Raphaël Thon

Wutharath Chin
email: wutharath.chin@u-psud.fr

Didier Chamma

Alejandro Gutiérrez-Quintanilla

Michèle Chevalier

Jean-Pierre Galaup

Claudine Crépin

W(CO) 6 in cryogenic solids: A comparative study of vibrational properties

Keywords: photon echo, vibrational dynamics, cryogenic solids

A comparative study of the vibrational properties of W(CO) 6 has been performed in different solids at cryogenic temperatures focusing on the IR absorption and the vibrational dynamics of the CO stretching mode of the organometallic compound. Guest-host interactions are investigated in doped solids through the linear IR spectroscopy and four-wave mixing techniques at different temperatures. We show how the host nature, the trapping site, the crystallographic ordering affect the properties of the guest molecule and in particular its vibrational dynamics.

Introduction

The advent of picosecond (ps) and femtosecond (fs) laser sources in the IR domain has enabled the study of the vibrational dynamics of a wide variety of systems spanning from biological molecules [START_REF] Hochstrasser | Special feature on Multidimensional ultrafast spectroscopy[END_REF][START_REF] Chung | Transient 2D IR spectroscopy of ubiquitin unfolding dynamics[END_REF][START_REF] Backus | 2D-IR study of a photoswitchable isotopelabeled alpha-helix[END_REF][START_REF] Ghosh | Two-dimensional sum-frequency generation (2D SFG) spectroscopy: summary of principles and its application to amyloid fiber monolayers[END_REF][START_REF] Panman | Communication: Nanosecond folding dynamics of an alpha helix: Time-dependent 2D-IR cross peaks observed using polarization-sensitive dispersed pump-probe spectroscopy[END_REF] to material sciences [START_REF] Donaldson | Gold nanoparticle capping layers: Structure, dynamics, and surface enhancement measured using 2D-IR spectroscopy[END_REF][START_REF] Mehlenbacher | Photoexcitation dynamics of coupled semiconducting carbon nanotube thin films[END_REF][START_REF] Grechko | Diffusion-Assisted Photoexcitation Transfer in Coupled Semiconducting Carbon Nanotube Thin Films[END_REF] through nonlinear four-wave mixing techniques such as IR photon echo [START_REF] Hesselink | Picosecond Photon Echoes Stimulated from an Accumulated Grating[END_REF] or 5 two-dimensional IR spectroscopy [START_REF] Asplund | Two-dimensional infrared spectroscopy of peptides by phase-controlled femtosecond vibrational photon echoes[END_REF]. Thanks to the very large transition dipole moment (µ = 1 D) of the asymetric CO stretch vibrational mode (T 1u mode near 2000 cm -1 ) W(CO) 6 organometallic complex is highly interesting since it yields a large nonlinear response. In this sense W(CO) 6 has been widely studied by means of nonlinear processes in various condensed media [START_REF] Tokmakoff | Infrared vibrational photon echo experiments in liquids and glasses[END_REF][START_REF] Rector | Vibrational echoes: A new approach to condensed-matter vibrational spectroscopy[END_REF][START_REF] Broquier | IR spectra and vibrational dephasing of the CO stretching mode in W(CO)6 doped cryogenic matrices[END_REF]. In particular W(CO) 6 represents a very sensisitive probe to characterize guest-host interactions and allows a very detailed insight into environment effects induced by the nature of the host on the molecular dynamics of W(CO) 6 . We have investigated the environment effects on the vibrational properties of W(CO) [START_REF] Donaldson | Gold nanoparticle capping layers: Structure, dynamics, and surface enhancement measured using 2D-IR spectroscopy[END_REF] in the condensed phase in different cryogenic lattices such as rare gas crystals (argon [START_REF] Broquier | IR spectra and vibrational dephasing of the CO stretching mode in W(CO)6 doped cryogenic matrices[END_REF], krypton [START_REF] Thon | Vibrational Perturbations of W(CO)6 Trapped in a Molecular Lattice Probed by Linear and Nonlinear Spectroscopy[END_REF]) and molecular hosts (nitrogen [START_REF] Thon | Vibrational Perturbations of W(CO)6 Trapped in a Molecular Lattice Probed by Linear and Nonlinear Spectroscopy[END_REF], methane [START_REF] Thon | Vibrational spectroscopy and dynamics of W(CO)6 in solid methane as a probe of lattice properties[END_REF]).

The vibrational properties of W(CO) 6 have been measured by linear and nonlinear (pump-probe and photon echo techniques) IR spectroscopy at different temperatures. We thus have access to T 1 population relaxation time and T 2 dephasing time. T 2 is related to the homogeneous broadening γ homo through the relation:

γ homo = 1 πT 2 = 1 2πT 1 + 1 πT 2 * (1)
where T 2 *, called pure dephasing time, is especially sensitive to the environment. In order to get an overview of the vibrational behavior of W(CO) 6 in cryogenic lattices, we performed additional experiments in neon (for probing a third rare gas host), in parahydrogen (a specific host with quantum properties) and in carbon tetrafluoride (following the series of methane solids CH 4 and CD 4 ). This paper is thus dedicated to the comparison of these various results allowing for conclusive remarks on the host dependence of W(CO) 6 vibrational properties. After a brief description of the experimental procedures, the results in the different hosts are summarized. They are discussed in the last part before the conclusions in terms of host effects on the absorption features, vibrational population relaxation and dephasing processes. We show how the host nature, the trapping site, the crystallographic ordering affect the properties of the guest molecule and in particular its vibrational dynamics. The conclusions highlight the main tendencies obtained from the comparison of all the results.

Experimental procedure and methods

The detailed experimental set-ups have been extensively described in our previous papers [START_REF] Thon | Vibrational Perturbations of W(CO)6 Trapped in a Molecular Lattice Probed by Linear and Nonlinear Spectroscopy[END_REF][START_REF] Galaup | Vibrational dynamics of CO stretching in W(CO)6-doped hybrid xerogels from 5 K to room temperature with the CLIO-FEL[END_REF] and only the main descriptions related to new results are presented.

In the case of CF 4 , as for the experiments described in Refs. [START_REF] Thon | Vibrational Perturbations of W(CO)6 Trapped in a Molecular Lattice Probed by Linear and Nonlinear Spectroscopy[END_REF][START_REF] Thon | Vibrational spectroscopy and dynamics of W(CO)6 in solid methane as a probe of lattice properties[END_REF] the matrix samples have been obtained by continuous deposition of a gaseous mixture onto a cold CaF 2 window of the cryostat. Gaseous samples are prepared at room temperature by mixing W(CO) 6 (Sigma Aldrich) with the carrier gas with [W(CO) 6 ]/[Host] ratio varying from 10 -5 to 10 -3 . Matrix thickness is kept below 100 µm. Concentration and deposition times are adapted to keep an optical density of the T 1u mode of W(CO) 6 of ≈ 1. Deposition temperatures can vary between 15 and 30 K depending on the host (30 K for CF 4 ).

Nonlinear measurements are obtained using an IR OPA source for fs pulses (see ref. [START_REF] Thon | Vibrational Perturbations of W(CO)6 Trapped in a Molecular Lattice Probed by Linear and Nonlinear Spectroscopy[END_REF] for details). The fs IR OPA is combined to a 3-pulse photon echo set-up. It is pumped by a 800 nm Ti:Sa laser/amplifier system and delivers an IR pulse centered at 1980 cm -1 , bandwidth 150 cm -1 , duration 145 fs, output ≈ 3 µJ. Resulting IR beam is then split into three beams (k 1 , k 2 and k 3 wave vectors) of equivalent intensities using two coated ZnSe beamsplitters. The echo signal is emitted in a well-defined direction given by phase-matching such

as k s =k 3 + k 2 -k 1 .
The signal beam is focused on an MCT (mercury cadmium telluride) detector. There are two independant delay stages giving access to two delay times τ and T, called coherence time and waiting time and corresponding to the delay between the first two pulses and the last two pulses, respectively.

The detected signal (quadratic detection) is:

S(τ, T ) = ∞ 0 dt P (3) (τ, T, t) 2 (2)
P (3) (τ, T, t) is the third order polarization created in the sample with the wave vector k s . In a rough way, the S(T) signal at fixed τ gives access to T 1 population lifetime and S(τ ) signal at fixed T to dephasing processes through the measure of T 2 dephasing time.

Absorption spectra have been recorded using an FTIR Mattson spectrometer at 0.25 cm -1 spectral resolution to check the quality of the sample and its evolution with temperature and time. A switching gold coated mirror brings the FTIR globar beam to probe the same matrix region as in photon echo experiments. Linear and nonlinear data have been measured using the same nitrogen-cooled MCT detector.

Additional experiments in neon and parahydrogen (pH 2 ) have been performed with another set-up dedicated to pH 2 experiments. Hydrogen is converted to parahydrogen in a first cryostat kept at 17 K and parahydrogen vapor is directly condensed onto a cold diamond window of a second cryostat (IceOxford) at the lowest temperature of 3 K. W(CO) 6 /pH 2 samples are obtained by flowing pH 2 over a tube containing W(CO) 6 and carrying its vapor before the deposition. The experimental procedure to produce doped pH 2 samples is the same as that described in ref. [START_REF] Ceponkus | Infrared study of glycolaldehyde isolated in parahydrogen matrix[END_REF]. W(CO) 6 /Ne samples are obtained in the same manner, replacing hydrogen by neon and keeping the first cryostat at 40 K to avoid any neon condensation. In this case, the first cryostat is used to trap all residual impurities. IR spectra of the samples are recorded by means of a

Nicolet FTIR spectrometer at 0.125 cm -1 spectral resolution. No time-resolved measurements have been conducted with this cryogenic set-up. Because Kr, Ar and Ne have different lattice parameters, trapping sites should be different in the three hosts. In that sense, the Ar spectrum seems the simplest and could reflect a smaller number of different trapping sites, i.e. a better match between the size of W(CO) 6 and that of the vacancies [START_REF] Broquier | IR spectra and vibrational dephasing of the CO stretching mode in W(CO)6 doped cryogenic matrices[END_REF]. Nevertheless spectra in the three rare gas solids show a major structure in the red side and a minor one in the blue side. The energy gap between these two bands is roughly 5±2 cm -1 with no obvious correlation with the lattice parameter. In Ne, the absorption spectrum spreads only over 8 cm -1 and this gap is reduced to ≈ 3 cm -1 (Figure 1). The frequency shift between matrix and gas phase (1998 cm -1 ) is also the smallest. This is a well-known consequence of the lowest polarizability of Ne which induces the smallest matrix effect on the transition frequencies of guest molecules.

