Abderzak El Farsy

Jean-François Pierson

Thomas Gries

Ludovic De Poucques

Jamal Bougdira

Abderzak El Farsy
email: abderzak.el-farsy@universite-paris-saclay.fr

On the correlation between the TiN thin film properties and the energy flux of neutral sputtered atoms in direct current magnetron discharge

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

In this study, the energy flux of sputtered atoms on a substrate was correlated to the properties 10 of titanium nitride (TiN) films deposited using direct current magnetron sputtering (dcMS) under 11 mixed Ar and N2 atmospheres. The neutral titanium sputtered atoms velocity distribution func-12 tions (AVDFs) were measured by tunable diode-laser induced fluorescence (TD-LIF), and the flux 13 of particles and their energy were derived. Mass spectrometry was used to characterize the 14 energy-resolved flux of the ions. It was found that the neutral sputtered atoms flux and deposi-15 tion rate were in good agreement, indicating that the flux of the neutral titanium ground state 16 represents the number of deposited atoms. Moreover, TiN films were deposited at different gas 17 pressures and at various Ar/N2 gas mixtures close to the conditions where stoichiometric TiN 18 was formed, without bias voltage and heating of the substrates. The energy flux of the sputtered 19 neutral Ti into the substrate was calculated from TD-LIF measurements. At a relatively low mag-20 netron discharge pressure of 0.4 Pa, we demonstrated that the energy of sputtered neutral Ti 21 impinging on the substrate is higher than the energy flux of ionized particles corresponding 22 mainly to Ar + . Thus, the influence of the energy flux of the sputtered atoms on the texture and 23 microstructure of the films is revealed. The (200) texture was obtained at 0.4 Pa when the energy 24 flux of the sputtered atoms was higher than the ion energy flux. At 1.3 Pa where the sputtered 25 atoms energy flux is one order lower compared to 0.4 Pa the (111) texture was obtained. The 26 high-energy flux of the ground state of Ti sputtered atoms seems to allow stress removal in the 27 films. 28 Keywords: dcMS, diode laser-induced fluorescence spectroscopy, TiN microstructure and tex-29 ture. 30

I. Introduction

In magnetron sputtering (MS), the growth of polycrystalline thin films begins with vapor condensation 32 on the substrate surface, which nucleates into islands and consolidates to form a continuous film. Thin 33 films and coatings are used in a wide range of technological applications including microelectronics, 34 optical devices, and surface protection. The performance of thin films and coatings depends on their [START_REF] Cemin | Low-energy ion irradiation in HiPIMS to enable anatase TiO2 selective growth[END_REF] physical properties, which are governed by film morphology and phase composition. These properties 36 depend on the interactions of the particles with the substrate. Thus, the energy and flux of atoms and 37 ions arriving at the substrate are of major importance for tailoring the forming film properties, such 38 as microstructure, stress, adhesion, electrical resistivity, stoichiometry, and crystalline properties. Ti-1 tanium nitride (TiN) was used in this study because of its excellent mechanical and optical properties, 2

and it has been used in several applications, such as decorative and wear-resistance [1,[START_REF] Wang | Influence of Substrate Negative Bias on Structure and 26 Properties of TiN Coatings Prepared by Hybrid HIPIMS Method[END_REF]. [START_REF] Depla | Handbook of deposition technologies for films and coatings: sci-29 ence, applications and technology[END_REF] Magnetron sputtering is a physical vapor deposition technique that can be operated with different 4 power supplies: direct current magnetron sputtering (dcMS) to sputter conductive targets, radiofre-5 quency magnetron sputtering primarily used to deposit dielectric materials, and high-power impulse 6 magnetron sputtering (HiPIMS) [START_REF] Depla | Handbook of deposition technologies for films and coatings: sci-29 ence, applications and technology[END_REF][START_REF] Anders | Tutorial: Reactive high power impulse magnetron sputtering (R-HiPIMS[END_REF]. In the dcMS process, most of the sputtered species remain in a 7 neutral state, and their energy is controlled by the degree of thermalization, i.e., the number of colli-8 sion events between the sputtered species and the processing gas. The number of collisions can be 9 directly controlled by the deposition pressure and the target-to-substrate distance [START_REF] Revel | Transition from ballistic to thermalized 33 transport of metal-sputtered species in a DC magnetron Plasma Sources[END_REF]. Their energy 10 ranges from the energy they gain in the sputtering process and at virtually no collisions (~ 3.2 eV in 11 average) to fully thermalized species at a larger number of collisions (~0.1 eV in average). Over the last 12 two decades, HiPIMS has been intensively studied because of its ability to generate sputtered atoms 13 with a high ionization rate (a few tens of percent). Such pulsed plasma discharges work at a peak 14 current of approximately two orders of magnitude (low duty cycle: 1 % and low repetition frequency: 15 < 5 kHz) compared with dcMS. 16

In conventional dcMS to deposit nitride thin films, the ion flux on the substrate mainly contains buffer 17 gas ions (Ar + and N2 + ), whereas the sputtered species are mainly in a neutral state. For titanium nitride 18 (TiN) deposition, the energy flux on the substrate, i.e., the product of particle flux and incident particle 19 energy determines the growth mode. The TiN grains are preferentially oriented along the [START_REF] Ehiasarian | Influence of high power 35 impulse magnetron sputtering plasma ionization on the microstructure of TiN thin films[END_REF]7,[20][21][22], and most of these studies investigated the impact of ion flux on the properties of TiN 37 films. The present study aims to correlate the energy flux of neutral sputtered atoms on a substrate 38 with the properties of TiN thin films (film texture, microstructure, and morphology) grown in dcMS 39 discharges where the sputtered particles are mainly neutral. To achieve this goal, we used a balanced 40 magnetron to reduce the ion flux on the substrate without bias and without intentional substrate 41 heating. Thus, simultaneous measurements of TD-LIF and mass spectrometry of magnetron discharge 42 under different gas mixtures (Ar/N2) were performed to characterize the energy flux of neutral sput-1 tered Ti atoms and the ion energy flux, respectively. 2

II. Experimental details 3

The growth of TiN thin films and plasma diagnostics were carried out in a stainless-steel cylinder, 30 4 cm in diameter and 35 cm in height. Using mechanical and turbomolecular pumps, the base pressure 5 obtained was approximately 2×10 -4 Pa. A titanium target, 50 mm in diameter, 3 mm in thickness, and 6 99.99 % pure, was installed on a 2-inches balanced magnetron cathode cooled by water. The power 7 source was a MELEC SIPP 2000 power supply (Umax =1 kV; Imax_peak= 200 A). The reactive gas mixture 8 (Ar and N2) was added to the chamber at various N2/(Ar+N2) flow rate ratios, and the total flow rate 9 was maintained at 18 sccm. We investigated the gas mixture range of 2 % to 5 % N2 where quasi 10 stochiometric TiN films were formed as shown latter by the measurements of the chemical composi-11 tion of the films, the same conditions were found in early work with another deposition system [START_REF] Petrov | Mass and energy resolved detection of ions and neutral 1 sputtered species incident at the substrate during reactive magnetron sputtering of Ti in mixed Ar+N2 2 mixtures[END_REF]. 12 For all the results presented in this work, the average power was fixed at 5 W cm -2 (100 W for the 13 target area). In addition, all plasma measurements and thin film depositions were performed at a tar-14 get-to-substrate distance of 5 cm (figure 1). 15 Plasma diagnostics and film depositions were performed in the same reactor, and the (100)-oriented 16

Si substrates were installed using configuration 2, where the magnetron cathode was installed atop 17 the chamber [figure 1 able diode laser (Toptica Photonics DL 100), which was accorded to probe the transition from 10 3d 2 s 2 ( 3 F2) to 3d 2 ( 3 F) 4s4p ( 1 P o ) of the ground state of neutral titanium sputtered atoms (λ0=398.17 11 nm). The diode laser was tuned to scan a 9 pm wavelength range with a locked single-mode, and the 12 spectral resolution was 0.005 pm, enabling an accurate description of the Doppler broadening profile. 13

The typical scanning frequency for measurements was 50 Hz. The probed volume in the TD-LIF meas-14

urements was approximately 3 mm 3 above the racetrack center, that is, at r=1.25 cm and z = 5 cm 15 (figure 1(a)). The combination of high spectral and spatial resolutions accurately measures the flux and 16 energy of the deposited species. 17

The ion energy distribution functions (IEDFs) of Ar + and N2 + were measured using a HIDEN EQP 300 1 instrument. The plasma was sampled by a grounded orifice of a 100 m diameter mass spectrometer 2 installed in the virtual position of the substrate (figure 1(a)). Because the mass spectrometer signal 3 depends on the differences in the acceptance angle for different ion energies and the unknown trans-4 fer function of the mass spectrometer, the measurements do not represent the absolute values of the 5 ion flux; therefore, we discuss only the qualitative signal variations. Herein, only the qualitative 6 changes in terms of energy are discussed. However, owing to the reactor geometry, mass spectrome-7 try measurements were only performed in front of the target center at r= 0 cm (see figure 1). 8

The deposition rate was measured via scanning electron microscopy using a cross-sectional view of 9 the specimens. The microstructure (crystallite size) and preferred orientation of the films were char-10 acterized by X-ray diffraction (XRD) analysis (Brüker D8 Advance with Cu K radiation, λ=1.54056 Å) in 11

