P Rosique

P Ruelle

M Khaledian

Sub surface drip irrigation using Chapin tapes Case study for a corn crop under a Mediterranean climate 1st experimental campaign

INTRODUCTION

This report is concerning the experimental characterization of the behaviour of the subsurface Chapin tapes (Jain) underneath tilling implemented in Montpellier according to the agreement between Jain and Cemagref. Two main objectives were assigned to this work:

1. the study of its capacity to feed with water a maize crop, the study of the amount of water saved by using subsurface drip irrigation in comparison with a sprinkler irrigation in the Mediterranean climate . 2. the study of the nitrogen fertigation and its capacity to decrease the risk of nitrogen leaching under maize crop while optimizing crop production.

Agriculture must match challenge and environmental issues: "agriculture must produce more food to meet increasing food needs but using less water … "1 According to FAO, irrigated agriculture will have to produce 80% of food increase needed for world population growth during next ten years. Drip irrigation is considered as a possible technique to face water savings challenges. Drip irrigation is now a well known technique, improvement was obtained by burying rigid drip equipment in the soil. But to use subsurface drip irrigation on a large extend for crops such as corn it is necessary to look for new less expensive equipments. New researches are needed to characterize the behaviour of such equipment in different pedoclimatic conditions over years and elaborate tools for advices on the best way to use it for a sustainable crop production. This study on subsurface drip irrigation realized in Montpellier at Lavalette experimental station under a Mediterranean climate with an important rainfall inter-annual variability, but there are few rainfalls and a high water demand during summer. These climatic conditions are favorable to achieve research results on irrigation.

The 2008 campaign was the first campaign of a three-year field experiment. A lot of field operations were done. The subsurface drip equipment was installed in April a short time before sowing a corn crop, so due to the modification of soil structure provoked when burying the drip tapes in the soil, the present results should be considered as preliminary ones. However interesting observations were collected.

In the first part of this document, the experimental design and measurement equipment are described. In the second part, agronomic and hydraulic results are analysed and data from the main experimental treatments are used to present soil water transfers. A conclusion summarizes the issues of the first year of experiment and the points to look at.

This work was realized by members of the Joint Research Unit G-EAU (Water Management, Actors, Usages) and has been partly supported by the JAIN IRRIGATION SYSTEMS Co. Ltd

EXPERIMENTAL DESIGN AND MEASUREMENT EQUIPMENT

PEDO-CLIMATIC CONTEXT

Location of the experimental site

The crop experimental station of Lavallette in Montpellier (43° 40'N, 3° 50'E, altitude 30m) is situated on the right bank of the Lez River at about 15 km from the Mediterranean sea.

Soil characteristics

The soil is from both colluvial and alluvial origin being very deep, with a water table which is deeper than 5 m in summer and does not contribute to water supply of crops. It has a favorable agronomic quality without any coarse element and a loamy sandy to loamy clayey sandy texture depending on its distance from the river which is in the Northern direction. As shown in table 1, the clay content is about 20% for the upper layer. Near the river there is a small increase of the clay and silt content of the layer 120-150 cm and at the opposite, the sand content is higher in the south part of the field. Due to these characteristics, the soil water storage capacity is high and ranges from 120 to 180 mm/m.

Climate

The climate is of Mediterranean type with a mean monthly temperature of 6°C in January and 22°C in July; rainfalls are variable along the year with a maximum in October (usually) and a total annual amount of 750 mm. There is a huge water deficit during summer of around 350 mm between PET (potential evapotranspiration) and rainfall. 1b). So the soil was very wet during the beginning of the cropping season and there was no need for emergence irrigation. Due to that situation, it wasn't possible to test, as planned, the efficiency of subsurface drip irrigation to wet the seed bed zone.

Measurements equipment and monitoring on the experimental plots

Climatic data were recorded by an agro-climatic station situated near the plots. Irrigation water depth was controlled for drip irrigation as well as for sprinkling irrigation treatments. Soil water status was monitored during the cropping season by a periodic measurement of soil water content with a neutron probe; additional capacitive measurements were used during short periods. During the first part of the season, soil matric potentials, using tensiometers, were determined to evaluate soil water fluxes. Crop growth was monitored by Leaf Area Index measurements. The characteristics of the equipment and sensors are described below. In 2008, the climatic conditions were far from the normal year with a dry winter but a rainy spring (Fig. 1a). The amount of rainfall from January to the 20 th of April was only 173 mm but then a lot of ring irrigation. They were compared on the other hand, with the values measured by volumetric water meter.

Agro-climatology

• Sprinkling Irrigation

A series of three rain gauges with a triangle arrangement around the neutron probe measurement site was used on the two treatments irrigated with a raingun: TS (tillage system) and Direct Seeding.

Rain gauges were regularly raised to be 10 cm higher than the top of crop.

Soil water status

• Neutron probe

An aluminium access tube of 2 m was driven down in the soil to realize neutron probe measurements of soil water content on each of the following treatment: SDI 120 South, SDI 120 North, SDI 160, DS DSI 160, TS, TCWI, and Direct Seeding. The Neutron probe is a 503 DR Campbell Pacific Nuclear; measurements took place every week on Monday morning, after water redistribution during drip irrigation and 5 days after watering on treatments with sprinkler irrigation.

• Capacitive probe

Two treatments were equipped with access tubes for automatic capacitive measurement of soil water content to monitor soil water content evolution during irrigation: SDI 160 and DS-SDI-160. The first access tube was of 15 cm from the tape and the second one on the row between two plants of corn. The equipment consists in two Envirosmart Sentek Water content profile probes with SDI outputs connected to a Datalogger from Campbell Sci. Ltd. Each probe was customized with 6 sensors at different depths. Measurements were registered with a time step of 20 min.

• Tensiomers

A series of tensiometers from SDEC (France) were placed from 10 to 150 cm depth in the main treatments. Values were collected every morning between 8:30 and 9:30 to avoid disturbance from temperature

Leaf Area Index (LAI) measurement

Measurement of LAI was realized about once a week in each treatment using a LAI 2000, LI-COR Plant Canopy Analyzer. The objective of these measurements was to monitor plant growth and possible water stress.

Experimental design

Tillage and cultural practices

Two types of tillage and cultural practices were used in this experiment: conventional tillage in the West side of the field and no-till with direct seeding into mulch in the East side of the field.

• Conventional tillage

After harvesting of the previous crop (corn for this experiment) a series of tillage operations: incorporation of plant residues, ploughing, fertilizer application and seedbed preparation were implemented before sowing. It's the classical technique used in the most farm

• No-till with direct seeding into mulch (DS)

With such a technique which belongs to conservation tillage family, the soil should never be bared and a "cover crop" is planted after harvest of the main crop (in our case, a mix of vetch, oat and rapeseed was planted after corn harvesting). These tillage practices where combined with irrigation techniques to obtain 9 experimental treatments as shown below

Experimental Treatments

Nine treatments were implemented in 2008:

DTS-MET: (1)

(Drip Tape Surface control treatment MET) Plot with a row spacing of 80 cm and 8 tapes on the surface of the soil with a spacing of 160 cm; well watered crop: V max. SDI 160: (2) ( Subsurface Drip Irrigation with a tape spacing of 160 cm ) Plot with a row spacing of 80 cm and 12 tapes buried at a depth of 35 cm in the soil with a tape spacing of 160 cm; restricted irrigation: 70%V max.

SDI 120 N: (3)

( Subsurface Drip Irrigation with a tape spacing of 120 cm ) Plot with a row spacing of 60 cm and 17 tapes buried at a depth of 35 cm in the soil with a tape spacing of 120 cm; restricted irrigation: 70%V max.

SDI 120 S: (4)

( Subsurface Drip Irrigation with a tape spacing of 120 cm ) Plot with a row spacing of 60 cm and 17 tapes buried at a depth of 35 cm in the soil with a tape spacing of 120 cm; restricted irrigation: 60%V max.

DS-SDI-ETM: (5)

(Direct Seeding Subsurface Drip Irrigation control treatment MET) Direct Seeding Plot with a row spacing of 80 cm and 7 tapes buried at a depth of 20 cm in the soil with a tape spacing of 160 cm; well watered crop: V max.

DS-SDI-160: (6)

(Direct Seeding Subsurface Drip with a tape spacing of 160 cm) Direct Seeding Plot with a row spacing of 80 cm and 12 tapes buried at a depth of 20 cm in the soil with a tape spacing of 160 cm; restricted irrigation: 70%V max.

TCR: (7)

(Treatment conventional Raingun irrigation) Plot with conventional tillage and a row spacing of 80 cm, irrigated with a raingun; restricted irrigation: 70%Vmax.

MAIN CROPPING SEASON INFORMATIONS

Crop variety

The corn crop variety was: Pioneer PR33TY65. This hybrid has a high yield potential. With a base temperature of 6 °C, this late variety requires 103 0 degree days from sowing to flowering and 2055 degree days from sowing to harvesting at 32% grain humidity.

Soil preparation and planting

• Soil preparation and fertilization

For conventional tillage plots, ploughing took place on 11/19/2007. Then 400 kg/ha of super phosphate 45% were applied on 03/20/2008 and two crossed harrow passes were done to achieve a relevant levelling of the soil as well as weed destruction. In direct seeding treatments, the cover crop was partly destroyed using a rototiller and an herbicide (glyphosate) was applied. The same amount of fertilizer were applied in these plots. • Planting

Corn was planted on 04/30/2008 for plots with a row spacing of 80 cm with 90 000-100 000 seeds/ha. The pneumatic SEMEATO ® drill was used for direct seeding into mulch plots and conventional plots. During sowing, an insecticide (curater) was applied beneath the sowing line as well as a fertilizer (30 kg N/ha) was applied.

For conventional tillage plots with a row spacing of 60 cm, corn was sown on 05/01/2008 with a pneumatic MONOSEM drill at the same density. In that case, due to drill equipment limitation no fertilizer was applied.

The rows orientation of the whole experiment was West-East. The soil was then packed down with a roller in all plots.

Nitrogen fertilization

The amount of N needed was calculated according to soil N content in the soil at the planting date (see below). On 06/11/2008 nitrogen fertilization (450 kg/ha of ammonitrate 33%) was spread on all plots except plots with subsurface drip irrigation. For those plots fertilizer was applied through drip irrigation (fertigation).

Weed control

Due to a lot of rain events during the first two months of the cropping season weed control wasn't very efficient. Herbicides couldn't be applied at the right time and were partly leached. However the effect on crop growth was limited (see below).

Irrigation and Fertigation

Water for irrigation is delivered by an automatic pumping station with pressure regulation in two points of the experimental field for drip irrigation and for raingun irrigation.

As noticed above, a comparison between theoretical water application depth calculated from equipments characteristics and measured volumes was made; using water meters for drip irrigation and local measurements with raingauge for raingun irrigation.

