L Lacroix
email: loic.lacroix@enit.fr

C Blanc

N Pébère

G E Thompson

B Tribollet

V Vivier

Simulating the galvanic coupling between S-Al 2 CuMg phase particles and the matrix of 2024 aerospace aluminium alloy

Keywords: A, Aluminium A, Sputtered films B, Polarisation B, LEIS C, Galvanic coupling

Study of the corrosion behaviour of a magnetron sputtered Al-Cu/Al-Cu-Mg model alloy couple in sulphate solutions has been undertaken to gain insight into the galvanic coupling between the matrix and S-Al 2 CuMg particles in the 2024 aluminium alloy (AA2024). Polarisation curves and local electrochemical impedance spectroscopy measurements (LEIS) were performed on the individual alloys and on the model alloy couple. SEM enabled correlation of electrochemical phenomena to the observed damage. The corrosion behaviour of the sputtered alloys was shown to be representative of the AA2024, with the Al-Cu-Mg alloy part undergoing localised corrosion and the Al-Cu alloy part remaining passive.

Introduction

2024 Aluminium alloy (AA2024) remains important for aerospace applications due to the high strength-to-weight ratio and damage tolerance. However, this alloy is susceptible to corrosion and, specifically, to intergranular corrosion which has been studied extensively [START_REF] Silva | Morphological analysis of pits formed on Al 2024-T3 in chloride aqueous solution[END_REF][START_REF] Garner | Direct observation of intergranular corrosion in Al-4 wt%Cu alloy[END_REF][START_REF] Zhao | In situ X-ray radiographic study of intergranular corrosion in aluminum alloys[END_REF][START_REF] Liu | In-situ observation of intergranular stress corrosion cracking in AA2024-T3 under constant load conditions[END_REF][START_REF] Li | Localized corrosion mechanism of 2ÂÂÂseries Al alloy containing S(Al 2 CuMg) and h 0 (Al 2 Cu) precipitates in 4.0% NaCl solution at pH 6.1[END_REF][START_REF] Guillaumin | Localized corrosion of 2024 T351 aluminium alloy in chloride media[END_REF][START_REF] Zhang | Transitions between pitting and intergranular corrosion in AA2024[END_REF]. The corrosion susceptibility of the AA2024 alloy is known to be due to the heterogeneous microstructure of the alloy, which is a consequence of the thermomechanical processing history. S-Al 2 CuMg particles are one of the coarse, primary intermetallic particles associated with the AA2024 alloy system, and their reactivity and tendency to constitute preferential initiation sites for corrosion have been widely investigated [START_REF] Blanc | The role of precipitates enriched with copper on the susceptibility to pitting corrosion of the 2024 aluminium alloy[END_REF][START_REF] Blanc | Mechanistic studies of the corrosion of 2024 aluminum alloy in nitrate solutions[END_REF][START_REF] Buchheit | Local dissolution phenomena associated with S phase (Al[sub 2]CuMg) particles in aluminum alloy 2024-T3[END_REF][START_REF] Buccheit | Evidence for Cu ion formation by dissolution and dealloying the Al 2 CuMg intermetallic compound in rotating ring-disk collection experiments[END_REF][START_REF] Buchheit | The electrochemical characteristics of bulk-synthesized Al 2 CuMg[END_REF][START_REF] Hughes | Co-operative corrosion phenomena[END_REF][START_REF] Suter | Microelectrochemical studies of pit initiation at single inclusions in Al 2024-T3[END_REF]. However, such mechanisms of intermetallic dissolution continue to be discussed. In order to explain the observed corrosion phenomena, galvanic coupling between the particles and the surrounding matrix are considered.

To study these phenomena, local techniques [START_REF] Suter | Microelectrochemical studies of pit initiation at single inclusions in Al 2024-T3[END_REF][START_REF] Shao | A study on pitting corrosion of aluminum alloy 2024-T3 by scanning microreference electrode technique[END_REF][START_REF] Schmutz | Characterization of AA2024-T3 by scanning Kelvin probe force microscopy[END_REF][START_REF] Lacroix | Statistical study of the corrosion behavior of Al 2 CuMg intermetallics in AA2024-T351 by SKPFM[END_REF][START_REF] Lacroix | Combination of AFM, SKPFM, and SIMS to study the corrosion behavior of S-phase particles in AA2024-T351[END_REF] such as atomic force microscopy (AFM) combined with scanning Kelvin probe force microscopy (SKPFM) are often used [START_REF] Schmutz | Characterization of AA2024-T3 by scanning Kelvin probe force microscopy[END_REF][START_REF] Lacroix | Statistical study of the corrosion behavior of Al 2 CuMg intermetallics in AA2024-T351 by SKPFM[END_REF][START_REF] Lacroix | Combination of AFM, SKPFM, and SIMS to study the corrosion behavior of S-phase particles in AA2024-T351[END_REF]. These local techniques provide high lateral resolution, which is often lacking in conventional electrochemical approaches. Other authors have studied the corrosion behaviour of model alloys representa-tive of the different metallurgical phases [START_REF] Idrac | Electrochemical behavior of magnetron-sputtered Al-Cu alloy films in sulfate solutions[END_REF][START_REF] Liu | Grain orientation effects on copper enrichment and oxygen generation during anodizing of an Al-1 at.%Cu alloy[END_REF][START_REF] Garcia-Vergara | Morphology of enriched alloy layers in an anodized Al-Cu alloy[END_REF]. Several mechanisms have been suggested for S-phase dissolution in the AA2024 alloy [START_REF] Blanc | The role of precipitates enriched with copper on the susceptibility to pitting corrosion of the 2024 aluminium alloy[END_REF][START_REF] Buchheit | Local dissolution phenomena associated with S phase (Al[sub 2]CuMg) particles in aluminum alloy 2024-T3[END_REF][START_REF] Buchheit | The electrochemical characteristics of bulk-synthesized Al 2 CuMg[END_REF][START_REF] Hughes | Co-operative corrosion phenomena[END_REF][START_REF] Lacroix | Combination of AFM, SKPFM, and SIMS to study the corrosion behavior of S-phase particles in AA2024-T351[END_REF][START_REF] Vukmirovic | Dealloying and Corrosion of Al Alloy 2024-T3[END_REF]. A two-step mechanism has been proposed that consists of preferential dissolution of aluminium and magnesium (Step 1), with the intermetallic particles acting as anodes and generating copper-enriched particles after some immersion time, the copper-enriched particles switch to a cathodic behaviour (Step 2) [START_REF] Lacroix | Combination of AFM, SKPFM, and SIMS to study the corrosion behavior of S-phase particles in AA2024-T351[END_REF]. In order to reproduce separately these two steps, simple systems such as a pure aluminium/pure magnesium couple (representative of the first step) and a pure aluminium/pure copper couple (representative of the second step) have been recently studied [START_REF] Jorcin | Galvanic coupling between pure copper and pure aluminum[END_REF][START_REF] Lacroix | Localized approach to galvanic coupling in an aluminum-magnesium system[END_REF]. Both systems were examined with physical contact between the two materials of the couple, and were demonstrated to be appropriate for understanding the corrosion mechanisms associated with copper-and magnesium-rich intermetallics in Al-Cu-Mg alloys.