Bragg-Brentano geometry (θ-2θ). This mode allows for the identification of planes parallel to the thin-12 film surface. The chemical composition of the films was determined by wavelength dispersive X-ray 13 spectroscopy (WDS), also known as electron probe microanalysis (EPMA), using a JEOL JXA-8530F in-14 strument. Ti, Fe4N, and MgO were used as standards to measure the Ti, N, and O concentrations, 15 respectively. For each sample, the reported chemical composition was obtained by averaging 50 dif-16 ferent spots measured on the surface (~ 200 × 200 μm 2 ). The topography and RMS roughness of the 17 TiN films were investigated in resonant mode using a nano-observer atomic force microscope (AFM) 18 developed by CSInstruments. 19

III. Results and discussion

20

III-1. Correlation between the deposited flux and deposition rate 21

Figure 2 shows the neutral Ti ( 3 F2) AVDFs in dcMS discharge at 0.4 and 1.3 Pa, for the different gas 22 mixtures (N2/Ar). We used the resonance fluorescence signal (λlaser = λlif = 398.17 nm), which signifi-23 cantly improved the TD-LIF signal compared with previous studies [START_REF] Revel | Transition from ballistic to thermalized 33 transport of metal-sputtered species in a DC magnetron Plasma Sources[END_REF]16]. Then, the AVDF profiles and 24 the atoms populations are accurately described: thermalized (centered at v = 0 km/s) and energetic [v 25 > 1 km/s ≈1 eV for titanium atoms] [5] are separated at relatively low and high magnetron pressures 26 (p=0.4 and 1.3 Pa). The dashed curves represent fitting of the TD-LIF signal. The measured velocity 27 field is the axial component (component perpendicular to the target surface as shown in figure 1 (a)), [START_REF] Maszl | Origin of the energetic ions at the substrate 10 generated during high power pulsed magnetron sputtering of titanium[END_REF] and two Gaussian functions were used to fit the experimental signal, which corresponded to the ther-29 malized and energetic atoms populations. Because the measurements were carried out 5 cm away 30 from the target, sputtered atoms undergo collision with the buffer gas, inducing the energetic popu-31 lation to be better fitted by a Gaussian function instead of the commonly known Thompson function 32 [24]. The fitting by these two Gaussians results in some discrepancy for negative velocity (v < 0), espe-33 cially at low pressure (0.4 Pa, top panel of figure 2). The main goal of the fitting is to better calculate 34 the flux and energy of the atoms with momentum towards the substrate (positive velocity) to correlate [START_REF] Cemin | Low-energy ion irradiation in HiPIMS to enable anatase TiO2 selective growth[END_REF] with the film properties. Only the measurements performed at the substrate position are shown at a 36 distance z = 5 cm from the target. For a detailed description of the AVDFs' fitting and titanium sput-37 tered atoms transport characterization combined with PIC Monte Carlo modeling in argon gas, the 38 reader is referred to Revel et al. [START_REF] Revel | Transition from ballistic to thermalized 33 transport of metal-sputtered species in a DC magnetron Plasma Sources[END_REF]. 39 The addition of nitrogen to the argon discharge completely altered the sputtering process. N2 mole-5 cules react with the target surface material, forming a nitride layer that induces variations in secondary 6 electron emission, electron temperature, and cathode voltage, but also induces variations in the ions 7 striking the cathode, that is, Ar + , N2 + , and N + allowing sputtering instead of only Ar + in pure Ar gas. 8

Figure 2 shows that the TD-LIF signal at the substrate positioned at a distance z = 5 cm from the target 9 decreased progressively with increasing N2 content. This decrease was observed for all atoms regard-10 less of their energy. This is due to two main changes: (i) poisoning of the target surface in which the 11 binding energy of Ti-N (8.04 eV [25]) is higher than that of Ti-Ti ones (6.6 eV [START_REF] Du | Sublimation crystal growth 6 of yttrium nitride[END_REF]) and (ii) plasma 12 variation in which the N + and N2 + ions can be less efficient for sputtering compared to the Ar + ion [START_REF] Rossnagel | Thin film deposition with physical vapor deposition and related technologies[END_REF]. 13 TD-LIF measurements performed near to the target surface (z= 1.1 cm) at low pressure of 0.4 Pa show 14 that the surface nitridation affects the surface binding energy, we measured an average energy of 15 4.0±0.2 eV at nitride mode and 3.2±0.2 eV in metallic mode (100% Ar). The gas mixture does not affect 16 the temperature of thermalized sputtered atoms since they are in thermal equilibrium with the buffer 17 gas. In terms of the energy of the sputtered atoms, an expected difference can be observed when the 18 gas pressure is increased; thermalized atoms are increased at a relatively high pressure (p=1. compared to the energetic atoms. Indeed, the sputtered atoms leaving the target with an average 1 energy of 4.0±0.2 eV (nitride mode, 3.2±0.2 eV in metallic mode) towards the substrate [START_REF] Revel | Transition from ballistic to thermalized 33 transport of metal-sputtered species in a DC magnetron Plasma Sources[END_REF] undergo 2 more collisions than at 0.4 Pa, efficiently transfer their energy to argon and nitrogen particles, and are 3 more thermalized when they reach the substrate position at p=1.3 Pa. 4

We calculated the deposition rate from the film thickness determined from the scanning electron mi-5 croscopy images. The flux of sputtered neutral Ti atoms ( 3 F2, 0 eV) was obtained from the AVDFs using 6 the following formula: 7

Ф 𝐽=2 (cm -2 s -1 ) = ∫ 𝑣 AVDF(𝑣) ∞ 0 𝑑𝑣, (1) 8
where, v is the axial velocity. Figure 3 (a) shows that the parameters, i.e., the flux of sputtered atoms 9 and the deposition rate, are in good agreement. 10

Because the TD-LIF measurements were performed on the lower level of the ground state (J = 2), we 11 assumed that neutral titanium atoms are in Boltzmann equilibrium and calculated the absolute value 12 of the flux of ground-state titanium atoms as 13

Ф absolute (cm -2 s -1 ) = Ф 𝑚 {1 + ∑ 𝑔 𝐽 𝑔 𝑚 exp (- 𝐸 𝐽 -𝐸 𝑚 𝑘 B 𝑇 ) 𝑚-1 𝐽=1 }, (2) 14
where EJ and gJ are the energy and statistical weight, respectively, of state J and kB is the Boltzmann 15 constant. The titanium ground state has a triplet structure, in which the levels J = 2, 3, and 4 are at 16 energies of 0, 0.021, and 0.047 eV, respectively. Therefore, Eq. ( 2) simplifies to 17

Ф absolute (cm -2 s -1 ) = Ф 𝐽=2 {1 + 𝑔 3 𝑔 2 exp (- 𝐸 3 -𝐸 2 𝑘 B 𝑇 ) + 𝑔 4 𝑔 2 exp (- 𝐸 4 -𝐸 2 𝑘 B 𝑇 )}.
(

3) 18

The temperature of the thermalized atoms was used to calculate the absolute flux of the Ti atoms. The 19 absolute flux and deposition rates are shown in figure 3 (b). The flux of Ti atoms reaching the substrate 20 at 2 % N2 and p = 0.4 Pa was 6.8×10 14 cm -2 s -1 and decreased to 5×10 14 cm -2 s -1 when 5 % N2 was added 21 to the gas mixture. Similarly, the deposition rate decreased from 1700 to 1350 nm h -1 when the gas 22 mixture varied from 2 to 5 % N2. By increasing the pressure p= 1.3 Pa, a slight decrease in the deposi-23 tion rate and Ti atoms flux was measured compared to p=0.4 Pa. The influence of the gas mixture was 24 similar at both pressures. These variations show good agreement between the flux and the deposition 25 rate for the 0.4 and 1.3 Pa pressures used in this work. In fact, increasing the percentage of nitrogen 26 induces poisoning of the target and decreases the number of sputtered titanium atoms, resulting in a 27 corresponding decrease in the deposition rate. In the studied pressure range, the pressure variation 28 slightly affected the deposition rate, whereas the sputtered atoms thermalization increased signifi-29 cantly when the pressure increased (figure 2). 30 As mentioned in the experimental section, TiN films were deposited in the dcMS discharge without 2 any heating or bias of the substrate. The Ar gas temperature was measured as a function of the dis-3 tance from the target using tunable diode laser absorption spectroscopy. It reaches a high 4 temperature of 1400 K near the target (z = 1.3 cm), but a low temperature of approximately 500 K was 5 measured at z = 5 cm [START_REF] Revel | Transition from ballistic to thermalized 33 transport of metal-sputtered species in a DC magnetron Plasma Sources[END_REF]. Under these conditions, the total energy flux towards the substrate is the 6 sum of the different contributions due to the kinetic energy of different deposited species. This section 7 reports the different contributions. 8

In dcMS using a balanced magnetron, the plasma is trapped close to the target surface, in which the 9 ion flux into the substrate decreases [START_REF] Anders | Tutorial: Reactive high power impulse magnetron sputtering (R-HiPIMS[END_REF]. Figure 4 shows the IEDFs of Ar + and N2 + at 0.4 Pa and 3 %N2 10 in gas mixture. The mass spectrometer signal represents the flux of ions, and two groups of ions arrive 11 at the substrate: the low-energy group (E < 6 eV) and high-energy group (E around 20 eV). The low-12 energy group of ions is thermalized with the buffer gas. The high-energy group has been studied in 13 many works, especially in HiPIMS discharge [START_REF] Maszl | Origin of the energetic ions at the substrate 10 generated during high power pulsed magnetron sputtering of titanium[END_REF][START_REF] Hecimovic | Anomalous cross-Bfield transport and spokes in HiPIMS plasma[END_REF][START_REF] El Farsy | Ionized particle 15 transport in reactive HiPIMS discharge: correlation between the energy distribution functions of neutral 16 and ionized atoms Plasma Sources[END_REF], and is generally attributed to ion acceleration 14 inside spokes in magnetron plasma. As shown in figure 4, the signal magnitude of this high-energy 15 group is three orders of magnitude lower than that of the thermalized ions. Thus, to calculate the 16 energy flux towards the substrate, only low-energy ions were considered. In an early study of Ar/N2 17 magnetron discharge, Petrov et al. [START_REF] Petrov | Mass and energy resolved detection of ions and neutral 1 sputtered species incident at the substrate during reactive magnetron sputtering of Ti in mixed Ar+N2 2 mixtures[END_REF] demonstrated that Ar + ions are the primary ions incident on 18 the substrate in Ar-N2 dcMS discharges, with a flux accounting for more than 92 % of the total ion flux 19 when the percentage of N2 was lower than 15 %. It worth to mention herein that ours mass spectrom-20 eter measurements are not calibrated. Thus, the corresponding ion energy flux to the substrate is 21 calculated using the following expression [START_REF] Bornholdt | Calorimetric Probes for Energy Flux Measurements in Process 18[END_REF]: 22

