Europhys. Lett., 61 (6), p. 762 (2003)
Time-resolved X-ray diffraction on laser-excited
metal nanoparticles
A. Plech 1 - S. Kürbitz 2 - K.-J. Berg 2 - H. Graener 2 - G. Berg 2 S. Grésillon 3 - M. Kaempfe 4 - J. Feldmann 4 M. Wulff 1 - G. von Plessen 5
1
ESRF - BP 220, F-38043 Grenoble, France
Fachbereich Physik der Martin-Luther-Universität Halle-Wittenberg
Friedemann-Bach-Platz 6, D-06108 Halle, Germany
3
ESPCI - 10 rue Vauquelin, F-75005 Paris, France
4
Physics Department and CeNS, University of Munich
Amalienstrasse 54, D-80799 München, Germany
5
I. Physikalisches Institut, RWTH Aachen - D-52056 Aachen, Germany
2
(Received 9 August 2002; accepted in final form 3 January 2003)
Abstract
The lattice expansion and relaxation of noble-metal nanoparticles heated by intense femtosecond
laser pulses are measured by pump-probe time-resolved X-ray scattering. Following the laser pulse,
shape and angular shift of the (111) Bragg reflection from crystalline silver and gold particles with
diameters from 20 to 100
are resolved stroboscopically using 100
X-ray pulses from a
synchrotron. We observe a transient lattice expansion that corresponds to a laser-induced
temperature rise of up to 200 , and a subsequent lattice relaxation. The relaxation occurs within
several hundred picoseconds for embedded silver particles, and several nanoseconds for supported
free gold particles. The relaxation time shows a strong dependence on particle size. The relaxation
rate appears to be limited by the thermal coupling of the particles to the matrix and substrate,
respectively, rather than by bulk thermal diffusion. Furthermore, X-ray diffraction can resolve the
internal strain state of the nanoparticles to separate non-thermal from thermal motion of the lattice.
PACS
61.10.Nz - Single-crystal and powder diffraction
65.80.+n - Thermal properties of small particles, nanocrystals, nanotubes
78.47.+p - Time-resolved optical spectroscopies and other ultrafast optical measurements in
condensed matter
Introduction
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 [1]. One interesting issue is what effects such different vibrational properties may
have on the rate of heat transfer across nanostructure interfaces [2]. 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 [3]. 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 timeresolved 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/Xray probe technique [17]. 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 [18].
Experimental
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).
We study spherical silver and gold nanoparticles of various sizes. The silver particles are prepared
in flat glass by ion exchange and subsequent tempering. The particle size is controllable by the
preparation conditions; it is derived from absorbance measurements (see inset of fig. 1a)) and TEM
analysis [19]. We investigate mean diameters from 24 to 100
, with size dispersions of below
10%. The analysis of the Scherrer width of the particles reveals that the small particles (diameter <
48
) are essentially single crystals, whereas the average grain size for the larger particles is less
than the particle size. For example, the average grain size in 100
particles is found to be about
57
. The second set of samples is prepared by self-assembly of gold colloids onto a
polyelectrolyte surface from aqueous solution as described in [20,21]. Commercial solutions
(BBInternational) containing spherical gold particles with defined diameters (20, 60, 80 and 100
) and dispersion (
) are used to deposit monolayered colloid films on polyelectrolytecoated silicon substrates, with surface coverages of around 10%.
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,
[17]. 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) [22]. The resulting Debye-Scherrer
rings are integrated azimuthally and corrected for polarization and geometry effects [23]. 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 [9]
by an accumulative effect that can reduce the size of the particles and create small precipitates
around them.
Figure 2: a) Relative lattice expansion for 86
embedded silver particles (full circles) and 100
supported gold
particles. The solid lines represent exponential fits to the data as explained in the text. b) Peak widths for the silver (full
circles) and gold (open circles) particles in a).
