D Mauduit
email: dmauduit@mines-albi.fr

G Dusserre
email: gilles.dusserre@mines-albi.fr

T Cutard

Influence of temperature cycles on strength and microstructure of spraydeposited Si-Al CE9F alloy

Keywords:

This paper investigates the effects of temperature cycles between -55 °C and 125 °C (the temperature range for intended space application) on the strength and microstructure of spray deposited Si-Al CE9F alloy. After 500 cycles, the strength is significantly improved of 9% (i.e., 26 MPa). Moreover the Weibull modulus also undergoes a significant increase. Microstructure characterizations by XRD, SEM, EBSD and DSC evidence recovery and recrystallization processes in the Al phase, and subgrain development at grain boundaries in the Si phase, leading to lower crystallite size. A Hall-Petch dependence of mean strength to average crystallite size in Si is proposed as strengthening mechanism.

Introduction

The usage of spray-deposited Si-Al alloys in space applications mainly encompasses chip boxes aiming at protecting the on-board electronic devices from the environment. Ensuring the tightness of the housing throughout the life cycle of the device is therefore required. In space application, the boxes are subjected to cyclic temperature changes, usually between -55 °C and 125 °C, that may result in structure damage or material properties changes. Therefore, the design of the boxes must take into account the influence of the successive temperature changes on the strength of the material. The present paper thereby focuses on the influence of cyclic temperature changes on the residual strength of a Si-Al CE9F alloy.

Several grades of alloys with various Si-Al ratios (named based on their coefficient of thermal expansion: CE7, CE9, CE11, CE13 and CE17) were recently studied [START_REF] Weinshanker | High performance, lightweight, hermetic AlSi Packages for military, aerospace, and space applications current packaging technology initial trials[END_REF][START_REF] Del Castillo | Robust, reworkable thermal electronic packaging: applications in high power TR modules for space[END_REF]. These alloys can be elaborated through several processes (direct metal deposition [START_REF] Zhao | Ultra-fine Al-Si hypereutectic alloy fabricated by direct metal deposition[END_REF], sintering [START_REF] Zhai | Effect of Si content on microstructure and properties of Si/Al composites[END_REF]) or spray-deposited by atomization [START_REF] Wang | Effect of Si content on the dry sliding wear properties of spray-deposited Al-Si alloy[END_REF]. The microstructure [START_REF] Raju | Effect of spray forming on the microstructure and wear properties of Al-Si alloys[END_REF] and the thermo-mechanical properties of the alloy change significantly depending on the processing route. The family of controlled expansion (CE) spray-deposited Si-Al alloys is processed by atomization by Sandvik Osprey™. The major influencing parameters of the atomization process [START_REF] Cui | Spray forming of hypereutectic Al-Si alloys[END_REF] (for instance: pressure and temperature during the hot isostatic pressing step to decrease the porosity [START_REF] Jia | Microstructure and thermal expansion behavior of spray-deposited Al-50[END_REF][START_REF] Yu | Microstructure characterization and thermal properties of hypereutectic Si-Al alloy for electronic packaging applications[END_REF] and gas/ metal mass flow ratio (Wei et al., 2007b)) were evidenced and optimized to obtain the desired specific microstructure and the corresponding material properties. Among these latter, the coefficient of thermal expansion is of prior interest for the intended applications, and several studies [START_REF] Jia | Microstructure and thermal expansion behavior of spray-deposited Al-50[END_REF][START_REF] Hogg | Microstructural characterisation of spray formed Si-30Al for thermal management applications[END_REF] focused on relating it to the specific two-phase microstructure of spray deposited hypereutectic Si-Al alloys.

The present paper deals with the Si-Al grade CE9F, an alloy that contains 60 wt.% silicon and 40 wt.% aluminum. The main characteristics of this material (i.e., a low coefficient of thermal expansion (9.10 -6 K -1 between -20 °C and 100 °C), a high thermal conductivity (130 W m -1 K -1 ) and a low density (2460 kg m -3 )) make it suitable as chip boxes material for space components. The thermal properties of this alloy are well known, since heat extraction is an important in-use function of the chip boxes. Previous studies [START_REF] Adolfi | Property Measurements on Osprey Spray-Deposited Al-Si Alloys[END_REF]Wei et al., 2007a) evidenced the quasi-linear variation of heat conductivity, heat capacity and diffusivity from room temperature up to 500 °C. Some basic mechanical properties, such as flexural strength and Young's modulus, are also available in literature, but most of the data were measured at room temperature and do not consider preceding temperature cycles.

In a previous paper [START_REF] Mauduit | Probabilistic rupture analysis of a brittle spray deposited Si-Al alloy under thermal gradient: characterization and thermoelastic sizing guidelines[END_REF], the strength of the Si-Al CE9F alloy has proved to be consistent with the Weibull's theory of brittle materials fracture between -50 °C and 130 °C. The fracture surface revealed cleavage mechanisms in the silicon phase. The Weibull's theory is based upon the role of flaws in the strength of brittle materials and accounts for volume effects on the probability of failure (Eq. ( 1)) [START_REF] Weibull | A statistical distribution function of wide applicability[END_REF][START_REF] Andreasen | Reliability-based design of ceramics[END_REF][START_REF] Trustrum | Statistical approach to brittle fracture[END_REF], without requiring any intrinsic feature of the flaws. Eq. ( 1) expresses the probability of failure, P, of a specimen as a function of stress, σ. m is the Weibull modulus, V eq is the equivalent volume of the sample calculated according to the Weibull's theory, V 0 is a reference volume and σ 0 is the scale parameter.

= P e x p V V 1 eq m 0 0
(1)

As shown in [START_REF] Mauduit | Probabilistic rupture analysis of a brittle spray deposited Si-Al alloy under thermal gradient: characterization and thermoelastic sizing guidelines[END_REF]), Weibull's theory accounts for differences between four-point and three-point bending strength of Si-Al CE9F, as a result of volume effects. The Weibull's parameters were found to be independent on temperature between -50 °C and 130 °C, but the material was only subjected to monotonous variation of the temperature and short dwell-times (a few tens of minutes) at -50 °C or 130 °C. In the case of temperature cycles, cyclic stresses are also induced in the material because of the mismatch of coefficient of thermal expansion between aluminum and silicon and may affect the material properties.

The present paper investigates the influence of preceding temperature cycles between -55 °C and 125 °C on the residual strength at room temperature of the Si-Al CE9F alloy. A significant increase in strength of 9% after 500 cycles is reported for the first time for such a material (to the best of the authors' knowledge). The microstructure of the asreceived material is described, and further investigations of microstructure changes after temperature cycles are reported in order to propose a strengthening mechanism.

Experiment

The spray deposited Si-Al CE9F alloy was prepared through atomization process by Osprey Metals Ltd [START_REF] Coombs | Atomizing Apparatus and Process Part 1[END_REF]. Ninety 45 × 4 × 3 mm 3 specimens were machined and split into 5 batches intended for different heat treatments. A first reference batch of 29 specimens was used for characterizing the as-received material. Four batches of 10 or 20 specimens were subjected to 80, 200, 500 or 700 temperature cycles performed inside a thermal chamber. The cycles consist of 15 min dwell-times at -55 °C and 125 °C, with heating and cooling rates of 20 K min -1 .

