H Fakih

S Jacques

O Dezellus

M P Berthet

F Bosselet

M Sacerdote-Peronnet

J C Viala
email: viala@univ-lyon1.fr

Phase equilibria and Re active Chemical Vapour Deposition (RCVD) of Ti 3 SiC 2

Keywords: carbides, chemical potential gradients, diffusion paths, experimental study, local equilibrium, multicomponent diffusion, non-equilibrium processes

The present paper addresses the issue of properly modelling the thermodynamic aspect of chemical reactions proceeding at the solid/gas interface in a multi-component system. Attention is more especially paid to the formation of Ti3SiC2 by reactive chemical vapour deposition (RCVD) on a silicon carbide substrate heated at 1100 °C. A deposition diagram has been calculated by Gibbs free energy minimization in the C-Cl-H-Si-Ti quinary system. It is shown that this deposition diagram can account for experimental results obtained by RCVD only for the short period of time during which the reaction layer is thin and discontinuous. For thick, dense and continuous reaction layers, the deposition diagram is no more appropriate and reaction-diffusion models developed for solid state diffusion couples have to be used in place of it.

Introduction

Chemical vapour deposition (CVD) is a general surface coating process in which a reaction layer grows from a gas phase flowing at the surface of a solid substrate held at high temperature [START_REF] Pierson | Handbook of Chemical Vapor Deposition -Principles, Technology and Applications[END_REF]. In conventional CVD (CCVD), the hot substrate is chemically inert and species present in the coating are all coming from the gas phase. This is for example the case for the deposition of pyrolytic carbon layers from CH4 [START_REF] Lucas | Pyrolytic Carbon Deposition from Methane: an Analytical Approach to the Chemical Process[END_REF] or of titanium carbide layers from TiCl4-CH4-H2 mixtures [START_REF] Vandenbulcke | Thermodynamic Approach to the Deposition of Nonstoichiometric Solids from the Gas Phase: Example of TiC[END_REF]. In reactive CVD (RCVD), the substrate plays an active part in the sense that a direct chemical reaction of at least one species present in it with the gas phase is a necessary condition for the coating to be grown. Many oxide, carbide or nitride layers on refractory metals are produced by RCVD [START_REF] Schaaf | Rapidly Produced Thin Films: Laser-Plasma Induced Surface Reactions[END_REF]. A RCVD process has also been developed to coat the surface of carbon fibres with a carbide layer [START_REF] Bouix | Process for Coating Carbon Fibers with a Carbide[END_REF].

As other refractory MAX-phases, the ternary compound Ti3SiC2 (hexagonal symmetry, space group P63/mmc, a = 0.3068 nm, c = 1.7669 nm [START_REF] Jeitschko | The Crystal Structure of Ti3SiC2[END_REF]) possesses a set of mechanical properties of special interest for structural applications at high temperature [START_REF] Barsoum | Synthesis and Characterization of a Remarkable Ceramic: Ti3SiC2[END_REF][START_REF] Barsoum | Thermal Properties of Ti3SiC2[END_REF]. Owing to its ability to form kink bands and delamination cracks, this compound could more especially be used as an interphase deflecting microcracks in ceramic matrix composites. It is with this aim in view that thin layers of Ti3SiC2 were produced by conventional CVD [START_REF] Racault | On the Chemical Vapour Deposition of Ti3SiC2 from TiCl4-SiCl4-CH4-H2 Gas Mixtures. Part II. An Experimental Approach[END_REF][START_REF] Pickering | CVD of Ti3SiC2[END_REF]. However, the crystal size and orientation in the layers thus obtained were not satisfying for interphase applications [START_REF] Racault | On the Chemical Vapour Deposition of Ti3SiC2 from TiCl4-SiCl4-CH4-H2 Gas Mixtures. Part II. An Experimental Approach[END_REF][START_REF] Pickering | CVD of Ti3SiC2[END_REF][START_REF] Tang | Growth Model and Morphology of Ti3SiC2 Grains[END_REF]. A possible way for changing the microstructure of the deposited layer consists in using low gas pressure RCVD instead of conventional CVD, combined if necessary with pressure pulses [START_REF] Jacques | Which Alternative to the Pyrocarbon Interphase in Ceramic Matrix Composites ?[END_REF][START_REF] Jacques | Pulsed Reactive Chemical Vapour Deposition in the C-Ti-Si System from H2/TiCl4/SiCl4[END_REF]. First attempts were thus made by reacting at 1100 °C a SiCl4 + H2 gaseous mixture with solid TiC: Ti3SiC2 was obtained by this way but difficultly and co-deposition of silicon carbide SiC was unavoidable [START_REF] Jacques | Pulsed Reactive Chemical Vapour Deposition in the C-Ti-Si System from H2/TiCl4/SiCl4[END_REF]. Layered structures containing Ti3SiC2 were easier to produce by reaction of a TiCl4 + H2 gas mixture with solid SiC at 1100 °C [START_REF] Fakih | The Growth of Ti3SiC2 Coatings onto SiC by Reactive Chemical Vapor Deposition Using H2 and TiCl4[END_REF].