Ф 𝑒𝑛𝑒𝑟𝑔𝑦, 𝐴𝑟 + ( 𝑚𝑊 cm -2 ) = 1 4 𝑒 𝑛 𝑖 𝑣 𝑖 𝑉 (4) 23
where ni and vi are the ion density and thermal ion velocity, e is the electron charge and V is the voltage 24 drop in the substrate sheath. Bradley et al [START_REF] Bradley | Measurement of the plasma potential in a magnetron 21 discharge and the prediction of the electron drift speeds[END_REF] measured the ions density in dcMS with a cathode of 25 15 cm in diameter, 0.26 Pa argon pressure, and a dc power of about 1.5 W cm -2 , they found an ions 26 density of about 10 16 m -3 at z= 5 cm. In ours deposition system at z = 5 cm away from the target and 27 PDC =5 W cm -2 , we assumed an ion density of 2×10 16 m -3 and an ion temperature of 600 K [START_REF] Revel | Transition from ballistic to thermalized 33 transport of metal-sputtered species in a DC magnetron Plasma Sources[END_REF]. Based 28 on our mass spectrometer measurements of the thermalized ions (figure 4), the voltage drop at the 29 substrate sheath was estimated to be 3 V. For these plasma parameters, the energy flux corresponding 30 to the ion contributions (equation 4) is approximately 0.075 mW cm -2 . 31

Regarding the energy flux of the electron contribution, the energetic secondary electrons accelerated 32 in the cathode sheath are trapped near the cathode surface for ionization by the magnetic field, and 33 only thermalized electrons can reach the substrate. Our substrate was grounded, and because the 34 plasma potential at z = 5 cm was positive, the thermalized electrons were pushed away from the sub-35 strate. Therefore, their energy flux contributions can be neglected. 36

2

For the neutral species reaching the substrate, the energy flux deposited by Ti atoms (J=2) is obtained 3 as follows: 4

Ф 𝑒𝑛𝑒𝑟𝑔𝑦,𝐽=2 = ∫ 1 2 𝑀 𝑣 2 𝑣 AVDF(𝑣) ∞ 0 d𝑣 , (2) 5
where M (amu) is the atomic mass of titanium and v is the axial velocity. The total energy flux of the 6 ground state Ti atoms was then deduced by applying equation (3). Figure 5 shows the variations in the 7 energy flux of the ground state of the neutral Ti atoms and Ar + ions as a function of the nitrogen per-8 centage. At p = 0.4 Pa, the energy flux gradually decreases from 0.27 to 0.20 mW cm -2 when the 9 nitrogen percentage increases from 2 to 5 %. This decrease was mainly due to the decrease in the 10 number of Ti-neutral atoms reaching the substrate. However, at p = 1.3 Pa, where the vapor is more 11 thermalized, the energy flux is one order of magnitude lower than that measured at 0.4 Pa. It is on the 12 order of 0.03 mW cm -2 . The most important result is that the energy flux of sputtered Ti atoms is 13 higher than that of Ar + ions at a low magnetron pressure of 0.4 Pa. Other sputtered species, such as 14 nitrogen atoms (N), could contribute to the energy flux towards the substrate, and its behavior as a 15 function of pressure is expected to be similar to that of neutral Ti atoms. The knowledge of their en-16 ergy flux requires further investigation. In other deposition system, Gauter et al. [START_REF] Gauter | Direct calorimetric measurements in a PBII and deposition 23 (PBII&D) experiment with a HiPIMS plasma source[END_REF] used direct 17 calorimetric probe to characterize the energy flux on the substrate during the deposition by HiPIMS 18 discharge with copper magnetron, they measured an averaged energy flux of 20 mW cm -2 . Calorimet-1 ric probe was also used by Bornholdt et al. [START_REF] Bornholdt | Characterization of the 25 energy flux toward the substrate during magnetron sputter deposition of ZnO thin films Plasma Sources 26[END_REF] to energy flux during the deposition of ZnO by a radio-2 frequency discharge of 15 W cm -2 (3 target with 5 W cm -2 ), they found a total energy flux of 30 mW 3 cm -2 . In those calorimetric probe experiments, the energy flux is higher than the obtained by our di-4 agnostics because (i) their measurements consider the contributions of all species arriving to the 5 substrate, (ii) the discharge power is higher than used in our work and (iii) the zinc and copper have 6 higher sputtering efficiency compared to titanium. 7 8

10

A. Film composition 11

Measurement of the chemical composition of thin films is not an easy task when the films contain light 12 elements, such as nitrogen. The TiN samples deposited were analyzed using EPMA, and the percent-13 ages of O, Ti, and N were obtained. The quantitative results are summarized in Table 2. For Ti and N, 14 the films are quasi-stoichiometric for both pressures (0.4 and 1.3 Pa). The Ti and N concentrations 15 were approximately 48 and 50 at. % at respectively for the films at 0.4 Pa. At 1.3 Pa, the Ti concentra-16 tion was 48 at. % and the N concentration is 46 at. %. Concerning the oxygen contamination, EPMA 17 measurements show that the concentration of O element increases in the films from 2 at. % at 0.4 Pa 18 to 6 at. % at 1.3 Pa. This contamination can be attributed to the residual oxygen in the chamber. Be-19 cause the amount of oxygen in the chamber is constant and weak, the increase in oxygen 20 concentration with the pressure is due to the decrease in the deposition rate. Indeed, films that grow 21 at a low deposition rate contain more oxygen. However, the deposition rate at 1.3 Pa is about 85% of 22 the deposition rate at 0.4 Pa. This decrease seems rather small to explain the increase of O concentra-23 tion, from 2 to 6%. The higher oxygen concentration seems induced by film density (denser at 0.4 Pa) 24 or by the plasma variation especially the electron density and temperature assuming that the oxygen 1 atoms are produced by the dissociation of oxygen molecule by electron impact. 2 planes exhibited the highest intensity for all percentages of N2 investigated. We also observed the 12 quasi-absence of the (200) planes. The two preferred orientations have different surface energies. In 13 fact, the family of (111) planes has an atom density greater than that of (200) planes, thus inducing a 14 lower surface energy of the (111) planes. Therefore, we can consider that the latter are more stable 15 and require less energy to be produced than the (200) plane. Thus, the preferred (111) orientation is 16 the result of deposition under conditions close to equilibrium [START_REF] Ehiasarian | Influence of high power 35 impulse magnetron sputtering plasma ionization on the microstructure of TiN thin films[END_REF]. Because the TiN films were depos-17 ited at ambient temperature and without substrate bias, the texture variation could only be affected 18 by the energy flux of the arriving species and the chemical composition of the films. 19 20

23

The gas composition and total pressure influence the number of sputtered Ti neutral atoms reaching 24 the substrate position (figure 3) and substantially affect the energy flux of neutral-sputtered Ti atoms 25 (figure 5). It should be noted that films with similar chemical compositions have different preferred 26 orientations. The preferred orientation has been studied in many previous works on dcMS under dif-1 ferent energetic ion bombardment conditions [START_REF] Ehiasarian | Influence of high power 35 impulse magnetron sputtering plasma ionization on the microstructure of TiN thin films[END_REF][START_REF] Cemin | Low-energy ion irradiation in HiPIMS to enable anatase TiO2 selective growth[END_REF][START_REF] Magnus | Morphology of TiN thin 31 films grown on SiO2 by reactive high power impulse magnetron sputtering[END_REF][START_REF] Viloan R P B | Bipolar high power impulse magnetron 33 sputtering for energetic ion bombardment during TiN thin film growth without the use of a substrate bias 34[END_REF], and it is well known that by increasing the ion 2 energy at the substrate, the preferred orientation switches from [111] to [200]. As shown in figure 5 XRD instrument was performed using the (004) diffraction peak observed from the Si substrate for all 2 samples (figure 6). The films deposited at 0.4 Pa exhibit a lattice constant around 4.24 Å. The lattice 3 constant of bulk TiN is 4.24 Å in the absence of stress. An increase in the nitrogen ratio in the gas 4 mixture from 2 % to 5 % induced a slight decrease in the lattice constant from 4.240 Å to 4.235 Å. This 5 decrease may be related to a slight variation in the concentration of N in the film, which was not 6 detected by EPMA. However, for the films deposited at 1.3 Pa the lattice parameter was approximately 7 4.215 Å, suggesting the presence of tensile stress in the films. As shown in figure 4, the energy flux of 8 sputtered Ti atoms at 0.4 Pa is one order of magnitude higher than at 1.3 Pa. Therefore, the high-9 energy flux of Ti atoms seems to allow stress removal in films at low pressures. 10 AFM measurements were performed to determine the morphology and roughness of the film surfaces 11

