Dr Karl Ridier

Alin-Ciprian Bas

Dr Victoria Shalabaeva

Dr William Nicolazzi

Dr Lionel Salmon

Dr Gábor Molnár
email: gabor.molnar@lcc-toulouse.fr

Azzedine Bousseksou

Dr Maciej Lorenc
email: maciej.lorenc@univ-rennes1.fr

Dr Roman Bertoni

Eric Collet

Dr Hervé Cailleau

Dr A.-C Bas

Prof H Cailleau

Prof E Collet

Finite size effects on the switching dynamics of spin-crossover thin films photo-excited by a femtosecond laser pulse

Keywords: photoswitching dynamics, spin crossover, thin films, size reduction effects, femtosecond optical spectroscopy

Using ultrafast optical absorption spectroscopy, we have studied the room-temperature spinstate switching dynamics induced by a femtosecond laser pulse in high-quality thin films of the molecular spin-crossover complex [Fe(HB(tz)3)2] (tz = 1,2,4-triazol-1-yl). These measurements reveal that the early, sub-picosecond, low-spin to high-spin photoswitching event, with linear response to the laser pulse energy, can be followed under certain conditions by a second switching process occurring on a tens of nanoseconds timescale, enabling nonlinear amplification. Such out-of-equilibrium dynamics is discussed in light of characteristic timescales associated with the different switching mechanisms, i.e. the electronic and structural rearrangements of photo-excited molecules, the propagation of strain waves at the material scale and the thermal activation above the molecular energy barrier. Importantly, size reduction effects are evidenced on the second switching step. Notably, this nonlinear process appears to be completely suppressed in the thinnest (50 nm) film due to the efficient heat transfer to the substrate, allowing the system to retrieve the thermal equilibrium state on the 100-ns timescale.

These results provide a first milestone towards the assessment of the physical parameters that

drive the photo-response of spin-crossover thin films, opening up appealing perspectives for their use as high-frequency all-optical switches working at room temperature.

Spin-crossover (SCO) solids of 3d 4 -3d 7 transition metal complexes constitute the archetypal example of multifunctional molecular materials able to switch reversibly between the so-called low-spin (LS) and high-spin (HS) states through the application of a variety of external stimuli (temperature, pressure, intense magnetic field, light irradiation, etc.). [1][START_REF] Gütlich | Spin Crossover in Transition Metal Compounds I-III[END_REF][START_REF] Bousseksou | [END_REF][START_REF] Halcrow | Spin-Crossover Materials: Properties and Applications[END_REF][START_REF] Bousseksou | [END_REF] The SCO phenomenon entails spectacular changes in the physical properties of the material, including optical, magnetic, mechanical and electrical responses. At the molecular scale, the electronic spin-state change is concomitant with an important structural rearrangement (in particular a sizeable increase of the metal-ligand bond lengths in the HS state), which gives rise to long-range elastic interactions and cooperative effects in the solid. Such a cooperative feedback between the molecular spin state and the lattice volume may result in a first-order isostructural phase transition between the LS and HS phases, characterized by a discontinuity in the evolution of the unit-cell parameters. [6] The recent progress in the nanoscale synthesis and organization of SCO materials allowed the elaboration of a variety of molecular nano-objects (nanoparticles, thin films, nanopatterns, nanoscale assemblies, etc.) exhibiting spin transition in some cases at technologically relevant temperatures. [7][8][9][10][11][12][13][14] These new nanometer-sized materials pave the way for the implementation of the SCO phenomenon in various applications including information processing, sensor and actuator devices. [15,16] Until now, the focus of these studies has been the investigation of size reduction and surface/interface effects on the thermal spin-transition behavior (transition temperature, hysteresis width, completeness of the transition). Beyond the LS-HS phase stability, however, another key issue is to understand the evolution of the dynamical properties of the spin-state switching process upon downsizing. This last subject has remained largely unexplored so far. Time-resolved pump-probe optical spectroscopic and X-ray diffraction measurements have been carried out on bulk single crystals to identify the fundamental mechanisms that drive the switching dynamics in SCO solids after light excitation, and thereby pave the way for the control of their macroscopic properties with ultrashort laser pulses. These studies have revealed the existence of multi-scale out-of-equilibrium dynamics in response to a femtosecond laser pulse, from the molecular to the material scale, described by a sequence of three consecutive steps (sic photo, elastic and thermal switching) at distinct timescales (ps, ns and µs, respectively). [17][18][19][20] While the first step corresponds to the ultrafast electronic and structural reorganization at the molecular scale, the second step is associated with the volume change of the lattice at the material scale, which is not instantaneous and requires strain propagation on the so-called acoustic timescale. Finally, the last step is triggered by an increase of the average temperature of the sample due to heat diffusion.

A current big challenge is to determine the evolution of these dynamical phenomena in the spinstate switching process with size reduction. [20][21][22][23] In a general manner, size reduction appears to be a promising route to achieve extremely fast switching dynamics because both strain wave propagation and heat diffusion take place on shorter timescales in nanoscale systems. The first femtosecond optical spectroscopic measurements performed on SCO nanoparticles dispersed in a polymer matrix have recently demonstrated the interplay between the sample size and the relative evolution (in terms of amplitude and timescale) of the three consecutive steps during the out-of-equilibrium photoswitching dynamics. [20,21] While the molecular photoexcitation process was noticeably enhanced in nanocrystals due to a better light penetration, the 'elastic' step was shifted towards shorter timescales and the microsecond 'thermal' step was found considerably attenuated (or even absent). Another interesting approach uses time-resolved electron diffraction to probe the photoresponse (in terms of structural dynamics) of SCO nanocrystals to pulsed laser excitations. [24] In particular, four-dimensional electron microscopy, which combines time-resolved electron diffraction and real-space imaging, has proven to be a powerful technique to investigate the spatiotemporal dynamics of individual SCO nanoparticles. [25,26] In bulk crystals, the finite laser penetration depth gives rise to an inhomogeneous distribution of photo-switched molecules as well as temperature and stress gradients within the sample, which induce delayed dynamical responses associated with strain wave propagation and heat diffusion. By contrast, the use of emerging, high-quality thin-film SCO samples offers the possibility to suppress these inhomogeneous 'bulk' effects and fine-tune the lattice response by adjusting the film thickness. Studying the spin-state switching dynamics in these SCO thin films is not only of strong interest from a fundamental point of view, but appears also essential in order to determine the accessible switching times and modulation frequencies in devices integrating such SCO nanomaterials.

To these aims, we have carried out a detailed investigation of the ultrafast switching dynamics in thin films of the molecular complex [Fe(HB(tz)3)2] (tz = 1,2,4-triazol-1-yl) (1). Crystals of (1) are known to exhibit an extremely abrupt first-order, isostructural spin transition above room temperature (334 K) [27] associated with an exceptionally high resilience upon repeated switching. [28] Recently, this complex was successfully deposited on different substrates by thermal evaporation allowing to obtain high-quality, nanocrystalline thin films in which the SCO properties are close to those encountered in the bulk counterpart. [29] The well-controlled, nanometric thickness and the high quality of these films offer unprecedented possibilities to investigate the ultra-fast spin-state switching dynamics in SCO nano-objects at room temperature, compared to previous studies performed on single crystals prepared by ultramicrotomy [24] or on nanocrystals dispersed in a polymer matrix. [20,21] For the experiments discussed below, thin films of (1) with different nominal thicknesses (50, 100 and 150 nm) were grown onto fused silica substrates by thermal evaporation as described previously. [29] A post-deposition solvent-vapor annealing treatment results in smooth, dense and highly-oriented nanocrystalline films (see Figures 1a and1b), growing with the orthorhombic c-axis normal to the substrate surface. Figure 1c shows the UV-vis absorbance spectra of the 100-nm-thick film at various temperatures between 293 and 393 K. At room temperature (LS state), the films exhibit intense absorption bands in the UV range between 250 and 340 nm (presumably corresponding to charge-transfer transitions), which are completely bleached upon heating the film above the transition temperature (HS state). The temperature dependence of the HS fraction, extracted from the variation of the optical density at  = 317 nm, is displayed in Figure 1d. The films of different thicknesses exhibit a very similar, abrupt, complete and well-reproducible spin transition around 336-337 K with a narrow thermal hysteresis of ca. 0.8 K width. As already observed and analyzed in a previous study, [30] a slight upshift of the transition temperature is observed when decreasing the film thickness (inset of Figure 1d), from 336 K to 337.4 K for the 150-nm and 50-nm-thick films, respectively.

