Patrick Marsaleix

Claude Estoumel

Veronique Kondrachoff

Raoul Vehil

A numerical study of the formation of the Rhone River plume

Keywords: river plume, Northwestern Mediterranean, the Rhone, JEBAR effect, twofold sigma coordinate

A three-dimensional primitive equation ocean model is applied to the Rhone River plume (northwestern Mediterranean).

The plume dynamics are analyzed through the vorticity balance of the depth-averaged current. This balance highlights the importance of the JEBAR and nonlinear terms. The topography induces the freshwaters to enter the Gulf of Fos and progress eastwards. The momentum advection is responsible for the large offshore extension of the plume. Northwestern winds (characteristic of the regional climate) may detach the plume from the coast. The wind stress magnitude required for this detachment is commensurate with Garvine's dimensional analysis. A satisfactory comparison is made between the numerical experiments and satellite observations for weak and strong wind conditions. Finally, a sensitivity test of the model to the vertical coordinate reveals that a double-sigma system preserves the salinity gradients and current intensity in the frontal zones of the plume better than a conventional sigma coordinate.

Introduction

The main characteristics of estuarine plumes are known, for the most part, through satellite imagery and modeling studies [START_REF] Chao | Onset of estuarine plumes[END_REF][START_REF] O'donnell | The formation and fate of a river plume: a numerical model[END_REF]Kourafalou et al., 1996a,b). Glob ally, after leaving the river mouth, the light waters enter an anticyclonic eddy which the coastal current extends. The three-dimensional structure of the cur rents as revealed by the models involves a cyclonic undercurrent beneath the anticyclonic bulge. Numeri cal studies have demonstrated the sensitivity of these characteristics to certain parameters: the two-layer flow inside the estuary constitutes a source fo r the surface circulation and a sink deeper down for the plume entering the adjacent sea. In nearly inviscid models, the Froude number determines the shape of the plume, and varies depending on whether the plume is supercritical or subcritical [START_REF] Garvine | Estuarine plumes and fronts in shelf waters: A layer model[END_REF][START_REF] Chao | River forced estuarine plumes[END_REF]: a supercritical plume is characterized by a bulge with a considerable seaward extension, followed by a narrow coastal current, while a subcrit ical plume is characterized by a bulge whose width is comparable to that of the coastal current. The width of the coastal current is comparable to that of the Rossby radius [START_REF] Stem | The intrusion of a density current along the coast of a rotating fluid[END_REF] in the inviscid case but may be significantly larger in the case of diffusive plumes. In many cases, river plume dynam ics may differ from the 'anticyclonic eddy-coastal current' system described by [START_REF] Chao | Onset of estuarine plumes[END_REF]. Indeed, the determining factor in the plume shape can be an alongshore current [START_REF] Garvine | Estuarine plumes and fronts in shelf waters: A layer model[END_REF], tidal currents or the wind (Lentz and Limeburner, 1995;Kourafalou et al., 1996a). The topography of the continental shelf also plays an important role since the effect of a seaward bottom slope is to limit the offshore development of the bulge by increasing the anticyclonic vorticity linked to the orographic lifting of the undercurrent [START_REF] Chao | River forced estuarine plumes[END_REF], while the presence of a canyon in fr ont of the mouth reinforces the barotropic circulation with the emission of coastally trapped waves [START_REF] Weaver | The influence of buoyancy flux from estuaries on continental shelf circulation[END_REF].

In this study, we examine the plume of the RhOne, which is one of the largest discharges of freshwater into the western Mediterranean. Its mean discharge is ab out 2000 m 3 / s, but frequent autumn and spring floods lead to discharges exceeding 5000 m 3 / s. These floods are of prime importance, since they transport to the sea considerable quantities of conti nental matter, whose fate needs to be studied. The three-dimensional circulation caused by the buoy ancy flux, characterizing the arrival of freshwaters into the sea, plays a role which is not yet fu lly understood. From a more fundamental point of view, the aforementioned parameters which govern plume circulation are significantly different in the case of the Rhone than the ones used in the numerical studies mentioned ab ove. For example, the width of the Rhone at its mouth (I km), small in comparison with the deformation radius, and its shallow depth (2 m), do not generally enable the development of three-dimensional estuarine circulation. The speeds at the ri ver mouth are high, greater than 2 m/s for a discharge of 5000 m 3 / s, and entail significant ad vective effects, as will be discussed below.

Our study of the Rhone River plume dynamics is conducted through three-dimensional numerical modeling. A two-fold sigma coordinate model is used, making it possible, on the one hand, to pre serve a fine vertical resolution in the surface fresh water layer despite the seaward bottom slope and, on the other hand, to accurately represent the effects of the topography on the circulation under the plume. The simulations performed in the ab sence of wind are analyzed by means of the depth-averaged current vorticity equation. This approach makes it possible to quantitatively take into account the set of pro cesses acting on the plume, including both intrinsic processes related to the density gradients and exter nal forcings caused by the topography. We will also examine the effect of offshore winds, dominant in this region, on the detachment of the plume from the coast. Satellite images of surface temperature illus trate the situations studied, thus making it possible to assess the validity of the model results.

Presentation of the model

Equations

The model used is an adaptation of the one de scribed by [START_REF] Pinazo | Spatial and temporal variability of phytoplankton biomass in upwelling areas of the northwestern Mediterranean: a coupled physical and biogeochemical modelling approach[END_REF]. The governing equa tions were obtained by assuming that mass, momen tum and salinity are conserved, and then applying the Boussinesq approximation and hydrostatic equilib rium. Within a rectangular Cartesian coordinate sys tem, Ox 1 x 2 x 3 in which the origin, 0, corresponds to the equilibrium level of the sea surface and Ox 3 is directed upwards along the local vertical, the Reynolds-averaged components of the velocity, (upu 2 ,u 3 ), satisfy:

au.

-1 =0 {1) ox j OU; au j ui at + �ei.j,du j

J for i = 1,2 (2)
where f denotes the Coriolis parameter, e the alter nating unit tensor, T/ the position of the sea surface, p 0 a reference density, ah= (o 2 /ox?) + (a 2 / oxD, and A the horizontal diffusivity, taken to be 10 m 2 /s. The displacement of the sea surface is de duced from a vertically integrated form of the equa tion of continuity (Eq. ( 1)), in which:

OTf a - 0 t + ( Hu j ) = O (3) ox j � 1, 2
where H denotes the total depth, and the overbar the average over depth. The density, p, is derived from the water salinity, S , using the fo llowing linearized equation of state:

P = Po [ 1 + {3 ( S -S0)] {4)
where the saline contraction, {3, is taken to be 7.45 X 10-4 psu -1, and S0 is the reference salinity corresponding to p0• For the sake of simplicity, we have omitted the effect of the temperature on the water density. The temperature of the Rhone River water at the mouth may fall below 8°C in the winter and can attain 22°C in the summer (CTGREF, 1977), while the monthly average of sea surface tempera ture in the Gulf of Lions generally ranges from 13°C to 22°C. We thus felt that temperature differences between the Rhone River and the ambient seawater may generally be considered small enough to assume in the remainder of this article that the buoyancy effects in the plume are represented by salinity gradi ents only.

