4D Imaging and Diffraction Dynamics of Single-Particle Phase

Jan 6, 2014 - Physical Biology Center for Ultrafast Science and Technology, Arthur Amos ... We found that the threshold temperature for phase recovery...
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4D Imaging and Diffraction Dynamics of Single-Particle Phase Transition in Heterogeneous Ensembles Haihua Liu,† Oh-Hoon Kwon,†,§ Jau Tang,‡ and Ahmed H. Zewail*,† †

Physical Biology Center for Ultrafast Science and Technology, Arthur Amos Noyes Laboratory of Chemical Physics, California Institute of Technology, Pasadena, California 91125, United States ‡ Research Center for Applied Sciences, Academia Sinica, Taipei 11529, Taiwan S Supporting Information *

ABSTRACT: In this Letter, we introduce conical-scanning dark-field imaging in four-dimensional (4D) ultrafast electron microscopy to visualize single-particle dynamics of a polycrystalline ensemble undergoing phase transitions. Specifically, the ultrafast metal−insulator phase transition of vanadium dioxide is induced using laser excitation and followed by taking electron-pulsed, timeresolved images and diffraction patterns. The single-particle selectivity is achieved by identifying the origin of all constituent Bragg spots on Debye−Scherrer rings from the ensemble. Orientation mapping and dynamic scattering simulation of the electron diffraction patterns in the monoclinic and tetragonal phase during the transition confirm the observed behavior of Bragg spots change with time. We found that the threshold temperature for phase recovery increases with increasing particle sizes and we quantified the observation through a theoretical model developed for singleparticle phase transitions. The reported methodology of conical scanning, orientation mapping in 4D imaging promises to be powerful for heterogeneous ensemble, as it enables imaging and diffraction at a given time with a full archive of structural information for each particle, for example, size, morphology, and orientation while minimizing radiation damage to the specimen. KEYWORDS: Vanadium dioxide, metal−insulator transition, 4D ultrafast electron microscopy, orientation mapping

S

In this contribution, we report another approach for structural dynamics studies at the single-particle level by integrating conical-scanning dark-field (DF) imaging with 4DUEM. Whereas in SAED the single-particle selectivity is limited to how well a particle of interest is isolated from the rest in the ensemble through the selected-area aperture, in our reported approach we reveal the single-particle dynamics from snapshots of the polycrystalline ensemble at once. The single-particle sensitivity is achieved by identifying the origin of all constituent Bragg spots on Debye−Scherrer rings from the ensemble with the use of the conical-scanning DF imaging. In this conical scanning imaging, the pulsed electron beam is tilted and conically scanned around the optical axis so that the Bragg diffracted beam can pass through a small enough objective aperture positioned at the center of the optical axis to form a DF image9,10 of the corresponding single particles (Figure 1). Thus, the reported methodology can reveal the structural dynamics of each particle that is embedded in a heterogeneous ensemble at a given time with a full archive of structural information for the particle, for example, size, morphology, and orientation. Here, to demonstrate the spatiotemporal visualization of single-particle dynamics we investigate the phase transition of vanadium dioxide (VO2). VO2 has been reported to undergo light-induced ultrafast structural transformation from the low-

ince its invention in the 1930s, transmission electron microscopy (TEM) has been a powerful and robust platform for the structural investigation of matter with the ultimate spatial resolution of the atomic scale and with applications in the physical, chemical, and biological sciences.1−3 The recent emergence of four-dimensional ultrafast electron microscopy (4D-UEM) has defined a new paradigm that includes the ultrafast temporal resolution using timed photoelectron packets as imaging pulses with time resolution as short as femtoseconds, the time scale of atomic motions.4−6 The combined spatiotemporal resolution of 4D-UEM now enables the visualization of structural dynamics at a singleparticle level.7,8 To date, the single-particle selectivity in 4D-UEM has been realized in two different modes of operation: convergent-beam electron diffraction (CBED)7 and selected-area electron diffraction (SAED).8 In the CBED mode, short electron pulses are tightly focused and probe a small volume of the specimen at the nanometer scale. The CBED patterns with the help of dynamic scattering simulations provide the dynamics of structures involved. In the SAED mode, a pulsed parallel electron beam is used and to probe a single nanoparticle a small selected-area aperture is introduced in the image plane of an objective lens. In contrast to the CBED mode, in the SAED mode radiation sensitive (bio) chemical samples can be examined due to the spread of the electron beam, not only in reciprocal space but also in real-space imaging. © 2014 American Chemical Society

Received: November 23, 2013 Published: January 6, 2014 946

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highly correlated upon electronic excitation;12 it is accompanied by pronounced changes in electrical resistivity and optical transmittance. Because of these unique properties of VO2, many potential applications have emerged, including thermochromic coatings, information processing systems, ultrafast optical switches, and optoelectronics.14−16 The nature of the phase transition from the monoclinic to the tetragonal phase and vice versa has been extensively investigated using ultrafast optical methods.17,18 Following electronic excitation, the recording of time-resolved diffraction (both X-ray19,20 and electron pulses12,21) provides direct observation of the atomic structural arrangement involved. The ensemble-averaged observation, however, lacks singleparticle characteristics of heterogeneous constituents that bear a distribution of size, morphology, orientation, and/or defects, and the interference with supporting material and/or among themselves. In fact, the role of interconnectivity between nanoparticles has been reported to play a role in the thermally driven phase recovery of a free-standing VO2 film in 4DUEM.22 When such scrutiny at the micro (nano) scale is attained, we can better understand the fundamental function of the macroscopic behavior and advance the related technologies. Therefore, it is necessary to map the structural dynamics at the single-particle level and with the required spatiotemporal resolutions. Materials. Polycrystalline VO2 films were grown on graphene substrates via the sol−gel method.23 This method consists of spin-coating and a subsequent annealing process under Ar atmosphere. The coating solution was prepared by dissolving the precursor vanadyl acetylacetonate (99.99% purity, Sigma-Aldrich, U.S.A.) in methanol and spin-coated onto graphene substrates of Cu TEM grids (2−6 layers, Graphene Supermarket) with a spin rate of 3000 rpm for 10 s.

