Symmetry breaking and restoring under high pressure: the amazing behaviour of the "simple" alkali metals

Angilella, G. G. N.; Siringo, Fabio; Pucci, R.

doi:10.1140/epjb/e2003-00105-8

Cited by 13 publications

(13 citation statements)

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“…14) and the orthorhombic C-facecentered (oC8) structure of ␣-gallium (7). Theoretical studies have explored the possibility of the onset of superconductivity in the solid phases (15,16), and suggest the possible onset of a dimerized phase at pressures Ͼ200 GPa (13,17). Here we are concerned with the crystal structure of the cI16 phase.…”

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confidence: 99%

Structure of sodium above 100 GPa by single-crystal x-ray diffraction

McMahon

Gregoryanz

Lundegaard

et al. 2007

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

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At pressures above a megabar (100 GPa), sodium crystallizes in a number of complex crystal structures with unusually low melting temperatures, reaching as low as 300 K at 118 GPa. We have utilized this unique behavior at extreme pressures to grow a single crystal of sodium at 108 GPa, and have investigated the complex crystal structure at this pressure using high-intensity x-rays from the new Diamond synchrotron source, in combination with a pressure cell with wide angular apertures. We confirm that, at 108 GPa, sodium is isostructural with the cI16 phase of lithium, and we have refined the full crystal structure of this phase. The results demonstrate the extension of single-crystal structure refinement beyond 100 GPa and raise the prospect of successfully determining the structures of yet more complex phases reported in sodium and other elements at extreme pressures.alkali metals ͉ crystal structure ͉ high pressure A t ambient pressure the alkali metals are simple metals; i.e., they can be described as nearly-free-electron metals that are characterized by a weak interaction between their single valence electron and the atomic core (1, 2). At ambient conditions the alkali metals all crystallize in the close-packed body-centered cubic (bcc) structure. However, under sufficient compression, they undergo a series of structural phase transitions. At pressures ranging from 2.2 GPa in cesium to 65 GPa in sodium, they transform from the bcc to the face-centered-cubic ( fcc) structure (3-5). Further compression leads to the formation of a wide variety of lower-symmetry and often very complex crystal structures (6, 7), which range from distorted variants of the bcc structure in lithium and sodium (5,8,9) to an incommensurate composite or ''host-guest'' crystal structure in rubidium (10, 11). The discovery of a whole series of these symmetry-lowering transitions over the last decade-not only in the alkali metals, but also in various other elements (6, 7, 9)-had been unexpected because it often involves a reduction in coordination number, which is opposite to the usual trend for pressureinduced phase transitions. The experimental discoveries have been complemented by computational studies, but the physical mechanisms that lead to the formation of the complex phases are not yet fully understood, and their physical properties not yet known in detail.Because of the low x-ray scattering power and relatively high transition pressures of sodium, it is only recently that it has become possible to investigate its high-pressure behavior. A number of high-pressure phases have been identified above 100 GPa (ref. 12 and M. Hanfland, K. Syassen, N. E. Christensen, and D. L. Novikov, unpublished data-see ref. 5), and the melting line was discovered to be very unusual: it first rises close to 1,000 K at Ϸ30 GPa and then falls to room temperature (Ϸ300 K) at 118 GPa (12) (see Fig. 1). Previous x-ray diffraction studies have shown that, with increasing pressure at room temperature, sodium transforms first from the bcc phase to fcc at 65 GP...

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confidence: 99%

Structure of sodium above 100 GPa by single-crystal x-ray diffraction

McMahon

Gregoryanz

Lundegaard

et al. 2007

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

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“…In order to emphasize the role of the coupling-constant integration and to hint at an upcoming result [equation (12)], this can be written as…”

Section: Ijmentioning

confidence: 99%

“…But upon further inspection of this equation, one might wonder about the absence of coupling between the induced densities themselves. The part of this interaction that is linear in V a or V b is included in (12), but the part that is nonlinear in both V a and V b is not. It turns out that some of these contributions can also be expressed intuitively in terms of δρ a and δρ b .…”

Section: Corrections Specific To Interacting Systemsmentioning

confidence: 99%

“…We can directly generalize equation (12) to an N-body potential treating all terms linear in N − 1 particles exactly by writing…”

Section: Bmany-center Potentialsmentioning

confidence: 99%

“…A derivation of the dynamical quadratic response function can also be found in Pitarke et al 11 . With the advent of density functional theory (DFT) and modern computers, response theory has lost some of its quantitative appeal, but as noted it is still being used for a qualitative understanding of general trends in metals [11][12][13] . Dynamic compression experiments have achieved metallization of hydrogen at high temperature 14 , and there is an expectation that low-temperature metallization might also be achieved in the relatively near future 15 .…”

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confidence: 99%

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Nonlinear response theories and effective pair potentials

Gravel

Ashcroft

2007

Phys. Rev. B

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We present a general method based on nonlinear response theory to obtain effective interactions between ions in an interacting electron gas, which can also be applied to other systems where an adiabatic separation of time scales is possible. Nonlinear contributions to the interatomic potential are expressed in terms of physically meaningful quantities, giving insight into the physical properties of the system. The method is applied to various test cases and is found to improve the standard linear and quadratic response approaches. It also reduces the discrepancies previously observed between perturbation theory and density functional theory results for proton-proton pair potentials in metallic environments.

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Symmetries and Physics

Pucci

2017

Correlations in Condensed Matter Under Extreme Conditions

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Symmetry breaking and restoring under high pressure: the amazing behaviour of the "simple" alkali metals

Cited by 13 publications

References 28 publications

Structure of sodium above 100 GPa by single-crystal x-ray diffraction

Structure of sodium above 100 GPa by single-crystal x-ray diffraction

Nonlinear response theories and effective pair potentials

Symmetries and Physics

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