Results

3

No significant change is observed when varying the temperature in Ar [START_REF] Broquier | IR spectra and vibrational dephasing of the CO stretching mode in W(CO)6 doped cryogenic matrices[END_REF] and Kr [START_REF] Thon | Vibrational Perturbations of W(CO)6 Trapped in a Molecular Lattice Probed by Linear and Nonlinear Spectroscopy[END_REF] in terms of band position or linewidth. On the contrary, annealing at 60 K in Kr leads to reorganization of the trapping sites yielding a small change in the relative intensities of the bands. We have also observed slight differences in W(CO) 6 /Ar spectra when varying the experimental deposition conditions.

However the relative intensities of the two main features remain constant. The occur to be rather simple. Time-resolved signals measuring T 1 and T 2 always exhibit long decay times in the hundreds of ps. Of course, since the IR laser pulses are spectrally broad, the time-resolved signals correspond to the nonlinear response of the entire absorption spectra. In Kr, there is no variation in the population decays when changing the temperature. The decay is not in fact mono-exponential and the S(T) signals are better fitted with two exponential contributions that take into account two different dynamics linked to the population relaxation from v = 1 excited state (T 1 ) and recovery to the ground state (T g ), suggesting a long-lived intermediate level in the vibrational relaxation. We find T 1 = 80±20 ps and T g ≈ 1.5 ns [START_REF] Thon | Vibrational Perturbations of W(CO)6 Trapped in a Molecular Lattice Probed by Linear and Nonlinear Spectroscopy[END_REF]. In Ar, a single exponential is found but the signal has not been recorded until the end of the relaxation, suggesting that the long T g time has not been actually measured. It gives a T 1 population relaxation time which slightly shortens when temperature increases with T 1 > 200 ps at 8 K and T 1 = 160 ps at 20 K [START_REF] Broquier | IR spectra and vibrational dephasing of the CO stretching mode in W(CO)6 doped cryogenic matrices[END_REF].

Similarly to S(T), the S(τ ) signals in Kr show no temperature effects between 25 and 50 K. The decay of the signal yields 100 ± 20 ps, equivalent to a γ homo homogeneous broadening of 0.106 cm -1 . It is smaller than the width of the narrowest lines of the absorption spectrum (FWHM≈ 0.5 cm -1 ): it means that the absorption structure is not composed of homogeneous substructures. In Ar, T 2 values are slightly longer than in Kr, they are not constant with temperature but they are in the same order of magnitude with T 2 (8 K) = 400 ps and T 2 (20 K) = 200 ps. Corresponding γ homo of 0.026 and 0.053 cm -1 are much less than the linewidths of the absorption structures (≈ 2.3 cm -1 ). In both rare gas solids we find T 2 comparable to twice T 1 , meaning that dephasing processes are essentially governed by population relaxation.

Molecular matrices

Nitrogen and methane

We have studied nitrogen and methane solids because the crystals also adopt an fcc structure similar to rare gas solids. Moreover, nearest neighbors distances d are of the same order of magnitude, and in particular close to that of Kr lattice: temperature increases [START_REF] Thon | Vibrational spectroscopy and dynamics of W(CO)6 in solid methane as a probe of lattice properties[END_REF]. This effect is assigned to a motional narrowing due to the complete rotational disorder and the large motional fluctuations of CH 4 hosts in phase I, which for this reason is also named plastic phase [START_REF] Bounds | Molecular dynamics simulation of the plastic phase of solid methane[END_REF].

185

There is no obvious temperature effect on the vibrational population relaxation of W(CO) 6 in N 2 and the decay times are in the hundreds of ps, similarly to the case of Kr (Figure 3a). As in Kr two times in the population decay can also be considered, a T 1 time around 180 ps and a very long recovery time T g > 1 ns [START_REF] Thon | Vibrational Perturbations of W(CO)6 Trapped in a Molecular Lattice Probed by Linear and Nonlinear Spectroscopy[END_REF]. They represent averaged population decay times for all the sites 190 as in Kr and Ar. On the contrary, a strong temperature effect is observed in 10 CH 4 in the S(T) signals corresponding to distinct dynamical behaviours above and below phase transition of CH 4 (Figure 3b): there is one long component around 200 ps at all temperatures (same order of magnitude as T 1 in N 2 ) but there is an additional shorter decay of 10 ps in phase I (red trace in Figure 3b).

The weight of the short component corresponds to the weight of high symmetry sites obtained in the analysis of the absorption spectra. Our analysis of the time-resolved signals suggests that the short 10 ps component reflects T 1 time of W(CO) 6 molecules in these high symmetry sites [START_REF] Thon | Vibrational spectroscopy and dynamics of W(CO)6 in solid methane as a probe of lattice properties[END_REF]. In these sites, W(CO) 6 does not significantly perturb the CH 4 lattice and fast relaxation involving a methane vibron can occur in phase I because of the strong broadening of methane modes in this crystallographic phase. Note that, whatever the temperature no very long (> 400 ps) decay has been measured in CH 4 precluding the existence of a very long T g time.

Photon echo measurements in N 2 and CH 4 both exhibit temperature effects. In low symmetry sites, T 2 is almost constant, around 50 ps, i.e. shorter than in rare gas matrices. The temperature dependence in high symmetry sites can be described as an enhancement of the homogeneous width by coupling with a libration mode of the nitrogen lattice [START_REF] Thon | Vibrational Perturbations of W(CO)6 Trapped in a Molecular Lattice Probed by Linear and Nonlinear Spectroscopy[END_REF].

In CH 4 , beside the large shortening of the population relaxation time in phase I assigned to high symmetry sites, T 2 is found to decrease with temperature increase in all sites. It is well depicted in Figure 4b where S(τ ) signals have in phase I. The corresponding homogeneous width of ≈ 0.4 cm -1 at 30 K for all sites is consistent with a predominant homogeneous broadening with a bandwidth of 0.5 cm -1 measured on the main component of the absorption spectrum at 30 K. In both N 2 and CH 4 solids, the S(τ ) signal becomes more symmetric with respect to τ (Figure 4) reflecting the increase of the homogeneous contribution to broadening but one can notice that, whereas the rise of the signal (at τ < 0) does not depend on temperature in N 2 , it is longer at high temperature in CH 4 indicating that the inhomogeneous contribution is simultaneously reduced, which is a signature of the motional narrowing [START_REF] Thon | Vibrational spectroscopy and dynamics of W(CO)6 in solid methane as a probe of lattice properties[END_REF].

Experiments have also been conducted in heavy methane (CD 4 ) for which two phase transitions can be explored. In fact, the T 1u mode of W(CO) 6 is found in resonance with the 2ν 4 overtone mode of CD 4 [START_REF] Thon | Vibrational spectroscopy and dynamics of W(CO)6 in solid methane as a probe of lattice properties[END_REF]. The consequence is a very fast population relaxation at all temperatures (≈10 ps) which prevents any analysis of environment effects on pure dephasing processes in this solid.

The absorption spectrum shows the same global structure as in CH 4 , with broad features in all the phases, suggesting a similar analysis based on low and high symmetry sites with a high/low ratio in CD 4 of 55:45.

Carbon tetrafluoride CF 4

In order to probe another crystallographic environment with molecular "spherical" hosts, we have studied CF 4 solid after CH 4 and CD 4 . CF 4 carbon tetrafluoride presents a phase transition at 76.2 K (at zero pressure) [START_REF] Sataty | Carbon tetrafluoride -phase II: Far infrared spectrum and crystal structure[END_REF], the high-and low-temperature phases are respectively designated by I and II. Phase I (or β) is also named "plastic" phase due to orientational disorder of CF 4 molecules [START_REF] Fournier | Vibrational Spectra of Liquid and Crystalline CF4[END_REF],

similarly to CH 4 . It corresponds to a rhomboedric structure. Phase II (or α) is a well-ordered crystal and the lattice structure changes to monoclinic [START_REF] Fitch | The structure of solid carbon tetrafluoride[END_REF].

It is therefore an interesting medium for trapping W(CO) 6 in terms of lattice structure and orientation of molecules.

In The consequence is a red shift and an increase of band 2 at 1989 cm -1 with temperature. At 35 K, there is only one main band at 1988.7 cm -1 . It is found to narrow slightly from 8 to 20 K and to broaden because of the previous effect.

Spectral changes observed when varying the temperature are reversible. CF 4 forms a larger "sphere" (0.43 nm diameter) than methane but as in the other solids studied, W(CO) 6 (0.78 nm diameter) replaces more than one host in the lattice. Because of the monoclinic structure in phase II, the O h symmetry of W(CO) 6 cannot be preserved and band splitting due to degeneracy removal is expected. It is thus not surprising that the spectral behavior is different in CF 4 .

Anyway, the comparison with the observations in N 2 and CH 4 suggests that the most intense band 2 at 1989 cm -1 contains the main components of highest symmetry sites. The frequency shift of some components in the absorption spectrum toward the main one when temperature increases looks like the band coalescence observed in CH 4 from phase II to phase I [START_REF] Thon | Vibrational spectroscopy and dynamics of W(CO)6 in solid methane as a probe of lattice properties[END_REF], although 35 K is rather far from the temperature of phase transition in CF 4 . One must remind that a lowering of this temperature was observed in methane when the solid was doped with W(CO) 6 [START_REF] Thon | Vibrational spectroscopy and dynamics of W(CO)6 in solid methane as a probe of lattice properties[END_REF] and such effect can also occur in CF the tens of ps as given by eq. 1 is present, that is temperature dependent. The molecular nature of the host could be at play in pure dephasing process, as in N 2 and CH 4 but data are too scattered for a more precise conclusion.