Figure 1. Schematic diagram of conical scanning dark-field imaging in 4D electron microscopy. In this study, time-resolved diffraction measurements were performed in the on-axis configuration for a pulsed electron imaging beam.

temperature monoclinic (insulator or semiconductor) to the high-temperature tetragonal (metal, rutile) phase.11,12 The firstorder phase transition can also be induced thermally near 340 K.13 The transition is reversible and nondestructive and is

Figure 2. Images, diffraction patterns, and orientation map obtained in our UEM. (A) UEM real-space image of vanadium dioxide. Scale bar, 300 nm. (B) Selected-area electron diffraction pattern. Scale bar, 5 nm−1. (C) Nanoparticles orientation map of the same sample area as shown in panel A with a tolerance of 2°. (D−H) Corresponding conical scanning dark-field images that come from the diffraction spot positions marked by numbers 1−5 on panel B, respectively, and their grain boundaries are sketched in panel A and are marked by a−e, respectively. 947

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Figure 3. Time-resolved bright-field images. (A,B) Snapshots of images recorded stroboscopically at two representative time delays, as indicated at the bottom right of each image, with respect to pulsed photoexcitation. Scale bar, 300 nm. (C) Image difference frame at t = 100 ns referenced to the image taken at t = −400 ns, which highlights the nanometer-scale image change with time. In the difference image, the regions of black or white indicate the contrast change, whereas the gray regions indicate no contrast change. (D) Ultrafast structural phase transition. Plotted are intensity changes of (606) (blue) and (091) (red) Bragg peaks with time, showing the two prominent time scales of femtoseconds and picoseconds during ultrafast phase transition from monoclinic to tetragonal phase; see ref 12. (E) Full phase transition dynamics of an ensemble. Shown is the time dependence of image cross correlation of the full image. A fit to a multiexponential function, corresponding to the initial, immediate, and the following recovery, is also given.

of an angle β which is the azimuthal angle. This permits us to follow a Debye−Scherrer ring of a diffraction pattern from the ensemble through a fixed small objective aperture. The diffracted beam passes through the objective aperture positioned along the main optical axis of the microscope at the back focal plane of an objective lens to form a central DF image of the corresponding particle. This procedure is repeated for a series of α depending on the lattice-spacings in a diffraction pattern. The conical-scanning DF imaging in this study was carried out at a step of 2° in the β direction along 16 different Debye− Scherrer rings in α direction to obtain DF images of good quality. The pair of (α, β) defines one reciprocal space point on the diffraction pattern from which the connection between a DF image and a diffraction pattern can be determined. The conical scanning and successive image recording were automatically controlled by a custom script in Digital Micrograph software. Finally, the obtained DF images and the diffraction patterns are numerically correlated according to crystallographic relations to reveal the origin of each Bragg spot and identify the corresponding single particle. By recording conical-scanning DF images at a wide range of sample tilt angles (±30 degree), the orientation of a particle can be reconstructed in the scheme of three-dimensional orientation mapping.25−27 The DF images were aligned and filtered in order to eliminate specimen drift and to improve the qualities of DF images. Accordingly, Figure 2C shows the orientation map of the sample area in Figure 2A in the laboratory coordinate system with the x-axis being upward and the z-axis is perpendicular to the image plane; the tilt axis is the x-axis. Different colors represent different crystallographic

The coated film was subsequently heated to 353 K on a hot plate for 20 min in the air to remove the excess solvent. During the procedure, the alkoxide film partially hydrolyzes with ambient moisture to form amorphous vanadium oxides. Polycrystalline VO2 films were formed upon heat treatment at 823 K for 30 min under Ar atmosphere. Subsequently, the VO2 film was slowly cooled to room temperature for measurements. Figure 2A shows a bright-field (BF) image of the film. The film is found to be heterogeneous. Figure 2B displays the SAED pattern from the same area as in Figure 2A showing the polycrystalliniety. Conically Scanned Imaging in UEM. Details of the experimental setup of UEM with femtosecond and nanosecond laser systems have been reported elsewhere.24 In brief, in this study for the full dynamic range of the phase transition the excitation was impulsively made using laser pulses of 10 ns duration at 532 nm. Time-framed diffraction patterns were taken with photoelectron pulses (wavelength of 2.5 pm), generated from the photocathode by laser pulses of 8 ns at 266 nm at a series of well-defined time delays with respect to the excitation (defined as time zero) and up to microseconds. Because the structural dynamics in this study is reversible and nondestructive, the pump−probe measurements were performed stroboscopically at the repetition rate of 2 kHz. To obtain a full archive of structural information from individual particles embedded in an ensemble, conical-scanning DF imaging, originally developed in steady-state studies for two-dimensional orientation mapping9,10 and now made possible also in three dimensions,25 is invoked. As shown in Figure 1, the incident electron beam is tilted at a specific angle α from the normal optical axis and rotated conically for a series 948

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Figure 4. Time-resolved diffraction of single nanoparticles (domains). (A,B) Snapshots of diffraction patterns taken stroboscopically at two representative time delays, as indicated at the bottom right of each pattern, with respect to pulsed photoexcitation. Scale bar, 5 nm−1. (C) Diffraction difference frame of t = 100 ns, referenced to the pattern recorded at t = −400 ns, which shows Bragg spot intensity and position changes with time. Note that the Bragg spots denoted as g are from the graphene substrate, showing neither intensity change nor displacement. (D) Bragg peak intensity change. Shown are the changes of intensities for Bragg spots denoted by 1 and 2 in panel A. Also shown is the time-dependent average intensity for a set of Bragg spots from the graphene substrate denoted as g. The kinetic profiles were fit to multiexponential functions and the time constants associated with the phase transition and recovery were deduced. (E) Bragg spot displacement. Shown are the time-dependent displacements of Bragg spots denoted as 3, 4, and 5 in panel A. Multiexponential fits are also given.