Irrigation doses for the different plots

For raingun irrigation (TCR and DSR plots) the calculated water application depth was very near the measured value (fig. 2 and table 2). . For DTS 160 ETM, where the tapes were placed on the surface of the soil, the result was the same: there was no gap between calculated and measured water depth. But it was different for all other plots with subsurface drip irrigation, the calculated values overestimate the water application depth given by the water meters. These differences can be explained by the influence of soil pressure on the tape. The outside pressure was not the atmospheric pressure and discharge was less than planed. Values for conventional tillage plots are summarized in table 2. A control of water pressure for each plot is necessary to apply the planned irrigation dose. A control and a comparison of all manometers and equipments will be done for the next experimentation seasons.

Fertilization

All treatments with drip irrigation were fertilized using a N fertilizer solution which was mixed with irrigation water by a pump (Dosatron). The amount of soil residual nitrogen and of fertilizer applied at sowing are summarized for all conventional tillage plots in fig. 3. According to mineralization previously observed and N crop requirement, a grain yield target of about 15 t/ha can be obtained unless in TCWI, where the yield target was less than 10 t/ha, depending on rainfall during the cropping season.

RESULTS AND DISCUSSION

Agronomic Results

Crop Yields

Due to the modification of soil structure during the installation of subsurface drip irrigation as indicated above, it is not possible to take into account the obtained yield for Direct Seeding plots in comparison with conventional tillage. We noticed that the abundant germination of weeds occurred in DS treatments and corn growth was disturbed and only some information on water monitoring for these treatments will be given farther.

. In conventional tillage plots, a lower amount of irrigation with subsurface drip irrigation did not reduce crop yield as shown in fig. 4. The same grain yield of 15 t/ha (for a standard humidity of 15%) was obtained for a row spacing of 80 cm as well as for 60 cm. The obtained yield reached the target yield for these treatments. The yield for the well watered treatment (DTS-MET ) was a few lower (14.5t/ha) due to a late application of N fertilizer.

For the raingun irrigated plot (TCR) water stress was probably most important: a part of the applied water was evaporated at the soil surface and submitted to wind effect. The plant density was around 80 000 plants/ha at harvest for all plots. Total Dry Matter yield was 24 t/ha for SDI 160 and SDI 120; so the Harvest Index is 0.53 which is a high value.

In the rainfed plot, the yield was very low, with no rain events during the flowering stage. The hypothesis is that this treatment cumulated both water and nitrogen stress.

Leaf Area Index analysis

LAI is a main factor for water consumption, total dry matter production and grain yield. The evolution of LAI depends on water stress but also on fertilizer supply to the plants. A continuous monitoring was done in three treatments (fig. 5) with a time step of around one week. We should remind that this measurement involves in constraint due to the fact that it must be done only under diffuse light, usually during a short time at sunset or sunrise. According to the values of standard deviation there is no significant difference between the two treatments i.e. SDI 160 and SDI 120 with conventional tillage. The maximum value of LAI is approximately 4.2 .

There is a decrease of LAI with a higher variability around the mean value at the beginning of August. As there was a strong lowering of water irrigation, the existence of a short stress period is possible.

For DS SDI 160, the values were lower; crop growth was less satisfactory due to the fact that plant density was lower.

Soil water content analysis

Soil water content profiles

From neutron probe measurements at different depths it is possible to look at soil water profiles and their evolutions during the cropping season. The evolution of the curves of soil water content, in fig. 7, points out the layers contributing to water uptake of the crop for a measurement made exactly on the row of corn plants. Plant water uptake is concerning a depth of 120 cm deeper on raingun irrigated plot (TCR) but the water uptake is limited at that depth. The situation is approximatively the same under drip irrigation. So we can say the soil water reserve was pretty well used with subsurface drip irrigation. Near soil surface, soil water content remains higher for SDl, especially at 20-30 cm which can be explained by water transfer from the tape (which is about 30 cm from the row and at a depth of 35 cm). No increase of soil water content is seen on TCR because of measurement protocol: neutron probe measurements were made the day before irrigation and the last irrigation had been done a week before. On the contrary for SDI, irrigation was applied only three days before. Such measurements are not sufficient to look for capillary rise up to the soil surface. During summer the surface of the soil above drip tapes was always dry, but we cannot conclude about possible capillary rise at the sowing date with a wet soil and higher application depth.

Water stocks

First we can notice in fig. 8, as foreseen, that water stock for the layer of 0-150 cm was lower for plots near the river where the clay content is lower. So SDI 160 stock was lower than SDI 120 but as the irrigation scheduling was the same most of the time, the evolution of the water reserve was similar all along the cropping season. It appeared only a small increase of soil water content on 75 th days after sowing due to a rainfall. Water stock during the cropping season was continuously decreasing: the crop was taking water from soil water reserve to complete water delivery in all plots with deficit irrigation. In rainfed treatment corn wasn't able to uptake a higher amount of water from the soil.

Characterization of the wetted zone by subsurface drip irrigation

An analysis of the zone wetted by the drip line is possible for SDI 160 where two series of capacitance Envirosmart sensors were placed at the beginning of August. Fig. 9 demonstrates the evolution of soil water content at different depths at a distance of 15 cm from the drip line (a), on the corn row at a distance of 40 cm (b) as well as in relation with irrigations and potential evapotranspiration (c). Irrigation was applied three times a week on this treatment and the dose was doubled on Monday and Friday, due to the fact that there was no irrigation during week-end; such irrigation scheduling allowed to examine the effect of irrigation dose. The vertical distribution of water near the drip line during irrigation can be observed from raw data registered at a time step of 15 min. As shown by the measured signal (fig. 9a) the applied water during the period reached only a depth of 45 cm: there is no increase of the signal of the deeper layers (55 and 65 cm). The higher effect was obtained at 25 cm and a significant one at 15 cm; but as indicated above the surface of the soil was dry. On the contrary of the phenomenon described on Monday and Friday, only a slight raise of the signals was observed on Wednesday with a single dose of irrigation: the water applied was immediately evaporated by the crop. We can also see that for the three upper depths, the values before next irrigation were equal to initial value: all the water applied was used. For the deeper layers, there was a small decrease of the signal during the period: the crop uptaked water from soil storage. For the curves (b) nearly no variation of the signal is visible, and slight ripples for 15 and 25 cm are difficult to connect to irrigations. So we can say that lateral diffusion did not reach the corn row. During the period the signal was decreasing slowly for all the sensors. All these observations are in fair agreement with neutron probe measurements, according to the difference of measurement volume between the two methods (some centimeters for capacitance method and about ten to fifteen for neutron probe).

From available data, it is difficult to give a representation of the wetted bulb around the drip tape for the monitored period. A crude representation of the wetted area is given in fig. 10. . The lateral limits are not known. Some more information could be obtained using another Envirosmart equipment in an oblique position, what was done in 2007 for surface drip irrigation.

Based on measurements, modelling can also be used to characterize water transfer during irrigation.

Analysis of root repartition

At harvest, a soil profile was dug by a backhoe to analyze rooting of the crop perpendicularly to the drip lines for SDI 160 and SDI 120. Root repartition was described on a grid of 5x5 cm (fig. 11) using a qualitative index from 0 for no root to 5 for maximum root quantity. A mean value of the index was calculated for each depth and on the North side and South side of the profile to examine possible effect of drip tape and its wet bulb on root repartition. The value of that index as a function of the depth is presented in fig. 12 for three drip irrigation treatments. We first can see that maximum rooting depth is around 1.2 m and most of the roots are observed in the first 40 to 50 cm. According to the drip tape position on the south side, there was a small increase of root density on that side: near the surface of the soil for DI 160, and approximately at the depth of the drip tape for Subsurface Drip Irrigation Treatments. From cumulative root index (fig. 12 d), we can see that root density was increased from SDI 160 to SDI 120 in comparison with DI 160. It can be a possible effect on reduction of soil compaction by the tool (a chisel) used to insert the tape inside the soil, so this aspect will be examined in 2009.

Direct seeding and Subsurface drip irrigation

Soil water content profile

As it was said this report presents only some specific aspects concerning water transfer in direct seeding plots.

If we look at soil water content profile (fig. 13) for DS SDI 160, it appears that soil water depletion was less important in comparison with conventional plots. There was few crop water uptake below a depth of 50 cm and nearly no uptake beneath 100 cm. In July the curves for the first layer (0-50 cm) followed a similar evolution and reached the same value at the end of August. But the situation was different for other layers, the crop on DS SDI 160 plot used only a limited amount of the water in 50-100 cm layer on the contrary of SDI 160. In the last layer a small decrease of around 10 mm was observed. These facts confirmed that a direct seeding plot used less water from soil than a conventional plot.

The same result was obtained in previous experiments with sprinkler irrigation.

Characterization of the wet zone

Same observations in DS SDI 120 as for DS SDI160 were made. The data were collected one week after measurement analysed above for SDI 160. As for the former plot, at 15 cm from the drip tape, a signal increase was measured for the first four layers (fig. 15) and no variation for the two last ones (53 and 63 cm). So we can confirm that the wet zone did not reached 53 cm depth. On Monday, the amplitude of signal variation was less important in that treatment and on Wednesday, the irrigation took place with a higher value of soil water content than on Monday and we were in the same situation on Friday. At the end of the period there was a slight increase of the value of the signal in the three upper layers that means that the soil water content is higher and a part of the water applied was not used. As shown in fig. 15c, PET was lower during this period of mid August than those observed one week before in SDI 160 plot. At last we must notice that signal undulation for sensor placed at 15 cm depth proved an increase of soil water content at night time, this can be explained by capillary rise which is favored by a more compacted soil and mulch on the soil surface. For the measurements on the corn row, being only 35 cm apart from the drip line (and the drip line is place at only 20 cm from soil surface) one can observe an increase of the signal of two upper layers. So lateral water transfers occurred for these layers, and the wetted zone seems to be larger than for conventional tillage

Conclusions and prospects

The implementation of this subsurface drip irrigation experimental set-up opens interesting prospects to identify possible improvements of water and fertilizers productivity in a Mediterranean context for cereals.

Results concerning experimental methods can be resumed as follow: Equipment used to set up subsurface drip tape in the soil proved to be relevant; water was delivered efficiently but measurement pointed out that delivered volume was lower than planned one, due to possible soil action on drip tape. Complementary observations will be realized to evaluate this effect.

The measurement devices based on tensiometers and neutron probe measurements demonstrated that they are suitable to characterize water flux and plant water uptake. With short time step automatic collect of data, capacitance sensors (Envirosmart from Semtek) gave information about the wetted zone around the subsurface drip tape during an irrigation. It showed that water transfer was limited vertically (< 50 cm) as well as laterally (< 40 cm) for water application depth of around 70% of water demand.

Corn yields were satisfactory in conventional tillage plots with subsurface drip irrigation surface.

For drip lines buried at 35 cm beneath soil, the same corn yield of around 15 t/ha was achieved in SDI 160 (subsurface drip irrigation with a distance between drip line of 160 cm) and in SDI 120 plots (distance between drip tapes 120 cm). This yield was higher than that of Sprinkler Irrigation plot (12,7 t/ha).