(figure 8). The films deposited at 0.4, 1.3 Pa, and 3 % N2 with approximately similar thicknesses (~ 2.9 12 m) were characterized. The film deposited at low pressure exhibited a very high roughness (RMS 13 surface roughness = 67 nm). The surface of this film showed large faceted grains, in agreement with 14 the XRD results. On the other hand, the film deposited at 1.3 Pa show a lower roughness (RMS surface 15 roughness = 11 nm) and small grains. Once again, the difference in the film surface morphology may 16 be explained by the high energy flux of sputtered Ti atoms at 0.4 Pa. 17

21

IV. Conclusion 22

The neutral titanium sputtered atoms velocity distribution functions (AVDFs) at the substrate position [START_REF] Petrov | Mass and energy resolved detection of ions and neutral 1 sputtered species incident at the substrate during reactive magnetron sputtering of Ti in mixed Ar+N2 2 mixtures[END_REF] were measured by a tunable diode laser induced fluorescence (TD-LIF) technique in direct current 24 magnetron sputtering (dcMS) discharge and correlated to the TiN thin film properties. The measured 1 velocity was perpendicular to the substrate (axial velocity in a planar circular magnetron). The flux of 2 the sputtered particles was then calculated and correlated with the deposition rate. Their evolutions 3 as a function of the N2 content in the gas mixture are in good agreement. TiN thin films were deposited 4 at 0.4 and 1.3 Pa, for different gas mixtures Ar/N2 close to the conditions where stoichiometric TiN was 5 formed, without bias voltage and heating of the substrates. Their microstructure, texture, and chem-6 ical composition were characterized using X-ray diffraction, EPMA. The films deposited at a low 7 pressure (0.4 Pa) show a [200] preferred orientations. For 1.3 Pa, the films were oriented along the 8

[111] direction and tensile stress was observed. Because the film growth was carried out without bias 9 and heating of the substrate, we studied the influence of the energy flux (i.e., the product of particle 10 flux and incident particle energy) of sputtered atoms deduced from TD-LIF measurements on the film 11 properties. At a relatively low magnetron discharge pressure of 0.4 Pa, we found that the energy of 12 the ground state of sputtered neutral Ti impinging on the substrate is higher than the energy flux of 13 ionized particles corresponding mainly to Ar + . This high energy flux of sputtered neutral atoms allows 14 the growth of TiN oriented along the [111] direction. In addition, it allows stress removal in the films. 15 At 1.3 Pa where the sputtered atoms energy flux is one order lower compared to 0.4 Pa the (111) 16 texture was obtained. 17 18

Figure 1 .

 1 Figure 1. Schematic of the experimental setup. The cathode magnetron is in position ① to measure titanium

  1

Figure 2 .

 2 Figure 2. TD-LIF signal of the neutral Ti(J=2) atoms as a function of the percentage of N2 in gas mixture at

4

 4

  Axial velocity (km/s)

31 1 2 Figure 3 . 4 PDC = 5 W

 312345 Figure 3. Variation of the flux of neutral Ti atoms [(a) J=2 level, (b) the absolute flux of neutral Ti] and the

III- 2 .

 2 Influence of deposited energy on the film microstructure, texture, and morphology 1

Figure 4 .

 4 Figure 4. IEDFs of Ar + and N2 + ions at z = 5 cm, 3 % N2, PDC = 5 W cm -2 , and p = 0.4.

Figure 5 .

 5 Figure 5. Energy flux of neutral of the ground state of Ti sputtered atoms as function of the percentage of N2 in

2 F

 2 energy (Ti) -0.4 Pa F energy (Ti) -1.3 Pa F energy (Ar + )

Figure 6

 6 Figure 6 shows the θ-2θ X-ray diffractograms of TiN films deposited in dcMS discharge for different 6 gas mixtures at pressures of 0.4 and 1.3 Pa. All films exhibited characteristic diffraction peaks corre-7 sponding to polycrystalline TiN with a cubic (NaCl-type) structure. At 0.4 Pa, the thin films exhibit a 8 mixed orientation with the (111) and (200) planes. Other planes with negligible intensities were de-9 tected and are not shown here. At 0.4 Pa, we observed that the (111) and (200) planes co-existed, but 10 the peak corresponding to the (200) planes was highly dominant. At 1.3 Pa, we observed that the (111) 11planes exhibited the highest intensity for all percentages of N2 investigated. We also observed the 12 quasi-absence of the (200) planes. The two preferred orientations have different surface energies. In 13 fact, the family of (111) planes has an atom density greater than that of (200) planes, thus inducing a 14 lower surface energy of the (111) planes. Therefore, we can consider that the latter are more stable 15 and require less energy to be produced than the (200) plane. Thus, the preferred (111) orientation is 16 the result of deposition under conditions close to equilibrium[START_REF] Ehiasarian | Influence of high power 35 impulse magnetron sputtering plasma ionization on the microstructure of TiN thin films[END_REF]. Because the TiN films were depos-17 ited at ambient temperature and without substrate bias, the texture variation could only be affected 18 by the energy flux of the arriving species and the chemical composition of the films. 19

Figure 6 .

 6 Figure 6. θ-2θ X-ray diffractograms of TiN films deposited by dcMS as a function of the percentage of N2 in the

2 Figure 7 .

 27 Figure 7. Variations of crystallite size (a) and lattice parameter (b) as function of the percentage of N2 in the gas

3

  mixture, in dcMS process.

4

  Similarly, peak fitting was used to calculate the lattice parameter, considering the shift in the 5 diffraction angle in the Bragg equation [figure7 (b)]. This was possible because the calibration of the 1

18 19Figure 8 .

 188 Figure 8. AFM images of the surface of the samples deposited in dcMS, at 2 % N2 in the gas mixture and p = 0.4

[ 7 ] 3 [ 8 ] 5 [ 9 ] 6 tific 35 dcMS

 73859635 Cemin F, Abadias G, Minea T and Lundin D 2019 Tuning high power impulse magnetron sputtering dis-1 charge and substrate bias conditions to reduce the intrinsic stress of TiN thin films Thin Solid Films 688 2 137335 Benedikt J, Kersten H and Piel A 2021 Foundations of measurement of electrons, ions and species fluxes 4 toward surfaces in low-temperature plasmas Plasma Sources Sci. Technol. 30 033001 Stahl M, Trottenberg T and Kersten H 2010 A calorimetric probe for plasma diagnostics Review of Scien-Instruments 81 023504 7 [10] Abolmasov S N, Cormier P A, Torres Rios A, Dussart R, Semmar N, Thomann A L and Roca i Cabarrocas P 8 2012 Probing dusty-plasma/surface interactions with a heat flux microsensor Appl. Phys. Lett. 100 011601 9 [11] Trottenberg T and Kersten H 2017 Measurement of forces exerted by low-temperature plasmas on a 10 plane surface Plasma Sources Sci. Technol. 26 055011 11 [12] Mahieu S and Depla D 2009 Reactive sputter deposition of TiN layers: modelling the growth by charac-12 terization of particle fluxes towards the substrate J. Phys. D: Appl. Phys. 42 053002 13 [13] Farsy A E, Ledig J, Desecures M, Bougdira J and Poucques L de 2019 Characterization of transport of tita-14 nium neutral atoms sputtered in Ar and Ar/N2 HIPIMS discharges Plasma Sources Sci. Technol. 28 035005 15 [14] Desecures M, de Poucques L, Easwarakhanthan T and Bougdira J 2014 Characterization of energetic and 16 thermalized sputtered atoms in pulsed plasma using time-resolved tunable diode-laser induced fluores-17 cence Applied Physics Letters 105 181120 18 [15] Desecures M, Poucques L de and Bougdira J 2014 Characterization of energetic and thermalized sputtered 19 tungsten atoms using tuneable diode-laser induced fluorescence in direct current magnetron discharge 20 Plasma Sources Science and Technology 24 015012 21 [16] Vitelaru C, Aniculaesei C, de Poucques L, Minea T M, Boisse-Laporte C, Bretagne J and Popa G 2010 Tun-22 able diode-laser induced fluorescence on Al and Ti atoms in low pressure magnetron discharges Journal 23 of Physics D: Applied Physics 43 124013 24 [17] Held J, Hecimovic A, von Keudell A and Schulz-von der Gathen V 2018 Velocity distribution of titanium 25 neutrals in the target region of high power impulse magnetron sputtering discharges Plasma Sources Sci-26 ence and Technology 27 105012 27 [18] Britun N, Palmucci M and Snyders R 2011 Fast relaxation of the velocity distribution function of neutral 28 and ionized species in high-power impulse magnetron sputtering Applied Physics Letters 99 131504 29 [19] Fekete M, Hnilica J, Vitelaru C, Minea T and Vašina P 2017 Ti atom and Ti ion number density evolution in 30 standard and multi-pulse HiPIMS Journal of Physics D: Applied Physics 50 365202 31 [20] Viloan R P B, Lundin D, Keraudy J and Helmersson U 2020 Tuning the stress in TiN films by regulating the 32 doubly charged ion fraction in a reactive HiPIMS discharge Journal of Applied Physics 127 103302 33 [21] Ghailane A, Larhlimi H, Tamraoui Y, Makha M, Busch H, Fischer C B and Alami J 2020 The effect of mag-34 netic field configuration on structural and mechanical properties of TiN coatings deposited by HiPIMS and Surface and Coatings Technology 404 126572 36 [22] Ghailane A, Oluwatosin A O, Larhlimi H, Hejjaj C, Makha M, Busch H, Fischer C B and Alami J 2022 Titanium

  37 nitride, TiXN(1-X), coatings deposited by HiPIMS for corrosion resistance and wear protection properties 38 Applied Surface Science 574 151635 39

Table 1 .

