Prediction of incommensurate crystal structure in Ca at high pressure

Abstract

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...

Exotic behavior and crystal structures of calcium under pressure

“…5). This result is similar to that recently reported by Arapan et al (36), who found this structure by educated guess based on a possible analogy with Sr. Such Fig. 2.…”

Competing phases, strong electron-phonon interaction, and superconductivity in elemental calcium under high pressure

“…At low pressure, our result is apparently different from the result by Arapan, Mao, and Ahuja. 26 In their results, sc Ca has the lowest enthalpy from 40 GPa to 77 GPa, lower than the P4 3 2 1 2 and Cmca structures. A possible reason is that the authors might not have taken into account the change in shape and internal coordinates of the Cmca structure in the 70-80 GPa pressure range.…”

“…Actually several other structures including Pnma, Cmca and P4 3 2 1 2 were proposed for the high pressure Ca-IV and Ca-V phases. 23,24,25,26 Their structural details are listed in Table I and their structures are pictured in reference [23,24,25]. I43m is a body-centered cubic structure, Pnma and Cmca Ca are orthorhombic, and P4 3 2 1 2 has a tetragonal symmetry.…”

“…So far the higher pressure phases Ca-IV and Ca-V have attracted the most attention, and considerable progress has been made in identifying these phases through a combination of experimental 9,22,23 and theoretical 24,25,26 work. However, satisfactory agreement between experimental and theoretical work is still lacking.…”

Structural and electronic properties of the alkali metal incommensurate phases

“…Previous computational studies have usually relied on the smallest possible commensurate approximants, although examples exist, for elementary and compound incommensurates, where the role of different host-guest ratios has been explored [35][36][37][38][39].…”