Ultrafast Three-Dimensional Imaging of Lattice Dynamics in Individual Gold Nanocrystals

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Science  05 Jul 2013:
Vol. 341, Issue 6141, pp. 56-59
DOI: 10.1126/science.1236034

Distorted Nanoparticle

Nanoparticles have found many applications in modern technology; however, the full characterization of individual particles is challenging. One of the most interesting mechanical properties is the particle's response to lattice distortion. This property has been probed for ensembles of nanoparticles, but the required averaging may distort the results. Clark et al. (p. 56, published online 23 May; see the Perspective by Hartland and Lo) were able to image the generation and subsequent evolution of coherent acoustic phonons from an individual perturbed gold nanocrystal on the picosecond time scale.


Key insights into the behavior of materials can be gained by observing their structure as they undergo lattice distortion. Laser pulses on the femtosecond time scale can be used to induce disorder in a “pump-probe” experiment with the ensuing transients being probed stroboscopically with femtosecond pulses of visible light, x-rays, or electrons. Here we report three-dimensional imaging of the generation and subsequent evolution of coherent acoustic phonons on the picosecond time scale within a single gold nanocrystal by means of an x-ray free-electron laser, providing insights into the physics of this phenomenon. Our results allow comparison and confirmation of predictive models based on continuum elasticity theory and molecular dynamics simulations.

Coherent lattice vibrations (phonons) in solids play an important role in many phenomena such as melting (15), phase transitions (6), bond softening (7) and hardening (8), and ferroelectricity (9). Ultrashort (femtosecond) laser pulses have been used to reveal great detail about the dynamics of these phenomena; however, many of these studies have been confined to bulk samples or ensembles of nanoparticles. With nanoparticles playing an increasingly important role in technology, from catalysis (10) and photonic devices (11) to single-particle mass spectrometry (12) and sensing, understanding the mechanical and dynamical properties of single nanoparticles becomes very important as many of the processes occur on femtosecond (fs) and picosecond (ps) time scales.

The characterization of lattice displacements in individual nanoparticles over very short time scales with atomic sensitivity has been challenging. The interrogation of individual particles is important, as ensemble heterogeneity can give the impression of considerably shorter-lived dynamics than actually exist (13, 14) and may hide the presence of high-order phonon modes or anharmonicity. Optical pump-probe experiments have shown promising results, particularly for single particles (15) over very short time scales; however, because of the long wavelength of the probe, atomic-scale motions cannot be measured without relying on interpretations from continuum elasticity theory. Pump-probe experiments on nanoparticles using electrons or x-rays overcome this problem by probing the atomic-scale motions directly (16, 17). The low scattering cross sections of x-rays and the (relatively) low number of photons in the ultrashort x-ray pulses from plasma sources (required for the short pulse duration) limit the ability to study individual nanoparticles. Likewise, for electrons, the small number of electrons per ultrashort pulse has meant that probing individual nanoparticles has been difficult. The increased flux of synchrotron sources in comparison to plasma sources provides a sufficient number of x-ray photons to probe individual nanoparticles, but at the expense of time resolution. This provides a strong motivation to develop ultrafast pump-probe x-ray diffraction methods on individual nanocrystals using x-ray free-electron lasers (XFELs) (18). Using this approach, one can elucidate the elastic response of the atomic lattice to laser irradiation while simultaneously obtaining high-resolution real-space images of the deformation field inside the nanocrystal by means of Bragg coherent diffraction imaging (BCDI) (19, 20).

BCDI is sensitive to very small variations in strain within nanocrystals as it recovers the projected distortion of the electron density with picometer (pm) sensitivity. The recovered image comprises the amplitude, which is related to the electron density, and the phase, ϕ(r), which is related to the (vector) displacement field u(r) of the atoms from the ideal lattice points and the scattering vector Q via ϕ(r) = u(rQ (21). Images obtained from noncoplanar Bragg peaks can be combined to recover the full displacement field (22).

Figure 1 shows a schematic of the experimental arrangement for ultrafast BCDI, which was performed at the x-ray pump probe (XPP) instrument at the Linac Coherent Light Source (LCLS). Truncated octahedra gold nanocrystals, ~300 to 400 nm in diameter (21), were placed at the center of a diffractometer. A Ti-sapphire laser with a wavelength of 800 nm and a pulse length of 50 fs [full duration at half-maximum (FDHM)] was used to generate coherent acoustic phonons in the gold nanocrystals. The incident fluence used in the experiment was 1 mJ/cm2. The sample was illuminated with 80-fs (FDHM), 9.2-keV x-rays generated by LCLS operating at a repetition rate of 120 Hz. A Si (111) monochromator was used to select ~1 eV bandwidth. Beryllium lenses were used to focus the illumination to an ~30 μm by 30 μm spot. Multiple nanocrystals were illuminated simultaneously, but orientation differences between them allowed Bragg peaks from individual nanocrystals to be spatially separated on the detector. The relative timing (accurate to sub-ps) of the optical and x-ray pulse was adjusted to provide the time-resolved data with the two beams almost parallel for spatial coincidence. Both fluences were below the damage threshold to allow repeated measurements. The coherent diffraction patterns were recorded with a Cornell-SLAC pixel array detector (CS-PAD) (23) positioned 1.2 m from the sample at the gold (111) Bragg peak, a sufficient distance to oversample (19) the diffraction patterns. A helium-filled bag was placed between the sample and detector to reduce absorption and scattering from air.