The present work is focused on the latter RCVD procedure. Attention will be paid to the relationships between the layer constitution and the phase equilibria in the Cl-H-C-Si-Ti quinary system. The objective is to achieve proper modelling of the chemical reactivity in the system, an approach that should be useful from an applied standpoint for optimizing both the deposition process and the coating properties.

Thermodynamic analysis

As a general rule, the thermodynamic approach of a CVD process consists in establishing a "deposition diagram" from thermodynamic calculations based on Gibbs free energy minimization. This diagram gives the nature of the solid phases that are likely to be deposited from the gas phase at a given temperature and a given pressure as a function of gas composition.

Many calculated deposition diagrams can be found in the literature as for example in references [START_REF] Lucas | Pyrolytic Carbon Deposition from Methane: an Analytical Approach to the Chemical Process[END_REF][START_REF] Vandenbulcke | Thermodynamic Approach to the Deposition of Nonstoichiometric Solids from the Gas Phase: Example of TiC[END_REF][START_REF] Pickering | CVD of Ti3SiC2[END_REF][START_REF] Jacques | Pulsed Reactive Chemical Vapour Deposition in the C-Ti-Si System from H2/TiCl4/SiCl4[END_REF][START_REF] Fakih | The Growth of Ti3SiC2 Coatings onto SiC by Reactive Chemical Vapor Deposition Using H2 and TiCl4[END_REF][START_REF] Goujard | Thermodynamic Study of the Chemical Vapour Deposition in the Si-B-H-Cl System[END_REF][START_REF] Racault | On the Chemical Vapor Deposition of Ti3SiC2 from TiCl4-SiCl4-CH4-H2 Gas Mixtures. Part I. A Thermodynamic Approach[END_REF].

Three different processes are generally distinguished in Conventional CVD [START_REF] Pierson | Handbook of Chemical Vapor Deposition -Principles, Technology and Applications[END_REF]. These are: (i) the transport of reacting species by the flowing gas, (ii) the gas phase diffusion of these species through a boundary layer adjacent to the surface coating and (iii) the development at the surface of the coating of chemical reactions including adsorption, nucleation, surface migration and desorption. In the calculation of any deposition diagram, it is assumed that "close to equilibrium conditions" tend to be established at the solid/gas interface. It can reasonably be assumed that the best situation to fulfil these conditions is when chemical reactions proceed at a fast rate compared with gas phase transport and diffusion. Practically, this situation occurs when the growth of the CCVD coating is controlled by the rate at which the gaseous species are brought to the deposition zone. From statistical probability considerations, it should take a shorter time to build a crystal by surface reactions with one type of atoms than with two or a fortiori three types. Therefore as the number of different atoms increases, the probability that surface reactions become rate limiting also increases. Consequently, fulfilling the "close to equilibrium conditions" should be easier for elements and binary compounds than for ternary ones. As a matter of fact, experimental results and calculated deposition diagrams are often in very good agreement for elements or binary compounds deposited by CCVD, provided that reliable data are used for Gibbs free energy minimization. For ternary compounds, conditions for a good fit between calculations and experiments might be more restrictive but the number of practical examples is not sufficient to derive a general law. In the special case of Ti3SiC2 deposited by CCVD, experimental and calculated results have been found in rather good agreement but some discrepancies have also been pointed out [START_REF] Racault | On the Chemical Vapour Deposition of Ti3SiC2 from TiCl4-SiCl4-CH4-H2 Gas Mixtures. Part II. An Experimental Approach[END_REF][START_REF] Pickering | CVD of Ti3SiC2[END_REF][START_REF] Racault | On the Chemical Vapor Deposition of Ti3SiC2 from TiCl4-SiCl4-CH4-H2 Gas Mixtures. Part I. A Thermodynamic Approach[END_REF]. According to the preceding reasoning, these discrepancies might be the consequence of some deviation to the "close to equilibrium conditions".

