Iterative Kriging-based Methods for Expensive Black-Box Models

Siyang Deng, Reda El Bechari, Stéphane Brisset, and Stéphane Clénet Univ. Lille, Centrale Lille, Arts et Metiers ParisTech, HEI, EA 2697 -L2EP -Laboratoire d'Electrotechnique et d'Electronique de puissance, F -59000 Lille, France

Reliability-Based Design Optimization (RBDO) in electromagnetic field problems requires the calculation of probability of failure leading to a huge computational cost in the case of expensive models. Three different RBDO approaches using kriging surrogate model are proposed to overcome this difficulty by introducing an approximation of the objective function and constraints. These methods use different infill sampling criteria (ISC) to add samples in the process of optimization or/and in the reliability analysis. Several enrichment criteria and strategies are compared in terms of number of evaluations and accuracy of the solution.

Index Terms-Infill sampling criteria, kriging model, reliability analysis, reliability-based design optimization.

I. INTRODUCTION ELIABILITY-BASED DESIGN OPTIMIZATION

(RBDO) approaches can be divided into Double-Loop (DLM), Single-Loop (SLM) and Sequential Decoupled Methods (SDM). They have emerged in the past few decades and become more and more popular in electromagnetics owing to their ability to account for uncertain parameters. However, for expensive black-box models, the computational burden can become unbearable.

To overcome this issue, iterative kriging surrogate models have been proposed to reduce the number of evaluations [START_REF] Lee | A sampling technique enhancing accuracy and efficiency of metamodel-based RBDO: Constraint boundary sampling[END_REF]- [START_REF] Lee | Sampling-based RBDO using the stochastic sensitivity analysis and Dynamic Kriging method[END_REF]. Infill Sampling Criterion (ISC) was used with the aim of improving the quality of the surrogate model, and searching for the solution of the optimization problem. However, the metamodel is established before starting RBDO and no enrichment is made during neither optimization nor reliability analysis.

With the purpose of enhancing the efficiency, different strategies including the choice of the ISC and the positioning of sample enrichments in the optimization process are investigated in this paper for each aforementioned type of RBDO approaches, so that the reliabilities are also analyzed by metamodels. A mathematical example is used to compare with classic RBDO, i.e. without kriging model, and highlight the most effective strategy. Then, RBDO of a transformer modelled by a time consuming model based on the Finite Element method is performed with the most effective strategy.

II. INFILL SAMPLING CRITERIA

Iterative surrogate-based optimization methods start with a small set of initial sampling points to create a preliminary metamodel. Then, the infill sampling criteria are considered as new objective functions to add points into the sample set and update the meta-model until the predicted error is less than a chosen tolerance. A great advantage of this approach is that it enhances the accuracy of meta-model and search the probabilistic optimum simultaneously with a small amount of samples.

Expected Improvement (EI) criterion [START_REF] Jones | Efficient global optimization of expensive black-box functions[END_REF] is widely used for surrogate-based optimizations without constraints.

𝐸𝐼 𝑓 = { (𝑓 𝑚𝑖𝑛 -𝑓 ̂)𝛷(𝑧) + 𝑠̂𝑓𝜙(𝑧) if 𝑠̂𝑓 > 0 0 if 𝑠̂𝑓 = 0 (1)
where 𝑓 𝑚𝑖𝑛 is the best current sampled objective function value, 𝑓 ̂ and 𝑠̂𝑓 are the predicted value and the mean square error (MSE), 𝜙(•) and 𝛷(•) denote the probability density function and the cumulative distribution function of the standard normal distribution respectively, and 𝑧 = (𝑓 𝑚𝑖𝑛 -𝑓 ̂) 𝑠̂𝑓 ⁄ . However, as EI is multimodal, more attention should be paid on the infill criterion to be sure to find the global solution. The Weighted EI (WEI) criterion [START_REF] Xiao | Adaptive weighted expected improvement with rewards approach in Kriging assisted electromagnetic design[END_REF] seems to be more suitable as it adds weights into EI expression to balance exploration (right part) and intensification (left part).