Fig. 1 Ultrafast time-resolved Bragg coherent diffraction imaging.

Optical pulses (red) perturb the sample (green), generating phonons. Coherent x-ray pulses (generated from an XFEL) (blue) arrive a short time later. The diffracted pulses are recorded by an area detector, such as a CS-PAD.

The coherent diffraction patterns that were recorded from an individual nanocrystal (Fig. 2, A and B) show the modulated diffraction fringes, a consequence of the coherent illumination and finite nanocrystal size, which was much smaller than the x-ray beam. The fringes are most prominent in the facetted directions of the nanocrystal. The diffraction pattern collected immediately before the pump laser (Fig. 2A) shows a relatively symmetric fringe pattern, whereas the diffraction pattern collected +60 ps after (Fig. 2B) is more asymmetric, which is attributed to inhomogeneous lattice distortions i.e., an elastic strain gradient. Homogeneous contraction and expansion of the lattice (radial breathing modes) are manifested as a shift of the entire diffraction pattern (21) as the average lattice spacing changes across the nanocrystal. Shown in Fig. 2, C and D, is the angular shift of the gold (111) Bragg peak for two nanocrystals, I and II. For each time delay, the center of mass from the sum of 100 diffracted LCLS pulses was used to obtain the angular shift, with the error for each delay point given by the standard deviation. At the center of the rocking curve, ~104 diffracted photons are recorded per pulse. The homogeneous lattice expansion and contraction are evident as harmonic motion of the Bragg peak angular shift. Immediately after the arrival of the optical pump laser (positive delay times), the diffraction pattern starts shifting to lower angles. Because the crystal is much bigger than the electromagnetic “skin depth,” this behavior is only consistent with an electron-mediated model, such as the “two-temperature” model (24) of heating in which electrons are excited first and subsequently transfer energy to the lattice through electron-phonon coupling. The peak shift, S(τ) as a function of delay time, τ, is fitted by S(τ)=n=1NAnexp[ττd,n]cos[2πTn(τ+τ0,n)]+Cn (1) where n is the mode number, N(=2) is the total number of fitted modes, A is the amplitude, τd is the decay time, T is the period of the oscillation, and τ0 is the time offset. Two oscillation modes (red solid curve) are sufficient to fit the data shown in Fig. 2, C and D, within their errors with the fitted parameters summarized in table S1. The fitted values of the two periods from the data for nanocrystal I were 101 and 241 ps, and for nanocrystal II were 90 and 256 ps; the different oscillation periods between nanocrystals were a consequence of unequal sizes. These two oscillation modes are well reproduced by a molecular dynamics (MD) simulation (21) (fig. S1). Using the thermal expansion coefficient for bulk gold of 14.4(2) × 10−6 K−1 and the maximum change in the lattice constant, we estimated the temperature increase on each pump-probe cycle to be 44 K for each of the two nanocrystals. The fitted vibration amplitudes correspond to a maximum displacement of 600 pm at the surface of the crystal.

Fig. 2 Time-resolved Bragg coherent diffraction data from single nanocrystals.

(A and B) Experimentally recorded coherent diffraction patterns from a single nanocrystal for delay times of –10 and +60 ps, respectively. The diffraction patterns are the sum of 100 shots and are scaled logarithmically. (C and D) Gold (111) Bragg peak angular shift as a function of delay time from the same nanocrystal [(C), nanocrystal I] and a different nanocrystal [(D), nanocrystal II]. The blue dots are the experimental data and the solid red line is the modeled peak shift.

The peak position versus delay time shown in Fig. 2 agrees well with previous studies of gold nanoparticles (13, 25, 26) or thin films (5). The important distinction in this study is that we can monitor the behavior of individual nanocrystals using x-ray diffraction rather than the behavior of an ensemble (13, 25, 26). X-rays provide the structural sensitivity evident in Fig. 2, C and D, where both in-plane and out-of-plane cylinder oscillations are observed owing to the coupling of the Q vector to both these directions. Notably, the lifetime of the oscillations is relatively long in comparison to previous studies, because there is no ensemble averaging of heterogeneous periods in our experiment (1315, 21).