Four-point bending tests were performed at room temperature according to the standard EN-843. The distance between the upper loading points was 20 mm and the distance between the lower supports was 40 mm. The tests were carried out at a constant crosshead displacement rate of 0.5 mm min -1 . Further details about the experiment are available in [START_REF] Mauduit | Probabilistic rupture analysis of a brittle spray deposited Si-Al alloy under thermal gradient: characterization and thermoelastic sizing guidelines[END_REF]. All the specimens of each batch were tested. For the batches subjected to 0, 80 and 500 cycles (29, 20 and 20 specimens per batch respectively), the results were analyzed in the framework of the Weibull's theory applied to the fracture of brittle materials (Eq. ( 1)). For those three batches, the model parameters, σ 0 and m, were identified from the strength values by the maximum likelihood method [START_REF] Wu | Methods for estimating Weibull parameters for brittle materials[END_REF][START_REF] Przybilla | Maximum likelihood estimation for the three-parameter Weibull cdf of strength in presence of concurrent flaw populations[END_REF].

For each batch, about ten samples were analyzed prior to mechanical test with an X-ray diffractometer (Philips X-PERT) with Cu Kα 1 radiation (wavelength of 0.154184 nm). The incidence angle 2θ ranged between 20°and 130°with a step of 0.0167°. The diffraction lines were analyzed using PANalytical X'Pert High Score software [START_REF] Degen | The High Score suite[END_REF]. A Williamson-Hall analysis [START_REF] Williamson | X-ray line broadening from filed aluminium and wolfram[END_REF][START_REF] Pelleg | Evaluation of average domain size and microstrain in a silicide film by the Williamson-Hall method[END_REF] was conducted both for silicon and aluminum phases in order to assess the changes in crystallite average size and lattice strain after heat treatment through a qualitative analysis of the peak broadening, β, as a function of 2θ. Once removed the instrumental broadening and assuming arbitrarily Cauchy-Lorentz distribution, β is additively decomposed into a size-induced broadening contribution, In Eq. ( 2), λ is the wavelength of the anticathode and k (the shape parameter of the Scherrer law [START_REF] Jones | The measurement of the particle size by the X-ray method[END_REF][START_REF] Stokes | The diffraction of X rays by distorted crystal aggregates-I[END_REF]) is set to 1 when integral width is considered. ɛ and D are respectively deduced from the slope and intercept of a linear fit of βcosθ versus sinθ. It is noteworthy that only qualitative results are obtained through this method (cf. [START_REF] Scardi | Line broadening analysis using integral breadth methods: a critical review[END_REF] for a critical discussion). However a comparative analysis of the different batches will provide an insight into the mechanisms at work during temperature cycles. In addition, some specimens of the reference batch were subjected to heat treatment at 130 °C and 200 °C for 20, 50 and 125 h (corresponding respectively to the time spent at 125 °C during 80, 200 and 500 cycles) and characterized by the same method.

From these results, the dislocation density, ρ, is calculated as a function of average crystallite size, average lattice strain and Burgers vector magnitude, b, by using Eq. ( 3) [START_REF] Williamson | Dislocation densities in some annealed and cold-worked metals from measurements on the X-ray Debye-Scherrer spectrum[END_REF][START_REF] Chowdhury | Studies of microstructural imperfections of powdered Zirconium-based alloys[END_REF][START_REF] Kapoor | X-ray diffraction line profile analysis for defect study in Zr-2.5% Nb material[END_REF][START_REF] Uday | An insight into microstructural evolution during plastic deformation in AA6061 alloy after friction welding with alumina-YSZ composite[END_REF]. For both Al and Si phases, = b a 2 /2 [START_REF] Uday | An insight into microstructural evolution during plastic deformation in AA6061 alloy after friction welding with alumina-YSZ composite[END_REF][START_REF] Godet | Etude par Simulations et calculs Atomistiques, de la Formation de Dislocations aux Défauts de Surface Dans un Cristal de Silicium Soumis à des Contrainte[END_REF], with a, the lattice parameter (a = 0.543 nm for Si and a = 0.404 nm for Al). K is a material constant that depends on crystallite shape and is generally close to unity [START_REF] Balzar | X-ray diffraction line broadening: modeling and applications to high-Tc superconductors[END_REF].

= K D b 2 3 . ( 3
)
The sin 2 ψ method, developed by Macherauch and Muller [START_REF] Macherauch | Das sin2ψ-verfahren der röntgenographischen spannungsmessung[END_REF], was used to assess the residual stresses in several samples of each batch after heat treatment. In a DRX experiment, the difference of Bragg angle between stressed and unstressed material, Δθ hkl , can be related to the lattice strain of the planes of {hkl} type, hkl (Eq. ( 4)).

= cotan

1 2 ( )* 2 hkl hkl hkl (4)
The difference of Bragg angle Δθ hkl of the planes of {hkl} type is both function of angles ψ and φ, parameters of the direction of the incident beam at the sample surface. φ is set to 0°in the experiment, and the normal stress is neglected (plane-stress at the surface of the sample), leading to a simplified sin²ψ law, Eq. ( 5). The method likewise assumes that the material is homogeneous, isotropic, and that the residual stresses are uniform. Due to the heterogeneity of the material only a comparative analysis of the results will be carried out.

= + + + S sin S S 1 2 1 2 sin(2 ) ( ) hkl hkl hkl hkl 2, 11 2 2, 13 1, 11 22 (5)
In Eq. ( 5), S 1, hkl and S 2, hkl are the radioelastic constants of the planes of {hkl} type and σ ij are the components of the residual stress tensor. Planes of {222} type in the Al phase (theoretical Bragg angle of 156.7°) were analyzed with chromium radiation (wavelength of 0.2085 nm). Assuming that = 11 22 , an elliptical fit of hkl versus sin 2 ψ provides the value of the components of the stress tensor = 11 22 and σ 13 . The former quantity will be referred to as the residual stress.

The microstructure of the material was characterized by Electron Backscattered Diffraction (EBSD HKL system), with a Scanning Electron Microscope (SEM) JSM-7100TTLS LV. A 50 × 50 μm² area of one asreceived specimen was prepared by Focused Ion Beam (FIB) to characterize the reference material microstructure. The microstructures of the reference material and of a sample subjected to 500 temperature cycles were compared on a larger area (200 × 150 μm²) prepared by standard mechanical polishing.

Differential Scanning Calorimetry (DSC) experiments were performed using a Perkin Elmer DSC8500 apparatus. Two samples of about

Results

Microstructure of the as-received material

The microstructure of the as-received material consists of two interpenetrating phases of almost pure Si (diamond cubic) and Al (facecentered cubic). Indeed, the position of the XRD peaks (Fig. 1) matches the data for either pure Si or pure Al (standard JCPDS cards No. 00-005-0565 and 00-004-0787, respectively). Moreover, a comparison of the relative peak intensity for each phase indicates that the grains are macroscopically equiaxed in both phases. The two-phase microstructure resulting from spray-deposition is shown in Fig. 2, where the silicon phase is in light gray and the aluminum phase in dark gray.

A quantitative analysis of 60 optical microscope pictures ( × 1000 magnification) taken in three perpendicular planes has shown that the material composition can be homogenized in a 200 μm edge cube (the composition assessed by image analysis is 59.74 ± 0.35 wt.% Si and 40.26 ± 0.35 wt.% Al). Moreover, from this analysis, the microstructure seems isotropic at this level.

EBSD analyses of 200 × 150 μm 2 areas provide an average grain diameter of 2.5 μm in the Si phase and of 5 μm in the Al phase. The distribution of Si grain diameter is quasi-uniform between 0.5 and 3 μm and includes a few grains up to 10 μm diameter. In the Al phase, the distribution is scattered with a lot of 2 μm diameter grains and several large grains of diameter up to 15 μm. It seems that the Al grain size is directly related to the gap available between the Si grains (Fig. 3).

EBSD analysis of FIB polished surface (50 × 50 μm 2 areas, Fig. 3) reveals low local misorientation inside the grains (i.e., lower than 0.5° [START_REF] Mohtadi-Bonab | Texture, local misorientation, grain boundary and recrystallization fraction in pipeline steels related to hydrogen induced cracking[END_REF] except in the vicinity of a subgrain boundary) irrespective of the phase considered.

