Low-Energy Linear Structures in Dense Oxygen: Implications for the $ε$-phase

4 Pages·0.15 MB·English

by  J. B. Neaton

Low-Energy Linear Structures in Dense Oxygen: Implications for the ǫ-phase
J. B. Neaton1 and N. W. Ashcroft2,3
1Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08854-8019
2Laboratory of Atomic and Solid State Physics and Cornell Center for Materials Research,
Cornell University, Ithaca, NY 14853-2501
3Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge, CB3-0HE, United Kingdom
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0 (January 25, 2002)
0
Usingdensityfunctionaltheoryimplementedwithinthegeneralizedgradientapproximation,anew
2
non-magnetic insulating ground state of solid oxygen is proposed and found to be energetically fa-

n vored at pressures corresponding to the ǫ-phase. The newly-predicted ground state is composed of
a linearherringbone-typechainsofO2 moleculesandhasCmcmsymmetry(withanalternativemon-
J
oclinic cell). Importantly, this phase supports IR-active zone-center phonons, and their computed
7
frequencies are found to be in broad agreement with recent infrared absorption experiments.
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PACS: 61.50.Ah, 78.30.Am
]
i
c Atlow temperaturesandordinarypressuressolidoxy- bonds has been suggested to account for the stability of
s
gen condenses into the only antiferromagnetic insulating low-symmetry structures above 150 GPa [16].
-
l phase known among the elemental solids. In its ground Although there exist several promising structures
r
t state, the well-known monoclinic α-phase [1], the molec- [9–14],todate x-raydiffractionstudieshavebeenunable
m
ularspinsarearrangedinnearly-closedpackedplanes(or to completely revealthe exactpositions of the molecules
.
t layers) perpendicular to the molecular axes; the axes of in the ǫ-phase. Likewise a previous first-principles study
a
m moleculesinsuccessiveplanesarecollinear[1–3](andap- recordedaprematuremagneticcollapseandconcomitant
parently so in all measuredphases). As the temperature metallization into to the ζ-phase near 12 GPa [17], by-
-
d is increased,oxygeneventually undergoesa transitionto passing the ǫ-phase. In this Letter we summarize results
n its familiar room-temperature gaseous phase, but as the of first-principles calculations that predict a new low-
o pressureis increased,its attributes departradicallyfrom enthalpy moleculararrangementin the pressurerangeof
c
those of an ensemble of weakly-interactingmolecules. In the ǫ-phase. Beginning with a symmetrical low-density
[
factatpressuresabove96GPa(atnearly3-foldcompres- structure,we observethat itis unstableto the formation

1 sion),bothdiamond-anvil[4,5]andshock[6]experiments ofextendedherringbone-typechainsofO2 molecules(in-
v
5 have reported an insulator-metaltransition and, at tem- stead of O4 units), strikingly similar to that suggested
peratures below 0.6 K, the metallic state (the ζ-phase) by Agnew et al. [11]. Non-magnetic and insulating, this
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4 even exhibits superconductivity [7]. While some of the newly-predicted phase is also consistent with recent in-
1 broaderaspectsoftheelectronicbehaviorareunderstood frared measurements.