The salinity is determined from:

-+ -1 - = -K -+ALlhS as au s a ( as ) at ax } ax3 ax3
(5)

The transfer coefficient K is defined in terms of the turbulence energy density, E, using the following relation:

K = cklkE11 2 (6)
E is determined from:

:� + ';�; � K [ ( :::r + ( :::)']

+ !._ K ap + � ( K aE ) -e Po ax3 ax3 ax3 d (7)
The rate of loss of the turbulence energy, e d , is represented by:

c,, £ 3 / 2 e d = ---1,, (8)
Following [START_REF] Gaspar | A simple eddy kinetic energy model for simulations of the oceanic vertical mixing: tests at station Papa and long-term upper ocean study site[END_REF], the turbulent scales le and lk are given by: lk = min(lu,l d ) l e = j l )d

g fx 3+1"( ( * ) ) * ( ) - p( x3) -p x3 dx3 = E x3 Po x, g fx3-l d( ( * )) * -. p( x3) -p x3 dx3 = £( x3) Po x, (9)
The empirical constants, c k and c,,, are respec tively taken to be 0.1 and 0.7.

Boundary conditions

The boundary conditions at the free surface and seafloor are:

E= p a/ c ,, ck as atx3 = T/ . h I= 1,2 atx3 = - at x3 = -h (10) ( 11) Po K-= 0 at x3 = T/ and at x3 = -h ( 12) ax3
where T, is the wind stress and Tb the bottom stress, calculated as in [START_REF] Blumberg | A description of a three dimensional coastal circulation model[END_REF]. where n is the coordinate normal to the boundary and c is the wave speed calculated according to [START_REF] Orlanski | A simple boundary condition for unbounded hyperbolic flows[END_REF].

The freshwater discharge of the Rhone into the sea debouches from a channel in which the model equations are reduced to a two-dimensional system 0x 1

x3 which consists simply in eliminating u 2 , the component of the current perpendicular to the river banks, as well as the terms in a;ax 2 of Eqs. (1)-( 12). The channel is 32 km long and 2 m deep. The width of the Rhone River mouth is fixed at 1 km, which closely approximates reality. As the horizontal reso- lution of the 3-D ocean model is also km, the coupling with the river model is simply:

'Priver = 'Pocean (14)
where cp represents any variable in Eqs.

(1)-( 12). Boundary conditions at the end of the channel are:

S=O F u = - 1 Id (15) (16)
where F is the river discharge, l the width and d the depth of the channel.

The model g rid

The region of the Rhone River plume, the hori zontal dimensions of the numerical domain and the bottom topography are shown in Fig. 1. The equa tions are solved in a three-dimensional 'staggered' C grid [START_REF] Arakawa | Vertical differencing of the primitive equations in sigma coordinates[END_REF]. The horizontal resolution is 1 km X 1 km. A leap-frog differencing scheme associated with an [START_REF] Asselin | Frequency filters for time integrations[END_REF] filter is used for the time-stepping. A mode-splitting tech nique [START_REF] Blumberg | A description of a three dimensional coastal circulation model[END_REF] is used to calcu late the free surface elevation. The vertical grid corresponds to the 'two-fold' sigma coordinate sys-tern described by Deleersnijder and Beckers (l 992) consisting in dividing the water column into two regions, each of which is associated with a sigma coordinate. Although it may be stretched by the bottom topography, the thickness of the upper region is restricted to a maximum value of l 0 m, which prevents a loss of vertical resolution near the surface in deeper areas. This system is quite suitable for the study of river plumes, especially when wind forcing pushes the thin freshwater layer offshore. Four-and five-sigma levels are, respectively, used for the up per and lower layers.

Vorticity equation of the depth-avera g ed current

The simulations of the Rhone River plume are analyzed using the equation of depth-averaged cur rent vorticity, g = e;,j,3 auj/ Bx;, which may be ex pressed as:

ag a [ 1 a 'l7 -=-e -- uu dx Bt i, j, 3 Bx H Bx f k j 3 i k = 1,2 -h + d * d S,J ,] g f '11 B ( f 11 ) 'T. • -Tb • 1 ----px x- PaH -h axj X3 3 3 PoH au k a -f +e - a i.j.3 a X k -1 � X ; x --+- au dx [(llj B 11 ) A f '11 ] H Bt H -h h 1 3 (17)
The term on the left-hand side of Eq. ( 17) will be referred to below as the change in vorticity over time, while on the right-hand side we find the non linear, JEBAR, friction and stretching terms. It should be noted that JEBAR is often expressed [START_REF] Mertz | Interpretations of the JEBAR term[END_REF] as:

( 18)

where g !'1/ x = - zpdz Po -h (19)
is the potential energy anomaly. The two rightmost terms of Eq. ( 17), which derive from the variation of the surface level and horizontal-diffusive effects, are negligible when compared to the others, and can thus be legitimately omitted. They are nevertheless calcu lated in order to attain an exact numerical balance in Eq. ( 17) (see Appendix A). If the initial state of the simulations is considered to be a zero velocity field, then g(t) can be simply calculated by g(t) = ag f11_ 0 atdt. Therefore, the sum over time of the dis- crete form of Eq. ( 17) is chosen as it provides a vorticity balance.

Initialization

The simulations described below are performed using the following assumptions: the freshwater dis charge of the Rhone is 5000 m3 /s, typical of the strong floods reported over the past few years, espe cially in autumn and spring. The initial velocity and salinity fields, which are homogeneous, are respec tively taken to be 0 m/s and 38 psu. The effects of sea temperature on the circulation are not taken into account. No large-scale forcing is applied at the open lateral boundaries, meaning in particular that we have ignored the influence of the large-scale circula tion, which can be of the order of 5 to IO cm/s on the continental shelf [START_REF] Millot | The Gulf of Lions' hydrodynamics[END_REF], as well as the tidal currents, which are practically nonexistent in this region [START_REF] Tsimplis | A two-dimen sional tidal model for the Mediterranean Sea[END_REF].

Vorticity analysis of the Rhone River plume

Fig. 2 shows the surface salinity field, surface circulation and bottom circulation after a 48-h simu lation without wind forcing. Globally, two main plume-shape characteristics may be discerned, as identified by the numerical studies of [START_REF] Chao | Onset of estuarine plumes[END_REF]. First of all, the plume forms a bulge of anticyclonic circulation in front of the river mouth. The circulation within the bulge is baroclinic and may be considered as a two-layer circulation system in which the direction of the bottom current is opposite to that of the near geostrophic surface flow. Secondly, the anticyclonic surface circulation returns to the coast about 10 km west of the mouth and then forms a westward coastal current.