The analysis of the misorientation at the grain boundaries in both Al (Fig. 3c) and Si (Fig. 3d) phases shows some subgrain boundaries with misorientation lower than 5°. The Si phase is characterized by the presence of coherent Σ3 60°/<111> twin boundaries in almost each grain (Fig. 3d). This kind of twin boundaries has a low surface energy (0.06 J m -2 ) [START_REF] Phillpot | Grain Boundaries in silicon from zero temperature through melting[END_REF][START_REF] Bristowe | Microscopic modelling of grain boundaries and stacking faults in C-Si[END_REF][START_REF] Kohyama | Reconstructed structures of symmetrical <011> tilt grain boundaries in silicon[END_REF].

Fig. 4a and b display IPF EBSD maps of large areas (200 × 150 μm 2 ) in Al and Si for a sample mechanically polished. These results confirm that the Si phase is highly equiaxed at this scale. The Al phase seems to exhibit large areas of a few tens of μm with similar crystallographic orientation (cf. the green area at the bottom right of Fig. 4a, and the pink area at the top right of Fig. 3a) even if the grains are not in contact in the image plane, and areas of fine equiaxed microstructure (at the left of Fig. 3a or at the center of Fig. 4a). Such features were already evidenced in the microstructure of Si-Al CE7F by [START_REF] Hogg | Microstructural characterisation of spray formed Si-30Al for thermal management applications[END_REF]. However, the histogram of misorientation between two adjacent grains indicates that the number of subgrain boundaries in Si (misorientation lower than 5°) is about twice in Fig. 4d (after 500 cycles) than in Fig. 4b (as-received).

Effect of temperature cycles 3.2.1. EBSD data

Strength

The mean four-point bending strength for each batch is plotted in Fig. 5 versus the number of temperature cycles. A significant increase of 9%, from 283 MPa up to 309 MPa, is evidenced between 0 and 500 cycles. The trend of the curve is not linear: an increase of 5% is already achieved after 80 cycles. Between 500 and 700 cycles, no significant change is evidenced, which indicates that the phenomena leading to strength increase do not occur any more after such numbers of temperature cycles.

Table 1 reports mean, minimum and maximum values of the strength for each batch, as well as the Weibull parameters for 0, 80 and 500 cycles, for which at least 20 values are available, allowing a proper identification [START_REF] Nohut | Influence of sample size on strength distribution of advanced ceramics[END_REF]. During the first 80 cycles, mean, minimum and maximum values increase in the same way, as well as σ 0 , whereas the Weibull modulus remains unchanged. Between 80 and 500 cycles, the increase in average strength is still significant, but the maximum value and scale parameter only slightly increase, and the minimum value does not change anymore. Moreover the Weibull modulus significantly increases, indicating that the strength distribution is narrower.

The experimental strength distributions after 0, 80, 200, 500 and 700 cycles are plotted in Fig. 6, as well as the identified Weibull curves for 0, 80 and 500 cycles. The shift toward higher values of the Weibull curve illustrates the increase in strength with the number of temperature cycles.

Residual stresses

The assessment of residual stresses in the Al phase by sin 2 ψ method provides compressive normal stress values about 20 ± 5 MPa and shear stress values of 5 ± 2 MPa for 0, 200, 500 and 700 temperature cycles and does not evidence any significant change in the residual stress level with the number of temperature cycles. It is noteworthy that the residual stress value is of the order of magnitude of the yield stress of pure aluminum (between 10 and 20 MPa for purity of 99.99 and 99.8% respectively (Davis, 1993), which indicates that the Al phase has probably undergone plasticity mechanisms during the elaboration of the material.

Williamson-Hall analysis

The Williamson-Hall analysis of the XRD spectra provides an assessment of the average crystallite size and the average lattice strain from Eq. (2), and therefore the dislocation density from Eq. ( 3), in both Al and Si phases. These data are plotted respectively in Fig. 7a, c ande versus the number of temperature cycles. For comparison purpose, the same data are plotted in Fig. 7b, d andf for samples subjected to heat treatment at 130 °C for 20, 50 and 125 h. These heat treatments correspond to the time spent at the maximal temperature during 80, 200 and 500 cycles respectively. The results obtained with heat treatments at 200 °C are identical to those obtained after heat treatments at 130 °C and are not reported here.

The average crystallite size in the Si phase decreases of about 30% during the first 200 cycles and seems to stabilize after 500 cycles with a total decrease close to 35% (Fig. 7a). On the other hand, it seems to stabilize after only 20 h at 130 °C, with a total decrease close to 25% (Fig. 7b). In the Al phase, the average crystallite size continuously increases with the number of temperature cycles, and achieves an increase of 90% after 700 cycles (Fig. 7a). Heat treatments at 130 °C lead to an increase of only 65% after 20 h and a stabilization afterwards (Fig. 7b). It is noteworthy that the average crystallite size in both phases is more than one order of magnitude lower than the grain size assessed in Section 3.1.

The lattice strain in Si phase strongly decreases of about 30% after 200 temperature cycles and then more slightly to achieve a decrease of 44% after 700 temperature cycles (Fig. 7c). Heat treatment at 130 °C implies a decrease of 29% after 20 h, but the lattice strain does not change anymore afterwards (Fig. 7d). In the same way, the lattice strain in the Al phase decreases of about 38% after 200 temperature cycles and 50% after 700 temperature cycles (Fig. 7c), but remains quite constant during heat treatment at 130 °C (Fig. 7d) after a very low decrease for the first 50 h. The dislocation density in the Si phase, assessed from the previous data using Eq. ( 3), does not undergo any significant change either during temperature cycling (Fig. 7e) or during heat treatment at 130 °C (Fig. 7f). On the other hand, in the Al phase, the dislocation density exponentially decreases with the number of cycles, with a decrease of 40% after 80 temperature cycles and 74% after 700 temperature cycles (Fig. 7e). After 20 h at 130 °C, the dislocation density has dropped of 50% and does not undergo any change afterwards (Fig. 7f).

DSC analyses

Fig. 8 compares the DSC thermograms obtained with the as-received material and with a sample previously subjected to 500 temperature cycles. Whereas no significant signal is noticeable for the sample subjected to 500 cycles, the as-received material exhibit two exothermic phenomena. The first one is spread around 150-200 °C and is of low magnitude and the second one is more sharp and manifests as a peak above 400 °C.

Similar results were reported for a strain hardened (H19) commercial 1XXX series alloy in [START_REF] Hildebrandt | Differential scanning calorimetry of recrystallization behavior in aluminum sheet[END_REF]. The low temperature signal consists of several overlapped peaks and is attributed to recovery processes. The high temperature peak is attributed to recrystallization. Recovery peaks were also reported for a recycled aluminum alloy subjected to severe plastic deformation by equal channel angular pressing between 90 and 200 °C (attributed to recovery), between 200 and 300 °C (attributed to recrystallization) and between 300 and 350 °C (attributed to grain growth) [START_REF] Rebhi | TEM and DSC investigation of the recovery of a recycled aluminum processed by equal channel angular extrusion[END_REF][START_REF] Makhlouf | Microstructural evolution of a recycled aluminum alloy deformed by equal channel angular pressing process[END_REF].

The results of Fig. 8 thus indicate that not only recovery processes, but also recrystallization may have occurred in the Al phase during the 500 temperature cycles since the high temperature peak is not present after 500 cycles. The enthalpy corresponding to the first recovery peak between 125 and 250 °C is about 0.03 J g -1 (assuming a nominal composition of 40 wt.% Al in the DSC sample). This value lies in the range reported in [START_REF] Rebhi | TEM and DSC investigation of the recovery of a recycled aluminum processed by equal channel angular extrusion[END_REF], between 0.01 and 0.06 J g -1 .

