Research Interests

KEDARNATH KOLLURI AND MICHAEL J. DEMKOWICZ PHYSICAL REVIEW B 85, 205416 (2012)

one in the negative direction and the other in the positivedirection. The number of distinct end states is also listed inTable I. The rates of individual transitions are determinedusing the harmonic approximation of transition state theory(TST) due to Vineyard64 where the frequency of each transition

is given by ! = "0e! Eact

kB T . We assume "0 = 1ns!1 for all ofthe transitions in Table I, which allows us to determine thetemperature dependence of the effective migration rate, butnot the absolute value of the rate itself.

The results of our calculation are shown as the black pointsin Fig. 16(a). The gray line shows the temperature dependencethat would be expected had the effective defect migration ratebeen governed only by the highest activation energy event(Eact

eff = 0.4 eV). The migration rates obtained from kMC dipbelow this simple prediction at high temperatures, indicatingthat the multiplicity of transitions occurring in a singlemigration event reduces the overall point defect migration rate.This reduction may be represented as a temperature-dependenteffective attempt frequency.

FIG. 16. (a) Comparison between effective defect migrationrates computed using kMC (black dots), a standard Arrhenius-typeequation using only the highest activation energy event (Eact

eff =0.4 eV, gray line), and the modified rate expression in Eq. (8) with atemperature-dependent prefactor (black line). (b) Fits of the modifiedrate expression to MD data (gray dots). Temperatures are plotted onan inverse scale.

To better understand the origin of this temperature de-pendence, we revisit harmonic TST.64 In this formalism, theinitial state (A) is separated from the final state by a uniquehypersurface (S) and the escape rate ! is given by

! =!

kBT

2#

"Se! ES

kB T dS"A

e! EA

kB T dA. (2)

Here, the numerator is the configurational partition functionof the saddle-point hypersurface, while the denominator isthe configurational partition function of the hyperspace (A)corresponding to the initial state. For a system with N degreesof freedom, the energy surfaces near the saddle point and initialstates may be approximated with Taylor expansions in phasespace, parametrized through modal coordinates qj and q "

j :

EA # E(A) +N#

j=1

12

(2#"j )2q2j , (3)

ES # E(S) +N!1#

j=1

12

(2#" "j )2q "2

j . (4)

"j and " "j are normal mode vibration frequencies about

the initial and the saddle points, respectively. The normalmode perpendicular to the saddle-point hypersurface has animaginary vibration frequency and is not part of the sum inEq. (4). Therefore, only N ! 1 degrees of freedom are takeninto account when computing the configurational partitionfunction for the saddle point.

When energies are expressed as in Eqs. (3) and (4), theconfigurational integrals in Eq. (2) become

! =

$

%&!

kBT

2#

'N!1j=1

1" "j

(kBT2#

'Nj=1

1"j

(kBT2#

)

*+e! E(S)

kB T

e! E(A)

kB T

. (5)

The terms in parentheses on the right-hand side of Eq. (5)together form the effective attempt frequency "o. Simplifyingthis expression, the attempt frequency is found to be indepen-dent of temperature:

! =

'N!1j=1

1" "j'N

j=11"j

e! E(S)!E(A)

kB T = "0e! Eact

kB T . (6)

This expression is only valid if the saddle-point configurationpartition function has just one degree of freedom less than theinitial state. In some cases, however, there may be additionalmodes that do not contribute temperature-dependent terms tothe configurational partition function, for example, when thesaddle point contains rotations or translations not present in theinitial state. Buttiker and Christen suggested that in some suchcases, the integration across the saddle cannot be treated by aGaussian approximation, as in the usual case where the saddlehas positive curvatures in all directions not along the MEP.Instead, the flatness of a saddle point in one direction can bemodeled as a “translational” degree of freedom accessible tothe system at the saddle point.65 A similar interpretation maybe applied in this work. Abstracting away from the detailedMEPs illustrated in Fig. 9, all the intermediate states in the

205416-10










! =!

kBT

2#

"Se! ES

kB T dS"A

e! EA

kB T dA. (2)


j :

EA # E(A) +N#

j=1

12

(2#"j )2q2j , (3)

ES # E(S) +N!1#

j=1

12

(2#" "j )2q "2

j . (4)




! =

$

%&!

kBT

2#

'N!1j=1

1" "j

(kBT2#

'Nj=1

1"j

(kBT2#

)

*+e! E(S)

kB T

e! E(A)

kB T

. (5)


! =

'N!1j=1

1" "j'N

j=11"j

e! E(S)!E(A)

kB T = "0e! Eact

kB T . (6)


205416-10










! =!

kBT

2#

"Se! ES

kB T dS"A

e! EA

kB T dA. (2)


j :

EA # E(A) +N#

j=1

12

(2#"j )2q2j , (3)

ES # E(S) +N!1#

j=1

12

(2#" "j )2q "2

j . (4)




! =

$

%&!

kBT

2#

'N!1j=1

1" "j

(kBT2#

'Nj=1

1"j

(kBT2#

)

*+e! E(S)

kB T

e! E(A)

kB T

. (5)


! =

'N!1j=1

1" "j'N

j=11"j

e! E(S)!E(A)

kB T = "0e! Eact

kB T . (6)


205416-10

Enabling designer materials using computational sciencesKedarnath Kolluri, Ph.D. UMass, Amherst

Los Alamos National Lab, NM 87545

This material is based upon work supported as part of the Center for Materials at Irradiation and Mechanical Extremes, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number 2008LANL1026.