Quantum matrix: parahydrogen pH 2

Only IR measurements are available in solid parahydrogen (pH 2 ). Parahydrogen is a very attractive environment as it possesses unique properties. It is a quantum crystal thanks to its light pH 2 mass and to the significant translational zero-point motion of the pH 2 molecules about their equilibrium positions within the solid. The weak pH 2 -pH 2 intermolecular forces, the J = 0 rotational state at cryogenic temperatures for all molecules, the spherical symmetry of the ground state, the minimal cage effect contribute to the "softness" of the matrix and result in weak perturbations on the guest molecules [START_REF] Silvera | The solid molecular hydrogens in the condensed phase: Fundamentals and static properties[END_REF]. By trapping W(CO) 6 molecules in pH 2 we thus expect that its spectroscopy and dynamics will qualitatively differ from the other solids studied so far. Solid pH are expected to be homogeneously broadened [START_REF] Momose | High-resolution laser spectroscopy of methane clusters trapped in solid parahydrogen[END_REF][START_REF] Yoshioka | Infrared spectra of CH3F(ortho-H2)n clusters in solid parahydrogen[END_REF][START_REF] Momose | High-resolution spectroscopy and the analysis of ro-vibrational transitions of molecules in solid parahydrogen[END_REF].

The IR spectrum of W(CO) 6 isolated in pH 2 at 3 K is displayed in Figure 1c.

It is simpler than in the other solids and the global feature is much narrower than in other hosts. However, it does not show a unique band, as in the isolated molecule but two doublets. The most intense doublet absorbs at 1992.2 and 1992.5 cm -1 and the weakest one is located at 1992.8 and 1993.3 cm -1 . The absorption spectrum exhibits a very slow time evolution, with a decrease of the bands at 1993.3 and 1992.5 cm -1 meaning that they correspond to metastable sites. The two weaker bands have half intensities of the two stronger ones. We conclude that the two doublets correspond to two sites where the triply degenerated T 1u mode gives rise to two components, one being doubly degenerated (the strongest one). Such degeneracy removal is consistent with the hcp structure. Bands are very narrow and their actual linewidth cannot be reached with our FTIR resolution (FWHM < 0.125 cm -1 ). It gives a 0.1 cm -1 limit to the value of γ homo . The corresponding T 2 dephasing time is thus longer than 100 ps. Time-resolved experiments are necessary to obtain more accurate values.

Discussion

Spectroscopy

The complex structures in the absorption spectra in the crystalline cryogenic solids mainly reflect site effects. In amorphous solids, like xerogels or glasses, only a non structured and broad absorption band has been observed [START_REF] Galaup | Vibrational dynamics of CO stretching in W(CO)6-doped hybrid xerogels from 5 K to room temperature with the CLIO-FEL[END_REF][START_REF] Heilweil | Population relaxation of CO (v=1) vibrations in solution phase metal carbonyl complexes[END_REF][START_REF] Tokmakoff | Vibrational spectral diffusion and population dynamics in a glassforming liquid: Variable bandwidth picosecond infrared spectroscopy[END_REF].

Since this band is inhomogeneously broadened, it corresponds to a continuum of different sites. Results in differents environments are summarized in Table 1.

The analysis of the structures in N 2 and CH 4 suggests the existence of high symmetry sites where the O h symmetry of W(CO) 6 is preserved [START_REF] Thon | Vibrational Perturbations of W(CO)6 Trapped in a Molecular Lattice Probed by Linear and Nonlinear Spectroscopy[END_REF][START_REF] Thon | Vibrational spectroscopy and dynamics of W(CO)6 in solid methane as a probe of lattice properties[END_REF]. In fcc lattices, with nearest neighbors distances around 0.4 nm, O h (or T d ) trapping sites large enough to contain the guest molecule are obtained when removing 13 hosts (one and its 12 nearest neighbors). The size of this big hole has a diameter of around 0.77 nm, which is well adapted to W(CO) 6 . Therefore, these "O h " trapping sites should also exist in Ar and Kr matrices and possibly in Ne. Similarly to the case of N 2 and CH 4 , we can also conclude that in all these fcc solids the weaker feature in the blue part of the spectra is assigned to a non degenerated component of the T 1u mode of W(CO) 6 in low symmetry sites.

A rough estimation of the integrated absorption of the weak and the strong bands (separated by few wavenumbers) can give an idea of the ratio of high/low symmetry sites. We find 40:60, 45:55, 45:55 in Kr, Ar and Ne respectively, it is as expected very similar to the 40:60 and 45:55 ratios obtained in the spectral analysis in N 2 and CH 4 respectively. The hcp structure of pH 2 is very close to the previously described fcc structure and with a nearest neighbors distance d of 0.379 nm, a hole of 13 pH 2 could also fit for the trapping of W(CO) 6 .

The symmetry of such trapping site is D 3h in the hcp structure, explaining the splitting of the T 1u mode in two components. The results in pH 2 in that sense confirm the previous assignment.

Figure 7a shows the IR spectra of W(CO) 6 in the different solids studied, CH 4 , Kr, N 2 , Ar, CF 4 , pH 2 and Ne from top to bottom. All these features are red-shifted from the gas phase frequency (1998 cm -1 ) [START_REF] Jones | Vibrational spectra and force constants of the hexacarbonyls of chromium, molybdenum and tungsten[END_REF], meaning that the gas to matrix shift is due to dispersive interactions. In Figure 7b xerogels [START_REF] Galaup | Vibrational dynamics of CO stretching in W(CO)6-doped hybrid xerogels from 5 K to room temperature with the CLIO-FEL[END_REF], 14.7 cm -1 in dibutylphtalate [START_REF] Tokmakoff | Infrared vibrational photon echo experiments in liquids and glasses[END_REF]. These values differ by 1.5%, to be compared with the 0.2% dispersion found for the corresponding fundamental frequencies.

Population relaxation

Vibrational relaxation of W(CO) 6 in liquids was found to be strongly solvent dependent [START_REF] Tokmakoff | Homogeneous Vibrational Dynamics and Inhomogeneous Broadening in Glass-Forming Liquids -Infrared Photon-Echo Experiments from Room-Temperature to 10 K[END_REF] because the vibrational pattern of the solvent can give intermediate levels in the vibrational relaxation depending on the vibrational energies of its modes compared to the probed T 1u mode of W(CO) 6 . The same is observed in cryogenic solids. In CD 4 a vibrational mode of the host is in quasi-resonance with the T 1u mode yielding a reduced T 1 value of 10 ps. We also suggest that the vibron of CH 4 at 1538 cm -1 can be efficiently involved in the population relaxation of W(CO) 6 in high symmetry sites because this energy corresponds to the energy gap between the probed T 1u mode and low energy modes of W(CO) 6 around 400 cm -1 , leading also to a strongly reduced T 1 time [START_REF] Thon | Vibrational spectroscopy and dynamics of W(CO)6 in solid methane as a probe of lattice properties[END_REF]. In all the other cases studied, T 1 of 100-200 ps has been measured.

In particular, T 1 is not shortened in phase II of CH 4 nor in low symmetry sites despite a rich vibrational pattern below 1900 cm -1 . At low temperature, the population relaxation pathway needs to include vibrational levels of the host of rather precise energies to be efficient. The same remark is verified in the case of CF 4 . The solid possesses indeed only vibrational fundamental modes of low energies (≤ 1320 cm -1 ) [START_REF] Fournier | Vibrational Spectra of Liquid and Crystalline CF4[END_REF] which cannot fill the gap between the T 1u mode and low energy modes of W(CO) 6 [START_REF] Amster | Vibrational spectra of some group VI hexacarbonyls[END_REF]. It means that lattice phonons are rather inefficient in the relaxation pathway, which is expected since the order of magnitude of their energy is once or twice lower than the probed vibration.

On the other hand, 100-200 ps values are short compared with T 1 = 800 ps obtained in CCl 4 at room temperature [START_REF] Tokmakoff | Temperature-Dependent Vibrational-Relaxation in Polyatomic Liquids: Picosecond Infrared Pump-Probe Experiments[END_REF]. There is no obvious reason for T 1 times to be shorter in matrices at temperatures below 20 K, especially in rare gas solids or N 2 with no vibrational levels below 1900 cm -1 . In these

Conclusions

By probing the vibrational properties of a guest molecule (W(CO) 6 ) in diverse cryogenic lattices, we have obtained several results highlighting the specificities of the different environments explored. The IR absorption of W(CO) 6 always exhibits a structured feature. It is a signature of the limited number of families of trapping sites due to the crystalline environment. The simplest structure is observed in solid pH 2 , a solid with specific properties minimizing site effects. Band broadening of each structure in pH 2 is expected to be homogeneous but no time-resolved experiment has yet been measured to confirm this assumption. In other cryogenic matrices, some substructures possess narrow linewidths (≈ 0.5 cm -1 ) but time-resolved experiments always show a significant inhomogeneous contribution to broadening. However strong homogeneous broadening is clearly observed in the absorption when temperature increases in a fraction of N 2 trapping sites.

Relaxation processes are found to be host-dependent and they are moreover site dependent as proved in N 2 or CH 4 . Except in the case of resonances between the probed vibration and the energy levels in the host + guest system, T 1 population relaxation times are long. In fact, values of 100-200 ps may reflect vibrational energy transfers between components of the T 1u mode of W(CO) 6 when a very long time in the ns range is detected, that would correspond to the v = 1 lifetime (as observed in rare gas and N 2 solids). Dephasing is enhanced in molecular hosts probably because of coupling between molecular motions. Acoustic phonons turn out to be very inefficient in the dephasing process, in contrast with phonons coming from rotational or vibrational motions of the molecular hosts. Librons and vibrons affect the vibrational dynamics and their effect appears to be strong in sites where the lattice is weakly perturbed, i.e. high symmetry sites.