The photoswitching dynamics of the three thin films were investigated by femtosecond pumpprobe optical spectroscopic measurements in transmission geometry with the experimental setup described in detail in ref. [19]. Thin films were excited with an 80-fs pump laser pulse and their transient optical transmission was probed using a delayed laser pulse. The delay between pump and probe pulses was controlled by combining a mechanical translation stage, to adjust the optical path difference for sub-ns measurements, with an electronic synchronization scheme of laser amplifiers for measurements in the ns-to-ms time domain. The film temperature was controlled in situ by a nitrogen gas flow. The experiments were carried out with a 500 Hz pump repetition rate, set to 570 nm on the weak d-d absorption band of the complex in its LS state. This absorption band centered around 535 nm is well evidenced on a thicker (700 nm) film of (1) (see Figure S1 in the Supporting Information). The laser beam of diameter ca. 150 µm propagates normal to the film surface. The pump energy was varied between 1 and 8 µJ. The probe wavelength was set to 320 nm (where the optical density change is maximum between the LS and HS states) to monitor the resulting LS-to-HS switching dynamics through the time variation of the optical density ∆OD(t). The time evolution of the HS fraction ∆nHS(t) was then extracted from ∆OD(t), knowing the absolute change of OD between the full LS and HS states measured, respectively, at 293 and 393 K:

∆𝑛 𝐻𝑆 (𝑡) = ∆𝑂𝐷(𝑡) 𝑂𝐷 𝐻𝑆 -𝑂𝐷 𝐿𝑆 (1)
Figure 2a displays the time evolution of the relative change of the optical transmission ∆T / T at  = 320 nm in the 100-nm-thick film on the ps timescale at two different temperatures (293 and 375 K) following a 2-µJ femtosecond laser excitation. At room temperature, the photoinduced signal reflects a decrease of the optical density, which is attributed to the photoconversion of a small amount of molecules from the LS to the HS state. A comparative measurement performed on the same area of the film above the transition temperature (375 K)

shows no detectable long-lived photo-induced signal. Finally, the same fraction of photoswitched molecules is retrieved on return to room temperature. Comparable observations were made in the three films (see Figure S2).

As depicted in Figure 2a, the photo-induced switching between the molecular LS and HS states, probed through the relative change of the optical transmission, typically occurs on the subpicosecond timescale. A biexponential fit appears necessary to reproduce the observed dynamics (see Figure S3). The shorter time constant (τ1 = 171 ± 8 fs) is related to the ultrafast dynamics of the intersystem crossing trajectory through transient excited states, that leads to the population of the HS state. Such an ultra-fast process, which takes place at the molecular scale, has been already observed in various SCO compounds, whether the switchable molecules are in solution or in a crystalline structure. [31][32][33][34][35][36][37] The second (longer) time constant (τ2 = 2.4 ± 0.4 ps) presumably describes the vibrational cooling of the "hot" excited molecules, which arrive in the final HS potential with excess vibrational energy. [21,38] This cooling process drains the population to the bottom of the HS potential and causes an additional slight variation of the optical density. After about ten picoseconds, the vibrational cooling is completed and the change of optical density can be directly related to the fraction of photo-converted HS molecules. Figure 2b shows that this HS fraction, hereafter denoted ∆nHS hν , remains constant during the first nanosecond. As displayed in the inset of Figure 2b, ∆nHS hν grows linearly with the excitation density, independently of the film thickness, as expected for an intramolecular process.

To probe the switching dynamics and the relaxation phenomena on longer timescales, we have performed measurements on a broader temporal range [100 ps -1 ms] after photoexcitation.

As depicted in Figure 3a, different photoresponses are evidenced at room temperature in the 100-nm-thick film within the ns-µs time domain depending on the excitation density. For fluences below 4 µJ, the photo-switched molecules return to the LS ground state through a single-step relaxation process occurring within 100 ns. Above a threshold excitation density (6 µJ), a pronounced increase of the fraction of HS molecules is observed in the 20-40 ns time window, which in turn leads to delaying noticeably the relaxation to the LS state. This two-step response in terms of ∆nHS has also been evidenced in the 150-nm-thick film at a lower threshold of 4 µJ, but does not appear in the thinner film of 50 nm, at least within the explored excitation energies (see Figure S4).

To determine the origin of this additional switching process occurring on the ns timescale, we have carried out temperature-dependent measurements. Figure 3b shows that for a given excitation density (4 µJ), the 25-ns peak grows progressively as the film temperature is increased while the sub-ns-timescale plateau remains constant (∆nHS hν ≈ 2.25 %). The temperature dependence of ∆nHS at t = 25 ns and its non-linear variation with the pump energy (threshold effect) demonstrate that the photo-response around t = 25 ns can be related to a thermally activated switching process (this will be hereafter denoted ∆nHS th ). Figure 3c compares the variations of ∆nHS hν and ∆nHS th with increasing excitation energy at two different temperatures (see also Figure S5). As discussed above, ∆nHS hν , measured on the picosecond timescale, is independent of the film temperature and increases linearly with the laser pulse energy. By contrast, ∆nHS th shows a strong dependence with the temperature and its evolution with the pump energy clearly departs from the linear regime. This non-linear behavior leads to a strong increase of ∆nHS (up to 14 %) at large excitation energies (8 µJ) and high temperatures (315 K) in the 100-nm-thick film. At room temperature, for excitations below ca. 4 µJ, the system relaxes and ∆nHS th < ∆nHS hν , whereas above this 'threshold' energy value, amplification occurs and ∆nHS th > ∆nHS hν . At 315 K, ∆nHS th is always higher than ∆nHS hν , even when using low pump energies.

Figure 3d compares the room-temperature photoresponse of the three films of (1) following a 6-µJ laser pulse. (The photoresponse to various excitation energies is shown in Figure S6.) As already mentioned above, the fraction of photoswitched molecules on the sub-ns-timescale plateau ∆nHS hν is identical in the three films for a given excitation energy, since the pump laser penetration depth ( ≈ 50 µm) is much larger than the thickness of the films. Size reduction effects are, however, clearly visible in the long-timescale dynamics. The main observation is that the additional switching step around 25 ns vanishes progressively when the film thickness is reduced. In the thinnest film (50 nm), regardless of the pump energy (0-6 µJ), the system directly recovers the LS ground state within ca. 100 ns. This relaxation time tends towards the molecular relaxation limit measured for similar Fe II SCO systems in solution, in which the lifetime of the photo-induced HS state falls in the typical 1-50 ns range at room temperature. [START_REF] Brady | Spin Crossover in Transition Metal Compounds III[END_REF] In the thicker films (100 and 150 nm), an additional amplification occurs (∆nHS th > ∆nHS hν ) and the recovery of the thermodynamic equilibrium appears noticeably delayed towards the μs timescale.

The physical picture hinges on the following lines.

(1) In contrast with a bulk crystal, the optical pump pulse excites the SCO molecules in a homogeneous manner along the direction of the laser propagation, owing to the small thickness of the films (L ≈ 100 nm) compared to the laser penetration depth ( ≈ 50 µm at 570 nm). This homogeneous distribution of photo-excited HS molecules within the LS lattice is clearly supported by the sub-ns experimental data in Figures 2b and3d, which displays no thickness dependence. During the initial LS-to-HS switching step, the swelling of the molecular volume gives rise to a substantial photo-induced stress within the material. The latter is also accompanied by a thermal stress, arising from the homogeneous increase of the lattice temperature (within a few picoseconds [START_REF] Li | [END_REF] ) due to the incoherent transfer of the electronic excess energy to the lattice via electron-phonon coupling.

(2) This thermal and non-thermal photo-induced stress builds up faster than the lattice can expand, so that the macroscopic volume remains constant at this stage. The mechanical equilibrium with the environment is then restored via the coherent propagation of collective strain waves within the sample, [17,19,41] on the so-called "acoustic timescale" defined by the ratio L / v, where L is a typical length and v is the longitudinal sound velocity (ca. 3 km.s -1 ). [42] Therefore, we can estimate that the photo-induced stress along the direction perpendicular to the substrate plane should rapidly relax (within only a few tens of ps), making a clear difference between thin films and bulk crystals. A sizeable expansion of the crystal lattice along the c-axis is then expected from the thermal variation of the unit-cell parameters (see Figure S7). [27] In addition, it is worth to mention that a second acoustic timescale should be considered, determined by the size of the irradiated area on the thin-film sample (beamwaist ca. 150 µm) and expected to occur on a 10's of ns timescale.

