Single-nanoparticle phase transitions visualized by four-dimensional ...

ARTICLES PUBLISHED ONLINE: 14 APRIL 2013 | DOI: 10.1038/NCHEM.1622

Single-nanoparticle phase transitions visualized by four-dimensional electron microscopy Renske M. van der Veen1, Oh-Hoon Kwon1, Antoine Tissot2, Andreas Hauser2 and Ahmed H. Zewail1 * The advancement of techniques that can probe the behaviour of individual nanoscopic objects is of paramount importance in various disciplines, including photonics and electronics. As it provides images with a spatiotemporal resolution, four-dimensional electron microscopy, in principle, should enable the visualization of single-nanoparticle structural dynamics in real and reciprocal space. Here, we demonstrate the selectivity and sensitivity of the technique by visualizing the spin crossover dynamics of single, isolated metal–organic framework nanocrystals. By introducing a small aperture in the microscope, it was possible to follow the phase transition and the associated structural dynamics within a single particle. Its behaviour was observed to be distinct from that imaged by averaging over ensembles of heterogeneous nanoparticles. The approach reported here has potential applications in other nanosystems and those that undergo (bio)chemical transformations.

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ecent technical advances in electron microscopy have driven the study of organic, inorganic and biological materials to an unprecedented level of detail1. Aberration-corrected and scanning electron microscopy techniques now provide atomic spatial images and structures of single particles, molecules and interfaces2,3. Moreover, high-resolution in situ electron microscopy visualizes transformations such as (catalytic) nanowire/nanotube growth4–7, dislocation dynamics8, ferroelectric switching9 and phase transitions10,11. However, the temporal resolution in these studies is limited by the speed of the acquisition time of the detector (30 ms), which leaves many phenomena that occur on shorter timescales inaccessible. Concomitant with these advances, progress has been made in the fields of ultrafast optical and X-ray techniques. Recently, ultrafast optical microscopy was applied to study electronic responses of single nano-objects, such as antennas, on photoexcitation12, but the exact particle size and morphology could not be measured in situ because of the limited spatial resolution and because direct structural dynamics information is not provided by these studies. Time-resolved X-ray methods are now capable of resolving atomic-scale dynamics with temporal resolutions that approach the femtosecond regime13–15, but in situ real-space X-ray imaging of single particles remains a major challenge. Four-dimensional electron microscopy (4D-EM) combines, in a table-top apparatus, high spatial resolution to resolve individual nano-objects with the ultrashort temporal resolution needed to address nanoscale chemical dynamics on laser excitation16. In this work, we use short parallel-beam electron pulses to realize combined real- and reciprocal-space probing of single, isolated nanoparticles on the intrinsic length and timescales of chemical phase transitions. In contrast to convergent-beam ultrafast electron diffraction17–19, in which the electron pulses are focused tightly on the nano-object, we spread the electron beam to avoid radiation damage of sensitive (bio)chemical samples, such as the molecular framework employed here, to obtain well-defined diffraction patterns from a single nanoparticle. To achieve this single-particle selectivity, we introduce a small aperture in the image plane of

the objective lens, the size of which projected in the sample plane is 1 mm, that is about twice the size of the nanoparticle, as demonstrated in Fig. 1. Here we demonstrate the spatiotemporal visualization of singlespin crossover (SCO) nanoparticles of the metal–organic framework Fe(pyrazine)Pt(CN)4 (Fig. 2a)20–29. The SCO phenomenon (Fig. 2b) represents a prototype example of molecular bistability and cooperative phase transformation in solids30–32, with many promising applications in molecular memory and data storage devices, optical displays and sensors33. The SCO process can be triggered by changes in temperature, pressure or magnetic field, or by light excitation. It involves the conversion between a diamagnetic lowspin (LS, S ¼ 0) state and a paramagnetic high spin (HS, S ¼ 2) state, each of which exhibits vastly different physical properties (for example, colour, magnetic, electric and structural). In particular, because of the population of antibonding transition-metal eg orbitals in the HS state, the metal–ligand bond distance elongates by as much as 0.2 Å for Fe–N SCO systems34. Consequently, in the case of Fe(pyrazine)Pt(CN)4 , the flexible 3D molecular structure accommodates an unusually large (anisotropic) unit-cell volume expansion of 13% (ref. 35). So far, most optical and X-ray studies have dealt with the dynamics of either SCO molecules in solution13,36, nanoparticle ensembles37 or bulk crystals38,39. However, the pertinent questions concerning individual SCO nano-objects and their interactions with the surroundings have remained largely elusive22,40. Such studies of nanoparticles are of fundamental interest and have relevance to technological applications of functional miniaturized materials, such as thin films, nanopatterns and nanoparticles. Open questions concern the effects of size reduction and the surrounding matrix on the phase-transition behaviour and cooperativity on the nanoscale, as compared to the bulk scale22,41. Surface and crystal defects are expected to play a progressively important role as the surface/volume ratio of nano-objects increases (phase transition processes at or near the particle surface can be inhibited because of strain and interface effects). From the temporal point of view, the effect of heat and matter inertia, which limit the macroscopic