In the present work more especially devoted to the formation of Ti3SiC2 by RCVD, thermodynamic calculations based on Gibbs free energy minimization have been worked out in the quinary system C-Cl-H-Si-Ti using the computer program Gemini 2 and data from the Scientific group Thermodata Europ, Saint Martin d'Hères, France. These data were already used in references [START_REF] Jacques | Which Alternative to the Pyrocarbon Interphase in Ceramic Matrix Composites ?[END_REF][START_REF] Jacques | Pulsed Reactive Chemical Vapour Deposition in the C-Ti-Si System from H2/TiCl4/SiCl4[END_REF][START_REF] Fakih | The Growth of Ti3SiC2 Coatings onto SiC by Reactive Chemical Vapor Deposition Using H2 and TiCl4[END_REF]. In a first step, isothermal sections of the C-Si-Ti ternary sub-system were recalculated in full agreement with previous evaluations [START_REF] Wakelkamp | Phase Relations in the Ti-Si-C System[END_REF][START_REF] Du | Experimental Investigation and Thermodynamic Calculation of the Titanium-Silicon-Carbon System[END_REF]; Fig. 1 shows the section recalculated at 1100°C. In a second step, solid-gas phase equilibria in the quinary system C-Cl-H-Si-Ti were considered. As the matter of concern was more especially the reaction between solid SiC and a gaseous mixture of H2 and TiCl4, a representation in the form of a triangle featuring SiC, H2 and TiCl4 at the three apices with axis graduations in mole fraction was chosen. Fig. 2 shows the deposition diagram thus calculated at 1100°C for a total gas pressure of 5kPa. From this diagram, reaction between a TiCl4 + H2 gas mixture and solid SiC should yield pure Ti3SiC2 for hydrogen-rich gas mixtures (H2/TiCl4 molar ratio R higher than 3). For intermediate values of the molar ratio (0.3 < R < 3), TiC (either mixed with Ti3SiC2 or pure) should be produced in the gas-solid reaction. For gas mixtures very poor in hydrogen (molar ratio R lower than about 0.3), a part of SiC should be converted into TiC while the other part should be decomposed into elemental carbon. Excess silicon and carbon produced in the gas/solid reaction should be evacuated in the gas phase under the form of silicon chlorides SiCl2 or SiCl3 and methane CH4. This is indicated by the equilibrium compositions calculated for the reaction of 1 mol of SiC with a great excess of TiCl4 + H2 gaseous mixture under a pressure of 5 kPa. These compositions are: xSiCl2 = 0.48 mol, xSiCl3 = 0.34 mol, and xCH4 = 0.05 mol a the R ratio R = 0.5; xSiCl2 = 0.45 mol, xSiCl3 = 0.34 mol and xCH4 = 0.036 mol at the R ratio R = 35.

Experimental procedure

A classical low pressure hot wall CVD reactor equipped with a silica tube was used, like in previous studies [START_REF] Jacques | Pulsed Reactive Chemical Vapour Deposition in the C-Ti-Si System from H2/TiCl4/SiCl4[END_REF][START_REF] Fakih | The Growth of Ti3SiC2 Coatings onto SiC by Reactive Chemical Vapor Deposition Using H2 and TiCl4[END_REF]. Each RCVD layer was deposited on a polycrystalline graphite disk (12 mm in diameter, Ellor 30, Le Carbone Lorraine France) previously coated with a dense 0.5-3 micrometers thick film of 3C-cubic silicon carbide SiC. This film was deposited by CCVD at 1100 °C from a H2 + CH3SiCl3 gaseous mixture at a pressure of 3 kPa (molar ratio H2/CH3SiCl3 = 4). RCVD was then performed by reacting at 1100 °C the SiC film with a gaseous mixture of H2 + TiCl4 at a total pressure of 5 kPa, the molar ratio R = H2/TiCl4 varying from 4 to 35.

Process Temperature Control Rings (LTH type from Ferro Electronic Materials B.V., Uden, The Netherlands) were used to determine the temperature within the deposition zone of the reaction tube. To facilitate characterization of the deposited layers and check the reproducibility of the RCVD process, several sequences consisting of an inner layer of CCVD-SiC and an outer layer of RCVD-coating were successively deposited on the same graphite discs.