(3) On the shortest acoustic timescale (tens of ps), despite the rise of the lattice temperature and the completion of lattice expansion along the c-axis, our experimental data do not show any additional spin-state switching. This result stems from the fact that the activated LS ↔ HS switching rate is governed by a significant intramolecular energy barrier, making the molecular spin states (LS or HS) locally "frozen" on the sub-ns timescale. Instead, the second jump of the HS fraction is observed only in the 20-40 ns range after the laser pulse. For low pump energies, we can notice that the photoswitched HS molecules directly relax towards the thermal equilibrium state within a few tens of ns, which gives a reliable estimation of the timescale of the thermally activated molecular switching phenomenon. For higher pump energies, the observed second jump occurs within the same timescale window, which hints at the role played by thermal activation in the process. It is also interesting to mention that the observed values of ∆nHS th are in agreement with a moderate increase of the lattice temperature, which can be estimated of the order of 3 K per % of ∆nHS hν . That said, we must mention the possible role played by in-plane elastic stress relaxation in this second switching step. Indeed, as discussed above, the in-plane relaxation can be estimated to occur on a tens of ns timescale, which is an intriguing coincidence with the delayed increase of the HS fraction.

(4) Finally, the recovery to a complete thermal equilibrium with the external environment is mainly governed by the transfer of the thermal energy, imparted by the laser pulse, into the substrate. To estimate the related timescale, we can mention that the characteristic time associated with heat diffusion across the thin films of thickness L can be approximated by the ratio τ = L 2 / DT ≈ 10-80 ns, where DT = 2.6 × 10 -7 m 2 .s -1 is the thermal diffusivity. [28] The actual heat transfer may require longer time at grain boundaries and/or at the film-substrate interface, [43] but will be completed in less than 1 µs. [44] This is in good agreement with our experimental observations for the recovery of the initial state within 0.1-1 µs (depending on the experimental conditions). In the absence of heat exchange with the external environment, the same transient temperature jump (i.e. the same response in terms of ∆nHS) would be expected in the three films. The large difference observed between the three samples proves that the reduction of the film thickness, and thereby the thermal exchange coupling with the substrate, plays a key role in the observed phenomena. Indeed, as the contribution of heat exchange follows the surface-to-volume ratio (and then varies as L -1 ), the reduction of the film thickness allows a better dissipation of the heat generated by the laser pulse. Consequently, size reduction contributes to lower the transient temperature jump undergone by the sample and thus accelerate the recovery of the thermodynamic equilibrium state.

To summarize, time-resolved optical spectroscopic measurements of the out-of-equilibrium switching dynamics induced by a femtosecond laser excitation were performed on nanocrystalline SCO thin films exhibiting first-order spin transition near room temperature. The well-controlled, nanometric thickness of the studied films allowed for quantitative measurements of the transient optical transmission and an accurate determination of the photoinduced HS fraction evolving on successive timescales. Contrary to bulk samples, an important asset of the present experiments is the homogeneous distribution of the photo-switched molecules and of the lattice temperature following the laser pulse. Crucially, these high-quality, thin films brought into light the consequences of delayed thermal activation and size reduction effects on the multiscale switching dynamics. Overall, the following new features have been evidenced:

(1) The absence of spin-state switching concomitant with the lattice expansion along the direction perpendicular to the film, presumably because the corresponding acoustic timescale in such nanometric films is too short compared to the time needed to activate the molecular switching above the energy barrier, making the latter a temporal bottleneck for the transition.

(2) The observation of a delayed, nonlinear, thermally activated response on the 20-40 ns timescale, governed by the intramolecular LS ↔ HS energy barrier. Further investigations are required to better understand if this additional switching step is purely of thermal origin or related to elastic contributions, as it may be suggested because the involved timescale is compatible with the in-plane strain propagation.

(3) The existence of another visible size reduction effect in the photoswitching dynamics related to a more efficient heat transfer to the substrate in the thinnest film, which has the effect of preventing the second switching step and accelerating the recovery of thermal equilibrium.

To conclude, we demonstrate that these newly synthesized high-quality SCO thin films pave the way for pioneering investigations on the switching dynamics at the nanometric scale, which are fundamental in order to control and manipulate the physical properties of SCO nanomaterials using ultrafast stimuli. Importantly, these films also offer an unprecedented opportunity to perform time-resolved diffraction studies of the structural dynamics in the near future. In terms of applications, while the sub-picosecond molecular photoswitching constitutes a well-known and appealing feature, the time needed by the system to recover its initial state has been less considered up to now, despite this being the main limiting factor for operation at high frequencies. In this context, the present results demonstrate that nanometric films of (1) can be used in ambient conditions as ultra-fast molecular switches in devices, driven by ultrashort laser excitations and working in the 1-10 MHz frequency range. Material engineering in terms of intramolecular energy barriers and thermal/mechanical couplings between the film and the substrate appear as the most promising ways for further improving/tuning the photoswitching properties of SCO nanomaterials. The growth kinetics of the HS fraction are described using a biexponential model. The shorter time constant (typically τ1 = 140-170 fs) is related to the ultrafast dynamics of the intersystem crossing process between the LS and HS states and the second (longer) time constant (τ2 = 1.9-2.7 ps) describes the vibrational cooling of the "hot" excited molecules, which populate the HS potential with an excess vibrational energy. Evolution of ∆nHS at room temperature on the ns-ms time window in the three films (a) 50 nm, (b) 100 nm and (c) 150 nm, following a femtosecond laser pulse with various excitation energies. In the thinner film (50 nm), the relaxation occurs through a one-step process regardless of the pump laser energy (0-6 µJ). In the 100-nm-thick film, a self-amplification of the fraction of HS molecules is observed around 20-40 ns above a threshold energy value of 6 µJ. The same behavior is observed in the 150-nm-thick film, but the additional switching step appears above a threshold laser energy of 4 µJ.

. Thermal variation of the unit-cell parameters and lattice volume extracted from Xray diffraction measurements on a bulk powder sample of (1) in the heating mode. [S1]

Figure 1 .

 1 Figure 1. (a) Photograph of the 100-nm-thick film of (1) deposited on a silica substrate. (b) Atomic force microscopy (AFM) topography image of this film (image size is 10 × 10 µm 2 ). (c) Optical absorbance spectra of the 100-nm-thick film acquired at selected temperatures between 293 K (LS) and 393 K (HS). Inset: optical density change ∆OD = OD293K -OD393K in the three films as a function of the wavelength. (d) Temperature dependence of the HS fraction extracted from the variation of the optical density at  = 317 nm along one heatingcooling cycle at 1 K / min scan rate for the three films. The inset shows the derivatives of the transition curves in the heating mode.

Figure 2 .Figure 3 .

 23 Figure 2. Photoresponse of the thin films of (1) on the ps-ns time range to a femtosecond laser pulse. (a) Time evolution of the relative change of the optical transmission ∆T / T at = 320 nm in the 100-nm-thick film at two different temperatures 293 K (initial LS) and 375 K (initial HS) after a 2-µJ laser pulse. (b) Time evolution of ∆nHS in the same film on the 0-1 ns timescale at 293 K in response to a laser pulse with various excitation energies. The inset shows the evolution of ∆nHS hν with respect to the laser pulse energy for the three filmsrevealing the same, size-independent linear behavior.

FiniteFigure S2 .Figure S3 .

 S2S3 Figure S2. Time evolution of the photo-induced HS fraction ∆nHS on the picosecond timescale in the three films (a) 50 nm, (b) 100 nm and (c) 150 nm, and at two different temperatures (room temperature, initial LS state and high temperature, initial HS state) after a 2-µJ laser pulse.

  Figure S4.Evolution of ∆nHS at room temperature on the ns-ms time window in the three films (a) 50 nm, (b) 100 nm and (c) 150 nm, following a femtosecond laser pulse with various excitation energies. In the thinner film (50 nm), the relaxation occurs through a one-step process regardless of the pump laser energy (0-6 µJ). In the 100-nm-thick film, a self-amplification of the fraction of HS molecules is observed around 20-40 ns above a threshold energy value of 6 µJ. The same behavior is observed in the 150-nm-thick film, but the additional switching step appears above a threshold laser energy of 4 µJ.

Figure S5 .Figure S6 .

 S5S6 Figure S5. Time evolution of the photo-induced HS fraction in the 100-nm-thick film following a femtosecond laser pulse with various excitation energies at two different temperatures: (a) 293 K and (b) 315 K. For the same used excitation energies, the second jump of the HS fraction at 25 ns, ∆nHS th , appears noticeably more pronounced at 315 K (i.e. 22 K below the transition temperature), indicating that this additional switching step occurs through a thermally activated process.

