Entropically Stabilized Local Dipole Formation in Lead Chalcogenides

Abstract

We report the observation of local structural dipoles that emerge from an undistorted ground state on warming, in contrast
to conventional structural phase transitions in which distortions emerge on cooling. Using experimental and theoretical probes
of the local structure, we demonstrate this behavior in binary lead chalcogenides, which were believed to adopt the ideal,
undistorted rock-salt structure at all temperatures. The behavior is consistent with a simple thermodynamic model in which
the emerging dipoles are stabilized in the disordered state at high temperature due to the extra configurational entropy despite
the fact that the undistorted structure has lower internal energy. Our findings shed light on the anomalous electronic and
thermoelectric properties of the lead chalcogenides. Similar searches may show that the phenomenon is more widespread.

Full text

Entropically Stabilized Local Dipole
Formation in Lead Chalcogenides
Emil S. Božin,
1
Christos D. Malliakas,
2
Petros Souvatzis,
3
Thomas Proffen,
4
Nicola A. Spaldin,
5
Mercouri G. Kanatzidis,
2,6
Simon J. L. Billinge
1,7
*
We report the observation of local structural dipoles that emerge from an undistorted ground state
on warming, in contrast to conventional structural phase transitions in which distortions emerge
on cooling. Using experimental and theoretical probes of the local structure, we demonstrate this
behavior in binary lead chalcogenides, which were believed to adopt the ideal, undistorted rock-salt
structure at all temperatures. The behavior is consistent with a simple thermodynamic model in
which the emerging dipoles are stabilized in the disordered state at high temperature due to the extra
configurational entropy despite the fact that the undistorted structure has lower internal energy.
Our findings shed light on the anomalous electronic and thermoelectric properties of the lead
chalcogenides. Similar searches may show that the phenomenon is more widespread.
Ferroelectric materials are characterized
by a spontaneous alignment of static local
dipole moments leading to a net electric
polarization that can be switched by an applied
electric field (1). Above their critical Curie tem-
perature, T
c
, they undergo a phase transition to
a higher symmetry, nonpolar state, which by anal-
ogy with ferromagnets is called paraelectric. Al-
though the question of whether the paraelectric
phase consists of fluctuating local dipole mo-
ments or entirely centrosymmetric arrangements
of atoms remains open (and likely depends on
material, temperature, and length scale), the tran-
sition from paraelectric to ferroelectric on cool-
ingalwaysinvolvesaloweringinsymmetrythat
is well described within the traditional Landau
picture of phase transitions, for example, in
BaTiO
3
(2). In PbTe and PbS, we have observed
the existence at high temperature of such a para-
electric phase of disordered, fluctuating dipoles,
but the ground state rather than being the ferro-
electric state is a dielectric with no local dipoles.
There is no macroscopic symmetry change asso-
ciated with the spontaneous local dipole forma-
tion, so the behavior is invisible to conventional
crystallographic techniques. We detect the local
atomic off-centering at high temperature using
recently developed local structural probes.
Lead chalcogenides such as PbTe and the
mineral galena (PbS) have been known and ex-
ploited since ancient times (3). They are partic-
ularly important today, with PbTe currently
the leading thermoelectric material in applica-
tions just above room temperature (4). Despite
their long history, their nanoscale structure has
only recently been studied in detail (5–7), mo-
tivated by the realization that intrinsic nanoscale
structural modulations are helpful in produc-
ing low thermal conductivity and, therefore,
high thermoelectric figures of merit (4,8). Such
studies of the nanostructure have been enabled
by powerful synchrotron-based local structure
probes, such as atomic pair distribution function
(PDF) analysis (9,10). The PDF is obtained by
Fourier transforming appropriately collected
and corrected x-ray or neutron powder diffrac-
tion data (9) and has peaks at positions corre-
sponding to interatomic distances in the solid.
We show in Fig. 1B the PDF of the simple rock-
salt structure (Fig. 1A) that the lead chalco-
genides were previously believed to adopt at all
temperatures. Because both Bragg and diffuse
scattering signals are used, the PDF yields local
structural information rather than just the aver-
age crystallographic structure.