There was no significant difference between the yields of both SDI treatments. Due to the rainy spring, these results have to be confirmed next year (in 2009).

In SDI treatments, water savings was obtained due to soil evaporation decrease; evaluation on water savings based on modelling are in progress and will be validated during the next cropping season. Corn crop had an efficient utilisation of soil water reserve up to a depth of about 120 cm; this observation was coherent with root profile descriptions.

The results on Direct Seeding plots should be only considered as preliminary ones, because of soil disturbance provoked by subsurface drip line installation (at a depth of 20 cm) and as a consequence the growth of weeds. However data collection and analysis pointed out a satisfactory soil water transfer and crop water uptake around subsurface drip tape in parallel with a lower utilization of soil water reserve below a depth of 50 cm as observed in previous experiment.

Observations will pay more attention on the effect of fertilizer placement in the soil by drip irrigation during next cropping season and on water saving.

As resumed above a series of provisional results obtained during this first experimental campaign, will be examined to be completed and validated in 2009.

However the present results enlightened that the use of drip tape subsurface irrigation is feasible e.g. for corn and other seed production. More studies to test the feasibility of this technique for different crops are needed as well as an economic evaluation based on life duration of subsurface drip tape equipment.

An information session for farmer on some new trends in agriculture will take place at the Lavalette station (Cemagref of Montpellier) in June 2009 in collaboration with extension services. A presentation and a visit of the experimentations on subsurface Jain drip tape will be included in the program and organized with the representative of Jain Irrigation System Ltd in France.

  Fig 1a: Monthly rainfall of in 2007-2008 rain events occurred and a total of 200 mm was recorded during the two next months (fig.1b). So the soil was very wet during the beginning of the cropping season and there was no need for

Fig. 2 :

 2 Fig. 2: Experimental design and different plots

Fig. 2 :

 2 Fig. 2: Comparison of cumulated calculated and measured water application depth on the different plots in 2008

Fig. 3 .

 3 Fig. 3. Amount of nitrogen in the soil and of nitrogen applied at sowing in the converntional plots in 2008

Fig. 4 :

 4 Fig. 4: Comparison of water application depth and yield on main conventional plots

Fig. 6 :

 6 Fig. 6: LAI evolution during two months for three irrigated plots

Fig. 7 :

 7 Fig. 7: Soil water content profile evolutions for raingun and subsurface drip irrigated plots

Fig. 8 :

 8 Fig. 8: Comparison of water stock evolution in layer 0 -150 cm in different plots

Fig. 9 :

 9 Fig. 9: Evolution of the Envirosmart sensors signal in SDI 160 Treatment at different depths for measurements at 15 cm from the drip line at 15 min time step (a), on the corn row, at 40 cm from the drip line (b) in comparison with potential evapotranspiration and irrigation depth in August 2008.

Fig. 10 :

 10 Fig. 10: Schematic representation of the wetted bulb for SDI 160

Fig. 11 :Fig. 12 :

 1112 Fig. 11: Position of the grid in the soil profile to analyze root repartition

Fig. 13 :

 13 Fig. 13: Soil water profiles during the cropping season for DS SDI plot

Fig. 14 :

 14 Fig. 14: Comparison of soil water stock evolution in 50 cm thick layers for SDI 160 and DS SDI 160 plots

Fig. 15 :

 15 Fig. 15: Evolution, in DS SDI 160 Treatment, of the Envirosmart sensors signal at different depths for measurements at 15 cm from the drip line at 15 min time step (a), on the corn row, at 35 cm from the drip line (b) in comparison with PET and irrigation depth (c) in August 2008

Table 1 .

 1 Granulometry analysis of Lavalette soil (2002)

	Depth (cm)	Clay (%)	Silt (%)		Sand (%)
		North	South	North	South	North	South
	0-30	18.4	22.2	42.0	48.7	39.3	29.1
	30-60	17.6	23.7	43.6	48.6	38.8	27.8
	60-90	20.2		47.4		32.4
	90-120	20.2		54.6		22.2
	120-150	26.7	24	48.0	44.0	25.2	32.0

Table 2

 2 Comparison of calculated and measured water application depth (mm) for drip irrigation

	Plots	Calculated Measured
	SDI 120 N	280	193
	SDI 120 S	270	182
	SDI 160	281	236
	DTS-MET	367	373
	TCR	269	280

15 cm 85 cm 35 cm 45 cm 65 cm 25 cm Trad SDI160 à 40 cm de la gaine : sur la ligne de maïs

		0.9
		0.85	Trad SDI160								35 cm
		0.8	à 15cm de la gaine
												25 cm
		0.75	35 cm								15 cm
	Indice	0.7		45 cm							45 cm
		0.65	15 cm		55 cm							55 cm
					65 cm
		0.6	25 cm								65 cm
		0.55
		0.5
		4 / 8 / 0 8 1 2 : 0 0 lundi	5 /8 / 0 8 1 2 : 0 0 mardi	6 / 8 / 0 8 1 2 : 0 0 mercredi	7 / 8 / 0 8 1 2 :0 0 jeudi	8 / 8 / 0 8 1 2 : 0 0 vendredi	9 / 8 / 0 8 1 2 : 0 0 samedi	1 0 /8 / 0 8 1 2 :0 0 dimanche	1 1 /8 / 0 8 1 2 :0 0 lundi	1 2 /8 / 0 8 1 2 :0 0
		0.8
				35 cm	45 cm
		0.75				85 cm
					65 cm
	Indice	0.7
			25 cm
		0.65	15 cm
		0.6
		4 / 8 / 0 8 1 2 : 0 0	5 / 8 / 0 8 1 2 : 0 0	6 / 8 / 0 8 1 2 : 0 0	7 / 8 / 0 8 1 2 : 0 0	8 / 8 / 0 8 1 2 : 0 0	9 / 8 / 0 8 1 2 : 0 0	1 0 /8 / 0 8 1 2 :0	1 1 /8 / 0 8 1 2 :0	1 2 /8 / 0 8 1 2 :0
		lundi	mardi	mercredi	jeudi	vendredi	samedi	dimanche	0	lundi	0	0
		12
		10									I
	Flux (mm/j)	4 6 8									ETP
		2
		0
		4	5	6	7	8	9	1		1		1
		/ 8 / 0	/ 8 / 0	/ 8 / 0	/ 8 / 0	/ 8 / 0	/ 8 / 0	0 / 8 /	1 /8 /		2 /8 /
		8	8	8	8	8	8		0 8	0 8	0 8

c b a DS SDI 160 DS SDI 160 At 15cm from drip line At 35 cm from drip line

		Monday	Wednesday		Friday		Monday
		Monday	Wednesday		Friday		Monday
	SCV SDI 160 8 DS SDI 160		I ETP
	6
	2
	1 8 / 0 8 / 0 8	1 9 / 0 8 / 0 8	2 0 / 0 8 / 0 8	2 1 / 0 8 / 0 8	2 2 / 0 8 / 0 8	2 3 / 0 8 / 0 8	2 4 / 0 8 / 0 8	2 5 / 0 8 / 0 8
		Monday		Wednesday		Friday		Monday

CemOA : archive ouverte d'Irstea / Cemagref

ICID congress conclusions, Cairo, Egypt, 1996 CemOA : archive ouverte d'Irstea / Cemagref

CemOA : archive ouverte d'Irstea / Cemagref


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Modelling vulnerability to flooding

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  Agriculture and flood risk on Rhône River Delta Applications and conclusions Conceptual modelling and damage simulation * UMR G-EAU (Montpellier) Contact: pauline.bremond@cemagref.fr Deltas in Times of Climate Change Rotterdam, 29 September -1 October 2010 Modelling vulnerability to flooding: a systemic approach on farms of the Rhône River Delta Bremond P.*, Abrami G.*, Blanc C.*, Grelot F.concern all farm components and farm recovery Rhône River delta: 3 000 farms are potentially exposed to flood risk. STEP 1: characterization of flood damage on farm technical capital (damage functions): -change of status (normal => damaged) -simulation of damage (€) =output 1 Characterization of farm vulnerability for different flood scenarios (damage type that represents the larger share of the total amount, see damage simulation) •Efficiency appraisal (Cost Benefit Analysis) of measures to mitigate farm vulnerability that are planned on Rhône River Delta: comparison of the cost of implementation and maintenance and the mean annual avoided damage for two farm types


Pavel Ondračka

David Nečas

Michèle Carette

Stéphane Elisabeth

David Holec

Agnès Granier

Antoine Goullet
email: antoine.goullet@univ-nantes.fr

Lenka Zajíčková
email: lenkaz@physics.muni.cz

Mireille Richard-Plouet
email: mireille.richard@cnrs-imn.fr

Unravelling local environments in mixed TiO 2 -SiO 2 thin films by XPS and ab initio calculations

Mixed Ti x Si 1-x O 2 oxide can exhibit a partial phase separation of the TiO 2 and SiO 2 phases at the atomic level. The quantification of TiO 2 -SiO 2 mixing in the amorphous material is complicated and was so far done mostly by infrared spectroscopy. We developed a new approach to the fitting of X-ray photoelectron spectroscopy data for the quantification of partial phase separation in amorphous Ti x Si 1-x O 2 thin films deposited by plasma enhanced chemical vapour deposition. Several fitting constraints reducing the total number of degrees of freedom in the fits and thus the fit uncertainty were obtained by using core electron binding energies predicted by density functional theory calculations on Ti x Si 1-x O 2 amorphous supercells. Consequently, a decomposition of the O 1s peak into TiO 2 , SiO 2 and mixed components was possible. The component areas ratios were compared with the ratios predicted by older theoretical models based on the atomic environment statistics and we also developed several new models corresponding to more realistic atomic structure and partial mixing. Based on the comparison we conclude that the studied films are mostly disordered, with only a moderate phase separation.