Figure captions

. 1 .

 1 Rare gas matrices: Ar, Kr, Ne W(CO) 6 has been isolated in Ar, Kr and Ne solids. The IR spectra have been recorded in the three hosts and photon echo experiments have been performed in Ar and Kr. The IR spectrum in Kr and Ne in the region of the asymetric νCO stretch of W(CO) 6 is displayed in Figure1. Spectra reveal a complex absorption spreading over 10 cm -1 in contrast to the gas phase where there is only one line at 1998 cm -1[START_REF] Jones | Vibrational spectra and force constants of the hexacarbonyls of chromium, molybdenum and tungsten[END_REF]. The complex structure reflects the complexity of the trapping sites. With a diameter around 0.78 nm, W(CO) 6 is a huge impurity to trap in these cristallographic lattices. Rare gas solids have an fcc structure with a nearest neighbors distance d of 0.40, 0.38 and 0.32 nm for Kr, Ar and Ne respectively, i.e. much smaller than the size of W(CO) 6 . Consequently, the guest molecule is trapped in multi-vacancy sites. The structure of the absorption spectra can result from two effects: the presence of many different trapping sites (differing for example by the number of hosts removed), and the possible degeneracy removal of the T 1u mode (triply degenerated in the isolated molecule) in trapping sites of lower degree of symmetry than O h group (the group of symmetry of the isolated molecule).

Figure 1 :

 1 Figure 1: IR spectra of W(CO) 6 in (a) Kr (35 K), (b) Ne (3 K) and (c) pH 2 (3 K). The inset shows a schematic of W(CO) 6 (W in blue, C in grey, O in red).

d 4 Figure 2 :Figure 3 :

 423 Figure 2: IR spectra of W(CO) 6 in N 2 at 6 and 22 K and CH 4 at 8 and 22 K. Low and high temperatures are respectively plotted as black and red traces.

Figure 4

 4 Figure 4 shows signals recorded at 9 and 20 K in N 2 and at 8 and 24 K in CH 4 . Experimental curves in N 2 are correctly modelled when considering T 2 times that depend on the family of sites. Only T 2 times of high symmetry sites are strongly temperature dependent: they vary from 130 ps at 6 K to 15 ps at 20 K. It is in perfect agreement with the temperature broadening of band 2 in the absorption, leading to a significant homogeneous contribution at 20 K.

  been measured with long waiting times (T > 30 ps) to get rid of this short 10 ps component in T 1 in phase I. T 2 times are found to decrease smoothly from 120-140 ps at 6 K to 25-30 ps at 30 K. The latter value is very close to twice T 1 of high symmetry sites, where dephasing is governed by the loss of population

Figure 4 :

 4 Figure 4: S(τ ) signals (normalized) of W(CO) 6 in (a) N 2 and (b) CH 4 . Red circles and black squares represent signals at high (20 and 24 K) and low (8 and 9 K) temperatures respectively.

Figure 5 :

 5 Figure 5: IR spectra of W(CO) 6 in CF 4 from 10 K to 40 K (top to bottom).

4 .

 4 Unfortunately, time-resolved measurements have been very difficult to obtain due to high scattering of the samples. The best signals have been recorded in a short temperature range only (30-45 K) corresponding to the best quality samples so only global behaviors can be extracted from the signals. Nevertheless a clear shortening of T 2 upon temperature increase is observed. T 2 of 50 ps ± 10 ps is obtained between 10 and 20 K, and this value continuously decreases to ≈ 20 ps at 50 K. The S(τ ) signal at 30 K is shown in Figure6a. The asymmetric profile indicates a predominant inhomogeneous contribution to broadening.The deduced value of T 2 = 38 ps is an average for all bands. It corresponds to a homogeneous broadening of 0.27 cm -1 , which is lower than the linewidth of the substructures (0.5 -1 cm -1 ) measured in the absorption spectra. The S(τ ) profile seems obviously more symmetric at 50 K (not shown), corresponding to the IR spectrum involving only one main band. T 1 is measured in the hundreds of ps in the explored temperature range, without any clear temperature effect. An example is given in Figure6bat 35 K, yielding T 1 = 240 ps ± 30 ps. No obvious long component can be extracted from the S(T) curves, suggesting that there is no long T g recovery time as in CH 4 . Similarly to the case of N 2 , no population relaxation enhancement takes place in CF 4 while a pure dephasing time T 2 * in

2

 2 adopts an hcp lattice structure with nearest neighbors distance d = 0.379 nm, i.e. a value very close to that of solid Ar. W(CO) 6 should thus replace a similar number of pH 2 hosts as Ar atoms in the respective lattices. Because of its softness, site effects are usually strongly reduced in this quantum solid and absorption bands

Figure 6 :

 6 Figure 6: Examples of time-resolved signals in CF 4 doped with W(CO) 6 (arbitrary units), (a) S(τ ) at 30 K, T = 20 ps, (b) S(T) at 35 K ("spike" at the origin as in Figure3a).

  is plotted the T 1u frequency measured in the different media as a function of the polarizability α of the host. It clearly shows a correlation between T 1u position and α, except for CF 4 . The weakest feature observed in all hosts is less down shifted from the gas phase. It corresponds to a CO stretch mode in a specific direction in low symmetry sites that is either weakly perturbed by the environment, or more sensitive to constraints as in Ne, where it is slightly above the gas phase value because of a more compact lattice (d = 0.32 nm) inducing more repulsive forces than in the other hosts. The red-shift of the T 1u frequency in the condensed phase can reach 20 cm -1 [30], i.e. 1% of its value. The anharmonicity of this mode has been measured in various environments by means of oscillations observed in photon echo signals and has been assigned to quantum beats between thev = 0 ↔ v = 1 and v = 1 ↔ v = 2 transitions[START_REF] Tokmakoff | Infrared vibrational photon echo experiments in liquids and glasses[END_REF]. The anharmonicity value measured in N 2 is 14.7 cm -1 [14], 14.5 cm -1 in CH 4[START_REF] Thon | Vibrational spectroscopy and dynamics of W(CO)6 in solid methane as a probe of lattice properties[END_REF], 14.5 cm -1 in

Figure 7 :

 7 Figure 7: (a) IR spectra of W(CO) 6 recorded in the region of T 1u mode in, from top to bottom, CH 4 , Kr, N 2 , Ar, CF 4 , pH 2 and Ne. Temperature is 20 K for all solids except in pH 2 and Ne where it is 3 K. The gas phase frequency (1998 cm -1 ) is marked with a dotted line. (b) ν wavenumber (in cm -1 ) of the T 1u mode of W(CO) 6 in the gas phase, Ne, pH 2 , Ar, Kr, N 2 , CH 4 and CF 4 plotted as a function of the polarizability α of the host ( Å3 ).

The temperature dependence of the long T 1

 1 (100-200 ps) has been difficult to measure, with very weak changes in the short temperature range accessible in the experiments. Because of the experimental difficulties to obtain precise measurements (low laser and sample stabilities in long acquisitions of hundreds of ps), signal changes are usually in the measurement errors. A slight effect has been measured in Ar without the possibility to extract a temperature law.

1 )Figure 8 :

 18 Figure 8: Plot of γ homo as a function of temperature in Kr rare gas solid (triangles) and in N 2 (squares), CH 4 (circles), CF 4 (stars) molecular hosts.

Figure 1

 1 Figure 1 IR spectra of W(CO) 6 in (a) Kr (35 K), (b) Ne (3 K) and (c) pH 2 (3 K). The inset shows a schematic of W(CO) 6 (W in blue, C in grey, O in red).

Figure 2

 2 Figure 2 IR spectra of W(CO) 6 in N 2 at 6 and 22 K and CH 4 at 8 and 22 K.Low and high temperatures are respectively plotted as black and red traces.

Figure 3 S

 3 Figure 3 S(T) signals (normalized) of W(CO) 6 in (a) N 2 at 20 K and (b) CH 4 at 14 K (black) and 25 K (red). The very steep rise ("spike") at T = 0 is due to additional nonlinear signals produced when the IR pulses simultaneously arrive onto the sample. It is not related to the probed dynamics [21].

Figure 4 S

 4 Figure 4 S(τ ) signals (normalized) of W(CO) 6 in (a) N 2 and (b) CH 4 . Red circles and black squares represent signals at high (20 and 24 K) and low (8 and 9 K) temperatures respectively.

Figure 5

 5 Figure 5 IR spectra of W(CO) 6 in CF 4 from 10 K to 40 K (top to bottom).

Figure 6

 6 Figure 6 Examples of time-resolved signals in CF 4 doped with W(CO) 6 (arbitrary units), (a) S(τ ) at 30 K, T = 20 ps, (b) S(T) at 35 K ("spike" at the origin as in Figure3a).

Figure 7 (

 7 Figure 7 (a) IR spectra of W(CO) 6 recorded in the region of T 1u mode in, from top to bottom, CH 4 , Kr, N 2 , Ar, CF 4 , pH 2 and Ne. Temperature is 20 K for all solids except in pH 2 and Ne where it is 3 K. The gas phase frequency (1998 cm -1 ) is marked with a dotted line. (b) ν wavenumber (in cm -1 ) of the T 1u mode of W(CO) 6 in the gas phase, Ne, pH 2 , Ar, Kr, N 2 , CH 4 and CF 4 plotted as a function of the polarizability α of the host ( Å3 ).

Figure 8

 8 Figure 8 Plot of γ homo as a function of temperature in Kr rare gas solid (triangles) and in N 2 (squares), CH 4 (circles), CF 4 (stars) molecular hosts.