In the present study, an Al-Cu model alloy representative of the a-Al AA2024 matrix and an Al-Cu-Mg model alloy representative the S-Al 2 CuMg phase were synthesised by magnetron sputtering to simulate the corrosion behaviour of the AA2024. Such thin film model alloys have been shown previously to give relevant data on the electrochemical behaviour of the metallurgical phases represented [START_REF] Blanc | Modelling the corrosion behaviour of Al 2 CuMg coarse particles in copper-rich aluminium alloys[END_REF][START_REF] Saenz De Miera | Modelling the anodizing behaviour of aluminium alloys in sulphuric acid through alloy analogues[END_REF][START_REF] Idrac | Galvanic corrosion of aluminium-copper model alloys[END_REF]. The present paper is focussed on macroscopic (open circuit measurements and polarisation curves) and local (local electrochemical impedance spectroscopy) techniques to study the electrochemical behaviour of each individual model alloys and of the couple. In the first step, the corrosion behaviour of each individual model alloy was studied using potentiodynamic polari-sation. In the second step, interpretation of the model couple behaviour was assisted by local electrochemical impedance spectroscopy (LEIS).

Experimental

Material and systems

The model alloys consisted of thin films sputtered on electropolished aluminium substrates. The alloys were synthesised using an Atom Tech DC magnetron sputtering system with provision for 50 mm diameter targets. In the present case, aluminium (99.99%), copper (99.95%) and magnesium (99.95%) targets were used. The substrates were placed on a large copper disk (300 mm diameter), which was rotated at 250 rpm to ensure composition and thickness uniformity of the alloys. The deposition was performed at room temperature. After evacuating to 6 Â 10 À7 mbar, deposition was performed at 5.5 Â 10 À3 mbar in 99.998% argon at room temperature. Three types of material were synthesised, namely the individual Al-Cu alloy, the individual Al-Cu-Mg alloy and the couple of both alloys. Concerning the Al-Cu model alloy, it was synthesised to be representative of the AA2024 matrix.

The AA2024 matrix was considered as the a-Al solid solution containing the hardening precipitation (mostly GPB zones) and dispersoids. It contains aluminium and copper but also other alloying elements. However, in this study, the only alloying element considered was copper and the composition of the Al-Cu model alloy expected was around Al-2.8 at.%Cu i.e. Al-4 wt.%Cu. Al-Cu-Mg model alloys were synthesised to be chemically representative of the S-phase particles with an expected composition of Al-25 at.%Cu-25 at.%Mg. As described in Fig. 1, to synthesise the model couple, the Al-Cu model alloy was first deposited on an electropolished aluminium substrate. Then, a mask was placed on the sample to cover a part of the surface and the Al-Cu-Mg model alloy was subsequently deposited. Finally, the mask was removed. A surface area ratio of 1:1 between both components of the couple was obtained. No surface preparation was performed on the specimens before the electrochemical studies.

Electrochemical measurements

The corrosion behaviour of the model alloys and the coupled system was studied in sulphate solutions at room temperature with the electrolyte in contact with air. The electrolytes were 10 À1 M Na 2 SO 4 and 10 À3 M Na 2 SO 4 solutions, and were prepared from analytical reagent grade chemicals dissolved in distiled water (pH values between 6 and 7). The specimen electrodes (Fig. 1) were prepared by connecting the substrates, on which the model alloys were deposited, to an electric wire using silver paint, then pasting them on a plastic support with epoxy resin and isolating the electric connection from the electrolyte using epoxy resin. Care was taken in electrode preparation to ensure artifacts were not introduced, i.e. galvanic couples, and to ensure only the model alloy was exposed to the electrolyte. The OCP measurements consisted of recording the free corrosion potential during immersion. In the following, all potentials are given with respect to the mercury/mercurous sulphate electrode (MSE), with saturated potassium sulphate solution (+0.65 V vs. SHE, the Standard Hydrogen Electrode, at 25 °C). Polarisation curves were recorded after immersion for 10 min when the corrosion potential was relatively stable. The potential was scanned from the cathodic domain (À1.4 V/MSE) to the anodic domain (+0.6 V/MSE) with a 1 V/h potential scan rate. Local electrochemical impedance spectroscopy (LEIS) was performed with a Solartron 1275 system, using a fiveelectrode configuration [START_REF] Baril | Local electrochemical impedance spectroscopy applied to the corrosion behavior of an AZ91 magnesium alloy[END_REF][START_REF] Jorcin | Delaminated areas beneath organic coating: a local electrochemical impedance approach[END_REF][START_REF] Jorcin | CPE analysis by local electrochemical impedance spectroscopy[END_REF]. The probe (i.e. a bi-electrode allowing local current density measurement) was stepped across selected points of the sample. The analyses were performed in the centres of the individual model alloys and along a line perpendicular to the Al-Cu/Al-Cu-Mg interface of the model alloy couple. The LEIS measurements were performed in a frequency range of 3 kHz-100 mHz with eight points per decade using 20 mV peakto-peak sinusoidal potential. With the experimental set up employed, only the normal component of the current was measured.

Optical and chemical characterisations

The samples were observed prior to immersion and after immersion for 600 min in 10 À3 M Na 2 SO 4 solution with an Olympus PMG3 microscope; in situ observations were also performed. Energy dispersive X-ray spectroscopy (EDS) was used for elemental analysis, employing a JEOL-JEM-2010 transmission electron microscope (TEM) and a Leo 435VP scanning electron microscope (SEM). The EDS analysis was performed at an electron beam accelerating voltage of 5 keV in order to reduce the electron interaction volume and to localise the chemical analysis within the model alloy layer.