Discussion

Microstructural changes in the Al phase

Compressive residual stresses of about 20 ± 5 MPa have been assessed in the Al phase irrespective of the number of temperature cycles. This value is close to the yield stress of pure aluminum [START_REF] Hildebrandt | Differential scanning calorimetry of recrystallization behavior in aluminum sheet[END_REF] and indicates that the Al phase has probably undergone plastic deformation during the elaboration process. This is supported by the dislocation density about 10 14 m -2 in the Al phase (as-received material). The compressive state of stress in Al probably develops during hot isostatic pressing, because the coefficient of thermal expansion of Al is higher than the one of Si (23 × 10 -6 K -1 for Al and 2.5 × 10 -6 K -1 for Si at 25 °C), what would lead to tensile stresses in Al phase during cooling down to room temperature.

The identical results obtained by Williamson-Hall analyses after heat treatments at 130 and 200 °C indicate that the static recovery phenomena are similar in this temperature range and that they are complete after 20 h at 130 °C and a fortiori at 200 °C. These recovery phenomena are probably related to the first DSC peak spread between 125 and 250 °C while scanning at 20 K min -1 (Fig. 8), and attributed to recovery in [START_REF] Rebhi | TEM and DSC investigation of the recovery of a recycled aluminum processed by equal channel angular extrusion[END_REF][START_REF] Makhlouf | Microstructural evolution of a recycled aluminum alloy deformed by equal channel angular pressing process[END_REF].

These static recovery phenomena manifest by a large increase of the average crystallite size and a large decrease of dislocation density, but only a low decrease of the lattice strain.

Thanks to cyclic thermomechanical stresses induced by the mismatch of coefficients of thermal expansion, temperature cycles are able to activate dynamic recovery mechanisms that continue the static recovery process. This results in further reducing lattice strain and dislocation density and by increasing the average crystallite size. The DSC thermograms indicate that the phenomena occurring during temperature cycles, involve mechanisms related to recrystallization since the high temperature peak (above 400 °C) related to recrystallization [START_REF] Hildebrandt | Differential scanning calorimetry of recrystallization behavior in aluminum sheet[END_REF] has almost fully disappeared after 500 temperature cycles (Fig. 8). It is noteworthy that recrystallization in super-purity aluminum has been reported at temperature as low as 200 °C [START_REF] Perryman | Observations on the structural changes accompanying recovery in super-purity aluminium[END_REF] or 250 °C [START_REF] Huang | Measurements of grain boundary mobility during recrystallization of a single-phase aluminium alloy[END_REF].

These static and dynamic recovery phenomena seem to interact during temperature cycles as suggested by the different microstructures obtained after 80 temperature cycles and after 20 h at 130 °C. Indeed, the increase in the average crystallite size is lower and the decrease in lattice strain is higher, after 80 temperature cycles than after 20 h at 130 °C, despite exposure to cyclic thermomechanical stresses in addition to equivalent thermal exposure. However after 200 cycles and 50 h at 130 °C, the microstructural features obtained by Williamson-Hall analysis are about the same and correspond to the stabilized state after heat treatment at 130 °C or 200 °C, which should indicate that the static recovery mechanisms are over. The additional microstructure changes occurring after more than 200 cycles are therefore mainly dynamic and involve recrystallization phenomena.

Microstructural changes in the Si phase

In the investigated temperature range, dislocation motion in Si is much more difficult [START_REF] Priester | Les Joints De Grains -de La Théorie à L'ingénierie[END_REF] than in Al and is not relevant to explain the changes revealed by Williamson-Hall analyses, as confirmed by the almost constant dislocation density provided by Eq. ( 3) (Fig. 7e andd). However the fraction of subgrain boundaries (misorientation lower than 5°) is about twice after 500 temperature cycles than in the as-received material (cf. Section 3.2.1), and this result is corroborated by the decrease in average crystallite size.

The rapid cooling of the droplets of molten Si during spray forming might have generated crystal defects such as dislocations, twins, but also vacancies and disordered or ill-defined grain boundaries. These latter defects are likely to reorganize and create subgrains with welldefined boundaries instead of ill-defined grain boundaries. Such a phenomenon is consistent with the microstructural changes reported here, i.e., increase in the fraction of subgrain boundaries and decrease of both average crystallite size and lattice strain.

The characteristics of Al and Si phase microstructure follow close trends (i.e., identical results obtained by Williamson-Hall analyses during heat treatments at 130 and 200 °C, slow down of microstructural changes after 200 temperature cycles, and similar values of average crystallite size and lattice strain after either 80-200 cycles or heat treatment for 20-50 h). Together with the previous assumption that changes in Si phase is mainly related to grain boundaries, this could indicate that the interfaces between Al and Si phases are, at least partially, the locus of microscopic changes in Si.

Strength versus microstructure relationships

The average strength of the material undergoes an important increase up to 80-200 cycles, and then still increases slowly up to 500-700 cycles. Such a two-step trend matches the microstructure changes in the Al and Si phases, as described in Sections 4.1 and 4.2.

However, the strength value, about an order of magnitude higher than the yield stress of pure aluminum (Davis, 1993), and the brittle behavior of the material [START_REF] Mauduit | Probabilistic rupture analysis of a brittle spray deposited Si-Al alloy under thermal gradient: characterization and thermoelastic sizing guidelines[END_REF] indicate that CE9F fracture is mainly related to the Si phase. Indeed, the temperature of brittle to ductile transition in Si is above 500 °C [START_REF] Hirsch | The brittle-ductile transition in silicon[END_REF].

The main fracture mechanism in silicon is cleavage along {111} planes [START_REF] Savage | Thermal shock cleavage of silicon (111) thin crystals[END_REF]. Evidences of such a fracture mechanism in Si-Al CE9F alloy have been reported in [START_REF] Mauduit | Probabilistic rupture analysis of a brittle spray deposited Si-Al alloy under thermal gradient: characterization and thermoelastic sizing guidelines[END_REF] (cleavage planes in fracture surfaces). It is well known from the early work of [START_REF] Petch | The cleavage strength of polycrystals[END_REF] that the Hall-Petch effect is relevant to describe the grain-boundary strengthening of materials undergoing brittle fracture by cleavage. Even if the grain size assessed by EBSD does not change with temperature cycles, the strengthening can be related to the decrease of the crystallites size evidenced by the Williamson-Hall analyses. Indeed the subgrain size is sometimes the quantity that controls the mechanical properties instead of the grain size [START_REF] Ghassemali | Effect of coldwork on the Hall-Petch breakdown in copper based micro-components[END_REF][START_REF] Mcqueen | Microstructures of aluminum compressed at various rates and temperatures[END_REF]. The plot of average strength as a function of average crystallite size (Fig. 9) shows a reasonable agreement of the experimental data with the Hall-Petch law, in view of the dispersion of the results.

Conclusion

Temperature cycles between -55 and 125 °C (in-use temperature range of space embedded systems) induce significant changes in the microstructure and strength of the Si-Al CE9F alloy prepared by spraydeposition.

Recovery and recrystallization occur in the Al phase with a large decrease of the dislocation density. Rearrangement at the grain boundaries (and probably at the interfaces between Al and Si phases, in view of the simultaneous microstructure changes in both phases) occurs in the Si phase, which leads to a decrease in the average crystallite size.

By Hall-Petch effect, the Si substructure refinement gives rise to an improvement of up to 9% of the strength after 500 cycles, and a lower dispersion of strength values.