According to the classification scheme of [START_REF] Chao | River forced estuarine plumes[END_REF], which is based on the offshore extension of the bulge and the width of the coastal current, the computed plume may be considered to be supercriti cal. Within the inviscid limit, this situation occurs when the internal Froude number, Fr, is greater than one [START_REF] Chao | River forced estuarine plumes[END_REF]. An estimation of this number may be given by V / c, where V is the surface velocity in the plume and c the phase speed associated with the first baroclinic mode, obtained by computing the eigenvalues of the normal mode equation on the model grid. We found that the plume was almost entirely characterized by a Froude number greater than 1 and that the baroclinic Rossby radius, R0 = c / f, was of the order of 3 to 5 km in the coastal current, whose width is about IO km. A Kelvin number, Ke, may be obtained from the ratio of the coastal current width to the baroclinic Rossby radius. Within the inviscid limit, Stern et al. (1982) have shown that Ke is about 0.4. Here, a value of Ke greater than 2 indicates the effect of mixing on the plume shape, which may be considered as diffusive, if Chao's classification scheme is once again used. The Kelvin number is the predominant parameter in the classification system of [START_REF] Garvine | A dynamical system for classifying buoyant coastal discharges[END_REF] for buoy ant coastal discharges. We have included here a table (Table 1) from [START_REF] Garvine | A dynamical system for classifying buoyant coastal discharges[END_REF] which lists values of Ke and Fr for various buoyant coastal discharges. One remarkable feature of Garvine's dimensional analysis, as may be seen in Table 1, is that low Kelvin numbers are normally associated with super critical plumes and, inversely, high Kelvin numbers with low Froude numbers. It is interesting to note that, according to our numerical experiments, the Rhone River plume does not satisfy this rule, with both Ke and Fr higher than one. This particular point will be discussed in Section 7. [START_REF] Chao | River forced estuarine plumes[END_REF] showed that the bottom slope re stricts the offshore extension of the bulge because of vorticity constraints. Below, the vorticity balance of the depth-averaged current will highlight the influ ence of the sloping bottom on the plume circulation through the JEBAR te�s. A similar approach was employed by [START_REF] Wheless | The evolution of density-driven circulation over sloping bottom topography[END_REF], who con sidered the case of buoyant, neutral and dense plumes. A direct relation may be observed between the structure of the depth-averaged current and the plume shape, as shown in Figs. 2 and3; indeed, the bulge may be considered as an anticyclonic gyre centered to the southeast of the mouth, and the coastal current as the northern branch of a cyclonic circulation which can be clearly distinguished from the former pattern.

Jn the vicinity of the river mouth

When the width of an estuary is larger than the baroclinic Rossby radius, a complex three-dimen- sional circulation may form inside the estuary [START_REF] Weaver | The influence of buoyancy flux from estuaries on continental shelf circulation[END_REF]. This is not the case here since the baroclinic radius calculated by the model is clearly larger than the estuary width ( ,.., 1 km). It should be noted that this fact justifies our numerical choice of two-dimensional fluvial circulation. One consequence of this simplification is that the flow is not constrained laterally by advection or the pressure gradient force. When the freshwater discharges into the sea, the flow is suddenly constrained by the baroclinic pressure forces generated by the surround ing seawater. The strong induced bottom current flows in approximately the opposite direction to the surface circulation and converges towards the mouth, mainly from the west and east due to the bathymetri-

E � Q) (.) c: � i5 20
cal constraints. At the mouth, the adjustment of the sea surface level to the convergence of the bottom current with the river discharge creates a sizable pressure gradient which increases the surface spread ing of the plume. The orographic lifting of the bottom current gen erates a vertical velocity component of the order of 1.5 X 10-3 m s -1 . It should be noted that if the realistic bathymetry is replaced with a flat bottom, the simulation yields a stronger undercurrent. Indeed, the bottom slope, due to the vertical movements generated, increases the conversion of kinetic en ergy, drawn from the bottom circulation, into poten tial energy.

The freshwater discharges into the sea through the entire water column, and then extends offshore as a bottom-to-surface plume up to a distance of 2 km from the mouth (Fig. 5a). Beyond this point, the freshwater is diluted with seawater through turbu lence and upwelling movements associated with the two-layer circulation. Upwelling movements explain the thinning of the plume, which occurs within a distance comparable to the internal Rossby radius. The thickness of the surface plume which then forms is of the order of 5 m. Mixing with the seawater lessens the plume's vertical stratification. It should, however, be noted that for small discharges, mixing with the seawater occurs in the estuary, and the freshwater thus discharges into the sea as a surface plume. A scale analysis reveals that the momentum Eq. ( 2) is, approximately, a balance between advective, pressure and friction terms within the first few kilo meters away from the mouth. Advection is signifi cant because of the strong inflowing current gener ated by the considerable river discharge and the relatively small mouth of the estuary (roughly 1 km X 2 m). Below, we will see that the effect of the advective terms is to lengthen the offshore extension of the plume.

Topographical effects in the Gulf of Fos

One remarkable feature of the plume shape is its eastward extension into the Gulf of Fos, as seen in Figs. 2 and3. Fig. 4 presents the vorticity balance of the depth-averaged current near the mouth. The net anticyclonic vorticity is associated with the eastward rotation of the depth-averaged current towards the Gulf of Fos. The net vorticity is small when com pared to the various terms of the vorticity balance, especially the nonlinear, JEBAR and friction terms. At the mouth ( x2 = 61 km) the nonlinear terms give a cyclonic tendency to the depth-averaged current. Fig. 4 clearly shows the opposition of the JEBAR term to the nonlinear terms. The JEBAR inversion in front of the mouth is to be expected, according to [START_REF] Wheless | The evolution of density-driven circulation over sloping bottom topography[END_REF]. Indeed, considering Eq. ( 18), the combination of the bottom slope, which is approximately aligned in the north-south direction, and the alongshore potential energy gradient, which is clearly negative to the east of the mouth and positive to the west (Fig. Sb), generates an anticy clonic tendency to the east of the mouth (and cy clonic to the west) in opposition to the nonlinear term. It should be noted that in these shallow areas, the vorticity effects of the bottom stress are signifi cant due to the high velocities of the bottom circula tion. The bottom friction tenn has a cyclonic ten dency which is globally opposed to the stretching term (Fig. 4).

Farther to the east, the bathymetry of the Gulf of Fos implies that the behavior of the JEBAR term will be opposite to its behavior for the conventional straight coastline and bathymetry case considered by [START_REF] Wheless | The evolution of density-driven circulation over sloping bottom topography[END_REF]. Indeed, in the latter case, the JEBAR term contributes to the anticyclonic rotation of the circulation to the east of the river mouth. Here, on the other hand, the bottom slope produces a cyclonic JEBAR in the eastern part of the Gulf of Fos, which helps keep the plume flowing alongshore up to Cap Couronne.

The anticyclonic bulge

To the south of the Gulf of Fos, the surface current traces a wide anticyclonic eddy characterized by upwelling movements. As in Chao and Boicourt (l 986), the lateral detrainment area found at the fr inge of the eddy is characterized by downwelling movements. The vorticity balance of the depth-aver aged current (Fig. 6) shows that the bulge is charac terized by a net anticyclonic vorticity. At the fringe of the bulge, the lateral detrainment zone displays a net cyclonic vorticity, itself mainly due to the nonlin ear terms. The behavior of the JEBAR and stretching terms is as expected: in the eastern half of the bulge, the JEBAR term is negative due to the negative west-east potential energy gradient, and the stretch ing term is positive due to the thickening of the water column associated with a mean southward current; in the western half of the bulge, the JEBAR term is positive and the stretching term negative for the opposite reasons. It may be observed, however, that these terms are more significant in the western half due to the relatively perpendicular orientation of the isobaths with respect to both the pressure con tours and to the mean current on the western side of the canyon extending in front of the river mouth (Fig. 3). A similar behavior of the JEBAR and stretching terms when confronted with a canyon is seen in [START_REF] Weaver | The influence of buoyancy flux from estuaries on continental shelf circulation[END_REF]. The effect of the nonlinear term on the depth-averaged current vortic ity in the bulge is in the same direction as the resulting vorticity, even within the detrainment areas.