Thus far, we have identified two clear vibration modes in the expansion of the crystal. Further modes, such as shear modes, can be identified only by imaging the crystal distortions directly because these do not result in a shift of the Bragg peak position. Three-dimensional (3D) images as a function of delay time were obtained for nanocrystal I by collecting 3D coherent diffraction patterns and then recovering the lost phase of the diffracted wavefield by using iterative phase retrieval (21, 27). Complete knowledge of the diffracted wavefield (both amplitude and phase) allows an image of the nanocrystal to be obtained by an inverse Fourier transform. To obtain the missing phase of the diffracted wavefield, an iterative procedure is used that enforces the a priori knowledge that the nanocrystal is isolated, as well as consistency with the measured amplitude of the diffracted wavefield (from the measured intensity). These two constraints are enforced successively until a self-consistent solution is reached.

Figure 3 shows images of the phase of nanocrystal I, displayed as orthogonal cuts through the center for selected times. This phase is the change in the displacement of the crystal, projected onto the diffraction vector Q, whose direction is also shown in Fig. 3. The homogeneous (linear) lattice expansion and contraction resulting from the breathing modes of the nanocrystal have been removed (21), leaving only the inhomogeneous component that would manifest itself as a broadening or distortion of the Bragg peak rather than a peak shift. To emphasize the changes, we have subtracted the image at –40 ps from the subsequent times, which removes the contribution of small, static residual stresses in the nanocrystal. The spatial pattern of oscillating regions of expansion and contraction are well within the resolution of the image (21), estimated as 51 ± 7, 22 ± 3, and 55 ± 6 nm in the x, y, and z directions, respectively.

Fig. 3 Imaging of acoustic phonons in a nanocrystal.

Orthogonal cut planes through the center of nanocrystal I showing the projected displacement as a function of delay time. Three different viewing directions are shown. The direction of the displacement field is given by the Q vector in red. For clarity, the range of displacement has been truncated to ±26 pm instead of the full range of ±53 pm.

What is particularly evident in Fig. 3 is that the regions of expansion become regions of contraction and vice versa as the delay time increases (movie S1). This spatial and temporal reversal of expansion and contraction is indicative of the presence of a shear vibration mode of higher order than a simple breathing mode. Figure 4 shows the location of selected slices (top row) used to compare the experimental images (middle row) with the theoretical (1, 1) mode of a cylinder (bottom row) with a radius of 200 nm and a height of 220 nm (21). The good agreement between the data, theory, and MD simulation (fig. S2) strongly supports the presence of this otherwise invisible higher-order mode. Our observation of this 50-pm amplitude mode in the presence of a 600-pm breathing mode shows the considerable sensitivity gain by BCDI imaging.

Fig. 4 Comparison of data with theory.

Orthogonal slices taken either side of the center (top) of nanocrystal I compare the projected displacement obtained from the experiment (middle) with a simulated (1, 1) mode for a cylinder (bottom). Comparison is made for a delay time of +110 ps. The separation between the x-y and y-z slices is 180 nm and for the x-z slices 120 nm.

The combination of intense, coherent, and ultrashort x-ray pulses provided by XFELs has enabled direct, unambiguous imaging of coherent acoustic phonons in gold nanocrystals in three dimensions. The technique demonstrated here can be applied widely to investigate other materials such as semiconductors and nanostructures and, with continued improvement in experimental design, it should be possible to image particles with sizes less than 100 nm. Many other applications will become possible with the advent of coherent, ultrashort electron sources (28), which could provide atomic-scale images when used with diffractive imaging.

Supplementary Materials

Materials and Methods

Figs. S1 and S2

Table S1

References (2940)

Movie S1

References and Notes

  1. Materials and methods are available as supplementary materials on Science Online.
  2. Acknowledgments: This work was supported by FP7 advanced grant from the European Research Council. I.K.R is appreciative of support from the Engineering and Physical Sciences Research Council (EPSRC) under grant EP/I022562/1 and from the Biotechnology and Biological Sciences Research Council (BBSRC) under grant BB/H022597/1. A.H. was supported by Atomic Weapons Establishment. J.S.W. is grateful for support from the UK EPSRC under grant EP/H035877/1. A.M.K. is grateful for support from the EPSRC under grant EP/I020691/1. B.A. acknowledges the support of the Australian Research Council Centre of Excellence for Coherent X-ray Science. The experimental work was carried out at the Linac Coherent Light Source, a National User Facility operated by Stanford University on behalf of the U.S. Department of Energy, Office of Basic Energy Sciences. We acknowledge S. Boutet for insightful discussion.
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