Results and discussion

Structure and composition of the model alloys before corrosion tests

The model alloy microstructure was characterised by transmission electron microscopy (TEM), with Fig. 2 showing a micrograph of the Al-Cu alloy (Fig. 2a) and the corresponding electron diffraction pattern (Fig. 2b). The Al-Cu alloy was relatively uniform in thickness (about 450 nm thick) and free of defects that may expose the underlying aluminium substrate to the electrolyte. Such model alloys are suitable for electrochemical tests with no risk of galvanic coupling with the aluminium substrate. A typical polycrystalline structure was observed for the Al-Cu alloy, which was assumed to be representative of the a-Al AA2024 matrix. It was confirmed by electron diffraction (Fig. 2b). The diffraction spots are indeed characteristic of a crystalline aluminium structure. Concerning Al-Cu model alloys, equilibrium phase diagram showed that, for a copper content of 4 wt.%, both a-Al and h-Al 2 Cu phases are to be observed. However, Idrac et al. showed that, for a copper content less than 5 at.%, magnetron sputtered Al-Cu model alloys are composed of a-Al supersaturated solid solution with very little or no h-Al 2 Cu phase [START_REF] Blanc | Modelling the corrosion behaviour of Al 2 CuMg coarse particles in copper-rich aluminium alloys[END_REF][START_REF] Idrac | Galvanic corrosion of aluminium-copper model alloys[END_REF], which is representative of the AA2024 matrix. In the present study, two kinds of grains are distinguished, namely fine equiaxed grains at the interface between the aluminium substrate and the sputtered alloy (grains marked 1-5 in Fig. 2a, the diameter of which are about 50 nm), and columnar grains that transverse the remaining alloy thickness (grains 6-13 in Fig. 2a). EDS analyses at the numbered locations were also performed, with the elemental analyses given in Tables 1 and2. The equiaxed grains, located at the inner part of the deposit, revealed a mean copper content around 24 at.%Cu, less than the theoretical copper content in the h-Al 2 Cu phase. However, it could be assumed that these grains corresponded to h-Al 2 Cu phase and the error in the chemical composition was attributed to the limited resolution of EDS analyses. The Al-Cu columnar grains, located at the outer part of the deposit (in contact with the electrolyte), appeared uniform in composition with an average copper content of about 2.7 at.%. This copper content is significantly higher to that corresponding to the a-solid solution (indeed, the solubility of copper in aluminium at room temperature is only 0.02 at.%) but this result is in agreement with previous works which showed that PVD process led to a supersaturated a-solution [START_REF] Blanc | Modelling the corrosion behaviour of Al 2 CuMg coarse particles in copper-rich aluminium alloys[END_REF][START_REF] Idrac | Galvanic corrosion of aluminium-copper model alloys[END_REF]. Besides, the experimental crystallographic data obtained from the diffraction pattern performed at the centre layer i.e., out of the equiaxed grains, confirmed the a-Al structure. An example is presented in Fig. 2b using the CaRIne Cristallographie software. The d-spacings calculated for several grains with a good reproducibility, and corresponding to the following crystal plane directions [1 1 1], [2 0 0] and [2 0 2] allowed the crystal lattice parameters to be calculated for the model alloys, respectively equal to 0.407, 0.400, and 0.404 nm. These values were close to the theoretical value of 0.405 nm for the fcc aluminium structure. The difference between the two sets of values i.e. the experimental crystal lattice parameter and the theoretical ones showed that the columnar grains could be considered to correspond to the a-Al supersaturated solid solution. As a conclusion, since the copper content of the columnar grains was close to that of the AA2024 matrix (Table 3), it was assumed that the Al-Cu alloy was representative of the AA2024 matrix. Fig. 3 shows a TEM micrograph of the Al-Cu-Mg alloy (Fig. 3a) and the corresponding electron diffraction pattern (Fig. 3b). Similar to the sputtered Al-Cu alloy, the Al-Cu-Mg alloy appeared uniform in thickness (about 650 nm thick) and free of defects. Unlike the binary alloy, the ternary alloy displayed an amorphous structure, confirmed by the electron diffraction (Fig. 3b). This is a classical result for ternary Al-Cu-Mg alloys deposited by magnetron sputtering. Blanc et al. [START_REF] Blanc | Modelling the corrosion behaviour of Al 2 CuMg coarse particles in copper-rich aluminium alloys[END_REF] studied the corrosion behaviour of such alloys. They have not attributed the amorphous structure to the high alloying element content but to the third alloying element (magnesium) in significant amounts. The authors assumed that the crystallographic structure of such model alloys is not as significant as the chemical composition. Indeed, in spite of the amorphous structure, the sputtered Al-Cu-Mg alloy was shown to be representative of the corrosion behaviour of the 2024 alloy in sulphate solutions and in the cathodic range [START_REF] Blanc | Modelling the corrosion behaviour of Al 2 CuMg coarse particles in copper-rich aluminium alloys[END_REF]. As for the latter, Liu et al. [START_REF] Liu | Grain orientation effects on copper enrichment and oxygen generation during anodizing of an Al-1 at.%Cu alloy[END_REF][START_REF] Liu | Anodic behaviour of a model second phase: Al-20 at.%Mg-20 at[END_REF] revealed that such model alloys were electrochemically representative of the S second phase (Al 2 CuMg) particles present in the AA2024 alloy. The chemical composition of the ternary alloy does not resemble that of any bulk alloys. Bulk Al-Cu-Mg model alloys have a microstructure very different from AA2024 S-phase particles since they are generally multiphase [START_REF] Buchheit | The electrochemical characteristics of bulk-synthesized Al 2 CuMg[END_REF]. PVD model alloys are difficult to obtain with a homogeneous and reproducible composition. However, unlike bulk alloys, the present ternary alloy was shown to be monophase and with the exact composition of the S-phase particles present in the 2024 aluminium alloy. Indeed, EDS analyses at the nine numbered locations are presented in Table 4; a uniform composition of Al-22.4 at.%Cu-24.2 at.%Mg was revealed for the nine analyses, which confirms that the deposited alloy is chemically representative of the S-Al 2 CuMg phase.

Corrosion behaviour of the individual model alloys

Fig. 4 shows the polarisation curves for the Al-Cu and Al-Cu-Mg alloys in 10 À1 M Na 2 SO 4 electrolyte. The polarisation curve of pure aluminium and AA2024 alloy in the same electrolyte are also reported for comparison. All the polarisation curves exhibit a cathodic current plateau corresponding to the oxygen reduction reaction (ORR). Results show that the ORR plateau is higher for the Al-Cu, Al-Cu-Mg and AA2024 alloys than for pure aluminium which could be related to enhanced kinetics of the ORR on copper in comparison to the kinetics on aluminium. Comparison of the cathodic current density for Al-Cu-Mg alloy to that for Al-Cu alloy confirms this result since the higher copper content in the model alloy the higher the cathodic current density. Results confirm the corrosion mechanisms proposed on the AA2024 alloy [START_REF] Buchheit | Local dissolution phenomena associated with S phase (Al[sub 2]CuMg) particles in aluminum alloy 2024-T3[END_REF][START_REF] Buchheit | The electrochemical characteristics of bulk-synthesized Al 2 CuMg[END_REF][START_REF] Lacroix | Combination of AFM, SKPFM, and SIMS to study the corrosion behavior of S-phase particles in AA2024-T351[END_REF]: the ORR takes place preferentially on the copper-rich intermetallic particles such as S-Al 2 CuMg phase particles and leads to the local alkalinisation of the medium and provokes the depassivation of the aluminium matrix around the particles, which is characterised by a trenching of the surrounding matrix. Concerning the anodic domain, it presents, for the Al-Cu alloy, a passive region plateau, which superimposes with that for pure aluminium, with current densities values of about 10 À6 A/cm 2 . On the contrary, the anodic domain for Al-Cu-Mg alloy presents a current peak (À300 mV/ MSE) followed by a passive region. Optical microscopy observations before and after the current peak in the 10 À1 M Na 2 SO 4 electrolyte showed that it may be attributed to local dissolution phenomena and subsequent repassivation of the Al-Cu-Mg alloy. Indeed, as shown by Mankowski et al. [START_REF] Mankowski | The pit morphology on copper in chlorideand sulphate-containing solutions[END_REF], sulphate ions can be responsible for pitting corrosion of copper.