Most of these microstructure changes mainly occur between 80 and 200 temperature cycles, and are also observed after heat treatment at 130 °C for 20 h. However, microstructure changes are higher after 500 temperature cycles than after heat treatment. This highlights the role, in the mechanisms a work, of the thermomechanical stresses, induced Even if the mechanisms at work are still hypothetic and must be further investigated, these results could be exploited to propose a new step in the processing route of chip boxes, in view of a lightening of the components thanks to higher mechanical properties. A suitable heat treatment has to be optimized by investigating the effects of heat treatment prior to or in place of temperature cycles.

Declarations of interest

None.

  a strain-induced broadening contribution, = tan

  Fig. 4c and d display IPF EBSD map of large areas (200 × 150 μm 2 ) in Al and Si for a sample mechanically polished after exposure to 500 temperature cycles between -55 °C and 125 °C. The microstructure of the sample subjected to 500 temperature cycles is similar to the one of the as-received material in terms of grain size and crystallographic orientation. No quantitative comparison was possible with the available data concerning the fraction of subgrain boundaries in Al, the fraction of twin boundaries in Si, and local misorientation in both phases.

Fig. 1 .

 1 Fig. 1. Diffraction pattern of Si-Al CE9F compared to the diffraction peaks of pure Si and Al (the intensity of Si and Al peaks are normalized in reference to the intensity of the first corresponding peak in Si-Al CE9F line) (preference for color: online only).

Fig. 2 .

 2 Fig. 2. Two-phase microstructure of Si-Al CE9F alloy (Si in light gray and Al in dark gray). SEM picture using back-scattered electron detector. The sample was mechanically polished following standard procedure and chemically etched with Keller's reagent.

Fig. 3 .

 3 Fig. 3. IPF EBSD maps with respect to the Z direction (a and b) and substructures (c and d) of the Al phase (a and c) and the Si phase (b and d). In c and d, red lines depict subgrain boundaries (misorientation <5°) and yellow lines depict twin boundaries (60°misorientation). The sample was polished by FIB. (preference for color: online only).

Fig. 4 .

 4 Fig. 4. IPF EBSD maps with respect to the Z direction in the Al phase (a and c) and the Si phase (b and d), as received (a and b) and after 500 temperature cycles (c and d). The sample was mechanically polished following standard procedure. (preference for color: online only).

Fig. 5 .

 5 Fig. 5. Increase in mean strength with the number of temperature cycles. The errors bars represent the 95% confidence interval.

Fig. 6 .

 6 Fig. 6. Cumulative strength distribution for each batch (markers) and Weibull model identified at 0, 80 and 500 temperature cycles (solid lines). The failure probability estimator for the i th of n values sorted into ascending strength order is (i-0.5)/n.

Fig. 7 .

 7 Fig. 7. Evolutions of the average crystallite size (a and b), lattice strain (c and d) and density of dislocations (e and f) in Si and Al phases as a function of temperature cycles number (a, c and e) and of heat treatment duration at 130 °C (b, d and f). The error bars represent the 95% confidence interval. A dwell time of 20, 50 and 125 h respectively corresponds to the exposure time at the maximal temperature for 80, 200 and 500 cycles.

Fig. 8 .

 8 Fig. 8. DSC Thermograms of as-received material and after 500 temperature cycles at 20 K min -1 .

Fig. 9 .

 9 Fig. 9. Hall-Petch plot of average strength of Si-Al CE9F, Rm, as a function of the Si average crystallite size, d. The errors bars represent the 95% confidence interval.

Table 1

 1 Strength distribution data as a function of number of temperature cycles.

	Number of temperature cycles, N Number of samples, n Mean value, Rm (std-dev) Minimum value Maximum value Weibull modulus, m Scale parameter, σ 0	--MPa MPa MPa -MPa	0 29 283 (12) 255 303 31 302	80 20 297 (10) 277 315 30 316	200 10 301 (10) 278 315 --	500 20 309 (11) 276 320 46 320	700 10 307 (12) 274 318 --

mg taken from a reference specimen (as-received) and from a specimen previously subjected to 500 temperature cycles, were heated from 50 up to 500 °C at 20 K min -1 under N 2 flow.

Acknowledgments

This work was supported by the French National Center for Space Studies, CNES (Centre National d'Etudes Spatiales). The authors gratefully acknowledge the CNES for its technical and financial support (grant CNES number 151313/00).


Noémie Gaudio
email: noemie.gaudio@inra.fr

Xavier Gendre
email: xavier.gendre@math.univ-toulouse.fr

Marc Saudreau
email: marc.saudreau@inra.fr

Vincent Seigner
email: vincent.seigner@irstea.fr

Philippe Balandier
email: philippe.balandier@irstea.fr

Impact of tree canopy on thermal and radiative microclimates in a mixed temperate forest: A new statistical method to analyse hourly temporal dynamics

Keywords:

Forest shelter buffers microclimate, decreasing daily ranges of solar radiation and temperature, yielding higher minimum and lower maximum temperatures than those of open field. The most common way to analyse sets of these data is to compare mean, maximum and minimum values of climate parameters of open field and understorey conditions at daily, monthly or seasonal scales; however, this approach loses information about temporal dynamics. This study developed a statistical method to analyse hourly dynamics of temperature (T) and radiation (Rad) together and quantify effects of canopy openness and seasonality on these dynamics. Eight experimental sites were chosen in small gaps located in a temperate oak-pine forest (France), and five plots were established in each along a light gradient (i.e. a total of 40 plots), which delimited a transect along which T and Rad were measured hourly at a height of 200 cm from May 2009 to March 2010. T and Rad were also measured in open field. A specific Principal Component Analysis (PCA) with an innovative graphical representation was performed on this dataset. This statistical method allowed hourly temporal dynamics of all data recorded to be analysed and included a chart to interpret the distribution of the data in the principal plane defined by the PCA. Except in winter, results demonstrate the well-documented buffering effect of the tree canopy on T, with higher minimum and lower maximum values in the forest understorey. This effect was especially pronounced for minimum T and increased as canopy grew denser. In summer, T remained higher than expected in the understorey and was lower than expected in the open field, indicating thermal inertia in the understorey and an a priori cooling effect linked to wind or radiative losses during the night in the open field. The newly developed statistical method offers an innovative approach to better understand the tree canopy's buffering effect on temporal dynamics.

Introduction

In the current context of climate change, many concerns about the sustainability of ecosystems and crop production exist [START_REF] Lobell | The influence of climate change on global crop productivity[END_REF], especially because temperatures are predicted to steadily increase in the near future and have a strong impact on many plant processes [START_REF] Atkin | Global variability in leaf respiration in relation to climate, plant functional types and leaf traits[END_REF][START_REF] Blessing | Allocation dynamics of recently fixed carbon in beech saplings in response to increased temperatures and drought[END_REF][START_REF] Duursma | The peaked response of transpiration rate to vapour pressure deficit in field conditions can be explained by the temperature optimum of photosynthesis[END_REF][START_REF] Kolari | Field and controlled environment measurements show strong seasonal acclimation in photosynthesis and respiration potential in boreal Scots pine[END_REF][START_REF] Sendall | Acclimation of photosynthetic temperature optima of temperate and boreal tree species in response to experimental forest warming[END_REF]. In forest ecosystems, understorey microclimate is controlled by characteristics (age, species, etc.) and the spatial structure of overstorey trees [START_REF] Aussenac | Interactions between forest stands and microclimate: ecophysiological aspects and consequences for silviculture[END_REF][START_REF] Malcolm | The transformation of conifer forests in Britain -regeneration, gap size and silvicultural systems[END_REF]. Most microclimate variables are buffered by the shelter which trees provide (e.g. [START_REF] Karki | Microclimatic differences between mature loblolly-pine silvopasture and open-pasture[END_REF][START_REF] Siegert | Stomatal conductance and transpiration of co-occurring seedlings with varying shade tolerance[END_REF][START_REF] Von Arx | Spatio-temporal effects of forest canopy on understory microclimate in a long-term experiment in Switzerland[END_REF]. Consequently, forest shelter creates cooler and wetter conditions for plant species sensitive to high temperatures or drought and thus thermophilisation of plant communities via macroclimate warming -i.e. favouring species adapted to warm conditions -could be limited [START_REF] De Frenne | Microclimate moderates plant responses to macroclimate warming[END_REF]. Therefore, both the macroand microclimate should be considered to adequately predict the future of ecosystems. Many researchers have demonstrated that mean climate change, especially average temperature, is probably not the best way to predict adverse consequences of climate change on ecosystems [START_REF] Thornton | Climate variability and vulnerability to climate change: a review[END_REF] and [START_REF] Henttonen | Response of radial increment variation of Scots pine to temperature, precipitation and soil water content along a latitudinal gradient across Finland and Estonia[END_REF] emphasised the need to use high-resolution climate data when analysing tree growth.