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Physical Biology Center for Ultrafast Science and Technology, Arthur Amos Noyes Laboratory of Chemical Physics, California Institute of Technology, Pasadena, California 91125, USA, 2 De´partement de Chimie Physique, Universite´ de Gene`ve, CH-1211 Gene`ve, Switzerland. * e-mail: [email protected]

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need to be considered in understanding the phase-transition dynamics of nanoscopic objects. Many of these factors are averaged out and remain unveiled when ensembles of nanoparticles are studied. It is thus of primary importance to assess the structural dynamics at the single-particle level and with the required spatiotemporal resolutions.

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Figure 1 | Single-nanoparticle 4D-EM. The laser pulse (hn, green) initiates the structural change at t ¼ 0 and acts as a clocking pulse, which gives rise to a temperature jump. The short, parallel-beam electron packet (e2, black), time delayed with respect to the clocking pulse (Dt), illuminates the ensemble of nanoparticles. By inserting a small aperture in the image plane of the objective lens, single-nanoparticle selectivity in diffraction can be achieved. Electron-propagation paths from the aperture are schematically denoted as dashed lines.

transformation time in the bulk, is expected to be less in nanoscopic systems, and so render the phase transition faster and more efficient. The environment is not just a spectator, but it generally selects the channels of (bio)chemical transformations and affects the rates involved, for example, solvation in solution-phase photochemistry42. Similarly, the nature and dynamics of the particle interface and the supporting substrate are expected to play a vital role and a

Equilibrium characteristics. The measurement of the steady-state SCO phase-transition behaviour of a single particle is technically challenging and has, to our knowledge, only been done spectroscopically on micron-sized particles, of which the exact size and morphology could not be ascertained43. In the experimental configuration described above (Fig. 1), without laser excitation, we recorded diffraction patterns of isolated nanoparticles as a function of temperature. Figure 3a depicts a representative SCO nanoparticle imaged in the bright-field mode (excluding all scattered electrons in the reciprocal plane before constructing the image), together with the shadow of the aperture that is used for spatial selection. The dark contrast contours in the square particle are related to the warping of the nanocrystal in the LS state, as discussed in the section Spatiotemporal visualization (see below). The corresponding diffraction pattern (Fig. 3b) comprises the Bragg-allowed reflections of the [001] crystal zone axis, in good agreement with the reported tetragonal crystal structure of Fe(pyrazine)Pt(CN)4 (refs 20,21). The nanoparticle has a plate-like morphology with an aspect ratio of about 20 (600 × 600 × 30 nm3), which reflects the underlying anisotropic crystal structure. The particles preferentially orient themselves with the large (001) crystal facets parallel to the substrate surface, so the electron pulses mainly probe dynamics in the quasi-2D FePt(CN)4 planes along the a,b crystallographic directions. Some particles are oriented with the crystal c-axis parallel to the substrate, as discussed in the section Particledependent dynamics (see below). The (110) diffraction peak position in reciprocal space is plotted for the heating and cooling loop of the phase transition (Fig. 3c), which reveals a hysteresis around 250 K. The decrease in diffraction-peak spacing as temperature increases reflects an increase in lattice spacing, as expected for the LS  HS transition. Compared to the phase-transition curve of a nanoparticle ensemble (Fig. 3d–f), c