W𝐸𝐼 𝑓 = { 𝜔(𝑓 𝑚𝑖𝑛 -𝑓 ̂)𝛷(𝑧) + (1 -𝜔)𝑠̂𝑓𝜙(𝑧) if 𝑠̂𝑓 > 0 0 if 𝑠̂𝑓 = 0 (2)
Choosing small weight 𝜔 prevents WEI from converging to a local minimum if the initial sampling is inside the security domain. This condition is quite difficult to satisfy for many devices, as their security domains may be small and sometimes discontinuous. To avoid this issue, a Modified WEI (MWEI) combined with the surrogate objective function is proposed:

MW𝐸𝐼 𝑓 = W𝐸𝐼 𝑓 -𝜔𝑓 ̂ (3)
Investigations on the same example as in [START_REF] Xiao | Adaptive weighted expected improvement with rewards approach in Kriging assisted electromagnetic design[END_REF] show that a weight equal to 0.1 provide to a global optimum with less iterations.

For constrained problems, an extended method consists in multiplying the value of EI by the probability of feasibility (PF) [START_REF] Schonlau | Computer Experiments and Global Optimization[END_REF]. However, PF may prevent the sampling on the constraint boundary where the deterministic optimum may lie. Another constraint handling method is the Expected Violation (EV) method [START_REF] Audet | A surrogate-model-based method for constrained optimization[END_REF] but the number of candidate points to evaluate can be very large. An alternative method is to use the predicted value of the constraint functions 𝑔 ̂ directly as constraints in the infill sub-problem [START_REF] Sasena | Flexibility and efficiency enhancements for constrained global design optimization with kriging approximations[END_REF].

R III. INFILL STRATEGIES FOR RBDO METHODS

RBDO is a combination of deterministic constrained optimizations and reliability analysis. For the first one, the design variables 𝑑 are the mean value of random variables 𝑋 and the standard deviations 𝜎 are constant. For reliability analysis, 𝑑 and 𝜎 are constants and the design variable 𝑥 is a realization of 𝑋. 𝛽 𝑡 is the given target reliability index.

A. Double-Loop Method

DLM like Performance Measure Approach (PMA) [START_REF] Tu | A new study on reliability-based design optimization[END_REF] has a nested structure: The outer loop seeks for the optimum and the inner loop searches the Most Performance Target Point (MPTP) that maximize the constraint subject to a given reliability index.

There are two places where ISC can be introduced to improve the accuracy of kriging model: Outer loop and inner loop. For the inner loop, EI of 𝑔 is used to find MPTP by solving the optimization problem in Eq. ( 4)-( 5) as the constraint on the reliability index is an explicit function of the design variables:

𝑥 * = argmax 𝑥 𝐸𝐼 𝑔 (𝑥) 𝑠. 𝑡. ‖(𝑥 -𝑑) 𝜎 ⁄ ‖ = 𝛽 𝑡 ( 4
)
𝐸𝐼 𝑔 = { (𝑔 ̂-𝑔 𝑚𝑎𝑥 )𝛷(𝑧 𝑔 ) + 𝑠̂𝑔𝜙(𝑧 𝑔 ) if 𝑠̂𝑔 > 0 0 if 𝑠̂𝑔 = 0 ( 5
)
where 𝑧 𝑔 = (𝑔 ̂-𝑔 𝑚𝑎𝑥 ) 𝑠̂𝑔 ⁄ , 𝑠̂𝑔 is the MSE of the constraint, and 𝑔 𝑚𝑎𝑥 is the maximum sampled constraint value.

For outer loop, the criterion MWEI is preferred to avoid local solutions and the implicit inequality constraints are computed by the inner loop. However, as the two loops are nested, the enrichment in inner loop may bring out thousands of model evaluations. To test it, two strategies are proposed: the first one (PMA1) adds new samples only inside the outer loop, whereas the second (PMA2) enriches inside both loops.

B. Single-Loop Method

For SLM like Single Loop Approach (SLA) [START_REF] Liang | A single-loop method for reliability-based design optimization[END_REF], the main point is that the inner loop optimization is replaced by an approximation based on a first order Taylor expansion to avoid the numerous evaluations required to find the MPTP.

It is important to note that due to its approximation, the method itself has already loose some precision. Therefore, it is expected that with a surrogate model, the two approximation errors will be added and the accuracy will be further reduced.

C. Sequential Decoupled Method

SDM like Sequential Optimization and Reliability Assessment (SORA) [START_REF] Du | Sequential optimization and reliability assessment method for efficient probabilistic design[END_REF] are based on a series of sequential deterministic optimizations and reliability assessments. The main point is to shift the boundaries of constraints inside the feasible domain based on the reliability information obtained in the former iteration. The first optimization aims at searching the global deterministic optimum. Reliability assessment is then conducted to locate the MPTP corresponding to the target reliability index. Finally, new optimizations are carried out by taking into account the shift 𝑡 computed with MPTP.