The RCVD layers thus produced were characterized by different techniques. X ray powder diffraction (XRD, CuKα radiation) was performed on the reaction layers as-deposited on the graphite discs using a X'Pert Pro MPD diffractometer from Panalytical equipped with a back monochromator and a X'Celerator detector. The depth thus analysed by XRD was of the order of 10 µm. Observations were made by scanning electron microscopy on transverse fractures (SEM, Hitachi S-800 operated at 15 kV). Electron probe micro-analysis (EPMA, Cameca) was used to determine the chemical composition of the reaction layers. This was achieved on polished transverse sections at an accelerating voltage of 10 kV for a beam current of 9 nA. Atomic contents were determined by reference to pure element standards after correction for atomic number, absorption and fluorescence. Accuracy was of the order of ± 1 at% for a lateral resolution of ± 0.7 µm.

Results

Thin RCVD layers

Reaction layers with a thickness lower than 1 µm were grown at 1100 °C onto SiC at molar ratios R = H2/TiCl4 ranging from R = 4 to R = 35. According to the deposition diagram shown in Fig. 2, these experimental conditions should have been favourable to the formation of Ti3SiC2.

In fact, the thin RCVD layers grown onto SiC at the molar ratio R = 4 only consisted of nearly stoichiometric titanium carbide TiC (cubic, Fm3m, a = 0.433 nm). Not any indication for the formation of Ti3SiC2 was found. The corresponding chemical reaction can be schematically written: SiC(sol.) + TiCl4(gas) + H2(gas) → TiC(sol) + SiCl2(g) + 2 HCl(g)

A layer sequence (SiC/TiC)n obtained by repeating deposition of SiC by CCVD for 8 min and subsequent partial conversion into TiC by RCVD for 20 min is shown in Fig. 3. It can be seen that the CCVD-SiC layers remains unconverted over a depth of about 200 nm. As to the layers of TiC grown by RCVD, they have a mean thickness of 800 nm and are made of round-shaped crystals with a diameter of the order of 200 nm. It is to note that SiC is intimately bonded to each underlying TiC layer onto which it was deposited by CCVD: the interface is even and there is not any lack of matter. Conversely, many voids are present at each interface between the TiC layer and the underlying SiC layer to the detriment of which TiC was grown.

To obtain RCVD thin layers containing the ternary carbide Ti3SiC2 instead of TiC, the molar ratio R had to be higher than 5. Fig. 4 shows the periodic layer sequence grown at 1100 °C with the molar ratio R = 35. SiC was deposited in 3 min and then exposed for 10 min to the gaseous mixture TiCl4 + H2. Only two constituents were characterized by XRD in the resulting coating:

Ti3SiC2 formed by RCVD and unconverted SiC (Fig. 5). The chemical solid-gas reaction can be schematically written:

2 SiC(sol.) + 3 TiCl4(gas) + 5 H2(gas) → Ti3SiC2(sol) + SiCl2(g) + 10 HCl(g)

As can be seen in Fig. 4, Ti3SiC2 forms continuous layers with a mean thickness of 1.3 µm. In these layers, the Ti3SiC2 crystals are bigger than the TiC crystals previously characterized and their shape is different. Indeed, the Ti3SiC2 crystals grown at R = 35 appear in the form of platelets with a mean size of 0.2x1.3 µm whereas the TiC crystals formed at R = 4 were globular with a diameter of 200 nm. The fact that most of these platelets are standing upright onto the incompletely converted SiC layers suggests a preferential orientation. Effectively, in the XRD patterns of such multi-layered coatings like that reported in Fig. 5, the (110) diffraction line characteristic for Ti3SiC2 is anomalously strong whereas the (008) reflection is lacking. This clearly confirms a preferential orientation of the c axis of the Ti3SiC2 crystals parallel to the SiC layer surface.

The foregoing results obtained for thin layers of TiC and Ti3SiC2 grown by RCVD onto SiC at 1100 °C are only in qualitative agreement with the deposition diagram shown in Fig. 2. Indeed, SiC is converted into Ti3SiC2 when the gas mixture is hydrogen-rich and into TiC when the gas mixture is hydrogen-poor as indicated by the deposition diagram. However, if the value of the R ratio is considered from a quantitative point of view, the experimental results do not fit well with the thermodynamic calculations. This misfit will be discussed later.

2. Thick RCVD layers

In order to produce thick reaction layers, the reaction time corresponding to the deposition of SiC by CCVD and its conversion by RCVD was increased up to 240 min.