excitation at t = −400 ns and at t = 100 ns, respectively. The peak fluence and the diameter of illuminated area of the excitation pulse on the specimen were 20.6 mJ/cm2 and 55 μm, respectively. In the first image at t = −400 ns, before the excitation pulse at t = 0, the typical feature of diffraction contrast of nanocrystallites is observed. In bright-field imaging, zone axis condition means more scattering to diffracted beams, intensity in direct beam goes down, and bright-field image has strong contrast. Changes in crystal orientations, or in local structures from grain-to-grain or within grains change the diffraction condition and hence the contrast. Therefore, the bright-field images provide a sensitive indication of the occurrence of structural change. At positive times (after t = 0), visual changes are observed through diffraction contrast change (Figure 3B). A series of such time-framed images can provide a movie of the phase-transition dynamics. To conveniently visualize the temporal structural evolution, image-difference frames were constructed. Figure 3C is a representative one at t = 100 ns when referencing it to the frame at t = −400 ns. In the difference image, the regions of

orientations of nanoparticles. As shown in Figure 2C, the VO2 nanoparticles are found to be randomly oriented. Figure 2D−H displays the DF images of the particles originating from the representative Bragg spots denoted by 1− 5, respectively, in Figure 2B. The boundaries of those particles are presented in Figure 2A. From the BF image, particle location and connectivity with adjacent particles can be deduced. However, the information of size and shape is ambiguous in the BF image because of the packing of the particles. The size and shape of embedded particles can be directly obtained from DF images due to the characteristic crystallographic orientation of each particle. Following the time dependence of the Bragg spot corresponding to each single particle, the particle-dependent characteristic of structural dynamics of all particles in the field of view can be revealed from time-framed diffraction patterns of the ensemble obtained at a given time, as shown below. Time-Resolved Images and Ensemble Dynamics. In Figure 3A,B, displayed are representative time-framed BF images of VO2 nanocrystallites taken with pulsed photo949

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excitation, which leads to the loss of Bragg intensity (spots 1 and 2), and continues to stay depleted for several hundred nanoseconds followed by recovery. The constant depletion of the intensity during hundreds of nanoseconds indicates that the temperature of the particle exceeded the threshold temperature for the phase transition during that period; the intensity of the monoclinic phase is gone due to the full transformation into the high-temperature tetragonal phase. Once the temperature of the particle decreases below the reverse phase-transition temperature (after the residence time for the tetragonal phase, τr), the two phases coexist until the monoclinic phase is fully recovered across the entire volume of the particle. We note that bulging or mechanical movement of the graphene substrate can also result in the alteration of Bragg intensity of the nanoparticles sitting on it,24 but as shown in the bottom panel of Figure 4D we observe negligible change of Bragg intensities from the graphene layers. Thus, the phase transition causing the alteration of symmetry is responsible for the observed intensity changes. Bragg spots from the graphene layers are used to calibrate long-term electron beam movement and intensity. The Bragg diffraction intensity loss can be counteracted by the gain of the intensity originated from the growing population of the tetragonal phase. The monoclinic phase has a lower symmetry than that of the tetragonal phase, and in general the symmetry-raising phase-transition process can result in intensity increase in Bragg diffraction. When Bragg spots of the tetragonal phase are better in phase with the Ewald sphere than those from the initial monoclinic phase, intensity enhancement is possible as a consequence of the phase transition. In addition, the attenuation of Bragg intensity can arise from the Debye−Waller effect, which results from the temperature increase of the system as a consequence of photoexcitation. However, a quantitative measure of the phase transition is provided by the time dependence of the Bragg spot displacement. Figure 4E shows the time dependence of the displacement of the Bragg spots denoted by 3, 4, 5 in Figure 4A, respectively. The Bragg spot 3 is found to immediately move upon excitation by 0.5° clockwise in the β direction. Then, in a few hundred nanoseconds the extent of displacement reaches a maximum as large as about 2 pixels (with 5.6 × 10−2 nm−1/pixel). The original location of the Bragg spot is restored in 1500 ns. On the other hand, the time-dependent displacement of the Bragg spots 4 and 5 shows longer recovery times, indicating the existence of heterogeneity in the phasetransition dynamics depending on the particle involved. The shift of Bragg spots takes place when lattice parameters change due to the phase transition and lattice expand/shrink due to thermal effects. The latter can cause the shift only toward/ outward the central direct beam. Theoretical and Experimental Considerations of Single-particle Transitions. The phase transition can occur in three types: nonthermal electronic excitation; internal thermal excitation; and external heat transfer. The electronic excitation of V−V, d−d transition induces the phase transition, as revealed by ultrafast structural and electronic dynamics studies.11,12 The photoexcitation of our experiment at 2.3 eV corresponds to a transition between the uppermost-occupied 3d band and the hybridized π* band (0.7 eV < hν < 2.5 eV).29 However, at sufficiently high pump fluence the temperature of illuminated areas can exceed the transition threshold temperature, following electron−phonon relaxation on the time scale

white or black indicate locations of lattice orientation changes (diffraction contrast change), whereas gray regions are areas without contrast change. Note that image-frame alignment was performed to ensure the elimination of specimen drift during the measurement because they can affect the apparent contrast change in the difference images and image cross-correlation (see below). The structural dynamics accompanying the phase transition is described by the following elementary processes. The initiating excitation at 2.3 eV (532 nm) primarily involves the bonding of the vanadium pairs in the unit cell and upon promotion of electrons to antibonding orbitals a constant repulsive force on the atoms is acquired and lead to separation of vanadium atoms along the bond axis on the femtosecond time scale; see Figure 3D.12 In several picoseconds, the unit cell rearranges toward the configuration of the tetragonal phase. All of these stepwise structural changes and following restoration of original structural configuration involve contrast changes in time-resolved images because of the Bragg intensity changes following lattice deformation. In order to quantify the changes in time-framed images, we used the method of cross-correlation.28 The normalized crosscorrelation of an image at time t with respect to that at time t′ is expressed as γ (t ) =

