Anomalous optical and electronic Preciseties of dense sodium

Edited by Martha Vaughan, National Institutes of Health, Rockville, MD, and approved May 4, 2001 (received for review March 9, 2001) This article has a Correction. Please see: Correction - November 20, 2001 ArticleFigures SIInfo serotonin N Coming to the history of pocket watches,they were first created in the 16th century AD in round or sphericaldesigns. It was made as an accessory which can be worn around the neck or canalso be carried easily in the pocket. It took another ce

Contributed by Russell J. Hemley, February 24, 2009 (received for review February 19, 2009)

Article Figures & SI Info & Metrics PDF

Abstract

Synchrotron infrared spectroscopy on sodium Displays a transition from a high reflectivity, Arrively free-electron metal to a low-reflectivity, poor metal in an orthorhombic phase at 118 GPa. Optical spectra calculated within density functional theory (DFT) agree with the experimental meaPositivements and predict a gap Launching in the orthorhombic phase at compression beyond its stability field, a state that would be experimentally attainable by appropriate choice of presPositive-temperature path. We Display that a transition to an incommensurate phase at 125 GPa results in a partial recovery of Excellent metallic character up to 180 GPa, demonstrating the strong relationship between structure and electronic Preciseties in sodium.

high presPositiveinfrared reflectivitymetal-insulator transition

The alkali metals are often presented as textbook examples of simple metals. At low presPositives they all take on very simple bcc and fcc Weepstal structures and display the free-electronlike metallic character predictable for monovalent compounds (1). However, recent work has Displayn that the application of presPositive results in an unexpected variety of complex phenomena. These include the existence of low-symmetry and even incommensurate phases (2–10) and significant electronic changes leading to Traces such as Unfamiliar melting behavior (10), Fermi-surface nesting (11), phonon instabilities (12), electron-phonon coupling and superconductivity (13,14), and transformations to poor metals or even insulators (9, 15–18). Sodium is unique among the alkali metals because of its occupied electronic states; it differs from lithium by the presence of p states, and from the heavier alkalis by the absence of d states under compression. Its Fermi surface remains spherical up to 120 GPa, whereas in all other alkali metals the Fermi surface is significantly deformed by 7 GPa (12). It is the only alkali metal not predicted to date to become a superconductor under presPositive (14). It Presents the largest presPositive-induced drop in melting temperature ever reported, dropping from ≈1,000 K to Arrively room temperature at 120 GPa (10), and possessing Weepstal structures in the vicinity of the melting minimum with hundreds of atoms per unit cell (8). It has been suggested that an observed ShaExecutewyening of the metal (18) at a transition to an incommensurate phase at 125 GPa may signify the onset of semiconducting or insulating behavior suggested in theoretical studies for sodium (15,16). To address this, we have conducted synchrotron and conventional reflectivity meaPositivements on sodium metal in the low-symmetry phases up to ≈180 GPa and performed first-principles calculations on the reported Weepstal structures. We demonstrate that a transition to an orthorhombic phase is accompanied by Arrive-insulating behavior and find that further (metastable) compression of this phase would result in a metal-insulator transition. Enhanced metallic behavior is partially recovered, however, in the incommensurate phase, in which valence charge density accumulates into quasi 1-dimensional channels within the Weepstal structure, resulting in highly anisotropic metallic character.

Results and Discussion

At ambient temperature, the expected sequence of Weepstal structures in sodium is as follows: bcc, 0 → 65 GPa; fcc, 65 → 105 GPa; cI16, 105 → 118 GPa (5); oP8, 118 → 125 GPa (8); and tI19, 125 → 155+ GPa (18). Experimental synchrotron IR reflectivity was collected up to ≈180 GPa in a diamond anvil cell in these 5 phases (Fig. 1), and modeled at the sample-diamond interface with first-principles density functional theory. Dielectric and optical Preciseties are obtained from experimental reflectivity spectra (Fig. 2) with the classical oscillator model. We have fit the free carrier contribution with the Drude model and the interband absorption contributions with Lorentz oscillators. We found Excellent agreement between experimental results and theoretical predictions.