0 throughout this density range, the crystal structure and Weexamineherethestabilityofthecommonsymmet-
2
magnetic properties of the so-called ǫ-phase, persisting ric phases of oxygen over the molar volume range 6.7-
0
as it does over the wide, intermediate pressure range of 13cm3/mole,the lowervalue correspondingto pressures
/
t
a 10-96 GPa, remain unknown. exceeding 100 GPa. Density functional theory (DFT) is
m Overtwodecadesago,adramaticcolorchangewasob- usedwithinthelocalspin-densityapproximation(LSDA)
- served (from light-blue transparent to darkening red) in [18] and with gradient corrections [19]. We utilize the
d experimentsabove10GPaatroomtemperature [8]. De- projectoraugmented-wave(PAW) method [20]as imple-
n
tailedopticalmeasurements[2]shortlythereafteratroom mented within the Vienna ab initio Simulations Package
o
temperaturerevealedanabruptonsetofinfrared(IR)ab- (VASP)[21]. OuroxygenPAWpotentialrelegatesthe1s
c
: sorptioninthefundamentalmolecularvibron,alsoatap- electrons to a frozen core but otherwise treats all other
v
proximately 10 GPa. Recent low-frequency opticalstud- electrons explicitly as valence; a 60 Ry plane wave cut-
i
X ies have uncovered another strong IR peak, ranging in off is used for all calculations. These methods provide
r frequencybetween300-500cm−1 from10to70GPa,but a particularly accurate picture of the free molecule for
a
at very much lower frequencies than that of the vibron which we correctly obtain the magnetic (S = 1) ground
[13–15]. TheformationofpairsofO2 moleculeswithD2h state; ourcalculatedbond lengthof1.236˚A,binding en-
(rectangular) symmetry–an O4 unit–has been suggested ergy of near 6.0 eV, and molecular vibron frequency of
to explainthese new low-frequencymodes [13,15]. Inter- 1550 cm−1 (within the harmonic approximation) are all
estingly enough the sudden increase in the intensity of slightly larger than experiment (1.207 ˚A) but quite con-
infrared activity in two quite different frequency bands sistent with the known tendency of gradient corrections
parallelsthecaseofdensehydrogen,whereaspontaneous to overestimate the bond length and binding energy of
polarization of the charge density along the molecular p-bonded diatomic molecules [22].
1
A primary physical issue centers on the notably high structure, possessing a two-molecule primitive cell and
linear dipole polarizability of the oxygen molecule. The Cmcm space-group symmetry. A plot of the enthalpies
along-axis tensor component is 15.9a3 and the off-axis asafunctionofpressureforallstructuresconsideredap-
0
components are 8.2a30 [23], where a0 is the Bohr radius. pears in Fig. 1. For comparison, we also evaluate the
These exceed the corresponding quantities in hydrogen enthalpy of the metallic C2mm phase, a candidate ζ-
by more than a factor of two, and the Hertzfeld crite- phase proposedby Serraet al. [17]. Interestinglywe find
rion (for the onset of a polarization divergence) would theCmcmstructuretobeunstabletoC2mmatacalcu-
require a compression of only about 1.8. There is a lated pressure of 47 GPa,resulting in an insulator-metal
large anisotropic fluctuating-dipole (or van der Waals) (IM) transition at a lower pressure than experimentally
attraction [24], and an accurate, effective, and fully observed(96 GPa [4]). Since the IM transition is associ-
non-local representation of these correlated fluctuations ated with band gap closure, this discrepancy may result
withindensity functionaltheoryhasproventobe achal- from the usual underestimate of the electronic band gap
lenge[25,26]. Thusthelocaldensityapproximationisnot by the gradient-correctedLDSA.
expected to be satisfactory until significant intermolecu-
lar density has accumulated, and accordingly we focus
our study on volumes less than 13 cm3/mole (8 GPa),
above which we obtain adequate agreement ( 5 GPa)
with the equation of state at 300 K [4]. ± (a) (b) (c)
0.05
e) Fmmm
ul 0
c
e
ol
m
V/ C2mm
(em -0.05 in-plane (z=0) chains
mm Cmcm out-of-plane (z=1/2)
H - HF -0.1 C2FmIGm.,a2n.dS(cch)enmeawtliyc-sporefd(i0c1te0d)Cacm-pcmlanpehsaosefs(.aT)hFemmmomlec,u(lbes)
inwhite(orientedalong[001])areshiftedbyhalfalatticevec-
-0.1510 20 30 40 50 60 70 80 toroutoftheplane. TheorthorhombicCmcmphase(having
Pressure (GPa) Wyckoffpositions8(g))resultsfromanintraplanardistortion
FIG.1. Enthalpy(H =E+pV)vs. pressurepforselected in which the center molecule moves off-site. Chains run per-
structuresofdenseoxygenwithrespect totheFmmmphase pendicular to the plane and are indicated by with bold gray
atT=0K.Ingeneralagreementwithapreviousstudy[17],we lines. Differences in, e.g., a or c/a are ignored in these illus-
observe that the Fmmm phase is unstable to C2mm above trations.