The bulge/ coastal current transition

When leaving the bulge, the plume impinges on the coast. Most of the surface plume turns cyclonicly to the west, forming a coastal current, while the remaining par t returns to the east, joining in with the anticyclonic circulation of the bulge (Fig. 2a). The bottom circulation consists, first of all, of a counter current detached from the coast and flowing towards the river mouth and, farther downstream, of a current flowing in the same direction as the surface circula tion (Fig. 2b). Along the coast, the circulation, when it leaves the bulge, is barotropic as well. This part of the plume is characterized by considerable bottom stress due to the acceleration of the mean current in shoaling areas. This calls to mind the numerical experiments of [START_REF] Chao | Onset of estuarine plumes[END_REF], showing that the inversion of bottom circulation in the coastal current is sensitive to the bottom fr iction, with strong fr iction encouraging barotropic circulation. The con vergence of the surface current generates a coastal downwelling with a maximal intensity of 0.3 m/h. If the vorticity balance is examined, it may be seen that the cyclonic tum of the plume when leaving the bulge is mostly caused by the JEBAR term, while the stretching term contributes, under the effects of the thinning of the water column, to the generation of vorticity, anticyclonic like the sizable friction term in the part of the plume closest to the coast.

The coastal current

During the first few hours of simulation, the plume has not developed long enough to be affected by the rotational effects. It is only when the size of the bulge exceeds ten or so kilometers that the anticyclonic circulation appears, with surface cur rents which are almost parallel to the salinity con tours. [START_REF] Ruddick | A model study of the Rhine discharge front and down welling circulation[END_REF] show that in the case of the Rhine River plume, the distance from the mouth at which the current adjusts itself to a quasi-geo strophic state corresponds to the internal Rossby radius. Here, this distance is greater due to the considerable influence of the advection. The conver gence of the anticyclonic current with the coast produces a barotropic coastal circulation. Indeed, a significant (> 1 cm/s) westward bottom current characterizing the barotropic circulation appears after 9 h of simulation, 11 km to the west of the river mouth. After 48 h, it attains about twenty cm/s downstream from the salinity front (Fig. 2). [START_REF] Weaver | The influence of buoyancy flux from estuaries on continental shelf circulation[END_REF] demonstrated that the presence of a canyon generates, through the JEBAR effect, a stronger barotropic circulation. It is possible that a similar effect is here created by the canyon extend ing in front of the Rhone River mouth.

Sensitivity of the plume dynamics to the nonlin ear terms

The previous simulation demonstrated that the momentum advection is a significant component of the circulation in the plume, not only near the river mouth, due to the high velocities of freshwater dis charge, but also throughout the bulge, where it con tributes to the vorticity tendency. The shape attained by the plume may thus be considerably different when the advection is omitted. It is in order to demonstrate this point that we now describe a simu lation, identical to the previous one, except for the fa ct that the momentum advection has not been taken into account. Fig. 7 shows the surface and bottom circulation. If it is compared with Fig. 2, the high sensitivity of the plume to the nonlinear terms be comes apparent. At the river mouth, most of the freshwater flows into the Gulf of Fos along the They de la Gracieuse. The mean current is much stronger here, and suggests that the advection terms in the previous simulation drain its energy by lateral mix ing. The cyclonic effects of the fr iction on the bot tom of this strong barotropic circulation keep this plume alongside the They de la Gracieuse. The generation of cyclonic vorticity by fr iction amply compensates for the vorticity generated by the advec tion, such that the cyclonic turning at the river mouth is stronger than in the simulation without advection. Farther east into the Gulf of Fos, the bottom current weakens, and the fr ictional effects become negligible while the JEBAR term generates an anticyclonic current rotation. In the simulation with advection, the anticyclonic vorticity generated by the JEBAR term is partially attenuated by the cyclonic tendency of the nonlinear terms. The absence of advection thus implies a stronger anticyclonic vorticity, resulting in a shorter offshore extension of the bulge. The center of the anticyclonic eddy is now found farther to the east of the river mouth. It is thus possible to observe an eastward offset in the transition between the bulge and the coastal current, which now appears only 4 km to the west of the river mouth, whereas in the case in which advection was included, this transition occurred 10 km farther west. It should be noted that these characteristics of the simulation without advec tion may also be found in simulations with a smaller discharge (not included in this article).

The reduced surface area of the bulge is compen sated for by a two-fold thickening of the freshwater layer, resulting from the stronger barotropic circula tion to the east of the river mouth, and by the longer westward extension of the plume (Fig. 7). The shape of the coastal current is affected as well: unlike the previous simulation where its width gradually dimin ished to the west, the nose of the plume is here wider than the coastal current. This effect is somewhat reduced here by the particularities of the coastline and, more specifically, by the Pointe de Beauduc. Indeed, simulations performed with a rectilinear coastline (not included in this article) show that this characteristic is even more pronounced, with currents displaying a fa n-shaped nose when the advection is not included. In the absence of advection, the mo mentum balance in the nose is dominated by the pressure gradient which, due to the unsteadiness of the circulation, widens the intrusion offshore. Farther upstream, the rotation effects are significant and induce a near-geostrophic circulation, involving cur rents with a shoreward component which tends to make the coastal current narrower behind the nose. The advection effect of the momentum is dominant in the nose because of the small length scale associ ated with the nose discontinuity and finally pushes the plume back against the coast at the front end of the intrusion.

The influence of the wind

The local climate of the Gulf of Lions is charac terized by strong northwestern winds associated with coastal upwelling [START_REF] Johns | On the wind-driven coastal upwelling in the Gulf of Lions[END_REF] and internal gravity waves. [START_REF] Demarcq | La dynamique superficielle du panache du Rhone d'apres l'imagerie infrarouge satellitaire[END_REF] demon strated that northwestern wind conditions may detach the Rhone River plume from the coast. In fa ct, [START_REF] Garvine | A dynamical system for classifying buoyant coastal discharges[END_REF] established, through a dimensional analysis of the equations of motion, an order of magnitude for wind stress beyond which the circula tion generated by the wind dominates the circulation of the plume itself. This order of magnitude may be expressed by:

p H P c 2 r=--- L ( 20
)
where H P and L are respectively the depth and the alongshore length scales of the buoyant structure, and c is the internal phase speed. If, in accordance with Section 3, we set c = O.Sm s -I, H P = Sm and L = 40km, then the plume circulation will be domi nated by the wind when the order of magnitude of the wind stress exceeds 3 X 10-2 N/m 2 , or, using the parameterization of [START_REF] Wu | Wind-stress coefficients over sea surface near neutral conditions-a revisit[END_REF], a 10-m wind of the order of 5 m/s. Plume simulations analogous to the reference simulation but forced by a northwest ern wind stress of 0.01 N/m 2 , 0.035 N/m 2 , 0.075 N/m 2 and 0.15 N/m 2 , corresponding approximately to winds of 3 m/s, 5 m/s, 7 m/s and 10 m/s, demonstrate the sensitivity of the plume shape to local atmospheric forcing and to the coastal circula tion generated by the wind. For a wind stronger than 7 m/ s, the plume is clearly deflected seaward (Fig. 8) in accordance with the observations of [START_REF] Demarcq | La dynamique superficielle du panache du Rhone d'apres l'imagerie infrarouge satellitaire[END_REF] and with the order of magnitude given by Eq. (17). measured on the island of Pomegues, ab out 30 km to the east of the river mouth, was blowing at 12 m/s from the northwest, and the Rhone River discharge was about 4000 m3 /s. The plume, darker than the surrounding waters, is clearly separated from the coast, and its overall orientation is towards the south west in accordance with the plume characteristics as calculated with a wind of 10 m/s (Fig. 8). It should be pointed out that the apparent similarity between Figs. 8 and 9a cannot be considered as a validation of the model, since the initialization and forcing conditions of the simulation took into account nei ther the variability of the wind and freshwater dis charge, nor the oceanic stratification corresponding to the satellite observation. Two salinity fronts may be discerned in the latter plume. The circulation is stronger near the external eastern front than to the west, where the pressure force and wind are in opposition. The circulation generated by the north western wind is characterized by the formation of coastal upwelling which increases the rising move ments associated with the discharge of freshwater in front of the river mouth. [START_REF] Chao | River forced estuarine plumes[END_REF] showed that high-frequency internal gravity waves propagate within the plume. We found that these waves are intensified by the wind and that their direction of propagation corresponds globally to the orientation of the plume (Fig. 10). The southwards orientation of the surrounding surface circulation converges to wards the internal western front of the plume, along which a downwelling develops (Fig. 10). On the opposite side, along the external eastern edge, the downwelling associated with the lateral detrainment is bounded by an upwelling (Fig. 10) resulting from the divergence of the surface current.