Table 1 :

 1 Summary of the results on the vibrational properties for the main features of W(CO) 6 in different environments.

	Host	T (K)	Absorption ( cm -1 )	T 1 (ps)	T 2 (ps)	References
			Major	Minor
			feature	feature
	Ar	7-8	1986	1991	240-270	400 ± 80	Ref. [13]
		20	1986	1991	160 ± 10	200 ± 40
	Kr	25	1983.9	1989.3	80 ± 20 &	100 ± 20	Ref. [14]
					> 1000 (T g )
	Ne	3 → 8	1995.9	1999	not measured
	N 2	6	1984.1	1989.3	180 ± 30 &	130 (high sym.) & Ref. [14]
					> 1000 (T g )	50 (low sym.)
		20	1983.7	1989	180 ± 30 &	15 (high sym.) &
					> 1000 (T g )	50 (low sym.)
	CH 4	6	1980.6	1987.0	200 (low sym.)	130	Ref. [15]
		25	1980.8	1986.6	10 (high sym.) & 30
					200 (low sym.)
	CD 4	15 → 30 1980.5	1986.3	≤ 10	10	Ref. [15]
	CF 4	20 → 50 1989	1992.9	240	38	this work
	pH 2	3	1992.5	1993.3	not measured
	CCl 4	300	1978		800	< 1	Ref. [29]
	dibutyl-	0 → 300 1982		33	33 → 13	Ref. [11]
	phtalate
	xerogels	4.5	1982		60-70	28	Ref. [16]
		300				4

  solids, a longer time (> 1 ns) has been measured and assigned to T g recovery time. This value compares well with the long T 1 recorded in CCl 4 . Assuming that this T g time would correspond to the lifetime of v = 1 in these cryogenic solids, the shorter T 1 would then be assigned to the population relaxation time of the component of the T 1u mode probed in the four wave mixing experiment, i.e. the time to leave the level probed by the first pulse and probably to reach another component of the T 1u mode (through intra molecular energy transfer).Components of the T 1u mode differ by less than few wavenumbers, which is lower than energies of phonons. It explains that this vibrational energy transfer is itself inefficient. Considering that T g times are T 1u lifetimes in rare gas and N 2 solids, our experiments therefore show that the lifetime in CH 4 and in CF 4 is reduced (no long T g has been detected) as expected because of the existence of vibrational mode of medium energies. The T 1 value (< 100 ps) found in xerogels at low temperature is consistent with this latter assumption[START_REF] Galaup | Vibrational dynamics of CO stretching in W(CO)6-doped hybrid xerogels from 5 K to room temperature with the CLIO-FEL[END_REF].Photon echo experiments give a direct access to the vibrational dephasing times. Thanks to the measurements of the population relaxation times, pure dephasing times are extracted by means of eq. 1. From the results reported in cryogenic solids, there are two kinds of environments where dephasing processes are governed by population relaxation. The first one is rare gas solids (Ar and Kr). Both T 1 and T 2 times are in the hundreds of ps in the explored temperature range. Because of quite large measurement errors, it is not possible to extract valuable values of T 2 * times, but in any case, at any temperature, we can conclude that T 2 * is longer than twice T 1 . Population relaxation is fast in the second kind of environment as in CD 4 , where T 1 ≤ 10 ps and T 2 ≈ 10 ps,

	4.3. Dephasing processes

Acknowledgements

This research was supported by the RTRA Triangle de la Physique grants no. 2010-004-T NOSTADYNE, 2012-053T DYMA and 2013-0436T REACMAQ.

The authors are grateful to Justinas Ceponkus for his help in the parahydrogen measurements. They also thank Bernard Bourguignon and Aimeric Ouvrard for the use of femstosecond laser system and their technical support.


Miguel Tarongi Chavarri

Vincent Bonhomme

Allowen Evin

Sarah Ivorra

Dani López Reyes

Natàlia Alonso Martínez

Laurent Bouby

A new way of seeing pulses: preliminary results of geometric morphometric analyses of Iron Age seeds from the site of La Font de la Canya (Barcelona, Spain)

Keywords: Legumes, Seed Outline, Distance measurements, Lens culinaris, Lathyrus sativus, Vicia faba

This study applied size and shape analyses through traditional and geometric morphometrics to quantify the differences between three taxa: Lathyrus sativus (grass pea), Lens culinaris (lentil) and Vicia faba (broad bean). This analysis represents a pilot study in view of a wider future application of this technique to identify the role of legumes throughout the Western Mediterranean in the Bronze and Iron Ages. Here, we quantify the morphological differences of seed species from the site of La Font de la Canya (Catalonia, Spain), an Iron Age (625-150 BC) centre of storage and trade which delivered a vast assemblage of cereal, fruit and legume remains. Our results reveal that seed outline analyses have a greater potential of prediction than length measurements.

The combination of the two, however, leads to even more precise predictions. Moreover, the quantitative differences between the lentils of the different samples confirm the potential of these analyses to further identify intra-species morphotypes.

Introduction

Along with cereals, legumes are one of the most important resources for human consumption due both to their large number of cultivated species and their nutritional properties. The domestication of the first cereals and legumes took place simultaneously during the Preceramic Neolithic (9000-8000 cal BC) of Southwest Asia [START_REF] Zohary | Domestication of Pulses in the Old World: Legumes were companions of wheat and barley when agriculture began in the Near East[END_REF][START_REF] Zohary | Domestication of Plants in the Old World: The origin and spread of domesticated plants in Southwest Asia, Europe, and the Mediterranean Basin[END_REF]. [START_REF] Kislev | The Legumes: The Earliest Domesticated Plants in the Near East?[END_REF] suggested that legumes were cultivated even earlier, as the processes for their preparation for consumption is straightforward, contrary to cereals.

Ethnographic and archaeological data nonetheless reveal that legumes were always secondary to cereals throughout the Mediterranean Basin. This could explain why they have been relegated in archaeobotanical literature to a secondary role behind cereals [START_REF] Tarongi | The storage of pulses during the Bronze and Iron Ages in the East of the Iberian Peninsula: examining the archaeological data through the lens of ethnography[END_REF].

The earliest cultivation of legumes in the Northeast of the Iberian Peninsula is evidenced by charred seeds of Vicia faba (broad bean) and Pisum sativum (pea) at the sites of La Draga and the Caserna de Sant Pau (Catalonia) in an Early Neolithic context (5400-5000 cal BC). The earliest Lens culinaris (lentil) identified in this region are from a late phase of the Early Neolithic (5000-4500 cal BC) of the site of Plansallosa. Other species such as Vicia ervilia (bitter vetch) and V. sativa (common vetch) are identified since the early phases of the Middle Neolithic (4500-4000 cal BC). The cultivation of this last species, nonetheless, is not assured due to the modest numbers of seeds encountered in the sites.

Throughout the remaining part of the Neolithic these species are poorly represented [START_REF] Antolín | Local, intensive and diverse? Early farmers and plant economy in the North-East of the Iberian Peninsula (5500-2300 cal BC)[END_REF]. A slight and progressive increase of frequency of legumes took place later in the Bronze Age (2200-700 BC) in the study area. This phase also saw the appearance of the earliest regional evidence of Lathyrus sativus/cicera (grass/red pea) [START_REF] Albizuri | Economia i canvi social a Catalunya durant l'edat del bronze i la primera edat del ferro[END_REF].

The frequency and number of seeds of cultivated legume species increased even more during the First Iron Age (700-575 BC). Concentrations of pulses appear for the first time in Catalan sites such as Font de la Canya [START_REF] López | Noves Aportacions Sobre Agricultura i Alimentació Durant La Primera Edat Del Ferro a Catalunya: Dades de l'assentament de Sant Jaume (Alcanar, Montsià)[END_REF] and Sant Jaume Mas d'en Serra [START_REF] López | Noves Aportacions Sobre Agricultura i Alimentació Durant La Primera Edat Del Ferro a Catalunya: Dades de l'assentament de Sant Jaume (Alcanar, Montsià)[END_REF][START_REF] López | L'agricultura i l'alimentació dels habitants de Sant Jaume a través de les análisis carpològiques[END_REF]. They are represented by large numbers of lentils, grass peas and broad beans at the first site and grass peas at the second. During the Iberian Period these high prevalences persist, as evidenced by a concentration of broad beans at Puig de Sant Andreu de Ullastret [START_REF] Buxó | Arqueología de las plantas: la explotación económica de las semillas y los frutos en el marco mediterráneo de la Península Ibérica[END_REF], as well as peas, grass peas and vetches at Mas Castellar de Pontós [START_REF] Canal | ed) Mas Castellar de Pontós (Alt Empordà). Un complex arqueològic d'època ibèrica (excavacions 1990-1998[END_REF], grass peas at Les Malesses [START_REF] López | L'Explotaciódels recursos vegetals al jaciment ibèric de Les Maleses: primers resultats de l'estudi arqueobotànic de les llavors i fruits[END_REF]) and lentils at Font de la Canya [START_REF] López | Primers resultats arqueobotànics (llavors i fruïts) al jaciment protohistòric del Turó de la Font de la Canya (Avinyonet del Penedès)[END_REF]).

The increase in taxa frequency and in the number of legume seeds during the Bronze and Iron Ages leads to speculation as to the role they played in changes of the agricultural system. This increase could be linked to extensive cultivation, which could be related to the introduction of crop rotation through this period.

The occurrence of grass pea may be indicative of the cultivation of less fertile lands, since this species can easily grow in poor, dry and uneven soils [START_REF] Sarpaki | The Paleoethnobotanical Approach: The Mediterranean Triad or is it a Quartet? In: Wells B (ed) Agriculture in Ancient Greece[END_REF][START_REF] Peña-Chocarro | History and traditional cultivation of Lathyrus sativus L. and Lathyrus cicera L. in the Iberian Peninsula[END_REF]. All these questions point to the necessity of studying in more detail the role of legumes during the Iron Age.

A characteristic of legumes, and the Fabaceae family as a whole, is the great interspecific morphological variability of their seeds. For instance, the position that a seed occupies in the pod can largely modify its shape. Also, the large number of genera and species in Fabaceae and the recognized variability within and between species of this family complicates their taxonomic identification. In spite of there being studies on how to identify these species through their seeds at the level of the genus [START_REF] Kirkbride | Fruits and Seeds of Genera in the Subfamily Faboideae (Fabaceae)[END_REF] and species [START_REF] Lersten | Testa characters in the tribe Vicieae, with notes about tribes Abreae, Cicerae and Trifolieae (Fabaceae)[END_REF], these do not necessarily serve to identify archaeobotanical seeds since they are based on the testa, hilum and lens, parts of the seeds that are rarely preserved among charred archaeological remains.