Figure 2a) displays the time evolution of the relative lattice expansion
derived from the peak
shift of embedded silver particles of 86
diameter and supported gold particles of 100
diameter at a laser fluence of 13
per pulse, corresponding to a peak irradiance of
. The expansion sets in around zero time delay. The true rise time of
is expected to be
much shorter [14] than the finite X-ray probe-pulse duration and thus cannot be resolved in our
experiment. This rise is followed by a relaxation indicating particle cooling. Finally, the lattice
parameters return to their room temperature values after several hundred picoseconds for embedded
silver particles, and several nanoseconds for supported gold particles. We will first discuss the
magnitude of the expansion immediately after the heating. In the regime studied here, the maximal
lattice expansion increases almost linearly with the applied power. From the maximal
in
fig. 2a) and the bulk expansion coefficients we calculate lattice temperature rises of
and 197 for the silver and gold particles, respectively. In comparison, an estimate of the energy
absorbed by each silver particle per pulse yields a
temperature rise, i.e., slightly higher
than derived from the measured expansion. Similar slight deviations of experimental results from
estimates are also observed at different pulse energies and may be caused by the constraint exerted
by the glass matrix, which is expected to somewhat reduce the particle expansion [24].
Figure 3: Relaxation times as a function of particle diameter. The full circles
represent the embedded silver particles. The solid line shows a fit based on eq. (1).
The broken line represents a simulation according to ref. [8]. The crosses
correspond to cooling times of embedded particles taken from refs. [4,6,7,8]. The
inset compares the relaxation times of the embedded silver particles to those for the
supported gold colloids (open circles).
The lattice relaxation displays a strong dependence on the particle size. This is shown in fig. 3,
where the relaxation time determined from an exponential decay fit taking into account the 80
probe time resolution around time zero (solid lines in fig. 2a)) is plotted vs. the particle diameter.
This dependence can be explained if one assumes that the heat transfer from the particles to the
glass matrix is limited by an interface resistance due to phonon-phonon coupling at the metal-glass
interface. Following standard macroscopic approaches [26], one obtains for the relative lattice
expansion
as a function of time t:
(1)
where , , c are the linear-expansion coefficient, density and heat capacity of silver (gold),
respectively, and Vand A are the particle volume and surface. The parameter hdenotes the heat
transfer coefficient of the boundary. In this approach the relaxation time, i.e. cooling time, will be a
linear function of the ratio V/A, therefore depending linearly on the particle diameter. Indeed this
relationship is found for a large range of sizes of the embedded silver particles, as shown by the
straight line in fig. 3. The heat transfer coefficient
determined from the
slope of the straight line lies at the upper edge of the range 0.2known from
planar solid-solid interfaces [3]. For comparison, fig. 3 also shows the cooling times for embedded
metal particles determined from all-optical time-resolved experiments in the literature
(crosses) [15,6,16,4,7]. The data in the particle size range 5-10
have been measured on silver
and gold particles in water using optical pump-probe or ultrafast lensing techniques [27,28,16,4].
They show cooling times between 20 and 150
, with relatively large deviations from each other.
The largest particles whose cooling times were reported in the literature (sol-gel embedded gold
particles of 30
diameter [7]) agree well with our results even for a slightly different system.
Alternatively to the scenario described above, the particle cooling could be limited by the bulk
thermal resistivity of the glass matrix, rather than by the interface resistance. For this scenario the
heat diffusion equation has been solved by Inouye et al. [8], leading to an algebraic expression
where the cooling time depends essentially on the square of the particle radius. The 1/e decay times
calculated using this approach are plotted as a dashed line in fig. 3, where a thermal diffusivity of
for glass has been assumed to fit the experimental data. Clearly, the fit is not
as good as in the first scenario. Another aspect casts additional doubt on the second scenario: Our
fit result of
disagrees with the literature value for flat glass of about
[26]. If we used this latter value for the calculation, the expected cooling times
would increase by a factor of 3, which is in clear contradiction to our findings. The second scenario
can only be saved by speculating that heat conduction in the glass is not entirely diffusive, but also
involves ballistic phonon transport, as the typical length scales approach the mean free path of
phonons in glass. Ballistic contributions to heat transport should be expected to accelerate the
particle cooling. Clearly, this issue requires further study in the future.
The inset of fig. 3 shows that the relaxation times for the supported gold colloids are about 5 to 10
times longer than for the embedded silver particles. This remarkable difference can be explained by
the reduced contact area between the supporting substrate and the particles, and thus by reduced
cooling. It is difficult to estimate the contact area quantitatively due to uncertainties in the faceting
of the particles and in the colloid-polyelectrolyte interaction, and due to a possible water wetting
meniscus.