Forest temperatures are often estimated from open field weather stations, sometimes located far from study sites, even though tree canopies modulate their own microclimate, and systematic differences between temperatures measured in forests and at open field weather stations have been identified [START_REF] Kollas | How accurately can minimum temperatures at the cold limits of tree species be extrapolated from weather station data?[END_REF]. As [START_REF] Körner | When it gets cold, plant size matters -a comment on tree line[END_REF] emphasised, plants experience temperatures that are rarely reflected by average data and "to advance vegetation ecologists need to collect bioclimatic data, rather than rely on weather station data". Most ecological or physiological studies have used climate data at a resolution of several kilometres or more, whereas organisms experience microclimate at a finer scale, from millimetres to metres [START_REF] Suggitt | Habitat microclimates drive fine-scale variation in extreme temperatures[END_REF]. While the general buffering effect of the tree canopy is known, i.e. a decrease in maximum temperatures and an increase in minimum temperatures, further investigation is needed into daily variations in temperature, and their relations to solar radiation below the canopy.

The buffered thermal range is influenced partly by reduced radiation in the understorey, as radiation and temperature are highly correlated [START_REF] Bristow | On the relationship between incoming solar radiation and daily maximum and minimum temperature[END_REF][START_REF] Jegede | Diurnal variations of net radiation at a tropical station -Osu, Nigeria[END_REF]. Daily temperature and radiation dynamics are rarely considered together in studies linking understorey plant behaviour to microclimate characteristics, even though temperature alone is often not enough to explain plant processes. For example, phenology of leaf senescence is mainly under thermal control at low and middle latitudes, while photoperiod becomes the primary factor at high latitudes [START_REF] Gill | Changes in autumn senescence in northern hemisphere deciduous trees: a meta-analysis of autumn phenology studies[END_REF]. Many studies address only radiation or temperature (often added to moisture). They mainly focus on i) impacts of these climate parameters on understorey plant behaviour (see e.g. [START_REF] Ammer | Growth and biomass partitioning of Fagus sylvatica L. and Quercus robur L. seedlings in response to shading and small changes in the R/FR-ratio of radiation[END_REF], [START_REF] Balandier | Six-year time course of light-use efficiency, carbon gain and growth of beech saplings (Fagus sylvatica) planted under a Scots pine (Pinus sylvestris) shelterwood[END_REF] and Gaudio et al. (2011a,b) for light, and [START_REF] Butt | Relationships between tree growth and weather extremes: spatial and interspecific comparisons in a temperate broadleaf forest[END_REF][START_REF] De Frenne | Microclimate moderates plant responses to macroclimate warming[END_REF] for temperature) or ii) the microclimate itself, as modified by forest shelter (see e.g. Balandier et al. (2006b) for light and [START_REF] Morecroft | Air and soil microclimates of deciduous woodland compared to an open site[END_REF] for temperature). This study's aim was to accurately characterise microclimate in the forest understorey by considering both temperature and radiation, as they strongly influence plant processes. The dual challenge was to consider i) temperature and radiation together because the relation between the two could differ in the forest compared to the open field and ii) hourly dynamics of these two variables, to extend analysis beyond daily mean, minimum and maximum values. To this end, we used an exploratory method based on Principal Component Analysis (PCA) with an innovative graphical representation. This article focuses on describing the statistical method and its ability to describe forest microclimate defined by hourly dynamic behaviour of two or more climate parameters. In particular, it describes the buffering effect associated with forest shelter: conditions under which buffering occurs (i.e. the influence of canopy density or cover) and how seasonality influences it.

Materials and methods

Study site and experimental design

The study was conducted from May 2009 to March 2010 in the Orleans plain forest in France (47 • 51 -47 • 77 N, 2 • 25 -2 • 36 E, mean elevation: 140 m). This region has a semi-oceanic climate, with mean annual precipitation of 740 mm evenly distributed throughout the year and mean annual temperature of 11.3 • C (data from 1981 to 2010). In winter 2008, a network of eight experimental sites was established in mixed oak (Quercus petraea Lieblein) -Scots pine (Pinus sylvestris L.) stands (Table 1). Mean, minimum and maximum distances between the experimental sites were respectively 5.2, 1.2 and 11.2 km; therefore, they were considered independent. An open field site was also identified near the selected experimental sites to provide a reference measurement of the microclimate for all measurements described hereafter.

At each experimental site, we took advantage of small gaps (779 m 2 ± 352 m 2 ) within the stand to increase the number of radiation situations explored. Each experimental site contained a transect with five 1 m 2 plots organised to capture the natural light gradient which occurs between a darker plot in the stand and a lighter plot in the middle of the gap (Fig. 1). As plot location was adapted to each stand's gap characteristics to capture the light gradient, the total length of transects ranged from 19 to 39 m, and the distance between two plots within a transect ranged from 3 to 25 m. The category "understorey conditions" grouped plots that were influenced by all degrees of tree canopy openness. All plots were kept free of understorey vegetation during the entire experiment. The experimental sites were fenced to protect them from wildlife.

Measurements

Temperature

In early spring 2009, experimental sites were equipped with temperature sensors, i.e. thermocouples (T type class 1, CETIB Dexis, Clermont-Ferrand, France), which measured temperature T with 0.01 • C precision. To measure air T instead of sensor T, each thermocouple was protected in a well-ventilated white shelter of 950 cm 3 to allow airflow. Data were recorded every minute, averaged at an hourly time step, and stored using a datalogger (CR800, Campbell Scientific Ltd, Loughborough, UK) powered by a 12 V battery. One thermocouple was placed at a height of 200 cm in each of the 40 plots (i.e. 8 sites × 5 plots). Another thermocouple was placed at a height of 200 cm in the open field to provide the reference T. Data were collected for eleven months, from May 2009 to March 2010.

Radiation

Incident quantum of Photosynthetic Active Radiation (PAR, 400-700 nm, mol m -2 s -1 ) was measured throughout the experiment (from May 2009 to March 2010) with a light sensor (DLT/BF3, Delta-T, Cambridge, UK) placed at a height of 200 cm in the open

Table 1

Forest stand characteristics for the eight experimental sites (S1,. . .,S8) sampled in mixed oak-Scots pine stands in the Orleans forest (France) within small gaps. Tree basal area (m 2 ha -1 ), number of stems (per ha), and mean height (m) were measured within a 20 m-radius of the darkest plot of the transect (Fig. 1), considering both dominant (overstorey) and dominated (understorey) tree strata. For the understorey, only trees higher than 2 m were considered. In July 2009, after light sensor calibration, PAR was measured at a height of 200 cm on each understorey plot using a light sensor (SKP 215, Skye Instruments, Llandrindod Wells, UK, mol m -2 s -1 ) connected to a datalogger (DataHog2, Skye Instruments, Llandrindod Wells, UK). Data were recorded every minute, averaged at an hourly time step, over a 24-h period. Transmitted PAR (PAR t ) in the understorey was then calculated as PAR measured in the forest divided by incident PAR (expressed as a percentage), thus eliminating the influence of differences in weather conditions on measurement days (Balandier et al., 2006a;[START_REF] Lieffers | Predicting and managing light in the understory of boreal forests[END_REF]. PAR t was considered a proxy of canopy openness.