 1 Summary of deposition conditions for the various realized coatings: reactive gas mixture, pressure,

	18	(b)]. No substrate bias or external heating was applied to the substrate during
	19	the film growth. The energy source on the substrate comes only from the deposited species, which
	20	are characterized by the diagnostic methods described below. Prior to deposition, all the substrates
	21	were ultrasonically cleaned in acetone for 10 min and ethanol for 10 min. Table 1 summarizes the
	22	deposition conditions.
	23
		cathode voltage and film thickness.

Table 2 .

 2 Concentration of Ti, N, and O elements measured with EPMA (top) for the samples deposited at 3%N2.

	3
			Ti	N	O
		0.4 Pa	50 ±1 %	48 ±1 %	2 ±1 %
		1.3 Pa	48 ±1 %	46 ±1 %	6 ±1 %
	4
	5	B. Film texture, microstructure, and morphology

Acknowledgments 19

The authors thank Mrs. Christine Gendarme and Mr. Denis Mangin from the Centre de Compétences 20 3M of the Institut Jean Lamour for WDS analyse. The Centre de Compétences X- of the Institut Jean 21

Lamour is also acknowledged for the access to the X-ray diffractometers. 22


Morgane Koval

Yvonne Jansen

How to Visualize Food Quantities to Prevent Food Waste? Examples and Challenges

Keywords:

Food quantity management involves planning and predicting in one's daily life. One has to estimate how much needs to be bought, how much the people eating together will want to eat, and how much needs to be prepared to have enough but not too much either. Wasting food raises sustainability and financial challenges. We present some of the issues linked to poor food management and then suggest two ways in which visualization may address two of them: over-buying and over-preparing. Finally, we discuss current limitations in order to identify future directions and research questions.

INTRODUCTION

Food is embedded in our everyday lives: we need it to survive. Whether consumed out of necessity or pleasure, poor food management leads to poor consequences. Throwing away food wastes money and resources, resulting in both financial and ecological repercussions. In 2011, the FAO reported that one third of the food produced ended up wasted. In 2016, the European report of the FUSIONS project indicated that 53% of food waste came from households. Reducing this waste thus appears relevant to address the problem of climate change. Here we focus on small individual actions by supporting a better food management to reduce food waste at the household level. We introduce two cases in which such visualizations could be used to help manage food quantity and discuss the existing challenges of designing such solutions.

FOOD WASTE

Many individual behaviors lead to food waste. For instance, overprovisioning, i.e., when purchases exceed needs, is a common behavior [START_REF] Evans | Beyond the Throwaway Society: Ordinary Domestic Practice and a Sociological Approach to Household Food Waste[END_REF][START_REF] Ganglbauer | Why and What Did We Throw out? Probing on Reflection through the Food Waste Diary[END_REF][START_REF] Hebrok | Household food waste: Drivers and potential intervention points for design -An extensive review[END_REF][START_REF] Parfitt | Food waste within food supply chains: quantification and potential for change to 2050[END_REF][START_REF] Schanes | Food waste matters -A systematic review of household food waste practices and their policy implications[END_REF] when grocery shopping. However, food is also wasted after being cooked due to over-preparing, i.e., too large portions are prepared. While leftovers may be put aside, some people report a aversion towards them, also leading to waste [START_REF] Hebrok | Household food waste: Drivers and potential intervention points for design -An extensive review[END_REF][START_REF] Schanes | Food waste matters -A systematic review of household food waste practices and their policy implications[END_REF].

What solutions then? Ens and Irani [START_REF] Ens | Spatial analytic interfaces: Spatial user interfaces for in situ visual analytics[END_REF] described a scenario in which someone wants to compare prices to their budget, and ElSayed et al. [START_REF] Elsayed | Situated analytics: Demonstrating immersive analytical tools with augmented reality[END_REF] studied a system that would help people make faster comparisons and decisions while grocery shopping. Even though, these researches were not motivated by food waste, they could be applied to the over-provisioning issue. We build on the latter example in the next section to illustrate how visualization could benefit our research's focus. Regarding over-preparing, some approaches have suggested community involvement. For instance, apps can connect individuals to share leftovers or other food items that would otherwise be lost [START_REF] Farr-Wharton | Food Talks Back: Exploring the Role of Mobile Applications in Reducing Domestic Food Wastage[END_REF]. However, food sharing also requires trust: do we want to take food from strangers [START_REF] Katzeff | Share or waste? : Using an ICT-platform to share food on a university campus[END_REF]? * e-mail: morgane.koval@inria.fr † e-mail: yvonne.jansen@cnrs.fr

VISUALIZATION EXAMPLES FOR FOOD QUANTITIES

We focus on the management of food quantities because it can be difficult to gauge how much food is needed for a meal, especially when trying out a new recipe, or when cooking for multiple people. Our goal is to highlight opportunities for visualization to assist in food management and ultimately in reducing household food waste. We use the example of Julia, a woman who lives alone but regularly has guests for whom she cooks.

She invited three friends over and is thus going to the grocery store in order to buy the necessary food items for a specific recipe she has in mind. Similar to the system studied by ElSayed et al. [START_REF] Elsayed | Situated analytics: Demonstrating immersive analytical tools with augmented reality[END_REF], the goods written on her shopping list are highlighted while she looks at different shelves so as not to be tempted by special offers and buy unnecessary items. When several products of the same type are available, she can compare them: the overall quantity expressed as the number of average meals for one person is displayed for each item she holds. Having 3 guests, Julia selects the one that shows 4 portions to avoid over-provisioning. However, in the next aisle, several products share the same quantity. In that case, the price and the composition are put forward instead and Julia can make a choice according to her budget and the diet of her guests. Once back home, Julia starts preparing the meal and only has access to the products she just bought along with those already in her cupboards. She wants to avoid generating leftovers since she knows that she likely will not eat them later. She puts all the ingredients that she intends to include in her recipe on her counter and checks the predicted final quantity (see Fig. 1). The prediction is based on data from her previous inputs, that is, how much she actually eats on average, but other criteria can also be included such as calorie counts or specific amounts of a given nutrient. With the current parameters, the system has already learned from her eating habits, so Julia is confident that the recommended amount is reasonable. She thus removes a zucchini from her work surface to meet the recommended goal. Julia notices over time that her predicted quantities are getting closer to the recommended quantity. As such, she believes she will soon be able to prepare suitable amounts of food without it, although she prefers to use it when inviting guests because she finds the task more difficult and more uncertain.

The rise and constant development of new technologies opens new doors, but which one to adopt? We described two types of use in the previous section, omitting the visualization system: is it augmented reality? Is it virtual reality? Should we stay on a screen with a 2D representation? Should we make use of the convenience of smart phones? Understanding the effects of these different technologies on the effectiveness of the visualization is essential in order to select the most appropriate one. This raises the question of how food quantities should be represented. While the perception of classic 2D shapes have been studied in detail [START_REF] Cleveland | An experiment in graphical perception[END_REF], food quantities may require different representations, possibly using concrete scales [START_REF] Chevalier | Using concrete scales: A practical framework for effective visual depiction of complex measures[END_REF] or more abstract 3D shapes. In the previous scenario, for example, we could choose between a realistic or an abstract representation of food quantity (see Fig. 1 and Fig. 2). Moreover, the computation of the final food quantities given raw ingredients would produce uncertainty (because goods are transformed, because some weight is lost when peeling or cooking vegetables for instance). We thus may need predictive visualizations, which are "uncertainty visualizations that show plausible outcomes" [START_REF] Koval | Do You See What You Mean? Using Predictive Visualizations to Reduce Optimism in Duration Estimates[END_REF]. We can take inspiration from existing work on how to represent uncertainty [START_REF] Fernandes | Uncertainty displays using quantile dotplots or CDFs improve transit decision-making[END_REF][START_REF] Greis | Investigating Representation Alternatives for Communicating Uncertainty to Non-experts[END_REF][START_REF] Kale | Visual Reasoning Strategies for Effect Size Judgments and Decisions[END_REF][START_REF] Kay | When (Ish) is My Bus? User-Centered Visualizations of Uncertainty in Everyday, Mobile Predictive Systems[END_REF], but studies investigating specifically how to display uncertainty for food quantities are still needed. Figure 2 presents potential designs. Finally, when designing for sustainability, one must take into account the system's impact on the environment: even if we manage to waste less food thanks to new technology, what is the net environmental cost? Would it be preferable to still waste some food? Or is the impact of such a system insignificant compared to food waste?

CONCLUSION

Food waste plays an important role in the current ecological crisis. We have described two everyday-life situations in which visualization may be able to assist in the management of food quantities, first during shopping and then when preparing a dish, but these could also apply when ordering at a restaurant or through food delivery apps. However, for such a system to be effective, issues such as what technology to use and how to appropriately represent these food quantities must be addressed.

Figure 1 :

 1 Figure1: On the left are the ingredients and on the right is a realistic representation of the predicted amount of food that would be produced with a red overlay to designate the surplus amount compared to the recommended quantity.

Figure 2 :

 2 Figure 2: Examples of abstract visualization representing predicted and recommended food quantities: (1) simple 2D bar chart ; (2) colored 3D bar chart ; (3) detailed diagram with nutrients ; (4) horizontal bar with uncertainty ; (5) cylinder with uncertainty.

ACKNOWLEDGMENTS

This work is part of the ANR Ember project, supported by a grant from Agence Nationale de Recherche (ANR-19-CE33-0012).


Sebastien Chalies
email: sebastien.chalies@univ-tlse2.fr

Sébastien Chaliès

Stefano Bertone

Prof Sébastien Chaliès

And if L. Wittgenstein helped us to think differently about teacher education?