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Figure 2 | Structure, spin crossover and dynamics of Fe(pyrazine)Pt(CN)4 nanoparticles. a, Crystal structure of the metal–organic framework Fe(pyrazine)Pt(CN)4 (ref. 20). The bridging pyrazine ligands are actually rotationally disordered, but shown in one orientation for clarity. b, The spin crossover process involves a rearrangement of electrons in the t2g and eg orbitals of the Fe atom, resulting in a LS configuration (shown in blue) at low temperatures (solid potential curves) and a HS configuration (red) at elevated temperatures (dashed potential curves) with elongated Fe–N bonds. The crossover in this case is induced by a temperature jump (DT) after the optical excitation (marked by a green arrow and involving higher-lying excited states marked in grey). c, Schematic phase-diagram plot showing the non-equilibrium temperature and time dependence of the HS fraction. After the fast temperature rise has exceeded the thermal threshold (red), the HS fraction nucleates and grows (green) until almost full conversion is achieved. The dynamics that involve cooling of the nanoparticle (200 ns, magenta then blue) and relaxation to the initial electronic LS state (100 ns around 250 K), determine the nature of the final state. 2

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Figure 3 | Equilibrium phase-transition behaviour. a, Bright-field image of an individual SCO nanoparticle at 90 K. The shadow (bright circle) of the round selected-area diffraction aperture is visible also. The dark contours (diffraction contrast) within the nanoparticle result from morphology warping, as described in the main text. b, Corresponding single-particle electron-diffraction pattern along the [001] zone axis. Some of the diffraction peaks are labelled in the pattern. c, Single-nanoparticle phase-transition behaviour exhibiting a small hysteresis (red, heating; blue, cooling). The (110) diffraction-peak position was used to follow the phase transition (order parameter). Solid curves are guides to the eye based on a fit to a sigmoid function (see the Supplementary Information). The uncertainty in momentum transfer is estimated to be 0.005 nm21, but the difference in behaviour between the heating and cooling curves is systematic and reproducible. d–f, Bright-field image (d), diffraction pattern (both at 90 K) (e) and phase-transition behaviour (f) of an ensemble of nanoparticles. The phase-transition behaviour of the single nanoparticle (a–c) is shallower than that of the ensemble (d–f), which can be related to the friction at the particle/substrate interface.

the curve for the single nanoparticle is shallower and the hysteresis is smaller. This is probably caused by interface-induced stress to the particle and/or the lack of surrounding nanoparticles that allow the propagation of the cooperative phase transition. Confinement effects in small nano-objects can also inhibit the phase transition44. The thermal expansion coefficient (which reflects the change in volume lattice in response to a change in temperature) could not be determined reliably from the diffraction data over this temperature range. However, a small negative thermal expansion coefficient (avolume ¼ dV/VdT ¼ 22 × 1025 K21), that is, a lattice contraction with a temperature increase, has been reported for the LS state of Fe(pyrazine)Pt(CN)4 (ref. 35). Consequently, the positive expansion dynamics on laser excitation observed in this study is a clear signature that the electronic SCO process dominates the non-electronic thermal expansion behaviour of the material. The steady-state phase transition behaviour of each nanoparticle is unique, depending on the characteristic surroundings and interactions at the substrate/particle interface. These particle-specific properties remain hidden when the phase transition behaviour of the nanoparticle ensemble is considered. Spatiotemporal visualization. The morphology and atomic structural changes that accompany the phase transition of the individual nanoparticles are visualized by real-space images and reciprocal-space diffraction dynamics. In Fig. 4a we display representative time-framed real-space images of a single nanoparticle on temperature-jump (T-jump) excitation

(7 ns, 532 nm, 12 mJ cm22); by this we mean the fast rise of temperature after photon excitation. The repetition rate was 600 Hz, that is we recorded the dynamics stroboscopically. The equilibrium sample temperature was kept at 90 K, at which the majority of the SCO centres were in the LS state. Using a cross-correlation technique, all images shown were corrected carefully for long-term drifts of the sample holder during measurements (see Methods). In the first image taken at –300 ns before the clocking pulse (t ¼ 0), characteristic dark features, such as bend contours in the single nanocrystal, are observed, as in Fig. 3a. These contours probably result from warping of nanocrystals, which originates from the large crystallattice contraction on cooling from the room-temperature HS state, in which the particles are synthesized, to the LS state at 90 K. Consequently, frictional forces at the interface, where the particle experiences a resistance to change in its structure, can result in a buckling/warping effect. The dark contours in the image thus belong to crystal-lattice planes that have a favourable orientation with respect to the incoming electron beam, such that they fulfil the Bragg condition and scatter electrons efficiently (which are blocked by an aperture prior to image formation); the warped morphology means this condition is not satisfied simultaneously across the whole crystal. At positive times after excitation, t . 0, dramatic changes in image contrast are observed. The dark-field images in Fig. 4b, collecting only the (110) Bragg peak (Fig. 4c) to form the real-space images, clearly reveal the complementary relationship between real- and reciprocal-space patterns. The initially localized scattered intensity spreads until it almost spans the entire nanocrystal at