Bottom line• Designer materials exhibit very rich phenomena

• But the design space is large

• We will identify most promising sub-space using computational sciences

Enhanced properties by tuning materials structure

Design space is huge for interfaces and particles

For example,

• Particle shape controls upconversion emission spectra

• Nanostructured ceramics conduct colossal amount of oxygen ions

• Internal interfaces trap and remove radiation-induced defects

Structure-transport relationships

Cu-Nb KS

L1

Cu-Mo KS

L2

Ea

Cu-V KS

K. Kolluri and M. J. Demkowicz, Phys. Rev. B., 82, 193404 (2010)Phys. Rev. B., 85, 205416 (2012)

! E

(eV

)s s

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

I

a 0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

b

I

Dislocation model

AtomisticsPoint defect MEP in CuNb

Transition between structures

B CC’

B’

A’

Fo

rma

tio

n e

ne

rgy (

eV

)

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

-4 -2 0 2 4 6 8 10

Energ

y (

eV

)

Ag-V NW

Cu-Nb KS

Cu-Mo KS

Size of point defect cluster at an MDI

A

Experience and expertise

Acknowledgments: UMass : Dimitrios Maroudas, Lakis Mountziaris, Rauf GungorMIT : Michael DemkowiczLANL : Blas Uberuaga, Amit Misra, John Hirth, Richard Hoagland

Proposed researchSuperionic conductors for solid oxide fuel cells

Current: Bulk electrolyte Future: Nano-structured electrolyte

Oxygen Fuel

e-

source Cathode

Anode

e-e-O2- Electrolyte

O2-O2-O2-O2-O2-O2-O2-O2-

e-e-e-e-e-e-e-e-e-e-e-e-e-e-

O2-

O2-

O2-

Cathode

AnodeOxygen Fuel

e-

source

e-e-O2- Electrolyte

O2-O2-O2-O2-O2-O2-O2-

e-e-e-e-e-e-e-e-e-e-e-e-e-e- O2- O2- O2-

O2- O2- O2-

O2- O2- O2-

O2- O2- O2-

O2- O2- O2-

O2- O2- O2-

O2- O2- O2-

O2- O2- O2-

O2- O2- O2-

High-capacity anodes for batteries

Nano-structured materials for nuclear reactors

Collision cascade (picoseconds)

Defect kinetics(up to several years)

trolyte material. So far, yttria-stabilized zirconia(Y2O3)x(ZrO2)1–x (YSZ) is the material mostlyused in SOFCs because of its mechanical sta-bility, chemical compatibility with electrodes, andhigh oxygen ionic conductivity. It is well knownthat doping ZrO2 with Y2O3 stabilizes the cubicfluorite structure of ZrO2 at room temperature andsupplies the oxygen vacancies responsible forthe ionic conduction, resulting in high valuesof the oxygen conductivity at high temperatures(5–7). Amaximumvalue of 0.1 S/cm (where 1 S =1 A/V) at 1000°C is observed for the 8 to 9 molepercent (mol %) yttria content (2–4). A severedrawback toward the final implementation ofSOFCs is the relatively low room temperatureionic conductivity of this material, which imposesrather high operational temperatures around 800°C(1–4). The search for alternative electrolytes hasnot yet been successful in reaching the conduc-tivity value of 0.01 S/cm desired for room tem-perature operation (1–4).

Only modest reductions in the operationtemperature of SOFCs (500° to 700°C) can beanticipated with the recently proposed optimizedelectrolytes such as gadolinia-doped ceria andlanthanum gallates (8–11). On the other hand, theone to two orders of magnitude increase of theelectrical conductivity reported (12–14) in nano-crystalline samples as compared with single crys-tals outlines the importance of processing as analternative route to increasing conductivity valuestoward the desired levels. Because modern thinfilm growth techniques allow a precise control oflayer thickness and morphology, they provide apathway for the production of solid electrolyteswith optimized properties. Maier et al. found asubstantial increase of the dc ionic conductivityof superlattices of CaF2 and BaF2 when thethickness of the individual layers was decreaseddown to 16 nm, assigned to a size effect due tothe space charge regions being smaller than thelayer thickness (15, 16). Kosacki et al. havereported enhanced conductivity in highly tex-tured thin films of YSZwith thicknesses between60 and 15 nm, reaching 0.6 S/cm at 800°C (17).Because reducing film thickness (and thereforeincreasing the fraction of material near the in-terface) produces such a noticeable conductivityenhancement, the interfaces themselves wouldseem to play a determining role in the outstand-ing conductivity properties observed.

To search for interface effects, we fabricatedheterostructures where YSZ layers (with 8 mol %nominal yttria content) in the thickness range from62 nm down to 1 nm were sandwiched betweentwo 10-nm-thick layers of insulating SrTiO3 (STO).Also, superlattices were grown, alternating 10-nm-

thick STO films with YSZ layers with thicknessbetween 62 and 1 nm (18). Figure 1A displays alow-magnification (inset) and a high-resolutionannular dark field (or Z-contrast) image of a[YSZ1nm/STO10nm]9 superlattice (with ninerepeats), showing the excellent crystalline qualityof the sample. The layers appear continuous andflat over long lateral distances (a few microns).The interfaces between the STO and the YSZare seen to be atomically flat. From the high-magnification image it is possible to count thenumber of unit cells of STO and YSZ, nomi-nally 25 of STO and 2 of YSZ. Most impor-tantly, the YSZ is perfectly coherent with theSTO, in agreement with x-ray diffraction (XRD)results (fig. S1), meaning that the ultrathin layerof YSZ grows rotated by 45° around the c axisand strains to match the STO lattice. Because thebulk lattice constants of STO and YSZ are

0.3905 (19) and 0.514 nm (20), respectively, theepitaxial growth of the YSZ on top of the STOensures a large, expansive strain in the thin YSZlayers of 7% in the ab plane. Increasing the thick-ness of YSZ (for constant STO thickness) resultsin a loss of structural coherence, as reflected by areduction of superlattice satellites in XRD. Elec-tron microscopy observations confirm that therelease of strain results in a granular morphology,although the growth remains textured.

We plotted the lateral electrical conductivity(real part s!) of the thinnest YSZ trilayer versusfrequency in a double logarithmic plot (Fig. 2).The characteristic electrical response of ionic con-ductors (21–23) is observed in the figure. The longrange or sdc ionic conductivity of the material isobtained from the plateau found in s! versusfrequency plots. In the presence of blocking effectsdue to grain boundaries or electrodes, a further

1Grupo de Física de Materiales Complejos, UniversidadComplutense de Madrid, Madrid 28040, Spain. 2MaterialsScience and Technology Division, Oak Ridge NationalLaboratory, Oak Ridge, TN 37831, USA. 3Escuela TécnicaSuperior de Ingenieros de Telecomunicaciones, Universi-dad Politécnica de Madrid, Madrid 28040, Spain.