Keywords: cultural anthropology, subjectivization, rules, subject, teacher education

HAL is a

Introduction

This article outlines a "research program" [START_REF] Lakatos | Histoire et méthodologie des sciences[END_REF] that has been inspired essentially by the analytical philosophy of Ludwig Wittgenstein and developed over the past fifteen years in the field of teacher education. As part of a broad enterprise in "culturalist anthropology" (e.g., [START_REF] Bertone | Contribution of an action theory for conceptualizing and evaluating reflexive practices in the initial training of teachers[END_REF][START_REF] Chaliès | Training teachers to improve their job satisfaction: theoretical proposals and empirical illustrations[END_REF][START_REF] Chaliès | Learning 'rules' of practice within the context of the practicum triad: A case study of learning to teach[END_REF] to study the construction of the subject in the context of professional education, the program grew out of a "core theory" [START_REF] Lakatos | Histoire et méthodologie des sciences[END_REF] and its main theoretical hypotheses: (i) the immanence of the subject is revealed by and through language experiences (Chauviré, 2009;[START_REF] Proudfoot | Meaning and mind: Wittgenstein's relevance for the "Does language shape thought? debate[END_REF][START_REF] Taylor | La liberté des modernes[END_REF], (ii) individuation leads to subjectivization (Laugier, 2010;[START_REF] Macherey | De Canguilhem à Foucault : la force des normes[END_REF] and (iii) subjectivization occurs by following rules and/or performing the actions governed by them [START_REF] Butler | The psychic life of power[END_REF]. As in any research program, the studies as a whole seek to stabilize these "hard core" assumptions and extend them through new "auxiliary" hypotheses [START_REF] Lakatos | Histoire et méthodologie des sciences[END_REF].

With respect to the theme of this collection of works, we present two of the theoretical hypotheses currently being explored in our research program, and they constitute the conceptual framework for this article. The original methodologies used in the empirical studies to (in)validate these hypotheses are then detailed. Last, these theoretical and methodological proposals are illustrated by a number of empirical results taken from studies in the field of teacher education.

Theoretical framework

The two theoretical hypotheses were chosen because the empirical results thus far been suggest that they are appropriate heuristics for addressing many of the problems in teacher education today. A notable issue that deserves attention is how to effectively implement the principle of alternation between the sequences of education at the university and in the schools with the sequences of classroom work.

First theoretical hypothesis

In this theoretical presentation, teaching someone (or being taught) how to teach means that the person will (learn to) carry out actions governed by "rules" (Wittgenstein, 1996, § §145-242) and/or (learn to) identify those actions that the community of teachers considers as exemplifying the rules of their profession. These rules have nothing to do with the "situated normative experiences" [START_REF] Lähteenmäki | On rules and rule following: Obeying rules blindly[END_REF] that are accepted by the community as rendering each teacher's actions intelligible, anticipatable, and evaluable [START_REF] Livet | Théorie de l'action et conventions[END_REF]. They instead carry the weight of authority as standards of correct practice within the community. Yet applying the rules can in no way be dictated, as every teacher who follows them is free at any moment to deviate from them, transgress them, or even refuse to follow them [START_REF] Descombes | Le complément de sujet. Enquête sur le fait d'agir soi-même[END_REF]. For preservice teachers (PTs), these rules are a kind of experiential "grammar," not yet fully mastered but useful in helping them to recognize and/or judge how well their actions [START_REF] Berducci | Vygotsky through Wittgenstein: A new perspective on Vygotsky's developmental continuum[END_REF] conform to professional prescriptions [START_REF] Clot | Travail et pouvoir d'agir[END_REF]. Nevertheless, this experiential grammar is certainly not the be-all and end-all, to be learned and interiorized as a precondition to being able to teach day after day. It is instead an "arbitrary reality" [START_REF] Searle | Construction of Social Reality[END_REF] composed of a complex system of endlessly shifting rules, constantly overwhelmed by the singularity of the situations and unexpected circumstances of teaching. What makes teacher education activities difficult from this theoretical perspective are the two registers of meaning and the heterogeneous, relatively autonomous actions.

(i) The first register of meaning is related to the emergence of normative capacities, which reveal "in some respects" the professional skills that make it possible to reduce dissimilarities between singular situations and see the "family resemblance" (Wittgenstein, 1996, § §46-49, § §67-73). Situational regularities can be identified and the teacher is able to consider the circumstances as meaningful with regard to a system of rules that is being "played out" at a given instant and a given context [START_REF] Du | La nature sociale de l'esprit[END_REF]. At this level, the normative capacities that have been developed let the teacher sample the lived experience, identify it as being more or less emblematic of the teaching profession, and make judgments on the pertinence, correctness or meaning of the actions being observed or carried out [START_REF] Descombes | Le complément de sujet. Enquête sur le fait d'agir soi-même[END_REF].

(ii) The second register of meaning is related to carrying out the actions that "significant others" (the other members of the teaching community) consider satisfactory and meaningful in an established context. In this register, reflexivity is a kind of self-presence [START_REF] Legrand | Pre-reflective self-as-subject from experiential and empirical perspectives[END_REF] that mobilizes neither symbolic representations nor clear awareness of what the actors are in the midst of doing. The meaning of an event becomes "transparent" only at the moment where it is apprehended in the course of action. Action is thus "governed by rules" (Wittgenstein, 1996, §219).

In this conception, alternation can be characterized by the activities in which each PT deploys a dual register of reflexivity [START_REF] Ogien | Les formes sociales de la pensée[END_REF].

(i) In classroom teaching situations, PTs are engaged in situated interactions with students and make decisions based on prereflexive consciousness. They carry out actions governed by rules, with these rules being "inherent" to action [START_REF] Ogien | Les formes sociales de la pensée[END_REF]. Preconscious rules can nevertheless be the object of reflexive activity in post-lesson training. These rules are indeed potentially sayable either because they were learned in earlier reflexive training or because learning them has occurred implicitly within a community of practice [START_REF] Lave | Situated learning: Legitimate peripheral participation[END_REF] through nonverbal interactions and/or informal alignments with the observed practices of other teachers [START_REF] Rogoff | Models of teaching and learning: participation in a community of learners[END_REF].

(ii) In other situations, PTs are engaged in dialogic activities or interactions whose object is classroom teaching as part of teacher education. The activities have characteristics that approach the idea of "consciousness as liaison" [START_REF] Vygotski | Conscience, inconscient, émotions[END_REF] wherein the PTs use a register of reflexivity on the order of "apprehending the inherent" [START_REF] Ogien | Les formes sociales de la pensée[END_REF]. In the course of these interactions, both verbal and nonverbal, they carry out actions of "following" the work rules, which enable them to identify, describe, comment on, and analyze lived experience. They thus act in accordance with the rules that are, at a given instant, both conscious and sayable because they have been learned in earlier reflexive training and through dialogic re-elaborations. Teacher education at the university and/or in the schools (e.g., during post-lesson interviews with the cooperating teacher (CT)) mainly call on this register of reflexivity. In order to understand the outcomes and limitations of this register, certain characteristics should be detailed.

Second theoretical hypothesis

In order for PTs to engage in reflexive thinking about their classroom work, they first need to learn the rules so that they can correctly assign meaning to their experiencesthat is, meaning in line with the expectations of the teaching community. Theoretically, learning these rules requires that the university supervisors (USs) or CTs engage in "ostensive teaching" (Wittgenstein, 1996, §6) by which they teach the meaning of those experiences considered as exemplary of the work rules. A US or CT will indeed judge a PT's action as inadequate by referring to the rules that structure the meaning of the teaching profession and that thus serve as yardsticks for measurement. For each of these experiences, judged and/or taught, the US or CT creates "meaningful links" (Bertone et al., 2009) that associate (i) a language experience that names a fact or action, (ii) examples that are described, shown and/or demonstrated, and used as samples or emblematic examples, and (iii) the results that are usually associated or expected in the teaching community. The meaningful links taught by the US or CT can then become real "benchmark" experiences [START_REF] Williams | Is everything interpretation?[END_REF] as PTs interact in the training situation and/or act in the classroom.

They are able to build on these samples of exemplary experience to give meaning to and judge observed events. This step is nevertheless not sufficient [START_REF] Bertone | Co-analysis work in the triadic supervision of preservice teachers based on neo-Vygotkian activity theory: case study from a French university institute of teacher training[END_REF], and theoretically the US or CT must next engage in a new activity of supporting the PTs as they begin to follow the rules [START_REF] Chaliès | Training teachers to improve their job satisfaction: theoretical proposals and empirical illustrations[END_REF]. Through this support, the US or CT not only makes it possible for the PTs to carry out the expected actions (e.g., by arranging the work situation), but they also and above all ensure that these first steps in following the rules lead to the usually associated and expected results. Only by observing these results will the PTs be able to relate a practical work intention to a rule that was taught [START_REF] Cash | Normativity is the mother of intention: Wittgenstein, normative practices and neurological representations[END_REF], and this connection is far from obvious: the intention to obtain the result cannot logically precede the expected action, prescribed by the US or CT but hitherto unknown to the PT, both in its execution and in its positive or negative outcome.

It is thus by correctly following the rules that were taught and observing the expected results in the classroom that the PTs complete their learning and can develop professionally and subjectively within the rules [START_REF] Nelson | Wittgenstein and contemporary theories of word learning[END_REF]. During these first efforts at rule following, the US or CT "monitors" compliance and intervenes, if necessary, with "ostensive explanation" [START_REF] Davis | Examples as method? My attempts to understand assessment and fairness in the spirit of the later Wittgenstein[END_REF]. This is accomplished by multiplying the examples described, shown and/or demonstrated so as to remove any possible misinterpretation [START_REF] Chaliès | Learning 'rules' of practice within the context of the practicum triad: A case study of learning to teach[END_REF]. It is only at this point, when the rules have been learned, that the PTs can free themselves from the control of the community members. They are now able to build a system for interpreting the rules [START_REF] Winch | L'idée d'une science sociale et sa relation à la philosophie[END_REF] that authorizes an "extended" use of the meaningful links outside of the original situations in which they were learned. This extended use is based on the identification of a "family resemblance" between the circumstances of the current situation and those of the original training situation.