The line width of the Scherrer ring also displays characteristic reactions upon laser excitation.
Generally, we find an increase in width immediately after excitation, which relaxes within
hundreds of picoseconds. In the case of embedded silver particles, the width relaxation (see
fig. 2b)) occurs on the time scale of the lattice cooling and can be fitted with the same relaxation
time. We attribute this Scherrer ring broadening to non-uniform laser heating of the particle
ensemble due to the finite optical extinction depth of the sample. In addition, the particles may be
heated non-uniformly due to particle-to-particle variations of their individual absorption spectra.
Summing up the scattering contributions from particles with different relative lattice expansions is
then expected to lead to an inhomogeneous broadening of the peak.
A different picture is present in the case of supported particles. Here we observe a relaxation of the
broadening that occurs on a time scale much smaller than the cooling time (see fig. 2b)). For
instance, we observe a width relaxation time of 800
vs. a cooling time of 18
for 100
particles, and 160
vs. 1.5
for 60
particles. Here we cannot ascribe the broadening to a
finite optical extinction depth, since the sample consists of a monolayer of colloids. Theoretically a
lattice in thermal equilibrium should not show broadening in the absence of lattice strain. On the
other hand, coherent lattice vibrations exert strain and are therefore expected to manifest
themselves as a broadening if the time resolution is insufficient to resolve individual vibration
periods. We therefore interpret the broadening of the Scherrer rings from the supported particles as
due to coherent lattice vibrations. Such lattice vibrations have previously been observed in alloptical experiments on metal nanoparticles [11,12,13,14]. They usually have picosecond time
periods and, in embedded particles, very short damping times below approximately 100
[29,11], due to an efficient damping of oscillations at the particle-matrix contact. In the case of
supported particles the contact area is strongly reduced and hence the damping should be much
weaker, thus making plausible the long relaxation times of the Scherrer width observed here for the
supported gold particles.
Non-thermal contributions are apparent for the embedded particles only for short time delays of
-100
(not shown here) from the analysis of the line shape of the Scherrer rings. A
shoulder at low angle appears in the Scherrer profiles for the smallest resolvable positive time
delays. This shoulder indicates a scattering contribution from an overshoot of the lattice expansion
as compared to adiabatic thermal expansion. The expansion determined from a fit to this shoulder
is, for instance, visible in the curve of the embedded 88
particles at a time delay of 100
in
fig. 2a), where a relative lattice expansion of
is reached. This data point represents a
strong deviation of the expansion from the assumed exponential decay and was therefore not
included in the fitting procedure used to determine the relaxation times. It indicates, however, that
coherent particle vibrations with amplitudes considerably exceeding the adiabatic thermal
expansion occur initially. This non-thermal motion seems to be damped out within the X-ray probepulse duration (i.e. within
).
Conclusion
In summary, we have investigated the lattice expansion and relaxation of noble-metal nanoparticles
heated by femtosecond laser pulses, using time-resolved X-ray diffraction. The lattice expansion
decays within several hundred picoseconds in embedded particles, and several nanoseconds in
supported particles, due to heat transfer to the embedding/supporting material. The decay rate
shows a strong dependence on particle size. We have also observed non-thermal contributions to
the structural dynamics. We expect that the experimental technique employed here will be of great
interest for future investigations of the structural dynamics of nanocrystalline matter.
References
1. Kara A. and Rahman T. S., Phys. Rev. Lett., 81 (1998) 1453. APS Link
2. edited by Majumdar A., Peterson G. P. and Poulikakos D. J. Heat Transfer (Special Issue),
124 (2002).
3. Cahill D. G., Goodson K. and Majumdar A., J. Heat Transfer, 124 (2002) 223, and
references therein.
4. Tokizaki T., Nakamura A., Kanedo S., Uchida K., Omi S., Tanji H. and Asahara Y., Appl.
Phys. Lett., 65 (1994) 941.