A similar current peak (at the same potential of about À300 mV/ MSE) had been observed previously for the AA2024 alloy in chloride-containing nitrate solution [START_REF] Blanc | Mechanistic studies of the corrosion of 2024 aluminum alloy in nitrate solutions[END_REF], which was attributed to Sphase particle dissolution. In the present study, such an anodic peak was not observed for AA2024 in sulphate solutions and only a passive plateau was recorded. It could thus be concluded that, in sulphate solutions, AA2024 is passive and breakdown of the passivity could locally appear on S-phase particles. However, here, the anodic currents corresponding to the dissolution of S-phase in AA2024 do not lead to a passivity breakdown: they are either too low or the dissolution of S-phase occurred during the cathodic polarisation.

Corrosion behaviour of the couple: LEIS measurements

Open circuit potential (OCP) measurements were performed initially to determine the time necessary for the potential to Interestingly, during the first 100 min of immersion (dotted vertical line in Fig. 5), the OCP of the Al-Cu alloy was more positive than that for the Al-Cu-Mg alloy (Step 1) whereas, after immersion for 100 min, the OCP of the Al-Cu alloy was more negative than that for the Al-Cu-Mg alloy (Step 2). The OCP of the model couple increased rapidly from À1.8 to À0.7 V/MSE at the beginning of immersion then stabilised after 60 min.

After OCP stabilisation, local electrochemical impedance spectroscopy was performed for different positions on the model couple. Fig. 6 shows a schematic representation of the model couple electrode with the position of the probe for the local impedance measurements. The x-axis origin corresponds to the interface between Al-Cu-Mg (negative values) and Al-Cu (positive values) alloy parts. Electrochemical impedance measurements were performed for short immersion times (after 60 min of immersion in the electrolyte) and for long immersion times (after 600 min of immersion in the electrolyte). It is worthy noticing that, for short immersion time, Al-Cu is cathodically polarised in the model couple while, for long immersion times (600 min for example), Al-Cu is anodically polarised. Moreover, 60 min corresponds to the stabilisation of the couple OCP (Fig. 5). Fig. 7 shows the local electrochemical impedance spectra obtained on the Al-Cu-Mg alloy part (Fig. 7a) and Al-Cu alloy part (Fig. 7b), after immersion for 60 min in the 10 À3 M Na2SO4 solution while the corresponding impedance spectra obtained after immersion for 600 min are given respectively in Fig. 7c andd. The spectra of the individual Al-Cu-Mg (Fig. 7a andc) and Al-Cu (Fig. 7b andd) alloys were reported for comparison. These spectra were plotted after 150 min of immersion, which corresponds in the stabilisation of the OCP values of the individual model alloys. For short immersion times, the spectra of the Al-Cu-Mg part (Fig. 7a) present an inductive loop and a capacitive loop. The size of the inductive loop is greatest near the interface of the Al-Cu-Mg/Al-Cu alloy and then decreases as the distance from the interface increases. This is related to the geometrical effect due to the equipotential line distribution over the surface of an embedded electrode, [START_REF] Frateur | Experimental issues associated with measurement of local electrochemical impedance[END_REF][START_REF] Blanc | The origin of the complex character of the Ohmic impedance[END_REF][START_REF] Huang | The apparent constant-phase-element behavior of a disk electrode with Faradaic reactions[END_REF][START_REF] Huang | Local electrochemical impedance spectroscopy: a review and some recent developments[END_REF]. The local impedance spectrum of the individual Al-Cu-Mg alloy shows slightly lower impedance values than those of the Al-Cu-Mg alloy part of the couple. Observations of the Al-Cu-Mg alloy electrode surface had revealed pitting corrosion during the initial period of immersion, in agreement with the low impedance values measured on this alloy material. The local impedance spectra of the Al-Cu alloy part (Fig. 7b andd) shows, for the position close to the interface (x = +1), a capacitive behaviour with two time constants ascribed to the oxygen reduction reaction (charge transfer process and semi-infinite diffusion). This is in accordance with the polarisation of the model couple for short immersion times with Al-Cu which acts as a cathode. When the measurements are performed far from the interface (x = +4), the impedance response is similar to that of individual Al-Cu alloy. Such a behaviour corresponds to the galvanic coupling effect between both alloys. Comparison of Fig. 7a and b reveals that the impedance values at low frequencies are higher (1.5 decades) on the Al-Cu alloy part than on the Al-Cu-Mg alloy part, revealing the capacitive behaviour of the Al-Cu alloy and the reactive behaviour of the Al-Cu-Mg alloy when both are coupled. No passivation of the latter alloy was observed and, conversely, dissolution phenomena have been identified. These results are in agreement with the polarisation curves plotted for each individual model alloy (Fig. 4). A current peak is present in the anodic part of the polarisation curve of the Al-Cu-Mg alloy revealing dissolution phenomena and a passive plateau on the polarisation curve of the Al-Cu alloy. For long immersion times, the impedance spectra plotted for Al-Cu-Mg model alloy showed that there was a decrease of the impedance when the immersion time increased. This showed that, despite of the inversion of the polarisation of the model couple (Fig. 5), corrosion phenomena went on occurring on Al-Cu-Mg alloy. For Al-Cu alloy, a strong capacitive behaviour was observed for long immersion times in agreement with the inversion of the polarisation of the model couple: Al-Cu model alloy became the anode of the couple and remained passive as shown by the polarisation curve plotted for individual Al-Cu model alloy (Fig. 4).

Results thus showed that, when the two alloys were coupled, the Al-Cu alloy part was polarised cathodically during the first 100 min (Step 1), with the Al-Cu-Mg alloy part being the anode. Some pits may be formed on the Al-Cu-Mg alloy, which explained the low impedance values obtained for this alloy after immersion for 60 min. After immersion for 100 min, ( Step 2) the corrosion potentials of the two individual materials were reversed (Fig. 5). Thus, the Al-Cu alloy became the anode of the system and passivated, since it did not develop any pits in the sulphate medium as shown on the current-potential curves. The Al-Cu-Mg alloy became the cathode of the system. It was assumed that, even if this alloy was the preferred site for the oxygen reduction reaction, the anodic component on it was significant, particularly with local dissolution phenomena. Further, these alloys are covered by a passive layer at the corrosion potential at the commencement of immersion. Even though galvanic coupling occurs and oxygen reduction on copper-rich parts then leads to a rapid depassivation of the zones due to subsequent alkalinisation. Such corrosion phenomena may be combined with changes in surface chemistry of the alloys, which could also explain the potential variations with time (Fig. 5). Optical microscopy observations and SEM characterisation combined with EDS analyses were conducted to characterise the corrosion damage and check the assumptions made previously about the electrochemical behaviour of both alloys in the couple.

Microscopic observations and chemical analysis of the corrosion damage

Fig. 8 shows a photograph (Fig. 8a) and the corresponding optical micrograph (Fig. 8b) of the model alloy couple after immersion for 60 min in the 10 À3 M Na 2 SO 4 solution. The couple after immersion for 600 min is presented in Fig. 8c, with magnified images on each part of the couple displayed in Figs. 8d ande. The large differences in reflectivity on both parts of the couple did not allow the simultaneous observation of both parts. Indeed the Al-Cu-Mg alloy part appeared corroded while the Al-Cu alloy part appeared almost intact (Fig. 8b). Interestingly, the Al-Cu-Mg alloy part was more corroded close to the interface, revealing the galvanic coupling effect. As explained before, sulphate ions are responsible for pitting corrosion [START_REF] Mankowski | The pit morphology on copper in chlorideand sulphate-containing solutions[END_REF], which is enhanced at locations of higher galvanic currents, i.e., at the interface between both model alloys. After 600 min, the Al-Cu-Mg alloy part appeared severely corroded compared with the Al-Cu alloy part. Further, many similarly sized pits (about 100 lm in diameter) were present on the Al-Cu-Mg alloy whereas, except for some small pits (about 10 lm in diameter) that are probably unstable, the Al-Cu alloy appeared passive. These observations were fully consistent with the assumptions made earlier after the analysis of local impedance measurements of the couple and the current-voltage curves for the individual alloys.