From these meaningful links, the PTs are finally able to organize a complex network of similarities, "understand" the new situation as it unfolds, and ultimately succeed in producing activities consistent with community expectationsall while gradually freeing themselves from the control of the teaching community. In these situations, the US or CT helps the PTs to engage in highly personal instances of following the rules and to experiment with their original meaning [START_REF] Butler | The psychic life of power[END_REF]) so as to be optimally equipped to adapt them to the ever-shifting circumstances of teaching.

Method

Essentially the same methods are used for all the studies in the research program [START_REF] Bertone | Construire un programme de recherche technologique sur la formation des enseignants : choix épistémologiques et théoriques[END_REF]. In all cases, four successive steps are respected.

Step 1: Establishing the research conditions

In this step, the researchers (Rs) (i) define a new hypothesis derived from the core hypotheses of the research program and (ii) select a field of potential study. They thus formalize a new hypothesis from the results of previous work. They then identify a professional education program as a potential field of study, and they proceed to an inventory and review of the international literature in the field of study.

Step 2: Establishing the research-working conditions

In this step, the Rs meet with the actors (US, CT and/or PT) in the selected program to present the hypothesis and the field of study. At this time, they are attentive to the actors' concerns or "requests for assistance." The Rs and the actors then agree to engage in (in)validating the hypothesis and finding solutions to some of the concerns.

Step 3: Data collection and processing

For each study, two types of data are collected and transcribed verbatim.

(i) "Extrinsic" data, usually audio-video recordings, are collected at each stage of the study using a video camera and a wireless microphone worn by each actor.

(ii) "Intrinsic" data are collected from the audio-video recordings of self-confrontation interviews (SCIs) conducted by an R with each actor at the end of each step in the program. These interviews are conducted to reconstruct a posteriori the rules learned and/or followed during situations of training and/or teaching. All interviews follow the same protocol. The interviews are semistructured and the R encourages the actors to talk about the meanings they attributed to the observed actions and any judgments that were made. By asking for clarification or provoking controversy, the R further invites them to substantiate these judgments. Last, the R invites them to talk about the results they had expected from the actions being viewed.

The data are processed so that each actor's activity, its evolution over time, and the articulation of all actors' activities (US, CT and/or PT) can be analyzed at each stage of the study. To achieve this, a four-step procedure was built [START_REF] Chaliès | Training preservice teachers rapidly: The need to articulate the training given by university supervisors and cooperating teachers[END_REF].

(i) The extrinsic and intrinsic data are transcribed verbatim and then decomposed into units of interaction. These units are delimited by the meanings that the self-confronted actor attributes to the events being viewed. A new unit of interaction is created every time the subject of the meaning attributed by the actor changes.

(ii) For each unit of interaction, the elements supporting the meaning attributed by the actor are then identified. By convention, these supporting elements correspond to all the circumstances mentioned by the actor to explain to R how to arrive at the same meaningthat is, by following the same rule for the events of the viewed training situation.

(iii) For each unit of interaction, the rule followed by the actor to understand and judge his or her experience is then formalized. By convention, every rule is labeled from (a) the subject of the meaning attributed by the actor, (b) all the circumstances mentioned by the actor to support this meaning, and (c) the results observed and/or expected. To minimize R's interpretations, each rule is labeled using vocabulary close to that of the actors.

(iv) A double synchronic and diachronic grammatical inquiry is then conducted. The synchronic investigation compares the rules followed and/or learned by the actors during the same step and the diachronic inquiry traces the historicity of the rules followed and/or learned by every actor over the entire training program. By convention, two actors are assumed to be following the same rule if the object of judgment, some of the supporting elements and the associated results are identical.

Step 4: Progress of the research program

The progress of the research program is assessed by the empirical results. The overall results are organized in line with the initially defined auxiliary hypothesis. If the hypothesis is validated, it is incorporated into the program and it will serve much as the earlier hypotheses did: as the starting point for defining a new hypothesis. Otherwise, it is rejected.

Empirical illustration

Elements of contextualization

The two theoretical hypotheses and the methodological choices detailed above are illustrated by empirical results from a study whose principal characteristics can be summarized as follows. In this study, the hypothesis was the following: The PT has to follow rules that need to be learned. This compels the educators to engage not only in ostensive teaching of the rules but also in supporting the first efforts at following them. To (in)validate this hypothesis, the educational component under study was the traditional situation of a CT and PT in the public school system (For a review see Chaliès, Cartaut, Escalié & Durand, 2009). This situation was modeled on the

Empirical results

Two results are presented, chosen because they illustrate and validate the hypothesis of the study. Excerpt 1 PT: So we need to review it (he mimes the action of hitting the shuttlecock toward the ground) because they (the students) are all like this (he mimes the action of hitting the shuttlecock upward). CT: Yes. PT: They're hitting it from underneath, like this (he mimes the student' action of hitting toward the ceiling)… CT: So we need to show them! PT: By holding the shuttlecock in front and we break the wrist to get under it from the bottom (he mimes the movement while speaking).

During the SCI, the PT justified his action with the CT. The excerpt that follows identifies the rule he followed during the lesson to engage with the CT (Excerpt 2).

Excerpt 2 PT: Here I'm practicing… with him (the CT) the points to review… I try almost to put myself in the situation. R: You're practicing with him, you mean? PT: I'm listing (the actions to do) so I don't forget anything… Break the wrist… somewhere in there, I sense that I'm going to have to say it (to the students)… R: So you're trying to prepare? PT: Sort of! R: You say, I'm practicing… can you explain that? PT: Almost like I'm explaining (to the CT)… I'm trying to verbalize, to clarify what I want to say…So that afterwards I can say it to the students…And it's something (verbalizing the instructions before giving them to the students) that he (the CT) does when we prepare together. When we were preparing (co-preparation of the lesson) he said it (what he would do) as if he were speaking to the students… In this excerpt from the SCI, the PT gave the R the supporting elements that indicated his use of a rule: "Prepare to tell the students what they have to do" which meant placing himself "in the situation" as if he were already speaking to the students. He did this in front of the CT by "trying to verbalize" and "practicing with him" and "listing" what had to be delivered, "as if he were explaining it." By following this rule, the PT expected to "clarify" and "not forget" the information he wanted to give the students during the demonstration.

Excerpt 2 provides access to the history of usages of this rule. The CT had initially taught the rule to the PT during the co-preparation of the lesson. The CT in fact revealed his own way of "preparing to explain what the students needed to do" by placing himself "in the situation" by simulation. The excerpt of the SCI that follows about the co-preparation meeting with the CT strengthens the idea that the PT started learning this rule during the co-preparation meeting (Excerpt 3).

Excerpt 3 PT: I listen to him (the CT). He builds the lesson directly here… I'm thinking that he's… When he's preparing the situation, he's already planning the instructions he's going to give the students… R: Can you be more specific? PT: He's letting the situation unfold there. He's preparing… In the way he prepares, he saves time and more than anything… He doesn't miss anything, he forgets nothing… Once on the field. Because while preparing, he's going to say… We're going to do… We're going to put them two on a court and then make them work on the wrist break… And he goes further than that… He says 'I serve, the other returns it'. Here, he's already… As if he were talking to the students. R: And you? PT: There I get it… how to prepare and be clear on the field… In fact, he practices… He already has a text prepared and he practices it. He worked out the instructions before giving them to the students… Excerpt 3 informs on the quality of the articulation between the co-preparation and the classroom work in the collaborative mentoring situation. It shows that the PT "understood how to prepare (the lesson) in advance to be clear while in class" during the co-preparation. By observing the CT's actions and taking them as an example of what to do, he began the process of learning a rule that he then tried to follow in the lesson. The PT thus constructed a meaningful link between an experience that labels a professional practice ("I'm thinking that he's… he's preparing the situation") and an experience that lets him sample a work action. The CT thus demonstrated a rule, or it was demonstrated without him quite being aware as he neither stated it nor deliberately addressed it to the PT. Yet the PT followed this rule in the co-intervention lesson, both to elaborate his work and to interpret his classroom experience ("I'm practicing the different points to make with him here… I'm trying to almost put myself into situation… As if I were explaining it to him… I try to verbalize, to clarify what I want to say… So that afterwards, I can give the instructions to the students", Excerpt 2). The co-intervention situation was therefore not merely a work situation for the PT. Because the CT was alongside him, the situation was in fact an occasion to follow the rule for the first time. Similar to and in continuity with the situation of copreparation, it can be considered a real training situation for supporting the PT as he tracked the outcome of a rule learned in training. Ultimately, learning this rule exceeded the co-preparation and resulted in a self-prescription that organized his classroom actions while co-teaching.

Making the classroom a training situation on and of work: arranging the work so that the PT can follow the rules

During his SCI about the co-intervention situation (Step C), the PT of Dyad 3 (subject: mathematics) said that for the first time he had noticed that following a rule taught by the CT had had the expected results (Excerpt 4).