Table of contents

 of Size reduction effects have been evidenced on the room-temperature photoswitching dynamics of spin-crossover thin films induced by femtosecond laser excitations. A delayed, thermally activated switching is observed on the 20-40 ns timescale, governed by the intramolecular energy barrier between the two spin states. This additional switching step is suppressed in the thinnest films and the thermal equilibrium state is recovered within 100 ns.

	Keyword:
	ultrafast spin-state photoswitching
	Karl Ridier, Alin-Ciprian Bas, Victoria Shalabaeva, William Nicolazzi, Lionel Salmon, Gábor
	Molnár,* Azzedine Bousseksou, Maciej Lorenc,* Roman Bertoni, Eric Collet, and Hervé
	Cailleau

Acknowledgements

This work was supported by the European Commission through the SPINSWITCH project (H2020-MSCA-RISE-2016, Grant Agreement No. 734322) and by the Agence Nationale de la Recherche through the ELASTICA project (ANR-16-CE30-0018). The grants of AB and VS were financed by the Région Occitanie (contract No. 15050123) and the CNRS (Emergence project), respectively.

Received: ((will be filled in by the editorial staff))

Revised: ((will be filled in by the editorial staff)) Published online: ((will be filled in by the editorial staff))

[1] P. Gütlich, A. Hauser, H. Spiering, Angew. Chem. Int. Ed. 1994Ed. , 33, 2024. .

Supporting Information

Supporting Information is available from the Wiley Online Library or from the author.

Supporting Information

Finite size effects on the switching dynamics of spin-crossover thin films photo-excited by a femtosecond laser pulse

Karl Ridier, Alin-Ciprian Bas, Victoria Shalabaeva, William Nicolazzi, Lionel Salmon, Gábor Molnár,* Azzedine Bousseksou, Maciej Lorenc,* Roman Bertoni, Eric Collet, and Hervé Cailleau


L Girolami

O Roche

T H Druitt

T Corpetti

Velocity fields and depositional processes in laboratory ash flows, with implications for the dynamics of dense pyroclastic flows

Keywords: Pyroclastic flow, fluidized granular flow, laboratory experiment, velocity profile, progressive aggradation

Velocity fields and depositional processes in laboratory ash flows, with implications for the dynamics of dense pyroclastic flows

Introduction

Pyroclastic flows are dense granular avalanches of hot particles and gas generated by gravitational collapse from lava domes or fallback of eruption columns. They travel at high speeds and constitute one of the most important hazards around active volcanoes (e.g., Wilson 1986;[START_REF] Druitt | Pyroclastic density currents[END_REF][START_REF] Freundt | Pyroclastic flow transport mechanisms[END_REF]. Their ability to travel large distances on slopes as gentle as a few degrees has been attributed to non-equilibrium pore pressures and associated fluidization effects generated either by gases released internally or by entrainment of air [START_REF] Sparks | Grain size variations in ignimbrites and implications for the transport of pyroclastic flows[END_REF]Wilson 1980;[START_REF] Druitt | Gas retention in fine-grained pyroclastic flow materials at high temperatures[END_REF]). Development of quantitative models of pyroclastic flows is a priority of modern volcanology, and this requires better understanding of their physical properties. While the physics of gravitational dry granular flows (in which it is assumed that particle interactions dominate and that interstitial gas plays a negligible role), has been explored extensively (for reviews, see [START_REF] Gdr Midi | On dense granular flows[END_REF][START_REF] Forterre | Flows of Dense Granular Media[END_REF][START_REF] Forterre | Flows of Dense Granular Media[END_REF], research on dense gas-particle flows dominated by fluid-particle interactions is much less advanced [START_REF] Roche | Experimental study of gas-fluidized granular flows with implications for pyroclastic flows emplacement[END_REF][START_REF] Roche | Experimental observations of waterlike behavior of initially fluidized, unsteady dense granular flows and their relevance for the propagation of pyroclastic flows[END_REF][START_REF] Girolami | Propagation and hindered settling of laboratory ash flows[END_REF].

Up to now the dynamics of pyroclastic flows has been largely based on field observations of active flows (e.g., [START_REF] Hoblitt | Obsevations of the eruptions of July 22 and August 7 1980 at[END_REF][START_REF] Levine | Hydraulics of the August 7 1980 pyroclastic flow at Mount St Helens[END_REF], and in particular inferred from textural studies of flow deposits [START_REF] Sparks | Grain size variations in ignimbrites and implications for the transport of pyroclastic flows[END_REF]Branney and Kokelaar 2002 and references therein). However in order to use deposits to infer flow dynamics, it is crucial to understand how such deposits form [START_REF] Branney | Pyroclastic density currents and the sedimentation of ignimbrites[END_REF]. Moreover, pyroclastic flows appear to be capable of a wide spectrum of behaviors, from depositional to strongly erosional, the physics of which are poorly understood.

The kinematics of gas-fluidized particulate flows can be investigated through quantitative analysis of laboratory experiments. Fluidization is the process whereby the drag exerted by an upward flow of gas through a granular bed reduces interparticle stresses, the fluidization state being determined by the vertical superficial gas velocity U g (gas volumetric flux divided by surface area at the temperature of operation) [START_REF] Rhodes | Introduction to Particle Technology[END_REF]. Once U g exceeds a minimum fluidization value U mf , gas drag balances particle weight, friction disappears, and the bed adopts a liquid-like behavior. Some fine-grained powders (group A of [START_REF] Geldart | Types of gas fluidization[END_REF] expand uniformly between U mf and the minimum bubbling threshold, U mb (>U mf ). If the gas supply to a uniformly expanded bed is cut, the bed re-sediments from the base upwards by hindered settling in what is called a bed collapse [START_REF] Lettieri | The influence of interparticle forces on the fluidization behavior of some industrial materials at high temperature[END_REF][START_REF] Druitt | Gas retention in fine-grained pyroclastic flow materials at high temperatures[END_REF]. Laboratory studies of dense gravitational gas-particle flows include those of both continuously fluidized flows [START_REF] Eames | Aerated granular flow over a horizontal rigid surface[END_REF]Takahashi and Tsujimoto 2000;[START_REF] Gilbertson | The effects of gas flow on granular currents[END_REF], and dam-break (i.e., transient) flows of initially fluidized particles released from a reservoir and that defluidize progressively during propagation [START_REF] Roche | Experimental study of gas-fluidized granular flows with implications for pyroclastic flows emplacement[END_REF][START_REF] Roche | Experimental observations of waterlike behavior of initially fluidized, unsteady dense granular flows and their relevance for the propagation of pyroclastic flows[END_REF][START_REF] Girolami | Propagation and hindered settling of laboratory ash flows[END_REF]. [START_REF] Roche | Experimental observations of waterlike behavior of initially fluidized, unsteady dense granular flows and their relevance for the propagation of pyroclastic flows[END_REF] showed that dam-break flows of small (<100 µm) group-A glass beads initially fluidized at U mb (with a corresponding bed expansion of 2-4%) propagate on a horizontal substrate in three distinct phases based on observations of the flow front: (1) a short initial acceleration phase as the reservoir empties, (2) a dominant phase in which the front has an approximately constant velocity U~√(2gh 0 ), where h 0 is the height of the initial material in the reservoir, and (3) a short stopping phase. Flow behavior during phases 1 and 2, which together account for ~80% of the flow runout, strongly resembles that of inertial fluids such as water (probably because of strong gas-particle interactions), and it is consequently inferred that inertia dominates flow motion during the first two phases of emplacement, while a granular-frictional regime may dominate the third phase [START_REF] Roche | Experimental observations of waterlike behavior of initially fluidized, unsteady dense granular flows and their relevance for the propagation of pyroclastic flows[END_REF].

Similar experiments were carried out by [START_REF] Girolami | Propagation and hindered settling of laboratory ash flows[END_REF] with hot volcanic ash. Hot ash differs from glass beads in that it can be expanded considerably (up to ~40 %) above loose packing when fluidized above U mf , allowing the effect of initial expansion on flow kinematics to be investigated. Heating the ash to ~200 °C was necessary to reduce interparticle cohesion due to atmospheric humidity, allowing the ash to behave as a group-A material [START_REF] Druitt | Gas retention in fine-grained pyroclastic flow materials at high temperatures[END_REF]). The ash-flow experiments showed that the runouts of initially expanded flows scale with the initial expansion, the first emplacement phase being governed by gravitational acceleration, and the second and third phases being dominated by both gravity and hindered sedimentation. Additional experiments with tracer particles revealed that deposition from initially expanded flows takes place incrementally at the flow base. A major finding of this work was that the upper surface of the deposit aggraded at a mean velocity identical to that inferred to take place at the base of a collapsing quasi-static bed of the same ash, expanded by the same initial amount, in the flume reservoir with the lock gate closed. High rates of shear therefore appeared not to affect deposit aggradation rate under collapsing layers of initially expanded ash.