Fig. 6 shows the reaction layer produced by heating SiC under a flowing gas mixture of TiCl4 + H2 for 240 min at 1100°C at a molar ratio R = 4. As at shorter reaction times, titanium carbide TiC is the sole constituent of the 3µm thick reaction layer thus obtained. This layer exhibits a duplex microstructure. In its inner part that extends over about 1µm in thickness, the reaction layer consists of equiaxed round-shaped crystals with a mean diameter of 200 nm, like previously. In its outer part, the TiC crystals tend to be elongated in the growth direction giving to that part a more columnar appearance. These observations suggest that the inner part of the TiC reaction layer is the oldest and the outer the most recently deposited. An EPMA line profile was recorded point by point across the reaction layer from its inner part to its outer. A slight deviation to unity of the C/Ti molar ratio was thus revealed: the layer composition varied within the limits TiC0.96 and TiC0.82.

The increase in thickness of the TiC reaction layers grown at R = 4 has been plotted in Fig. 7 as a function of the deposition time. It can be seen that the rate of growth of TiC continuously decreases as the deposition time increases: initially of 30 nm min -1 , that rate becomes null for reaction times higher than or equal to 200 min. Such an important variation in deposition rate indicates that different processes successively control the growth of the reaction layer during the period of time investigated. More especially, three main stages can be distinguished:

-(i) as it is generally the case for most interface reactions [START_REF] Dibkov | Growth kinetics of chemical compound layers[END_REF], surface reactions should predominate in a former stage. In the present instance, unevenness has been noticed in Fig. 3 at the CCVD-SiC/RCVD-TiC interface. This suggests that he TiCl4 + H2 gas mixture would attack the SiC surface in some places while in other places, this surface would be protected by TiC crystallites that nucleate and grow from the gas phase. When a gastight reaction layer is formed by stacking of TiC crystals (200 nm in diameter), surface reactions stop. The duration of this first stage controlled by surface reactions is less than 30 min under our experimental conditions; -(ii) for reaction times ranging from 30 to 120 min, one enters a second stage in which evolution with time of the layer thickness, e, can be described by a branch of parabola having, when expressed under the reduced form e 2 = K t, the following equation:

e 2 = 1.60 10 -15 t (3)
with t in second and e in meter (0.6 < e < 2.5 10 -6 m). It is generally accepted that such a parabolic law characterize a growth process by solid state diffusion of atoms [START_REF] Dibkov | Growth kinetics of chemical compound layers[END_REF][START_REF] Van Loo | Multiphase Diffusion in Binary and Ternary Systems[END_REF]. At the same temperature (1100 °C), a parabolic constant K of the same order of magnitude (K = 2.9 10 -15 m 2 s -1 ) was reported for the diffusion-controlled growth of layers of small TiC crystals (100-200 nm in diameter) by reaction between a solid carbon substrate and a Sn-1wt%Ti melt [START_REF] Pastor | Fabrication of C/Al composite wires and effect of an interfacial TiC layer[END_REF]. Given that in the thick TiC reaction layers we have produced by RCVD, the carbide composition varies from TiC0.96 to TiC0.82, a Fick's coefficient of interdiffusion can be evaluated using the Fick's first law expressed as:

DFick interdif. = (K/2) . (Nc/ΔNc) (4)
K being the parabolic growth constant in m 2 s -1 and ΔNc/Nc the relative variation of the carbon molar fraction in the composition range TiC0.98-TiC0.82. An interdiffusion coefficient of 9.4 10 - 15 m 2 s -1 has thus been obtained. On the other hand, an averaged Fick's coefficient of interdiffusion can be calculated at 1100 °C for the composition range TiC0.96 to TiC0.82 from the data by van Loo and Bastin [START_REF] Van Loo | On the Diffusion of Carbon in Titanium Carbide[END_REF]. The value of this calculated coefficient is of 4.23 10 -17 m 2 s - 1 , i.e. about 200 times smaller than our experimental value. Very likely, the reason for that difference lies in the fact that grain boundary diffusion is predominant in TiC layers made of small crystals (200 nm) whereas van Loo and Bastin's data refer to volume diffusion in TiC layers consisting of very big grains (100 µm or more). On a comparison basis, a factor of 10 4 is reported for grain boundary versus volume diffusion in ZnO [START_REF] Neves Nogueira | Diffusion of the 65 Zn radiotracer in ZnO polycrystalline ceramics[END_REF]; -(iii) for TiC reaction layers with a thickness larger than 2.5 µm, the growth rate more and more deviates from the parabolic law and finally, no growth at all occurs for reaction times longer than 200 min. Two additional processes can be invoked to explain why growth stops.

