PhD; Jean-Michel Martinez

Jean-Loup Guyot

Naziano Filizola

Francis Sondas

Keywords: Hydrology, sediment concentration, Amazon, remote sensing, HYBAM, MODIS

This study addresses the quantification of the Amazon River sediment budget which has been assessed by looking at data from a suspended sediment discharge monitoring network and remote sensing estimates derived from MODIS spaceborne sensor. Surface suspended sediment

concentration has been sampled every 10 days since 1995 (390 samples available) by the international HYBAM program at the Óbidos station which happens to be the last gauged station of the Amazon River before the Atlantic Ocean. Remote sensing reflectance is derived from continuous time series of 554 MODIS images available since 2000 and calibrated with the HYBAM field measurements. Discharge shows a weak correlation with the suspended sediment concentration during the annual hydrological cycle, preventing us from computing sediment discharge directly from the water discharge. Accordingly, river sediment discharge is assessed by multiplying daily water discharge measurements by the suspended sediment concentration averaged on a monthly basis. Comparisons of annual sediment discharge assessed using both field and satellite datasets show a very good agreement with a mean difference lower than 1%.

Both field and satellite-derived estimates of the sediment concentration of the Amazon River are combined to get an uninterrupted monthly average suspended sediment discharge from 1995 to 2007. Unlike the water discharge which exhibits a steady trend over the same period at Óbidos, the 12-year suspended sediment discharge increases by about 20% since 1995, significant at the 99% level. In particular, the interannual variability is much more significant in the sediment discharge than in the river discharge.

Increase in suspended sediment discharge of the Amazon River

1 assessed by monitoring network and satellite data 2 3 JM Martinez 12* , JL Guyot 12 , N. Filizola 3 and F. Sondag 12 samples available) by the international HYBAM program at the Óbidos station which 7 happens to be the last gauged station of the Amazon River before the Atlantic Ocean. 8

Remote sensing reflectance is derived from continuous time series of 554 MODIS 9 images available since 2000 and calibrated with the HYBAM field measurements. 10 Discharge shows a weak correlation with the suspended sediment concentration during 11 the annual hydrological cycle, preventing us from computing sediment discharge 12 directly from the water discharge. Accordingly, river sediment discharge is assessed by 13 multiplying daily water discharge measurements by the suspended sediment 14 concentration averaged on a monthly basis. Comparisons of annual sediment discharge 15 assessed using both field and satellite datasets show a very good agreement with a mean 16 difference lower than 1%. Both field and satellite-derived estimates of the sediment 17 concentration of the Amazon River are combined to get an uninterrupted monthly 18 average suspended sediment discharge from 1995 to 2007. Unlike the water discharge 19 which exhibits a steady trend over the same period at Óbidos, the 12-year suspended 20 sediment discharge increases by about 20% since 1995, significant at the 99% level. In 21 particular, the interannual variability is much more significant in the sediment discharge 22 than in the river discharge. 23 KEYWORDS : Hydrology, sediment concentration, Amazon, remote sensing, INTRODUCTION 1 2 With a drainage basin area of 6.1 10 6 km 2 [START_REF] Goulding | The Smithsonian Atlas of the 42 Amazon[END_REF] and a mean annual 3 discharge estimated at 209 000 m³/s at the river mouth [START_REF] Molinier | Les regimes 25 hydrologiques de l'Amazone et de ses affluents[END_REF], the 4 Amazon basin is the largest river system in the world. Given its large size, the Amazon 5 basin experiences significant climate variability [START_REF] Marengo | Interdecadal variability and trends of rainfall across the Amazon 3 basin[END_REF]. At Óbidos, the most 6 downstream gauged station on the Amazon River in Brazil offering long term 7 hydrological monitoring, annual data for the 1903-1999 period indicate a steadily 8 increasing discharge trend (+9%) over the century, and a recent period of decrease over 9 the last decade of the past century [START_REF] Callède | Evolution du débit de l'Amazone à Obidos de 1903 à 1999[END_REF]. In recent decades, several 10 suspended sediment discharge budgets have been published for the Amazon (Dunne et 11 al., 1998;[START_REF] Filizola | Transfert sédimentaire actuel par les fleuves amazoniens[END_REF][START_REF] Gibbs | Amazon rivers: Environmental factors that control its dissolved and 40 suspended load[END_REF][START_REF] Meade | Storage and 18 remobilization of suspended sediment in the lower Amazon river of Brazil[END_REF][START_REF] Meade | Sediment loads in the Amazon River[END_REF], but the 12 time variability of the sediment concentration, based on 10-day sampling has only been 13 recently made available thanks to the HYBAM program (http://www.ore-hybam.org). [START_REF] Martinez | Amazon floodplain water quality monitoring using MERIS and MODIS 16 data[END_REF] 15 [START_REF] Gibbs | Amazon rivers: Environmental factors that control its dissolved and 40 suspended load[END_REF] provides the first estimate of the sediment discharge of the Amazon River 16 at the Óbidos station of about 500 million tons per year using data from only two 17 sampling campaigns at low and high water levels. Using two additional sampling 18 campaigns conducted during a high water period, [START_REF] Meade | Sediment loads in the Amazon River[END_REF] assessed during 18 field sampling campaigns allowing SSS estimates to be related to the 19 river reach average suspended sediment concentration [START_REF] Filizola | Transfert sédimentaire actuel par les fleuves amazoniens[END_REF]; 20 21 (c) 8-day estimates of the surface-suspended concentration over the river reach assessed 22 from remote sensing images, i.e. 8-day composite MODIS images, calibrated and 23 validated locally with the 10-day SSS measurements [START_REF] Martinez | Surface water quality monitoring in large rivers with 8 MODIS data -Application to the Amazon basin[END_REF].

Most past and present satellites are unsuited to water quality monitoring in rivers and 1 lakes because the sensors used fail to offer an adequate tradeoff between spatial 2 resolution, spatial coverage, revisit frequency and radiometric resolution. A significant 3 amount of research has been devoted to the use of remote sensing data for monitoring 4 inland water quality parameters. However, it is often limited to one-off studies based on 5 high resolution imagery. In this study, we intend to make use of more robust remote 6 sensing data offering daily coverage and for which we previously studied the possibility 7 of retrieving suspended sediment concentration [START_REF] Martinez | 11 Analysis of multitemporal MODIS and Landsat 7 images acquired over 12 Amazonian floodplain lakes for suspended sediment concentration retrieval[END_REF]Martinez et al., 8 2004). The combination of field sampling and remote sensing data supports the 9 provision of robust long term monitoring of the Amazon River sediment discharge for 10 the 1995-2007 period. 11

12

DATA AND METHODS 13 14

Surface-Suspended Sediment Estimates 15 16 The Óbidos hydrological station managed by the Brazilian water agency 17 (www.ana.gov.br) has been furnishing uninterrupted data since 1968. At Óbidos, the 18 watershed covers 4.8x10 6 km² and the river mouth is located 900 kilometers 19 downstream (Figure 1). Discharge has been derived from the rating curve established 20 within the HYBAM project (Callede et al., 2002;[START_REF] Callède | Etablissement de la relation hauteur-16 débit de l'Amazone à Obidos : méthode de la dénivelée normale à géométrie 17 variable[END_REF]. Figure 2 shows 21 the monthly average Amazon River discharge from 1968 to 2007. The Amazon River 22 average annual discharge is 173,000 m 3 /s, with, during the last decade, a noteworthy dry 23 year (-15%) in 1997/1998 marked by a strong El Niño episode. The river discharge 24 shows a very stable value over the period considered for the study of sediment 1 discharge : 1995-2007. 2 3 From March 1995 to December 2007, 390 500-ml SSS samples were collected. 4