The aim of the present study is to investigate in more detail the internal kinematics and deposition behavior of experimental flows of volcanic ash similar to those described by [START_REF] Girolami | Propagation and hindered settling of laboratory ash flows[END_REF]. For this, we made high-speed videos of the experiments, which were subsequently treated with sophisticated techniques of motion field estimation. For a range of initial bed expansions, we analyzed the temporal and spatial development of both the deposit and the velocity profile in the overlying flowing ash. We first present the method of image sequences analysis and the results obtained, then discuss possible implications for the depositional mechanisms and erosive capacities of pyroclastic flows.

Experimental procedures

The high-temperature flume

The experiments were carried out in a linear flume consisting of a fluidization reservoir and a horizontal channel built of aluminium and pyrex in order to withstand temperatures of up to 200° C (Figure 1; see [START_REF] Girolami | Propagation and hindered settling of laboratory ash flows[END_REF] for a detailed description). The high temperature was provided by external heating tapes regulated by thermostats and covering both the reservoir and an underlying windbox, and all experiments were carried out with the incoming gas and reservoir contents at the same temperature. The ash was fluidized and expanded in the rectangular reservoir (length 30 cm, height 50 cm) and was subsequently released by means of a lock gate into the channel (length 300 cm, height 30 cm). The width of both the reservoir and the channel was 15 cm. The ash rested on a porous plate of mean pore size of 17 m that separated the windbox from the reservoir. The gas flux entering the windbox was controlled by flowmeters and was recalculated according to the operating temperature and the ideal gas law. The fluidization state of ash in the reservoir was given by the pressure drop across the bed measured by a pressure transducer. By means of a three-way valve, the incoming gas could be either directed into the windbox or vented outward during bed collapse tests as the gas supply was suddenly cut. The reservoir gate had a 20-kg counterweight allowing upward motion at a consistently high speed, and had a heat-resistant seal and a downward-tapering shape to prevent leakage and reduce resistance during opening . Releasing the fluidized ash across the impermeable floor of the flume in the manner of a dambreak formed a fast-moving, short-lived, shear current that defluidized progressively during propagation until motion ceased.

Experimental material and procedure

The volcanic ash involved in the experiments was that used by [START_REF] Girolami | Propagation and hindered settling of laboratory ash flows[END_REF]. It contained a broad spectrum of particle sizes, from ~ 1 to 250 m, and was obtained by disaggregating the matrix of a 0.58-Ma non-welded trachytic ignimbrite from Neschers (Massif Central, France) and removing particles >250 m. The ash was then fluidized in the flume reservoir in the bubbling regime (U g >U mb ), so that the finest particles were elutriated from the bed. The operation was stopped when the elutriation rate became negligible, and this resulted in a slightly fines-depleted material that was subsequently used to generate the flows. We could use the same batch for all experiments since no subsequent elutriation occurred and the grain-size distribution remained constant (see Table 1 in [START_REF] Girolami | Propagation and hindered settling of laboratory ash flows[END_REF].

The ash was dried at 200° C during 24 hours before each experiment, then transferred to the lock-gate reservoir where it was fluidized and expanded as required. The operating temperature of all experiments was fixed at 170 °C, which was high enough to avoid humidity-related cohesive effects [START_REF] Druitt | Gas retention in fine-grained pyroclastic flow materials at high temperatures[END_REF]. All experiments were limited to the nonbubbling state (U mf ≤U g <U mb ), and the bed expansion was defined as

E =h 0 /h mf , (1)
where h 0 and h mf are respectively the expanded and non-expanded (i.e., at U mf ) heights of initial bed of ash (Figure 1). Under these conditions, the maximum value of E (at U mb ) was 1.45.

No detectable particle-size segregation occurred during expansion or re-sedimentation of the ash, either during quasi-static expansion and collapse in the reservoir, or during horizontal flow, as confirmed by sieving. It is known that even strongly polydisperse suspensions of particles may settle without segregation provided the initial concentration is high enough [START_REF] Davies | Experimental investigation into the settling behaviour of suspensions[END_REF]Lockett and Al-Habboby 1974;[START_REF] Druitt | Settling behaviour of concentrated, poorly sorted dispersions and some volcanological applications[END_REF]. This enabled us to assign bulk properties to the ash (e.g., flow velocity, deposit aggradation velocity), and interpret the results quantitatively.

In some experiments, tracer particles of 500-m silicon carbide (SiC) were added to the ash in proportions up to 10 vol%. This was done to permit visual estimation of particle motions from videos for comparison with those calculated using the optical-flow algorithm. Video footage revealed no disturbance by the tracer particles of the flow or sedimentation dynamics, and this is consistent with previous findings that low amounts of large particles are advected passively in flows of fluidized group-A particles [START_REF] Roche | Inviscid behaviour of fines-rich pyroclastic flows inferred from experiments on gas-particle mixtures[END_REF].

We first studied the hindered settling behavior of the ash under quasi-static (nonshearing) conditions in bed-collapse tests in the reservoir of the apparatus with the gate shut. After expanding the bed to a known amount, we then cut the gas supply and measured the descent rate of the surface [START_REF] Druitt | Gas retention in fine-grained pyroclastic flow materials at high temperatures[END_REF]). The second part of our investigation involved the study of the flows in the channel. Once at temperature, the bed was first mixed to avoid channeling, then mixing was stopped to allow homogeneous bed expansion, and the lock gate was opened by the required amount. The experimental conditions were the same as in experiment series 2 of [START_REF] Girolami | Propagation and hindered settling of laboratory ash flows[END_REF]: h mf was fixed at 16.5 cm in all experiments, so that h 0 increased proportionally with E and flows were generated at four different values of E: 1.00 (non-expanded), 1.09, 1.17 and 1.35.

Method of velocity-field estimation

Principle of the method

Flow velocity fields and vertical profiles were determined using the particle-tracking technique of [START_REF] Corpetti | Fluid experimental flow estimation based on an optical-flow scheme[END_REF], which is based on the theory of optical flow. Optical-flow techniques are commonly used in the computer-vision community, and were introduced by [START_REF] Horn | Determining optical flow[END_REF] for the tracking of rigid objects (particles in the present context) in image sequences. They allow estimation of a dense motion field (i.e. the velocity at each point of the image) from the intensities (also called luminance) of a pair of consecutive images.

The fundamental principle is to minimize an energy function based on two assumptions: 1) luminance conservation and 2) spatial consistency of the velocity-vector field. The first assumption is that all points of the first image conserve their intensities on the second image. This enables us to use the image pair to generate an estimate of the flowvelocity field. However, in areas of the images where no spatial or temporal variations of luminance are apparent, this leads to an undetermined equation with an infinity of possible solutions. To solve this problem, [START_REF] Horn | Determining optical flow[END_REF] introduced a spatial-smoothing term that roughly assumes that all neighborhood points have a similar motion (assumption 2). This generates smooth flow fields where spatial gradients of motion are very low.

Our optical-flow method [START_REF] Corpetti | Fluid experimental flow estimation based on an optical-flow scheme[END_REF]) is a modified version of the original [START_REF] Horn | Determining optical flow[END_REF], where instead of generating very smooth flow fields, we estimate velocity vectors where some properties of fluid flows such as divergence and vorticity, are conserved.

Film acquisition and validity of the algorithm

For each experiment, the whole channel was filmed with a standard video camera (25 images per second) to determine the flow front velocity. Parts of the flows were filmed in detail with a high-speed video camera (1000 images per second) placed at a distance that depended on the flow runout, in order to focus the analysis on flow phase 2. The camera was then located at various distances (20-30 cm -50-60 cm -80-90 cm -110-120 cm) from the lock gate, and this was done using a single camera and by repeating each experiment multiple times, as permitted by the high reproducibility of the experiments. [START_REF] Girolami | Propagation and hindered settling of laboratory ash flows[END_REF] showed that the flows slipped along the pyrex wall of the channel, so that particle movements observed through the wall were inferred to be representative of the flow interior.

