The vibrational properties of nanocrystalline materials, such as the vibrational density of states, can substantially differ from those of bulk crystals, with significant implications for their thermodynamics . One interesting issue is what effects such different vibrational properties may have on the rate of heat transfer across nanostructure interfaces . In comparison to macroscopic situations, heat transfer processes may be considerably modified as structure sizes approach the length scales of electron and phonon wavelengths and mean free paths. Relatively little is known experimentally on the rate of heat transfer from two- or three-dimensionally confined nanostructures, presumably due to difficulties in measuring such rates on extremely small length scales . From an applied point of view, an improved knowledge and understanding of heat transfer processes from such nanostructures appears desirable, as feature sizes of microelectronic devices continue to shrink to nanometer dimensions, leading to increased power dissipation per unit volume and aggravated cooling problems, with the risk of device failure if local overheating occurs.
Here we investigate the thermal dynamics of metal nanoparticles that are heated by femtosecond laser pulses and subsequently cool down via heat transfer to the environment. The electron and lattice dynamics of this model system has previously been investigated in a number of time-resolved optical pump-probe experiments [4,5,6,7,8,9,10,11,12,13,14,15,16]. It is known to be controlled, on femto- and picosecond time scales, by thermalization of the laser-excited electrons and subsequent electron cooling concomitant with lattice heating. The lattice expansion associated with the lattice heating triggers coherent particle vibrations observable as picosecond periodic signal modulations [11,12,13,14]. However, the heat transfer from the nanoparticles into the embedding material, which usually occurs on much longer time scales, has attracted little attention. For example, it is unclear whether the heat transfer rate is limited by the thermal coupling of the nanoparticles to the embedding matrix, or by bulk thermal diffusion in the embedding material. In the present work, we address this and related issues, using a novel time-resolved optical pump/X-ray probe technique . It gives us much more direct access to the lattice dynamics in the nanoparticles than was available from previous all-optical experiments. The advantage of X-ray scattering methods is that they directly probe the lattice parameter and strain state of the metal particles. Therefore they give direct access to structural properties such as lattice temperature and coherent motion, as recently shown in the case of semiconductor surfaces .
Figure 1: Debye-Scherrer ring profiles for a) embedded silver particles of 79 diameter and b) supported gold particles of 20 diameter at different delay times after excitation. Full circles: non-excited profile; open circles in a): ; crosses: . Open circles in b): . Insets: absorbance of the samples. Sketches: experimental geometries, i.e. transmission geometry for embedded particles and reflection geometry for supported particles (X denoting incoming X-ray beam, L laser beam, S sample and X-rays scattered under twice the Bragg angle onto the area detector D).
By synchronizing a femtosecond laser to the pulse structure of X-rays emitted from the synchrotron radiation source ESRF (Grenoble), we resolve the (111) Bragg reflection of the metal lattice as a function of delay time between exciting laser pulse and probing X-ray pulse, . The laser system at the station ID09B is an amplified Ti:sapphire femtosecond laser that is phase-locked to the RF clock of the storage ring. The laser delivers pulses of 150 duration at a wavelength of 800 , which are frequency doubled in a BBO crystal to excite the plasmon resonance of the particles (see insets of fig. 1). The chirped pulse amplifier runs at a repetition rate of 896.6 , the 392832th subharmonic of the RF clock. The X-ray pulses are diluted to the same 896.6 repetition rate by a ultrasonic mechanical chopper wheel. The powder scattering from the samples of the monochromatic X-rays (16.45 , (111) double monochromator, toroidal mirror) is collected on a two-dimensional CCD camera (Mar Research) . The resulting Debye-Scherrer rings are integrated azimuthally and corrected for polarization and geometry effects . The X-ray pulse length lies between 90 and 110 (FWHM), depending on the ring current. The delay time is varied by means of electronic delay units, with a typical jitter of 10 (RMS), which is small compared to the X-ray pulse duration. The scattering from X-ray probe pulses is accumulated on the detector at each . As the volume filling factor of the embedded particles is only of the order of 10-4, the Scherrer rings have an intensity of about 5 to 10% of the scattering from the glass matrix. This background is used for a normalization of the profiles prior to baseline subtraction. The embedded particles are excited and probed in transmission geometry through the 0.1-0.2 thick glass substrates, whereas the supported particles are excited and probed in reflection geometry (see insets of figs. 1a) and b)). Grazing angles of 8 degrees for X-rays and 30 degrees for the laser are used in the latter geometry.
Results and discussion
Azimuthally integrated profiles of the Debye-Scherrer rings are presented in fig. 1 for various time delays of the X-ray probe pulses with respect to the laser excitation pulses, . A shift of the peak position is observed for small positive . This shift is a direct measure of the lattice expansion caused by the laser heating of the particles. Peaks split in position at times around 0 , where the earlier part of the X-ray pulse probes the non-excited sample and the later part the excited sample. This splitting allows a determination of the shift even at times shorter than the X-ray pulse duration. The effective time resolution for measuring the onset of the laser-induced lattice expansion is therefore lowered to about 80 .
The laser fluence on the silver samples is optimized for highest lattice expansion without noticeable damage of the sample on the time scale of the experiment (several hours of exposure, corresponding to approximately 107 laser pulses). We note that irreversible damage at higher fluences shows itself as a gradual decrease of the Bragg intensity, followed by Scherrer profile changes. It is known that the particles can be deformed upon excitation with intense laser pulses  by an accumulative effect that can reduce the size of the particles and create small precipitates around them.