Suspended sediment concentration at the river surface has been sampled by local 5 operator in a small boat every 10 days at a fixed point, near the middle of the river reach 6

where the stream is about 2-km wide. Bottles were stored and sent approximately every 7 6 months for filtering to the UnB (Brasilia National University 1995-2003) and recently 8 to the Amazonas State University at Manaus. In the laboratory, the samples were 9 filtered using 0.45 μm cellulose acetate filters, previously dried for 24 hours at 50°C and 10 weighted. The weight difference before and after filtration allows the amount of 11 suspended matter to be determined by unit of liquid. 12 13 Figure 3 displays the clockwise hysteresis in the relation between SSS concentration 14 and river discharge from 1995 to 2003. It shows that there is no simple and robust 15 relationship between river flow and the suspended sediment. The concentration peak 16 occurs two to three months before the annual flood peak during the rising water stage. 17

Around the flood peak, the SSS concentration reaches a minimum. During each year, 18 the SSS concentration is highly variable, from 9 to 260 mg/l. Nevertheless, the pattern is 19 relatively stable from year to year. A specific sampling campaign was conducted to 20 assess the SSS concentration heterogeneity across the river reach. From 66 samples 21 collected on a regular grid of 250 by 250 meters, we calculated a coefficient of variation 22 of 18 %. 23 24 Average suspended sediment concentration 25 1 Eighteen sampling campaigns were conducted between 1995 and 2003 to relate the 10-2 day surface samples to the average suspended sediment (ASS) concentration across the 3 whole river reach. During these campaigns, the discharge was measured with Acoustic 4 Doppler Current Profilers (ADCP). Fifteen 10-liter water samples were collected at 5 three verticals and five different depths using horizontal oceanographic bottles suitable 6 for the Amazon River's operational and environmental conditions (Filizola and Guyot, 7 2004). Each sample was first filtered through 62 μm filters to remove the coarser 8 material. Then, each sample was processed using the same protocol as for the 10-day 9 HYBAM measurement network. Comparison of the results derived with our technique 10 and a depth integration method used by the USGS and the Brazilian Water Agency 11 during the same sampling campaign indicated a difference of less than 5% (Filizola and 12 Guyot, 2004). 13 14 From the 320 samples collected over the whole river reach at Óbidos, we calculated a 15 ASS concentration of 150 mg/l, which is twice the mean SSS concentration of 72 mg/l 16 for 390 samples. Figure 4 shows the SSS concentration as a function of the ASS 17 concentration for the 18 campaigns. A good agreement is found and makes it possible to 18 assess the ASS concentration for the whole river reach from the 10-day SSS 19 measurement network or from satellite data [START_REF] Guyot | Régime et bilan du flux sédimentaire de 44 l'Amazone à Óbidos (Pará, Brésil) de 1995 à[END_REF]. For calculation of 20 sediment discharge we will make use of the following equation relating the average 21 concentration to the surface concentration: 22 ASS = 1.24 . SSS + 43.5

(1) 23

24

The same equation will be used to derive ASS concentration from SSS concentration 1 over the whole period considered (1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007). (http://modis.gsfc.nasa.gov). Band 1 is centered at 645 nm and band 2 at 858.5 nm 25 (infrared). MODIS surface reflectance 8-day composite data were acquired between 1 March 2000 and October 2007 from the NASA Earth Observing System (EOS) data 2 gateway. We chose composite images because i) the 8-day composite is compatible 3 with the 10-day field measurement sampling frequency; ii) it reduces the amount of data 4 to be analyzed as a large number of daily images cannot be used in view of the 5 persistent cloud cover and iii) it significantly reduces the directional reflectance effects 6 and atmospheric artifacts. For each date, the composites from Terra and Aqua are 7 automatically scanned and the image with the lowest cloud coverage is selected. When 8 both composites exhibit low cloud coverage, the composite acquired with the lowest 9 satellite viewing angle is preferred. 10 11 A pixel-based river mask covering nearly 10,000 pixels is manually outlined over the 12 Óbidos station to automatically extract the reflectance in each MODIS image. Retrieval 13 of river stream reflectance using MODIS data however, is greatly hampered by the low 14 spatial resolution that may result in few pure (non-mixed) water pixels, depending on 15 the river width and image acquisition geometry. Along the river bank, the occurrence of 16 multiple materials such as water, vegetation and sand results in a composite pixel with a 17 mixed spectral signal. Starting with the spectra of each pure component or 18 "endmember", the pixel value observed in any spectral band is usually modeled by a 19 linear combination of the spectral responses of the components. The spectra of the 20 vegetation and sand endmembers may be directly assessed from each image from stable 21 and large targets. River pixels are partitioned into homogeneous clusters using the K-22 means algorithm (Martinez et al., submitted). The fraction of each endmember in each 23 cluster is obtained by applying a least squares technique to minimize the unmodeled 24 residual. The set of linear equations is then solved by testing every cluster as a possible 25 "pure" water endmember. The cluster leading to the lowest residual is retained as the 1 water endmember (Martinez et al., submitted). The general bootstrap approach involves resampling of the dataset with repeated 1 replacements [START_REF] Wehrens | The bootstrap: a tutorial[END_REF] to generate an empirical estimate of the sampling 2 distribution. Accordingly, a large number of 'bootstrap samples' is generated, each with 3 the same size as the original dataset. For each bootstrap sample, a linear model using 4

York regression is built and tested against those objects present in the sample to 5 compute the RMSE  and the objects omitted from the resampled set to compute the 6 RMSE ε. To achieve a better estimate of the prediction error, we use the 0.632 7 bootstrap b 632 . Practical and theoretical evidence suggests that this is a very reliable 8 estimator [START_REF] Efron | An introduction to the bootstrap[END_REF]. The final bootstrap estimate is the average value 9 of b 632 over N iterations of the procedure : 10

11      N i i i N b 1 632 632 . 0 ) 632 . 0 1 ( 1   12 13
The factor 0.632 is used because it corresponds to the probability of getting an 14 observation in a bootstrap sample. Although two hundred bootstrap samples are usually 15 sufficient, two thousand bootstrap samples have been routinely used. The dataset for 16 regression and validation consists of 77 reflectance/SSS estimates, from 17 to 235 mg/l 17 with a mean value of 75 mg/l. Based on this dataset the b 632 estimate of the retrieval is 18 29 mg/l (36 % relative error). Field assessment of SSS concentration heterogeneity 19 during one sampling campaign showed a CV of 18 % using 66 samples. Comparison of 20 both estimates highlights the fact that a significant part of the difference between field 21 measurements and satellite-derived estimates should be attributed to SSS concentration 22 heterogeneity across the river reach. which complete records are available for both field measurements and satellite images. 17

The relative difference is -3.0 % (sediment discharge of 788.10 6 tons with field 18 measurements and of 811.10 6 tons using satellite images) for the hydrological cycles of 19 2001 (November 2000 -October 2001) and +1.8 % for 2005 (sediment discharge of 20 797.10 6 tons with field measurements and of 782.10 6 tons using satellite images). Field-21 derived and satellite-derived SSS estimates complement each other for monitoring the 22 suspended sediment discharge. On the one hand, the field measurements provide 23 estimates at fixed and regular dates but fail to provide an assessment of the sediment 24 concentration heterogeneity across the river surface. Additionally, the monitoring 25 network is prone to many potential sources of failure including variable sampling 1 location, operator reliability or loss of samples. When a problem occurs, it may take a 2 few weeks or even months before it can be fixed, resulting in a significant loss of data. 3