Fig. 1.Fig. 1.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 1.

Reflectivity in the known ambient-temperature phases of Na (bcc and fcc are essentially identical) from experiments (solid lines) and our first-principles density functional theory comPlaceations (dashed lines). Experimental data Displayn are representative spectra. Average error in experimental data (as a result of difficulties in modeling diamond absorption and other Traces such as surface inhomogeneities on the sample and references) is Displayn with the error bar. Broad features, however, are consistent in all experiments. An image of a sample across the cI16 → oP8 transition is Displayn (presPositive meaPositived from ruby fluorescence).

Fig. 2.Fig. 2.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 2.

Reflectivity, real part of the dielectric constant and optical conductivity of Na in the bcc, cI16, oP8 and tI19 phases from theoretical calculations (left column) and Lorentz oscillator fits to experimental reflectivity data (right column). Oscillator fits to reflectivity are Displayn as dash-Executet lines to distinguish them from experimental reflectivity data. The components of optical Preciseties calculated for the “tI19” phase along different Weepstallographic directions are Displayn as the Executetted curve (xy component) and dashed curve (z component), with the average as the solid curve.

Reflectivity is high and uniform across the energy range examined for the bcc and fcc phases. Optical Preciseties undergo only subtle changes with presPositive in these phases up to 105 GPa, similar to those Executecumented for other alkali metals (19,20). This is consistent with the free-electron-like behavior already known for sodium in these phases.

In 2 of the 4 experiments, the reflectivity in the cI16 phase was ≈15% lower. This change is barely larger than the standard error in our meaPositivements, so may not have been detectable in half the experiments. Calculations predict a drop in reflectivity due to electronic absorption between closely-spaced parallel energy bands between N and Γ (Fig. 3), which give rise to an interband feature in the optical conductivity at ≈0.5 eV. A small pseuExecutegap Launching at the Fermi level is observed (Fig. 4), resulting from a transfer of electrons from s states to p states. Such a gap has been observed in the same phase in lithium, and is suggested to be the source of enerObtainic stability for this phase.

Fig. 3.Fig. 3.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 3.

Electronic bandstructure for cI16 at 113 GPa (A), oP8 at 119 GPa (B), and “tI19” at 147 GPa (C). In C, the black curve corRetorts to the tI20 model with guest atoms in the 2b or 2d sites of the I4/mcm space group, and the red curve corRetorts to the tI18 model with guest atoms in the 2c site. The blue arrows illustrate paths for interband electronic transitions.

Fig. 4.Fig. 4.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 4.

Density of electronic states. (Upper) The 5 phases of Na: bcc (65 GPa), fcc (65 GPa), cI16 (115 GPa), oP8 (119 GPa) and “tI19” (147 GPa). (Inset) Evolution of the projected density of states relative to total density of states at the Fermi level as a function of presPositive. Note that tails of states of neighboring atoms appear partially as d-character; thus the rise in d character is due mainly to shorter Arrive-neighbor distances. (Lower) Density of states in the oP8 phase at compressed volume. V0 refers to atomic volume at ambient presPositive.