The films were analyzed using the optical-flow algorithm; in each case, a series of velocity fields were determined from motion estimation between two images at a time interval of 1/500 s, which was sufficient for detectable motion. The high-speed video camera was placed 30 cm from the transparent channel wall, so that the algorithm determined particle motion in vertical strips ~10 cm wide. Velocity profiles were then extracted from strips ~1 cm wide perpendicular to the upper surface of the aggrading deposit. Inconsistent velocity fields at flow boundaries due to sidewall-reflection or perspective-related-shadow effects were avoided using a masking technique [START_REF] Corpetti | Fluid experimental flow estimation based on an optical-flow scheme[END_REF]. Generating the mask consisted of grouping pixels outside the flow and associating them with a color that contrasted markedly with that of the flow, so that the algorithm encountered no ambiguity.

In order to test the validity of the algorithm, we measured the thickness of the basal deposit (i.e., no velocity) as a function of time from videos of ash flows without SiC tracers. For comparison, we also measured the deposit thickness by visual inspection of videos of flows with SiC. Both methods revealed similar results (Figure 2), thus showing that the algorithm was suitable for the aim of our study. This also confirmed that tracer particles had no noticeable influence on deposit aggradation rate.

Results

Bed collapse tests and general flow behavior

The results of the quasi-static bed collapse tests in the reservoir are presented in Figure 3 for initial expansions from 1.06 to 1.43, along with data for flows in the channel that will be discussed later. As observed previously [START_REF] Druitt | Gas retention in fine-grained pyroclastic flow materials at high temperatures[END_REF][START_REF] Girolami | Propagation and hindered settling of laboratory ash flows[END_REF]), the hindered settling velocity (V, in cm s -1 ) of the ash given by the descent rate of the upper surface increases with E, the best-fit relationship in the present case being :

V = 2.44E-2.15
(2)

Note that the value of V for a given E is higher than for the ash of [START_REF] Girolami | Propagation and hindered settling of laboratory ash flows[END_REF] (grey region of Figure 3), owing to the presence of the SiC particles.

The general behavior of the flows was described by [START_REF] Girolami | Propagation and hindered settling of laboratory ash flows[END_REF]. When released, the ash flowed down the channel until defluidization was complete and frontal motion ceased. Propagation took place in the three main phases typical of dam-break granular flows: the first, brief initial acceleration phase (1) lasted 0.1-0.2 s; the second, dominant phase (2) during which the front had an approximately constant velocity lasted 0.6-0.8 s and accounted for about two thirds of the flow duration and 70-80 % of the flow runout; and the third, brief stopping phase (3) lasted 0.1-0.4 s. The non-expanded flow (E=1.00) had a phase-2 velocity of ~1.1 m s -1 , a runout distance of 0.6 m and a runout duration of 0.8 s, whereas the most expanded flow (E=1.35) had a phase-2 velocity of ~2.1 m s -1 , a runout distance of 2.2 m and a runout duration of 1.4 s.

Characteristics of velocity fields and profiles

The velocity fields revealed a basal (static) deposit beneath the overriding flow for the whole range of initial bed expansions investigated (Figures 4567). Sedimentation commenced ~0.05-0.10 s (~5-20 cm) behind the flow front at all distances from the lock gate, and the deposit took the form of a wedge that thickened with time at the expense of the flow until the latter was entirely consumed. The upper surface of the deposit was steeply inclined (up to 20-25°) and remained approximately constant with time beneath the initially non-expanded flow (E=1.00). In contrast, it was much more gently inclined beneath the initially expanded flows (E>1.00), and decreased from 2° to 0.8° as E increased from 1.09 to 1.35. The flow fronts were typically rounded in cross section near the lock gate, but became progressively more triangular in form with increasing distance downstream. Immediately behind the front, the flowing region thickened to a maximum of 3-4 cm, before then decreasing in thickness, both temporally at a given location as the deposit aggraded, and longitudinally down the flume. In the initially expanded flows, the angle of the flow surface was slightly greater than that of the underlying deposit, whereas the reverse was true in the non-expanded flow.

By analogy with pure fluids, flows were "laminar" on scales larger than individual grains. Velocity vectors in the initially expanded flows had significant downward components within 20-25 cm of the lock gate inherited from the initial phase-1 collapse, but beyond this the vectors became sub-horizontal. A downward flow component was maintained to the distal limit in the initially non-expanded flow, owing to the steep surface of the aggrading deposit.

Velocity profiles revealed different flow behaviors before and after the onset of deposition (Figure 8). The fronts of both expanded and non-expanded flows slid along the channel floor on a basal slip zone < 1 mm thick with only a weak vertical velocity gradient in the over-riding flow. Once deposition had commenced, however, shear was accommodated more uniformly throughout the flow and velocity increased more progressively towards the deposit surface. In the initially non-expanded flows, velocity increased rapidly upwards over a few mm above the deposit surface, then increased more slowly towards the flow surface and reached a maximum of about 1.6 m s -1 . In contrast, in the initially expanded flows, velocity increased upwards in a quasi-linear manner (though velocity profiles were slightly concave upward), but then decreased again near the flow surface. Maximum velocity increased with E, from 1.6 m s -1 (E=1.09) to 1.9 m s -1 (E=1.35), these being similar to the phase-2 frontal velocity in each case. As the deposit aggraded at a given site, the velocity profile was translated upwards while maintaining approximately the same shape. Velocity gradients increased as the flows thinned progressively downstream. Consequently, the highest shear rate estimated 25 cm from the lock gate was ~125-150 s -1 , while that at 85 cm was ~275-300 s -1 .

Aggradation of the basal deposit

Figure 9 shows the evolution of deposit thickness with time for the different flows, t=0 marking the passage of the flow front at various distances from the reservoir gate. The formation of the basal deposit started after passage of the front, and the time interval was about 0.05 s for the initially non-expanded (E=1) flow, and increased slightly from 0.05 to 0.10 s when as E increased from 1.09 to 1.35. Regarding aggradation of the deposit, the data reveal three main features. First, the mean aggradation velocity was dependent on E. Second, aggradation velocity at each value of E was almost independent of distance down the channel, showing that it was sufficient to measure this parameter at a single location down the flume to obtain representative values. Third, the aggradation velocity (at a given E) was approximately constant with time at each location. Initial aggradation occurred at ~4.9 cm s -1 at E=1.09, ~4.1 cm s -1 at E=1.17, and ~2.4 cm s -1 at E=1.35. In the E=1.00 flow, this rate remained constant until sedimentation was complete. In the initially expanded flows, however, there is an indication that aggradation speeded up during the final increments (0.7-0.9 s) of sedimentation, although this behavior is defined by only a few data points for measurements at a distance of 20-30 cm from the gate. We note, however, that this increase in aggradation rate occurred at a time corresponding approximately to the transition between the second (constant-velocity) and third (stopping) phases of the flows. In the initially moderately expanded flows (at E=1.09 and 1.17) this late-stage aggradation velocity resembles that of the non-expanded flow, whereas in the most expanded flow (E=1.35), it does not. We stress, however, that to a first approximation the aggradation rates at each value of E are constant throughout most of the duration of sedimentation. The deposit aggradation rates measured for the flows are now compared to those inferred from the quasi-static bed-collapse tests carried out in the flume reservoir with the lock gate closed. For an initially expanded bed collapsing at a velocity V, the deposit aggradation velocity S given by mass flux balance is S=V/(E-1) [START_REF] Druitt | Gas retention in fine-grained pyroclastic flow materials at high temperatures[END_REF]). Hence from equation 2 the quasi-static aggradation velocity for the ash is S = (2.44E-2.15)/(E-1) cm s -1 . In Figure 10, deposit aggradation rates beneath the expanded flows are compared with values calculated from the settling rates measured in the collapse tests and reported earlier. Values are plotted both for the rate of initial aggradation and for a mean value for the entire duration of deposition. Irrespective of which value is used, aggradation rates beneath the E>1 flows agree to within measurement error with those inferred beneath quasi-static collapsing beds of the same initial expansion.