For winds weaker than 5 m / s, the calculated plume clings to the coast and has a form which closely resembles that of the re ference circulation without wind. The satellite observation of the plume shown in Fig. 9b is characterized by a wind of the order of 3 m/s during the 18 h which precede the image and a Rhone River discharge of 1700 m3 / s, and is thus an example of a plume subjected to a low wind stress, as is attested by its standard form com posed of a bulge near the river mouth and the westward alongshore structure. The plume shape, as well as the characteristic size scales of the bulge and coastal current, coincide quite well with those shown in Fig. 8 for the numerical experiment subjected to a wind of 3 m/s, even though the forceful discharge of 5000 m3 /s overestimates the reality (a simulation performed with a discharge of 1700 m3 / s resulted in a similar plume shape). A few characteristics high lighted by the numerical experiment have thus been confirmed by this satellite image, such as, for exam ple, the semi-circular shape of the anticyclonic bulge whose seaward extension is ab out 18 km, the flow of a fraction of the river water towards the Gulf of Fos along the They de la Gracieuse, and a westward alongshore coastal current a few kilometers wide.

Once again, the external forcings, and here espe cially the ambient circulation, would have to be accurately represented in order to truly validate the model. Indeed, for mild wind conditions, the conti nental shelf circulation is generally characterized by a westward alongshore current, often designated as the 'Liguro-Proven�al' current [START_REF] Millot | The Gulf of Lions' hydrodynamics[END_REF]. Ac cording to [START_REF] Millot | The Gulf of Lions' hydrodynamics[END_REF], it seems that this coastal current may be reasonably estimated at 5-10 cm/s. We thus tested the sensitivity of the simulation de scribed in Section 3 to an ambient westward current of the order of 5 cm/s. Our results come close to O'Donnell's description of the effects of ambient current on the shape of the plume (O'Donnell, 1990): the general plume shape is slightly modified by the crossflow, which however enhances the downstream spreading while tending to restrict the upstream and offshore extension of the bulge. It may therefore be assumed that the eastward extension towards the Gulf of Fos can be influenced by the coastal circula tion. An accurate representation of the continental shelf circulation associated with the 'Liguro-Proven�al' current should enable future studies to test this hypothesis.

6. Sensitivity to the vertical coordinate system

The double-sigma coordinate system was intro duced into our model since, as it offers the advantage of preserving the horizontal resolution of the surface layer despite the variable bottom topography (unlike the conventional sigma system), it was felt that the vertical structure of the plume would be better repre sented in the open sea, which would clearly lead to a better representation of the resultant pressure gradi ents and circulation. We thus assessed the sensitivity of the model to the vertical coordinate system by performing a simulation analogous to the reference simulation, except that the restriction on the thick ness of the upper layer was removed, thus implying that the vertical grid would be similar to a conven tional sigma grid.

The general shape of the plume as calculated by the conventional sigma version is not very different from the one calculated by the reference simulation. The seaward extension of the anticyclonic bulge is slightly shorter than in the reference simulation, but the westward alongshore extension of the plume is longer. A truly significant difference finally appears in the horizontal salinity gradients: the reference simulation results in a much more pronounced salin ity front, in particular in the bulge, while the simple sigma simulation results in a gradual dilution of the plume as it gets farther from the river mouth. One consequence of the salinity front dilution is a de crease of ab out 30% in the maxima of the velocities calculated inside the bulge.

A likely explanation of the salinity front dilution in the case of the simple sigma simulation is that, as the plume flows seaward, the model distributes the freshwater over a larger and larger vertical mesh, and the value of S at the surface consequently increases simply by considering the salt conservation criterion. This flaw is accompanied by an excessive thickening of the plume.

Discussion and conclusion

The Rhone River plume was studied by means of a 3-D model with a I-km horizontal mesh, which made it possible to solve for the internal radius of deformation, of the order of 4 km inside the plume, and to represent the complex topographical charac teristics, principally the canyon extending in front of the river mouth and the Gulf of Fos, which exercise a considerable influence on the plume shape. Simi larly, a double-sigma vertical coordinate was used, as it enabled a finer representation of the effects of the bottom topography all the while conserving the vertical resolution required for the accurate represen tation of the surface plume. This choice proved to be more suitable for the representation of the frontal areas than a conventional sigma coordinate, which artificially increases the plume dilution and reduces the currents associated with it. Since the purpose of this study was to understand the mechanisms control ling the formation of the plume, a depth-averaged current vorticity analysis was performed. Mean flood conditions were chosen since, even though they rep resent a period of only about one month per year, they are accompanied by the discharge of a large portion of the solid continental matter transported by the river over the scale of one year. An understand ing of the plume dynamics is fundamental to predict ing the fate of this matter on the continental shelf. When compared to the plumes simulated in idealized conditions [START_REF] Chao | Onset of estuarine plumes[END_REF][START_REF] Chao | River forced estuarine plumes[END_REF][START_REF] O'donnell | The formation and fate of a river plume: a numerical model[END_REF], the Rhone River plume has cer tain unique characteristics resulting from the particu larities of the coastline and bottom topography, and the high speed of the current as it leaves the river. The plume calculated by our model may be consid ered as supercritical-diffusive according to the classi fication scheme defined by [START_REF] Chao | River forced estuarine plumes[END_REF]. There may be several reasons for this: the high current speeds inside the plume, resulting on the one hand from the considerable buoyancy created by the discharge of the freshwater onto the continental shelf, which oc curs over the entire water column (due to the ab sence of estuarine circulation), and on the other hand from the high speed of the current in the river. The diffusive characteristic may be attributed to the verti cal movements, brought about by the bottom topog raphy, which are the cause of the gradual dilution of the plume.