One of these is the development of Kirkendall voids at the SiC/TiC interface. Effectively, carbon is virtually the only diffusing component in TiC1-y, whatever the value of y (0 < y < 0.5) [START_REF] Van Loo | On the Diffusion of Carbon in Titanium Carbide[END_REF]. By reducing the contact area, such voids could slow down solid state diffusion. The other process is the evaporation of carbon at the solid gas interface under the form of gaseous CH4.

This possibility is sustained by equilibrium calculations that give at R = 0.5 a non negligible mole fraction of CH4 (xCH4 = 0.05) for 1 mol of SiC converted into TiC. Combination of diffusion controlled growth of TiC with evaporation of carbon can thus result under steady state conditions in a reaction layer that keeps a constant thickness, as demonstrated in ref [START_REF] Dibkov | Growth kinetics of chemical compound layers[END_REF]. At this point it is interesting to compare the layers characterized after solid/gas RCVD at 1100°C with reaction layers formed by interface reaction in SiC/Ti solid state diffusion couples.

For such couples annealed at 1100 °C or less, the reaction zone mainly consists of a two-phased layer of TiC and Ti5Si3Cx [START_REF] Wakelkamp | Phase Relations in the Ti-Si-C System[END_REF][START_REF] Choi | Interaction between Titanium and SiC[END_REF][START_REF] Gotman | Interaction between SiC and Ti Powder[END_REF][START_REF] Goesmann | Temperature-Dependent Interface Reactions and Electrical Contact Properties of Titanium on 6H-SiC[END_REF][START_REF] Gorsse | A New Approach in the Understanding of the SiC/Ti Reaction Zone Composition and Morphology[END_REF][START_REF] Martina | Production and characterization of titanium aluminide or silicide intermetallic matrix composites[END_REF], the presence of an additional Ti3SiC2 layer between SiC and the two-phased layer being sometimes mentioned [START_REF] Wakelkamp | Phase Relations in the Ti-Si-C System[END_REF][START_REF] Martina | Production and characterization of titanium aluminide or silicide intermetallic matrix composites[END_REF]. As a matter of fact, our results

for thick layers formed at 1100 °C by RCVD are in relation with these data but do not match exactly. In this regard, it is worth noting that under our experimental conditions, the chemical activity of the titanium source is not equal to the unity but smaller. The driving forces for solid state volume diffusion are also smaller, which reduces the rate of growth of the reaction layer and may slightly modify the layer sequence. More especially, phases that are mixed in the same layer at a high titanium activity (TiC and Ti5Si3Cx) may grow in two distinct layers at low titanium activity. This phenomenon has already been observed in solid state diffusion couples.

For instance, the layer sequence SiC/ Ti3SiC2/ TiC + Ti5Si3Cx/ Ti characterized at 1100 °C in the presence of pure Ti was observed to turn to the sequence SiC/ TiC/ Ti3SiC2/ Ti5Si3Cx/ Ti3Al, the same reaction layer as in the present work, when pure Ti was replaced by the intermetallic compound Ti3Al [START_REF] Martina | Production and characterization of titanium aluminide or silicide intermetallic matrix composites[END_REF].

If the latter results obtained for thick layers grown at R = 35 are compared with the deposition diagram (Fig. 2), no fit at all can be found. Indeed, the thick reaction layers consist of three solid phases TiC, Ti3SiC2 and Ti5Si3Cx and there exists no phase field in the deposition diagram featuring these three compounds in equilibrium. Anyway, the three phases are arranged in three successive sub-layers and the gas phase or the SiC substrate are only in contact with one of these sub-layers. As a matter of fact, the deposition diagram is no more valid to account for these results.

Discussion

In the following discussion, we will first try to provide a rational explanation to the points of agreement and discrepancy that have appeared between the calculated deposition diagram (Fig.

2

) and the experimental results obtained by RCVD (Figs 345678). Then we will point out some principles for properly modelling the thermodynamic aspect of chemical reactions proceeding at the solid/gas interface in a multi-component system.

It has been recalled in Section 2 that "close to equilibrium conditions" at the solid/gas interface are needed for a good fit between calculations and experiments in CCVD and that these conditions are generally fulfilled when reactions at the surface of the growing coating proceed at a fast rate compared with the rate at which the reactive species are supplied via the gas phase.