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Figure 4 | Single-nanoparticle morphology dynamics. a, Bright-field images taken at three different time delays. The red and blue lines (labelled 1 and 2) refer to the particle directions used to quantify the dimension changes with time (see Fig. 5a). The yellow dashed box indicates the region (SAI) that is used to plot the dynamics in Fig. 5b. b, Corresponding dark-field images at the three time delays. The (110) diffraction peak (see c) was selected to construct the images and visualize the contrast dynamics. c, Single-nanoparticle diffraction pattern. The incoming electron beam is slightly tilted away from the [001] zone axis. The diffraction peaks that belong to the supporting graphite substrate are encircled in grey. The (110) reflection used for dark-field imaging is encircled in red. d, Schematics of the morphology dynamics on spin crossover (HS, red; LS, blue). Before t ¼ 0 the nanoparticle shape is buckled/strained, and after t ¼ 0 the structure expands and relaxes.

around t ¼ þ50 ns, but at later times (for example, at t ¼ þ400 ns), the localized feature partially reforms. These dynamics directly map the local lattice motion when the strained, buckled particle in the LS state releases the stress on excitation into the structurally relaxed HS state, as schematically depicted in Fig. 4d. The homogenization of the scattered intensity shortly after excitation and the concomitant diffracted intensity increase indicate that additional lattice planes ‘rotate’ into the Bragg condition as the particle undergoes SCO with a large concurrent volume expansion. The homogenization of diffraction contrast (such as at t ¼ þ50 ns) could not be obtained by tilting the sample for t , 0; in this case, the bend contours move across the crystal without changing their extent. However, steady-state heating of the particle to room temperature could reproduce similar dispersed contrast features across the nanoparticle. This confirms that the time-dependent contrast change in the images represents the morphological dynamics of the nanoparticle undergoing SCO; that is, flattening and expanding towards the HS state on excitation, and rebuckling and shrinking during relaxation towards the LS state. Series of time-framed images, including those of Fig. 3a,b, were collected to construct nanomovies to visualize the effect of SCO on the morphology of the single particle (Supplementary Movies S1 and S2). To quantify the described real-space dynamics we took line profiles along the two principal axes of the particle and plotted the integrated intensity for different time delays. From the obtained cross-sections the positions of the particle edge were determined by taking their derivatives, which were fitted to Gaussian functions. The resulting expansion dynamics, referenced to the particle size before t ¼ 0 (605 nm), are depicted in Fig. 5a. The expansion directly visualizes the difference in molecular size between the two electronic spin states. It exhibits a clear spatiotemporal anisotropy (0.8% and 1.9% along directions 1 and 2, respectively) in the a,b plane, which indicates an appreciable 4

friction force at the interface that hinders the motion of the particle parallel to the substrate45. Figure 5b shows the summed imageintensity dynamics within a selected-area image (SAI, see Fig. 4a) that spans the entire particle as a function of time delay and referenced to the intensity before t ¼ 0. The intensity profile is characterized by an immediate decrease around t ¼ 0, followed by a partial recovery on the timescale of 150 ns and, finally, a longlived component that recovers on a much longer timescale (greater than milliseconds). These trends are corroborated by time-dependent diffraction dynamics, shown in Fig. 5c. From the single-nanoparticle diffraction patterns, Bragg peak separations, intensities and widths were obtained by Gaussian peak fitting as a function of time delay. We focus here on the symmetric (110) and (21210) Bragg peaks; other reflections of the [001] zone axis showed similar responses. On excitation, the (110) conjugate peaks abruptly (,15 ns) move closer to each other; at later times they partially recuperate within 230+26 ns. The maximum diffraction-peak contraction at t ≈ 50 ns corresponds to a unit-cell expansion in the a,b crystal plane of 1.7%, or 0.12 Å. This represents 75% of LS  HS conversion in the nanocrystal, taking into account a small (,0.2%) counteracting thermal lattice contraction over the observed temperature range. The onset of the phase-transition dynamics is delayed by about 10 ns with respect to the exact temporal overlap of laser and electron pulses (at t ¼ 0), as discussed in the section Non-equilibrium phase-transition model (see below). The single-nanoparticle diffraction dynamics are significantly faster than the dynamics of an ensemble (containing 100 particles, 5 kHz, 11.6 mJ cm22), as depicted in Fig. 5d. The azimuthally averaged (110) diffraction ring of the ensemble (see Fig. 3e) contracts within 29+3 ns after excitation, compared to ,15 ns for the single particle. The signal almost entirely recovers within 980+50 ns, with a minor long-lived component.