Introduction

The mixed TiO 2 -SiO 2 oxides have attracted considerable attention in the area of photocatalysis as it has been shown that they are more active than pure TiO 2 [START_REF] Jung | Photoactivity of SiO 2 /TiO 2 and ZrO 2 /TiO 2 mixed oxides prepared by sol-gel method[END_REF][START_REF] Fu | Enhanced photocatalytic performance of titania-based binary metal oxides: TiO 2 /SiO 2 and TiO 2 /ZrO 2[END_REF][START_REF] Anderson | An improved photocatalyst of TiO 2 /SiO 2 prepared by a solgel synthesis[END_REF]. The mixed oxides serve as base components for complex nanomaterials with applications in photoluminescence [START_REF] Jeng | Light emission and atomic coordination structure of sol-gel derived erbium-doped SiO 2 -TiO 2 thin films[END_REF], electrochemical sensors [START_REF] Da Fonseca | Study of the characteristics, properties and characterization of new SiO 2 /TiO 2 /Sb 2 O 5 ternary oxide obtained by the sol-gel process[END_REF] or catalytic hydrogenation [START_REF] Huang | Performance of SiO 2 -TiO 2 binary oxides supported Cu-ZnO catalyst in ethyl acetate hydrogenation to ethanol[END_REF] dehydrogenation [START_REF] Lu | Hydrodeoxygenation of guaiacol catalyzed by high-loading Ni catalysts supported on SiO 2 -TiO 2 binary oxides[END_REF] and hydrodeoxygenation [START_REF] Saputera | Light-induced synergistic multidefect sites on TiO 2 /SiO 2 composites for catalytic dehydrogenation[END_REF]. There are also multiple possible optical application for those coatings [START_REF] Li | Ion impingement effect on the structure and optical properties of Ti x Si 1-x O 2 films deposited by ICP-PECVD[END_REF], with demonstrated use in waveguides [START_REF] Karasiński | Optical rib waveguides based on sol-gel derived silica-titania films[END_REF][START_REF] Brusatin | Microstructural and optical properties of sol-gel silica-titania waveguides[END_REF], laser mirrors [START_REF] Chao | Low-loss dielectric mirror with ion-beam-sputtered TiO 2 -SiO 2 mixed films[END_REF] and rugate filters [START_REF] Poitras | Design and plasma deposition of dispersioncorrected multiband rugate filters[END_REF].

The atomic structure of mixed TiO 2 -SiO 2 films has been studied quite extensively as it influences both the optical and catalytic activity. Often debated topic is the dominant coordination number for Ti and Si atoms. In the crystalline TiO 2 and SiO 2 , the Ti cation is present in the 6coordinated octahedral position and the Si cation in the 4-coordinated tetrahedral position, with the only exception being some high pressure polymorphs such as stishovite. The majority of reports on TiO 2 -SiO 2 shows that Si atoms are also almost always 4-coordinated [START_REF] Baur | Rutile-type compounds. IV. SiO 2 , GeO 2 and a comparison with other rutile-type structures[END_REF], whereas for Ti the coordination depends on composition. Ti evolves from mostly 4-coordinated at low Ti concentration towards dominantly 6-coordinated at higher concentration -nevertheless, 5-coordinated Ti atoms were also reported [START_REF] Cheng | Coordination and optical attenuation of TiO 2 -SiO 2 glass by electron energy loss spectroscopy[END_REF][START_REF] Landmann | The atomic structure of ternary amorphous Ti x Si 1-x O 2 hybrid oxides[END_REF][START_REF] Gracia | SiO 2 /TiO 2 thin films with variable refractive index prepared by ion beam induced and plasma enhanced chemical vapor deposition[END_REF][START_REF] Rosenthal | Molecular dynamics study of amorphous titanium silicate[END_REF][START_REF] Sandstrom | Coordination of Ti in TiO 2 -SiO 2 glass by X-ray absorption spectroscopy[END_REF]. There are however some contradictory reports mentioning dominantly 6-coordinated Ti atoms even at low TiO 2 concentrations [START_REF] Green | The formation of Ti-O tetrahedra and band gap reduction in SiO 2 via pulsed ion implantation[END_REF][START_REF] Greegor | Investigation of TiO 2 -SiO 2 glasses by X-ray absorption spectroscopy[END_REF]. It has been also established, both experimentally and theoretically, that there are no direct Ti-Ti, Si-Si or Ti-Si bonds, and the Ti and Si atoms are always interconnected through the bridging oxygen atoms [START_REF] Landmann | The atomic structure of ternary amorphous Ti x Si 1-x O 2 hybrid oxides[END_REF][START_REF] Larouche | Microstructure of plasma-deposited SiO 2 /TiO 2 optical films[END_REF][START_REF] Netterfield | Ion-assisted deposition of mixed TiO 2 -SiO 2 films[END_REF].

An extensively studied topic for mixed TiO 2 -SiO 2 films is whether the TiO 2 and SiO 2 phases are well mixed at the atomic scale or whether they consist of more than one separated phases. Multiple reports show that TiO 2 -SiO 2 phase separation can be easily induced by annealing [START_REF] Smith | Chemical vapor deposition of Ti x Si 1-x O 2 films: precursor chemistry impacts films composition[END_REF][START_REF] Permpoon | Natural superhydrophilicity of sol-gel derived SiO 2 -TiO 2 composite films[END_REF], especially for samples prepared by the sol-gel method and high TiO 2 concentrations [START_REF] Stakheev | XPS and XAES study of titania-silica mixed oxide system[END_REF][START_REF] Dirken | 17 O and 29 Si Solid State NMR Study of Atomic Scale Structure in Sol-Gel-Prepared TiO 2 -SiO 2 Materials[END_REF][START_REF] Rigden | The role of titanium in mixed sol-gels: an X-ray and neutron diffraction study[END_REF]. However, it was also shown that it is possible to prepare homogeneous mixtures of the TiO 2 and SiO 2 phases in the whole composition range [START_REF] Larouche | Microstructure of plasma-deposited SiO 2 /TiO 2 optical films[END_REF][START_REF] Gracia | SiO 2 /TiO 2 thin films with variable refractive index prepared by ion beam induced and plasma enhanced chemical vapor deposition[END_REF][START_REF] Busani | Electrical and physical properties of room temperature deposited, mixed TiO 2 /SiO 2 oxides[END_REF]. The thorough ab initio report on atomic structure of a-Ti x Si 1-x O 2 by Landmann et al. [START_REF] Landmann | The atomic structure of ternary amorphous Ti x Si 1-x O 2 hybrid oxides[END_REF] reported no phase separation at x as high as 0.8, suggesting that the atomically mixed phases can be formed even at high Ti concentrations, the possibility of phase separation was not ruled out though and more recent ab initio reports agree that the TiO 2 and SiO 2 mixing (in bulk) is not energetically preferable [START_REF] Ondračka | Optical properties of Ti x 1-x O 2 solid solutions[END_REF][START_REF] Cuko | Stability of mixed-oxide titanosilicates: dependency on size and composition from nanocluster to bulk[END_REF].

Larouche et al. [START_REF] Larouche | Microstructure of plasma-deposited SiO 2 /TiO 2 optical films[END_REF] proposed a simple statistical model to quantify the probability of occurrences of Si-O-Si, Ti-O-Si and Ti-O-Ti groups under the assumption of 4-coordinated Si and Ti atoms and 2-coordinated O atoms for the two cases of perfectly random mixing and separate phases. Busani et al. [START_REF] Busani | Electrical and physical properties of room temperature deposited, mixed TiO 2 /SiO 2 oxides[END_REF] calculated the same probabilities numerically using Monte Carlo simulations.

The most often used method for the determination of the mixing in TiO 2 -SiO 2 films is the infrared (IR) absorption spectroscopy [START_REF] Gracia | SiO 2 /TiO 2 thin films with variable refractive index prepared by ion beam induced and plasma enhanced chemical vapor deposition[END_REF][START_REF] Larouche | Microstructure of plasma-deposited SiO 2 /TiO 2 optical films[END_REF]. Absorption around 950 cm -1 is attributed to the Ti-O-Si stretching vibrations [START_REF] Ricchiardi | Vibrational structure of titanium silicate catalysts. A spectroscopic and theoretical study[END_REF] and by comparing the relative intensities of the Si-O-Si and Ti-O-Si vibration modes in the absorbance measurements with the statistical Larouche's model some effort was dedicated to quantify the mixing [START_REF] Gracia | SiO 2 /TiO 2 thin films with variable refractive index prepared by ion beam induced and plasma enhanced chemical vapor deposition[END_REF][START_REF] Larouche | Microstructure of plasma-deposited SiO 2 /TiO 2 optical films[END_REF]. Unfortunately, there are some difficulties with this approach. It is unclear whether the Larouche's statistical model works well for high TiO 2 concentrations when the Ti atoms are mostly 6-coordinated and the O atoms mostly 3-coordinated. Moreover, the existing attempts [START_REF] Gracia | SiO 2 /TiO 2 thin films with variable refractive index prepared by ion beam induced and plasma enhanced chemical vapor deposition[END_REF][START_REF] Larouche | Microstructure of plasma-deposited SiO 2 /TiO 2 optical films[END_REF] show only the evolution of the Si-O-Si and Ti-O-Si components and the Ti-O-Ti component was not quantified at all, possibly due to the overlap with rocking Si-O-Si mode, rather broad nature of the Ti-O-Ti peak, weak activity, and its position in the far IR range, partially extending beyond the measurement range. Further problem arises from the unknown infrared absorption cross section (oscillator strength) of the Ti-O-Si vibrations. While it can be estimated from the pure phases for the Ti-O-Ti and Si-O-Si modes, this is not possible for the Ti-O-Si mode and hence its normalization factor is unknown. Another issue is related to the large refractive index difference between TiO 2 and SiO 2 . Especially at high TiO 2 concentrations the effects such as multiple reflections in the films might be significant due to the high refractive index and hence a simple extraction of absorbance might not be enough to properly quantify the absorption, a proper fitting of the spectra might be needed. All those factors increase the uncertainty in the mixing determination.

X-ray photoelectron-spectroscopy (XPS) is a suitable method for obtaining the atomic composition of TiO 2 -SiO 2 films [START_REF] Larouche | Microstructure of plasma-deposited SiO 2 /TiO 2 optical films[END_REF][START_REF] Li | Structural and optical properties of PECVD TiO 2 -SiO 2 mixed oxide films for optical applications[END_REF] and it can be also used to extract information about atomic environments; in this case to detect the presence of the mixed phase [START_REF] Permpoon | Natural superhydrophilicity of sol-gel derived SiO 2 -TiO 2 composite films[END_REF][START_REF] Lassaletta | Spectroscopic characterization of quantum-sized TiO 2 supported on silica: influence of size and TiO 2 -SiO 2 interface composition[END_REF][START_REF] Gallas | SiO 2 -TiO 2 interfaces studied by ellipsometry and x-ray photoemission spectroscopy[END_REF][START_REF] Orignac | Structural study of SiO 2 -TiO 2 sol-gel films by X-ray absorption and photoemission spectroscopies[END_REF]. The analysis of TiO 2 -SiO 2 mixing by a careful evaluation of the XPS spectra (specifically the O 1s and Ti/Si 2p) does not suffer from some of the shortcomings of the IR analysis. Specifically, we can easily observe all the three components (TiO 2 , mixed Ti-O-Si and SiO 2 ) and their intensity depends on the concentration only. However, while in IR spectra the peaks for components are well separated, this is not the case in XPS. A careful fitting of the XPS peaks for different compositions of TiO 2 -SiO 2 films is necessary because even the sub-peaks belonging to the same component (e. g. TiO 2 ) shift with the composition [START_REF] Gallas | SiO 2 -TiO 2 interfaces studied by ellipsometry and x-ray photoemission spectroscopy[END_REF]. Another downside of XPS is that, contrary to the IR spectroscopy, it is just a surface technique. This introduces additional challenges; for example some reports show different atomic concentration at the surface and in the bulk [START_REF] Stakheev | XPS and XAES study of titania-silica mixed oxide system[END_REF], or surface contamination [START_REF] Permpoon | Natural superhydrophilicity of sol-gel derived SiO 2 -TiO 2 composite films[END_REF]. The work of Orignac et al. [START_REF] Orignac | Structural study of SiO 2 -TiO 2 sol-gel films by X-ray absorption and photoemission spectroscopies[END_REF] is a rare attempt to quantitatively analyse the mixed TiO 2 -SiO 2 films (with x between 0.05 and 0.3), by fitting the XPS O 1s peak using the three components' contributions. The results for these sol-gel films were somewhat surprising because the TiO 2 component had a larger area than the mixed component in the whole deposited x range. This differs significantly from the ratios expected from the Larouche's model for random mixing, and suggests a significant phase separation. Several recent reports highlighted the possibility of using ab initio calculations in order to achieve a better understanding and help with the analysis of XPS measurements [START_REF] Aarva | Understanding X-ray spectroscopy of carbonaceous materials by combining experiments, density functional theory, and machine learning. Part I: Fingerprint spectra[END_REF][START_REF] Lee | Single-particle excitation of core states in epitaxial silicene[END_REF][START_REF] Gavrielides | A poly-epoxy surface explored by Hartree-Fock ΔSCF simulations of C1s XPS spectra[END_REF].