Discussion

Processes in the laboratory flows

The velocity fields and profiles of Figures 4-8 are to our knowledge the first measurements of internal motion in fluidized flows of hot natural ash. High-speed images show that the laboratory flows behaved to a first approximation as sheared-out collapsing beds, with a fast-moving flow below which a deposit aggraded progressively until the flow ran out of volume. The flows propagated in three distinct phases, and the measured phase-2 velocities were about √(2gh 0 ), typical of inviscid dam-break flows [START_REF] Roche | Experimental observations of waterlike behavior of initially fluidized, unsteady dense granular flows and their relevance for the propagation of pyroclastic flows[END_REF]. Flow at all expansions was "laminar" with no turbulent eddies significantly larger than the particle scale. It cannot be ruled out that this was in part a boundary-layer effect against the flume wall, but it is consistent with absence of surface vorticity reported by [START_REF] Girolami | Propagation and hindered settling of laboratory ash flows[END_REF]. An important observation is that at all expansions the frontal regions of each flow, up to 5-20 c m (0.05-0.10 s) behind the leading edge, slipped across the channel floor with only weak internal velocity gradients, whereas once deposition had begun a no-slip basal condition was established and shear was accommodated more uniformly throughout the flow. The origin of this effect is unclear and requires further study, but it may relate to differences in fluidization state between the flow head and body. In initially expanded flows, the data also revealed the existence of a superficial layer of decreasing velocity, possibly due to air drag since surface flow-velocity decrease is correlated positively with initial bed expansion. In flows of all initial expansions, the dynamics were probably constant over time at a given distance from the lock gate, as suggested by the simple upward translation of velocity profiles. When the flow traveled down the channel, the internal shear rate increased because the maximum internal velocity, about equal to the frontal velocity, was approximately constant, whereas the flow thickness decreases. [START_REF] Girolami | Propagation and hindered settling of laboratory ash flows[END_REF] estimated time-averaged deposit aggradation rates from initially expanded ash flows assuming (1) that deposition began immediately behind the flow front, and (2) that aggradation rate depended only on E and was independent of time or distance within a given flow; they then divided the final deposit thickness by total deposition time. The new data confirm these assumptions to a first approximation. In detail, however, sedimentation began 5-20 cm (0.05-0.10 s) after passage of the flow front. The dependence of aggradation rate on initial bed expansion can be explained by comparing the flow values with those of our quasi-static bed-collapse tests. As shown in Figure 10, the rates of deposit aggradation beneath the expanded (E>1.00) flows determined from video analysis were similar to those inferred from the bed-collapse tests. Hence, despite rates of shear of up to 300 s -1 in the flows, shear had little effect on deposit aggradation rate, as also concluded by [START_REF] Girolami | Propagation and hindered settling of laboratory ash flows[END_REF] based on their less accurate approach. While aggradation rate was almost independent of distance from the lock gate, there were some indications that it increased slightly with time at a given location in initially expanded flows. Note that this cannot be due to segregation of the dense SiC tracer particles towards the base of the flow, since this would result in higher initial deposition rates, the inverse of what is observed. As the aggradation rate increased approximately when the flows entered the stopping phase after about two thirds of the flow duration, this suggests a relationship between the internal dynamics of the flow and the kinematics of the front. Furthermore, the late-stage aggradation rates of the moderately expanded flows (E=1.09 and 1.17) were similar to those of the nonexpanded flow, which could suggest that all initially expanded flows defluidized rapidly once they had thinned beyond some threshold value. This may be consistent with the observed evolution of flow-front shape from rounded to progressively triangular, the latter being typical of non-expanded flows.

The initially non-expanded flows behaved in a similar manner to the expanded ones: shearing throughout and depositing progressively. Particle sedimentation is theoretically not possible from an initially non-expanded fluid-particle mixture. A one-dimensional granular bed just fluidized at U mf defluidizes by pore-pressure diffusion, rather than settling [START_REF] Druitt | Gas retention in fine-grained pyroclastic flow materials at high temperatures[END_REF]. Either defluidization of the E=1.00 flow indeed took place by pore-pressure diffusion, from the base upwards, at a rate we cannot quantify, or the ash was slightly expanded by a combination of Reynolds dilation and particle agitation during shear, then underwent re-sedimentation like the other flows. If the latter is true, then an expansion of a few % is implied by extrapolation of the quasi-static curve (Figure 10), which agrees well with values reported for Reynolds dilation of sheared granular masses [START_REF] Hutter | The Savage-Hutter avalanche model: how far can it be pushed?[END_REF].

One implication of this observation could be that even a flow generated from initially nonexpanded (but just fluidized) ash may deposit by settling because the shear generated by flow will always slightly expand the gas-particle mixture above loose-packing. Further investigation of this possibility is required.

Implications for pyroclastic flows

The experimental results provide information on the possible flow and deposition behavior of dense pyroclastic flows propagating on a sub-horizontal slope. Fluidization in pyroclastic flows is believed to affect only the sub-mm size fractions, so that lapilli and blocks are transported in suspension or as bedload within a matrix of partially or fully fluidized ash [START_REF] Sparks | Grain size variations in ignimbrites and implications for the transport of pyroclastic flows[END_REF]). As our experimental ash is representative of that matrix, the behavior of the laboratory flows is likely to resemble that of natural flows containing particles of a larger size range, and this idea is supported by laboratory experiments [START_REF] Roche | Inviscid behaviour of fines-rich pyroclastic flows inferred from experiments on gas-particle mixtures[END_REF]. The presence of very large and/or dense clasts may, however, complicate this simple picture.

Understanding the manner in which a pyroclastic flow deposits its load is fundamental to using deposits to reconstruct eruptive processes. The deposition mechanisms of pyroclastic flows have been widely debated, possible mechanisms including frictional freezing or progressive aggradation [START_REF] Sparks | Grain size variations in ignimbrites and implications for the transport of pyroclastic flows[END_REF]Branney andKokelaar 1992, 2002, andreferences therein). The conceptual difference between these mechanisms is that freezing is envisaged to occur only at a late-stage following long transport, whereas progressive aggradation takes place throughout flow runout. Textural studies have been used to infer that the individual flow units and thick massive layers that constitute large ignimbrite sheets were laid down by progressive aggradation, not freezing (Branney andKokelaar 1992, 2002). However, such flows may travel as dense turbulent suspensions, so it is less clear to what extent progressive aggradation also takes place in pyroclastic flows of small volume in which whole-body turbulence is less likely (e.g., [START_REF] Sparks | Erosion by pyroclastic flows on Lascar Volcano, Chile[END_REF]). However, the experiments of [START_REF] Girolami | Propagation and hindered settling of laboratory ash flows[END_REF] and this paper now show that even non-turbulent dam-break flows of ash as thin as a few cm deposit progressively. Moreover, this behavior also characterizes even the initially non-expanded ash flows, so it seems to be a general feature of dense gas-particle flows, irrespective of thickness, expansion or degree of turbulence.

The apparent insensitivity of deposit aggradation rate to shear may offer a means of parameterizing deposit aggradation rates in flow models by using sedimentation rates measured in quasi-static rigs. Mathematical models taking into account progressive deposition have been developed for granular flows, but only for dry (i.e., non-fluidized) flows and assuming empirical aggradation rates [START_REF] Doyle | Static and flowing regions in granular collapses down channels: insights from a sedimenting shallow water model[END_REF]). On the other hand, some numerical models simulate (partially) fluidized geophysical flows, but do not yet include progressive deposition [START_REF] Iverson | Flow of variably fluidized granular masses across three-dimensional terrain 1. Coulomb mixture theory[END_REF][START_REF] Denlinger | Granular avalanches across irregular three-dimensional terrain: 1. Theory and computation[END_REF]. In this context, the results presented in this paper could serve as a guide for including deposit aggradation in models of fluidized flows. Such an approach would be limited to the modelling of relatively dense fluidized flows propagating on a sub-horizontal slope and in which turbulence is absent on a scale comparable to that of the flow thickness.