Moreover, although legumes have received less attention than cereals and certain fruit, there are nonetheless notable studies of pulses: [START_REF] Kislev | Origins of the cultivation of Lathyrus sativus and L. cicera (Fabaceae)[END_REF], [START_REF] Butler | Legumes in antiquity: a micromorphological investigation of seeds of the Vicieae[END_REF][START_REF] Butler | Pulse agronomy: Traditional systems and implications for early cultivation[END_REF], [START_REF] Jones | Ancient and modern cultivation of Lathyrus ochrus (L.) DC. in the Greek islands[END_REF], [START_REF] Sarpaki | The Paleoethnobotanical Approach: The Mediterranean Triad or is it a Quartet? In: Wells B (ed) Agriculture in Ancient Greece[END_REF], [START_REF] Peña-Chocarro | History and traditional cultivation of Lathyrus sativus L. and Lathyrus cicera L. in the Iberian Peninsula[END_REF], [START_REF] Fuller | The archaeobotany of Indian pulses: identification, processing and evidence for cultivation[END_REF], [START_REF] Valamoti | An investigation of processing and consumption of pulses among prehistoric societies: archaeobotanical, experimental and ethnographic evidence from Greece[END_REF][START_REF] Caracuta | The onset of faba bean farming in the Southern Levant[END_REF][START_REF] Montes-Moya | Las prácticas agrícolas en la Alta Andalucía a través de los análisis carpológicos[END_REF][START_REF] Filatova | Environmental imposition or ancient farmers' choice? A study of the presence of "inferior" legumes in the Bronze Age Carpathian Basin (Hungary)[END_REF] and [START_REF] Tarongi | The storage of pulses during the Bronze and Iron Ages in the East of the Iberian Peninsula: examining the archaeological data through the lens of ethnography[END_REF]. Yet, as opposed to the studies of cereals (notably the data compiled by Jacomet 2006), there is no systematic listing of the criteria serving to identify legumes. This dearth of points of reference is even evidenced by a lack of terminology for describing and orienting archaeological seeds when photographing them. This absence of consensus was in fact discussed at the 18th Conference of the International Workgroup for Palaeoethnobotany celebrated in Lecce in 2019.

In this study, geometric morphometry has been applied to the archaeological legumes of Font de la Canya in order to investigate their potentiality for establishing quantitative differences between the shape of different species and samples. The choice of this technique stems from the significant breakthrough obtained with other archaeological taxa of cereals [START_REF] Bonhomme | Identification of inter-and intraspecies variation in cereal grains through geometric morphometric analysis, and its resilience under experimental charring[END_REF]) such as barley [START_REF] Ros | Geometric morphometric analysis of grain shape and the identification of two-rowed barley (Hordeum vulgare subsp. distichum L.) in southern France[END_REF]) and millet [START_REF] García-Granero | Geometric morphometric analysis of Setaria italica (L.) P. Beauv. (foxtail millet) and Brachiaria ramosa (L.) Stapf. (browntop millet) and its implications for understanding the biogeography of small millets[END_REF], and with fruit taxa such as olives [START_REF] Terral | Historical biogeography of olive domestication (Olea europaea L.) as revealed by geometrical morphometry applied to biological and archaeological material[END_REF], grapes [START_REF] Terral | Evolution and history of grapevine (Vitis vinifera) under domestication: new morphometric perspectives to understand seed domestication syndrome and reveal origins of ancient European cultivars[END_REF][START_REF] Pagnoux | Inferring the agrobiodiversity of Vitis vinifera L. (grapevine) in ancient Greece by comparative shape analysis of archaeological and modern seeds[END_REF][START_REF] Ucchesu | Earliest evidence of a primitive cultivar of Vitis vinifera L. during the Bronze Age in Sardinia (Italy)[END_REF][START_REF] Bouby | Back from burn out: are experimentally charred grapevine pips too distorted to be characterized using morphometrics?[END_REF], dates [START_REF] Terral | Insights into the historical biogeography of the date palm (Phoenix dactylifera L.) using geometric morphometry of modern and ancient seeds[END_REF]) and melons [START_REF] Sabato | Molecular and morphological characterisation of the ldest Cucumis melo L. seeds found in the Western Mediterranean Basin[END_REF]. This study uses these morphometric approaches and examines for the first time only well-preserved archaeological seeds from the site of Font de la Canya (Fig. 1) in the Northeast of the Iberian Peninsula. Some investigations analyse the shape of the current legume seeds through different techniques. [START_REF] Cervantes | Seed shape quantification in the model legumes: methods and applications[END_REF] quantitatively calculated the area of overlap between the seeds of some legume species, obtaining the J index (common area divided by the total area of both images) and the circularity. Other studies obtain photographs of lentils to obtain the volume and surface area of two varieties of lentils [START_REF] Firatligil-Durmuş | Image vision technology for the characterisation of shape and geometrical properties of two varieties of lentil grown in Turkey[END_REF] or to obtain size ranges for subsequent marketing [START_REF] Lemasurier | A digital image analysis method for assessment of lentil size traits[END_REF]. However, the use of these techniques on archaeological individuals does not seem to be very effective since it compares the seeds with predetermined shapes and uses a single view of each one.

The main objective of this study is to prove the efficiency of the application of geometric morphometry to archaeological seeds from different legume species, determining if it is possible to quantify the differences between them. To verify its potential, we decided to study the seeds of pulses from a site whose species have significant morphological differences. Once the efficiency of this method has been verified, future studies will be carried out on a larger taxonomic, spatial and chronological scale. Another objective of this article is to verify the differences in shape and size of the same species in the different phases of the same site through geometric morphometry. This technique requires the complete outline of the seeds, so individuals in a poor state of conservation cannot be used. This study is part of a research project led by the University of Lleida on the wider role of legumes in agri-food practices in the western Mediterranean throughout the second and first millennium BC.

Materials and methods

Archaeological materials

Due to the favourable conditions of preservation (charring) of the archaeological seeds of Font de la Canya, optical identification was straightforward [START_REF] López | Primers resultats arqueobotànics (llavors i fruïts) al jaciment protohistòric del Turó de la Font de la Canya (Avinyonet del Penedès)[END_REF], always taking into account that carbonization leads to an unequal reduction in length, width and thickness of the seeds, producing deformations with respect to current individuals [START_REF] Kislev | Influence of experimental charring on seed dimensions of pulses[END_REF][START_REF] Braadbaart | Laboratory simulations of the transformation of peas as a result of heat treatment: changes of the physical and chemical properties[END_REF][START_REF] Caracuta | The onset of faba bean farming in the Southern Levant[END_REF]. Grass peas identified in prior research as Lathyrus sativus [START_REF] López | Primers resultats arqueobotànics (llavors i fruïts) al jaciment protohistòric del Turó de la Font de la Canya (Avinyonet del Penedès)[END_REF]) have been classified as Lathyrus sativus/cicera in this study, as the smaller current varieties of L. sativus may overlap with L. cicera, a similarity that is more pronounced in archaeological seeds (Mahler-Slasky and Kislev 2010).

The only parameter serving to clearly differentiate them is the testa [START_REF] Chernoff | Characters and testa texture in species of the Vicieae: their taxonomic significance[END_REF], which is most often not preserved after carbonisation.

The site of Font de la Canya can be broken down into three well-defined chronological phases: Early Iron Age (625-550 BC), Early Iberian period (550-400 BC) Middle Iberian period (400-200 BC) [START_REF] López | Noves Aportacions Sobre Agricultura i Alimentació Durant La Primera Edat Del Ferro a Catalunya: Dades de l'assentament de Sant Jaume (Alcanar, Montsià)[END_REF]. The site's features are dominated by about 1,000 underground silos. Although the site reveals no evidence of dwellings, there are certain buildings designed for storage or craftwork such as metallurgy [START_REF] López | Noves Aportacions Sobre Agricultura i Alimentació Durant La Primera Edat Del Ferro a Catalunya: Dades de l'assentament de Sant Jaume (Alcanar, Montsià)[END_REF]. All of the archaeobotanical remains come from the silos, with cereals standing out above the rest of the taxa, although legumes and grape seeds are also of great importance. These Early Iron Age grape pips and pedicels are in fact the earliest evidence of viticulture in the Northeast of the Iberian Peninsula [START_REF] López | Noves Aportacions Sobre Agricultura i Alimentació Durant La Primera Edat Del Ferro a Catalunya: Dades de l'assentament de Sant Jaume (Alcanar, Montsià)[END_REF].

Only assemblages containing more than 10 seeds from any cultivated leguminous species were retained for the study. Additionally, only the taxa with more than 10 individuals in the whole settlement were retained for the study. The final dataset gathered 1,403 seeds of three taxa: Lens culinaris (N=1082), Lathyrus sativus/cicera (N=181) and Vicia faba (N=140). These seeds originate from 16 different stratigraphic units, 11 from the Early Iron Age, 1 from the Early Iberian period, and 4 from the Middle Iberian period (Table 1). All were collected in secondary non-domestic silo filling contexts. Their combination with finds of other archaeological materials proves they are not in situ but part of waste that ultimately filled the structures [START_REF] López | Primers resultats arqueobotànics (llavors i fruïts) al jaciment protohistòric del Turó de la Font de la Canya (Avinyonet del Penedès)[END_REF]. 984 lentils, 173 grass peas and 139 broad beans are from the Early Iron Age. 18 lentils are from Middle Iberian period and 80 lentils, 8 grass peas and 1 broad bean are from the Early Iberian period.