Our main results, obtained from temperature-
dependent neutron diffraction studies, are sum-
marized in Fig. 1, C to I. Because PbTe and PbS
behave qualitatively similarly, we present only
the PbTe results in the figure; data for PbS are
contained in figs. S1 and S2 in the supporting
online material (11). The dramatic effect of tem-
perature on the structure of PbTe is evident in
the powder diffraction pattern, shown in the form
of the corrected and normalized diffraction in-
tensity function F(Q)(11) in Fig. 1C. This figure
also serves to illustrate the high quality and good
statistics of the neutron powder diffraction data
collected over a wide range of momentum trans-
fer, Q(Q=4psinq/l,whereqis the Bragg angle
and lthe wavelength of the x-rays or neutrons).
The dramatic loss of intensity in the Bragg peaks
at high Qin the 500 K data (red) compared with
the 15 K data (blue) is clear. The attenuation is
due in part to the usual Debye-Waller effects (12)
from increased thermal motion; however, the
extent of the changes is extraordinarily large. In
Fig. 1, D and E, we show the PDFs at 15 K and
500 K, respectively; the effect of temperature on
the PDFs is anomalous, with notable broadening
evident at 500 K compared with 15 K. (The scale in
Fig. 1E is one-fifth that in Fig. 1D.)
To study the temperature-induced local struc-
tural effects in more detail, we next analyze the
temperature dependence of the low-rregion,
where ris the interatomic pair separation dis-
tance, of the PDF (Fig. 1F), where measured PDFs
are shown every 50 K from 15 K to 500 K. The
PDF peak broadening is reflected in the drop in
the maxima of the peaks. Particularly striking is
the drop in the nearest-neighbor peak, which oc-
curs as rapidly as those in the higher-neighbor
peaks. This strong broadening of the nearest-
neighbor PDF peak does not occur in conventional
materials. This is because of the highly correlated
dynamics of nearest-neighbor atoms (13), which
results in the relative motion of directly bonded
atom pairs having a much smaller temperature
dependence than the higher-neighbor pairs.
In Fig. 1, G and H, we show the Pb-Te nearest-
neighbor peak on an expanded scale. At 15 K
(Fig. 1G), the peak appears as a sharp, single-
Gaussian function with small ripples coming
from the finite Qrange of the Fourier transform,
so-called termination ripples (9).Theredlineis
a calculated PDF peak with a pure Gaussian
line-shape, convoluted with a sinc function to
simulate the effects of the finite Fourier trans-
form (9). This is characteristic of a single aver-
age bond length with harmonic motion taking
place around that position, indicating that the
ground state of PbTe at 15K is ideal rock-salt in
both the local and average structures, as expected.
However, at 500 K (Fig. 1H), the peak is consid-
erably broadened and qualitatively non-Gaussian,
with extra intensity apparent on the high-rside
of the peak. This unambiguously indicates the
appearance of nonharmonic effects with increas-
ing temperature.
We have quantified the asymmetry of this
peak, and in Fig. 1I we plot the temperature de-
pendence of a PDF peak asymmetry param-
eter, ∆R
ASYMM
(11). It has a value of zero for
a perfectly symmetric peak such as a Gaussian,
and its numerical value increases as the peak be-
comes more asymmetric. As evident in Fig. 1I,
the asymmetric nature of the first PDF peak
increases continuously from 15 K to ~250 K,
where it saturates.
The non-Gaussian asymmetry can be inter-
preted either in terms of strong anharmonicity in
a single-welled potential probed by the atomic
motions or by the appearance of multiple, incom-
pletely resolved, short and long bond lengths
under the nearest-neighbor PDF peak, charac-
teristic of quasistatic structural dipoles in ma-
terials studied using the PDF (14,15). Figure 1F
points to the latter interpretation because it is
evident that higher-neighbor peaks are also losing
their Gaussian character at high temperature.
Despite being globally rock-salt, characteristic
of lone-pair–inactive Pb
2+
compounds (6), the
local structure behaves like that in ferroelectrically
distorted lone-pair–active Pb
2+
compounds such as
PbTiO
3
(14). The off-centered ions are disordered
1
Condensed Matter Physics and Materials Science Depart-
ment, Brookhaven National Laboratory, Upton, NY 11973,
USA.
2
Department of Chemistry, Northwestern University,
Evanston, IL 60208, USA.
3
Theoretical Division, Los Alamos
National Laboratory, Los Alamos, NM 87545, USA.
4
Lujan
Neutron Scattering Center, Los Alamos National Labora-
tory,LosAlamos,NM87545,USA.