*To whom correspondence should be addressed. E-mail:[email protected]

Fig. 1. (A) Z-contrast scanning transmission electron microscopy (STEM) image of the STO/YSZ interface ofthe [YSZ1nm/STO10nm]9 superlattice (with nine repeats), obtained in the VG Microscopes HB603Umicroscope. A yellow arrow marks the position of the YSZ layer. (Inset) Low-magnification image obtainedin the VGMicroscopes HB501UX column. In both cases a white arrow indicates the growth direction. (B) EELspectra showing the O K edge obtained from the STO unit cell at the interface plane (red circles) and 4.5 nminto the STO layer (black squares). (Inset) Ti L2,3 edges for the same positions, same color code. All spectraare the result of averaging four individual spectra at these positions, with an acquisition time of 3 s each.

Fig. 2. Real part of the lateralelectrical conductivity versus fre-quency of the trilayer with 1-nm-thick YSZ in a double log plot.Isotherms were measured in therange of 357 to 531 K. The solidline represents a NCL contribution(s! ~ Aw, where A is a temperature-dependent proportionality factorand w is the angular frequency),as explained in the text. Stars iden-tify the value of sdc. The uncertain-ty of conductance measurements is1 nS (10!2 S/cm in conductivity forthe sample shown, see error bar).(Inset) Imaginary versus real partof the impedance (Nyquist) plots at492, 511, and 531 K. Whereas thehigh-frequency contribution is a Debye-like process characterized by a conductivity exponent n = 0, the“grain boundary” term observed in the Nyquist plots shows a clear deviation from a Debye behavior, asreflected by the distorted impedance arcs.

www.sciencemag.org SCIENCE VOL 321 1 AUGUST 2008 677

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decrease of s! (below bulk sdc values) may occurtoward lower frequencies. For clarity, the value ofsdc has been identified by using stars. The sdcvalue is found to be thermally activated, so whenthe temperature is reduced the conductivity curvesshift downwards in Fig. 2. The inset in Fig. 2displays Nyquist plots for the same sample. Todetermine the nature of the charge carriers, wemeasured the conductance of the samples bymeans of dc measurements. As can be observed infig. S2, the dc conductance (open circles) is threeto four orders of magnitude lower than the valuesobtained from ac measurements (solid squares) inthe entire temperature measurement range. Thisresult indicates that the electronic contribution tothe ac measurements can be considered negligi-ble, and thus, the measured ac transport isattributable to an ionic diffusion process.

In Fig. 3, the temperature dependence of thesdc of [STO10nm/YSZXnm/STO10nm] trilayers isshown together with data corresponding to a singlecrystal and the 700-nm thin film from (7). Whereasthe “bulklike” samples (the thin film and the singlecrystal) show the well-known Arrhenius behaviorwith an activation energy of ~1.1 eV, the trilayersshow much larger conductivity values and smallervalues of the activation energy. The thickest trilayer(62-nm YSZ) already shows an increase of abouttwo orders of magnitude in the high-temperature dcconductivity, and the dc activation energy decreasesto 0.72 eV. When decreasing the thickness of theYSZ layer to 30 nm, the dc conductivity increasesanother three orders of magnitude, and the activa-tion energy decreases to 0.6 eV. The high values ofthe pre-exponential factor of ~107 (ohm·cm)!1 arecomparable to those found in other ion conductors(24) [see supporting onlinematerial (SOM) text]. Ifthe thickness is further reduced all the way downto 1 nm (two unit cells of YSZ), the conductivityis observed to increase as the inverse of the YSZlayer thickness, but the conductance is essentiallythickness-independent (bottom inset in Fig. 3).We can think of three parallel conduction pathsdue to the interfaces and the bulk YSZ and STOlayers. The bulk conductivity of YSZ is 10!7 S/cmat 500 K, which would yield a conductance valueof ~10!14 S for 1-nm-thick layers. This value ismuch lower than the 10!6 S value measured withthe ac technique. If we instead assume that the highconductance (G = 10!6 S) is due to electronicconduction in the STO, both ac and dc techniqueswould provide this same value, contrary to what isobserved (fig. S2).Moreover, reported conductivityvalues in STO thin films (25) are also much lowerthan those necessary to explain the high conduct-ance observed. Because bulk YSZ or STO contri-butions can be ruled out, an interface conductionmechanism is inferred.

To further test this scenario, we grew super-lattices repeating the [YSZ1nm/STO10nm] growthunit. We found (top inset in Fig. 3) that con-ductance scales nowwith the number of interfacesup to a number of eight (four bilayer repetitions).There is a scaling breakdown in the figure, ob-served for a larger number of bilayer repetitions,

most likely resulting from disorder building up inthis highly strained structure. The experimentaldata indicates that the first STO/YSZ interfacedoes not contribute to the large ionic conductivityobserved in the samples, probably because the firstSTO layer is somehow different from the others asit is grown directly on the substrate. This scaling,together with the invariance of the conductancewith the thickness of the YSZ, shows that the largeconductivity values in these heterostructures orig-

inate truly at the interfaces between YSZ and STO.Our results indicate a superposition of two parallelcontributions—one due to the bulk and one at-tributable to the interface—and the colossal ionicconductivity is observed as long as the interfaceconductance is larger than that of the bulk. Theabrupt conductivity decrease when the thicknesschanges from 30 to 62 nm is most likely due to adegraded interface structure when the YSZ layersexceed the critical thickness.

Fig. 3. Dependence of the logarithm of thelong-range ionic conductivity of the trilayersSTO/YSZ/STO versus inverse temperature. Thethickness range of the YSZ layer is 1 to 62 nm.Also included are the data of a single crystal(sc) of YSZ and a thin film (tf) 700 nm thick[taken from (7)] with the same nominalcomposition. (Top inset) 400 K conductanceof [YSZ1nm/STO10nm](ni/2) superlattices as afunction of the number of interfaces, ni.(Bottom inset) Dependence of the conduct-ance of [STO10nm/YSZXnm/STO10nm] trilayers at500 K on YSZ layer thickness. Error bars areaccording to a 1 nS uncertainty of the con-ductance measurement.