Data acquisition

Photography

The geometric morphometric analysis was carried out on two orthogonal photographs of each seed. The ventral view was defined as that where the radicle and the hilum (when conserved) occupy the centre of the image. For the purposes of this study, the radicle is placed so that it occupies the top of the image with the hilum (or its scar) also to the top. The lateral view is orthogonal to the first (Fig. 2). These criteria in ventral view, with the exception of a downward orientation of the radicle, were discussed during the 18th IWGP Conference (Lecce) and serve in certain publications [START_REF] Caracuta | From Natural Environment to Human Landscape: New Archaeobotanical Data from the Neolithic Site of Nahal Zippori 3, Lower Galilee[END_REF][START_REF] Caracuta | The onset of faba bean farming in the Southern Levant[END_REF][START_REF] Caracuta | Farming legumes in the pre-pottery Neolithic: New discoveries from the site of Ahihud (Israel)[END_REF].

Each seed was manually positioned, photographed, and two landmarks were sampled. These were oriented and photographed at the Institute of Evolution Sciences of Montpellier (France) with an Olympus SZ-ET stethoscope stereoscopic microscope and at the University of Lleida (Spain) with a Motic SMZ 168 microscope. The total margin of error, chiefly parallax distortions and landmark positioning, as well as potential variations due using two different types of equipment, was tested on groups of five seeds of differing species.

Distance measurements and outline shape analyses

We quantified differences between the three species using: 1) traditional morphometrics with distance measurements, 2) geometric morphometrics using outline analysis, and 3) the combination of these two. The values of distance measurements were measured from the photographs (Fig. 2) with Image J v. 1.50 software. Length on the ventral view corresponds to the Feret's diameter of the longitudinal axis; width corresponds to the Feret's diameter of the transversal axis; thickness corresponds to the Feret's diameter of the longitudinal axis of the lateral view (Fig. 2). All distance measurements were log-transformed.

Outline analyses were performed on the different seeds using elliptical Fourier transforms (hereon abbreviated to EFT). All the photographs were processed with Image J to remove the background. In the ventral view the two landmarks correspond to the intersection between the contour and the suture between the two cotyledons. In the lateral view, they are equivalent to the upper and lower ends of the seed (Fig. 3). Finally, the image was converted into a binary mask (black and white).

The (x; y) coordinates of the outline (Fig. 3), were obtained with the Momocs package in the R environment [START_REF] Bonhomme | Momocs: Outline Analysis Using R[END_REF]R Core Team). The next step consisted of normalising (centre, scale and homogenise the first point) the outlines using the two landmarks.

EFT turns outline coordinates into morphometric coefficients associated with the progressive decomposition of the outline into a series of trigonometric functions called harmonics (H). Each harmonic was associated with four coefficients, (two for x-, and two for y-coordinates). Here, eight harmonics led to an accurate description of the shape and we thus used 32 morphometric coefficients for the shape description.

Statistical analysis

The differences in distance measurements and outline coefficients were explored using Principal Component Analysis (PCA) and tested with Multiple Analysis of Variance (MANOVA). The differences between species and assemblages were modelled using Linear Discriminant Analyses (LDA) paired with leave-one-out cross-validations. We considered two thresholds for posterior probabilities of seed classification, minimal (50%) and very accurate (90%) [START_REF] Pagnoux | Inferring the agrobiodiversity of Vitis vinifera L. (grapevine) in ancient Greece by comparative shape analysis of archaeological and modern seeds[END_REF]. As the assemblages were unbalanced and since the variations in the number of seeds per group can affect the cross-validation results, a baseline was estimated using 1,000 permutations of balanced and re-sampled groups [START_REF] Evin | The long and winding road: Identifying pig domestication through molar size and shape[END_REF])

Results

Testing for error in positioning of the seeds and landmarks

We tested for errors in the positioning of the seeds and of the landmarks on the seeds using samples of 5 seeds of lentil and broad bean, each photographed twice in ISEM and twice in the University of Lleida, with different equipment. The computation of Analyses of Variance (ANOVA) yielded results with p-values ranging from 0.97 for lentils to 0.74 for broad beans, showing that the samples photographed at the two places cannot be distinguished. Therefore, human error in seed positioning does not provide significant differences.

Comparing the species by means of distance measurements

Distance measurements of the three species clearly differed (MANOVA P<10 -16 for length, width and thickness) (Table 2, Figs. 4 and5). A Linear Discriminant Analysis (LDA) was carried out based on the distance variables. The mean precision accuracy of the Linear Discriminant analysis (LDA) obtained with 1,000 permutations is 94%, far better than 33% of the random value of the three taxa.

Leave-one-out cross validation allowed prediction of whether each seed belongs to the pattern established by the archaeobotanical identification (Fig. 5). The results range from 98% correct identification for lentils to 68% for broad beans (when only retaining the posterior probability >90%).

Comparison of species using outline shape descriptors

The Principal Component Analysis (PCA) carried out on the EFT coefficients only partly distinguishes the three species from each other along the PC1 axis.

There is in fact a large overlap, particularly between Lathyrus sativus and Vicia faba (Fig. 5). The MANOVA test carried out applying all the components is P

<10 -16

As in the previous case, the prediction of the probability of each seed belonging to each morphotype was calculated through the Leave-one-out cross validation paired with a LDA. The accuracy of the LDA obtained with 1,000 permutations is better than in the previous case, with an average of 97%. The results of the classifications for each species are clearly superior to those based on distance measurements in the case of broad beans and grass peas (Table 3) and quite similar for lentils.

Size and shape combination

The third model combined length measurement and outline shape (Fig. 5). It is clear from the biplot that discrimination of the three species is greater when combined analysis is used. This is confirmed by the cross-validation of the LDA (Table 3). The accuracy of the LDA obtained with 1,000 permutations was the best of the three analyses, with an average of 98%.

Chronological comparison of lentils

Lentil is the only species represented in all three chronological phases of the site of La Font de la Canya, but its presence from one phase to another is disproportionate: 984 in the Early Iron Age (625-575 BC), 18 in the Early Iberian period (550-450 BC) and 80 in the Middle Iberian period (400-200 BC). In spite of the differences in sample size, it is possible to compare the individuals of the Early Iron Age with those of the Middle Iberian period as they each comprise enough individuals to offer reliable results.

Differences in length and outline shape descriptors can be observed between the seeds of the first and last phase (Fig. 6). The average length of the lentils in the Early Iron Age is 3.27 mm with a standard deviation of 0.42 while in Middle Iberian period it is 2.90 mm with a deviation of 0.37. The mean widths are 2.01 mm with a deviation of 0.34, and 1.59 mm with a deviation of 0.25. The mean thicknesses, in turn, are 3.04 mm with a deviation of 0.42, and 2.64 mm with a deviation of 0.34. A stronger difference in shape is observed when comparing the PC1 of the PCA carried out with on EFT coefficients.

The MANOVA (P<10 -16 ) confirms the differences between the chronological phases. The result of the ANOVA and the Tukey test in each variable, combine the Early Iron Age and the Early Iberian (in group a) and separate the Middle Iberian (in group b).

A similar analysis performed on shape descriptors and distance measurements but considering all the samples of lentils separately allowed the confirmation of the broad chronological differences and the identification of two Early Iron Age samples that coincide in size and shape with those of the Middle Iberian (Fig. 7).

Two groups clearly stand out when subjected to Tukey's multiple comparison test.

The first, made up of smaller seeds, comprises samples from the Middle Iberian and two from the Early Iron Age (0002, 0006, 0019 and 0020) while the second comprises seeds 20.2 % larger, all from the Early Iron Age, except for one sample (0007) from the Early Iberian.

Discussion

The three analyses performed confirm the existence of significant quantitative differences in size and shape between the three species. The outline shape analyses facilitate discrimination between species of similar size, such as grass pea and broad bean. The LDA of outline analyses with a posterior probability of 90% increases the accuracy of the prediction of grass peas and broad beans by 20.5% and 28.5% with respect to the distance measurements analysis. Lentils have similar results in both analyses. This therefore confirms that morphotypes (Fig. 8) gleaned from the values of outline shape are more accurate than those acquired through distance measurements. The values yielded by combining both analyses, in turn, increase the predictive model beyond 95% for each species.

In view of the results obtained in this study as well as in other species such as grapes [START_REF] Terral | Evolution and history of grapevine (Vitis vinifera) under domestication: new morphometric perspectives to understand seed domestication syndrome and reveal origins of ancient European cultivars[END_REF], dates [START_REF] Terral | Insights into the historical biogeography of the date palm (Phoenix dactylifera L.) using geometric morphometry of modern and ancient seeds[END_REF], olives [START_REF] Terral | Historical biogeography of olive domestication (Olea europaea L.) as revealed by geometrical morphometry applied to biological and archaeological material[END_REF]Netwon et al. 2014), barley [START_REF] Ros | Geometric morphometric analysis of grain shape and the identification of two-rowed barley (Hordeum vulgare subsp. distichum L.) in southern France[END_REF][START_REF] Wallace | Searching for the Origins of Bere Barley: A Geometric Morphometric Approach to Cereal Landrace Recognition in Archaeology[END_REF]) and millet [START_REF] García-Granero | Geometric morphometric analysis of Setaria italica (L.) P. Beauv. (foxtail millet) and Brachiaria ramosa (L.) Stapf. (browntop millet) and its implications for understanding the biogeography of small millets[END_REF], the potential of geometric morphometrics to characterise and differentiate legume seeds is confirmed. Although the species studied do not present many taxonomic doubts in their identification, the great results obtained by combining biometric data and outline analysis, offers the possibility of applying this method to help identify seeds of questionable status.

Distance measurements, although simple, are quite accurate for discrimination between species. Shape is nonetheless clearly superior but the best accuracies in identification were obtained by combining both. Distance measurements has traditionally served to distinguish between taxa such as Lathyrus sativus and Lathyrus cicera that are difficult to identify through optical observations alone [START_REF] Buxó | Arqueología de las plantas: la explotación económica de las semillas y los frutos en el marco mediterráneo de la Península Ibérica[END_REF]. Distance measurements have also served to compare broad bean seeds from different chronological phases of the Chalcolithic and Bronze Age from various sites in Upper Andalusia (Montes-Moya 2014), or simply as a means to identify them or compare archaeological seeds with current species.