5
Department of Materials,
ETH, Zurich, Switzerland.
6
Material s Science Division, Argonne
NationalLaboratory, Argonne, IL 60439, USA.
7
Department of
Applied Physics and Applied Mathematics, Columbia Uni-
versity, New York, NY 10027, USA.
*To whom correspondence should be addressed. E-mail:
sb2896@columbia.edu
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among symmetry-equivalent displaced sites sim-
ilar to the Ti in the high-temperature phases of
BaTiO
3
(14). Although the PDF does not yield
information directly on the dynamics, it is likely
that the local dipole moments are fluctuating
between the symmetry equivalent displaced sites.
Further confirmation of this unexpected result
has been obtained by modeling the PDF using a
least-squares fitting procedure (11). In Fig. 2A, the
reduced c
2
(goodness of fit) values of a number
of competing models are shown as a function of
temperature. Undistorted models give the best
agreement at low temperature, but above 100 K
distorted models give better agreement, with a
model including displacements along 〈100〉crys-
tallographic directions being clearly preferred.
In Fig. 2, B and C, we show the Tdependence
of Pb isotropic atomic displacement parame-
ters (ADPs) and the lattice parameter, respec-
tively, refined from the simplest undistorted
model. In this model, any off-centering must be
accommodated in the refined ADP. The tem-
perature dependence of both lattice parameters
and the ADPs are linear, as expected, in the high-
temperature region. In contrast, both properties
show a downward deviation from this linear
behavior below room temperature, precisely in
the region where the PDF peak asymmetry is
changing. This cannot be explained in any har-
monic or quasiharmonic model for the lattice
dynamics, such as the Debye model (16), shown
as solid lines in the figure. The combined temper-
ature dependences of the PDF peak asymmetry
and the ADPs suggest that local ferroelectric-
like Pb
2+
off-center displacements, absent at T=
0 K, gradually emerge over the temperature range
up to 250 K. At higher temperatures, the dis-
placed ions show more conventional dynamics,
resulting in a linear ADP and lattice expansion.
The amplitude of the Pb
2+
ion off-centering dis-
tortion, refined in the favored 〈100〉-displacements
model, is shown in Fig. 2E. The refined distor-
tion saturates at a maximum value of 0.24 Å.
This is comparable in magnitude to ferroelectric
displacements in, for example, BaTiO
3
(2). The
vicinity of a ferroelectric instability is also im-
plicated in first-principles electronic structure
calculations (7), including our recently devel-
oped self-consistent ab initio lattice dynamical
(SCAILD) method (17), as evident in fig. S3 (11).
Although the behavior observed in the PDF
is highly unusual—we know of no other obser-
vation of local dipoles emerging from an un-
distorted ground state on heating—we rationalize
it using a simple thermodynamic argument. In
Fig. 3A, we plot the familiar schematic of the
thermodynamic free energy, F,versustemper-
ature for a series of phases.
The curves slope downward with increasing
temperature, T, due to the increased contribution
of the entropy term in the free energy at higher
temperature: F=U−TS,whereUis the internal
energy. Phases with higher entropies, S, slope
down more steeply and may cross below phases,
with lower internal energy becoming the stable
phase at high temperature. This is the classic
explanation of the solid-liquid phase transition.
In Fig. 3A, we represent the free energy of an
ordered ferroelectric phase as a light blue line
and that of the disordered paraelectric phase in
olive green. In the absence of competing phases,
the ferroelectric phase transition occurs at T
F
,where
these lines cross as indicated in the figure. Above
T
F
, the stable state is the paraelectric phase.
Another metastable state may exist that is
undistorted but has a higher internal energy
than the distorted phase. This is represented as
a dashed gray line in Fig. 3B. Its configurational
entropy should be the same as the ordered ferro-
electric phase (light blue curve), so in the sche-
matic we give these a similar slope, although
factors such as vibrational entropy differences
will change this somewhat in practice. Because
it is higher in energy and has a similar slope,
the free energy of this phase never crosses the
ferroelectric phase, and it is never the stable
state. However, consider the special situation in
which this competing undistorted state is very
close but slightly lower in energy than the fer-
roelectric state at T= 0. This situation is de-
picted as the red line in the figure. In this case,
A
C
FG
H
I
E
BD
Fig. 1. (A) The rock-salt structure of PbTe with various interatomic distances color coded and (B)the
respective PDF peaks marked with arrows using the samecolorcodetoillustratehowthePDFisbuiltup
from atom-pair distances in the structure. (C) Experimental total scattering structure function F(Q)atT=
15 K (blue) and T= 500 K (red), with the corresponding PDFs (open symbols) shown in (D)and(E). The
PDF of the rock-salt structure model is superimposed as a solid red line, with the difference curve (green)
offset for clarity. (F) A stack of experimental PDFs from 15 K (blue) to 500 K (red) in ~50 K increments.