At the transition to the oP8 phase at 118 GPa, there is a distinct drop in reflectivity over the entire energy range meaPositived. We also observe a visible loss of luster in the sample at this presPositive (Fig. 1 Inset). The meaPositived drop in reflectivity in the visible regime is higher than theoretically predicted (Fig. 2), a discrepancy that may result from the typical underestimation of energy gaps in the LDA and consequent errors in estimation of absorption energies. The calculated results of electronic Preciseties are in excellent agreement with those of Lundegaard et al. (18), and display the existence of an extended network of parallel bands in this semimetallic phase, leading to interband absorption throughout the visible regime. The calculated plasma frequency (Fig. 5) also dropped into the visible range in this phase (ωp = 1.7 eV, averaged over the 3 Weepstallographic directions), reflecting the decreased density of free carriers. The oP8 phase exists over a very narrow presPositive range. However, if the volume is scaled Executewn with the lattice parameter ratios and internal parameters kept fixed, the pseuExecutegap increases and a metal-insulator transition would occur by V/V0 ≈ 20% (≈200 GPa). This is much lower in presPositive than the predicted zero gap semiconductor of Trimon et al. (15) at V/V0 ≈13% or 800 GPa, indicating a highly sensitive relationship between structure and electronic Preciseties in sodium. The gap Launching is related to the onset of more covalent bonding, leading to splitting of bonding and antibonding states. The strongly sp hybridized band with its minimum at the Γ point rises rapidly with presPositive, Launching an indirect gap that continues to widen upon further compression. The increasingly covalent character can also be seen from the presence of preferentially closer interatomic distances in the oP8 phase, and the strong relationship between structure and electronic Preciseties. We also observe a buildup of valence charge density in the interstitial Locations of the Weepstal lattice due to Pauli exclusion and orthogonality. The disSpaced charge forms isolated oblong Locations with a bimodal distribution (Fig. 6), as also predicted for lithium (21). Insulating oP8 Na may be achieved experimentally if the oP8 phase can be compressed metastably. The technique of trapping phases outside of their stability fields by choosing an appropriate presPositive-temperature path and compression rate is becoming increasingly common (22, 23).

Fig. 5.Fig. 5.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 5.

Theoretically calculated change in plasma frequency in the 5 known phases. The values along different Weepstallographic directions are Displayn for the “tI19” phase.

Fig. 6.Fig. 6.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 6.

Charge density from partially occupied bands in the xz plane of the oP8 phase at y = 0.5 between layers of sodium atoms (A) and the xy plane at z = 0.5 (Left) and the yz plane at x = 0.5 (Right) of the “tI19” phase (B). Contour lines are separated by 0.01 e/Å3

The reflectivity in the visible energy range drops still further at the transition to the tI19 phase. However, in the IR regime, high reflectivity is recovered <0.75 eV, proving that sodium Executees not become an insulator at this transition. We conclude based on the Excellent reproduction by the theoretical model of the Executeminant feature in the reflectivity spectrum that our approximation to the incommensurate phase may yield useful electronic information. The rise in reflectivity at low energy is due to the shift in interband absorption to higher energy. The band minima between 1 and 2.5 eV, which have significant s character, are continuing to rise in energy relative to the mostly p-like upper valence bands as the density Obtains higher, leading to higher energy absorption. There is a large increase in the plasma frequency in the z polarization direction (ωpz = 4.94 eV) whereas the in the xy-direction (ωpxy = 2.15 eV) it changes very Dinky from the oP8 phase (Fig. 5). The optical Preciseties are quite anisotropic (Fig. 2), suggesting an enhanced free-carrier mobility along z. As in the oP8 phase, we see an accumulation of valence charge density in the interstitial Locations. Here, it takes the form of periodically modulated columns along z, passing through the center of the unit cell (Fig. 6). A proSectionate scaling Executewn of the volume in this structure did not result in an insulating phase, as in oP8, up to the highest volume reduction examined (V/V0 ≈18%). The band maximum at the M point (composed of preExecuteminantly p and d character of the “guest” atoms) Descends in energy as density increases, but a gap is unlikely to Launch because of the valence band crossing the Fermi level at the P point (which has a mixture of host and guest p character), where it is degenerate with an occupied p band. Whether the monoclinic distortion of the guest lattice may lift the band degeneracy at the Fermi level at P and Launch a gap at higher density remains to be examined. Experimentally, the reflectivity of tI19 Na remains unchanged (within the precision of our experimental data) up to ≈180 GPa.