On the other hand, satellite measurements must first be calibrated using field 4 measurements and availability depends primarily on the weather. Furthermore, during 5 the rainy season, a clear sky is a remote possibility which may lead to interruptions in 6 the monitoring service. Nonetheless, MODIS images were constantly available for 93 7 consecutive months. This shows that the daily coverage offered by the MODIS sensor is 8 a prerequisite for long term monitoring of tropical areas by remote sensing means. 9

Finally, satellite imagery provides unprecedented knowledge of the surface 10 heterogeneity for much larger areas than a monitoring network would allow. 11 12 Yearly averaged field and satellite-derived suspended sediment discharges were merged 13 to produce a continuous assessment of the inter-annual variability of the sediment 14 discharge of the Amazon River. When available and complete, field-based data records 15 were considered while the remote sensing data was used for the period without 16 complete field measurements (2002, 2003, 2004, 2006 and 2007 cycles). Thus, a 17 complete and continuous assessment of the sediment discharge of the Amazon River 18 was obtained from 1995 to 2007, representing twelve consecutive hydrological cycles 19 (with the beginning of a hydrological cycle in November). Yearly average discharge 20 and yearly average sediment discharge were calculated summing the monthly estimates 21 for each variables. Over this period, the mean river discharge has been 173,000 m³/s 22 with a coefficient of variation of 6.2 %. Between 1996 and 2007, the annual mean 23 sediment discharge is about 754.10 6 tons / year with a coefficient of variation of 8.6 %. 24 This value is consistent with previous studies by [START_REF] Bordas | Evaluation des risques 7 d'erosion et de sedimentation au Bresil a partir de bilans sedimentologiques 8 rudimentaires[END_REF], [START_REF] Filizola | Transfert sédimentaire actuel par les fleuves amazoniens[END_REF] 25 and [START_REF] Guyot | Régime et bilan du flux sédimentaire de 44 l'Amazone à Óbidos (Pará, Brésil) de 1995 à[END_REF] and much higher than the river bed transport, assessed to be of 1 about 4.7 10 6 tons / year at this station [START_REF] Strasser | Bottom structures geometry of the 41 Amazon river[END_REF]. The 1997/1998 2 hydrological cycle shows a very low discharge (-15 % relative to the rest of the time 3 series). If we remove this particular hydrological cycle from the statistics, the mean 4 river discharge remains almost constant at 175,000 m³/s but the coefficient of variation 5 falls to 4.1 %. Clearly, the sediment discharge exhibits a much greater variation over 6 time than the discharge. Finally, the intra-annual variation in sediment discharge is 7 much more regular than inter-annual variation. For example, half the annual sediment 8 budget (51 % on average) is discharged between January and April for every year 9 considered. 10 11 Over the 1996-2007 period, an increasing trend of sediment discharge significant at the 12 99% level can be noticed. More specifically, the Amazon River sediment discharge time 13 series exhibits two contrasting periods, that is, before and after the 2001 hydrological 14 cycle. Before 2001, the annual mean sediment discharge was approximately 688.10 6 15 tons / year (coefficient of variation of 4.4 %). Then the annual mean sediment discharge 16 increased to 801.10 6 tons / year (coefficient of variation of 4.0 %) accounting for an 17 increase of 16 % in terms of absolute sediment discharge between both periods. These 18 observations suggest a significant change in the sediment transport regime of the 19 Amazon River even though the river discharge fails to exhibit a specific trend and the 20 time series is not long enough to reach a definitive conclusion on this topic. 21

22

An increase in sediment discharge may be attributed to stronger erosion processes 23 caused either by a global change (rainfall), or regional changes (land cover change 24 resulting from deforestation for example) or both. On the one hand, Callède et al. 25 [START_REF] Callède | Evolution du débit de l'Amazone à Obidos de 1903 à 1999[END_REF]) assessed the Amazon river discharge at Óbidos and observed a 1 rather stable river discharge since the seventies. However, for the same period, the 2 runoff coefficient, assessed from discharge and rainfall records for the whole basin, is 3 shown to increase, thereby pointing to a possible impact of land cover change (Callede 4 et al., 2008). On the other hand, Espinoza Villar et al. (Submitted) showed that the 5 stability of the mean discharge on the river main stem at Óbidos may be accounted for 6 by opposite regional features upstream : a decrease in low stage runoff, particularly in 7 the southern sub-basins, and an increase in high stage runoff in the north-western 8 region. The same authors [START_REF] Espinoza Villar | Spatio-temporal rainfall variability in the Amazon 32 basin countries (Brazil, Peru, Bolivia, Colombia and Ecuador)[END_REF]) also point out a stronger intra-9 annual variability of rain causing more extreme events in terms of discharge even 10 though the mean discharge tends to remain stable over time. Stronger rainfall variability 11 upstream may support a more efficient production and transportation of sediments. 12 Thus, a change in rainfall pattern may account as well for sediment discharge variation. 13 14 CONCLUSION 15 16 This study contributes to the quantification of erosion processes in one of the main 17 surviving natural ecosystems. Although our work only covers the last 12 years, it 18 demonstrates the interest of new techniques such as remote sensing for long term 19 monitoring of inland waters. The surface reflectance data appears to be robustly linked 20 with the suspended sediment concentration at the river surface over a large range of 21 concentration and for several consecutive hydrological cycles. By combining an 22 excellent temporal resolution and a fine calibration quality, MODIS data may be used 23 operationally along field observations to provide more observations in poorly gauged 24 basins, such as the large-scale river basins. However, the quest for a universal algorithm 25 for suspended sediments retrieval from satellite data is never likely to succeed because 1 the scattering efficiency of suspended particles is very much a function of average 2 particle size that is quite variable from one catchment to another. Thus, local calibration 3 of satellite data would have to be developed and tested for each river basin. 4 5 Our results confirm the independence of river discharge and suspended sediment 6 concentration at the Óbidos station. No major trend during the 1996-2007 period has 7 been found for the river discharge. On the contrary, there exists a significant increase in 8 the sediment budget of the Amazon with a suspended sediment discharge 20 % higher 9 in 2007 relative to 1996. To get further insights into these results, the inter-annual 10 budget of the Amazon River's two main tributaries in terms of sediment discharge i.e., 11 the Madeira River and the Solimões River, that drain the southern and northern part of 12 the Andean Cordillera respectively, will be assessed. 13 Figure 1 : Location of Óbidos on the Amazon River, 900-km upstream from the river 3 mouth. At Óbidos, the Amazon River has received most of its tributaries including the 4 Madeira River (the main tributary in terms of suspended sediment concentration) and 5 the Negro river (volumetrically the main tributary). At Óbidos, the drainage area is 4.8 6 10 6 km². 7 8

Figure 2: Monthly average river discharge of the Amazon River at Óbidos. Over the 9 period considered in this study , the average discharge is 173,000 m³/s.