S1

In December 2009, canopy openness was estimated using one hemispherical photograph taken at a height of 200 cm in each plot, at sunrise or sunset. The equipment included a digital single lens reflex camera body (EOS-5D, Canon, Tokyo, Japan) with a circular fish-eye lens (8 mm F3.5 EX DG, Sigma, Kawasaki, Japan) with a 180 • angle view. Then, photographs were thresholded in black and white using PiafPhotem software [START_REF] Adam | PiafPhotem -Software to Threshold Hemispherical Photographs. Version 1.0[END_REF] to render pixels as vegetation (black) or sky (white). Finally, canopy openness (%) was calculated with Gap Light Analyzer software (http://ecostudies.org/ gla/). Hemispherical photographs were also taken in July 2009 at a height of 200 cm to compare canopy openness estimated from hemispherical photographs to that measured by sensors; they were strongly correlated (p < 0.0001, R 2 = 0.89) [START_REF] Gaudio | Interactions pour la lumière au sein d'un écosystème forestier entre les arbres adultes, les jeunes arbres et la végétation du sous-bois[END_REF].

Canopy openness calculations represented two contrasting forest canopy states: i) winter canopy openness, when oaks had no leaves, and ii) summer canopy openness, when oak foliage was fully developed. The short states of oak budding and leaf senescence are dynamic and intermediate between these two states, corresponding respectively to the first 15 days of May and November in French temperate forests [START_REF] Balandier | IMPREBIO: Impact de l'intensité des prélèvements forestiers sur la biodiversité -Impact of Wood Harvest Intensity on Forest Biodiversity (Final Report)[END_REF]. For these two short sates, the two canopy openness values measured in summer and winter were averaged.

Radiation (Rad) in the understorey (Rad understorey , J m -2 s -1 ) was calculated at an hourly time step for each plot throughout the experiment based on the Rad measured in the open field (Rad Openfield ) and canopy openness (Eq. ( 1)):

Rad understorey (J m -2 s -1 ) = Rad Openfield (mol m -2 s -1 ) × 0.48 × canopyopenness (1)
where 0.48 is the conversion coefficient from mol s -1 m -2 to J s -1 m -2 provided by the light-sensor supplier.

Winter

Microclimate during the experiment

Based on T measured in the open field, the experiment was divided into four periods (Table 2): winter (December, January, February), summer (June, July, August), intermediate warm (May, September) and intermediate cold (March, October, November). For most statistical analyses, the two intermediate periods were grouped into a single intermediate period.

Because understorey conditions consisted of multiple degrees of canopy openness, they can be considered as a single group or separated into different groups to capture the light gradient from the dense forest shelter to the forest gap. As the experiment was conducted in mixed oak-pine stands and oaks lost their leaves in winter, canopy openness in the open field and the understorey differed less in winter than in summer. For instance, canopy openness of the 25% most shaded plots in the understorey ranged from 17 to 25% in winter, 1-12% during the intermediate period and 1-6% in summer (Fig. 2).

Data analysis

Data were analysed using R software (http://www.r-project. org).

First, analyses of variance (ANOVAs) were performed to estimate T differences between the understorey (for all understorey plots) and the open field, considering daily mean (T mean ), maximum (T max ) and minimum (T min ) values for the entire experiment and the four seasonal periods. For these analyses, the canopy openness gradient in the understorey was ignored, as all understorey plots were grouped into a single "understorey" category. Regardless of the period considered, homogeneity of variance was systematically Each subset had a different location in the principal plane, but it is not possible to interpret these differences without componentwise interpretation. Common approach to do so is based mainly on correlations between initial variables and principal components using the correlation circle method, in which arrow lengths and directions provide information about each variable (see e.g. [START_REF] Gomes | Trees modify the dynamics of soil CO2 efflux in coffee agroforestry systems[END_REF]). Due to the large number of variables (i.e. 48) used to build the principal plane, this classic graphical representation of PCA was illegible, making it difficult to understand the principal plane. Therefore, a new graphical method using innovative readout tools was developed to understand PCA axes and locations of observations in the principal plane.

Method for constructing a chart to interpret PCA axes

Each component of interest (C1 and C2) was a continuous variable that was discretely summarised by five quantiles (0.10, 0.25, 0.50, 0.75 and 0.90) to ensure sufficient representativeness of the sample along the component (Fig. 5). The two first components were then summarised by focusing on intersections of these quantiles. A second step provided representative 24-h (T, Rad) curves for each quantile intersection, following two precautionary measures:

-to smooth atypical 24-h (T, Rad) values (e.g. weather changes, short cloudy periods), the ten closest 24-h (T, Rad) curves of each quantile intersection were averaged instead of considering only the closest one, -to avoid isolated quantile intersections (i.e. not representative of the dataset), the moment of inertia I of the ten closest 24-h (T, Rad) curves was calculated with respect to each quantile intersection.

If I was higher than 10% of the inertia explained by the principal plane, the quantile intersection was considered isolated and was excluded from subsequent analyses (Fig. 5).

In this study's dataset, 22 quantile intersections were retained, each represented by the average of the ten closest 24-h (T, Rad) curves. These 22 averaged curves were kept to summarise distribution of observations in the principal plane, providing a chart to interpret the principal axes (Fig. 8). Each of the 22 cells in the chart illustrated the combined behaviour of the average T and Rad measurements representative of the 22 quantile intersections. One main advantage of the chart is a synthetic view of the dataset's spatial distribution in the principal plane, thus enabling easier interpretation.

PCA interpretation

Looking at the chart (Fig. 8) from left to right, component C1 showed a positive association between T and Rad, i.e. the higher the daily Rad range, the higher the daily T range, regardless of vertical location in the principal plane. Ranges of T and Rad were simultaneously lower on the left of the principal plane and higher on the right. Looking at the chart from bottom to top, component C2 showed opposite behaviour of T and Rad ranges. In a given column (i.e. horizontal location in the principal plane), high daily Rad ranges were associated with low daily T ranges at the bottom, and low daily Rad ranges were associated with high daily T ranges at the top. Information from the chart helps to interpret the locations of the observations in the principal plane.

In summer, when microclimate differences between open field and understorey were greatest (Table 3), the more the canopy was open, the more the associated subsets related to canopy openness moved from left to right along C1 (Fig. 6). Specifically, in the darkest understorey conditions, both Rad and T ranges were low, whereas as the forest canopy opened, Rad naturally increased, which increased the T range. Canopy openness subsets also showed a vertical gradient along C2 from the top for darkest conditions to the bottom for the lightest. These variations illustrate that T ranges in the understorey were higher than expected given the low Rad ranges. This was more evident as the canopy grew denser. Conversely, T ranges in sparse understorey and open field were smaller than expected given the high Rad ranges. This non-horizontal phenomenon was also observed when considering whether seasonality has the same impact on the relation between T and Rad in open field and in understorey (Fig. 7). In both open field and understorey conditions (all plots combined) the data subsets spread horizontally from winter to summer along C1, i.e. when the weather was warmer, Rad and T ranges increased regardless of the presence of a forest shelter. Along the vertical axis C2, the seasonal movement spread to the bottom for the open field and to the top for the understorey.

