anharmonic and entropic contributions play a significant role for the stabilization of the sc-like rh phase.…”

Section: Resultsmentioning

confidence: 99%

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

Mao

Wang

Ding

et al. 2010

Proc. Natl. Acad. Sci. U.S.A.

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“…Fig. 3 shows that in the pressure range 100-130 GPa there are several energetically extremely close structures, and the most stable structure at 89-116 GPa is the P4 3 2 1 2 − 8 structure proposed by Ishikawa et al (20), this structure also can be derived from sc by a large distortion and has recently been experimentally confirmed for Ca-IV phase (25). The Pnma-4 structure is the stable phase at higher pressures, 116-134 GPa, and is the last stable structure related to sc.…”

Section: Results Of Evolutionary Simulations: New Phases Of Calciummentioning

confidence: 99%

“…Whereas the sc phase is already superconducting, the most intriguing high Tc values are found in the stability fields of other phases; a recent x-ray diffraction study (2) found two further phases beyond sc-Ca-IV (stable at 113-139 GPa) and Ca-V (stable above 139 GPa). First structural models, proposed in (20), gave a structure possessing the P4 3 2 1 2 space group and 8 atoms in the unit cell (here denoted as P4 3 2 1 2-8) for Ca-IV and Cmca-8 for Ca-V. The P4 3 2 1 2-8 structure, proposed for Ca-IV, has indeed been confirmed experimentally (21).…”

mentioning

confidence: 82%

“…We also note that because Ca-IV is related to the sc structure, finding it with a neighborhood search method (metadynamics, starting from the sc structure, was used in ref. 20) is very efficient, whereas Ca-V would be more challenging to neighborhood algorithms and a fully global search based on evolutionary algorithms should be preferred.…”

Section: Results Of Evolutionary Simulations: New Phases Of Calciummentioning

confidence: 99%

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Exotic behavior and crystal structures of calcium under pressure

Oganov

Ma²,

Xu³

et al. 2010

Proc. Natl. Acad. Sci. U.S.A.

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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...

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Theoretical study of the structure of calcium in phases IV and V viaab initiometadynamics simulation

Cited by 33 publications

References 16 publications

Prediction of incommensurate crystal structure in Ca at high pressure

Prediction of incommensurate crystal structure in Ca at high pressure

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

Exotic behavior and crystal structures of calcium under pressure

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