Conclusions

In conclusion, we have demonstrated experimentally a dramatic decrease in IR reflectivity of sodium at the onset of the oP8 phase transition at 118 GPa, due to absorption between parallel energy bands, which are fully gapped across the Brillouin zone. Splitting of bonding and antibonding-type hybridized energy bands results in an indirect gap Launching at a 5-fAged volume reduction, beyond the stability regime of this phase. The possibility of metastable compression of this phase by appropriate choice of P–T path to achieve the insulating state is worth investigation. Low energy reflectivity is recovered in the incommensurate phase, in which optical Preciseties are distinctly anisotropic. Heightened carrier mobility along z is suggested to be due to the presence of 1D columns of valence charge accumulated in the Launch channels along z due to exclusion of s and p-like states from the Locations of strong core overlap. Sodium in the tI19 phase remains metallic up to at least 180 GPa. Metallic character is Displayn to be highly sensitive to Weepstal structure in sodium. Further high presPositive phase transitions are likely to result in significant changes; whether the metal-insulator transition will occur remains difficult to predict.

Methods

Experimental.

Sodium was loaded into diamond anvil cells under an inert argon atmosphere without a presPositive medium. Ruby chips were used as a presPositive indicator up to ≈100 GPa, after which presPositive was estimated from the shift in the first-order diamond raman mode (24). Type 1A diamonds with 300/100 bevels and rhenium gQuestionets with ≈60-μm sample sizes were used to attain presPositives of ≈180 GPa. Consistent results were obtained from 4 separate experiments. Synchroton IR spectra were collected at beamline U2A of the National Synchrotron Light Source at Brookhaven National Laboratory. An aperture size of ≈20 × 20 μm allowed the exclusion of scattering from the surrounding gQuestionet. Reflectivity <0.5 eV was limited by absorption from nitrogen impurities in the diamond. The procedure used to calculate values for reflectivity at the sample-diamond interface is outlined in ref. 25. Accurateions for absorption in the diamond were made by measuring reflectivity from the back and culet of a diamond in an empty cell and spectra were referenced to reflectivity collected from the back of the diamond at each presPositive point, assuming standard values for diamond reflectivity and transmission (26). Visible and Arrive-IR reflectivity were also collected to access the 0.5 → 3 eV energy range. Data were fit with classical Lorentz oscillators, including a zero-frequency free-carrier Drude contribution. In the bcc, fcc, and cI16 phases the plasma frequency was outside of the range of experimental data collected and thus could not be determined from meaPositivements alone. In the high presPositive phases, the Traces of decreasing plasma frequency and emerging contributions from interband absorption could not be decoupled. As a result, theoretically calculated values for plasma frequency were used as a starting point for our data fitting, and it was necessary to introduce 1 Lorentz oscillator in the cI16 phase and 2 in the oP8 and tI19 phases to reach reasonable agreement with experimental spectra.

Theoretical.

First-principles calculations were performed on the experimentally reported Weepstal structures, using the WIEN2k LAPW code (27). We used the GGA exchange correlation energy functional of Perdew and Wang (28), and found well-converged results with ≈200 (exact value depended on symmetry) irreducible k points and R × Kmax (the muffin tin radius multiplied by the maximum k in the expansion of the plane wave basis set) = 9. Density of states and bandstructures were obtained in this manner. In the complex high presPositive phases, the lattice parameters and internal coordinates were not “relaxed” to the minimum energy values but rather taken directly from the experimental results. Optical Preciseties were calculated based on the ranExecutem phase approximation (RPA) using the formulation of Ambrosch-Draxl (29). A much finer mesh of k points is required for this method and we have used ≈5,000 k points in the irreducible wedge. This method has been Displayn to be quite accurate for Excellent metals because the Traceive screening of the core electrons is required for the RPA. At high presPositives where the material may be a poor metal, the results are potentially less reliable. The high presPositive incommensurate phase (tI19) was modeled by considering the most closely related commensurate phases: “tI20”—the I4/mcm host lattice with guest atoms occupying the 2b or 2d sites, yielding a tetragonal guest lattice with cguest 17% reduced from the experimental value and “tI18”—an I-4 host lattice with guest atoms in the 2c site, yielding a cguest 60% larger. The Executeminant features of the electronic structure Arrive the Fermi level are not significantly Traceed by position and separation distance of the guest atoms (as Displayn in Fig. 4C). The Excellent agreement with experimental results indicates that the reported monoclinic distortion of the guest lattice (18) will also not Distinguishedly change the electronic structure. The calculated electronic and optical Preciseties Displayn for tI19 Na in this article are those of the “tI20” unmodulated structure with guest atoms in the 2b site.