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Figure 5 | Real- and reciprocal–space time profiles. a, Real-space particle expansion dynamics along the two principal particle axes relative to the particle dimensions at t , 0. The blue and red plots are obtained along directions 1 and 2 in Fig. 4a, respectively. b, Contrast dynamics of a SAI (see Fig. 4a) representing the crystal-strain relaxation and revival. The summed intensity within the SAI is plotted as a function of time delay relative to the intensity at t , 0. c, Reciprocal-space diffraction dynamics of the single nanoparticle under the same excitation conditions. d, Diffraction dynamics of the nanoparticle ensemble of Fig. 3d–f. The solid curves are fits to the data (see the Supplementary Information). The inset shows the initial changes just after excitation.

Particle-dependent dynamics. Having established the significant differences between dynamics of the isolated and ensemble of nanoparticles, the particle-selective probing capability now allows us to investigate the factors that affect the dynamics on a particleby-particle basis. Figure 6a depicts two neighbouring nanoparticles that exhibit largely different structural dynamics on T-jump excitation (11.7 mJ cm22, 2 kHz). Shown in Fig. 6b are three time-framed maps of difference images at t ¼ 2100 ns, þ70 ns and þ400 ns, referenced to the images before t ¼ 0. The first particle (labelled as 1 in Fig. 6a) displays a large expansion on excitation, emerging as dark contours in the image difference maps for t . 0. Surprisingly, the neighbouring nanoparticle (labelled as 2) exhibits the opposite behaviour; it abruptly shrinks on excitation resulting in bright contours in the difference image at t ¼ þ70 ns. At later times, after hundreds of nanoseconds, this particle entirely returns to its initial size. Time profiles of the relative particle-dimension changes along the two principal axes are shown in Fig. 6c. Whereas the contraction of particle 2 (600 × 600 nm2, 10 nm thickness) is isotropic along both directions, the expansion of particle 1 (540 × 830 nm2, .100 nm thickness) exhibits a pronounced anisotropy (the longer particle axis expands more than the shorter axis). Series of time-framed bright-field and difference images were collected to construct nanomovies of the expansion/contraction dynamics (Supplementary Movies S3 and S4). The aperture for diffraction dynamics selects both particles simultaneously. The peaks in the resulting composite diffraction pattern can be assigned unambiguously to the two nanoparticles using dark-field imaging, as shown in Fig. 6d. The diffraction dynamics corroborates the real-space expansion; an increase in

peak spacing for the shrinking particle and a decrease for the expanding particle. The equilibrium peak position of the expanding particle 1 can be identified as the (111) reflection of the LS Fe(pyrazine)Pt(CN)4 structure. Diffraction-pattern simulations show that the (111) reflection series becomes predominately visible when the incoming beam is perpendicular to the c-axis where it bisects the a,b crystal axes. In contrast to the square-shaped nanoparticles, particle 1 thus predominately grew along the crystal c-axis being parallel to the substrate. The anisotropic real-space expansion can then be explained by the expected anisotropic expansion of the reported unit-cell parameters (5.5% along c versus 2.7% along a,b) for the LS  HS transition20. In contrast to the thin squareshaped particles, friction at the particle/substrate interface is minimal for this thicker nanoparticle and the dynamics are intrinsic to the material. The edge-on viewing direction entails a reduction by sin 458 ¼ 0.71 of the observed real-space expansion magnitude along the short (a,b) nanoparticle direction, and the long axis exhibits the full c-axis expansion. The expected ratio between longitudinal and lateral expansions from the known crystal structures then becomes 2.9 (including thermal expansion between 90 K and 290 K), which is reasonably close to the experimentally observed anisotropy ratio of 2.6 at t ¼ 1.4 ms, when the nanoparticle has cooled back to 90 K. The slight difference between these ratios is probably related to an anisotropy of the thermal expansion coefficients along the a,b and c directions (that is, positive expansion along c, and negative expansion along a,b). The phase-transition rise (105+30 ns) and decay (248+72 ns) times of this nanoparticle are longer than those of the particle in Figs 4 and 5.