4 5 6 1

 6 Université de Toulouse; UPS (SVT-OMP); LMTG; 14 Av, Edouard Belin, F-31400 7 Toulouse, France 8 2 IRD; LMTG; F-31400 Toulouse, France 9 3 UEA, Av. Darcy Vargas, 1200; 69000-000 Manaus, Brazil 10 Issue : "Sediment Sources and sediment delivery under 15 environmental change" 16 network and remote sensing estimates derived from MODIS spaceborne sensor. Surface 5 suspended sediment concentration has been sampled every 10 days since 1995 (390 6

  got a higher sediment 19 discharge of 900 million tons per year. From the results of eight CAMREX sampling 20 campaigns, Meade et al. (1985) obtained an even higher sediment discharge value of 21 1200 million tons per year. More recently, using quarterly data from the Brazilian water 22 quality network, Bordas et al. (1988) and subsequently Filizola et al. (1999) derived a 23 new estimate for the annual sedimentary flux at the Óbidos station of 600 million tons 24 per year, a value close to the first estimate provided by Gibbs. Based on a 10-day 25 sampling from the HYBAM program, Guyot et al. (2005) suggest an increasing 1 sediment discharge from 2000 to 2003 and also noted that the trend in suspended 2 sediment concentration is not correlated with discharge. In other words, it is not 3 possible to derive a simple relationship between river flow and suspended sediment 4 concentration. It is therefore not possible to derive sediment discharge from the daily 5 measurement of river water flow alone but instead, simultaneous monitoring of 6 sediment concentration and of water discharge is required. In the current study, based 7 on an updated HYBAM dataset (1995-2007) and surface suspended sediment 8 concentrations calculated by MODIS reflectance inversion (Martinez et al., 2004) for 9 the 2000-2007 period, new results are presented highlighting improved monitoring of 10 suspended sediment. To quantify the Amazon River mean annual sediment discharge as 11 well as the inter and intra-annual variability, various datasets from the Óbidos station 12 have been used, namely : 13 14 (a) 390 surface-suspended sediment (SSS) point samples collected every 10 days 15 between 1995 and 2007 at Óbidos for the HYBAM program (Guyot et al., 1999); 16 17 (b) intensive sampling of the river reach over the width and depth of the cross-section 18

2 3sensing images 4 5

 24 RemoteNumerous papers deal with the sensitivity of remote sensing reflectance to the 6 suspended sediment concentration in oceanic and inland waters. A significant number 7 of researchers have reported a strong positive correlation between surface suspended 8 concentrations and spectral radiance[START_REF] Bhargava | Spectral refletance relationships to turbidity 1 generated by different clay materials[END_REF] Bhargava and 9 Mariam, 1991;[START_REF] Doxaran | Spectral signature 22 of highly turbid waters. Application with SPOT data to quantify suspended 23 particulate matter concentrations[END_REF][START_REF] Hinton | Application of eigenvector analysis to remote sensing of coastal 1 water quality[END_REF][START_REF] Martinez | Amazon floodplain water quality monitoring using MERIS and MODIS 16 data[END_REF] Mertes et al., 10 1993; Novo et al., 1989a; Novo et al., 1989b;[START_REF] Ritchie | Comparison of measured suspended sediment 35 concentrations with suspended sediment concentrations estimated from Landsat 36 MSS data[END_REF] Ritchie et al., 11 1987) and have noted that the relation may depend on the range of concentration, water 12 types and suspended matter origin. Most studies agree that the best correlation between 13 reflectance and SSC is between 700 and 800 nm in turbid inland waters. In this study 14 we propose to use data from the latest generation of spaceborne sensors such asMODIS 15 that are promising in terms of inland water monitoring because they offer the spatial 16 resolution and spatial coverage that are compatible with the dimensions of river systems 17 while allowing for fine temporal resolution. 18 19 The Collection 5 atmospherically-corrected surface reflectance products from the Terra 20 and Aqua MODIS spaceborne sensors are utilized in this study. The MODIS data 21 product MOD09Q1 (Terra on-board sensor) and MYD09Q1 (Aqua on-board sensor) 22 provides calibrated reflectance for two radiometric bands measured at a 250 m pixel 23 resolution while offering near-daily time coverage over tropical areas 24

2 3 17 Figure 5

 2175 Figure5shows the relationship between the water endmember reflectance extracted 18

Figure 6 7 8Figure 7

 677 Figure 6 compares the monthly average SSS concentration measurements with the 3

14 ACKNOWLEDGMENTS 15 16

 1415 FIGURE CAPTIONS 1 2Figure1: Location of Óbidos on the Amazon River, 900-km upstream from the river 3 mouth. At Óbidos, the Amazon River has received most of its tributaries including the 4 Madeira River (the main tributary in terms of suspended sediment concentration) and 5 the Negro river (volumetrically the main tributary). At Óbidos, the drainage area is 4.8 6 10 6 km². 7 8Figure2: Monthly average river discharge of the Amazon River at Óbidos. Over the 9 period considered in this study, the average discharge is 173,000 m³/s. 10 11 Figure 3 : Surface suspended sediment concentration at Óbidos as a function of the 12 Amazon river discharge. Suspended sediment concentration measurements have been 13 collected every 10 days by the HYBAM program since 1995. 14 15 Figure 4 : Average suspended sediment concentration as a function of the surface 16 suspended sediment concentration assessed during 18 field sampling campaigns. 17 Sampling within the water column was based on 15 point samples at 3 different 18 verticals and 5 increasing depths. Error bars stand for the standard deviation of all 19 points collected at a given campaign, either at the river surface (3 points) or within the 20 water column (12 points). 21 22 Figure 5 : Surface reflectance of the Amazon River water derived from MODIS 8-day 23 composite (Terra and Aqua Satellite) as a function of the surface suspended sediment 24 concentration. Surface reflectance was extracted from the infrared channels available in 25 the 250-meter resolution mode. Measurements represent monthly average values and 26 error bars stand for the standard deviation each month. 27 28 Figure 6 : Comparison of surface suspended sediment concentration derived from the 29 10-day HYBAM samples and of satellite-derived estimates previously calibrated with 30 field measurements. Error bars for the satellite-derived estimates stand for the 95% 31 confidence interval of the prediction previously calibrated with field measurements. 32 33 Figure 7 : Comparisons of monthly average river discharge with suspended sediment 34 discharge derived from field measurements and MODIS images. 35 36 Figure 8 : Annual Amazon river discharge and sediment discharge between 1996 and 37 2007 at Óbidos. 38 39

10 11 Figure 3 : 15 Figure 4 :Figure 5 : 28 Figure 6 :Figure 7 : 36 Figure 8 :

 11315452867368 FIGURE CAPTIONS 1 2Figure1: Location of Óbidos on the Amazon River, 900-km upstream from the river 3 mouth. At Óbidos, the Amazon River has received most of its tributaries including the 4 Madeira River (the main tributary in terms of suspended sediment concentration) and 5 the Negro river (volumetrically the main tributary). At Óbidos, the drainage area is 4.8 6 10 6 km². 7 8Figure2: Monthly average river discharge of the Amazon River at Óbidos. Over the 9 period considered in this study, the average discharge is 173,000 m³/s. 10 11 Figure 3 : Surface suspended sediment concentration at Óbidos as a function of the 12 Amazon river discharge. Suspended sediment concentration measurements have been 13 collected every 10 days by the HYBAM program since 1995. 14 15 Figure 4 : Average suspended sediment concentration as a function of the surface 16 suspended sediment concentration assessed during 18 field sampling campaigns. 17 Sampling within the water column was based on 15 point samples at 3 different 18 verticals and 5 increasing depths. Error bars stand for the standard deviation of all 19 points collected at a given campaign, either at the river surface (3 points) or within the 20 water column (12 points). 21 22 Figure 5 : Surface reflectance of the Amazon River water derived from MODIS 8-day 23 composite (Terra and Aqua Satellite) as a function of the surface suspended sediment 24 concentration. Surface reflectance was extracted from the infrared channels available in 25 the 250-meter resolution mode. Measurements represent monthly average values and 26 error bars stand for the standard deviation each month. 27 28 Figure 6 : Comparison of surface suspended sediment concentration derived from the 29 10-day HYBAM samples and of satellite-derived estimates previously calibrated with 30 field measurements. Error bars for the satellite-derived estimates stand for the 95% 31 confidence interval of the prediction previously calibrated with field measurements. 32 33 Figure 7 : Comparisons of monthly average river discharge with suspended sediment 34 discharge derived from field measurements and MODIS images. 35 36 Figure 8 : Annual Amazon river discharge and sediment discharge between 1996 and 37 2007 at Óbidos. 38 39

  Figure 1 Click here to download high resolution image

Figure 7

 7 Figure 7 Click here to download high resolution image


Q Liebgott

A Borroto

Z Fernández-Gutiérrez

S Bruyère

F Mücklich

D Horwat
email: david.horwat@univ-lorraine.fr

Deposition rate controls nucleation and growth during amorphous/nanocrystalline competition in sputtered Zr-Cr thin films

Keywords: thin films, competitive growth, nucleation, growth

Dual-phase Zr-based thin films synthesized by magnetron co-sputtering and showing competitive growth between amorphous and crystalline phases have been reported recently.