Fig. 4. (A) EELS chemical maps. The ADF image in the upper panel shows the area used for EELSmapping(spectrum image, marked with a green rectangle) in the [YSZ1nm/STO10nm]9 superlattice. The middle panelshows the averaged ADF signal acquired simultaneously with the EEL spectrum image, showing the STO(low-intensity regions) and YSZ (higher-intensity) layers. The lower panel shows the Ti (red) and Sr (darkyellow) EELS line traces across several consecutive interfaces. These line traces are averaged from theelemental 2D images shown in the insets, each framed with the same color code (red for Ti, dark yellow forSr). Data was obtained in the VG Microscopes HB501UX. Because the STEM specimen was relatively thick(several tens of nanometers), the wide chemical interface profiles are most likely attributable to beambroadening. (B) Solid spheres model of the YSZ/STO interface showing: (1) The compatibility of theperovskite and fluorite (rotated) structures. (2) A side view of the interface between STO (at the bottom)and YSZ (on top) with realistic ionic radius. The shaded oxygen positions in the interface plane arepresumed absent or displaced because of volume constraints, enabling the high ionic conductivity. (3) A3D view of the interface, with the ionic radius reduced by half to better visualize the plane of oxygenvacancies introduced in the interface. The square symbol in the legend indicates the empty positionsavailable for oxygen ions at the interface.

1 AUGUST 2008 VOL 321 SCIENCE www.sciencemag.org678

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J. Garcia-Barriocanal et. al., Science, 321, 676 (2008)

Xingchen Ye et. al., PNAS, 107, 22430 (2010)

temperature by 33 keV He+ ions with a dose of 6 · 1016/cm2 (referred to as case 2 hereafter), whereas annealed1 mm thick Cu sheet, Cu 2.5 nm/Nb 2.5 nm (referred toas Cu/Nb 2.5 nm hereafter) and Cu/Nb 100 nm multilayerswith a total film thickness of around 500–600 nm wereimplanted by 150 keV He+ ions with a dose of 1 · 1017/cm2 (referred to as case 3 hereafter). Evolution of micro-structures before and after ion-irradiation was examinedby cross-section transmission electron microscopy(XTEM). TEM and high-resolution TEM (HRTEM) wereperformed on a JEOL 3000F microscopes operated at300 kV.

3. Results and discussions

SRIM calculation of He ion-irradiation has been per-formed on Cu/Nb multilayer films with a nominal layerthickness of 80 nm each layer. Three ion-irradiation cases

were simulated. Case 1 represents ion-irradiation experi-ments performed recently in Cu/Nb multilayers [23]. Thesimulation parameters for case 2 and 3 are used for currentexperiments. Fig. 1 shows the variation of He concentra-tion versus implantation depth. The peak He concentrationfor the first case is about three times higher than that of theother two cases. The simulation shows that implantation inthe last two cases will produce similar peak He concentra-tion. The peak He concentration occurs much deeper underfilm surface, !425 nm, at 150 keV, compared to approxi-mately 150 nm under surface for He ion-irradiated at33 keV. Implantation of the first two cases will generateHe peak concentration at similar depth under film surfacedue to the usage of same implantation energy (33 keV).

XTEM reveals radiation induced He bubbles and inter-stitial loops in Cu thin sheet irradiated in case3, as shownin Fig. 2(a). These types of defects are typical in ion-irradi-ated bulk fcc Cu. He bubbles with diameter on the order of2–3 nm were observed in 500 nm thick Cu films irradiatedin case 2, as shown in Fig. 2(b). Theoretical calculationsof contrast from cavities and gas bubbles have been carriedout by a number of researchers [24–26]. Experimentallysmall cavities and gas bubbles are easily visible with theimages slightly out of focus and under kinematical di!rac-tion conditions. Generally in an underfocus condition thecavities or gas bubbles is bright relative to backgroundand the image has a dark rim [26,27], as shown inFig. 2(b). The reverse is true of an overfocus conditionwhen the void is a dark image with a faint bright rim.For all TEM studies in this research, both underfocusand overfocus conditions have been examined, but onlyunderfocus conditions are presented in this paper. We alsoexamined the microstructure of Cu/Nb 100 nm multilayers(600 nm total film thickness) ion-irradiated in case 3, asshown in Fig. 3(a). Magnified images of two boxes inFig. 3(a) are shown in Fig. 3(b) and (c). Region 1, close

0 200 400 600 8000

4

8

12

1633keV1.5 x1017/cm2

33keV6 x1016/cm2

He

conc

entra

tion

(1021

ions

/cm

3 )

Depth (nm)

150keV1017/cm2

Fig. 1. SRIM calculations that simulate the variation of He concentrationversus irradiation depth at various irradiation conditions. Case 1: 33 keV/1.5 · 1017/cm2; case 2: 33 keV/6 · 1016/cm2; case 3: 150 keV/1017/cm2.

Fig. 2. Underfocused XTEM micrograph of bulk Cu sheet ion-irradiated with He ions of 150 keV at a dose of 1 · 1017/cm2 (a), and 33 keV with a dose of6 · 1016/cm2 (b). Vacancy clusters, interstitial loops and He bubbles were observed in (a) and mostly He bubbles with 2–3 nm in diameter were seen in (b).

1130 X. Zhang et al. / Nucl. Instr. and Meth. in Phys. Res. B 261 (2007) 1129–1132

JOM • September 200762

Research SummarySmall Scale Mechanical Behavior

Interfaces act as obstacles to slip and sinks for radiation-induced defects. Hence, nanolayered composites that contain a large volume fraction of inter-faces provide over an order of magnitude increase in strength and enhanced radia-tion damage tolerance compared to bulk materials. This paper shows the experi-mental and atomistic modeling results from a Cu-Nb nanolayered composite to highlight the roles of nanostructur-ing length scales and the response of interfaces to ion collision cascades in designing composite materials with high radiation damage tolerance.