∑x , y Cx , y(t )Cx , y(t ′) ∑x , y Cx , y(t )2 ∑x , y Cx , y(t ′)2

(1)

where the contrast Cx,y(t) is given by [Ix,y(t) − I(̅ t)]/I(̅ t), and Ix,y(t) and Ix,y(t′) are the intensities of pixels at the position of (x,y) at times t and t′; I(̅ t) and I(̅ t′) are the means of Ix,y(t) and Ix,y(t′), respectively. The correlation coefficient γ(t) of eq 1 is a measure of the temporal change in the “relief pattern” between the two images compared, which can be used as a measure of the change as a function of time in the image. As shown in Figure 3E, the full time scale for image change over all pixels is covered in the range of the time delay, unveiling the ensemble averaged structural dynamics in the phase transition. On the nanosecond time scale, the initial response to the photoexcitation was observed to be biphasic, one fast component within 10 ns and the other in 250 ns. The structural recovery then follows on a time scale of 320 ns. Time-Resolved Diffraction and Single-Particle Dynamics. Single-particle sensitivity in the phase transition dynamics is achieved by momentum-transfer selection in the time-framed diffraction patterns of the ensemble. Figure 4A,B displays two representative diffraction patterns taken at t = −400 and 100 ns, respectively. At t = 100 ns, after photoexcitation it is observed that numerous Bragg spots have undergone intensity change and position displacement. Figure 4C is the difference diffraction pattern for t = 100 ns with respect to the pattern for t = −400 ns, clearly showing such changes. The time dependence of Bragg spots was quantified following changes in amplitude, width, and position extracted from 2D Gaussian peak fitting. A few examples of the time dependencies are given in Figure 4D. The Bragg spots denoted by 1 and 2 belong to (1, 0, −2) and (−3, 0, 2), respectively, of the initial monoclinic phase, and they disappear in the tetragonal phase. Therefore the timedependent intensity changes for such Bragg spots mainly reflect the evolution of the phase transition. From these results one can observe that monoclinic VO2 at room temperature undergoes the phase transition immediately following photo950

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For the remaining portion of the Gaussian pulse, from time τm and afterward, the heat absorbed by the tetragonal phase is given by

of several picoseconds, then inducing a thermal phase transition.30,31 Lastly, the thermal phase transition can also take place via heat transfer from the graphene substrate to the VO2 nanocrystallites. The large optical absorption cross-section of the graphene layers at 532 nm and their high thermal conductivity make them an efficient heat source mimicking a “hot plate.”8,32 In our case here, the system undergoes the nonthermal phase transition with the fluence being above the threshold for the phase transition, and this occurs on the femtosecond and a few picoseconds time scales (see Figure 3D). The electronically excited tetragonal phase then relaxes to the initial monoclinic phase in a few nanoseconds.22,30 When the excitation fluence is high enough to open the thermal pathway, the forward transition may accompany electron−phonon and phonon− phonon interactions on the time scale of several picoseconds. The resulting hot tetragonal phase relaxes to the lowtemperature phase upon the cooling of the system, which strongly depends on the thermal property of the supporting substrate.30 In our experiments, we found that the restoration of the initial phase after photoexcitation takes as long as ∼300 ns, which is 2 orders of magnitude longer than the reported lifetime of nonthermally generated tetragonal phase. This indicates that the driving force for the transformation in this work follows the thermal pathway. Accordingly, the temperature jump (ΔT) induced by photoexcitation needs to be rationalized in order to understand the observations made here. The Gaussian excitation laser pulse with a τfwhm of 10 ns has the following fluence distribution 2

ΔHt = (1 − R t)F0

1 − exp( −amL) × L

τm 2σ

(4)

τm 2σ

( )