The 150 K data set is highlighted in green, and the 300 K data are in purple. The inset focuses on the
behavior of the nearest-neighbor PDF peak. (G) Fit of the rock-salt crystallographic model to the near-
neighbor PDF peak data at 15 K and (H)at500K.(I) Asymmetry of the near-neighbor PDF peak.
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the ground state is undistorted, but on warming
the stable state becomes the paraelectric phase,
and local fluctuating dipoles emerge out of an
undistorted ground state. This crossover is in-
dicated by T
E
in the figure. These thermodynamic
arguments do not explain the phenomenon, but
they give an intuitive rationalization for this be-
havior and suggest that it may be more wide-
spread than in the PbQ compounds studied here.
The thermodynamic arguments do not ad-
dress the microscopic mechanisms that could
give rise to this situation, nor do they address the
precise nature of the transition from the undis-
torted to the paraelectric phase, that is, whether
it is an abrupt transition or a diffuse crossover.
The short-range nature of the dipole fluctuations
suggests the latter, although characterizing this
will require further study. Although there is no
change in crystal symmetry, so it is not possible
to identify a macroscopic order parameter, there
is evidence for the transition in a macroscopic
structural parameter: An anomaly is evident in
the temperature dependence of the lattice param-
eter (Fig. 2B), which shows a similar negative
deviation from linear behavior at 250 K.
The structural effects we report should be
considered in future explanations of the peculiar
properties of these materials; for example, the
very low lattice thermal conductivity (18)atele-
vated temperatures. The ferroelectric-like moment
fluctuations would also explain the well-known
strong temperature dependence of carrier scatter-
ing, which is unique in PbQ and not found in
other semiconductors such as Si, Ge, and Bi
2
Te
3
.
This dependence causes the rapid degradation
of carrier mobility with rising temperature with
aT
−2.5
dependence (19). Generally, the power
exponent for the mobility in semiconductors is
~T
−1.5
, and it is due to the increase in vibrational
amplitude of the lattice. The high power expo-
nent in PbQ implies additional scattering mech-
anisms for the carriers that would come from
the local off-centering fluctuations of the Pb
2+
ions. Similarly, our electronic structure calcu-
lations (11) find an enhanced band gap for the
locally distorted structure, indicating that the
observed anomalous increase in the band gap,
E
g
, with increasing temperature observed in
PbTe (20), may be explained by the appearance
of the local distortions.
The emergence of structural dipoles from
normal, undistorted states in materials may be
more ubiquitous than currently recognized. There
are some similarities of the present situation to
the search for a hidden broken symmetry in the
pseudogap phase of high-temperature supercon-
ductors, where a short-range nematic orbital or-
dering may be relevant but is only apparent in
probes of local structure (21). The PDF is a
powerful experimental tool for probing these
effects. Finally, we may now begin to contemplate
new ways to control these fluctuations through
appropriate chemical modifications that could
lead to large increases in the thermoelectric per-
formance of PbTe-based materials. We suggest in
particular that new thermoelectrics should be
sought among materials that, like PbTe, are close
to a ferroelectric instability. It is remarkable that
binary compounds with such simple structures,
which have been known about and exploited for
thousands of years, can still harbor surprises
when studied using modern experimental and
theoretical tools.
References and Notes
1. F. Jona, G. Shirane, Ferroelectric Crystals (Dover,
New York, 1993).