Discussion

As expected, regardless of season T mean was statistically the same in the forest and open field. [START_REF] Körner | When it gets cold, plant size matters -a comment on tree line[END_REF] demonstrated that T mean eliminates the signal range that is integrated into the integrative variables T max and T min . This highlights the well-documented buffering effect of the forest canopy on daily T, with higher T min and lower T max in forest understorey than in open field (Ferrez et al., 2011; [START_REF] Karki | Microclimatic differences between mature loblolly-pine silvopasture and open-pasture[END_REF][START_REF] Morecroft | Air and soil microclimates of deciduous woodland compared to an open site[END_REF]. This effect occurred only during summer and the intermediate warm period. This is explained by the absence of oak foliage in winter, when open field and forest understorey have more similar conditions because less Rad is intercepted by the forest canopy. The buffering effect of forest canopy depends greatly on tree leaf area index (LAI). von Arx et al. ( 2013) identified an LAI threshold of 4 (sparse canopies), below which the buffering effect of temperate forest stands tend to disappear. The higher the T (i.e. in summer), the greater the effect of forest shelter [START_REF] Renaud | Comparison between open-site and below-canopy climatic conditions in Switzerland during the exceptionally hot summer of 2003[END_REF]. This buffering effect was especially pronounced for T min in our study. [START_REF] Renaud | Comparison between open-site and below-canopy climatic conditions in Switzerland during the exceptionally hot summer of 2003[END_REF] illustrated that, depending on the main tree species in the forest, the buffering effect can be higher for T min (oak and pine) or T max (beech, beech-silver fir, and oak-silver fir), due to differences in canopy closure.

Even though T and Rad are linked by definition, the relation between them was weakened under forest shelter, with Spearman correlations substantially lower in the understorey than in open field. Specifically, T can become high despite low Rad in understorey conditions, which suggests thermal inertia in the understorey [START_REF] Jegede | Diurnal variations of net radiation at a tropical station -Osu, Nigeria[END_REF]. For instance, daily T mean can reach 25 • C at a daily Rad mean of approximately 10 J m -2 s -1 in summer (Fig. 3). This highlights the need to include all climate parameters when studying microclimate. For instance, the presence of a forest shelter also decreases wind speed and buffers relative air humidity [START_REF] Balandier | Conséquences de l'application de sylvicultures dynamiques sur la biodiversité floristique du sous-bois en forêt: les apports d'un réseau d'expérimentation (Rapport Final De Projet)[END_REF][START_REF] Renaud | Comparison between open-site and below-canopy climatic conditions in Switzerland for different types of forests over 10 years (1998-2007)[END_REF], which can influence T.

The previous results were obtained from classic statistical analysis (ANOVA) considering microclimate at the seasonal scale, i.e. pre-defined time divisions. Approaches using pre-defined time divisions, which cause a loss of information, have been applied at the seasonal scale [START_REF] Renaud | Comparison between open-site and below-canopy climatic conditions in Switzerland during the exceptionally hot summer of 2003[END_REF] and the daily scale (e.g. morning, afternoon) [START_REF] Karki | Microclimatic differences between mature loblolly-pine silvopasture and open-pasture[END_REF]. Although they provide information about microclimate behaviour, they depend greatly on weather conditions and seasonality and exclude information. Conversely, the method developed in this study makes no assumptions about time divisions, focusing instead on variations in hourly time-scale curves around their daily means, which thus includes all recorded data. The PCA procedure and the chart focused on 24-h (T, Rad) curves. The first component of the principal plane, C1, illustrated the well-documented buffering effect of tree canopy, with lower T and Rad ranges in dense understorey than in open field. The differences were greatest in summer and decreased when the canopy opened (Fig. 6). This confirmed the importance of considering microclimate variations in the understorey, with a buffering effect based on tree canopy structure and density. The value of our results is linked mainly to interpretation of the second component, C2. In forest understorey, when seasons became warmer, T was higher than expected assuming a linear relation between T and Rad. In understorey conditions, thermal inertia seemed to overcome the Rad effect, i.e. air T in forest stands decreased much more slowly in the afternoon on summer days than would be expected given the Rad alone. This is important to consider, especially for understorey vegetation and trees, which would experience greater thermal stress, and for a longer period, than assumed, even in shaded environments. However, extreme T was buffered in the understorey compared to the open field, particularly in summer. Based on these two points, a trade-off exists in the degree of canopy openness that ensures sufficient Rad for understorey vegetation and trees growth while also providing sufficient shelter to ensure the thermal buffering effect that may protect some species from climate change. Results demonstrated that even in shaded environments, T can remain high without high Rad, thus creating higher than expected thermal stress for understorey vegetation and trees. Conversely, T was lower than expected in the open field when seasons became warmer, suggesting that other parameters could have an influence. For example, during warm and sunny days, it is assumed that wind would buffer T. T min can also decrease relative to the heat lost from reflected longwave infrared energy during the night.

The R code developed for the PCA was written to consider 1 to n climate parameters together, e.g. air humidity and wind speed can be used to characterise forest microclimate if measurements are available. The method was designed for application to microclimate parameters measured at any time step (e.g. 1 min, 3 h).

Conclusion

The statistical method developed in this study adds substantive value to traditional analysis of a microclimate, especially because it can process all the data, whereas classic analyses usually begin by reducing the dataset (e.g. to mean, minimum and maximum values), which conceals several important features of microclimate dynamics. Thus, beyond than the demonstrated buffering effect of the canopy, the relation between temperature and radiation differed between forest understorey and open field conditions. Thermal inertia led to relatively high temperatures in more shaded conditions where canopy was dense and the opposite in more open conditions. Effects of other factors such as wind and nocturnal radiation losses decreased temperatures despite high radiation. Better understanding of forest microclimate behaviour could help improve predictions of future forest microclimates under climate change [START_REF] Renaud | Comparison between open-site and below-canopy climatic conditions in Switzerland for different types of forests over 10 years (1998-2007)[END_REF]. The method described in this article can help do this and would become more powerful if other climate parameters are included.

Fig. 1 .

 1 Fig. 1. Diagram of an experimental site (located in Orleans forest, France). Each experimental site consisted of one transect made up of five 1 m 2 plots organised to catch the light gradient at the stand -gap interface, i.e. the first plot was inside the forest stand (the darkest plot) and the fifth plot was in the middle of the gap (the lightest plot).

Fig. 2 .

 2 Fig.2. Distribution of canopy openness (%) in mixed temperate oak-pine forest stand understorey (France). Canopy openness was considered in winter (December, January, February), intermediate months (May, September, October, November, March) and summer (June, July, August).

Fig. 6 .Fig. 7 .

 67 Fig. 6. Level sets in the principal plane containing 75% of the 24-h (temperature, radiation) curves in summer according to canopy openness. The grey dashed line represents open field. Solid lines represent understorey, which was classified according to four canopy openness quantiles ranging from 0 (black) to 1 (light grey) with a 0.25 step, i.e. Canopy openness (%) = [1-6],]6-12],]12-26], >26. Dotted lines represent the quantiles defined in Fig. 5.

Fig. 8 .

 8 Fig. 8. Representative centred pairs of 24-h (temperature, radiation) curves (no meaningful unit) corresponding to the quantile intersections described in Fig. 5. Dotted line = radiation, solid line = temperature.

Acknowledgements

The authors thank Yann Dumas, Aurélien Brochet, Sandrine Perret, Michel Bonin and Florian Vast for their field assistance. This study was partly supported by a grant from the "Office National des Forêts", France.

Appendix A. Supplementary data

Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.agrformet.2017. 02.010.