Structure stability in the simple element sodium under pressure

Abstract

The simple alkali metal Na, that crystallizes in a body-centred cubic structure at ambient pressure, exhibits a wealth of complex phases at extreme conditions as found by experimental studies. The analysis of the mechanism of stabilization of some of these phases, namely, the low-temperature Sm-type phase and the high-pressure cI16 and oP8 phases, shows that they satisfy the criteria for the Hume-Rothery mechanism. These phases appear to be stabilized due to a formation of numerous planes in a Brillouin-Jones zone in the vicinity of the Fermi sphere of Na, which leads to the reduction of the overall electronic energy. For the oP8 phase, this mechanism seems to be working if one assumes that Na becomes divalent metal at this density. The oP8 phase of Na is analysed in comparison with the MnP-type oP8 phases known in binary compounds, as well as in relation to the hP4 structure of the NiAs-type.

Simple metal and binary alloy phases based on the hcp structure: Electronic origin of distortions and superlattices

“…This core ionization will lead to increasing the valence electron count to four as in the case of group-IV elements with the hcp structure. The valence band -core level overleap was considered previously for Na in the high pressure oP8 structure [11]. Valence electron count equal to four is suggested for alkali metals K, Rb and Cs in the high pressure structure oC16-Cmca which is similar to that in four-valent metals Si and Ge [44].…”

“…That leads to additional electron energy gaining and should be considered as origin of superlattice formation. The regular 12-sided polygon is formed by BZ planes if the superlattice period is defined by 3 / tan15 o (=6.4641), as was estimated by consideration of the incommensurate superstructure Au 11 In 3 based on the hcp structure [47,48]. This phase corresponds to the electron concentration value z = 1.43 giving k F accommodating well the 12-sided polygon (dodecagon) with small exceed of k F above the corner of polygon (at ~1.04) satisfying the Hume-Rothery rule.…”

Simple Metal and Binary Alloy Phases Based on the <em>fcc</em> Structure: Electronic Origin of Distortions, Superlattices and Vacancies

“…Jones model can be used to account for the phase stability in tetrahedral cluster structures, icosahedral and trigonal-prismatic clusters as building blocks. Formation of the complex structures of elemental metals under pressure can also be related to the Hume-Rothery mechanism [12][13][14][15][16][17].…”

Double-diamond NaAl via pressure: Understanding structure through Jones zone activation

“…As noted in several recent articles, 14,15 x-ray diffraction patterns are often useful in revealing the strengths of lattice potentials. Ackland and Macleod 14 and Degtyareva, 15,16 in particular, have productively explored this association. X-ray diffraction intensity is proportional to the square of the Fourier transform of the electron density, which for most elements resides largely within the cores.…”

“…In particular, it has been pointed out, notably by Ackland and Macleod 14 and by Degtyareva,15,16 that the Jones 17 and later Mott and Jones 18 stability arguments often play a critical role in determining structures in novel metallic phases under high pressure. 7 The essence of this reasoning resides in an argument that the contact of bands with Brillouin zone ͑BZ͒ planes, associated with crystal ͑pseudo͒po-tentials V K ͑generally local͒, and states near the Fermi level can be a key stabilizing factor.…”