As mentioned in Section 3, the Rhone River plume does not agree with the general rule derived from Garvine's classification by Kelvin number, since both Ke and Fr are higher than 1. A compari son with the case of the Rhine seemed worthwhile since the Rhine shares certain characteristics with the Rhone system, such as the mean freshwater dis charge (about 2000 m3 /s) and the Kelvin number (about 3). Moreover, recent studies on the Rhine River plume, conducted with a 3-D model similar to the one used here [START_REF] Ruddick | A model study of the Rhine discharge front and down welling circulation[END_REF][START_REF] Ruddick | Haline stratification in the Rhine-Meuse freshwater plume: a three-dimensional model sensitivity analysis[END_REF] provide substantial material for comparison with our results. While there is some disagreement between Garvine's classification (Table 1) and [START_REF] Ruddick | A model study of the Rhine discharge front and down welling circulation[END_REF] estimate of the Froude number (Ruddick's estimate is indeed ab out 0.9), it seems that the Rhine River plume may reasonably be considered to be subcritical. The case of the Rhine differs from that of the Rhone when it comes to the plume shape as well. Indeed, Ruddick's experiments demonstrate that the tidal currents and the relatively shallow bathymetry induce considerable turbulent mixing which en hances the dilution of the Rhine River plume. On the other hand, the Rhone River plume is characteristic of a weak ambient current situation (for no wind conditions), because of the lack of tidal currents and the low velocity of large-scale circulation on the shelf [START_REF] Millot | The Gulf of Lions' hydrodynamics[END_REF]) when compared to the plume velocity. This, added to the steep bathymetry which diminishes the effects of bottom friction, prevents the generation of turbulent mixing and encourages the relatively long extension of a thin surface plume with strong currents (Fr > I).

One remarkable characteristic of the Rhone River plume is the size of the anticyclonic eddy, which flows from the river mouth to the Gulf of Fos, extending considerably eastwards and then seawards. The mechanisms governing this progression seem tightly linked to the topography on the one hand, and to the momentum advection on the other hand. Upon exiting the river mouth, the plume acquires cyclonic vorticity which enables it to penetrate the Gulf of Fos. Once the components of this vorticity were analyzed, it was possible to demonstrate that this effect is caused by the stretching term, generated by the bottom slope, and by the nonlinear terms. The advection plays an important role here, since it is the dominant term in the vorticity balance. A simulation in which the advection is not taken into account shows that due to the shallow depth, the friction becomes the preponderant term, intensifying even further the cyclonic turning of the circulation, which has itself become highly barotropic against the west ern coast of the Gulf of Fos, thus encouraging the penetration of the river water up to the far end of the Gulf. Inside the Gulf of Fos, the plume begins its anticyclonic rotation, which is one of the main char acteristics of the river water flow in front of the river mouth. The JEBAR term is the cause of this negative vorticity, due to the orthogonality of the isopycnals and of the bathymetrical contours. Here as well, the significant role of the nonlinear terms needs to be emphasized, as they generate the cyclonic vorticity whose effect is then embodied by a relatively low net anticyclonic vorticity, and thus by a bulge with a long seaward extension.

We decided to test the sensitivity of the model to advection, since it was felt that the depth-averaged current was insufficient for analyzing the effect of the nonlinear terms on the net vorticity, due to the vertical shear. The analysis of the sensitivity to advection demonstrated that this term is in fact deter-minant in the size of the bulge since, unlike the situation near the river mouth, the friction here is not able to compensate for the absence of advection, which greatly increases the anticyclonic vorticity by reinforcing the preponderance of the JEBAR term. The result of a negligible advection is thus a signifi cant decrease in the size of the anticyclonic bulge. Simulations which have not been included in this article have demonstrated that in this part of the plume, the advection is only negligible for low val ues of river discharge ( < 1000 m 3 /s), thus indicat ing that the plume shape as shown in Fig. 2 is representative of the majority of situations. The per tinence of the numerical experiment without wind is moreover confirmed by a satellite observation which clearly highlights the anticyclonic bulge and the advance of the plume towards the Gulf of Fos.

An interesting fact which should also be noted, and which is not represented in idealized situations, is the rise in the bathymetry encountered by the plume in the eastern part of the Gulf of Fos. The JEBAR term then generates a cyclonic vorticity which pushes the plume against the coast until it reaches Cap Couronne, and thus participates in the eastward advancement of the freshwaters. The anti cyclonic bulge is the center of the rising movements which dilute the river waters considerably. The diffu sive effects result in a much wider coastal current than the value predicted in the inviscid case, since it attains about 10 km, i.e. more than twice the value of the internal Rossby radius. The momentum advection plays a particularly significant role here in keeping the nose of the plume pushed against the coast and thus reducing the loss of mass by lateral detrainment. When the momentum advection is omitted, it may effectively be observed that the salinity front which bounds the plume is more diluted than in the refer ence simulation. It should be noted that unlike the behavior previously observed in the bulge, the effect of the advection is always strong on the nose of the plume, regardless of the discharge, due to the hori zontal gradients which characterize the nose and the unsteadiness linked to the advance of the front.

The study of sensitivity of the plume to a north western wind resulted in a plume shape which closely resembles the satellite observation statistics of De marcq and Wald (1984). For a discharge of 5000 m 3 /s lasting 48 h, it seems that the plume detaches itself from the coast when the order of magnitude of the wind stress is at least 0.03 N/m 2 • This value is relatively comparable to the estimate calculated us ing dimensional analysis by [START_REF] Garvine | A dynamical system for classifying buoyant coastal discharges[END_REF]. The interface between the plume and the subjacent sea water is characterized by the propagation of internal gravity waves.

  A no-flux condition is applied across closed lat eral boundaries. At the open lateral boundaries, a zero gradient condition is applied to the density field. It should be noted that, because of the initially homogeneous density field, the results described here are not affected by the boundary condition on den sity since the simulations were ended before the nose of the plume reached the open boundaries. The surface elevation at the lateral open boundary is calculated by the following radiation condition:

  Fig. I. Coastline and depth contours (in m) of the numerical model. Inset: map of the northwestern Mediterranean Sea. The area covered by the model is shaded.

Fig. 2 .

 2 Fig. 2. (a) Computed surface salinity and current, and (b) bottom current after 48 h of simulation. Interval between salinity isocontours: 2 psu. For the sake of clarity, contours lower than 21 psu and one out of every two vectors in both directions have not been plotted.

  Fig. 3. Depth-averaged current (plotting one out of every two vectors in both directions) after 48 h of simulation, and depth contours in m.

Fig. 4 .

 4 Fig. 4. West-east profile of the time-integrated vorticity compo nents taken 2 km in front of the river mouth (its location is indicated on the included model map by a dotted line). For the sake of clarity, the change in elevation over time and the horizon tal-diffusive terms, which are small in comparison to the others, are not plotted. The black square indicates the position of the river mouth.

Fig. 5 .

 5 Fig. 5. (a) Vertical north-south section of the salinity taken in front of the river mouth, and (b) vertical west-east section of the salinity taken 2 km south of the river mouth. The interval between salinity isocontours is 4 psu.

Fig. 6 .

 6 Fig. 6. West-east profile of the time-integrated vorticity compo nents taken 13 km in front of the river mouth (its location is indicated on the included model map by a dotted line). For the sake of clarity, the change in elevation over time and the horizon tal-diffusive terms, which are small in comparison to the others, are not plotted. The black square indicates the position of the river mouth in the west-east direction. Detrainment areas are indicated.

Fig. 7 .

 7 Fig.7. Computed surface salinity and current after 48 h of simulation. Interval between salinity isocontours: 2 psu. For the sake of clarity, contours lower than 21 psu and one out of every two vectors in both directions were not plotted. Advective terms in the momentum equations were omitted.

Fig. 8 .Fig. 9 .