Geometric morphometric methods have proved their efficiency in characterization of seeds at infra-specific or varietal level for barley [START_REF] Ros | Geometric morphometric analysis of grain shape and the identification of two-rowed barley (Hordeum vulgare subsp. distichum L.) in southern France[END_REF][START_REF] Wallace | Searching for the Origins of Bere Barley: A Geometric Morphometric Approach to Cereal Landrace Recognition in Archaeology[END_REF]) and grapes [START_REF] Pagnoux | Inferring the agrobiodiversity of Vitis vinifera L. (grapevine) in ancient Greece by comparative shape analysis of archaeological and modern seeds[END_REF] for example, a fact that opens the door of these types of analyses to legumes. The identification of two types of lentils shows how this method can establish quantitative differences in the shape and size of archaeological seeds of the same pulse species. In this paper, only the lentil assemblages of two chronological phases are numerous enough to allow reliable comparisons. Grass pea and bean seeds do not present variations in the different chronological phases or between the different samples, but this fact may be due to the smaller number of individuals of these species. The MANOVA tests carried out on distance measurements and on outline shape descriptors in lentil seeds confirm a significant difference between those of the Early Iron Age and the Middle Iberian period. However, these differences are not only chronological as two samples of the Early Iron Age are similar to those of the Middle Iberian.

Unfortunately, the lack of grass peas and bean seeds among the samples in which these differences are observed does not permit determination whether this is the case for all three species.

The change in size and shape of the lentils from Font de la Canya seems to be unrelated to different steps in the domestication of the species. Although recent studies indicate that it was a slow process [START_REF] Purugganan | Archaeological data reveal slow rates of evolution during plant domestication[END_REF][START_REF] Fuller | Cultivation as slow evolutionary entanglement: comparative data on rate and sequence of domestication[END_REF][START_REF] Fuller | Convergent evolution and parallelism in plant domestication revealed by an expanding archaeological record[END_REF] lentils were already domesticated when they arrived in the Iberian Peninsula in the sixth millennium BC. On the other hand, the changes observed during the domestication of lentils show an increase in size and not a reduction, as is the case of this site. The lack of a wild ancestor in the Western Mediterranean also rules out the possibility of hybrids.

This study advances two hypotheses, potential lines of future research, to explain the causality of these two groups. The first hypothesis is that differences in morphometrics could be evidence of the cultivation of different varieties of lentils at Font de la Canya. Several varieties of lentils are known today, which can be grouped into two taxonomic levels, microspermae and macrospermae, designated as subspecies by [START_REF] Barulina | Lentils of the U.S.S.R and of the other countries[END_REF] but identified today as groups of varieties [START_REF] Cubero | Origin, taxonomy and domestication[END_REF][START_REF] Toker | Mutation breeding[END_REF]. Microspermae are characterised by small seeds (2 to 4 mm in diameter) with pigmented testae, whereas macrospermae have larger seeds (6 to 9 mm) with slightly pigmented testae [START_REF] Mishra | Genetics and cytogenetics of lentil[END_REF].

Bearing in mind that the lengths in the current study correspond to the diameter of the seed and that lentils contract by about 20% when charred [START_REF] Kislev | Influence of experimental charring on seed dimensions of pulses[END_REF], the group of larger seeds would increase in mean length from 3.54 to 4.25 mm, and the smallest from 2.82 to 3.48 mm. The second group, in fact, could clearly fall within the range of the microspermae group while the first group could correspond to an intermediate level between the ranges of the two types.

Macrospermae offer higher yields in dry climates while the harvest of microspermae is higher in more humid environments [START_REF] Ghassemi-Golezani | Effects of seed size and aging on field performance of lentil (Lens culinaris Medik.) under different irrigation treatments[END_REF]. A phenotypic study of 101 traditional (yet unspecified) varieties in the Iberian Peninsula [START_REF] Lázaro | Relationships between agro/morphological characters and climatic parameters in Spanish landraces of lentil (Lens culinaris Medik.)[END_REF] has noted that varieties of heavier seeds, associated with macrospermae, predominate in drier regions while lighter seeds, presumably microspermae are common to humid areas. Hence, each of the groups of archaeological lentils from the site of Font de la Canya could belong to two different varieties of microspermae as the climate and size of the seeds at this site are adapted to this group. If these two varieties finally belong to the same type of group with equivalent ecological characteristics, their coexistence may be due to culinary preferences

The second hypothesis assumes that all the lentil seeds belong to the same variety, so the morphological changes are due to other factors, such as environmental conditions. Differences in size between lentil samples during the Early Iron Age may be due to the presence of lentil crops in irrigated and non-irrigated fields.

Following the line of thought, the smaller lentils of the Middle Iberian period could correspond exclusively to non-irrigated crops. Irrigation, in particular, is interpreted as responsible for the change in size of broad bean seeds in Upper Andalusia during the Chalcolithic and Bronze Age (Montes-Moya 2014).

Irrigation has also been associated with an increase in plant and pod size among lentils [START_REF] Oweis | Lentil production under supplemental irrigation in a Mediterranean environment[END_REF]. At the same time, extreme droughts affect the number of lentil flowers and pods, but not the size of the seeds [START_REF] Shrestha | A water deficit during pod development in lentils reduces flower and pod numbers but not seed size[END_REF], rejecting [negating?] the idea that the smallest ones occur in dry years.

Plants reveal a preference for carbon 12 (C 12 ) over carbon 13 (C 13 ) in the process of photosynthesis, a fact bolstered by irrigation. It is possible to calculate the value of C 13 of archaeological seeds through stable isotope analyses and compare the results with those of current seeds with known hydric values. In the case of broad beans, the most often studied species, the average of the current Δ 13 C values is 14.91 among dry crops and 16.67 among irrigated crops [START_REF] Araus | Identification of Ancient Irrigation Practices based on the Carbon Isotope Discrimination of Plant Seeds: A Case Study from the South-East Iberian Peninsula[END_REF]). In the western Mediterranean there are several cases such as that of three broad beans samples from the Chalcolithic and Bronze Age levels of the settlement of Las Eras del Alcazar (Jaén, Spain) with Δ13C values of 17.06, 16.92 and 15.99.

The first two are interpreted as having been cultivated in irrigated fields while the third was cultivated in dry lands (Mora 2017). Broad beans from the Southwest of the Iberian Peninsula also reveal evidence of irrigation [START_REF] Araus | Identification of Ancient Irrigation Practices based on the Carbon Isotope Discrimination of Plant Seeds: A Case Study from the South-East Iberian Peninsula[END_REF].

Hence it would be of great interest to carry out stable isotope analyses of the lentils from Font de la Canya, in combination with geo-morphometric analyses, to explore the question of ancient irrigation in this context. In order to improve this result, an experimental study could be carried out in which different varieties were grown with and without irrigation, quantifying the differences in the shapes of the seeds through geometric morphometry and isotope analysis. Finally, we could compare the results with the archaeological data and estimate whether the changes we have observed are due to irrigation.

Conclusions

In this study it has been possible to quantify the differences between archaeological legume seeds through two different methods, obtaining an increase in the accuracy of seed description of 20-30% through geometric morphometrics rather than by size measurements alone. Combining both models helps to further improve this accuracy. Therefore, the results are very positive in inter-and intraspecific comparisons.

Moreover, this method validates the notion that two morphotypes of lentils were cultivated at Font de la Canya during respectively the site's Early Iron Age and Middle Iberian phases. The method should now be applied to a larger framework so as to explore the role of legumes in ancient communities throughout the Western Mediterranean Basin. Different morphotypes within the same species can also be linked to different taxonomic varieties or growing conditions. Another notion to explore is that irrigation can account for the differences in size and shape. In any case, this study offers new lines of future research and sheds light on legumes and their agricultural processes in past societies. 3 Comparison of the archaeobotanical identification of the seed (rows) with LDA morphometric identification (columns). Listing of the values of the results of the LDA of distance measurements, outline shape and the combination of the previous two. Left: the number of seeds with a posterior probability of 50% or greater chance of matching the statistical pattern. Right: the number of seeds with a posterior probability of 90% or more chance of matching

Figure captions

Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 6

 12346 Fig. 1 Location of the site of Font de la Canya in the Northeast of the Iberian Peninsula Fig. 2 Example of photographs of seeds and the positioning of the distance measurements in red. Top: ventral and lateral view of Lens culinaris. Medium: ventral and lateral view of a Lathyrus sativus/cicera. Bottom: ventral and lateral view of a Vicia faba Fig. 3 Example of the outline of a seed transformed into x and y coordinates. The red points correspond to the landmarks of the ventral and lateral views Fig. 4 Boxplots depicting the logarithmic values of length, width and thickness of the three species under study Fig. 5 PCA (top) and LDA (bottom) based on distance measurements (left), outline analysis (middle) and the combination of the two (right) Fig. 6 Boxplot comparing the length and the first component of outline shape of lentils from the different chronological phases from the site of Font de la Canya Fig. 7 Boxplot comparing the length of the different samples according to chronological phase. It is noteworthy that samples 0002, 0006, 0019 and 0020 reveal a very similar distribution Fig. 8 Visual comparison of the differences between the superimposed ventral (top) and lateral (bottom) views of the three species under study. Red colour corresponds to the taxon of the rows and blue colour to the taxon of the columns

Table 2

 2 Minimum, mean, maximum and standard deviation values for each species and variable

	Table

Acknowledgements

This study was by funded by the projects HAR2016-78277-R (Ministerio de Economía y Competitividad, Spain) and SGR2017-1714 (Generalitat de Catalunya, Catalonia) of the University of Lleida. The original English draft of this paper was reviewed by T. J. Anderson. The Font de la Canya site is part of the project "El canvi sociocultural a la Cessetània oriental durant la protohistòria i l'època romana republicana" of the University of Barcelona.