In such films, the amorphous phase grows as columns, while the crystalline phase grows as separated cone-shaped crystalline regions made of smaller crystallites. In this paper, we investigate this phenomenon and propose a model for the development of the crystalline regions during thin film growth. We evidence using X-ray diffraction (XRD), scanning electron microscopy (SEM) and transmission electron microscopy (TEM), that this competitive selfseparation also exists in co-sputtered Zr-Cr thin films with Cr contents of ~84-86 at.%, corresponding to the transition between the amorphous and crystalline compositions, and in the Zr-V system. Then, to assess the sturdiness of this phenomenon, its existence and geometrical characteristics are evaluated when varying the film composition and the deposition rate. The variation of geometrical features, such as the crystalline cone angle, the size and density of crystallites, is discussed. Is it shown that a variation in the deposition rate changes the nucleation and growth kinetics of the crystallites. The surface coverage by the crystalline phase at a given thickness is also calculated for each deposition rate. Moreover, comparison is made between Zr-Cr, Zr-V, Zr-Mo and Zr-W dual-phase thin films to compare their nucleation and growth kinetics.

Introduction

During the last decades, interest for new functional surfaces has continuously been growing [START_REF] Yang | Comparison of two-step surface treatment on surface roughness and corrosion resistance of TC4 alloy parts prepared by SLM and SEBM[END_REF][START_REF] Ma | Materials and structure engineering by magnetron sputtering for advanced lithium batteries[END_REF][START_REF] Garcia-Giron | Combined surface hardening and laser patterning approach for functionalising stainless steel surfaces[END_REF]. This is because the functionalities of surface-modified materials are manifold: antibacterial surfaces [START_REF] Müller | Increasing Antibacterial Efficiency of Cu Surfaces by targeted Surface Functionalization via Ultrashort Pulsed Direct Laser Interference Patterning[END_REF][START_REF] Ji | Corrosion and antibacterial performance of novel selective-laser-melted (SLMed) Ti-xCu biomedical alloys[END_REF][START_REF] Yi | Antibacterial Ti-35Nb-7Zr-xCu alloy with excellent mechanical properties generated with a spark plasma sintering method for biological applications[END_REF], solar cells [START_REF] Wu | Surface Passivation Using 2D Perovskites toward Efficient and Stable Perovskite Solar Cells[END_REF], wear or corrosion protection [START_REF] Tabish | Construction of NiCo/graphene nanocomposite coating with bulges-like morphology for enhanced mechanical properties and corrosion resistance performance[END_REF][START_REF] Purcek | Microstructural, mechanical and tribological properties of ultrafine-grained Cu-Cr-Zr alloy processed by high pressure torsion[END_REF][START_REF] Zhu | Microstructures, wear resistance and corrosion resistance of CoCrFeNi high entropy alloys coating on AZ91 Mg alloy prepared by cold spray[END_REF], to name a few. Many advances in the field of thin films have been made thanks to elaboration techniques such as magnetron sputtering, allowing to inexpensively synthesize thin films at low temperatures. Among these thin films, Zr-based thin film metallic glasses (TFMGs) have been intensively investigated due to their good mechanical properties such as hardness beyond 10 GPa, improvement of fatigue resistance of 316L stainless steel, and their corrosion resistance, for instance [START_REF] Deng | The fabrication and property evaluation of Zr-Ti-B-Si thin film metallic glass materials[END_REF][START_REF] Jia | Thin-film metallic glasses for substrate fatigue-property improvements[END_REF][START_REF] Liu | Micro-scratch study of a magnetron-sputtered Zr-based metallic-glass film[END_REF].

The ease to synthesize such TFMGs is characterized by the glass-forming ability (GFA). The higher the GFA, the easier to sputter-deposit a TFMG. For the GFA to be the highest, the sputtered film must contain different elements, with a difference greater than 10 % in atomic radii, have a negative mixing enthalpy, and a high quenching rate [START_REF] Inoue | Glass-forming ability of alloys[END_REF]. Moreover, in the case of Zr-X systems (X = Cr, V, Mo, W), intermetallic phases can be found in the equilibrium phase diagram, which increase the GFA, despite the atomic radii of the different elements is rather close and the mixing enthalpy is only slightly negative (-4 to -12 kJ/mol) [START_REF] Takeuchi | Classification of Bulk Metallic Glasses by Atomic Size Difference, Heat of Mixing and Period of Constituent Elements and Its Application to Characterization of the Main Alloying Element[END_REF]. This means that although it is possible to find amorphous films in a wide range of compositions, it is still possible to sputter-deposit crystalline films outside of this range. Thus, sputtering films at the transition between the amorphous and crystalline compositions could lead to new microstructures, such as the dual-phase crystalline and amorphous thin films that have been reported in the literature. This dual-phase morphology has already been observed in Zr-W [START_REF] Borroto | Composition-driven transition from amorphous to crystalline films enables bottom-up design of functional surfaces[END_REF][START_REF] Zeman | Self-formation of dual glassy-crystalline structure in magnetron sputtered W-Zr films[END_REF][START_REF] Borroto | Growth kinetics and origin of residual stress of two-phase crystalline-amorphous nanostructured films[END_REF] and Zr-Mo [START_REF] Borroto | Controlling surface morphology by nanocrystalline/amorphous competitive self-phase separation in thin films: Thickness-modulated reflectance and interference phenomena[END_REF]. Moreover, similar morphologies have been reported in the literature for different systems (Ti-Al [START_REF] Kolkovsky | Electrical and structural properties of direct current magnetron sputtered amorphous TiAl thin films[END_REF], Ti-O [START_REF] Gago | Surface morphology of heterogeneous nanocrystalline rutile/amorphous anatase TiO2 films grown by reactive pulsed magnetron sputtering[END_REF], Al-N [START_REF] Miska | olumnar growth of AL by r.f. magnetron spu ering Role of the } planes[END_REF]), where it has only been mentioned without much attention given to its development. These dual-phase thin films are the result of a competitive growth between the amorphous and crystalline phases during film growth, leading to unique surface morphologies [START_REF] Borroto | Composition-driven transition from amorphous to crystalline films enables bottom-up design of functional surfaces[END_REF][START_REF] Borroto | Controlling surface morphology by nanocrystalline/amorphous competitive self-phase separation in thin films: Thickness-modulated reflectance and interference phenomena[END_REF]. A possible origin for crystallization in a given range of composition is that GFA is favored, meaning that the liquid is relatively stable compared to the crystalline phase. In other words, when the composition gets closer to the crystalline composition nucleation becomes easier. Moreover, Borroto et al. have evidenced that, in the Zr-W system, films undergo evolution from amorphous, to nucleation at the column boundaries, to random nucleation as the tungsten content increases and nucleation rate increases [START_REF] Borroto | Composition-driven transition from amorphous to crystalline films enables bottom-up design of functional surfaces[END_REF].