In this paper, we develop a more quantitative approach to the determination of the phase separation in mixed TiO 2 -SiO 2 films. At first, the XPS spectra of Ti x Si 1-x O 2 are modelled from the first principles using the density functional theory (DFT) in order to check the fitting assumptions (e. g. whether the different types of environments have indeed significant differences in mean energy) and suggest some approaches for the fitting procedure. In the following section, an experimental approach to the fitting of XPS data is introduced and discussed with application to a series of TiO 2 -SiO 2 films deposited by plasma enhanced chemical vapour deposition (PECVD). The last section discusses several possible generalizations of the Larouche's statistical model for the case of a more realistic structure and also for the case of a partial phase separation.

Methods

DFT calculations

Structural models of amorphous Ti x Si 1-x O 2 were produced for seven different mixture ratios: x = 0, 0.1875, 0.34375, 0.5, 0.65625, 0.8125, and 1. The size of the amorphous cell was 96 atoms, with 64 oxygen atoms and the remaining 32 atoms were titanium or silicon, depending on the particular composition (0, 6, 11, 16, 21, and 26 Ti atoms, respectively). The structures were initiated with mass densities linearly decreasing from 3.8 g/cm 3 for TiO 2 to 2.2 g/cm 3 for SiO 2 and were generated using the ab initio simulated annealing approach described elsewhere [START_REF] Ondračka | Optical properties of Ti x 1-x O 2 solid solutions[END_REF] followed by a structural relaxation at 0 K. These steps were done using Vienna Ab initio Simulation Package (VASP) [START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF][START_REF] Kresse | Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set[END_REF] with GGA-PBE [START_REF] Perdew | Generalized gradient approximation made simple[END_REF] PAW-enabled pseudopotentials [START_REF] Kresse | From ultrasoft pseudopotentials to the projector augmentedwave method[END_REF], a plane wave cut-off energy of 400 eV and a × × 3 3 3 k-mesh. The resulting models of amorphous structures were used to evaluate the core electron binding energies (BE) for the O 1s, Ti 2p and Si 2p core levels. The linearized augmented plane wave method (LAPW) as implemented in the Wien2k density functional theory package [START_REF] Blaha | Wien2k, an augmented plane wave + local orbitals program for calculating crystal properties[END_REF] was employed. We used a standard PBE exchange-correlation functional [START_REF] Perdew | Generalized gradient approximation made simple[END_REF], with a × × 3 3 3 k-grid and the R K • mt max matrix size parameter was 7.5. The Slater transition state method was used to obtain the core electron binding energies. In this method, half of an electron is removed from the corresponding core state (compensated by a background charge) and the binding energy is calculated as a difference between the Fermi energy and the eigenvalue of this state [START_REF] Slater | The Self-consistent Field for Molecules and Solids[END_REF]. We note that our calculations do not produce energies directly comparable to the experimental ones. The Fermi level is always at the valence band maximum (VBM) in the calculations due to the perfect stoichiometry of the simulated cells. This is not the case in experiment, where, for example, the Fermi level for TiO 2 was reported to lie just below the conduction band minimum due to n-doping [START_REF] Pfeifer | Energy band alignment between anatase and rutile TiO 2[END_REF][START_REF] Scanlon | Band alignment of rutile and anatase TiO 2[END_REF]. Hence all the calculated BEs are aligned to the VBM and we denote them the modified binding energies (MBEs) in the following text to make this distinction clear. More details about the ab initio methodology can be found in the Supplemental Material.

The chemical environment corresponding to each atom was estimated by the coordination number analysis. To obtain the coordination number for each atom, a fixed radius r min was selected using the values of the first minimum in the pair distribution function [START_REF] Landmann | The atomic structure of ternary amorphous Ti x Si 1-x O 2 hybrid oxides[END_REF][START_REF] Ondračka | Optical properties of Ti x 1-x O 2 solid solutions[END_REF]. The coordination number (and the specific environment) were obtained as the number and types of neighbour atoms inside this radius.

Preparation of Ti x Si 1-x O 2 Films

Thin Ti x Si 1-x O 2 films were prepared by PECVD in a low pressure plasma reactor consisting of an inductively coupled plasma (ICP) source (13.56 MHz) and a diffusion chamber with the substrate holder, mounted below the source. The reactor details are described by Granier et al. [START_REF] Granier | Diagnostics in helicon plasmas for deposition[END_REF] and the PECVD of Ti x Si 1-x O 2 films is discussed in the previous paper [START_REF] Li | Structural and optical properties of PECVD TiO 2 -SiO 2 mixed oxide films for optical applications[END_REF]. The deposition proceeded from hexamethyldisiloxane (C 6 H 18 OSi 2 , HMDSO, 98%, Sigma Aldrich Ltd.) and titanium isopropoxide (Ti(-OC 3 H 7 ) 4 , TTIP, 99.999%, Sigma Aldrich Ltd.) vapours mixed with oxygen. Oxygen was introduced at the top of the ICP source, while both precursors were injected into the diffusion chamber via a dispersal ring, 15 cm in diameter, located 8 cm above the substrate. The TTIP vapours were kept in a heated container (60 °C) and introduced through a heated line (63 °C) with an MKS mass flowmeter (80 °C). Another MKS mass flowmeter was used to control the amount of the HMDSO vapours. HMDSO was kept in a container heated to 35 °C and the vapours were injected into the diffusion chamber through a line heated to 40 °C. Both precursors were introduced into the chamber at the same time. The film composition was varied by changing the flow rates of HMDSO and TTIP (Table 1) whereas the flow rate of O 2 was constant, 16.4 sccm. The deposition times were selected to keep the film thickness around 250 nm. Crystalline (1 0 0)-oriented silicon wafers with thickness of (381 ± 25) µm were used as substrates for the deposited films. The substrate holder was at the floating potential.

Characterization of films

XPS spectra were recorded using a Kratos Axis Ultra operating at 1486.6 eV (Al source). The pass energy to measure the region of interest was fixed to 20 eV allowing an resolution in energy equal to 0.1 eV. Due to the insulating character of the samples a charge neutralization was used when acquiring the spectra. The C 1s signal from adventitious carbon was used afterwards for energy calibration, setting its position at 284.7 eV.

The atomic composition determined from XPS measurements was used to calculated the titanium-to-silicon ratio, i. e. the titanium stoichiometry x in the Ti x Si 1-x O 2 films, for varied alkoxide flow rates. The results are summarized in Table 1 and revealed that it was possible to prepare films with a controlled x from pure SiO 2 till TiO 2 .

After removal of a Tougaard-type background, an approximate Voigt lineshape (70% Gaussian, 30% Lorentzian) in the product form [START_REF] Evans | Curve synthesis and optimization procedures for X-ray photoelectron spectroscopy[END_REF] was used for peak fitting. The fitting of highly-resolved atomic signals of Ti 2p, Si 2p and O 1s involved a multisample fitting procedure combined with some constrains of the fitting parameters. This advanced procedure was developed to unravel the local chemical environment of Ti x Si 1-x O 2 material prepared by PECVD and it is described in a later section together with its results and implications.

The films were previously characterized by optical spectroscopic methods [START_REF] Ondračka | Optical properties of Ti x 1-x O 2 solid solutions[END_REF] and their basic characterization concerning morphology, crystallinity and chemical structure was carried out by scanning electron microscopy, X-ray diffraction and infrared spectroscopy, respectively [START_REF] Li | Structural and optical properties of PECVD TiO 2 -SiO 2 mixed oxide films for optical applications[END_REF]. The TiO 2 film has a polycrystalline anatase structure, all samples containing Si are amorphous. The film density, given in Table 1, was determined from the film thickness measured by ellipsometry and the film mass.

Results and discussion

Ab initio modelling

Ab initio modelling techniques were employed to test if a decomposition of the O 1s peak into just the TiO 2 , mixed and SiO 2 parts in a real three dimensional structure can be justified and to reveal any trends which could be used to reduce the uncertainty during the experimental fits.

As can be seen in Fig. 1, the DFT results are in a good qualitative agreement with the normalized experimental spectra. Although the qualitative agreement is excellent, a more quantitative test is needed to verify the aforementioned assumptions. With the information from analysis of coordination numbers and first neighbours we can easily sort the binding energies into components corresponding to the various atomic environments. The amorphous structure, represented by our model at least to the degree possible by the limited supercell size, contains a variety of local environments. An oxygen atom can have two, three or four neighbours with different number of Ti or Si atoms -see Fig. 2a for the environments found in structures with = x 0.5. This fine- grained decomposition of the spectra is interesting from the fundamental point of view, but it has to be simplified for the experimental data evaluation. Fitting this many overlapping, poorly resolved peaks would lead to highly correlated components with huge uncertaintiesessentially, the results would be random and hence useless.

Therefore, we simply group the different atomic environments into the three simplified components. The Ti 2 , Ti 3 and Ti 4 local O environments into the TiO 2 component, the TiSi, TiSi 2 , SiTi 2 environments into the mixed Ti-O-Si component and the Si 2 environment into the SiO 2 component (subscripts denote the total numbers of neighbours of each

Table 1

The list of Ti x Si 1-x O 2 films prepared at varied flow rates of HMDSO and TTIP, Q HMDSO and Q TTIP . The titanium stoichiometry x in the films was determined by XPS and the density was determined from the film thickness measured by ellipsometry and film mass. kind; not all are always present due to limited statistics of our rather small supercells). Fig. 2b shows the O 1s peak for one selected concentration = x 0.5 and highlights that the initial assumption, i.e. that overall peak shape can be fitted by three separate components, seems reasonable. Now we take a look at the structural models and try to explain some of the differences between the calculated and experimental data. While a perfect agreement cannot be expected due to the different mixing in the calculations and the experiment, there are a few noteworthy features.