In order to further characterise the phenomena occurring on the Al-Cu-Mg alloy, chemical analyses were performed. Fig. 9 shows optical (Fig. 9a) and SEM (Fig. 9b) micrographs of the Al-Cu-Mg alloy part presented in Fig. 8 after immersion for 600 min in 10 À3 M Na 2 SO 4 solution. EDS spectra performed on the previous corroded sample are shown in Fig. 8c. Spectra analysis locations are marked in Fig. 9b from N°1 (far from the pit) to N°4 (in the pit).

Spectrum N°0 corresponds to analysis performed on the Al-Cu-Mg alloy before immersion. No significant composition differences were observed between spectrum N°1 and spectrum N°0; far from the pit, the Al-Cu-Mg alloy composition did not change after immersion for 600 min. Further, EDS spectra revealed a gradual variation of the chemical composition from the S-phase composition (N°1) to a composition almost exclusively copper and oxygen (N°4). Indeed, it is revealed that the aluminium and magnesium contents decreased from spectrum N°1 to spectrum N°4. For spectrum N°4, the magnesium peak was absent and the aluminium peak was very low. The chemical analysis thus showed that the Al-Cu-Mg alloy had undergone preferential dissolution of aluminium and magnesium in the vicinity of the pit, leading to a strong copper enrichment. This behaviour is consistent with the phenomena presented to explain S-phase particle reactivity in the AA2024 alloy. A schematic diagram of the corrosion behaviour of the model couple is presented in Fig. 10. In the initial state, both Al-Cu-Mg and Al-Cu parts are passivated (Fig. 10a). During immersion, because of the presence of magnesium, the Al-Cu-Mg alloy had a more cathodic potential than the Al-Cu alloy. In the couple, the Al-Cu-Mg alloy part was anodically polarised and localised corrosion phenomena occurred, leading to a preferential dissolution of aluminium and magnesium, which corresponds to the first step of the diagram (Fig. 10b). This first step resulted in a strong copper enrichment. The chemical composition change could explain the observed reversal of the corrosion potentials of the two model alloys. In the couple, after immersion for 100 min (Step 2), the Al-Cu alloy became the anode of the system, but it remained passive in the sulphate medium (Fig. 10c). However, it was assumed that the pits continued to grow on the Al-Cu-Mg alloy. In Fig. 8, the Al-Cu-Mg alloy appeared more damaged at the interface with the Al-Cu alloy part. These observations can be correlated with the changes observed with the probe position for the impedance spectra performed on the Al-Cu-Mg alloy part of the couple after immersion for 90 min in sulphate medium. Indeed, the gradual reduction of the magnitude of the high frequency inductive loop with distance from the interface had been observed before (Fig. 7). These observations are a sign of the galvanic coupling phenomenon.

Conclusions

As a prerequisite for the simulation of the galvanic coupling, the individual Al-Cu and Al-Cu-Mg model alloys were shown to be representative of the corrosion behaviour of the AA2024 alloy. Anodic and cathodic current densities measured on the Al-Cu-Mg alloy were about ten times higher than those on the Al-Cu alloy; this was attributed to the high copper content of the Al-Cu-Mg alloy. Thereby, the high copper content increased susceptibility of the Al-Cu-Mg alloy to pitting corrosion due to the presence of sulphate ions. An anodic current peak was observed on the Al-Cu-Mg alloy polarisation curve. This current peak was attributed to dissolution phenomena, which are totally representative of the dissolution of the S-phase particles of the AA2024 alloy.

LEIS showed a capacitive behaviour of the Al-Cu alloy part of the couple while the Al-Cu-Mg alloy part appeared to be the location of strong reactivity. While the Al-Cu alloy part remained in a passive state, the Al-Cu-Mg alloy part underwent significant localised corrosion. The preferential dissolution of magnesium observed in the commercial AA2024 alloy was highlighted in the magnetron sputtered couple model alloy.

The results showed that model couples constitute an original and efficient approach to study corrosion mechanisms involving galvanic coupling. The study of model alloys used to simulate events highlighted on the commercial AA2024 alloy was relevant, although the thin nature of the sputtered layers may limit long term testing. The macroscopic model systems (centimetre scale), studied by stationary and transient electrochemical methods, were shown to be representative of submicron phenomena that occur on the intermetallic particles of the commercial AA2024 alloy.

Fig. 1 .

 1 Fig. 1. Schematic representation of the realisation steps of a Al-Cu-Mg/Al-Cu model couple electrode.

Fig. 2 .

 2 Fig. 2. (a) TEM micrograph of the Al-Cu model alloy and (b) electron diffraction pattern realised on one of the columnar grains in the [1 0 1] zone axis.

Fig. 3 .

 3 Fig. 3. (a) TEM micrograph and (b) electron diffraction pattern of Al-Cu-Mg model alloy and (b) electron diffraction pattern realised on one of the point of the layer.

Fig. 4 .

 4 Fig. 4. Polarisation curves of Al-Cu and Al-Cu-Mg model alloy in a 10 À1 M Na 2 SO 4 solution. The polarisation curves of pure aluminium and AA2024 alloy in a 10 À1 M Na 2 SO 4 solution were reported for comparison. Potential scan rate v b = 1 V/h.

Fig. 5 .

 5 Fig. 5. Open circuit potentials of Al-Cu alloy, Al-Cu-Mg alloy and the couple in a 10 À3 M Na 2 SO 4 solution. The dotted vertical line indicates the transition between Step 1 (short immersion times) and Step 2 (long immersion times).

Fig. 6 .

 6 Fig. 6. Schematic representation of the different LEIS measurement locations on a model alloy electrode. The distance values are given in millimetres.

Fig. 7 .

 7 Fig. 7. LEIS spectra in Nyquist representation above (a and c) the Al-Cu-Mg alloy part and (b and d) the Al-Cu alloy part of the couple after short immersion time (60 min) and long immersion time (600 min) in a 10 À3 M Na 2 SO 4 solution. An inset, representing a magnification of the spectra in the high-frequency range was added in each graph. LEIS spectra of individual Al-Cu-Mg and Al-Cu alloy were reported for comparison, for short immersion time (150 min) and long immersion time (600 min).

Fig. 8 .

 8 Fig. 8. Photograph and optical micrographs of the couple interface after (a and b) 60 min and (c-e) 600 min of immersion in 10 À3 M Na 2 SO 4 solution. Magnification on each part of the couple after 600 min of immersion (d and e).

Fig. 9 .