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Figure 6 | Particle-dependent dynamics. a,b, Steady-state bright-field image (a) and image-difference maps (b) at three different time delays. The difference images are referenced to the images before t ¼ 0. One particle expands and the other shrinks on T-jump excitation. The labels (1, 2, H and V) refer to the nanoparticles and directions used to plot the dynamics in (c). c, Real-space expansion dynamics along the two principal particle axes of each nanoparticle (NP). The directions are labelled as shown in (a). d, Dark-field imaging to correlate the diffraction peaks with the individual particles. The diffraction peaks used to construct the images are encircled in the diffraction patterns displayed as insets (scale bar, 2 nm21). e, Diffraction dynamics corroborate the opposite expansion dynamics of the two particles. The solid curves are fits to the data (see the Supplementary Information).

The equilibrium peak position (2.1 nm21) of the shrinking particle 2 is larger and the peaks are azimuthally broader than those for Fe(pyrazine)Pt(CN)4 , which indicates a sheet-like crystal structure with a rotational disorder of the a,b planes around the c-axis. Starting from the original Fe(pyrazine)Pt(CN)4 phase before laser irradiation, the particle is found to have undergone an irreversible chemical transformation on in situ T-jump photoexcitation, in which the pyrazine ligands undergo reactive change. The resulting material exhibits an exceptionally large negative thermal expansion coefficient underlying the thermal excitation of transverse vibrational modes of the flexible bridging cyanide ligands in the absence of SCO46. On thermal excitation, the crystal lattice therefore unexpectedly contracts; in contrast to the common positive thermal expansion based on bonding anharmonicity. The contraction is short-lived following the temperature profile in the nanoparticle; no evidence for the SCO phase transition is found for this material. Details about this peculiar behaviour will be reported elsewhere. On average, nearly one out of ten nanoparticles is found to show the negative expansion dynamics. The unique spatiotemporal resolution and selectivity of 4D-EM enable these particle-dependent observations, which are not available from ensemble-averaged data. The bright-field and diffraction dynamics of a fourth nanoparticle are provided in the Supplementary Information. Non-equilibrium phase-transition model. In this work, the nanoparticles are excited through a T-jump starting from the LS 6

state at the equilibrium temperature of 90 K. The following picture emerges from the non-equilibrium model simulations, which are described briefly in the Supplementary Information but will be detailed in a forthcoming publication. By means of electron–phonon coupling and heat diffusion, the absorbed photons in the substrate and the nanoparticle are converted into heat on the nanosecond timescale. Consequently, four key steps in the phase-transition cascade that applies to the majority of nanoparticles can be distinguished, as schematically depicted in Fig. 2c. The temperature in the nanoparticle rises fast, initially without increasing the HS fraction. A laser fluence of 12 mJ cm22 induces a T-jump of 300 K in the nanoparticle, which traverses the phase-transition region around 250 K. Once the temperature passes the thermal threshold for the phase transition, the particle experiences a thermodynamic driving force and undergoes the transition from the LS state into the HS state. The HS fraction begins to grow on a timescale of tens of nanoseconds, as determined by the LS  HS reaction and nucleation kinetics. The time necessary to reach the thermal threshold for SCO results in an ‘incubation’ period between excitation and the onset of the observed phase-transition dynamics. In addition, because diffraction requires long-range structural order to give detectable signals of the new phase, strictly the peak positions (excluding thermal expansion) are not linearly related to the fractions of HS and LS phases. Early events of nucleation and growth are therefore precluded from the observation.