Even if this dual-phase morphology has been observed in different binary systems, the underlying mechanisms governing the development of competitive growth of the two phases are currently not well understood. Also, the sturdiness of the phenomenon regarding the deposition conditions is still unknown, and it is unknown if this phenomenon is present regardless of the deposition conditions, such as deposition rate, or not. This is mainly due to the facts that this phenomenon has only been first observed recently, and the composition range in which it occurs is narrow, making it difficult to observe experimentally.

In this study, we show that this phenomenon can be extended to Zr-Cr co-sputtered thin films. The competitive growth is tested by changing the deposition rate between 3.8 and 74 nm/min to test if it can exist over a wide range of deposition rates, if the composition range in which it occurs changes, and to compare the geometrical features of the obtained crystalline regions. Finally, nucleation and growth evolutions are explored in order to explain our results and generalize our understanding of the competitive growth process in Zr-based sputtered thin films. It is shown that the angle of crystalline cones decreases when increasing the deposition rate, and that it is due to a difference in nucleation and growth kinetics of the crystallites inside the cones. Then, these results are compared with dualphase Zr-V, Zr-Mo and Zr-W thin films in regard to the geometrical features of the crystalline phase.

Materials and methods

Thin films synthesis

Nanostructured Zr-Cr thin films were deposited onto (100) monocrystalline Si substrates ( 15x 15 mm²) using DC magnetron co-sputtering of Zr and Cr metallic targets (targets dimensions: 2 inches diameter, 3 mm thickness and purity higher than 99.9 %) in an argon atmosphere. The two targets were in confocal configuration and the substrate-holder rotation was set at 15 rpm to ensure homogeneity of the deposited films. The sputtering chamber was pumped down via a mechanical and a turbo-molecular pumps allowing a base pressure of 10 -8 mbar. The working argon pressure was 2 Pa, and the targets to substrate distance was set at 9 cm for the two targets. The deposition rate was controlled by the discharge current applied to the Zr target (0.04 A, 0.075 A, 0.15 A or 0.3 A). To each discharge current value corresponds one deposition rate reference (respectively 5, 11, 30 and 63 nm/min). For each deposition rate reference, the discharge current applied to the Cr target varied from 0.09 A to 0.72 A. This allowed controlling the chemical composition of the sputtered thin film, as the ratio of atoms sputtered from each target was changed with minor modification of the deposition rate around the reference rate (for more information, see Fig. S1 in Supplementary Information).

This allowed changing the composition between 82 and 88 at.%Cr for deposition rates between 3.8 and 74 nm/min. The deposition time for these films varied from 20 to 240 min, the first being for the highest deposition rate and the latter for the lowest deposition rate. This allowed to synthesize thin films with a thickness of 1-1.2 µm. For Zr-V thin films, the chamber parameters were the same as for Zr-Cr thin films. The discharge currents applied to Zr and V targets (the V target has the same dimensions as Zr and Cr targets, with a purity higher than 99.9%) were 0.1 A and 0.42 A, respectively. The deposition time was 105 min. This resulted in 2 µm thick thin films containing 86 at.%V.

For comparison purposes, a Zr-Mo and a Zr-W thin film have also been deposited. For Zr-Mo, a 3.7 µm thick thin film has been deposited in 150 min (24 nm/min deposition rate) with 0.3 A and 0.28 A applied to the Zr and Mo targets, respectively. The chamber parameters and target geometry are the same. For Zr-W, a 3.1 µm thick thin film has been deposited in 60 min (52 nm/min deposition rate) at a 3 Pa working pressure with 0.3 A and 0.5 A applied to the Zr and W targets, respectively. The W target geometry was the same as for the other targets used in this study.

During the experiments, the substrate temperature has been monitored using a thermocouple and did not exceed 45 °C for all depositions.

Thin films characterization

Film thickness was measured with a Bruker Dektak XT contact profilometer. X-ray diffraction (XRD) measurements were conducted in the Bragg-Brentano configuration with KαCu radiation (λ = 1.5406 Å) using an AXS Bruker D8 Advance diffractometer. Scanning electron micrographs were taken with a Zeiss GeminiSEM 500 scanning electron microscope (SEM) to analyze the surface morphology and the cross-section of the films. Film composition was obtained using X-ray energy dispersive spectroscopy (EDS) integrated in the SEM.

Transmission electron microscopy (TEM) analysis was conducted using a cold FEG JEOL ARM200 microscope. Cross-sectional TEM samples of films were prepared using a focused ion beam (FIB) scanning electron microscope dual beam system (FEI Helios 600). Throughout the FIB process, the time during the ionic cuts was the shortest possible to avoid any heating effect.

Image processing

Surface coverage by the crystalline phase was obtained using a homemade image treatment MatLab program on at least 3 different cross-section SEM micrographs and analyzing it at a film thickness of 750 nm (for more information, see Fig. S3 and Fig. S4 in Supplementary material). We defined the linear coverage by the crystalline phase as the ratio between the length corresponding to the crystalline phase and the total length of a line drawn at a given thickness of the film, and we extrapolated it to be equal to the surface coverage by the crystalline phase. Cone angles and size of crystallites were determined from cross-section SEM micrographs using ImageJ software using at least 10 cones for each calculation. For the crystalline geometry results, the deposition rates will be presented as reference deposition rates, with each reference corresponding to a given applied current on the Zr target, which means that 4 points representing each applied discharge current on the Zr target will be studied. The number of crystallites per cone was obtained by calculating the ratio of the average crystalline cone volume divided by the average crystallite volume. The average cone volume was calculated using the formula , where h is the height of the cone (set at 500 nm, to avoid miscalculation due to coalescence of the crystalline cones), and α the crystalline cone angle. The average crystallite volume was obtained by considering the crystallite as a cylinder; its volume was calculated using the formula , where R is the radius of the crystallite, and h its length. The obtained ratio is the number of crystallites per crystalline cone, and was used to extrapolate the nucleation rate of crystallites inside the cones.

Results and discussion

When synthesizing Zr-Cr thin films by magnetron sputtering, a composition-driven transition from amorphous to crystalline Cr(Zr) solid solutions has been reported at ~89 at.%Cr [START_REF] Kim | The corrosion behavior of sputter-deposited amorphous Chromium-Zirconium alloys in 6M HCl solution[END_REF].

This work aims to study what happens at the transition range, and aims to search for a competitive growth between an amorphous and crystalline phases, as has been seen for other Zr-based binary systems in magnetron sputtering [START_REF] Borroto | Composition-driven transition from amorphous to crystalline films enables bottom-up design of functional surfaces[END_REF][START_REF] Zeman | Self-formation of dual glassy-crystalline structure in magnetron sputtered W-Zr films[END_REF][START_REF] Borroto | Growth kinetics and origin of residual stress of two-phase crystalline-amorphous nanostructured films[END_REF][START_REF] Borroto | Controlling surface morphology by nanocrystalline/amorphous competitive self-phase separation in thin films: Thickness-modulated reflectance and interference phenomena[END_REF]. For this purpose, different thin films at compositions around the transition between these two phases were deposited at a 11 nm/min deposition rate. X-ray diffractograms of three of these thin films are shown in Fig. 1 (a), with compositions ranging from 83 to 88 at.%Cr, close to the 89 at.%Cr reported in [START_REF] Kim | The corrosion behavior of sputter-deposited amorphous Chromium-Zirconium alloys in 6M HCl solution[END_REF]. The film with 83 at.%Cr is totally X-Ray amorphous, and the film with 88 at.%Cr is totally crystalline. However, for a composition between these two (at 85 at.%Cr), we can see a mixture of the two XRD signals, showing that the two phases coexist in the same film. The shift in diffraction angle for the (110) bcc Cr plane is due to a change in the lattice parameter.