 9 Fig. 9. (a) Optical and (b) SEM micrograph of the framed pits of the Fig. 8c and d. (c) EDS spectra at different distances from a pit (point marked 1-4 in b). The spectra N°0 was performed on the Al-Cu-Mg alloy before immersion.

Fig. 10 .

 10 Fig. 10. Schematic diagram of the corrosion behaviour of the model couple alloy, (a) initial state, (b) Step 1, up to 100 min of immersion in 10 À3 M Na 2 SO 4 and (c) Step 2, after 100 min of immersion.

Table 1

 1 Aluminium and copper contents of the Al-Cu model alloy for equiaxed grains (points 1-5) reported in Fig.2a.

	at.% 1	2	3	4	5	Mean value Standard deviation
	Al	75.7 79.8 73.7 76.4 75.5 76.2	2.0
	Cu	24.3 20.2 26.3 23.6 24.5 23.8	2.0

Table 2

 2 Aluminium and copper contents of the Al-Cu model alloy for columnar grains (points 6-13) reported in Fig.2a.

	at.%	6	7	8	9	10	11	12	13	Mean value	Standard deviation
	Al	97.1	97.7	97.2	96.7	97.9	96.9	97.9	97.7	97.4	0.4
	Cu	2.9	2.3	2.8	3.3	2.1	3.1	2.1	2.3	2.6	0.4

Table 3

 3 Chemical composition of the 2024 aluminium alloy.

	Elements	Al	Cu	Mg	Mn	Fe	Si
	wt.%	Base	3.8-4.9	1.2-1.8	0.3-0.9	60.5	60.5

Table 4 Aluminium

 4

	at.%	1	2	3	4	5	6	7	8	9	Mean value	Standard deviation
	Al	53.4	52.5	53.2	51.9	53.1	55.6	54	53.2	54.3	53.5	1.0
	Cu	21.1	22.7	23	24.6	25.1	18.5	21.8	23.3	21.3	22.4	1.9
	Mg	25.5	24.8	23.8	23.5	21.8	25.9	24.2	23.5	24.4	24.2	1.1

, copper and magnesium contents of the Al-Cu-Mg model alloy for the points reported in Fig.

3a

.

Acknowledgements

The authors thank Mirnali Saenz and Peter Skeldon for their help in the PVD model alloy deposition and the support of the EPSTRC LATEST2 Programme Grant.


Paul Girard

The plan: a spontaneous and sustainable mark Le tracé, marque spontanée et durable

Keywords: plan, line, context, haptics, memory, spontaneity tracé, ligne, contexte, haptique, mémoire, spontanéité

The city is produced by drawing, which is a thrown through the plan accumulation of knowledge. The plan does not lack cultural context. There is a contextual content in the container of the draw, what offers a continuity of the surveyed contexts which is less and less met in the urban treatment, more disconnected. The sustainable development is to take hold again contexts.

Résumé : La ville naît du dessin, qui est une accumulation de savoir projetée à travers le tracé, lequel n'est pas dénué de contexte culturel. Il y a un contenu contextuel dans le contenant du trait, ce qui offre une continuité des contextes arpentés qui se retrouve de moins en moins dans le traitement urbain, davantage décousu. Le développement durable, c'est se ressaisir des contextes.

Urban, suburban spreading, division into sectors… are "monsters" indicated by those who make the city and this in the name of the democratization (the signs of a participative democracy in Europe are attested within the urban dialogues: UBA in Germany).

Maybe, nowadays, supplying answers adapted to variety of our cities is more necessary than comparing models of spaces between them. The modern city shows certainly a failure as regards the connections between the architecture and the urbanism. (Invention of a very sophisticated and individualized architecture, absence of intermediaries of investment on public spaces).

I suggest thinking about certain necessities of relations, asserted formerly by the city, and become less evident. I shall take the example of the association between the functionality and theater. The plan 1 of the city and the drawing of the architect always joined thanks to the meetings between the individuals within cities. Plans and lines placed the run-ups of our bodies in the geometrical. For this, they were tools guarantors of a human memory. The ephemeral and the local were thus bound with the universal.

The question of the ephemeral taps us today. I take the example of more and more common projects proposing the investment of said spaces "intermediaries": I can quote the example of these places between the place of residence and the street. We see them in Japan, in Brazil (traditionally), as in some projects of the Grand Paris.

These wills mark a new worry about links between areas and means to be found to invest this caesura between private and public places. This text does not propose new solutions, but reminds the inscription of the plan in the town planning, and the idea of line within the common areas.

It tries to evoke the paradox of the short-lived in the long-lasting city.

1) Observations on the feeling of the unity.

I often wonder if the town planning of our cities does not evade too quickly the implicit narrative dimensions which are on the base of any spatial device. While I am held within a landscape, I move between different points of view (imaginary and practicable since a concrete knowledge of places). Since this capacity, I can share a place, because I take under consideration the share of identities. If I take the example of a place which I cross, I live in it since the unity which it represents, through which I conceive the hypothesis that everyone can find there a meaning. An incoherent immediacy is not enough for me, a parcel of land, which does not depend on the unitary appreciation of a landscape.

Any collective understanding has narrative contents.

The points of the map of a territory have to be joinable; they must not exclude each other since every habitation. So it is rather a whole, and since it a symbolic sharing is made possible.

Lessing distinguishes about the painting an organic modality (of the presenting and of the seeing), which articulates a matter next to another one, and a poetic modality, which considers the order of succession of matters, a matter after another one.

I reason thus: if it is true that painting and poetry, in their imitations, make use of entirely different media of expression, or signs -the first, namely, of form and colour in space, the second of articulated sounds in time; -if these signs indisputably require a suitable relation to the thing betokened, then it is clear, that signs arranged near to one another, can only express objects, of which the wholes or parts exist near one another; while consecutive signs can only express objects, of which the wholes or parts are themselves consecutive.

Objects, whose wholes or parts exist near one another, are called bodies. Consequently, bodies, with their visible properties, are the peculiar objects of painting.

Objects, whose wholes or parts are consecutive, are called actions. Consequently, actions are the peculiar subject of poetry. (Lessing, 1853, p.101)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! " !#$%&!$'!%(&!%)*'+,*%-$'.!%(&!/$)0!12,*'3!-+!4$)!%(&!5)&'6(!1%)*6738!%(&!/$)0!10)*/3!4$)!%(&!5)&'6(!1%)*-%39!
An architecture which places objects and bodies one next to the other may be said organic; an architecture which articulates temporalities and successions between matters is closer to a symbolic, cosmogonical, or poetic, order. (Let us think of the Arabic architecture of Alhambra in Grenada, Spain. Let us remember maps of Leonardo da Vinci, in which the sight in oblique translates a relation between a physical crossing of the territory and a poetic-symbolic crossing of the territory.) I choose to hold these observations about the urban and landscaped recognition. A space opens on the different present successions, not on situations placed one next to the other. In other words, the conditions of appreciation of the frames of temporality must be accessible to everyone who lives here, without encroachment or threat of the one upon others. (An example is the skilful and playful dimension of the architecture which claims Le Corbusier).

2) The power of the haptic perception.

The difficulty envisaging the idea of spaciousness results from the character multi-leveled of the perception and of human needs.