17 GPa. Convergence with respect tok-points is achieved at
1 meV/molecule using 10x10x12 Monkhorst-Pack k-meshes Atomic arrangements for the three phases considered
for 2-molecule primitive cells; more k-points are used for
hereappearinFig.2. IntheCmcmstructuretheoxygen
the metallic phase. Relaxations are performed until Hell-
molecules order into symmetric herringbone-type chains
mann-Feynmanforcesarelessthan10−2 eV/˚A.Theenthalpy
HwasdeterminedbyfittingtheenergyEtoP2 a V−n/3. along [010] (the b-axis) and perpendicular to the molec-
n=−2 i ular bonds. They form through the shearing of adjacent
(010)planes ofthe Fmmmstructure, reducingthe coor-
At room temperature and under a moderate com-
dination of the molecules from four to two. An ǫ-phase
pression of 8 GPa, the antiferromagnetic δ-phase (space
havingmonoclinicsymmetryhasbeensuggested[3,4,12],
groupFmmm)ofsolidoxygenhasbeenparticularlywell-
and in this context we note that a monoclinic primi-
characterized[2,3,8]. Howeverrecentx-raydatasuggests
tive lattice vector c′ can be chosen for Cmcm (where
a direct α-to-ǫ transition at low temperatures [12]. Fur-
c′ = 1√a2+c2). (Asimilarrelationshipexistsbetween
ther, IR spectra [14] and Raman [27] between 2-8 GPa | | 2
theα(C2/m)andδ (Fmmm)phases[12].) Nevertheless
and below 20 K appear to be inconsistent with Fmmm
wefindthatdistortionsofitsorthorhombiclatticevectors
symmetry. Thus in order to examine the possibility of
lowersymmetrygroundstatesthatdopossessIRactivity a and c (resulting in P21/c symmetry) do not lower the
total energy [28]. The Fmmm phase is related through
attheobservedfrequenciesandremaininsulating,were-
continuous distortion to the nearly close-packed C2mm
leasedthe symmetry constraintsofa 4-molecule Fmmm
phase by a displacement of (001) planes in the [100] di-
orthorhombiccellandcompletely relaxed the internal co-
ordinates and lattice parameters, all with dense k-point rection [29]. Interestingly, the dimer length is found to
decrease by about 1% with increasing pressure in this
sampling. Thisimmediatelyresultedinasignificantrear-
newphase,from1.224˚Aat8GPato1.209˚Aat54GPa.
rangementofthe crystalandanew,stableorthorhombic
2
The distance between neighboring molecules along the tric state, whose physical origin may in turn be under-
chainisreducedfrom2.081˚Ato1.986˚Aoverthisrange, stoodthroughconsiderationofamean-fieldargumentfor
a modest overbinding with respect to experiment, where a dynamic lattice as given for hydrogen [16]. Thus self-
these distances are thought to be in the range 2.2-2.5 ˚A consistent Lorenz fields compensate energetic costs as-
[13]. Similarly, the a, b, and c lattice parameters decline sociated with the low-symmetry Cmcm structure in the
from 3.805 to 3.333 ˚A, 2.990 to 2.718 ˚A, and 7.034 to intermediate pressure range below 50 GPa. Increasing
6.216 ˚A, respectively, as pressure is increased from 8 to intermolecular overlap at higher densities lowers kinetic
54 GPa. Notably,c diminishes slightly faster than either and exchange energies, and the metallic C2mm phase is
aorbwithincreasingpressure;experimentally,theb-axis thuseventuallyfavored. Examinationofthespindensity
is observed to decrease most rapidly [14]. As the c-axis indicates that oxygenis non-magnetic within this phase,
spacingismuchlargerthaneitheraorb,remnantvander consistent with other studies [13,31]; total energies and
Waals interactions (see above) may still be particularly forces obtained from spin- and non-spin-polarized calcu-
important between adjacent (001) planes, and therefore lations are essentially identical.
it is here that our treatment of exchangeandcorrelation
is likely to be most inadequate. 1900
Ag
1700
-1)m 1500 B3u
cy (c 1930000
en B1g
qu 700 B2u
Fre 500 BA2gg
B3g
300 B2g
100
FIG. 3. Charge density slice of Cmcm at a calculated 0 20 40 60 80 100
pressure of 20 GPa (10.26 cm3/mole) plotted in an (001) (or Pressure (GPa)
FIG. 4. Calculated zone-center phonons of Cmcm as a
ab)planepassingthroughthemolecularcenters(theunitcell
is outlined in black). Anatural logarithmic scale isused; the function of pressure. Modes having B2u and B3u symmetry
are IR-active (red-dashed); the remaining are Raman-active
highest contour (blue) are 54 times larger than the lowest
(black-solid). Lines guidethe eye.