INTRODUCTION

The performance of materials in extreme environments of irradiation and temperature must be significantly improved to extend the reliability, life-time, and efficiency of future nuclear reactors.1 In reactor environments, damage introduced in the form of radia-tion-induced defects and helium from transmutation reactions results in embrit-tlement and dimensional instability of both structural and fuel components. Therefore, the ability to remove radia-tion-induced point defects and control helium bubble nucleation and growth are crucial to improving the mechani-cal properties of irradiated metals. This challenge calls for novel approaches to designing materials that resist radiation damage while maintaining high strength and toughness. Using nanolayered metallic composites as model systems, this article highlights how tailoring the length scales (layer thickness) and inter-face properties can provide insight into the design of radiation-damage-tolerant structural materials. Chemical and morphological stability of interfaces is a necessary factor in the design of nanolayered composites where

The Radiation Damage Tolerance of Ultra-High Strength Nanolayered Composites*A. Misra, M.J. Demkowicz, X. Zhang and R.G. Hoagland

interfaces are to act as sinks for radia-tion-induced defects. Studies conducted on sputter-deposited Cu-Nb multilayers

and single-layer copper and niobium led to considerable insight into the morpho-logical stability of these nanolayered materials. Copper and niobium have a positive heat of mixing, very limited solid solubility, and no tendency to form intermetallic compounds. Thus, the interfaces between copper and nio-bium layers are atomically sharp, with no evidence of mixing. Furthermore, unlike grain boundaries in single-ele-ment polycrystals, Cu-Nb interfaces are compositionally constrained against migration. Some nanolayered materials are known to exhibit spheroidization upon thermal annealing. Similarly, radiation may destroy the geometrical arrange-ment of layered morphologies because the flow of radiation-induced point defects into an interface changes its atomic configuration, perturbing its shape from flat to meandering. Such undulations provide an opportunity for adjacent nanometer-spaced interfaces to react and pinch off. Because the stability of the layered structure relies upon the planarity of the interfaces, such reactions can destabilize the structure and trigger the onset of recrystallization. There is a competition between restoring forces acting to flatten the interface and the undulations induced by rapid adsorption of defects. Remarkably, vacuum annealing stud-ies conducted on Cu-Nb nanolayered composites revealed their thermal sta-bility with no evidence of spheroidiza-tion up to 800°C.2 This finding formed the basis for exploring the stability of nanolayered composite materials under irradiation conditions, studied by He+ implantation over a broad range of irradiation conditions and layer thicknesses.3–6 The results presented are organized to highlight the roles of

Figure 1. (a) No helium bubbles are detected in under-focused TEM image in a 2.5 nm layer thickness Cu-Nb multilayer implanted at room temperature (150 keV helium, 1 1017/cm2). Note that the layered morphology is well preserved. (b) High-resolution TEM image of a Cu-Nb interface from implanted region showing sharp interface with no detectable amorphous regions. (c) At higher doses (33 keV helium, 1.5 1017 /cm2, 5 nm Cu-Nb multilayer), 1–2 nm diameter helium bubbles are detected as bright spots in under-focused TEM images. The dotted white line represents the end of range of implanted helium.

c

b

a

A. Misra et. al., JOM, 59, 62 (2007)

X. Zhang et. al, Nucl. Inst. Meth. Phys. Res. 261 (2007)

Cathode

Anode

charge

discharge

Anode in itsdischarge state

Anode in itscharge state

Li C6

Li4.4 Si

Sandwiched Si and Li4.4+ Si

Si

nc-Si

C

Low capacity

Mechanically stable

High capacity

Mechanical nightmare

High capacity

Mechanical stability possible

Epitaxial growth of polydisperse particles

Analytical models of observed phenomena

Modifications to existing models

PROGRESS ARTICLE

A

B

C

D

E

F

G

H

Surface coverage(patchiness)

Aspect ratio

Faceting

Pattern quantization

Branching

Chemical ordering

Shape gradient

Roughness

Figure 2 Anisotropy ‘dimensions’ used to describe key anisotropy attributes of particles. Homologous series of particles as the attribute corresponding to the anisotropy axisis varied from left to right. A: Interaction patchiness via surface coverage, B: aspect ratio, C: faceting, D: interaction patchiness via surface pattern quantization, E: branching,F: chemical ordering, G: shape gradient, H: roughness. Further dimensions, such as chirality, are not shown.

we consider several of the particles in Fig. 1. The key anisotropydimension of the tetrapods in the top row is branching (axis E).However, the two tetrapods diVer in aspect ratio (axis B) becausethe tetrapod on the left (which resembles a ‘plus’ sign) may beroughly circumscribed by a disc, whereas the tetrapod on theright is circumscribed by a sphere. Thus, these two particles havedimensionality 2 in anisotropy space. Adding gold tips48 to eitherobject increases their dimensionality to 3 with the addition of axisA. The colloidal molecule at the far right of the second row isdescribed by the same two key anisotropy dimensions (E and B)and thus also has dimensionality 2. It diVers from its smoothbranched counterpart by roughness (axis H). The surfactant-striped nanoparticle at the far left of the bottom row may bedescribed as a particle of dimensionality 2 in anisotropy space,comprising axes A and D. (If the striped particle is faceted, and notspherical, then a third dimension, axis C, is needed and the particlehas dimensionality 3.)

Other cases of equivalency such as that described in Fig. 3 arepossible. One example is that of dimension C (faceting), whichcharacterizes an attribute of particle shape. As shown, axis C isapplied to a convex tetrahedron to generate the Platonic solids.This axis may be equally applied to other objects to generateother convex or convex-faceted shapes. Of course, we can considermore refined descriptions of various types of anisotropy, includingfaceting anisotropy. For truncated polyhedra or polyhedra withunequal facets, for example, further anisotropy attributes maybe needed if a higher degree of detail is desired. However, ourclaim is that a limited set of key dimensions is suYcient to allow

experiment, theory and simulation to fruitfully interact to explorethe potential for anisotropic particle design and assembly.

SEEKING DESIGN RULES FOR ASSEMBLY THROUGH ANISOTROPY

What might the future hold for assembling these new shapes,and where do the opportunities and challenges lie? By combiningvarious sets of anisotropy dimensions, the interplay among thedimensions can be studied systematically. For example (Fig. 4),combining the dimensions of material homogeneity (axis A; notshown in 3D projection), aspect ratio (axis B), faceting (axis C) andpatch quantization (axis D) allows us to tune continuously froma Janus sphere to a Janus cube to a striped irregular tetrahedron(oV-axis; not shown). Then a systematic investigation of how thesymmetries of the bulk assemblies vary as we move along eachof the axes independently would provide a wealth of informationfor materials design. Theory, simulation and experiment would allbenefit from a conceptual framework based on ‘anisotropy space’.