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The temperature of the nanoparticle decreases on the timescale of 100–200 ns by heat dissipation to the substrate. During this time window the cooling rate competes with the back-relaxation rate for the HS  LS conversion. The latter is quite fast at elevated temperatures (thermally activated), but becomes increasingly slower when the particle cools down. Below a certain temperature the electronic lifetime becomes sufficiently long that a part of the particle is effectively trapped in the HS state. At the equilibrium temperature of 90 K, the timescale of the spin-forbidden HS  LS relaxation becomes several milliseconds, as determined by optical pump probe experiments on an ensemble of nanoparticles (see the Supplementary Information). The HS lifetime at 90 K is longer than the separation between consecutive laser pulses for the repetition rates employed. This leads to an accumulation of HS fraction and a steady-state offset before t ¼ 0. Single-shot experiments are desirable to ensure a pure starting phase. The balance between cooling and back relaxation thus sensitively determines the observed partial-recovery rate and the long-lived trapped HS fraction. In the case of a thin single nanoparticle (Fig. 5c), heating and cooling are efficient because of the good thermal contact at the particle/substrate interface. The phase transition and partial recovery dynamics are consequently fast and the trapped HS fraction is high. In the nanoparticle ensemble (Fig. 5d) the thermal contact is, on average, reduced; the dynamics are slower and the trapped HS fraction is much smaller. Compared to the thin particle (Fig. 5c), the thicker nanoparticle 1 in Fig. 6 exhibits slower dynamics because of its thermal inertia (larger volume), assuming similar thermal contact and excitation for both particles.

Conclusion Using 4D-EM, we demonstrate the combined real- and reciprocalspace visualization of structural dynamics at the level of a single nanoparticle. Whereas studies of an ensemble of heterogeneous nanoparticles provide an averaged characterization, the visualization of each constituent particle can unveil its unique behaviour, for instance with regard to its specific orientation, the nature of nucleation sites, crystal defects and the particle/substrate interface characteristics. Here, this distinction was observed for SCO phase transitions, and the pronounced differences in dynamics emphasize the importance of particle-selective probing methods. With the simultaneous imaging and diffraction capabilities of 4D-EM, in a table-top implementation, we anticipate numerous future applications for various nanoscale materials, such as single nanotubes, biological fibres and heterogeneous ensembles of interfacial or embedded structures.

Methods Apparatus and data acquisition. Overviews of the concept of 4D-EM and apparatus are detailed elsewhere47. Briefly, Caltech’s second-generation apparatus is used, which is equipped with both femtosecond and nanosecond laser capabilities. Here, we use 10 ns electron pulses (200 keV) through photoemission from a LaB6 cathode incorporated in a field-emission gun assembly. The repetition rate of the electron-pulse arrival and laser excitation (7 ns, 532 nm) can be varied by means of a digital delay generator, which adjusts the time delay between laser pump and electron-probe pulses. The laser is guided onto the sample by a mirror inside the microscope column with an angle of 58 with respect to the incoming electron beam; the laser polarization is approximately parallel to the sample plane. The power and pointing stability of the laser beam was monitored in situ by a beam-profiler camera located at an equivalent image plane of the specimen (see the Supplementary Information). Slight laser-beam drifts between measurements were corrected for. The beam size and fluence were also obtained from the beam profiler image. The alignment of the diffraction aperture for the selected area was verified and corrected by comparing the selected area in the image with the shadow image of the defocused direct beam in diffraction. The camera length and the ellipticity in the measurement of diffraction patterns were calibrated and corrected for, respectively, using a polycrystalline aluminium film as a reference. The sample was carried in a liquid-nitrogen cryoholder and kept at 90 K. To measure the temperature-dependent phase-transition curves, the temperature was varied with a rate of 2–4 K min21, which should be slow enough to assure thermodynamic equilibrium at the sample during the temperature change.