= (T − Tc)Cp,tρt

(5) −1

Here, αt is absorbance of 9.3 × 10 cm at 532 nm, Cp,t is the heat capacity of 787 J/(kg·K),35 ρt is the density of 4.653 g/ cm3,36 and Rt is the reflectivity of 0.22137 for tetragonal phase. Also, T is the final temperature reached in the film caused by laser heating. After τm is calculated in eq 3, the only unknown parameter of T in eq 5 can be obtained, and then the temperature jump ΔT = (T − 298) in the film caused by laser heating can be calculated. As an example, for a 90 nm thick VO2 thin film, the temperature jump ΔT is 197 K. The temperature jump ΔT is size dependent, decreasing with increasing film thickness. After the fast heat equilibration, the additional ΔT gained by the particles at equilibrium with the substrate is estimated to be as small as 10 ± 5 K, considering the average thickness of the substrate is ∼1 nm and that of the VO2 film is 90 nm; on the basis of the above considerations, the heat transfer from the graphene substrate to VO2 nanocrystals is not significant.38 This causes the total ΔT in the particles in the probed area of the film to be up to 207 K, and this value exceeds the phase transition temperature by 165 K and explains the occurrence of τr process until cooling back. This description conforms to our finding of the absence of separation change in conjugate Bragg spots from the graphene layers due to significant temperature change in the time series of diffraction patterns. Finally, thermal diffusion in the substrate does occur laterally and heat dissipation to the copper grids makes the combined graphene/copper grids an ideal heat sink. With an initial zindependent heat profile of absorption of the heating pulse in graphite, we estimated, using a 2D heat diffusion in a homogeneous medium,51 the time scale for an in-plane transfer with thermal conductivity λ = 700 W/(m·K) for graphite,42 density ρ = 2.26 g/cm3,40 and specific heat CV = 707 J/(K· kg).41 For the radius at half height of the initial pulse heat distribution r0 = 28 μm, the time for the axial temperature to drop to a half of its initial value (t1/2) is deduced to be ∼645 ns; for graphene with λ = 5000 W/(m·K), t1/2 is obtained to be 90 ns. The recovery time of 320 ns observed in Figure 3E falls well into this range of time scales. From the heat dissipation time of 320 ns in turn we can deduce our own λ value to be 1410 W/ (m·K), which is in good agreement with the reported value of 1250 W/(m·K) for 1 nm thick graphene.42 Size Effect and Heterogeneity of Phase Transition. The size of the particle plays a critical role in determining the nature of insulator−metal phase transition and the characteristic of the hysteresis loops in VO2.52−54 After the particle reaches its highest temperature during the photoexcitation, the particle cools down through the substrate and copper grids with the temperature decrease following an exponential decay 4

τm

∫−∞ f (t )dt τm 2σ

(2)

The first portion of the heat absorbed is for the temperature rise in the thin film of the monoclinic phase from room temperature of 298 K and up to the phase transition temperature Tc of 340 K. The latent heat (per unit volume) for the subsequent phase transition to the tetragonal phase can be equated to ΔHm by the following expression τm 2σ

( )

= ΔHL + (Tc − 298)C P,mρm

f (t )dt

m

1 − erf 1 − exp( −a tL) (1 − R t)F0 × 2 L

( )

1 + erf 1 − exp( −amL) × (1 − R m)F0 2 L

∞

( )

2σ 2

1 + erf 1 − exp( −amL) = (1 − R m)F0 × 2 L

∫τ

1 − erf 1 − exp( −a tL) = (1 − R t)F0 × L 2

during the pulse profile: f (t ) = 1/[(2π )1/2 σ ]e−t / e , where σ = τfwhm/(8 ln 2)1/2 ≈ 4.25 ns. In our case of a very small incident angle for the laser, it is a good approximation to ignore the angle and polarization dependence for the reflectivity considered by Fresnel.33 For a light pulse of peak fluence F0 and reflectivity Rm, in a thin film of thickness L, the monoclinic phase VO2, heat absorption, ΔHm, changes with and up to the time and τm is given by ΔHm = (1 − R m)F0

1 − exp( −a tL) × L

(3)

Here, αm is absorbance of 7.9 × 104 cm−1 at 532 nm,34 ΔHL is the latent heat of 2.37 × 102 J/cm3,35 Cp,m is the heat capacity of 656 J/(kg·K),35 ρm is the density of 4.571 g/cm3,36 and Rm is the reflectivity of 0.28737 for the monoclinic phase. 951

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behavior. The cooling rate, which is related to τc, was obtained from the fits to the experimental data in Figure 4D,E. From knowledge of the size dependent τc and the temperature jump ΔT after fast heat redistribution in the particle upon photoexcitation, we can deduce the threshold temperature of the phase recovery (Tr) for each nanoparticle from the relationship, Tr = ΔT·e−τr/τc + 298 K. τr can be obtained from the position of the vertical dash line in Figure 4D,E according to the top-truncated exponential fitting of the intensity or displacement of the time-dependent diffraction patterns. Figure 5A shows the experimental threshold temperature (Tr) of phase

temperature for phase recovery from the tetragonal to monoclinic phase increases with the particle size and the threshold temperature for phase transition from monoclinic to tetragonal phase almost remains constant, which indicates that the width of thermal hysteresis loop decreases with increasing particle size. The thermal heating and cooling results show a similar size-dependent behavior. Details of the microstructure, including defect structures within the grains, grain boundaries and relative orientation, contribute to critical size issues in the phase transition of VO2.54 The defects around the grain boundaries in bigger nanoparticles work as nucleation sites for the heterogeneous phase transition, thus reducing the energy requirement as quantified by the width of the thermal hysteresis.59 As shown in Figure 2D−H, the bigger particle has less uniform DF image contrast, which indicates that there is higher defect density within the grain and requires reduced energy at higher threshold temperature for phase recovery. The size-dependent characteristics of the hysteresis in phase transition of VO2 is very interesting for device applications of different functions, like smaller hysteresis for sensor-type device applications and a wider hysteresis for optical memory-type applications.54 Dynamic Scattering Simulations. We simulated the diffraction patterns of VO2 using a dynamic scattering model.60 The unit cell structure of VO2 at the low temperature has the following monoclinic lattice dimensions: a = 5.75 Å; b = 4.53 Å; c = 5.38 Å; β = 122.60°; and space group P21/c.21 The tetragonal phase of VO2 at high temperature has the unit cell parameters of a = b = 4.55 Å and c = 2.86 Å, and space group P42/mnm.21 During the phase transition, the atoms in the unit cell move from the coordinates at the low-temperature to the high-temperature phase, and the lattice symmetry and lattice parameters change from monoclinic to tetragonal structure.12,61,62 On the basis of the structural information of VO 2 nanoparticles of interest, the crystallite orientation change during the phase transition can be derived from the crystallographic analysis in the laboratory coordinate system. From the result in Figure 2C, the orientation matrix, in the laboratory coordinate system defined above of crystallite c in the monoclinic phase is given by

Figure 5. Threshold temperature and cooling rate of single particles. (A) Threshold temperature, Tr, of phase recovery from the metal to insulator phase in vanadium dioxide as a function of particle size, defined as the geometric mean of the long and short axes of an ellipseshaped grain. Tr is found to decrease with decreasing particle size. (B) The cooling rate, which is expressed by τc, as a function of particle size. Two dotted lines show the main distributed ranges of experimental cooling rate.