Excerpt 4

PT: Here, it's working. They (the students) are listening. R: It's working? PT: Well, here I'm lowering my voice in fact, and it's pretty quick, they realize it… and they stop (talking). R: And so? PT: There it's kind of relief. In my head, I say 'finally! Oof, that's it, it's OK now, it's done. R: And you feel better? PT: Totally… It took a while but I'm finally there. R: But you were looking for what? PT: Well, there, it's a thing I'd been working on (with the CT) for a while now. To gain control, we work with silence. R: Meaning? PT: To make them (the students) listen to me I can raise (my voice) louder and louder, and they do the same. So the idea was to do this less. He (the CT) suggested that I speak more quietly to make them listen… They actually listen better when I keep my voice low… And that's what happened there. They listened better… so there I had better control of them. This excerpt documents the PT's satisfaction with both his correct following of a rule taught by the CT ("Manage the students" stands for "play with silence" meaning "speaking more quietly to the students") and the result (they were "more attentive" and "listening"). The excerpt also indicates that "it took time" and required the PT's repeated attempts to follow the rule in order to finally see the expected results and end this part of his learning. The question now is whether or not the mentoring situation contributed to his learning.

The following excerpt is taken from the co-preparation of the lesson. It illustrates the CT's engagement in ostensive teaching of the rule (Excerpt 5).

Excerpt 5 CT: You don't always want to talk like that, louder and louder. I don't know if you realize it but you end up yelling… So in this case, to better manage the class… I would suggest you do the exact opposite. Get silence by silence. The idea is to play on your voice. You speak more quietly… And they are forced to stop, to listen up. PT: Yes, but… CT: It's not easy. For sure… But it still works really well. You keep lowering your voice until they start listening. You make them become attentive… At that moment, the CT was engaged in ostensive teaching of the rule (he deliberately addressed it to the PT). By doing so, he created a meaningful link between the statement ("Manage the class") and the practices ("play with silence", "lower your voice") of the experiential circumstances that were clearly identified ("you end up yelling"). He also pointed out the results expected from following this rule ("you make them become attentive"). From this perspective, the CT helped the PT to become engaged in following the rule. The excerpt from the CT's SCI about the co-intervention sequence documents the efficient training activity that allowed the PT to correctly follow the rule and observe the classroom effects (Excerpt 7).

Excerpt 7 CT: It's like before. I don't know if you saw but, well, for the instructions, every time he gives them to his group I try to be there. Just before, I actually left my group of students to be there (…) R: Did you plan to help him that way? CT: Yes, I tried to simplify those moments when he had to give the instructions… So there, I took a seat next to a couple of agitated students. This excerpt illustrates not only the importance of supporting the PT in class, but also and above all the need to arrange the circumstances in which he would try to follow a rule he had just learned. The CT's engagement in managing the PT's students (by trying to be "more present" and by leaving his own group) "simplified" the task of "giving instructions". By showing himself and/or by positioning himself differently in the classroom ("I took a seat next to a couple of agitated students"), the CT calmed the class and thereby allowed the PT to follow the rule and, most importantly, to see the result of doing so.

Discussion

The empirical results presented above validate the prediction of new developments linked to the hypothesis of the study. These results indicate that CTs should not stop at ostensively teaching the rules and therefore that the hypothesis is good. CTs in fact need to complete ostensive teaching by "supporting the first steps of rule following" as soon as the PT is next in the classroom. Although certain aspects of the complexity of professional development (especially with regard to its temporality) will no doubt be overlooked, we nevertheless have chosen to focus the discussion on two points.

The PTs were able to self-address a rule learned in the co-preparation session or reflexive training while they were in the classroom because an "expectation" had emerged, but this resulted in a "resolved action" only because of the CTs' attentive classroom support. Two distinct training activities were notably identified: ostensible teaching (not deliberate) and ostensive teaching (deliberate) of a rule. The observation that these activities were complementary and relatively autonomous suggests the specificity and limited contributions of training related to a reflexive system of meaning and the analysis of PT classroom experience. Although identifying a problem and prescribing a rule to resolve it favored the emergence of new capacities to "perceive" notable classroom events and to even "expect" them, ostensive training was not enough to transform the PTs' power to act in the classroom. This result was previously reported (Bertone et al., 2009) but this time our in-depth analysis revealed something unexpected: new teaching activities emerged in ordinary circumstances and under real classroom constraints when an expert (the CT) was there to facilitate this emergence by arranging the circumstances. Satisfactory rule-following required more than the CTs' mere presence in the classroom. Instead, the CTs played a very active role in ensuring the PTs' success in following a rule and finding personal confirmation that the rule had indeed produced the effects usually expected by the teaching community. These results provide greater detail on the findings in the international literature that indicate that real changes in PTs' classroom actions are only observed when their mentors' work is intense and systematic [START_REF] Miller-Rigelman | Creating foundations for collaboration in schools: Utilizing professional learning communities to support teacher candidate learning and visions of teaching[END_REF] and constructed within a reassuring and supportive community of practice (Roerhrig et al., 2008).

This "discovery" of results late in the training process aout what a newly learned action can produce echoes the findings in a recent study [START_REF] Rozelle | Opening the black box of field experiences: How cooperating teachers' beliefs and practices shape student teachers' beliefs and practices[END_REF]. These authors documented the effectiveness of PTs' genuine imitations of their CTs after systematically observing them. They notably reported that these PTs reproduced the lessons to the point of giving the exact same explanations, examples and anecdotes, although their actions were (i) too rapid and (ii) too rigid to allow for any improvisation that would take into account their personal interaction with students. These actions, which Rozelle and Wilson called "carbon copies", were considered satisfactory by the CTs. Moreover, when the PTs were no longer able to observe their CTs' actions due to an increasing number of teaching placements, they managed to gradually free themselves from these expert models through a growing capacity to adjust their actions in the classroom.

Conceptually, these findings raise questions about CTs and the precise circumstances when switching from ostensive rule teaching to actively supporting PTs in the classroom is effective and relevant. Regarding the PTs, they raise questions about the shift from an initial capacity to unambiguously "apply" rules to the capacity to handle multiple interpretations adapted to the particularities of each classroom situation.

In this regard, this study suggests that learning a rule can be considered as completed only when both registers of meaning (the inherent and understanding the inherent) have been constructed and "following the rules" is consubstantially associated with actions that are "governed by the rules". This model of alternation in teacher education provides a detailed look at the nature of the interactions in training situations needed for the effective development of professional activity. It strengthens and clarifies earlier results on PT satisfaction with their teaching activity in the classroom and in training [START_REF] Chaliès | Training teachers to improve their job satisfaction: theoretical proposals and empirical illustrations[END_REF]. Two phases appeared in the development of the PTs' professional activity. First, the PTs acted in compliance with the rules, hesitant and shaky though this may have been. They were less driven by the desire to be efficient and clear, not having fully grasped the importance of this, and were more focused on "pleasing" their CTs.

Sometimes, the PTs even thought that the advice they were trying to apply was irrelevant to their situation.

In this phase of learning the rules, the CTs' arrangement of the PTs' classroom situation and their help were crucial. Support in the classroom was not limited to simple note-taking and silent observation, but was an active co-intervention to bring about the expected results and thereby demonstrate the value of following the rules. Second, the PTs not only performed satisfactory actions ("resolved") but they were able to shape and adapt them to the unexpected circumstances of new classroom situations. In this phase, the PTs felt free from the control of their CTs and training was done.

The results of this study do not support the conception of alternation in teacher education as a sequence of classroom visits and post-lesson interviews. Instead, they point to the need to carry advisory and teaching activities into PTs' field work to ensure that they can "track" the outcomes of rule following in the classroom. In other words, this study suggests that PT education should be supported by specific activities that are arranged and implemented in the unique situations of training. This is undoubtedly at the heart of the complexity of supporting preservice teachers. The support must be considered as embodying the principle of "alternation" between learning the rules and interpreting them, and this within a framework of training programs broadly conceived along the principle of "continuity" between teacher education in the university and/or in the school system and work situations that are more or less arranged.

  notion of educative mentoring (Feiman-Nemser, 2001), which theoretically mitigates the separation between training (meetings of the CT and PT before and after lessons) and teaching. The collaborative mentoring in each PT/CT dyad comprised four successive steps over two consecutive weeks. Each mentoring sequence occurred once per trimester of the school year: -Step A: The CT observed the PT's lesson; -Step B: After the lesson, the CT and PT assessed the lesson and planned the next lesson (copreparation); -Step C: This planned lesson was carried out by the CT and the PT with the PT's students the following week (co-intervention); -Step D: After this lesson, the CT and the PT assessed it (co-assessment).

  They also suggest the need to reconsider the usual principle of alternating between training situations and suggest a new hypothesis related to rethinking the time of classroom work as a genuine time of training. 4.2.1. Making the classroom a training situation on and of work: arranging the work so that the PT can simulate professional practice At the time of the co-intervention lesson (Step C), the PT and CT of Dyad 1 (subject: physical education) were standing in a corner of the gym to observe the students. They did not think that the students were doing what they had been asked to do during this badminton lesson ("Score a point by hitting the shuttlecock with a downward movement [of the racket]"). They were thus talking about the reasons for this difficulty and the possible solutions (Excerpt 1).

  Two distinct steps in training emerged in the analysis of this case. The first is the CT's verbalization of examples of the rule. Quite removed from the actual circumstances of the PT's classroom work, this description alone can only guarantee the "tracking" of the outcome of rule following. The second step is the support to the PT in his classroom attempts to follow the rule. The excerpt of the PT's SCI about this moment in the co-preparation sequence documents the developmental impact of Step 1 of training and indicates that the PT has constructed an "expectation" (Excerpt 6). Excerpt 6 PT: Here it's clearer. I know what I have to do. R: Which is what? PT: He (the CT) told me to stop trying to speak louder and louder… I have to try to lower my voice so that they listen more. R: So there you have a solution. And before that there were no solutions? PT: Yes. But I had to wait to see what would happen in class.