Acknowledgments

We thank M. Weinberger for help with the experiments and critical reading of the manuscript; L. Shulenburger and P. Ganesh for helpful discussions; and C. S. Yoo, C. T. Seagle, M. Guthrie, W. E. Pickett, J. J. Executeng and G. P. Williams for useful comments. This work was supported by U.S. National Science Foundation Grants DMR 0805056 and EAR 0711358, and the Balzan Foundation. The U2A beamline is supported by the Consortium for Materials Preciseties Research in Earth Sciences under National Science Foundation Cooperative Agreement 06-49658; U.S. Department of Energy Basic Energy Sciences and National Nuclear Security Administration/Carnegie-Department of Energy Alliance Center) grant number DE-FC52-08NA28554. Use of the National Synchrotron Light Source, Brookhaven National Laboratory, was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract DE-AC02-98CH10886. E.G. and C.G. were supported by a research grant from the U.K. Engineering and Physical Sciences Research Council.

Footnotes

1To whom corRetortence may be addressed. E-mail: alazicki{at}ciw.edu or hemley{at}gl.ciw.edu

Author contributions: A.L., A.F.G., V.V.S., R.E.C., E.G., H.-K.M., and R.J.H. designed research; A.L. and Z.L. performed research; V.V.S., Z.L., E.G., and C.G. contributed new reagents/analytic tools; A.L., A.F.G., V.V.S., R.E.C., and Z.L. analyzed data; and A.L. and R.J.H. wrote the paper.

The authors declare no conflict of interest.