For example, I cannot observe the fact of living without evoking the theatrical motive, which is implicit: we have an address because we find within places the possibilities of establishing our theaters there.

Architecture does not separate theater and functionality.

While the traditional city (ancient, for example) contains the device of the theater, the modern city is inseparable of the idea of projection and cinema. Therefore, a more internal space is thrown on the urban and landscaped unity. The scales of the city and the framings send back to more mental marks. The technology makes our gaze more precise and more rational, and makes them taken within more and more material and individualized cultural marks.

I wish to observe openings, closings and impounding of territories since the exposure of the human being and his attachments within the city.

Two analyses invite me to approach very concretely this value of the exposure. The first one is made by the French art historian and philosopher Hubert Damisch, and the second one by the American sociologist Richard Sennett.

Hubert Damisch takes under consideration a capacity of delight and capture since the device of showcase. An exhibition proceeds of a hierarchy of presentation, from the human being captivated to the one captive or captivating (for a woman). The showcase, in the fact that it participates of a motive where movements and actions can be cut and exposed again, plays with the limits of our own capacities of distinction or empathy: I am suddenly touched, as marked since possibilities and impossibilities of contact, from where appear effects of fascination, splitting and mirror. The showcase inaugurates new contacts since the haptic intimacy of touches (Damisch, 2004, p.68-69).

Richard Sennett replaces the touch as the center and the generator of the movement in human beings [START_REF] Richard | The Conscience of the Eye: The design and social life of cities[END_REF]. Human being moves when he touches; thus this capacity of action is a fundamental and premier link, a necessity to remain and move. Our cities must be considered since a history of these different contacts which the human being establishes with his environment. A first report comes from the avoidance to register the marks of borders and differences within a generic city, become unlimited, without particular tensions, monotonous, and without putting in show our borders. Nevertheless the show of the border participates in this idea of overtaking, place of a common conflict where everyone meets.

In his history of a city captured by the obsession of the touch, the sociologist analyzes the imprint of a Christian culture. He reviews various models.

The modern city, following the example of Mies Van der Rohe, proposes an ice-cold contact, a shape closes, which produces a fantastical and terrible encroachment of an almighty presence: the immobilizing moment of the ' to be seen' imposes upon the 'to be able to see'.

The contemporary western city asserts its incapacity to propose a theater of its conflicts, of its varieties, of powers. All which allows the recognition of common conflicts within the city is repressed, strengthening the divisions between the public and the private places. Nevertheless the city shows every day its failure since an absolutist, apathetic and generic regularization. The absences accumulated of possibilities of contact exclude definitively spaces, again since this treason.

3) Memory, image and urbanity.

This Richard Sennett's last proposition is not maybe forgotten by the cinema: recently, the cartoon Waltz with Bashir (Folman, 2008) convinced me of it.

The central figure remembers himself an image, that of the city under the crashes of the war, the explosions, the "pyrotechnicians" fires where the vision going from yellow browns to the frontal and deep black invades the spectator since this truth that the city is also the sharing and the exhibition of the death: while a rain of splinters explode at night above a city, three military companions appear from the sea and approach this rain.

The director deliberately seems to have put within this recurring nightmare for the central figure, the motives for a terrible fascination which holds us and asks us especially to hold on: this image, with its colors, contains a forgotten truth.

The character will find besides the reasons of its neurosis.

Sublime image of the city, of a city merged with one of its symbolisms, a victory on the individual death. The city registers the possibility of the sharing of the death under a shape of proclamation where even nightmares, I would even say especially nightmares, are shared.

So, this modern city, carnivorous and nevertheless beautiful city, which explodes of beauties with the cinema of Murnau, with George Grosz's paintings, with aerial panoramas, surrounded between skies and lands, being afraid of an ethereal space in Nick Ray's movies, with John Cassavetes' family universes or facetious confusions in Tim Burton's movies.

If the possibility of memory was the object of a cinema, that of Chris Marker, of Alain Resnais, who both investigate the necessary presences and the unforgivable absences of our societies, the question of the images as symbols and the question of their memorial manners proceed of an eclipse by the city.

Nevertheless, the ambition of memory establishes the plan of the city.

We find again the question of the body and its exposure, that is to say a relation between images and architecture. More exactly, we see there at work the relations between the perceptions and the images (Sitte, 2006: about the memory of the draw).

Nowadays, the architecture and urbanism historian Bernard Gauthiez envisages the spatial partition as one of the objects-guards of the memory of our territories.

Before reviewing the discernible elements on a plan, it remains to enlighten a major difficulty, a source of numerous errors. It consists in mechanisms of the fact that Pierre Lavedan called the obstinacy of the plan, and that I prefer to name the memory of the fragmented, of which we saw that it could be total. Without this effect of memory, the introductory hypothesis would be groundless. So that forms are passed on, mechanisms of preservation have to be at work; they concern, for what interests us, the limits of the plots of land, and the buildings. The fragmented limits can be divided into two categories. The first one includes the limits between a private domain and a public domain. The factor determining their obstinacy is mainly based on the exercise of the control of the public authority, whatever this authority is, on a space of its competence, in front of possible private encroachments. (...)

The second fragmented category of the limits includes the separations between private domains. The mechanism in the work in their preservation is the control by the parts concerned by their own ground. (Gauthiez, 1999, pp.17-25) Let us observe, since this attempt of clarifying the authorities of a matrix, one moment of relation between the drawing of a village and the places that are proposed to the glance. In other words, let us try to see how the line sometimes operated in connection with the prerogatives of an initial Greek optical device.

4) The line in the plan.

The surrounding wall of the village of Monterigioni can be defined as the marker of a spatial shared limit (cf. Fig. 1 2 ).

The photographic image shows us that the plan, the line and the draw are bases which allow a meeting between human beings within places, as a relation between the extents. (We shall agree that any art results from the conquest of the spacing between human beings.3) The various walls, which join, establish hollows and extents in the place where they divide the territory. With these regulations of distance allowing the projections and individual theaters, these lines, with the distances they imply, establish the characters of time and space within the architecture. (Therefore, an architecture lets be understood from the parameters ordered by the topological and by the topographic [START_REF] Michel | L'homme spatial[END_REF]).

Let us try to see how these various lines stemming from the plan made by human beings are organized in the space and establish this unity of spacing.

In the representation of the space in perspective, we use to speak about the groundline, about the skyline, but hardly about the draw. The notion of draw rather sends back to the raw and carnal mark of the chalk on the blackboard, that is to say to the convocation through a hard line of all the parameters, materials, stories contained and brought back since the place where the sign is inscribed. The draw becomes thus a generic, rupestral and ancestral shape of the line. I shall bring it closer to the imprint, wanted by the hand and measured since the step of the man, but also to the meeting between the sky and the ground: where verticality is justified by horizontality. Are contained in draw the holding of a body still badly assured in the usage of the signs, or the holding of a body that is inscribed above all in the main part of the environmental parameters where he tries to be held. The draw convokes the concrete and cosmic characters of the presence and the place of the body.