⎛ 0.2982 − 0.3068 − 0.9039 ⎞ ⎜ ⎟ UM = ⎜ 0.9101 0.3768 0.1723 ⎟ ⎜ ⎟ ⎝ 0.2877 − 0.8740 0.3916 ⎠

As shown in Figure 4E, upon excitation crystallite c immediately undergoes phase transition from the monoclinic to tetragonal phase configuration within 10 ns. Its crystalline orientation matrix in the laboratory coordinate system changes to

recovery in VO2 as a function of the particle size extracted from time-resolved diffraction patterns. The Tr decreases with decreasing particle size. Figure 5B shows the size dependent τc for the particles analyzed in Figure 5A. τc also depends on the distance of the particle away from the copper grid.55 Considering the constant threshold temperature (Tc) of phase transition in VO2, Tr increases with particle size, making the hysteresis width narrow with increasing particle size which is in agreement with the previous reported results.53,56−59 We also examined the heating and cooling loop of the ensembled VO2 sample. The diffraction intensity change of single particles during the heating and cooling cycle are analyzed with the single-particle selection of the conical scanning DF imaging method, as shown in Figure S2A−C. From the insert in Figure S2D, it is found that the threshold

⎛ 0.6008 0.3068 − 0.7381 ⎞ ⎜ ⎟ UT = ⎜−0.6354 − 0.3768 − 0.6739 ⎟ ⎜ ⎟ ⎝ −0.4848 0.8740 − 0.0314 ⎠

Figure 6A,B gives the simulated electron diffraction patterns of crystallite c in the monoclinic and the tetragonal phase, respectively. Figure 6C is a difference image for Figure 6B referenced to Figure 6A in order to follow changes of Bragg spots in position and intensity. In Figure 6A, the (4, 2, 0) Bragg spot of the monoclinic phase is highlighted, which corresponds to spot 3 in Figure 4A. Upon phase transition, the spot moves 952

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embedded in the polycrystalline ensemble has characteristic structural dynamics associated with the particle size. The conical scanning dark-field imaging allows us to identify diffraction spots from a polycrystalline ensemble to track constituent single nanoparticles. The single-particle-selection precision is affected by the size of an objective aperture to form dark-field images and by the separation of adjacent Bragg diffraction spots or that of Debye−Scherrer rings. In the reported methodology, we were able to characterize the structural dynamics of 11 nanoparticles out of about 200, but with the fabrication of smaller objective apertures for finer selection and measurement of smaller volume, more resolved Bragg spots in Debye−Scherrer rings will in future studies improve the single-particle selectivity. The ability to spatially and temporally characterize a single particle’s dynamics and orientation promises many applications, especially in heterogeneous ensembles.

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ASSOCIATED CONTENT

* Supporting Information S

Additional information and figures. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address §

(O.-H.K.) Department of Chemistry, School of NanoBioscience and Chemical Engineering, Ulsan National Institute of Science and Technology (UNIST), Ulsan 689−798, Republic of Korea. Notes

The authors declare no competing financial interest.

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Figure 6. Electron diffraction pattern simulation of phase-transition of vanadium dioxide. Simulation of electron diffraction patterns of grain c in the low-temperature monoclinic phase (A) and in the hightemperature tetragonal phase (B). The spot marked by red circles in (A) and (B) represents diffraction spot 3 in Figure 2B. (C) The difference image is obtained by subtracting (A) from (B). The diffraction spots contrast change shows the movement of diffraction spots between monoclinic and tetragonal phases. The red arrow represents the spot movement direction.

ACKNOWLEDGMENTS This work was supported by the National Science Foundation and Air Force Office of Scientific Research in the Physical Biology Center for Ultrafast Science and Technology supported by the Gordon and Betty Moore Foundation at Caltech. We thank Dr. Kiwook Hwang for the help in the preparation of specimens and Dr. Sang Tae Park and Dr. J. Spencer Baskin for their valuable discussions.

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upward by 1.5 pixel and turns into the (2, −2, 2) spot of the tetragonal phase in Figure 6B. The arrow in Figure 6c shows the movement direction of spot 3. The direction and the amount of the spot shift in the simulation are found to be similar to those observed in the experiments as shown in Figure 4. The difference can be explained with thermal effects accompanied by nanosecond photoexcitation. As depicted in Figure 6C, most of the spots shift and undergo intensity change while phase changes; some spots disappear because of lattice symmetry increase, which is consistent with the results in ref 12. Concluding Remarks. By integrating conical scanning dark-field imaging with 4D-UEM, we are now able to observe structural dynamics of single nanoparticles undergoing phase transitions and embedded in heterogeneous polycrystalline ensembles. The spatiotemporal visualization of single-particle dynamics is demonstrated following the time-dependent Bragg diffraction of each vanadium dioxide nanoparticle of interest and upon laser excitation. It is revealed that each particle