Ultimately, what is needed are phase diagrams able to predictthe self-assembled structures possible for building blocks ofarbitrary anisotropy. This task poses great challenges for theory,and simulation may provide key guidance for experiment andtheory for the foreseeable future. Traditionally, phase diagramsplot a thermodynamic parameter (for example, temperature)versus another thermodynamic parameter (for example, density)to indicate regions of solid, liquid and gas phases, crystalstability fields and so on. In the 1980s with the advent ofblock copolymers and liquid crystals, ‘phase diagrams’ showing a

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centration but also the surface functionalities of the UCNPs canbe an effective means of tuning the upconversion luminescence.

To demonstrate the generality of the synthesis method andfurther tailor the upconversion emissions, we try several otherdopant combinations including Yb/Tm, Yb/Ho, and Yb/Ho/Cefor the !-NaYF4-based UCNPs. TEM images of the NaYF4:Yb/Tm (22∕0.2 mol%) UCNPs with different morphologies areshown in Fig. 1B (spherical NCs), Fig. 1E (NRs), Fig. 1H (hex-agonal nanoprisms), and Fig. 1K (hexagonal nanoplates), respec-tively. Upon 980 nm excitation, these hexagonal phase UCNPs(SI Appendix: Fig. S12) emit bright blue upconversion lumines-cence arising from the trivalent thulium 1D2 !

3F4 and 1G4 !3H6 transitions (Fig. 2F). In addition, predominantly greenupconversion emissions are observed from the hexagonal phase(SI Appendix: Fig. S14) NaYF4: Yb/Ho (20∕2 mol%) NRs andnanoprisms UCNPs (Figs. 1 F and I and 2G). The intensity ratioof green to red emission from the NRs increases as the Ho3! con-centration increases from 1% to 2%, owing to the enhancedenergy transfer from the Yb3! sensitizers to adjacent Ho3! ions(37). Furthermore, trivalent Ce3! ions are introduced to modu-late the upconversion profiles of the NaYF4: Yb/Ho (20∕2 mol%)UCNPs. The parity-allowed 4f ! 5d transition in the Ce3! ionscan effectively depopulate the green-emitting 5F4∕5S2 statesof Ho3! while increasing the population of the red-emitting5F5 state of Ho3! through two cross-relaxation pathways (SIAppendix: Fig. S8): 5F4∕5S2"Ho3!# ! 2F5∕2"Ce3!# ! 5F5"Ho3!#!

2F7∕2"Ce3!# and 5I6"Ho3!# ! 2F5∕2"Ce3!# ! 5I7"Ho3!#!2F7∕2"Ce3!# (38). The as-synthesized NaYF4: Yb/Ce/Ho(20∕11∕2 mol%) spherical NCs (Fig. 1C) and hexagonal nano-plates (Fig. 1L) display predominantly red emission under980 nm excitation although the total intensity of emission is muchweaker than other UCNPs (SI Appendix: Fig. S15). Powder XRDpatterns confirm that both samples are of pure hexagonal phase(SI Appendix: Figs. S16 and S17). The systematic peak shifts tolower angles compared to the standard XRD pattern of!-NaYF4 imply the partial substitution of Y3! ions by largerCe3! ions in the !-NaYF4 lattice (Y3!, r $ 1.159 �Å; Ce3!,r $ 1.283 �Å) (39), which results in the expansion of the unit cell.This Ce3! doping differs from previous reports where lanthanideelements with large ionic radii (e.g., La3! $ 1.300 �Å) could notbe incorporated into the !-NaYF4 lattice (23). In addition,uniform undoped !-NaYF4 NRs can also be synthesized by thepresent method (SI Appendix: Fig. S19).

Superlattices composed of anisotropic NCs have attractedgreat interest due to the rich phase behaviors and the potentialfor emergent collective properties (40). Here we explore the in-triguing structural diversity of ordered nanocrystal assembliesusing !-NaYF4 NRs and the !-NaYF4-based UCNPs. We employan interfacial assembly strategy that can produce continuous anduniform nanocrystal superlattice films (41). When 15 μL of hex-ane solution of the !-NaYF4 NRs with an aspect ratio (AR) of∼1.4 is drop-cast onto the viscous and weakly polar ethylene gly-col (EG) surface and the solvent is allowed to slowly evaporate,large-area NR superlattices comprised of monolayer and double-layer domains are obtained depending on the concentration ofNRs in the dispersion (Fig. 3 A and B). The NRs preferentiallyalign with their c-axis parallel to the substrate, exhibiting bothpositional and orientation order on the scale of tens of micro-meters, as confirmed by the sharp small-angle electron diffractionpatterns (SAED). The striking in-plane ordering of the NR super-lattices is also revealed by the selected-area wide-angle electrondiffraction patterns (SAWED), whose spots are due to diffractionof crystallographic lattice planes. Specifically, the strong (002)diffraction spots are arising from the anisotropic rod-shape ofthe individual NCs and their mutual alignment along the c-axis.Interestingly, the appearance of (h00) and simultaneous absenceof (110) diffraction spots, together with the recognition that the!-NaYF4 NRs are enclosed by the f10 10g facets, allow us to con-clude that the NRs are azimuthally aligned along their f10 10gcrystal facets (SI Appendix: Fig. S22). The superlattice formationis accounted for by the in-plane, dense packing of the !-NaYF4