(red). Since the chains are equally spaced in the cell, the
development of an alternating polarization perpendicular to
themolecule is evident by inspection. Sincethere aretwomoleculesineachprimitiveCmcm
cell, we expect nine optical phonons (plus three purely
SolidoxygenisrobustlyinsulatingintheCmcmstruc- translational modes). At the zone-center, there are
ture, and the calculated band gap (a considerable un- eight irreducible representations, as permitted by the
derestimate of the true band gap) decreases from 0.95 D2h point group: four allow Raman activity (Ag, B1g,
eV (direct gap) near 8 GPa to about 0.55 eV (indirect B2g, and B1g), three are IR-active (B1u, B2u, and B3u),
gap) at 55 GPa. The optical threshold of the ǫ-phase and a single remaining Au mode is silent. Gorelli et
has been∼measured to be around 3 eV (blue) near 10 al. [13,15] have proposed a structure made up of two
GPa,declining to 2.0 eV (orange-red)near 55 GPa [5], molecules (actually O4 units) having D2h symmetry. In
∼
for light polarized perpendicular to the molecular axis. agreementwithRef.[15],ourpredictedgroundstatepos-
These are larger than our computed direct gaps at these sesses D2h point symmetry, but also includes additional
pressures (for the smallest, by a factor of three) but, lattice translationsassociatedwith the herringbone-type
as stated above, this is to be expected given our use of chain structure. Corresponding force constants are ob-
the LSDA; corrections through approximate inclusion of tained through analysis [32] of a series of frozen-phonon
many-electron effects via, for example the GW approxi- calculations; phonon frequencies are then computed by
mation [30], would be of considerable interest for accu- diagonalizationof block-diagonaldynamical matrices.
rately reproducing this gap and likewise describing the The pressure dependence of zone-center optical fre-
onset of metallization. quencies computed between 8 and 86 GPa appears in
The charge density is plotted in Fig. 3 in the ab-plane Fig. 4, and we obtain remarkably good agreement with
(perpendicularto [001]),andisseento developanasym- the existing spectroscopic data, quite apart from the
metryoccurringperpendiculartothemolecularbondbut fact that C2mm is favored above 47 GPa in our cal-
centered on each molecule, as is evident by inspection of culations. Consistent with observations [15], we predict
Fig. 3, providing insight into the stability of this phase. two IR-active modes over this range. The B3u mode is
Theasymmetrymaybeviewedasaweaklyantiferroelec- an antiphase vibron; its computed frequencies are in the
3
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experimentally,whichincreasefrom300to600cm−1 be-
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The Raman-active vibron (A ) is in the range 1500-
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50 (1996).
interest are close in frequency to observed Raman peaks
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We gratefully acknowledge M. H. Cohen, M. P. Teter,
(1991).
and D. Vanderbilt for useful commentary; and we thank
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G. Kresse for providing the PAW potentials. This 80, 4153 (1998).
work was supported by the National Science Founda- [27] J. Yenand M. Nicol, J. Phys. Chem. 91, 3336 (1987).
tion(DMR-9988576). ThisworkmadeuseoftheCornell [28] Relaxation of larger supercells containing up to 36
Center for Materials Research Shared Experimental Fa- randomly-displaced molecules (constructed from 4-
cilities, supportedthroughthe NationalScience Founda- moleculeorthorhombiccellstripledalong[100]and[010])
tionMaterialsResearchScienceandEngineeringCenters did not result in phases with lower enthalpy.
program (DMR-9632275). [29] Our predicted lattice parameters for antiferromagnetic
Fmmm below 20 GPa yield b/a ∼ 0.95 and c/a ∼ 2.
Above50GPanon-magneticC2mmisverynearlymolec-
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(1996).
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