Three strategies are proposed. In the first one (SORA1), the reliability analysis is the same as in the inner loop of PMA and enrichment is made with EI criterion. For the deterministic optimizations, the constraints are computed with the metamodel 𝑔 ̂(𝑑 -𝑡) and the MWEI is preferred in order to find the global solution.

The second strategy (SORA2) differs from the first one by the fact that enrichment of the kriging models with MWEI criterion is made at first iteration only. For all other iterations, the deterministic optimization is made with the meta-models 𝑓 ̂ and 𝑔 ̂.

For the third strategy (SORA3), if the deterministic optimum found in 𝑘-th cycle 𝑑 𝑘 is close to any optimum of other 𝑘 -1 cycles, as the former reliability assessments have already added points in this region, the accuracy is considered to meet the requirement so there is no need to add samples any more. The proximity criterion defined in ( 6) is checked before entering reliability analysis:

‖(𝑑 𝑘 -𝑑 𝑖 )/𝜎‖ < 𝛽 𝑡 , 𝑖 = 1, … , 𝑘 -1 (6)
where 𝑑 𝑖 is the deterministic optimum found by the 𝑖-th cycle. If ( 6) is satisfied, the meta-model of constraints is used directly and only MPTP are evaluated. For the deterministic optimizations, it takes the same strategy as SORA2. The flowchart of SORA3 is shown in Fig. 1 where 𝑥 𝑘 is the MPTP of 𝑘-th cycle.

IV. COMPARISON OF STRATEGIES

To assess the efficiency of kriging-based RBDO methods, the mathematical example in [START_REF] Kim | A Single-Loop Strategy for Efficient Reliability-Based Electromagnetic Design Optimization[END_REF] with two variables and three constraints is analyzed. Noting that the random variables are Gaussian and their standard deviations are all equal to 0.3. Lower and upper bounds are 0 and 10 respectively for both variables. The target reliability index 𝛽 𝑡 is chosen equal to 2, so that the target probability of failure 𝑃 𝑡 = 𝛷(-𝛽 𝑡 ) = 2.28%. The results are given in Table 1 with an initial sampling of 20 points. The probability of failure 𝑃 𝑓 is calculated by Monte-Carlo Simulation (MCS) with 10 6 samples. For comparison purpose, results given by classic RBDO methods without kriging are also presented.

All the iterative kriging-based RBDO methods lead to a reduced number of evaluations. SLA with kriging has the minimum number of evaluations but is not accurate enough as the maximum probability of failure is much greater than 𝑃 𝑡 due to the approximation used to simplify the reliability analysis. As expected, PMA with infill during inner loops requires thousands of samples to evaluate. The other PMA strategy is faster but the accuracy is not sufficient. Kriging-based SORA strategies lead to the best result and the third one SORA3 is the most efficient. Fig. 2 shows two iterations of SORA3.

As SORA3 seems to be the most efficient meta-model strategy on this mathematical example, it is tested on the RBDO of a transformer with FEM.

V. ELECTROMAGNETIC DEVICE

The electromagnetic device is a single-phase safety isolating transformer with grain-oriented E-I laminations designed for installation in electric cabinet [START_REF] Tran | A Benchmark for Multi-Objective, Multi-Level and Combinatorial Optimizations of a Safety Isolating Transformer[END_REF]. The primary and secondary windings are wound around the frame surrounding the central core (Fig. 3, left).

A. Finite Element Models

Thermal and magnetic phenomena are modeled by using 3D FEA on the eighth of transformer due to symmetries. There are about 43,000 nodes and 290,000 edges in the model. The right part of Fig. 3 shows the mesh in the magnetic circuit, the insulating, the air gap, the frame and the opposing direction of currents in the primary and secondary windings that create flux in the gap between the coils (leakage flux).

For the electromagnetic modeling, all magnetic and electric quantities are assumed sinusoidal. Full-load and no-load simulations are used to compute all the characteristics. The iron losses are computed with the Steinmetz formula and the leakage inductances are calculated with the magnetic co-energy. The core magnetic nonlinearity is taken into account.

In the thermal modeling, some assumptions are considered: the insulator between the core and the coils is in perfect contact with both parts; there is no thermal contact between the exterior coil and the magnetic circuit; there is no thermal exchange with the air trapped between the coils and the iron; there is no convection on the upper and lower sides of the coil; there is no temperature gradient in the copper and the iron, and all surfaces have the same convection coefficient.