Each image or diffraction pattern was taken in a single acquisition with an integration time of 5–10 s; at a repetition rate of 600 Hz, 3,000–6,000 electron shots were accumulated on the charge-coupled device. No images or patterns were averaged together after data acquisition. The typical accumulated electron dose is 1 e2 Å22 per diffraction time scan. Within our experimental sensitivity, no sample damage was observed during the measurements; the diffraction patterns and real-space appearance of the particles before and after the measurements were identical. Drift-correction and dynamics quantification. The specimen at low temperature is prone to slight temperature fluctuations, so the drift in the sample plane was appreciable (5–10 nm min21). By keeping the total acquisition time of the scans short, we made sure that the nanoparticles stayed within the view of the selecting aperture. For typical acquisition times per image or diffraction pattern of 10 s, 100 delay steps per scan result in an acceptable drift of 100–200 nm. To quantify the dynamics and to produce the 4D-EM movies, we employed postacquisition drift correction based on image cross-correlation. A small recognizable area in the image was selected, and for each time delay the cross-correlation matrix with respect to a reference image before t ¼ 0 was calculated using fast Fourier transform procedures. The necessary drift correction to obtain a maximum cross-correlation was derived. This procedure was also applied to the diffraction patterns, which undergo drifts caused by magnetic hysteresis of the imaging lenses of the microscope. The diffraction dynamics were quantified by 2D Gaussian fitting of the diffraction peaks, which were paired according to the inversion symmetry of the diffraction pattern (Friedel pairs). Prior to peak fitting a median filter was applied to the diffraction patterns. Reliable laser-induced changes in the peak widths could not be observed, as the widths (15 pixels) were much larger than the laser-induced peak shifts (maximum of four pixels). Each diffraction pattern in a time-delay scan was normalized to the total integrated intensity. No laser-induced intensity/width changes of the direct beam were observed, which excludes possible laser-induced charging effects on the sample. Several time profiles (typically five, including forward and reverse delay scans) were averaged together during data processing. Real-space dynamics were quantified by taking line profiles along the two perpendicular directions of the square nanoparticles. For each line profile, the image intensity was integrated along the mutually perpendicular direction up to the particle borders. By taking the derivative of the resulting cross-sections, the edge positions could be determined accurately. All images were normalized to the totally integrated intensity in an area of the image showing only the substrate. Diffraction and real-space time profiles were fitted with a multiexponential function and the equilibrium phase-transition curves in Fig. 3 were fitted with sigmoid functions. Fitting details are provided in the Supplementary Information. Sample preparation. The synthesis of the Fe(pyrazine)Pt(CN)4 nanoparticles was adapted from Boldog et al.23. First, two aqueous solutions of reactants were prepared: (1) 0.2 mmol Fe(BF4)2.H2O þ 0.8 mmol pyrazine (in excess) dissolved in deionized water (4 ml), and (2) 0.2 mmol K2Pt(CN)4 dissolved in deionized water (4 ml). Then, two starting microemulsions were prepared by the slow addition of these aqueous solutions to 44.5 mmol of dioctyl sodium sulfosuccinate previously dissolved in n-heptane (88 ml). Both solutions were stirred until stabilization and then mixed quickly under intensive stirring. Orange precipitates began to appear after one hour of stirring. After 24 hours, the precipitate was collected by centrifugation (10 minutes at 10956 relative centrifugal force) and washed several times by redispersion in ethanol and centrifugation to remove the traces of surfactant around the particles. The nanoparticle powder was dispersed in ethanol and sonicated for 20 s. A small droplet of the solution was delivered onto a graphite substrate on a 2,000 mesh copper frame and dried in air. The grid was heated at 110 8C for two hours to remove residual crystal water. Between measurements on different days, the sample was kept under vacuum and heated at 90 8C for three hours. Sample characterization data (powder X-ray diffraction and ultraviolet–visible spectroscopy) are given in the Supplementary Information.

Received 27 November 2012; accepted 6 March 2013; published online 14 April 2013

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Acknowledgements This work was supported by the National Science Foundation and the Air Force Office of Scientific Research in the Gordon and Betty Moore Center for Physical Biology at the California Institute of Technology. R.M.V. acknowledges funding from the Swiss National Science Foundation. We thank S. Tae Park for helpful collaboration in the phase-transition simulations, which will be published later in a full report.

Author contributions R.M.V., O.H.K. and A.H.Z. conceived and designed the experiments. R.M.V. and O.H.K. performed the experiments. A.H. and A.M.T. contributed materials and performed sample characterization. R.M.V., O.H.K., A.M.T., A.H. and A.H.Z. discussed the results and commented on the manuscript.

Additional information Supplementary information is available in the online version of the paper. Reprints and permissions information is available online at www.nature.com/reprints. Correspondence and requests for materials should be addressed to A.H.Z.

Competing financial interests The authors declare no competing financial interests.

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