Exactly the same requirements are needed in RCVD, but the situation is more complex since the substrate that is inert in CCVD plays an active part in RCVD. Consequently in CCVD all the elements that constitute the coating are coming from the flowing gas phase. Therefore, the rate at which all species are brought to the growing coating remains constant under steady state conditions and if close to equilibrium conditions are established at the beginning of the deposition process, they will no more change. Conversely in RCVD at least one reactive species is coming from the substrate. The deposition rate may thus continuously decrease as the substrate is partly and then completely covered by a reaction layer of increasing thickness.

From there, two different stages have to be distinguished in a RCVD process:

-a first stage during which the RCVD coating is discontinuous or porous, which allows a direct contact to be established between the gas phase and the solid substrate;

-a second stage where a dense and continuous reaction layer has formed at the substrate surface isolating it from the gas phase.

The important change in deposition rate observed in our experiments between thin and thick layers produced at R = 4 as well as at R=35 corresponds to the transition from the first stage to the second one.

During the first stage of the RCVD process, i.e. during the fast rate growth of thin layers of TiC or Ti3SiC2, experimental results are qualitatively in agreement with the deposition diagram. By analogy with CCVD, one can consider that "close to equilibrium" requirements are grossly met at the solid/gas interface or, in other words, that the surface reaction processes involved in the consumption of SiC and formation of TiC or Ti3SiC2 crystals develop at a sufficiently fast rate compared wit gas phase transport or diffusion. Quantitatively, however, there is a shift between calculated and observed results with respect to the H2/TiCl4 molar ratio R. For a part, it can be considered that the real value of the R ratio in the hot deposition zone near the SiC substrate surface is smaller than that fixed in the gas mixture entering into the reactor: several technical reasons have been given to account for that assumption [START_REF] Fakih | The Growth of Ti3SiC2 Coatings onto SiC by Reactive Chemical Vapor Deposition Using H2 and TiCl4[END_REF]. It can also be thought that another part of the shift traduces some "supplementary" deviation to the close to equilibrium conditions that should be specific to the formation of the ternary compound Ti3SiC2, as previously evoked in Section 2.

Fig. 9 shows the variations of the chemical potentials of C, Si and Ti in the vicinity of the solid/gas interface in the case of thin RCVD coatings. Activity values for solid phases were taken from reference [START_REF] Wakelkamp | Diffusion and Phase Relations in the Systems Titanium-Silicon-Carbon and Titanium-Silicon-Nitrogen[END_REF]. Meeting the "close to equilibrium requirements" implies that the chemical potentials of the constituting elements monotonously vary without discontinuity at the crossing of the different interfaces (only the compositions change abruptly). As long as a threephased equilibrium tends to be established between the gas phase, the growing coating and the SiC substrate, the degrees of freedom for the system are limited and chemical potentials vary only slightly in the deposition zone. In that first stage where gas phase diffusion is rate limiting, most of the variations in chemical potential occur in the boundary layer, δ, as shown in Fig. 9.

Once a continuous and dense reaction layer is formed at the substrate surface by RCVD, this layer naturally acts as a (permeable) diffusion barrier. From that moment, further reaction between the substrate and the gas phase can only proceed by solid state diffusion of atoms through the barrier layer. Solid state diffusion being much slower than gas phase diffusion, the former process will rapidly become rate limiting. Under kinetic control by solid state diffusion, there is no more need for a three-phased equilibrium to be established between the gas phase, the growing coating and the substrate. Only two-phased solid-solid or solid-gas equilibria are required at the different interfaces. This increases the degrees of freedom for the system and while the chemical activity gradients of the constituents will tend to disappear in the boundary layer, δ, they will develop in the barrier layer, as shown in Figs. 10. As a general rule for interface reaction layers growing by diffusion, intrinsic diffusion of one type of atoms can only proceed down its activity gradient [START_REF] Van Loo | Multiphase Diffusion in Binary and Ternary Systems[END_REF]. It is clear from Fig. 10 that carbon and silicon can diffuse outwards while titanium diffuses inwards. For these thick RCVD layer configurations the gas phase is no more in contact with the substrate and for that reason, the deposition diagram is no more valid.