5. Bigot J.-Y., Merle J.-C., Cregut O. and Daunois A., Phys. Rev. Lett., 75 (1995) 4702. APS
Link
6. Roberti T. W., Smith B. A. and Zhang Z., J. Chem. Phys., 102 (1995) 3860.
7. Perner M., Bost P., Lemmer U., von Plessen G., Feldmann J., Becker U., Mennig M.,
Schmitt M. and Schmidt H., Phys. Rev. Lett., 78 (1997) 2192. APS Link
8. Inouye H., Tanaka K., Tanahashi I. and Hirao K., Phys. Rev. B, 57 (1998) 11334. APS Link
9. Kaempfe M., Rainer T., Berg K. J., Seifert G. and Graener H., Appl. Phys. Lett., 74 (1999)
1200.
10. Nisoli M., de Silvestri S., Cavalieri A., Malvezzi A. M., Stella A., Lanzani G., Cheyssac P.
and Kofman R., Phys. Rev. B, 55 (1997) R13424. APS Link
11. Hodak J. H., Henglein A. and Hartland G. V., J. Chem. Phys., 111 (1999) 8613.
12. del Fatti N., Voisin C., Chevy F., Vallée F. and Flytzanis C., J. Chem. Phys., 110 (1999)
11484.
13. Qian W., Yan H., Wang J. J., Zoua Y. H., Lin L. and Wu J. L., Appl. Phys. Lett., 74 (1999)
29.
14. Perner M., Grésillon S., März J., von Plessen G., Feldmann J., Porstendorfer J., Berg K.-J.
and Berg G., Phys. Rev. Lett., 85 (2000) 792. APS Link
15. Harata A., Taura J. and Ogawa T., Jpn. J. Appl. Phys., 39 (2000) 2909.
16. Link S. and El-Sayed M. A., Int. Rev. Phys. Chem., 19 (2000) 409, and references therein.
17. Schotte F., Techert S., Anfinrud P. A., Srajer V., Moffat K. and Wulff M., in ThirdGeneration Hard X-ray Synchrotron Radiation Sources edited by Mills D. John Wiley &
Sons, Inc. (2002).
18. Reis D. A., DeCamp M. F., Bucksbaum P. H., Clarke R., Dufresne E., Hertlein M., Merlin
R., Falcone R., Kapteyn H., Murnane M. M., Larsson J., Missalla Th. and Wark J. S., Phys.
Rev. Lett., 86 (2001) 3072. APS Link
19. Berg K.-J., Berger A. and Hofmeister H., Z. Phys. D, 20 (1991) 309.
20. Schmitt J., Mächtle P., Eck D., Möhwald H. and Helm C. A., Langmuir, 15 (1999) 3256,
and supporting information.
21. Schrof W., Rozouvan S., Van Keuren E., Horn D., Schmitt J. and Decher G., Adv. Mater., 3
(1998) 338.
22. Techert S., Schotte F. and Wulff M., Phys. Rev. Lett., 86 (2001) 2030; APS Link Neutze R.,
Wouts R., Techert S., Davidsson J., Kocsis M., Kirrander A., Schotte F. and Wulff M.,
Phys. Rev. Lett., 87 (2001) 195508-1 APS Link.
23. Hammersley A. P., Svensson S. O., Hanfland M., Fitch A. and Häusermann D., High Press.
Res., 14 (1996) 235.
24. The confinement of the metal particle in a low-expansion matrix can influence the
expansion coefficient [25]. In the present case, this means that the matrix can restrict the
expansion of the particle, leading to an effectively lowered expansion coefficient.
25. Dubiel M., Brunsch S., Seifert W., Hofmeister H. and Tan G. L., Eur. Phys. J. D, 16 (2001)
229; EDPS Link Brunsch S., Doctoral Thesis at the University of Halle-Wittemberg,
Germany (2000).
26. Bejan A., Heat Transfer John Wiley & Sons, New York (1993).
27. Ito K., Tsuyumoto I., Harata A. and Sawada T., Chem. Phys. Lett., 318 (2000) 1; Harata A.,
Taura J. and Ogawa T., Jpn. J. Appl. Phys., 39 (part 1) (2000) 2909.
28. Roberti T. W., Smith B. A. and Zhang Z., J. Chem. Phys., 102 (1995) 3860.
29. del Fatti N., Voisin C., Chevy F., Vallée F. and Flytzanis C., J. Chem. Phys., 110 (1999)
11484; Voisin C., del Fatti N., Christofilos D. and Vallée F., J. Phys. Chem., 105 (2001)
2264.