2. G. H. Kwei, A. C. Lawson, S. J. L. Billinge, S.-W. Cheong,
J. Phys. Chem. 97, 2368 (1993).
3. P. Walter et al., Nano Lett. 6, 2215 (2006).
Fig. 2. (A) Reduced c
2
of best fits for competing models of the local structure (11). (B)Thegraydots
are the isotropic ADPs for Pb refined from the undistortedmodel.Thesolidlinesrepresentthebehavior
expected from the Debye model, using the same Debye temperature, but with different offset param-
eters, accounting for static disorder, for the red and blue lines. (C) The PbTe lattice parameter (gray dots)
as obtained from Rietveld refinement. The vertical dashed line indicates the temperature 250 K where
the asymmetry of the nearest-neighbor peak saturates (Fig. 1I). (D) Schematic of the rock-salt structure
showninprojectiondownthecaxis, showing Pb (blue) and Te (red). (E) Same view of the proposed model
for the distorted rock-salt structure above room temperature. The amplitude of the Pb displacements have
been highly exaggerated to show the displacements more clearly. (F) Amplitude of Pb local off-centering
refined from the 〈100〉displaced model.
AB
Fig. 3. Schematics of the temperature dependence of the thermodynamic free energy F.(A)Thelight
blue curve represents F(T) for a ferroelectric state with ordered dipole moments (shown schematically as
blue arrows), and the olive green curve is for the paraelectric state where the dipoles are fluctuating
and only short-range ordered at best. It is more steeply sloping because of the extra configurational
entropy. Where these curves cross is the ferroelectric transition temperature, labeled T
F
. The blue arrows
show schematically the ordered dipole moments in the ferroelectric phase and disordered moments in
the paraelectric phase. (B) As in (A) but superimposed are additional free-energy curves for putative
undistorted states. The gray dashed curve represents F(T) for a metastable undistorted state. The red
curve shows the case where the competing undistorted state is slightly lower in energy than the ferro-
electric state. In this case, there is a crossover from an undistorted to a paraelectric phase at a tem-
perature T
E
, as shown schematically. In the insets, the blue dots indicate the absence of dipoles at low
temperatureandthebluearrowsthedisorderedfluctuatingdipolesathightemperature.
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and enthusiasm for the project and dedicate the paper
to him. We acknowledge useful discussions with A. Millis,
P. Allen, R. Cohen, C. Farrow, and J. Hill. Work in the
Billinge group was supported by the U.S. Department
of Energy, Office of Basic Energy Sciences (DOE-BES),
under contract DE-AC02-98CH10886. Work in the
Kanatzidis group was supported by the Office of Naval
Research. Work in the Spaldin group was supported by
the NSF under award DMR-0940420. The neutron
diffraction measurements were carried out at the Lujan
Center at Los Alamos National Laboratory, and the x-ray
experiments were carried out at the Advanced Photon
Source, Argonne National Laboratory, both of which
are supported by DOE-BES, and the calculations were
performed at the San Diego Supercomputer Center,
which is supported by NSF.
Supporting Online Material
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Materials and Methods
SOM Text
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24 May 2010; accepted 16 November 2010
10.1126/science.1192759
Large Variations in Southern
Hemisphere Biomass Burning
During the Last 650 Years
Z. Wang,
1
J. Chappellaz,
2
K. Park,
1
J. E. Mak
1
*
We present a 650-year Antarctic ice core record of concentration and isotopic ratios (d
13
C and
d
18
O) of atmospheric carbon monoxide. Concentrations decreased by ~25% (14 parts per billion
by volume) from the mid-1300s to the 1600s then recovered completely by the late 1800s. d
13
C
and d
18
O decreased by about 2 and 4 per mil (‰), respectively, from the mid-1300s to the 1600s
then increased by about 2.5 and 4‰by the late 1800s. These observations and isotope mass
balance model results imply that large variations in the degree of biomass burning in the Southern
Hemisphere occurred during the last 650 years, with a decrease by about 50% in the 1600s, an
increase of about 100% by the late 1800s, and another decrease by about 70% from the late
1800s to present day.
Carbon monoxide (CO) plays a key role in
the chemistry of the troposphere, largely
determining the oxidation potential of the
atmosphere through its interaction with hydroxyl
radical (OH). CO also interacts with atmospheric
methane, a gas whose preindustrial variability is
the topic of continuing debate (1,2). Little is
known about the variability of CO before the
industrial age (3) or about the anthropogenic im-
pact on its budget, although both affect atmospheric
CH
4
and O
3
budgets and related climate-chemistry
interactions.
The main sources of atmospheric CO include
atmospheric oxidation of methane and nonmethane
hydrocarbons (NMHCs), biomass burning, and fos-
sil fuel combustion (4). These sources account
for about 90% of today’s global CO budget (4).