Indeed, increasing the Zr content in the Cr(Zr) solid solution increases the lattice parameter as Zr has an atomic radius larger than that of Cr, thus making the peak to shift towards lower diffraction angles.

The same thin films have been characterized with SEM, and their surface micrographs are shown in Fig. 1 (b-d). As can be seen, the amorphous and crystalline films present different surface morphologies. At the composition of the transition, however, two different regions can be observed, an amorphous and a crystalline, separated by an interface. According to previous works [START_REF] Borroto | Composition-driven transition from amorphous to crystalline films enables bottom-up design of functional surfaces[END_REF][START_REF] Zeman | Self-formation of dual glassy-crystalline structure in magnetron sputtered W-Zr films[END_REF][START_REF] Borroto | Growth kinetics and origin of residual stress of two-phase crystalline-amorphous nanostructured films[END_REF][START_REF] Borroto | Controlling surface morphology by nanocrystalline/amorphous competitive self-phase separation in thin films: Thickness-modulated reflectance and interference phenomena[END_REF], the crystalline region is in the form of disks on the surface, surrounded by an amorphous matrix. From this micrograph, it is also noticeable that, at some point, the crystalline regions coalesce. A cross-section SEM micrograph, Fig. 1 (e),

shows that the amorphous phase grows in a columnar microstructure, while the crystalline phase grows as cones, with a dome on the surface. These cones do not nucleate from the beginning of deposition, but after a certain thickness, and the origin of each cone is not at the same thickness. This explains why the area of each cone emerging at the surface is different. Indeed, the surface of the crystalline region on the surface depends on the thickness where the cone nucleates, because the larger the cone, the larger its surface area.

The obtained microstructure for Zr-Cr thin films is the same as what has been observed in the other Zr-based systems. Moreover, the cone angle is nearly the same whatever its nucleation thickness. (e) Cross-section SEM micrographs showing the dual-phased sample, with amorphous columns and crystalline cones with a dome shape on the surface.

Interestingly, the surface morphology can be tailored by changing the film thickness. Indeed, as thickness increases, the surface coverage by the crystalline phase increases, until it eventually covers the whole surface. Moreover, changing the composition inside the transition zone can also be used to control the surface morphology [START_REF] Takeuchi | Classification of Bulk Metallic Glasses by Atomic Size Difference, Heat of Mixing and Period of Constituent Elements and Its Application to Characterization of the Main Alloying Element[END_REF], as the nucleation density of the crystalline cones increases with an increasing Cr content. Therefore, combining thickness and composition can help tailoring the surface of the deposited Zr-Cr thin films. Nonetheless, the range of this competitive growth is less than 5 at.%Cr, thus very careful investigations are required to observe what happens during growth and create models.

To further understand how the competitive growth develops and can be manipulated, the deposition rate of the Zr-Cr thin films has been varied in the range 5-63 nm/min reference deposition rates. Fig. 2 shows the surface coverage by the crystalline phase as a function of the film composition and for various deposition rates. The value is measured at a 750 nm thickness for all the films. Films with a 0% surface coverage are totally amorphous, while films with a 100% surface coverage are totally crystalline at the surface, meaning they either are crystalline from the start of deposition or that crystalline cones overgrew the amorphous phase and covered the whole surface. The existence of the competitive growth is approximately in the range of 84 to 86 at.%Cr for all the deposited films. Yet, due to the narrow composition range to observe this competitive growth, it is difficult to conclude whether or not the deposition rate affects the transition composition range.

Fig. 2: Values of the surface coverage by the crystalline phase at 750 nm thickness, extrapolated from cross-section SEM micrographs, for each deposition rate range. Some error bars are too small to be seen.

However, it is important to note that in this wide range of reference deposition rates, from 5

to 63 nm/min, the competitive growth has always been observed, which indicates that it is a process resilient to changes in deposition conditions and is encouraging to find it in other

systems. Yet, it is important to notice that the overall geometry of the structures is affected by the deposition rate, as shown in Fig. 3 (a-b). As can be seen, the crystalline cone angle for low deposition rates, in Fig. 3 (a), is larger than for high deposition rates, in Fig. 3 (b). Hence, a reduction of the crystalline cone angle is observed when increasing the deposition rate.

Furthermore, a difference is observed depending on the alloy deposited, as can be seen when comparing Zr-Cr thin films with Zr-V thin films in Fig. 3 (c). Note that Fig. 3(c) proves that the competitive growth also exists in the Zr-V system. For the Zr-Cr thin films, Fig. 6 (a) gives the crystalline cone angle as a function of deposition rate. When the deposition rate increases, the crystalline cone angle decreases. However, this decrease is quite small, given the fact that the deposition rate has been increased approximately 12-fold. The Zr-V thin films were deposited at a single deposition rate of 18 nm/min, resulting in the cones having an average angle of 48.4°, which is much larger than for Zr-Cr thin films. Zr-Mo thin film deposited at a 24 nm/min deposition rate resulted in a 39.9° cone angle, while the Zr-W thin film deposited at a 52 nm/min resulted in a 45.4° cone angle. For the nucleation of a crystalline cone to occur, an energy barrier has to be overcome. The energy needed can mainly be obtained chemically, thermally or mechanically. As suggested by the EDS results on the TEM sample, the composition regarding Zr and Cr elements is the same throughout the whole sample, so it is unlikely that a local chemical gradient is at the origin of the nucleation. Moreover, during the whole deposition, the substrate temperature did not exceed 45 °C, which makes the hypothesis of thermal energy being the precursor of the nucleation less plausible. The mechanical energy originates from local changes of the strain energy due to an uneven distribution of the stress through the film. It has been shown that these dual-phase thin films exhibit a change of internal mechanical stress at the first stages of the crystallite nucleation. Thus, it is likely that the origin for the nucleation of the first crystallite lies in the mechanical energy aquired thanks to mechanical stress [START_REF] Borroto | Growth kinetics and origin of residual stress of two-phase crystalline-amorphous nanostructured films[END_REF].

It can be seen on the SEM micrographs (Fig. 3) that some crystallites grow from the beginning of the cone, and some other nucleate at the interface between a crystallite and the amorphous matrix, or between crystallites. It is easier to observe on the Zr-V thin film, as the crystalline phase is less dense and the size of the crystallites is larger than for Zr-Cr. On Fig. 3 (c), on the cone on the right of the micrograph, vertical crystallites can be seen at the axis of the cone. In contrast, crystallites that nucleated at the interface between the first crystallites and the amorphous matrix on the right, and on the left some crystallites show a larger angle, indicating that they nucleated higher in the cone between different crystallites.

Using this model, the change in crystalline cone angle with deposition rate might find its origin either in a difference in nucleation rate of the crystallites inside the cones, a difference in their growth kinetics, or both.

The first explanation for the decrease of the crystalline cones angle with increasing deposition rate is the surface diffusion of adatoms. Indeed, an increased deposition rate means less time for the adatoms to diffuse, and thus less in-plane growth of the crystalline cones, reducing the cone angle. Nevertheless, given the high increase in deposition rate, the in-plane growth rate would need to be 8 times higher if the diffusion was the only parameter affecting the cone angle, following the equation given by Borroto et al. [START_REF] Borroto | Composition-driven transition from amorphous to crystalline films enables bottom-up design of functional surfaces[END_REF]:

With the in-plane growth rate, the deposition rate, and the crystalline cone angle, as shown on Fig. 3.