REFERENCES

(1) Knoll, M.; Ruska, E. Z. Phys. 1932, 78, 318−339. (2) Science of Microscopy; Hawkes, P. W., Spence, J. C. H., Eds.; Springer: New York, 2007, and references therein. (3) Williams, D. B.; Carter, C. B. Transmission Electron Microscopy - A Textbook for Materials Science; Springer Science Business Media: New York, 2009, and references therein. (4) Zewail, A. H.; Thomas, J. M. 4D Electron Microscopy: Imaging in Space and Time; Imperial College Press: London, 2009, and references therein. (5) Zewail, A. H. Science 2010, 328, 187−193, and references therein. (6) Flannigan, D. J.; Zewail, A. H. Acc. Chem. Res. 2012, 45, 1828− 1839. (7) Yurtsever, A.; Zewail, A. H. Science 2009, 326, 708−712. (8) Van der Veen, R. M.; Kwon, O.-H.; Tissot, A. M.; Hauser, A.; Zewail, A. H. Nature Chem. 2013, 5, 395−402. (9) Dingley, D. J. Mater. Sci. Forum 2005, 495−497, 225−230. (10) Dingley, D. J. Microchim. Acta 2006, 155, 19−29. (11) Cavalleri, A.; Rini, M.; Schoenlein, R. W. J. Phys. Soc. Jpn. 2006, 75, 011004, and references therein. 953

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Nano Letters

Letter

contrast, the thermal conductivity {6 W/(m·K)}46 of VO2 is very slow, on the order of several hundreds of nanoseconds, 2 orders of magnitude slower than the grid. It follows that the graphene substrate cools fast enough and can be used as an ideal heat sink (in this work) in which a thermal boundary resistance (Rbd) can play a role in the thermal diffusion across the interface.30 With Rbd of 10−8 m2·K/W for typical solid/graphite interfaces,47−49 the time for heat to escape from the VO2 film (τh) is estimated to be ∼3 ns according to the relation, τh = Rbd·d·Cv, where d is the thickness of the film and Cv is the specific heat per unit volume of the film, under the approximation given above.50 The time scale of heat transport across the interface is fast or comparable with respect to the duration of the nanosecond heating pulse, indicating the establishment of uniform heat distribution in the film and the substrate of the small area. (39) Nair, R. R.; Blake, P.; Grigorenko, A. N.; Novoselov, K. S.; Booth, T. J.; Stauber, T.; Peres, N. M. R.; Geim, A. K. Science 2008, 320, 1308. (40) Pierson, H. O. Handbook of Carbon, Graphite, Diamond and Fullerenes: Properties, Processing and Applications; Noyes Publications: Park Ridge, NJ, 1993. (41) Picard, S.; Burns, D. T.; Roger, P. Metrologia 2007, 44, 294− 302. (42) Balandin, A. A.; Ghosh, S.; Bao, W.; Calizo, I.; Teweldebrhan, D.; Miao, F.; Lau, C. N. Nano Lett. 2008, 8, 902−907. (43) Rathore, M. M.; Kapuno, R. R. Engineering Heat Transfer; Springer Press: London, 2010; p 349. (44) Wang, Z. Q.; Xie, R. G.; Bui, C. T.; Liu, D.; Ni, X. X.; Li, B. W.; Thong, J. T. L. Nano Lett. 2011, 11, 113−118. (45) Chen, J.; Chen, W. K.; Tang, J.; Rentzepis, P. M. Proc. Natl. Acad. Sci. U.S.A. 2011, 108, 18887. (46) Oh, D.-W.; Ko, C.; Ramanathan, S.; Cahill, D. G. Appl. Phys. Lett. 2010, 96, 151906. (47) Norris, P. M; Smoyer, J. L.; Duda, J. C.; Hopkins, P. E. J. Heat Transfer 2012, 134, 020910. (48) Duda, J. C.; Hopkins, P. E.; Beechem, T. E.; Smoyer, J. L.; Norris, P. M. Superlattices Microstruct. 2010, 47, 550−555. (49) Prasher, R. Phys. Rev. B 2008, 77, 075424. (50) Zeuner, S.; Lengfellner, H.; Prettl, W. Phys. Rev. B 1995, 51, 11903−11908. (51) Kwon, O.-H.; Barwick, B.; Park, H. S.; Baskin, J. S.; Zewail, A. H. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 8519−8524. (52) Pergament, A.; Velichko, A. Thin Solid Films. 2010, 518, 1760− 1762. (53) Lopez, R.; Haynes, T. E.; Boatner, L. A.; Feldman, L. C.; Haglund, R. F., Jr. Phys. Rev. B 2002, 65, 224113. (54) Narayan, J.; Bhosle, V. M. J. Appl. Phys. 2006, 100, 103524. (55) The cooling rate of a single particle is only weakly related to the distance away from the copper grids because of the rather high thermal conductivity of the graphene substrate. The particles studied are all located at small distance ranges from the copper grids so that we assume the distance effects on cooling rate are similar among them. (56) Babkin, E. V.; Charyev, A. A.; Dolgarev, A. P.; Urimov, H. O. Thin Solid Films 1987, 150, 11−14. (57) Baik, J. M.; Kim, M. H.; Larson, C.; Wodtke, A. M.; Moskovits, M. J. Phys. Chem. C 2008, 112, 13328−13331. (58) Appavoo, K.; Haglund, R. F., Jr. Nano. Lett. 2011, 11, 1025− 1031. (59) Appavoo, K.; Lei, D. Y.; Sonnefrud, Y.; Wang, B.; Pantelides, S. T.; Maier, S. A.; Haglund, R. F., Jr. Nano Lett. 2012, 12, 780−786. (60) Sugio, K.; Liu, H. H.; Poulsen, H. F.; Huang, X. Nanostructured Metals − Fundamentals to Applications; Grivel, J.-C., et al., Eds.; Risø DTU: Roskilde, Denmark, 2009; pp 337−342. (61) Okimura, K.; Sakai, J. Jpn. J. Appl. Phys. 2009, 48, 045504. (62) Yao, T.; Zhang, X. D.; Sun, Z. H.; Liu, S. J.; Huang, Y. Y.; Xie, Y.; Wu, C. Z.; Yun, X.; Zhang, W. Q.; Wu, Z. Y.; Pan, G. Q.; Hu, F. C.; Wu, L. H.; Liu, Q. H.; Wei, S. Q. Phys. Rev. Lett. 2010, 105, 225405.