A magneto-thermal weak coupling is considered and the computational time is equal to10 minutes on a single core of an Intel Xeon CPU E5-2690 at 2.60 GHz. The copper and iron losses are computed with the magnetic AC solver and introduced as heat sources in the thermal static solver. The copper temperature is used to compute the coils resistors introduced in the magnetic solver and this loop continues until change in temperatures is less than 0.1 °C. Both solvers use the same mesh and are included in Opera3D software.

B. Analytical Model

In order to motivate the need of a time expensive 3D FEA model, an Analytical Model (AM) is also used to compare RBDO results with both models.

The physical phenomena within the transformer are electric, magnetic and thermal. The assumptions for AM are uniform distribution of the magnetic flux density in the iron core and no voltage drop due to the magnetizing current. The thermal assumptions are the same than the 3D FEA except that the temperatures are uniform within the coils and laminations.

The weakest points of AM are the assumption of uniform temperature in copper and iron, and the approximation of the leakage inductance values.

C. Optimization Problem

The optimization problem contains 7 design variables. There are three parameters (𝑎, 𝑏, 𝑐) for the shape of the lamination, one for the frame (𝑑), two for the section of conductors (𝑆 1 , 𝑆 2 ), and one for the number of primary turn (𝑛 1 ) (Fig. 3

, left).

There are 7 inequality constraints in this problem. The copper and iron temperatures 𝑇 𝑐𝑜 , 𝑇 𝑖𝑟 respectively should be less than 120℃ and 100℃. The efficiency 𝜂 should be greater than 80% . The magnetizing current 𝐼 𝜇 𝐼 1 ⁄ and drop voltage Δ𝑉 2 𝑉 2 ⁄ should be less than 10% . All these constraints are computed with FEM or AM model. Finally, the filling factors of both coils 𝑓 1 , 𝑓 2 should be lower than 0.5.

The goal is to minimize the mass 𝑚 𝑡𝑜𝑡 of iron and copper materials. Thus, the optimization problem is expressed as: min 𝑚 𝑡𝑜𝑡 (𝑎, 𝑏, 𝑐, 𝑑, 𝑆 1 , 𝑆 For RBDO, all constraints are considered with a target probability of failure equal to 0.13%, which means a reliability index of 3. The standard deviation of each design variable is equal to 1% of its lowest bound.

D. Results

Table 2 shows optimal values, objective, probabilities of failure calculated by MCS with 10 6 samples computed with the meta-model, and the number of evaluations. For AM, SORA without meta-model is also tested and the number of evaluations is greater than 10,000, so it can be seen that SORA3 with kriging meta-model (SORA3 + AM, center column in Table 2) can find a solution almost satisfying all constraints with less evaluations. However when the same solution is reevaluated with FEM (FEM reeval., right column in Table 2), the highest probability of failure is 90%, so RBDO cannot be performed with AM only. The mass computed with FEM is slightly different from the one with AM because the voltage drop is considered to calculate the number of turns for the secondary coil.

SORA3 with FEM (SORA3 + FEM, left column in Table 2) leads to a probability of failure close to its target value. The objective value is higher with FEM because AM underestimates constraints. The initial sampling includes 7,000 points evaluated in parallel on 24 cores in about 49 hours then the 265 infill sampling points are evaluated sequentially in about 44 hours. The first advantage of SORA3 with FEM is that a significant computing time can be saved as it reduces the number of evaluations. The second advantage is that kriging model gives accurate derivatives that enable the use of fast gradient-based algorithm. Contrarily, as FEM provides noisy derivatives it requires a noise-free costly algorithm when directly connected with it. VI. CONCLUSION According to the mathematical example, the third strategy of kriging-based SORA is the most efficient without losing too much accuracy among the 6 approaches proposed.

RBDO of a single-phase safety isolating transformer is also performed here with FEM and the kriging-based SORA shows its applicability in dealing with this highly constrained problem by reducing the number of evaluations. Then, compared with analytical model of the same device, this approach with FEM could get a more accurate solution.

Fig. 1 .

 1 Fig. 1. The process of SORA3 strategy.

Fig. 3 .

 3 Fig. 3. Design variables of transformer and mesh.

Fig. 2 .