Hence, changing the deposition rate affects the in-plane growth of the crystallites. This is confirmed in Fig. 6 (b), where a ~15 % decrease in crystallite size is observed when increasing the deposition rate from 5 to 63nm/min, due to the fact that the adatoms have less time to diffuse on the surface of the film when the deposition rate is higher, and that means less inplane growth for the crystallites.

However, this ~15 % decrease in crystallite size alone does not explain the ~30 % decrease in cone angle. According to our model, it means that there could be another phenomenon happening, such as a difference in nucleation rate of the crystallites inside the cones. Thus, if this model of nucleation and growth of the crystalline phase is correct, a decrease of the nucleation rate should be observed when increasing the deposition rate.

To quantify the difference in nucleation inside the cones, the number of crystallites in a cone must be known. Yet, two problems arise when counting the number of crystallites per cone.

The first is due to the density of the crystallites in the cones, making it difficult to count them. Some interfaces can be easily seen, and have been used to calculate the average crystallite size for each deposition rate range, but it is not the case for the vast majority of the crystallites, where it becomes difficult to see the separation. The second problem is that when observing a cross-section SEM micrograph, the cones are not always cut in their center, and it is of great difficulty to know exactly where a cone has been cut, which means counting the crystallites from SEM micrographs is misleading.

To overcome these issues, the average number of crystallites per cone will be calculated by dividing the average cone volume by the average crystallite volume. To calculate the first one, the volume is calculated by using the cone angle and setting the height to 500 nm, which means for cones that have not already coalesced. For the latter, the crystallite is assumed to be a cylinder, of radius half of the crystallite size shown in Fig. 6 (b), and of length half of the 500 nm height used for the cone, as all crystallites don't nucleate at the origin of the cone. Then, the average cone volume is divided by the average crystallite volume, giving the plot in Fig. 6 (c). As can be seen, for a deposition rate between 5 and 30 nm/min, the nucleation density in a cone does not significantly change. However, when depositing films at 63nm/min, a 40 % reduction of number of crystallites is observed, which means that the nucleation rate is lower for this deposition rate, contributing to reducing the crystalline cone angle.

It should be noted that this calculation gives the same results no matter the length of the crystallites as compared to the cone height. As can be seen in Fig. 6, when increasing the deposition rate from 5 nm/min up to 30 nm/min, the decrease in crystalline cone angle is mostly due to the reduction of the crystallite size, and the nucleation density does not significantly change. Hence, at these deposition rates, the change in crystalline cone angle is mostly governed by the diffusion of the adatoms on the surface of the film during growth, whereas increasing the deposition rate from 30 to 63 nm/min did not significantly change the crystallite size. Instead, the number of crystallites per cone decreased by nearly 40 % as compared to other deposition rates, which means that the decrease in crystallite cone angle for very high deposition rates is mostly due to a lower nucleation density of the crystallites in the cones.

As a comparison, for the Zr-V thin films, as can be seen in Fig. 6 (a), the crystalline cone angle is much higher than that of Zr-Cr thin films, being 48° and from 21° to 32°, respectively.

Moreover, it can be seen in Fig. 6 (b) that the crystallite size is 87 nm, approximately 2 times higher than that of Zr-Cr films, and the number of crystallites per cone is nearly the same as for Zr-Cr thin films as Fig. 6 (c) shows. Thus, the higher cone angle in Zr-V dual phased thin films as compared to Zr-Cr thin films might find its origin in the higher surface diffusion of V adatoms as compared to Cr adatoms, leading to higher in-plane growth of the crystallites in Zr-V crystalline cones and thus a higher cone angle.

An explanation for the higher surface diffusion of V adatoms as compared to Cr adatoms in the studied Zr-V and Zr-Cr alloys lies in their different melting temperatures and solidification intervals. According to the literature, the stable equilibrium peritectic temperature of our Zr-V thin films is 1573 K [START_REF] Štrof | Laves phases in the -Zr system below room temperature: Stability analysis using ab initio results and phase diagram[END_REF] and solidification interval is close to 400 K at the composition range of interest, while for the Zr-Cr thin films the peritectic temperature is 1832 K and the solidification interval is close to 100 K [START_REF] Lu | Thermodynamic modeling of Cr-Nb and Zr-Cr with extension to the ternary Zr-Nb-Cr system[END_REF]. During sputtering, the surface diffusion directly depends on the ratio between the deposition temperature and the melting temperature of the deposited material [START_REF] Thornton | Influence of Apparatus Geometry and Deposition Conditions on the Structure and Topography of Thick Sputtered Coatings[END_REF]. At a similar deposition temperature, a lower melting temperature means a higher adatom surface diffusion. Thus, the adatom diffusion for the Zr-V system might be higher than for Zr-Cr, allowing a higher in-plane growth of the crystallites for the Zr-V crystalline cones, explaining the higher cone angle as compared to Zr-Cr for the same deposition rate. Similarly, higher solidification interval means more time for the adatoms to diffuse during the solidification process occurring at the film surface. The Zr-W peritectic temperature is 2483 K, according to its phase diagram [START_REF] Ren | Microstructure and mechanical properties of W-Zr reactive materials[END_REF], and the crystallites are smaller than in Zr-Cr and Zr-V. However, the Zr-Mo peritectic temperature is 2194 K [START_REF] Pérez | Thermodynamic assessment of the Mo-Zr binary phase diagram[END_REF],

but its crystallites are even smaller than for Zr-W. Again, the potential reason for the lower diffusion length of in Zr-Mo is the smaller solidification interval (approximately 300 K compared to 700 K for Zr-W), leading to a faster solidification, which allows less time for diffusion.

Conclusion

To summarize, the competitive growth phenomenon that occurs between amorphous and crystalline phases that has been observed in the literature for sputtered Zr-Mo, Zr-W and Zr-V films has been also found in the Zr-Cr system. This study shows that it exists in a wide range of deposition rate, indicating its resilience against changes of deposition conditions and giving promises for its experimental observation in other systems. However, changing the deposition rate also changes the geometrical features of the crystalline phase such as the cone angle, which can be used as a new parameter to control the growth of the film, together with the film composition and film thickness. The size and density of crystallites inside a cone also depend on the deposition rate and the material deposited. Furthermore, we proposed a model of nucleation and growth for the crystallites inside the crystalline cones to explain the development of this competitive growth, which is a step towards the understanding of the mechanisms underlying this process. This allows a fine tuning of the surface morphology, and hence of the functional properties. We showed that depending on the deposition rate, the change in the crystalline cone angle can be due to either the nucleation kinetics of the crystallites, or their lateral growth.

Fig. 1 :

 1 Fig. 1: (a) X-ray diffractograms of Zr-Cr thin films with 83 at.%Cr (blue), 85 at.%Cr (black), and

Fig. 3 :

 3 Fig. 3: SEM micrographs showing Zr-Cr thin films (~85 at.%Cr) deposited at 5nm/min (a), 63

Fig. 4 :

 4 Fig. 4: HRTEM micrograph (a) showing the interface between a cone (in the middle) and a

Fig. 5 :

 5 Fig. 5: Bright field TEM image showing the thin film with a crystalline cone surrounded by

Fig. 6 :

 6 Fig. 6: Graphs showing the change in crystalline cone angle (a), in crystallite size (b) and in

Fig. 7 :

 7 Fig. 7: Proposed nucleation and growth model for the crystalline cones in Zr-based thin films.

Acknowledgements

The "Université Franco-Allemande" (UFA) and the "Ministère de l'Enseignement Supérieur et de la Recherche" are deeply acknowledged for the PhD scholarship of Quentin Liebgott within the PhD-track in Materials Science and Engineering at UFA.