Thus the plan of a city carries all the spontaneous and rationalized social practices, coordinated in a most frontal way in the space. (There are hard draws and soft draws.) I consider, through this image, rather the notion of line than the notion of draw. But it seems to me important to replace the idea of draw (and of trace) within the distinction between soft line and hard line and, more exactly, in their meeting. Let us take an example: John Ford inscribes the credits of his film Young Mr. Lincoln "in the marble". Abraham Lincoln's name is engraved officially in the reflected light of America, within the show of its history and its geography. The mark made by writings and by signs reports an absolute truth which transcends as much as this mark is inscribed since a hegemony which exceeds us. It contains an immemorial time.

The plan participates of a recovering of temporality between hard lines and soft lines.

In the image of the village, the plan is what presides over the establishment of the ground under the light, while the objects of the architecture and of the spatial division (enclosure, walls…) operate their spacings. Phenomena of resonance and of resistance connect traces and lines between them.

The question of the line in architecture has to consider a synthesis of rules and parameters of our perceptions since a vision unified by the optics.

The enclosure and the walls of this village participate in an example: the enclosure separates the city from a shared inviolable (a shared invisible), and inscribes all the houses connected between them in the parameters of diverse, multiple, multi-leveled extent).

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Limitations and theater of this ban are then connected. The borders can be shared by all because a spectacular device exists, which connects human beings with the world. Every house is connected to the other one and to the universal: streets make houses joining between them since lines "of flight". The plans, which separate, order and associate while they separate.

There is an optical combination of the values of transversality and of longitudinality combined by the line. The line thus participates in invisible and dumb draws connecting objects between them within extents which build the three-dimensionality of a space. Since the hand and the will of human beings, they were a tool allowing the space to accommodate the sounds and the images of the dramatizations. The line inscribes the draws of construction so that the optical and geometrical orders coordinate towards an overtaking of the organic dimension.

It is necessary to understand here the establishment of this enclosure and of these streets by the line. The notion of architectural line, protective of the invisible, corresponds to all the assembled organic layouts, building units of spacing. The spacing is here the historic value which legitimizes the presence and the human culture. The line sets down a capacity to live, to contain, to distribute, to articulate. (Cf. Fig. 2)

There is a history of the spacing to be defined. This one can be apprehended only since the drawing of this line-shape which contains the multiplicities of distances, rhythms… which human beings need to recognize within a place: closing, opening, human theater… The line, stemming from the hand, connects the limits of the body to the necessary spacings between the expressions, the needs and the human functionalities.

Since this ancient Greek transversal and longitudinal organization which shares the territories of the human beings and the territories of the gods within the optical devices of representation [START_REF] Françoise | Du masque au visage[END_REF], the line allows that becomes established on earth a theater between the human beings, where spaces lead a war of the images then pacified.

5) The paradox of the intermediate spaces.

If we have a look at the nowadays city within the framework of the technicalities put in the service of the human beings, we make the report of a city where the urban spreading is more and more agree with the influence of the virtual utopia.

The image itself is observed since the validation of an explosion of time (the cheap digital support does not make any more necessary the calculation of the temporal economy). History of the image and history of the space are upset again in their referents.

Nevertheless, the optical scale of the dimensions of the human being was the object of a device in ancient Greece: transversal glance of the gods, longitudinal glance of the human beings.

The conflict between the line and the color, the risk of an opus incertum, the "indistinction" between human vision and divine vision, revealed the necessary preservation of these territorial divisions between sacred and profane since the oral and written dimensions by the image during XVIth century.

The virtual places us within an expansion, that of the cancer of the spot: the photography restored the power to the spot against the line, the virtual allows the inflation of this surface.

The white-black frames of the colors of the Attic ceramic reveal the entropy of the meetings between darkness and brightness since which the ancient human beings were remotely put.

The Renaissance replays the division of the mixité of the shade and the light. The Hogarth's printings of Elizabethan England and their serpentine allow us to evolve between the limits of drawn objects (the undulations and the convolutions of the smoke).

English garden cities of the XXth century define these "closes", devices of the space built around the public streets connecting private ways.

These "intermediate" spaces, glorified in certain western cities like Lyon, Venice, Prague, or by the urbanism of the cities of Latin America, are more than the places of meeting between diverse temporality (private-public) and diverse varieties of the ephemeral. These passages offer occasions of distances, contingencies and mixités where the most extreme positions of spectators and actors are met between individuals and community.

There, on these entries and exits tumble down the aggression, the firm, maintained, constructed and spontaneous hatred revealed in a little controllable way… If it is not by the regulation of flows. These places today mistreated ("gated Communities", dullness of the generic city, urban spreading, franchising of the big brands…) show phenomena of individual captures and strategic relinquishments ("non-places"). Nevertheless, it is important to connect them with the screen of the romantic shows and romanesques reasons of our cities. The direction of the limits, of the borders, has to can be recognized as moments of restoring of the social differences to be accepted. The tragedies and their compulsive contents, as shows it us the shot of the movie of Ari Folman.

The place of the death (its eclipse) in the contemporary city reappears on this incapacity of sharing.

It takes place behind this absence of shared recognition a disorder of the impossible autonomy of our bodies (is it inside a narrative, outside a narrative? What is there instead of it?). It results from it the incapacity to die and to born again, to recognize and to meet within the community.

The Portuguese cemeteries, the Spanish ones, and, closer of us, those in the Vosges, dominate the city, are at the feet of the churches, at the feet of those who open the landscape, linking the various cities within the landscapes. Once again the writing of the line is eluded.

What is drawing for an architect? This question joins the question of the implicit in the codes of representation and of perception, and the question of the creative necessities of human beings when they build a city, necessities where could be find our needs to live, to expose ourselves within the functional economies.

Walter Benjamin establishes a hierarchy of the show of the body, of his empowerment from the human being by the time it's exposed: passage covered in front of showcases, body in movement, the address, the hand (envisaged as original mode of expression)…

The ephemeral aspects of our devices contain more strongly that these, the reasons of the division of the profane and sacred territories.

The city can die and born again only by asserting the power of the spontaneity.

Even if this sharing is the object of a struggle to death.

Ari Folman shows us the ephemeral or the possibility of being able to die on the meeting of a show moved since the tragic of the night. Plans and screens transposed and transported since the devices of walls, low walls, surrounding walls, facades, are to be observed since the consideration of the human plan. The art of the line in the architecture, such a technology stemming from the draw, is defined by its capacity to build perspective feuilletages, imaginary and real, visible and invisible laminations, but resounding between them in a unity of tone defining the genius loci. There are layouts of plans, of screens, of directions of flight, of horizons, of grounds, of spots, of borders, of limits, of thresholds, of edges, which were combined since this art to make a correspondence between optical order and geometrical order. An analysis of the topological and topographic relations asks for example the organizations and the more invisible knots of invisible lines of construction to be envisaged.

Legends of the illustrations.

Fig. 1 .

 1 Fig.1. Monterigioni, Tuscan village.

Fig. 2 .

 2 Fig.2. Monterigioni, Tuscan village.

Personal drawings had as a base an aerial photograph of the village named Monterigioni (Tuscany) found in a book written by NorbergSchulz (1981, p.167).

On this subject, the analysis of the notion of spacing in the writings of architecture of Françoise Choay (2006) could be envisaged since certain perspectives of André[START_REF] André | Gesture and Speech[END_REF].