NRs, possessing a hexagonal cross section and also the interac-tion of ligands, contributing to the attractions between adjacentNRs. Further evidence that supports the explanation is the lateraldisplacement between neighboring layers in the !-NaYF4 NRsuperlattices (SI Appendix: Fig. S23). Liquid crystalline orderhas been observed in concentrated NR dispersions (42) andNR films prepared by controlled evaporation (43, 44) or by Lang-muir-Blodgett assembly (45). Here we have also employed polar-izing optical microscope to study the ordering of NR films.Optical micrographs (Fig. 3C and SI Appendix: Fig. S25) indicatedomains that are strongly birefringent due to the alignment ofNRs. The multidomain nature of the NR films is also confirmedby the atomic force microscopy (AFM). We anticipate that NRswith larger AR (>3) would be better suited for the formation ofliquid crystalline phases using the present assembly methodology.!-NaYF4 NRs with an AR of ∼2.0 have also been used to studythe shape-directed assembly behavior: monolayer and double-layer superlattices are obtained by depositing 15 μL of NR dis-persion (Fig. 4 A and B). However, when 40 μL of NR dispersionis used, the NRs tend to orient vertically in the film with wellcrystallized domains up to ∼200 μm2 (Fig. 4C), as seen fromthe corresponding SAWED pattern. Each domain is composedof hexagonally closed-packed perpendicularly aligned NRs

Fig. 2. Structural and optical characterization of the !-NaYF4-based UCNPs.(A) Powder XRD patterns of the NaYF4: Yb/Er (20∕2 mol%) UCNPs withdifferent shapes. The peaks are indexed according to the standard XRDpattern of !-NaYF4 (JCPDS file number: 28-1192). Insets are the correspond-ing geometrical models. (B) HRTEM image of a spherical NaYF4: Yb/Er(20∕2 mol%) UCNP. (C) HRTEM image of a NaYF4: Yb/Er (20∕2 mol%) NR.(D) HRTEM image of a NaYF4: Yb/Er (20∕2 mol%) hexagonal nanoprism.(E) HRTEM image taken from the edge of a NaYF4: Yb/Er (20∕2 mol%)hexagonal nanoplate. (F) Room temperature upconversion emission spectraof the NaYF4: Yb/Er (20∕2 mol%) and NaYF4: Yb/Tm (22∕0.2 mol%) UCNPsdispersed in hexane. Inset: Photographs of the upconversion luminescencefrom the NaYF4: Yb/Er (20∕2 mol%) (left) and NaYF4: Yb/Tm (22∕0.2 mol%)(right) NR dispsersions under 980 nm diode laser excitation. (G) Room tem-perature upconversion emission spectra of the NaYF4: Yb/Ho (20∕2 mol%)and NaYF4: Yb/Ho (20∕1 mol%) UCNPs dispersed in hexane. Inset: Photo-graphs of the upconversion luminescence from the NaYF4: Yb/Ho(20∕2 mol%) nanoprism (left), NaYF4: Yb/Ho (20∕2 mol%) NR (center) andNaYF4: Yb/Ho (20∕1 mol%) NR (right) dispersions under 980 nm diode laserexcitation.

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shapes and compositions are shown in Fig. 1. For the case ofNaYF4: Yb/Er (20∕2 mol%)-an optimized composition for effi-cient upconversion (36), the morphologies of the UCNPs canbe tuned from spherical NCs (Fig. 1A), to nanorods (NRs)(Fig. 1D), to hexagonal nanoprisms (Fig. 1G), and finally to hex-agonal nanoplates (Fig. 1J) by adjusting the reaction time and/orthe ratio of sodium to lanthanide trifluoroacetates. Powder X-raydiffraction (XRD) patterns confirm that all the NaYF4: Yb/Er(20∕2 mol%) UCNPs are of pure !-NaYF4 phase (Fig. 2A). TheXRD patterns of the spherical NCs and the NRs exhibit en-hanced (h00) as well as diminished (002) reflections whereas areversed trend is observed in the case of hexagonal nanoprismsand nanoplates. These results imply that the majority of sphericalNCs and NRs are lying with a preference for the [0001] direction(c-axis) parallel to the glass substrates used for XRD whilehexagonal nanoprisms and nanoplates are generally sitting withthe c-axis perpendicular to the substrates (similar trends are con-firmed separately by TEM). High-resolution TEM (HRTEM) im-age of a single spherical NC shows clear lattice fringes associatedwith the !10 10", !10 11", and (0001) crystal planes, respectively(Fig. 2B). Lattice fringes corresponding to the (0001) planes ap-pear along the NRs, indicating that the NRs grow along the c-axis(Fig. 2C and SI Appendix: Fig. S2A). HRTEM analysis also re-veals that the “cube-like” projections are coming from hexagonalprisms composed of six square or rectangular f10 10g side facetswith two hexagonal bases belonging to the {0001} planes (Fig. 2Dand SI Appendix: Fig. S2B). The formation of NRs and hexagonalnanoprisms is determined by a delicate interplay between thegrowth rates of {0001} and f10 10g planes at different growthstages. This observation contrasts with previous studies whereshape evolution of the !-NaYF4 NCs was dominated by control-ling the Ostwald-ripening process (35). Furthermore, dynamiclight scattering experiments that probe the hydrodynamic size ofthe dispersed NRs and hexagonal nanoprisms show results con-sistent with the largest dimensions of individual NCs measured

from the TEM images (SI Appendix: Fig. S4). In addition, quan-titative elemental analyses based on inductively coupled plasmaoptical emission spectrometry (ICP-OES) indicate the propor-tional incorporation of precursor lanthanide elements into thefinal UCNPs (SI Appendix: Table S2). By increasing the sodiumto lanthanide ratio and the reaction time, hexagonal nanoplateswith an edge length of 133# 5 nm and a thickness of 104# 8 nmare obtained (Fig. 1J and SI Appendix: Fig. S5). HRTEM imagetaken from the edge region confirms its high crystallinity(Fig. 2E). Although the present results do not rule out the pos-sibility of cubic to hexagonal (" ! !) phase transition very earlyduring the growth, no definitive signature of ! phase is observedand the high reaction temperature (∼330 °C) favors the formationof !-NaYF4 UCNPs.