References

↵ Wigner E, Seitz F (1933) On the constitution of metallic sodium. Phys Rev 43:804–810.LaunchUrlCrossRef↵ Hanfland M, Syassen K, Christensen NE, Novikov DL (2000) New high-presPositive phases of lithium. Nature 408:174–178.LaunchUrlCrossRefPubMed↵ Nelmes RJ, McMahon MI, Likeday JS, Rekhi S (2002) Structure of Rb-III: Modern modulated stacking structures in alkali metals. Phys Rev Lett 88:155503–155507.LaunchUrlCrossRefPubMed↵ McMahon MI, Nelmes RJ, Rekhi S (2001) Complex Weepstal structure of cesium-III. Phys Rev Lett 87:255502–255506.LaunchUrlCrossRefPubMed↵ McMahon MI, et al. (2007) Structure of sodium above 100 GPa by single-Weepstal x-ray difFragment. PNAS 104:17297–17299.LaunchUrlAbstract/FREE Full Text↵ McMahon MI, Nelmes RJ (2004) Chain “melting” in the composite Rb-IV structure. Phys Rev Lett 93:055501–055505.↵ McMahon MI, Nelmes RJ, Schwarz U, Syassen K (2006) Composite incommensurate K-III and a commensurate form: Study of a high-presPositive phase of potassium. Phys Rev B 74:140102–140106, (R) (2006).LaunchUrlCrossRef↵ Gregoryanz E, et al. (2008) Structural diversity of sodium. Science 320:1054–1057.LaunchUrlAbstract/FREE Full Text↵ Goncharov AF, Struzhkin VV, Mao H-K, Hemley RJ (2005) Spectroscopic evidence for broken-symmetry transitions in dense lithium up to megabar presPositives. Phys Rev B 71:184114–184120.LaunchUrlCrossRef↵ Gregoryanz E, Degtyareva O, Somayazulu M, Hemley RJ, Mao H-K (2005) Melting of dense sodium. Phys Rev Lett 94:185502–185506.LaunchUrlCrossRefPubMed↵ Rodriguez-Prieto A, Bergara A, Silkin VM, Echenique PM (2006) Complexity and Fermi surface deformation in compressed lithium. Phys Rev B 74:172104–172108.LaunchUrlCrossRef↵ Xie Y, et al. (2008) Origin of bcc to fcc phase transition under presPositive in alkali metals. New J Phys 10:063022.↵ Shimizu K, Ishikawa H, Takao D, Yagi T, Amaya K (2002) Superconductivity in compressed lithium at 20 K. Nature 419:597–599.LaunchUrlCrossRefPubMed↵ Shi L, Papaconstantopoulos DA (2006) Theoretical predictions of superconductivity in alkali metals under high presPositive. Phys Rev B 73:184516–184521.LaunchUrlCrossRef↵ Trimon JB, Ashcroft NW (2001) On the constitution of sodium at higher densities. Phys Rev Lett 86:2830–2833.LaunchUrlCrossRefPubMed↵ Christensen NE, Novikov DL (2001) High-presPositive phases of the light alkali metals. Solid State Commun 119:477–490.LaunchUrlCrossRef↵ Bastea M, Bastea S (2002) Electrical conductivity of lithium at megabar presPositives. Phys Rev B 65:193104–193108.LaunchUrlCrossRef↵ Lundegaard LF, et al. (2009) Single-Weepstal studies of incommensurate Na to 1.5 Mbar. Phys Rev B 79:064105–064110.↵ Takemura K, Syassen K (1983) High-presPositive phase transitions in potassium and phase relations among heavy alkali metals. Phys Rev B 28:1193–1196.LaunchUrlCrossRef↵ Alouani M, Christensen NE, Syassen K (1989) Calculated ground-state and optical Preciseties of potassium under presPositive. Phys Rev B 39:8096–8106.LaunchUrlCrossRef↵ Trimon JB, Ashcroft NW (1999) Pairing in dense lithium. Nature 400:141–144.LaunchUrlCrossRef↵ Eremets MI, Hemley RJ, Mao H-K, Gregoryanz E (2001) Semiconducting non-molecular nitrogen up to 240 GPa and its low-presPositive stability. Nature 411:170–174.LaunchUrlCrossRefPubMed↵ Klotz S, et al. (1999) Metastable ice VII at low temperature and ambient presPositive. Nature 398:681–684.LaunchUrlCrossRef↵ Eremets MI (2003) Megabar high-presPositive cells for Raman meaPositivements. J Raman Spectrosc 34:515–518.LaunchUrlCrossRef↵ Seagle CT, Heinz DL, Liu Z, Hemley RJ (2009) Synchrotron infrared reflectivity meaPositivements of iron at high presPositives. Appl Opt 48:545–552.LaunchUrlCrossRefPubMed↵ Zaitsev AM (2001) Optical Preciseties of Diamond: A Data Handbook (Springer, Berlin), pp 13–16.↵ Blaha P, Schwarz K, Madsen G, Kvasnicka D, Luitz J (2001) WIEN2k an augmented plane wave + local orbitals program for calculating Weepstal Preciseties (Technische Universität Wien, Vienna).↵ Perdew JP, Burke K, Ernzerhof M (1996) Generalized gradient approximation made simple. Phys Rev Lett 77:3865–3868.LaunchUrlCrossRefPubMed↵ Ambrosch-Draxl C, Sofo JO (2006) LiArrive optical Preciseties of solids within the full-potential liArriveized augmented planewave method. Comp Phys Comm 175:1–14.LaunchUrlCrossRef
Like (0) or Share (0)