 89 Fig. 8. 35 psu surface salinity isocontours for different values of the northwesterly wind stress, after 48 h of simulation. The numbers indicate the wind speed (in m/s).

Fig. 10 .

 10 Fig. 10. Vertical component of the current in meters per hour, 5 m beneath the sea surface. Dark and light areas, respectively, indicate downwelling and upwelling movements.

Table l

 l Values of Ke and Fr for various buoyant coastal discharges (from[START_REF] Garvine | A dynamical system for classifying buoyant coastal discharges[END_REF]

	Name	Ke	Fr
	Point Beach	0.1	2.0
	Mississippi	0.2	1.0
	Amazon	0.6	0.6
	Niagara	1.0	1.0
	Alaska	1.0	0.3
	Gaspe	2.0	0.4
	Algerian	3.0	0.3
	Rhine	3.0	0. 1
	Delaware	4.0	0. 1
	Norwegian	4.0	0. 1
	Scottish	10.0	0. 1

Acknowledgements

This study was supported by the Programme Na tional d'Oceanologie Cotiere (we thank H. Masse who coordinated the program in the Gulf of Lions) and by the European Community under contract MAS3-CT96-0049 (METRO-MED project). Didier Pont is thanked for helpful discussions on the Rhone River Mouth. We are also grateful to S. Prieur, Y. Meyerfeld and A. Urielli.

Appendix A

The calculation of the vorticity balance Eq. ( 17) on the model grid is performed using the depth-in tegrated momentum equations employed by the model in order to calculate the external mode solu tion [START_REF] Blumberg | A description of a three dimensional coastal circulation model[END_REF]. These equations are expressed as:

The time splitting technique is based on the de composition of the various terms in Eq. (Al) into a barotropic component and a depth-dependent compo nent (notably for the advection and the pressure gradient). This last point, which does not play a part in the discussion below, will not be developed here. The reader is referred to [START_REF] Blumberg | A description of a three dimensional coastal circulation model[END_REF] for more details. After division by H and crossed horizontal derivatives, Eq. (Al) becomes:

a { 1 aHu j ) ei . j, 3 ax; H --;;(

It may be observed that the pressure, Coriolis and advection terms are equivalent to the JEBAR, stretching and nonlinear terms of Eq. ( 17), meaning that it is easy to determine the latter in a manner consistent with the model calculations. On the other hand, this is not the case for the terms of horizontal diffusion and change in vorticity over time. It may also be observed that the term representing change in surface elevation over time: a { u j a71 ) ei j3 ax; Hat is missing in Eq. (A2). In fact, it is simple to make this latter term appear, as well as the term represent ing change in vorticity over time, by considering that: [ a { 1 aHu j )] a� [ a ( u j a77 )] ei . j . 3 ax; H ar -at = e i, j , 3 ax; H at

Finally, identical results may be obtained between the right-and left-hand sides of Eq. ( 17) if Eq. ( A3) is chosen as the finite-difference equivalent of the change in surface elevation over time, and if the horizontal diffusion term is calculated as in Eq. (Al).


V Bornand

Lithium Niobate Tantalate thin films deposited by r.f. sputtering

Keywords: Lithium niobate tantalate, Thin films, Sputtering, Atomic Force Microscopy, Ferroelectricity

Ta-modified lithium niobate (LiNb 1-x Ta x O 3 ) thin films were deposited on ITO-covered Si(111) substrates by r.f. sputtering. Experimental results reveal that Ta content (0<x<0.75) influences strongly the grain size as well as the ferroelectric and piezoelectric properties of the deposited materials. Increasing Ta induces a significant decrease of the grain size, while the polarization capability and the piezoelectric activity decrease. The film crystallinity and preferential orientation can be enhanced by the use of a two-steps growth process.

Introduction

Owing to their attractive electro-optical, acousto-optical, piezoelectric and non-linear properties, LiNbO 3 (LN) and LiTaO 3 (LT) are among the most promising materials for integrated and guided-waves devices. Both components exhibit the same crystal structure (space group R3c) with only slight differences in the lattice and positional parameters and belong to the small group of ferroelectric materials. Furthermore, lithium niobatelithium tantalate LiNb 1-x Ta x O 3 (LNT) forms a continuous solid solution that is also ferroelectric.

Within the last decades LN and LT thin films have been the subject of many works. To take advantages of the useful properties of these materials, it is essential to fabricate polar-axis oriented thin films with good surface morphology. In contrast, only few studies report on LNT deposition, even though these materials can be potentially attractive, since their properties can be tuned by varying the composition to meet engineering specifications [1][2][3][4][5][6][7][8][9][10][11].

In the present paper, we report on LNT thin films deposited in ITO-covered Si(111) substrates by r.f. sputtering. As LN has been much more investigated than LT [12][13][14], it appeared reasonable to use LN as the starting point in the considerations of the current mixed systems.

Four compositions were more particularly studied (x=0, 0.25, 0.5 and 0.75). Two approaches were applied. In a first part, employing a one-step process (6 hours), the effect of composition on the structural and physical properties has been investigated. In a second part, focusing on the LiNb 0.5 Ta 0.5 O 3 (LN50T50) solid solution, a two-steps process was adopted. By creating a high-nucleation density during the initial stage (1 hour), films with higher crystalline properties and preferential orientation could be deposited during the second step (5 hours).

Experimental details

LNT layers were deposited by r.f. sputtering from home-made ceramics targets. All experiments were performed with a Ar/O 2 (60:40) mixture, at 40 mTorr and 80 W. To avoid overheat of the sputtering device, the deposition temperature was limited to 260°C in the chamber, well-below the optimum temperature (600-660°C) necessary to grow preferentiallyoriented films [15][16]. (Poly)crystallization was induced by post-annealing treatment at 750°C during 1 hour for both 1-step and 2-steps processes. Since the results could be affected by the film thickness, all the samples were grown to have a similar thickness of about 1 m.

The structure and crystallographic orientation were determinded by X-ray diffraction (XRD) using and X'PERT diffractometer in / configuration with Cu K 1 radiation ( = 0.154 nm).

The surface morphology and film cross-section images were obtained by Atomic Force Microscopy (AFM) and Scanning Electron Microscopy (SEM). Secondary Ion Mass Spectrometry (SIMS) depth profiling was used to assess both film composition and interdiffusion phenomena. Ferroelectric hysteresis loops were measured with a RT66A tester while nanometric scale characterizations were performed using the piezo-response mode of the AFM (Piezoelectric Force Microscopy: PFM).

Results and discussion

Figure 1 shows the variation of LNT film XRD patterns within the composition range. The use of a 1-step deposition process followed by an external annealing treatment leads to polycrystalline materials without preferential orientation growth. The Lotgering factor f(006) estimating the degree of orientation along the polar c-axis -never exceeds 15% for 1-step depositions. Besides, for Ta-rich composition (x=0.75), a weak peak of the Li-rich phase (Li 3 Nb 0.5 Ta 0.5 O 4 ) near =18.5° can be observed. It is often reported in the literature a degradation of the crystallinity when x<0.3 in LNT thin films, whatever the deposition methods or the underlying substrates [17][18][19][20].