Q HMDSO (sccm) Q TTIP (sccm) x in Ti x Si 1-x O
The already mentioned absolute difference in the energies is unfortunately a problem of the DFT method (or the Slater transition state approach), and is also highly dependent on a particular choice of the xc functional. When replacing the GGA-PBE xc potential with local density approximation (LDA), the absolute values shift by ~4 eV; however, the relative shifts stay the same.

It can also be noticed that the calculated broadened MBEs do not shift as much with compositional changes as the experimental ones. This is due to the fundamental differences between the calculated and experimental values, specifically as the experimental values are given with respect to the Fermi level, a shift of Fermi level with respect to VBM between TiO 2 and SiO 2 can cause this discrepancy.

Due to the perfect composition and stoichiometry of the calculated structures, the spectral features associated with the OH-groups such as the shoulder around 531.5 eV are missing. The presence of the OH peak, which is hidden in the pure SiO 2 such as seen in [START_REF] Permpoon | Natural superhydrophilicity of sol-gel derived SiO 2 -TiO 2 composite films[END_REF], can also explain why the experimental peak of pure SiO 2 is broader than of TiO 2 , although they seem quite similar in the calculated spectra.

To do a more thorough analysis of the fitting constraints, mean peak positions for the components of the O 1s peak and also for the Ti 2p and Si 2p peaks were calculated as a mean value of the individual binding energies. The results are shown in Fig. 3a, c andd.

Only the mean MBE of the mixed O 1s components is constant, all other components show dependence on x. The mean MBE of the SiO 2 O 1s component and of the Si 2p peak show similar trends, especially for the Si-rich compositions. It is possible that some fluctuations are caused by uncertainty in the VBM determination, hence we show also the relative energy shifts between them as well as between the Ti-O-Ti O 1s component and Ti 2p 3/2 peak. These can be seen in Fig. 4. The relative trends are also more relevant for the experimental fitting, since the absolute mean MBE values cannot be compared directly to the experimental BE due to aforementioned differences.

The shift between the Ti-O-Ti component of the O 1s and Ti 2p 3/2 peaks is mostly constant for the compositions with > x 0.2, with one notable outlier from this trend being =

x 0.19. This composition has nevertheless a big uncertainty, since there are only a few atoms contributing to the Ti-O-Ti component in the Si-rich compositions. This large uncertainty of the mean value is also due to the fact that for Tirich compositions the number of possible environments is larger. The shift between the Si-O-Si component of the O 1s and Si 2p peaks is constant with the only exception being the pure SiO 2 phase. Full widths at half maximum (FWHMs) of the components were obtained as the standard deviation of the MBEs and are shown in Fig. 3b. The FWHM of the mixed peak is bigger than that of the pure components due to the more diverse specific environment. Obviously, there are no clear trends in the peak widths. Due to the nature of DFT calculations, this is only the part of the peak broadening associated with the structural disorder as other contributions, such as lifetime broadening, instrumental broadening or temperature (phonon) broadening, are not easily accessible by ab initio methods (at least not by the Slater transition state approach). The question is whether the structural disorder is comparable, larger or smaller as the rest of the contributions. In the first approximation, the FWHM B can be estimated as

= + B B B dis 2 other 2
, where B dis is the broadening associated with the structural disorder and B other are the other contributions such as the instrumental, lifetime and temperature broadening.

The calculated FWHM (which originates only from the disorder) is 0.61 eV for TiO 2 and 0.46 eV for SiO 2 . The values extracted from the experimental data are 1.1 eV for pure TiO 2 and 1.4 eV for SiO 2 . Surprisingly, the trends are reversed here, but it must be noted that the experimental TiO 2 is actually polycrystalline anatase and hence its FWHM is expected to be somewhat narrower than in the amorphous material. On the contrary, the Si-O-Si part in SiO 2 can not be easily distinguished from the impurity component, so the resulting peak is broader. Additionally, there can also be small differences due to different conductivity of TiO 2 and SiO 2 . Using those values, nevertheless, the total broadening from all the other contributions has FWHM in the range between 0.9 eV and 1.3 eV. When compared with the calculated values in Fig. 3b, it can be seen seen that the disorder broadening is the most significant for the mixed component where it is the dominant broadening factor, while it is less significant for the TiO 2 and SiO 2 components.

XPS data analysis

As indicated by the DFT results, it is reasonable to fit the O 1s peak with the three (Gaussian-Lorentzian) components in order to compare their ratios and hence to deduce the overall mixing. Unfortunately, while the mean position of the components are in fact separated, the energy differences are not very big, e. g. as small as 0.6 eV for the TiO 2 and mixed component and the components are not resolved well enough. Moreover, as can be seen from peak shapes in Fig. 1, the O 1s peak can be fitted with only two components for many compositions (if the areas, positions and FWHMs are left free). The situation is also further complicated by the oxygen engagement in other bonds (e. g. OH).

To reduce the uncertainty, the degree of freedom during fitting must be reduced. The areas under the peaks need to stay as free parameters in order for the method to work. It is also not possible to fix the energy of the components completely even when the MBE seems constant (as for example the mixed components of the O 1s peak), since the VBM to E F distance changes significantly between TiO 2 and SiO 2 . We must therefore utilize relative shifts. The first choice is to fix the relative shift between the SiO 2 component of the O 1s peak and Si 2p peak, which is quite constant as seen in Fig. 4b. It would be convenient to fix also the same for the TiO 2 component of the O 1s peak and Ti 2p 3/2 peak, but although the difference (as shown in Fig. 4a) is constant for x 0.5, it decreases significantly for < x 0.5. This originates form the downshift of MBE of the TiO 2 O 1s component as seen in the Fig. 3a. However, besides the large uncertainties, this is likely an artefact of the DFT calculations as already discussed in the previous section, since this corresponds to the right shoulder in the spectra and this feature is seen neither in our experimental data nor in any other reported spectra [START_REF] Larouche | Microstructure of plasma-deposited SiO 2 /TiO 2 optical films[END_REF][START_REF] Permpoon | Natural superhydrophilicity of sol-gel derived SiO 2 -TiO 2 composite films[END_REF][START_REF] Gracia | Correlation between optical properties and electronic parameters for mixed oxide thin films[END_REF]. Hence it seems reasonable to neglect those two points and assume the distance between the TiO 2 component of the O 1s peak and Ti 2p 3/2 peak to be constant as well. The same can be then reasoned for the energy difference between TiO 2 and mixed components of the O 1s peak. This three fixed energy shifts are the basis of our fitting approach. The shift between O 1s TiO 2 and mixed components was 0.65 eV, obtained as average value from the DFT data. The shift between the TiO 2 component of the O 1s peak and Ti 2p 3/2 peak was 71.26 eV, and the shift between the SiO 2 component of the O 1s peak and Si 2p peak was 429.28 eV. These values were extracted from the pure TiO 2 and SiO 2 experimental samples.

Our preliminary fits also indicated, that it is necessary to impose some other constraints regarding the FWHMs. For some fitting parameters, when left completely free, non-physically small values were obtained together with unrealistic fluctuations between the compositions. They cannot be completely fixed either, since such fixing leads to bad fits. The calculated disorder-dependent contribution to the FWHMs are smaller then the rest of contributions to the peak FWHM (as estimated in previous section) for the TiO 2 and SiO 2 parts, and comparable for the mixed part. We can therefore choose one composition-independent parameter expressing the disorder part B i of FWHM of each component i and one sample-dependent parameter B j , where the total FWHM for the given component and composition (sample) is calculated as

= + B B B . i j i j , 2 2 (1)
This allows for some freedom compensating the fluctuations and at the same time it reduces the number of free FWHM-related parameters in the multisample fit of n samples from n 3 to + n 3. In order to facilitate compositionally independent (global) parameters in the fits, all the spectra were fitted simultaneously.

The last difficulty is a proper treatment of oxygen atoms bonded to atoms other than Ti and Si, such as O in OH and CO groups, which we will together denote impurities. They are even worse resolved than the three main components, and fitting them independently was out of the question. Instead, we linked their positions and areas to the main components. The peak shapes of the pure TiO 2 and SiO 2 samples were decomposed into the MO 2 (M = Ti or Si) and impurity components (Fig. S1 in Supplemental Material). Area ratios and relative energy shifts between MO 2 and impurity components from these fits were fixed in the subsequent multisample fit. Both impurity components had one common global disorder-dependent FWHM parameter, similar as for the other three components, and followed the same scheme for calculation of the total FWHM (Eq. 1).

This approach was at first tested for a reference bi-layer sample constituted of SiO 2 (2 nm) on TiO 2 (20 nm). A very good agreement between the experimental and calculated spectra was obtained using only the TiO 2 and SiO 2 components as expected (Fig. S2 in Supplemental material). It indicated that the chosen fitting procedure works very well for the sample containing simultaneously both SiO 2 and TiO 2 materials. The same approach fails for the PECVD Ti x Si 1-x O 2 = x 0.57 sample as shown in the same figure, hence indicating that a reasonable fit without the mixed component is impossible in such case.

Example fit of the O 1s peak from the aforementioned multisample fitting approach including all the constraints is shown in Fig. 5 and displays a nice agreement with the measured peak shape. The full multisample fit including the Ti 2p and Si 2p peaks is shown in Fig. S3 in Supplemental Material.

Fig. 6 shows the evolution of the peak positions for the O 1s components as well as for the Ti 2p 3/2 and Si 2p peaks. The positions decrease significantly in the SiO 2 -rich region and are mostly constant for the x 0.3. Such significant changes are not seen in the calculated MBEs and hence they most likely originate in the shift of the Fermi level with respect to the VBM. This interpretation is further supported by the fact that the shifts are the same for O 1s, Ti 2p and Si 2p peaks, and, as will be shown in the next section, especially the Si environment is almost constant over the whole composition range and therefore no shifts due to local environment changes could be expected. In fact the nonlinear trend is very similar to the trends in the evolution of the band gap [START_REF] Ondračka | Optical properties of Ti x 1-x O 2 solid solutions[END_REF] and hence we can conclude that the Fermi level is just below the minimum of the conduction band for majority of the compositions; only for the SiO 2 -rich compositions it shifts towards the middle of the band gap as expected for SiO 2 .

It is plausible that with a high resolution measurements of the valence bands it would be possible to align the spectra according to VBM and then fix the component position to absolute energy values to simplify the fitting procedure.

The proportions of the O 1s components as a function of the Ti metal fraction, x, in the films are plotted in Fig. 7. The percentage in oxygen atoms engaged in a TiO 2 -like framework increases with x whereas those belonging to a SiO 2 -like environment decreases as expected. Surprisingly, the fraction of the O 1s mixed component is significantly smaller than predicted by the Larouche's mixing model [START_REF] Larouche | Microstructure of plasma-deposited SiO 2 /TiO 2 optical films[END_REF] and shows some asymmetry. The implications are thoroughly discussed in the following section.