To sum up, modelling the evolution of thick RCVD reaction layers comes to describe the growth of reaction layers by solid state diffusion in an opened system. Qualitatively, the diffusion path concept may be useful to understand the development of complex reaction zones [START_REF] Van Loo | Multiphase Diffusion in Binary and Ternary Systems[END_REF][START_REF] Kirkaldy | Diffusion Behaviour in Ternary Multiphase Systems[END_REF]. Assuming that local phase equilibria exist at the different interfaces under steady state growth conditions, intrinsic diffusion of atoms proceeds down their chemical potential gradient, as shown in Fig. 10. For a quantitative description of the growth of thick reaction layers by RCVD, the solid state reaction-diffusion models based on the Fick's law [START_REF] Van Loo | Multiphase Diffusion in Binary and Ternary Systems[END_REF][START_REF] Wakelkamp | Diffusion and Phase Relations in the Systems Titanium-Silicon-Carbon and Titanium-Silicon-Nitrogen[END_REF][START_REF] Kirkaldy | Diffusion Behaviour in Ternary Multiphase Systems[END_REF][START_REF] Kidson | Some Aspects of the Growth of Diffusion Layers in Binary Systems[END_REF][START_REF] Wagner | The Evaluation of Data Obtained with Diffusion Couples of Binary Single-Phase and Multiphase Systems[END_REF][START_REF] Adda | La Diffusion dans les Solides[END_REF] or on the Nernst-Einstein formalism [START_REF] Barge | Analysis of the Diffusion Controlled Growth of Cobalt Silicides in Bulk and Thin Films Couples[END_REF] should be the most appropriate.

Conclusion

A deposition diagram" was calculated at 1100 °C by Gibbs free energy minimization in the C-Cl-H-Si-Ti quinary system in view to produce Ti3SiC2 layers by RCVD onto a SiC substrate.

In qualitative agreement with that diagram, thin layers of pure Ti3SiC2 (up to 1.3 µm thick)

were produced in 10 min onto SiC by reactive CVD from a TiCl4 + H2 mixture (total gas pressure: 5kPa; molar ratio H2/TiCl4 = 35). Under the same experimental conditions but for longer reaction times (30 min or more), the reaction layers were thicker and two sublayers were observed to develop at each side of the Ti3SiC2 first formed layer: an inner TiC sublayer and an outer Ti5Si3Cx one. As a matter of fact, the calculated deposition diagram was no more appropriate to account for the growth of these thick multiphased layers. Valuable qualitative description of a RCVD process in the case of thick, continuous and multiphased layers has to be based on the diffusion path concept and chemical activity considerations. As to quantitative modelling, it needs use of diffusion-reaction models specially developed for solid state diffusion couples.

Figure captions

Fig. 8

 8 Fig.8shows the 6.5 µm thick reaction layer produced by RCVD after 90 min reaction at 1100 °C at a R ratio R = 35. From XRD and EPMA characterization, this reaction layer consists of three different compounds arranged in three sublayers: a very thin sublayer of TiC in contact with unconverted SiC, a Ti3SiC2 intermediary sublayer only slightly thicker than after 10 min reaction (1.7 µm instead of 1.3 µm) and a Ti5Si3Cx outer layer. The Ti3SiC2 intermediary layer exhibits the same columnar microstructure as that previously observed in thin layers, with a slight increase in crystals elongation. Exactly the same results were obtained for a thick RCVD layer grown on SiC in 30 min at 1100 °C at R = 35: simply, the total thickness was of 3.5 µm instead of 6.5 µm.

Fig. 1 .Fig. 2 .Fig. 3 .Fig. 4 .Fig. 5 .Fig. 6 .Fig. 7 .Fig. 8 .Fig 9 .Fig 10 .FiguresFig. 1

 123456789101 Fig. 1. Isothermal section of the C-Si-Ti phase diagram re-calculated at 1100 °C in full agreement with previous data [17-18] Fig. 2. Partial deposition diagram applicable to the formation at 1100 °C of RCVD coatings by reaction between solid SiC and a H2 + TiCl4 gaseous mixture at a total gas pressure of 5 kPa (phase fields very close to the border of the triangle are not represented) Fig. 3. Thin TiC layers grown in 20 min at 1100 °C onto SiC by RCVD from a TiCl4 + H2 gas mixture with a molar ratio R = 4 (R = H2/TiCl4) Fig. 4. Thin layers of Ti3SiC2 grown in 10 min onto SiC from a TiCl4 + H2 gas mixture with a molar ratio R = 35 (R = H2/TiCl4)

Fig. 2 21Fig. 3

 23 Fig. 2

Fig. 4 22Fig. 5

 45 Fig. 4

Fig. 6 23Fig. 7

 67 Fig. 6

Fig. 8 24Fig. 9

 89 Fig. 8

Fig. 10

 10 Fig. 10