The experiments also provide insight into the way in which shear may be accommodated vertically in different parts of a pyroclastic flow. The bases of pyroclastic flow deposits are commonly erosional on the underlying substrate, especially on steep slopes, the substrates exhibiting deep erosional channels, striations, furrows and percussion marks [START_REF] Rowley | Pyroclastic-flow deposits[END_REF][START_REF] Sparks | Erosion by pyroclastic flows on Lascar Volcano, Chile[END_REF][START_REF] Cole | Deposits from dome-collapse and fountain-collapse pyroclastic flows at Soufrière Hills Volcano, Montserrat[END_REF][START_REF] Pittari | Sole marks at the base of the late Pleistocene Abrigo Ignimbrite, Tenerife: implications for transport and depositional processes at the base of pyroclastic flows[END_REF]. These features show that pyroclastic flows can exert high shear stresses on the ground over which they travel. The erosion and incorporation of substrate lithic clasts, as well as the shear-laminations common in some ignimbrite basal layers are also indicative of high basal shear [START_REF] Buesch | Incorporation and redistribution of locally derived lithic fragments within a pyroclastic flow[END_REF]Susuki-Kamata 1998;[START_REF] Branney | Pyroclastic density currents and the sedimentation of ignimbrites[END_REF]. Erosional features at Lascar Volcano were interpreted to form when highly concentrated flows slid over the bedrock, and they were favored by basal segregation of lithic clasts as well as flow acceleration caused by topographic restrictions and local steep slopes [START_REF] Sparks | Erosion by pyroclastic flows on Lascar Volcano, Chile[END_REF]). Similar conclusions have been reached for the Abrigo Ignimbrite on Tenerife, where impact and sole marks are interpreted as the consequence of the passage of a highly energetic flow head enriched in pebble-to cobble-sized lithic clasts [START_REF] Pittari | Sole marks at the base of the late Pleistocene Abrigo Ignimbrite, Tenerife: implications for transport and depositional processes at the base of pyroclastic flows[END_REF]. In contrast, the typically massive interiors of flow units preserve evidence only for lower levels of shear at the aggrading depositional surface, such as magnetic fabrics, clast imbrication and flow-parallel orientation of elongated particles, crystals and logs (e.g., Suzuki and Ui 1982; [START_REF] Knight | Stratigraphy, palaeomagnetism, and magnetic fabrics of the Toba Tuffs: constraints on the sources and eruptive styles[END_REF][START_REF] Potter | Vent sites and flow directions of the Otowi ash flows (lower Bandelier Tuff), New Mexico[END_REF]Hughes and Druitt 1998 and references therein). Possible features indicative of intense shear, such as shear laminations and truncated clasts are generally absent within the massive interiors of flow units. This suggests that high basal shear stresses are probably limited to the frontal regions of pyroclastic flows and that, once the deposit starts to aggrade, shear stress at the base of the moving flow (i.e., the depositional surface) falls to lower values.

Velocity profiles associated with the leading edges of the laboratory flows show that the flow front slides over the flume floor. It is therefore inferred that the flow front exerts a strong shear stress (at the scale of the flow) on its substrate. Although the effects of this basal shear are not visually evident because the floor is rigid, high basal stress is inferred from the very steep velocity gradient at the base of the flow front. In a natural pyroclastic flow such a process might give rise to strong substrate erosion, as commonly observed. Frontal sliding has been proposed previously for highly concentrated pyroclastic flows with poorly-fluidized bouldery snouts (Iverson and Vallance 2001 and references therein), but our experiments show that it can occur even in the absence of coarse segregated particles. The experiments also show that as the flow front passes by and sedimentation commences, the flow develops a no-slip boundary with its aggrading deposit and shear is accommodated more pervasively throughout the flow. Textural evidence for shear may therefore be expected to be less common in the interiors of flow deposits, as is indeed the case.

Conclusions

We carried out experiments on dam-break flows of initially fluidized volcanic ash in order to better understand the transport and sedimentation processes in dense pyroclastic flows propagating on sub-horizontal slopes. The ash was representative of the matrices of natural flows and was expanded to amounts of up to 35% before release. The internal kinematics of the flows was documented by measuring the velocity fields of the constituent particles and their spatial and temporal variations. High-speed videos were acquired at 1000 frames per second, and subsequently analyzed using a particle-tracking algorithm.

The results revealed that the experimental flows behaved to a first approximation as sheared-out collapsing beds, with a fast-moving flow overriding a basal deposit that aggraded progressively until the flow was consumed. The overriding flow was non-turbulent and pervasively sheared, with a slightly concave-upward velocity profile. In initially expanded flows, the maximum internal velocity was close to that of the flow front, with shear rates up to ~300 s -1 ; some decrease in velocity was observed near the flow surface, possibly due to air drag. Flows of all initial expansions were characterized by a frontal region that slid across the floor of the flume on a thin, highly sheared basal layer. Deposit aggradation commenced ~0.05-0.10 s (~5-20 cm) behind the flow front and took place at a rate of a few cm per second that was similar to that inferred for quasi-static bed collapse tests at the same values of initial expansion. Once deposition had begun, a no-slip condition was established at the base of the flow. At a given distance from the lock gate, the velocity profile of the flow was translated upward as the deposit aggraded, suggesting time-invariant flow dynamics. The aggradation rate decreased as the initial bed expansion increased, and (within a flow of given expansion) was independent of the distance travelled. It was approximately constant with time at a given location, though it apparently increased when the flows entered their last, decelerating phase of emplacement. Initially non-expanded flows deposited progressively in a manner similar to initially expanded ones, even though particle sedimentation is theoretically not possible from the packed state. This suggests that the non-expanded flows may have undergone shearinduced dilation of a few percent during initial slumping.

Our study has some implications for our understanding of the kinematics of dense pyroclastic flows in nature. First, it shows that progressive aggradation of a basal deposit and pervasive shear of the overlying flow are likely mechanisms. Second, substratum erosion and lithic incorporation observed in the field could be the consequences of intense shear stresses at the base of a sliding flow front. Third, the deposit aggradation rates essential for the modeling of pyroclastic flows may in principle be determined from simple quasi-static bedcollapse tests. The data are approximated by a linear best fit V=2.44E-2.15 cm s -1 (black line). The grey zone shows the equivalent data on the raw ash (lacking SiC particles) used by [START_REF] Girolami | Propagation and hindered settling of laboratory ash flows[END_REF]. The effect of the SiC particles is to increase hindered settling velocity at a given expansion.

Figure 4

Velocity fields at 20-30 cm from the reservoir gate and at different times after release of the initially non-expanded flow (E=1.00). The dashed white line represents the interface between the flow and aggrading deposit. White lines show where the flow velocity was extracted to build the profiles of Figure 8.

Figure captions Figure 1 .

 captions1 Figure captionsFigure1. Sketch of the experimental apparatus used in this study. The widths of both the reservoir and the channel are 15 cm. Heights h mf and h 0 are those of the bed at the minimum fluidization velocity (U mf ) and of the expanded bed (at U g >U mf ), respectively.

Figure 2 .

 2 Figure2. Thickness of the basal deposit as a function of time in an initially moderately expanded flow (E=1.17) 20 cm from the lock gate. Comparison of data determined on the one hand by visual analysis, and on the other by using the optical-flow algorithm. The good agreement serves to validate the algorithm results.

Figure 3 .

 3 Figure 3. Quasi-static hindered settling velocities of the SiC-laden ash as a function of initial expansion. Measurements were carried out in the flume reservoir with the lock gate closed.The data are approximated by a linear best fit V=2.44E-2.15 cm s -1 (black line). The grey zone shows the equivalent data on the raw ash (lacking SiC particles) used by[START_REF] Girolami | Propagation and hindered settling of laboratory ash flows[END_REF]. The effect of the SiC particles is to increase hindered settling velocity at a given expansion.

Figure 5 .

 5 Figure5. Velocity fields at 20-30 cm from the reservoir gate and at different times after release of an initially expanded flow with E=1.09. The dashed white line represents the interface between the flow and aggrading deposit. White lines show where the flow velocity was extracted to build the profiles of Figure8.

Figure 6 .

 6 Figure6. Velocity fields at 20-30 cm from the reservoir gate and at different times after release of an initially expanded flow with E=1.17. The dashed white line represents the interface between the flow and aggrading deposit. White lines show where the flow velocity was extracted to build the profiles of Figure8.

Figure 7 .

 7 Figure 7. Velocity fields at 20-30 cm from the reservoir gate and at different times after release of an initially expanded flow with E=1.35. The dashed white line represents the interface between the flow and aggrading deposit. White lines show where the flow velocity was extracted to build the profiles of Figure 8.

Figure 8 .

 8 Figure 8. Velocity profiles determined from the velocity fields in Figures 4-7 for different initial expansions (E). (a, b) At a distance of 25 cm from the lock gate and at different times after release, and (c) at a time of 0.6 s and different distances. Heights and velocities in the flows were measured perpendicular and parallel to the depositional surface, respectively.

Figure 9 .

 9 Figure 9. Deposit thickness as a function of time for different initial bed expansions (E) and distances from the gate. Δt is the time delay between the passage of the flow front and the onset of deposition.

Figure 10 .

 10 Figure10. Deposit aggradation velocity in the flows as a function of E. Black squares are the initial aggradation velocity; white triangles are the mean aggradation velocity including the slightly faster late-stage phase (cf. Figure7). White circles are aggradation velocity inferred by mass-flux balance calculation from the quasi-static bed-collapse values of Figure3. The curve is the best-fit function S=(2.44E-2.15)/(E-1) cm s -1 to the quasi-static data (see text for details). The horizontal arrow shows that deposit aggradation beneath the initially nonexpanded (E=1.00) flow took place at a rate expected for an expansion of a few percent.

  Figures

  Figures 9

Acknowledgments

We thank J. L. Fruquière and G. Carazzo for technical assistance throughout the experiments involving the high-speed video camera.