(12) Baum, P.; Yang, D.-S.; Zewail, A. H. Science 2007, 318, 788− 792. (13) Morin, F. J. Phys. Rev. Lett. 1959, 3, 34−36. (14) Coy, H.; Cabrera, R.; Sepúlveda, N.; Fernández, F. E. J. Appl. Phys. 2010, 108, 113115. (15) Wu, J. M.; Liou, L. B. J. Mater. Chem. 2011, 21, 5499−5504. (16) Cao, J.; Fan, W.; Zhou, Q.; Sheu, E.; Liu, A.; Barret, C.; Wu, J. J. Appl. Phys. 2010, 108, 083538. (17) Cavalleri, A.; Rini, M.; Chong, H. H. W.; Fourmaux, S.; Glover, T. E.; Heimann, P. A.; Kieffer, J. C.; Schoenlein, R. W. Phys. Rev. Lett. 2005, 95, 067405. (18) Kübler, C.; Ehrke, H.; Huber, R.; Lopez, R.; Halabica, A.; Haglund, R. F., Jr.; Leitenstorfer, A. Phys. Rev. Lett. 2007, 99, 116401. (19) Cavalleri, A.; Tóth, Cs.; Siders, C. W.; Squier, J. A.; Ráksi, F.; Forget, P.; Kieffer, J. C. Phys. Rev. Lett. 2001, 87, 237401. (20) Hada, M.; Okimura, K.; Matsuo, J. Appl. Phys. Lett. 2011, 99, 051903. (21) Grinolds, M. S.; Lobastov, V. A.; Weissenrieder, J.; Zewail, A. H. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 18427−18431. (22) Lobastov, V. A.; Weissenrieder, J.; Tang, J.; Zewail, A. H. Nano Lett. 2007, 7, 2552−2558. (23) Chae, B.-G.; Kim, H.-T.; Yun, S.-J.; Kim, B.-J.; Lee, Y.-W.; Youn, D.-H.; Kang, K.-Y. Electrochem. Solid State 2006, 9, C12−C14. (24) (a) Barwick, B.; Park, H. S.; Kwon, O.-H.; Baskin, J. S.; Zewail, A. H. Science 2008, 322, 1227−1231. (b) Park, H. S.; Baskin, J. S.; Barwick, B.; Kwon, O.-H.; Zewail, A. H. Ultramicroscopy 2009, 110, 7− 19. (25) Liu, H. H.; Schmidt, S.; Poulsen, H. F.; Godfrey, A.; Liu, Z. Q.; Sharon, J. A.; Huang, X. Science 2011, 332, 833−834. (26) (a) Schmidt, S.; Olsen, U. L.; Poulsen, H. F.; Soerensen, H. O.; Lauridsen, E. M.; Margulies, L.; Maurice, C.; Juul, J. D. Scr. Mater. 2008, 59, 491−494. (b) Schmidt, S., http://sourceforge.net/apps/ trac/fable/wiki/ (accessed 2011). (27) Poulsen, H. F. Three Dimensional X-Ray Diffraction Microscopy; Springer: Berlin, 2004, and references therein. (28) Kwon, O.-H.; Barwick, B.; Park, H. S.; Baskin, J. S.; Zewail, A. H. Nano Lett. 2008, 8, 3557−3562. (29) Gavini, A.; Kwan, C. C. Y. Phys. Rev. B 1972, 5, 3138−3143. (30) Lysenko, S.; Rúa, A.; Vikhnin, V.; Fernández, F.; Liu, H. Phys. Rev. B 2007, 76, 035104. (31) Lysenko, S.; Rúa, A. J.; Vikhnin, V.; Jimenez, J.; Fernández, F.; Liu, H. Appl. Surf. Sci. 2006, 252, 5512−5515. (32) Kwon, O.-H.; Ortalan, V.; Zewail, A. H. Proc. Natl. Acad. Sci. U.S.A. 2011, 108, 6026−6031. (33) Jackson, J. D. Classical Electrodynamics, 3rd ed.; Wiley Press: New York, 1998. (34) Fu, D.; Liu, K.; Tao, T.; Lo, K.; Cheng, C.; Liu, B.; Zhang, R.; Bechtel, H. A.; Wu, J. J. Appl. Phys. 2013, 113, 043707. (35) Berglund, C. N.; Guggenheim, H. J. Phys. Rev. 1969, 185, 1022− 1033. (36) Leroux, Ch.; Nihoul, G.; Van Tendeloo, G. Phys. Rev. B 1998, 57, 5111−5121. (37) Kana Kana, J. B.; Ndjaka, J. M.; Vignaud, G.; Gibaud, A.; Maaza, M. Opt. Commun. 2011, 284, 807−812. (38) Because of the large optical absorption cross section of the graphene layers at 532 nm, the substrate can in principle significantly heat up upon photoexcitation. However, because the VO2 film of nanocrystals is resting on top of the graphene substrate, the actual available surface for graphene to absorb incident laser beam is low. About 10% of the laser light is absorbed by the substrate of 1 nm thickness. From α, ρ, and Cp of 2.9 × 105 cm−1,39 2.26 g/cm3,40 and 700 J/(kg·K),41 respectively, ΔT was estimated to be 370 K. The Cp value for graphite is known to increase rapidly from 700 J/(kg·K) at room temperature to 2000 J/(kg·K) at 3000 K,42 which gives 130 K for the minimum of ΔT. We also considered the effect of the copper grids. The thermal conductivity of copper is 384 W/(m·K),43 and for graphene it is around 5000 W/(m·K).44 In typical laser heating and cooling experiments of a copper film, the heat dissipation ends in a few hundred picoseconds or at most in a time on the order of 1 ns.45 In 954

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