 2 Fig. 2. Iterations of SORA3 for the mathematical example (green points are initial sampling, pink points are enrichment samples during deterministic optimizations, yellow ones are added by reliability analysis and blue ones are MPTPs at the current iteration, dashed lines and contours present the real constraints and objectives respectively while solid ones present the metamodels).

TABLE 1 RESULTS

 1 OF MATHEMATICAL EXAMPLE USING DIFFERENT STRATEGIES

	Strategy	Number of evaluations	Optimal solution	Optimal value	Maximal 𝑃 𝑓 (%)
	SLA (exact model)	165	[2.2512; 1.9677] -1.9953 2.32
	PMA/SORA (exact model)	3183/531	[2.2513; 1.9691] -1.9945 2.27
	SLA	26	[2.2466; 1.9617] -1.9996 2.59
	PMA1	29	[2.2494; 1.9649] -1.9972 2.44
	PMA2	1804	[2.2513; 1.9691] -1.9945 2.27
	SORA1/2/3	142/97/45	[2.2513; 1.9691] -1.9945 2.27

TABLE 2

 2

	RESULTS OF TRANSFORMER OPTIMIZATION WITH META-MODEL
	Values	SORA3 + FEM SORA3 + AM FEM reeval.
	𝑎	12.902	13.153
	𝑏	46.042	51.039
	𝑐	18.183	16.532
	𝑑	42.318	43.098
	𝑛 1	659.06	641.75
	𝑆 1	0.3254	0.3216
	𝑆 2	2.7552	2.8956
	𝑚 𝑡𝑜𝑡	2.4028	2.3552	2.3520
	𝑃(𝑇 𝑐𝑜 > 120℃)	0%	0%	0%
	𝑃(𝑇 𝑖𝑟 > 100℃) ⁄ > 0.1) 𝑃(∆𝑉 2 𝑉 2 𝑃(𝐼 μ 𝐼 1 ⁄ > 0.1)	0.1506% 0% 0.1348%	0.1567% 0% 0.1420%	90.05% 0% 0.3281%
	𝑃(𝑓 1 > 0.5)	0.1327%	0.1236%	71.20%
	𝑃(𝑓 2 > 0.5)	0.1282%	0.1307%	0.0014%
	𝑃(𝜂 < 0.8)	0%	0%	0%
	Evaluations	7265	7242	1


M Larchevêque

Virginie Baldy
email: virginie.baldy@up.univ-mrs.fr

Nathalie Korboulewsky

Elena Ormeño

Catherine Fernandez

M Larcheve ˆque

E Ormen ˜o

Compost effect on bacterial and fungal colonization of kermes oak leaf litter in a terrestrial Mediterranean ecosystem

Keywords: Mediterranean ecosystem, Sewage sludge compost, Leaf litter, Ergosterol, Bacterial numbers, Microbial biomass, Quercus coccifera L

published or not. The documents may come   L'archive ouverte pluridisciplinaire

Introduction

Soils under Mediterranean climate are undergoing degradation due to water erosion and recurrent fires, which affect their fertility [START_REF] De Luis | Climatic trends, disturbances and short-term vegetation dynamics in a Mediterranean shrubland[END_REF].

Nitrogen, which is often a limiting plant nutrient in soil, is easily lost by volatilisation during wildfires. [START_REF] Guerrero | Reclamation of a burned forest soil with municipal waste compost: macronutrient dynamics and improved vegetation cover recovery[END_REF] pointed out that organic matter addition is a suitable technique for accelerating the natural recovery process of burned soils. The spreading of biosolids, defined as the nutrient rich product of wastewater treatment, can improve the low fertility of soils and constitutes an alternative to landfill disposal. Biosolids are a source of organic matter and plant nutrients [START_REF] Brockway | Forest floor, soil, and vegetation responses to sludge fertilization in red and white pine plantations[END_REF][START_REF] Martinez | Biowaste effects on soil and native plants in semiarid ecosystem[END_REF] and can improve soil physical, chemical and biological properties [START_REF] Mckay | GB experience in the last decade: from research to practice[END_REF][START_REF] Caravaca | Aggregate stability changes after organic amendment and mycorrhizal inoculation in the afforestation of a semiarid site with Pinus halepensis[END_REF]. But biosolids present potential environmental risks. Their use can induce heavy metal and organic contaminants accumulation in soils [START_REF] Brockway | Forest floor, soil, and vegetation responses to sludge fertilization in red and white pine plantations[END_REF], as well as the discharge of nutrients, especially N and P, to surface and ground waters [START_REF] Martinez | Biowaste effects on soil and native plants in semiarid ecosystem[END_REF]. To decrease risks of heavy metal and salt leaching, the organic matter of biosolids can be stabilized by composting [START_REF] Garcia | The influence of composting and maturation processes on the heavy-metal extractability from some organic wastes[END_REF][START_REF] Planquart | Distribution, movement and plant availability of trace metals in soils amended with sewage sludge composts: application to low metal loadings[END_REF]. In addition, mixing biosolids and other organic wastes with large C/N ratios (such as green wastes) can reduce the rate of nitrogen leaching [START_REF] Mckay | GB experience in the last decade: from research to practice[END_REF]. Therefore, compost presents better agronomic potential than biosolids.