Phase separation modelling

Larouche et al. [START_REF] Larouche | Microstructure of plasma-deposited SiO 2 /TiO 2 optical films[END_REF] proposed a simple statistical model for the O 1s components. Under the assumption of 2-coordinated O atoms, 4-coordinated Ti and Si atoms, and a perfect random mixing, the expected fractions are x x x , 2 ( 1)

2 and x (1
) 2 for the TiO 2 , mixed and SiO 2 components, respectively. For completely separated phases, the fractions are the straight lines x and x 1

, with the mixed component absent.

The experimentally determined fractions of the three components are plotted as functions of composition x in Fig. 8 alongside the model curves for phase separation and random mixing. It is evident that real PECVD film structures are far from either of these theoretical border cases. Interpretation of the results thus requires a model incorporating a partial phase separation.

A complete model would include not only the evolution of the atomic network topology with changing x, as studied by Landmann et al. [START_REF] Landmann | The atomic structure of ternary amorphous Ti x Si 1-x O 2 hybrid oxides[END_REF], but also its realistic dependence on phase separation, and possibly additional parameters and peculiarities. This is beyond the scope of this work. Nevertheless, even relatively simple approaches allow progressing beyond the Larouche's model. Two important aspects to consider are an improvement of statistics of O environments based on ab initio calculations and a physical order-disorder model describing partially separated phases.

Oxygen environment statistics

The assumptions of Larouche's model are actually not valid in the Ti x Si 1-x O 2 case [START_REF] Landmann | The atomic structure of ternary amorphous Ti x Si 1-x O 2 hybrid oxides[END_REF], as also illustrated in Fig. 9. While Si is approximately 4-coordinated over the majority of compositional range, there is a significant amount of 5 and 6-coordinated Ti atoms and 3-coordinated O atoms. It was already argued [START_REF] Gracia | SiO 2 /TiO 2 thin films with variable refractive index prepared by ion beam induced and plasma enhanced chemical vapor deposition[END_REF] that this can be the cause of differences between the model and measured components. Is this explanation supported by our calculations?

We start by analysing the effect of changes in the average coordination numbers in the case of random mixing. Two factors come into play here. First, in the Larouche's model the probabilities that a , respectively. However, as Ti atoms have larger average coordination number, O atoms tend to have more Ti neighbours than Si neighbours. Hence, looking at a single random M-O bond, the probability of finding Ti-O

= + p x xC x C x x C x ( ) ( ) ( ) (1 ) ( ) O Ti Ti Ti Si (2)
is larger than for Si-O

= + p x x C x xC x x C x ( ) (1 ) ( ) ( ) (1 ) ( ) O Si Si Ti Si (3)
in more than half of the composition range. Here C t denotes the average coordination number of the atom = t Ti, Si and O. Note that the de- nominators can be simplified using the relation

+ = xC x C C (1 ) 2 , Ti Si O (4)
which follows from the stoichiometry. Second, a 3-coordinated oxygen has lower probabilities of pure environments than 2-coordinated simply due to having more neighbours.

The fraction of a pure component MO 2 is 3 , where the f O2 and f O3 are the fractions of 2 and 3-coordinated O atoms, respectively. If we disregard 4-coordinated O, which occurs only rarely, they can be written simply as

= + f p f p ( ) ( ) M O2 O M 2 O3 O M
= f C 3 O2 O and = f C 2 O3 O
. The mixed component fraction is then a complement to unity = 1 mixed Ti

Si . Therefore, if we know the average coordination numbers C Ti , C Si and C O we can construct a model for component fractions , Ti Si and mixed for random mixing. The average coordination numbers can be taken from our DFT structural models or the extensive Landmann's review (Fig. 9). Looking at the Landmann's data, C Ti is almost perfectly linear

+ C x C 4 2 ,

Ti

Si is close to 4 in the majority or the compositional range and can be approximated by

+ C x 4 0.5 Si 2
, and C O is then obtained from the rela- tion (4). Our DFT data are less smooth than Landmann's due to the smaller size of the cells. Nevertheless, the trends are similar and the main difference is that all coordination numbers are somewhat smaller due to a lower mass density [START_REF] Ondračka | Optical properties of Ti x 1-x O 2 solid solutions[END_REF]. The average coordination number for Ti ends at 5.6 and the highest average coordination number for Si is 4.16 at = x 0.8125. Hence, Si is essentially 4-coordinated in the entire range.

The result of feeding our coordination number trends into the model can be seen in Fig. 10. The final curves are surprisingly similar to the Larouche's model. A decrease in the SiO 2 component and corresponding increase of the mixed component are visible, whereas the TiO 2 component is largely unchanged. We note that the differences increase when Landmann's data are used instead, but only moderately. The overall shapes match nicely the data points from the DFT model, confirming that the DFT cells are well mixed. Indeed, it would be surprising to see phase separation in the DFT models because the cooling was quite fast. There are small discrepancies in the ratios of the 2 and 3coordinated parts of the TiO 2 and mixed component. However, they can be explained by either the small cell size or not taking into account in the model that some groups might be more energetically preferable. We can conclude that the simple Larouche's statistical model is a good approximation even though its initial assumptions are not justified.

Since the DFT cells correspond well to random mixing, they can serve directly as models of perfectly mixed structures. Instead of utilizing just the average coordination numbers, we can incorporate the complete structural data by taking the calculated fractions f x ( ) t of all possible O environments types = t Si 2 , TiSi, Ti 2 , Ti 3 , Ti 2 Si, … found in the simulated structures. They can be classified further to individual coordination polyhedra types [START_REF] Landmann | The atomic structure of ternary amorphous Ti x Si 1-x O 2 hybrid oxides[END_REF]; nevertheless, the chemical identity of the neighbours is sufficient here.

Components , Ti Si and mixed are then obtained by sorting the environments t into three groups, Ti -only Ti neighbours, Si -only Si, and mixed -all combinations of different metal atoms. The individual Fig. 8. Dependencies of environment fractions for perfect random mixing (dashed lines) and complete phase separation (dotted lines), compared with experimental dependencies. The solid curves correspond to fits of the experimental data using ( 6) with a simple quadratic formulae for .

Fig. 9.

Compositional dependence of the average coordination numbers for Ti, Si and O atoms, with spreads displayed using error bars corresponding to one standard deviation. Full points are our a-Ti x Si 1-x O 2 DFT structures [START_REF] Ondračka | Optical properties of Ti x 1-x O 2 solid solutions[END_REF], empty points are from DFT calculations by Landmann et al. [START_REF] Landmann | The atomic structure of ternary amorphous Ti x Si 1-x O 2 hybrid oxides[END_REF]. contributions in each group are then summed, for instance

= + + + f f f f Ti Ti Ti Ti Ti 2 3
4 for the titania component. Of course, in this case the resulting dependencies are very similar to the approximate model because the contribution of disregarded environments is negligible.

As a final remark we note that the presented splitting of O environments into simple pure and mixed components is unambiguous for 2-coordinated O, but for higher coordination numbers another scheme is possible. It considers all M-O-M configurations that can be found in the environment of a specific O atom and weights them accordingly. For instance, an O atom in Ti 2 Si environment would contribute 2/3 to the mixed component and 1/3 to the TiO 2 component. One serious disadvantage of this scheme is that the components are then combinations of more individual environment types. This results in rather odd component line shapes if we plot them as combinations of individual peaks as obtained from DFT, bringing additional uncertainty to the peak fitting constraints. Nevertheless the results of one approach can be in principle recalculated to the other using the nearest neighbour statistics.

Simple partial phase separation models

The simplest partial phase separation model can be constructed by considering the material as a combination of mixed and separated materials. For each environment, the compositional dependence for separated phases (chemically ordered structures) is the straight line

+ xf x f (1) (1 ) (0) t t
constructed from the fractions in pure materials. For a material composed of mixed and separated phases with fractions q and q 1

, the dependence can be expressed

= + + f x f qf x q xf x f ( , ) ( ) (1 )[ (1) (1 ) (0)]. t t t t
(5) Formula ( 5) is not a realistic description of an order-disorder evolution. However, it allows modelling and quantification of partial phase separation using simulation results without having to produce structures covering the entire two-dimensional space of composition x and disorder q.

It is not necessary to use the detailed O environment data f t as the input. The average coordination numbers can also serve as the starting point, as well as the Larouche's model. In the latter case there are only three environments, Ti 2 , Si 2 and TiSi, with parabolic dependencies 1) TiSi , respectively. Plugging them into (5) yields expressions

= f x Ti 2 2 , = f x (1 ) Si 2 2 and = f x x 2 (
= = = qx x x q x x qx 2 (1 ), [1 (1 )], (1 )(1 ), mixed Ti Si (6)
providing a simple analytical model for partial phase separation. Expressions (6) can be also derived in an alternative manner which leads to an interesting interpretation of the parameter q. We imagine traversing -M-O-M-O-M-chains in the atomic network. In a random mixture the metal atoms M we encounter are randomly Ti or Si, while for separate phases we see long chains of one type of metal atom. The sequences of encountered atoms can be constructed as Markov chains [START_REF] Grimmett | Probability and Random Processes[END_REF]. If we propose that the probability of switching between Ti and Si is reduced by a factor q (0, 1] with respect to random mixture (in- dependently on composition) then the transition matrix is [START_REF] Lu | Hydrodeoxygenation of guaiacol catalyzed by high-loading Ni catalysts supported on SiO 2 -TiO 2 binary oxides[END_REF] The limit values = q 1 and q 0 correspond to perfect random mixture and complete phase separation, respectively. In other words, chain segments or 'clusters' composed of pure phases are, on average, q 1/ larger than in the random mixture. The transition matrix [START_REF] Lu | Hydrodeoxygenation of guaiacol catalyzed by high-loading Ni catalysts supported on SiO 2 -TiO 2 binary oxides[END_REF] gives the stationary distributions of O environments [START_REF] Huang | Performance of SiO 2 -TiO 2 binary oxides supported Cu-ZnO catalyst in ethyl acetate hydrogenation to ethanol[END_REF].

By fitting this simplest model to the experimental dependencies we already improve the agreement, as illustrated in Fig. 8 (curve Larouche/ Markov). The expressions [START_REF] Huang | Performance of SiO 2 -TiO 2 binary oxides supported Cu-ZnO catalyst in ethyl acetate hydrogenation to ethanol[END_REF] are symmetrical with respect to swapping the metals and simultaneously x with x 1

. Hence, the model is not capable of capturing the evident asymmetry in experimental XPS data. The asymmetry is probably in part related to the larger average coordination numbers of O in the Ti-rich region compared to the Si-rich region. Nonetheless, even curves calculated from the ab initio structural data exhibit only a slight asymmetry, so this is unlikely the full explanation; see the fit with a model obtained by analysing oxygen neighbours in DFT cells in Fig. 11 (curve DFT neighbours). The theoretical compositional dependence is asymmetrical, but only very slightly.