Stable isotopic ratios (d
13
Candd
18
O) in atmo-
spheric CO help to resolve the relative contribu-
tions of these sources and thus to better estimate
the global CO budget (5). To date, no isotopic ratios
from CO in ice have been reported, and few CO
mixing ratio measurements have been reported
(1,3,6). Through use of a recently developed ana-
lytical technique (7), we present measurements of
CO concentration ([CO]), d
13
C, and d
18
O from a
South Pole ice core [89°57'S 17°36'W; 2800 m
above sea level (asl)] and from the D47 ice core
(67°23'S 154°03'E; 1550 m asl) in Antarctica (Fig. 1).
The combined changes in [CO], d
13
C, and d
18
O
during the past 650 years should reflect variations
in both total CO flux and a shift in relative source
strengths over time. [CO] shows a decreasing trend
from 53 T5 parts per billion by volume (ppbv) in
the mid-1300s to a minimum of 38 T5ppbvinthe
1600s. CO mixing ratio then increases to a rel-
atively constant value of 55 T5ppbvinthelate
1800s. Good agreement was observed between
our [CO] data and previous measurements on
Antarctic ice samples (3,6). Trends in both d
13
C
and d
18
O look similar to the [CO] record up to the
late 1800s. d
13
C [Vienna Pee Dee belemnite
(VPDB)] and d
18
O [Vienna standard mean ocean
water (VSMOW)], respectively, decreased from
–28.0 T0.3‰and 0.6 T0.7‰in the mid-1300s
to –30.2 T0.3‰and –3.4 T0.7‰in the 1600s,
then increased to –27.4 T0.3‰and 0.8 T0.7‰
by the late 1800s. Minimum values of [CO], d
13
C,
and d
18
O roughly coincide with the Little Ice Age
(LIA; circa 1500–1800), as defined in the North-
ern Hemisphere.
Observations from Berkner Island (79°32.90'S
45°40.7'W; 890 m asl) firn and present day sam-
ples are also shown in Fig. 1. The slight decrease
of [CO] from the late 1800s to present day is thus
accompanied by large shifts in both d
13
Candd
18
O,
which is a result of variations in relative source
strengths during the past century. In particular,
methane-derived CO, which is dependent upon
methane concentration and depleted in both d
13
C
and d
18
O, increased dramatically—by 13 ppbv—
during this time (Fig. 2). Because there was
little difference in overall [CO] between the late
1800s and present day, contributions from other
CO sources must have decreased by a similar
amount. Data from Berkner Island firn air show
an increase in [CO] and a decrease in d
13
Csince
1970 (8), reflecting the increase in atmospheric
methane (9).
The contribution from fossil fuel combustion
is negligible before the 1900s according to his-
toric CO
2
emissions data (10). In addition, simu-
lations from the Model for Ozone and Related
chemical Tracers (MOZART-4) (11)showthe
fossil fuel combustion contribution to today’sCO
budget in Antarctica is only 2 to 3 ppbv. Thus, the
main sources of CO able to explain our signals are
biomass burning and NMHC oxidation.
We can use isotopic compositions to help dis-
tinguish combustion-derived CO (such as bio-
mass burning) from noncombustion-derived CO
(such as hydrocarbon oxidation). C
18
O is a useful
tracer for this because of large differences in the
oxygen isotopic composition between combus-
tion and noncombustion sources of CO (12). The
d
18
O signature from combustion sources is sig-
nificantly enriched as compared with the d
18
O
signature from hydrocarbon oxidation processes
(12,13). The d
18
O value for biomass burning–
derived CO is generally between 15 and 22‰,de-
pending on specific combustion conditions (13–15).
We used an isotope mass balance model to es-
timate the ratio of combustion to noncombustion
1
Institute for Terrestrial and Planetary Atmospheres/School of
Marine and Atmospheric Sciences, Stony Brook University,
Stony Brook, NY 11794–5000, USA.
2
Laboratoire de Glaciologie
et Géophysique de l’Environnement (LGGE), CNRS, University of
Grenoble, BP 96, 38402 St. Martin d’Hères Cedex, France.
*To whom correspondence should be addressed. E-mail:
john.mak@stonybrook.edu
www.sciencemag.org SCIENCE VOL 330 17 DECEMBER 2010 1663
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