The NaYF4: Yb/Er (20∕2 mol%) UCNPs exhibit intense up-conversion luminescence under 980 nm excitation (Fig. 2F andSI Appendix: Fig. S6). Three visible emission bands centered at525, 542, and 655 nm are observed, attributable to the radiativetransitions from the (2H11∕2,

4S3∕2) (green) and from the 4F9∕2(red) excited states to the 4I15∕2 ground state of Er

3$, respectively.The activator Yb3$, capable of absorbing the 980 nm near-infra-red light efficiently, transfers its energy sequentially to nearbyEr3$ through the 2F5∕2!Yb3$" ! 4I11∕2!Er3$" process, pumpingthe Er3$ to its emitting levels. The multiphonon relaxationprocesses help bridge the different excited states of Er3$, givingrise to distinct emission peaks (SI Appendix: Fig. S8). The NaYF4:Yb/Er (20∕2 mol%) UCNPs obtained display size-dependentoptical properties (Fig. 2F and SI Appendix: Fig. S9): Both thetotal intensity of emission and the intensity ratio of green to redemission increase as NCs get larger. These relationships can beascribed to the fact that as the size of the NCs decreases, surfacedefects- and ligands-induced quenching of upconversion becomemore important, which modifies the relative population amongvarious excited states through phonon-assisted nonradiativerelaxations (36). Therefore, engineering not only the dopant con-

Fig. 1. TEM images of the !-NaYF4-based UCNPs. (A, D,G, J) NaYF4: Yb/Er (20∕2 mol%) UCNPs. (B, E, H, K) NaYF4: Yb/Tm (22∕0.2 mol%) UCNPs. (F, I) NaYF4: Yb/Ho (20∕2 mol%) UCNPs. (C, L) NaYF4: Yb/Ce/Ho (20∕11∕2 mol%) UCNPs. All scale bars represent 100 nm.

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shapes and compositions are shown in Fig. 1. For the case ofNaYF4: Yb/Er (20∕2 mol%)-an optimized composition for effi-cient upconversion (36), the morphologies of the UCNPs canbe tuned from spherical NCs (Fig. 1A), to nanorods (NRs)(Fig. 1D), to hexagonal nanoprisms (Fig. 1G), and finally to hex-agonal nanoplates (Fig. 1J) by adjusting the reaction time and/orthe ratio of sodium to lanthanide trifluoroacetates. Powder X-raydiffraction (XRD) patterns confirm that all the NaYF4: Yb/Er(20∕2 mol%) UCNPs are of pure !-NaYF4 phase (Fig. 2A). TheXRD patterns of the spherical NCs and the NRs exhibit en-hanced (h00) as well as diminished (002) reflections whereas areversed trend is observed in the case of hexagonal nanoprismsand nanoplates. These results imply that the majority of sphericalNCs and NRs are lying with a preference for the [0001] direction(c-axis) parallel to the glass substrates used for XRD whilehexagonal nanoprisms and nanoplates are generally sitting withthe c-axis perpendicular to the substrates (similar trends are con-firmed separately by TEM). High-resolution TEM (HRTEM) im-age of a single spherical NC shows clear lattice fringes associatedwith the !10 10", !10 11", and (0001) crystal planes, respectively(Fig. 2B). Lattice fringes corresponding to the (0001) planes ap-pear along the NRs, indicating that the NRs grow along the c-axis(Fig. 2C and SI Appendix: Fig. S2A). HRTEM analysis also re-veals that the “cube-like” projections are coming from hexagonalprisms composed of six square or rectangular f10 10g side facetswith two hexagonal bases belonging to the {0001} planes (Fig. 2Dand SI Appendix: Fig. S2B). The formation of NRs and hexagonalnanoprisms is determined by a delicate interplay between thegrowth rates of {0001} and f10 10g planes at different growthstages. This observation contrasts with previous studies whereshape evolution of the !-NaYF4 NCs was dominated by control-ling the Ostwald-ripening process (35). Furthermore, dynamiclight scattering experiments that probe the hydrodynamic size ofthe dispersed NRs and hexagonal nanoprisms show results con-sistent with the largest dimensions of individual NCs measured

from the TEM images (SI Appendix: Fig. S4). In addition, quan-titative elemental analyses based on inductively coupled plasmaoptical emission spectrometry (ICP-OES) indicate the propor-tional incorporation of precursor lanthanide elements into thefinal UCNPs (SI Appendix: Table S2). By increasing the sodiumto lanthanide ratio and the reaction time, hexagonal nanoplateswith an edge length of 133# 5 nm and a thickness of 104# 8 nmare obtained (Fig. 1J and SI Appendix: Fig. S5). HRTEM imagetaken from the edge region confirms its high crystallinity(Fig. 2E). Although the present results do not rule out the pos-sibility of cubic to hexagonal (" ! !) phase transition very earlyduring the growth, no definitive signature of ! phase is observedand the high reaction temperature (∼330 °C) favors the formationof !-NaYF4 UCNPs.

The NaYF4: Yb/Er (20∕2 mol%) UCNPs exhibit intense up-conversion luminescence under 980 nm excitation (Fig. 2F andSI Appendix: Fig. S6). Three visible emission bands centered at525, 542, and 655 nm are observed, attributable to the radiativetransitions from the (2H11∕2,

4S3∕2) (green) and from the 4F9∕2(red) excited states to the 4I15∕2 ground state of Er

3$, respectively.The activator Yb3$, capable of absorbing the 980 nm near-infra-red light efficiently, transfers its energy sequentially to nearbyEr3$ through the 2F5∕2!Yb3$" ! 4I11∕2!Er3$" process, pumpingthe Er3$ to its emitting levels. The multiphonon relaxationprocesses help bridge the different excited states of Er3$, givingrise to distinct emission peaks (SI Appendix: Fig. S8). The NaYF4:Yb/Er (20∕2 mol%) UCNPs obtained display size-dependentoptical properties (Fig. 2F and SI Appendix: Fig. S9): Both thetotal intensity of emission and the intensity ratio of green to redemission increase as NCs get larger. These relationships can beascribed to the fact that as the size of the NCs decreases, surfacedefects- and ligands-induced quenching of upconversion becomemore important, which modifies the relative population amongvarious excited states through phonon-assisted nonradiativerelaxations (36). Therefore, engineering not only the dopant con-

Fig. 1. TEM images of the !-NaYF4-based UCNPs. (A, D,G, J) NaYF4: Yb/Er (20∕2 mol%) UCNPs. (B, E, H, K) NaYF4: Yb/Tm (22∕0.2 mol%) UCNPs. (F, I) NaYF4: Yb/Ho (20∕2 mol%) UCNPs. (C, L) NaYF4: Yb/Ce/Ho (20∕11∕2 mol%) UCNPs. All scale bars represent 100 nm.

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