Statistical model

For a more physical approach to phase separation, we return to regular atomic networks with 2-coordinated O and describe a model based on the concept of quenched disorder in a regular solid solution. This type of model is known under many names, such as Ising or lattice gas model [START_REF] Ising | Beitrag zur Theorie des Ferromagnetismus[END_REF][START_REF] Peierls | On Ising's model of ferromagnetism[END_REF][START_REF] Landau | Statistical Physics[END_REF][START_REF] Baxter | Exactly Solved Models in Statistical Mechanics[END_REF][START_REF] Rothman | Lattice-gas models of phase separation: Interfaces, phase transitions, and multiphase flow[END_REF][START_REF] De With | Liquid-State Physical Chemistry: Fundamentals, Modeling, and Applications[END_REF]. While separated phases are energetically preferred, the non-equilibrium deposition process produces an atomic network with a relatively large disorder (large mixing), corresponding to a high temperature. The network is frozen in this state as the energy barriers impeding further relaxation are too high compared to k T B at room temperature T (k B denotes the Boltzmann constant). The disorder then depends on = E k T / B , where T is the effective temperature and E is the interchange energy

= + E E E E (Ti O Si) 1 2 [ (Ti O Ti) (Si O Si)], (8)
which is related to the energy of formation [START_REF] Ondračka | Optical properties of Ti x 1-x O 2 solid solutions[END_REF] E f of a perfect random mixture as follows (see Supplemental Information):

= + + E x xE x E x x E ( ) (TiO ) (1 ) (SiO ) 4 3 (1 )
.

f f 2 f 2 (9)
An explicit solution is known for one-dimensional (1D) chains that are equivalent to the 1D Ising model [START_REF] Baxter | Exactly Solved Models in Statistical Mechanics[END_REF], leading to expressions with the same overall form as [START_REF] Huang | Performance of SiO 2 -TiO 2 binary oxides supported Cu-ZnO catalyst in ethyl acetate hydrogenation to ethanol[END_REF]. However, q is no longer a constant; it is now a function of both and x (see Supplemental Information):

= + + q x x 2 1 1 4 (1 )(e 1) . 2 (10)
As a result, the mixed curve is flatter around = x 0.5 compared to the parabolic dependencies obtained with constant q. The fit of the experimental dependencies with this model is also illustrated in Fig. 11.

The 1D model can be considered realistic when the material is actually formed mostly by linear chains or the phase separation is relatively low (small ) and the topology of the atomic network plays little role because there is no long-range order yet. For larger , the 1D model exhibits a gradual progression to separated phases. This is typical for such 1D systems with short-range interactions and generally differs from the behaviour of higher-dimensional systems where a phase transition between disordered and phase-separated states is observed [START_REF] Baxter | Exactly Solved Models in Statistical Mechanics[END_REF].

To obtain x ( , ) dependencies that capture this phenomenon at least qualitatively, we performed a simple numerical simulation of twodimensional (2D) atomic networks using the Metropolis-Hastings algorithm [START_REF] Metropolis | Equation of state calculations by fast computing machines[END_REF][START_REF] Hastings | Monte Carlo sampling methods using Markov chains and their applications[END_REF][START_REF] Ibarra-García-Padilla | The hobbyhorse of magnetic systems: The Ising model[END_REF]. For simplicity, a square geometry in which both metals are 4-coordinated was used. By annealing atomic networks of varying composition x to different finite temperatures, corresponding to different values, we sampled the function in a mesh of x ( , ) points. Values for arbitrary x and could then obtained by interpolation, permitting fitting the experimental data with the 2D model.

The resulting theoretical mixed curve plotted in Fig. 11 is even flatter in the centre than for the 1D model. This effect is even more marked for smaller degree of disorder, when the function becomes almost constant over a wide range of compositions (not shown). We can expect that for 3D structures the dependence would have the same overall character because the Ising model behaviour changes qualitatively only between 1D and higher dimensions, despite the various effects influencing it in detail: different topology of the atomic network, including mean coordination numbers and ring size (that are on average larger and smaller, respectively, in realistic atomic networks [START_REF] Landmann | The atomic structure of ternary amorphous Ti x Si 1-x O 2 hybrid oxides[END_REF]), 3D structures being generally closer to a mean field model than for 2D [START_REF] Baxter | Exactly Solved Models in Statistical Mechanics[END_REF], etc.

For both the 1D and 2D models, the most notable discrepancy is nevertheless still the asymmetry, which they cannot describe because they are inherently symmetrical with respect to the two metals. We also note that even though the theoretical mixed curves have dissimilar shapes for the individual models, the sums of squared residuals differ by about 10% between all the various fits. Hence, the differences are not significant.

Considering how the model was constructed, one is of course curious what is the thermodynamic temperature T corresponding to the observed disorder. An estimate of E is necessary, which can be ob- tained by fitting the formation energy dependencies on composition [START_REF] Ondračka | Optical properties of Ti x 1-x O 2 solid solutions[END_REF] by formula [START_REF] Li | Ion impingement effect on the structure and optical properties of Ti x Si 1-x O 2 films deposited by ICP-PECVD[END_REF]. For the amorphous phase, which is probably the most relevant, we obtain E 0.17 eV, giving T 2400 K. Although this temperature may seem high at the first sight, it is consistent with similar approaches also considering only configurational entropy. For example, the maximum temperature for spinodal decomposition in

Ti Al

x x 1

N system was theoretically predicted to be 5000-8000 K [START_REF] Mayrhofer | Ab initio calculated binodal and spinodal of cubic Ti 1-x Al x N[END_REF][START_REF] Alling | Mixing and decomposition thermodynamics of c-Ti 1-x Al x N from first-principles calculations[END_REF] while experimentally the decomposition starts at around 1300 K [START_REF] Rachbauer | Decomposition pathways in age hardening of Ti-Al-N films[END_REF]. Later theoretical reports suggested that this discrepancy is mostly due to neglecting other entropic terms (e. g. related to lattice vibration or anharmonic effects [START_REF] Shulumba | Lattice vibrations change the solid solubility of an alloy at high temperatures[END_REF]). Consequently, also the here predicted temperature for phase separation is actually expected to be significantly lower in reality.

It should be also noted that the phase separation transition occurs around of unity, depending on the dimension and composition. The fitted value is somewhat smaller, but relatively close. Disorder close to critical may arise naturally when the deposition process only heats the material locally and the energy dissipates as is the case of PECVD, because decreasing temperature also means falling probabilities of overcoming potential barriers and the progress of phase separation beyond the critical point is very slow in such case.

Conclusions

We quantified from XPS measurements the phase separation in 10 amorphous thin Ti x Si 1-x O 2 films prepared by PECVD for a series of compositions x covering the entire interval x [0, 1]. The analysis was based on structural models constructed using ab initio DFT calculations, which provided O 1s, Ti 2p and Si 2p binding energies of each individual atom in simulated amorphous cells. The DFT results showed that the O 1s peak can be decomposed to three simple components, corresponding to the TiO 2 , SiO 2 and mixed environment of the O atoms. The necessity for a mixed component was further demonstrated by the impossibility to fit O 1s peaks by just the two peak shapes obtained for pure materials. The DFT results also justified several constraints for BEs and FWHMs of the components that were utilized in the XPS data fitting, in particular constant relative shifts between pairs of components, O 1s TiO 2 and mixed (0.65 eV), O 1s SiO 2 and Si 2p (429.28 eV), and O 1s TiO 2 and Ti 2p 3/2 (71.26 eV). Using a multisample analysis of all samples, we then obtained dependencies of the TiO 2 , SiO 2 and mixed components on x. The dependencies did not lie close to either of the previously published simple models of random mixing and phase separation. They also exhibited a notable asymmetry, with the mixed component being more prevalent in Ti-rich materials. Since it had been previously suggested that the asymmetry can arise from changes in average coordination numbers with x, we utilized the O environment statistics from ab initio results to construct more realistic models. However, the resulting theoretical curves were still only slightly asymmetrical, and we have to conclude the changes in coordination number alone do not explain the observed asymmetry. Finally, we presented several models suitable for fitting the functional dependencies of partial phase separation obtained from XPS data. The models range from a simple Markov chain-like model, which does not require any detailed information about the material, to models utilizing the coordination number and environment statistics and also a statistical phase separation model. They all agree that the studied PECVD are mostly disordered, with only a moderate phase separation tendency. Since modelling and methods form a large part of this work, we should also comment on their applicability to other materials and analyses. Although concrete DFT calculations need to be done anew in each case, the overall procedure is quite general. We utilize theoretical BEs from DFT to derive constraints which then provide guidance for XPS spectra fitting. Importantly, this approach remains practical even when DFT modelling of spectra is not feasible, such as for complex amorphous materials. The presented phase separation models can be adopted more directly. Individual models vary in complexity, assumptions and required information about the material -and this decides their suitability in specific cases. Nonetheless, all enable the characterization of disorder by combining XPS analyses for a range of material compositions.

Fig. 2 .

 2 Fig. 2. Decomposition of the calculated O 1s peak a) based on the specific firstneighbour environment, b) into the three simplified groups. A histogram of calculated binding energies is shown in b) as well to illustrate how the broadened lineshapes were produced (more details in the Supplementary Material).

Fig. 3 .

 3 Fig. 3. a) Calculated mean modified binding energy (MBE) of the simplified components of the O 1s peak. b) Calculated FWHMs of the simplified components of the O 1s peak. c) Calculated mean MBE of the Ti 2p 3/2 peak. d) Calculated mean MBE of the Si 2p peak.

Fig. 4 .

 4 Fig. 4. Energy difference between the a) TiO 2 component of the O 1s peak and Ti 2p 3/2 peak, b) SiO 2 component of the O 1s peak and Si 2p peak.

Fig. 5 .Fig. 6 .Fig. 7 .

 567 Fig. 5. Fit of the O 1s peak with three components for = x 0.57.

Fig. 10 .

 10 Fig. 10. Theoretical model for expected component fractions based on the DFT results. Points represent component fractions from DFT, solid lines approximations based on parabolic dependence of C Si on x and dotted lines the Larouche's model.

Fig. 11 .

 11 Fig. 11. Fit of experimental XPS results by dependencies corresponding to the three theoretical models: DFT nearest neighbour data, 1D statistical model and 2D Monte Carlo simulations.

Acknowledgement

This work was supported by Ministry of Education, Youth and Sports of the Czech Republic under the project CEITEC 2020 (LQ1601), by the MOBILITY projects 7AMB15AT017 and 7AMB15FR036, and from the Large Infrastructures for Research, Experimental Development and Innovations project IT4Innovations National Supercomputing Center -LM2015070. The computational results presented have been also in part achieved using the Vienna Scientific Cluster (VSC). This work has been supported by Campus France, the French agency for the promotion of higher education and international mobility.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.