The lattice parameters for LNT films with various Ta content ratios calculated from the XRD patterns are also indicated in figure 1. As expected, Ta-richer materials show a smaller c parameter and a higher a parameter. Indeed, according to the Joint Committee in Powder Diffraction Standard (JCPDS, PDF Nos. 20-631, 38-1252 and 29-836) data for bulk materials, these parameters evolve from a = 5.1494 Å (c = 13.862 Å) for LN to a = 5.1539 Å (c = 13.8152 Å) for LN50T50 to a = 5.154 Å (c = 13.755 Å) for LT. Somewhat smaller lattice parameters of LNT films compared with those of bulk materials are believed to be due to tensile stress. This stress results from a large lattice mismatch and a large difference between the thermal expansion coefficients of LNT and ITO underlying substrate.

The surface morphologies observed by AFM are presented in Figure 2. Introduction of Ta progressively leads to a grain size reduction which makes the film surfaces smoother by decreasing the depth of grain-boundary grooves. The mean roughness of 1m-thick films decreases from 20 nm to 13 nm, 10 nm and 6 nm for LN, LN75T25, LN50T50 and LN25T75, respectively. In the case of solid solutions with increasing Ta content, the film surfaces are relatively smooth with closely-packed grains of uniform size. Average grain sizes of 200 nm, 150 nm, 100 nm and 70 nm could be estimated for LN, LN75T25, LN50T50 and LN25T75, respectively.

SIMS studies show that such as-grown films possess a uniform composition within the whole thickness with limited interdiffusion phenomena. Well-defined interface lines can be observed on both SEM micrographs and SIMS curves. An example is given in figure 3 for LN50T50 films.

To investigate the ferroelectricity at micro-scale, the P-E hysteresis loops were recorded in figure 4. The experiments confirm the existence of a capacitor behavior despite the lake of a marked preferential orientation of the films. Positive remanent polarizations are obtained, even though the values are well below those measured in highly-textured thin films. The polarization capability is mainly influenced by the crystallinity but also strongly depends on the morphology. As expected, introduction of Ta progressively induces a decrease of the remanent polarization. This result is in good accordance with both the literature (LT is less efficient than LN in terms of polarization ability) and the microstructural investigations (smaller grains sizes increase the possibility of leakage phenomena at the grain boundaries and could make more difficult the polarization reversal under the application of an external electric field).

The ferroelectricity at nanoscale was investigated by PFM. Figure 5 shows the vertical deflection signal (V f ) of the cantilever versus the amplitude of the testing voltage (U f ) where a linear response is apparent. The slope is directly proportional to the piezoelectric coefficient of the layers and represents the film vibration with varying electric field in the surface normal direction. Because of the lack of texturation of these 1-step deposited films, we could not get a quantitative measurement of these coefficients and only a qualitative analysis could be done.

In good accordance with micro-scale experiments, the piezoelectric activity decreases with Ta-content.

Based on these previous studies, a general growth strategy was developed for the LN50T50 composition which involves (1) enhancing the crystallinity to get preferentially-oriented structures and (2) minimizing the surface roughness by maintaining a small grain-size and a homogeneous morphology during the film growth. The XRD pattern in figure 6 clearly shows that highly c-axis oriented films can be grown by using an appropriate 2-steps (1h + 5h) deposition process in which nucleation and growth stages can be optimally separated and controlled. The first step (1h) consists of creating a high nucleation density during the initial stage of film growth, while the second step (5h) consists in enhancing the crystallinity of the film. A Lotgering factor f(006) as high as 90% could calculated. The first LNT homo-buffer layer acts as a real seed-layer, promoting the oriented-growth of the bulk of the film during the second step. The polar c-axis is well known to be one of the fastest growth direction in LNT materials [21,22]. (006) Rocking curve full-width at half-maximum values of ~0.4° could be achieved which is comparable with those of LN, LT and LNT films of similar thicknesses and grown by other conventional deposition techniques [23].

The P-E hysteresis loop recorded in figure 7 confirms the ferroelectric activity at micro-scale.

Concomitant with the enhancement of the crystallinity and predominant c-orientation of the films, the use of a 2-steps process seriously increases the ferroelectric properties of the deposited material. A remanent polarization up to 6.9 C/cm 2 could be obtained.

The ferro-and piezo-electricity at nano-scale were investigated by PFM. Figure 8b shows simultaneously acquired images of the surface morphology and the ferroelectric domain structure of an upoled LN50T50 sample. The comparison of the topography and domain structure images shows that the domains appear to be essentially confined by grain boundaries. Note that the use of a 2-steps process influences the crystallinity (predominantly c-oriented growth) but does not affect the overall size of the crystallites. In the piezoresponse image, black and white regions correspond to opposite directions of the out-of-plane spontaneous polarization (polarization vectors oriented upward and toward the bottom electrode, respectively) [24]. Grains with gray tone correspond to polarization vectors deviating from the direction of the normal of the films [25]. The existence of well-evidenced bright and dark areas in these un-poled samples is a manifestation of the so-called self-polarization effect that is frequently observed in thin films [26]. The self-polarization is concomitant to the self-organization of the films. However, a c-preferential growth is not enough to get a full 1-direction of the polarization and a dispersion of the polarization still subsists within the layer. Mismatches between film and substrate, annealing treatments, boundary effects, stress-induced depolarization are as many factors that contribute to the nonuniformity at the nanoscale of the ferroelectric behavior.

Figure 8a shows the vertical deflection signal (V f ) of the cantilever versus the amplitude of the testing voltage (U f ). As illustrated by the equation in figure 8a, the slope is directly proportional to the piezoelectric coefficient (d 33 in case of highly c-oriented materials). As expected, increasing the degree of orientation along the c-axis of the ferroelectric structure by using a 2-steps deposition process induces an increase of the slope of the V s versus U f linear plot which highlights higher piezoelectric properties. In order to ensure the reliability and accuracy of the measurements, experiments were performed in the same conditions on LT (d 33 = 15.1 pm/V) and LN (d 33 = 25.2 pm/V) monocrystals. The linear relationship between the lock-in-amplifier voltage and applied voltage is shown in every case, the slope being proportional to the out-of-plane piezoelectric coefficient. Knowing the d 33 coefficients of these crystals [27,28], we could get the calibration constant of the photodetector sensitivity () and calculate an effective piezoelectric coefficient d 33 of 13.3 pm/V for a c-oriented 2-steps grown LN50T50 layer. The inherent reduction in the piezoelectric coefficient for this composition (middle region of the solid solution) compared with those of bulk materials in both edges might be due to boundary and size effects as well as to internal defects (stressinduced depolarization) in the films.

Conclusions

This work clearly demonstrates the effectiveness of a 2-steps growth process in producing good quality thin films directly on ITO-covered Si(111) substrates by r.f. sputtering.

Nucleation and growth stages could optimally separated and controlled, thus leading to strongly c-oriented LNT layers. These results suggest that it may be possible to deposit LNT thin films with tunable properties by only varying the composition of either the whole film or only the first and second layers.

Figure 1 .Figure 2 .Figure 3 .Figure 4 .Figure 5 .Figure 6 . 2 Figure 7 .Figure 8 .

 123456278 Figure 1. XRD patterns of LNT films deposited on ITO/Si(111) versus Ta content (*, parasitic Li-rich phase) (inset, variation of the lattice parameters versus Ta content)

Acknowledgments

The authors wish to thank Xavier Defay (Master student), M. Ramonda (Montpellier University), F. Fernandez (Montpellier University) and C Merlet (Montpellier University) for their contribution in film syntheses, AFM/PFM, SEM and SIMS experiments, respectively.