Compost amendment has been frequently shown to increase soil fertility [START_REF] Caravaca | Aggregate stability changes after organic amendment and mycorrhizal inoculation in the afforestation of a semiarid site with Pinus halepensis[END_REF][START_REF] Martinez | Biowaste effects on soil and native plants in semiarid ecosystem[END_REF], plant biomass [START_REF] Guerrero | Reclamation of a burned forest soil with municipal waste compost: macronutrient dynamics and improved vegetation cover recovery[END_REF] and nutrition [START_REF] Moreno | Transference of heavy metals from a calcareous soil amended with sewage-sludge compost to barley plants[END_REF]. As a consequence, it could lead to a high nutrient content litter and enhance litter breakdown. Litter breakdown is the principal pathway of nutrients' return to soil in a form available to plants [START_REF] Kavvadias | Litterfall, litter accumulation and litter decomposition rates in four forest ecosystems in northern Greece[END_REF]. This aspect is especially important on Mediterranean nutrient-poor soils where plant communities rely, to a great extent, on the recycling of litter nutrients [START_REF] Can ˜ellas | Litter fall and nutrient turnover in Kermes oak (Quercus coccifera L.) shrublands in Valencia (eastern Spain)[END_REF]. Factors contributing to the litter breakdown are: soil fertility, litter quality and supply and climatic conditions [START_REF] Kavvadias | Litterfall, litter accumulation and litter decomposition rates in four forest ecosystems in northern Greece[END_REF] The litter breakdown process involves three types of organisms: invertebrates, fungi and bacteria. The crucial role of microorganisms is clearly established, and consecutive changes in fungal and bacterial biomass dynamics are a useful way to investigate the impact of factors controlling leaf breakdown [START_REF] Gessner | Importance of stream microfungi in controlling breakdown rates of leaf litter[END_REF][START_REF] Isidorov | Volatile organic compounds from leaves litter[END_REF]. Moreover, the soil microbial biomass is often regarded as an early indicator of changes which may occur in the long term with regard to soil fertility. Likewise, [START_REF] Wardle | Response of soil microbial biomass dynamics, activity and plant litter decomposition to agricultural intensification over a seven-year period[END_REF] showed that microbial biomass responds to addition of fertilizers and of organic residues.

Most studies deal with total microbial biomass (fumigation-incubation, fumigation-extraction, substrate induced respiration and ATP methods; [START_REF] Martens | Current methods for measuring microbial biomass C in soil: potential and limitations[END_REF], i.e. bulked fungi and bacteria [START_REF] Borken | Application of compost in spruce forest: effects on soil respiration, basal respiration and microbial biomass[END_REF][START_REF] Khan | Effects of metal (CD, Cu, Ni Pb or Zn) enrichment of sewage sludge on soil microorganisms and their activities[END_REF][START_REF] Kunito | Copper and Zinc fractions affecting microorganisms in long-term sludge-amended soils[END_REF].

However, the respective roles of bacteria and fungi in the litter breakdown process are different. Fungi are able to decompose and assimilate as refractory compounds as lignin or tanins [START_REF] Criquet | La litie `re de che ˆne vert (Quercus ilex L.). Aspects me ´thodologiques, enzymologiques et microbiologiques. Etude pre ´liminaire des relations in situ entre microorganismes, enzymes et facteurs environnementaux[END_REF], although bacteria are not thought to assume notable importance before the leaf material has been partially broken down and decomposed by fungi [START_REF] Jensen | Decomposition of angiosperm tree leaf litter[END_REF]. Thus, it is of great interest to study separately their reactions to compost amendment.

In this study, bacterial and fungal biomass were determined on kermes oak (Quercus coccifera L.) leaf litter on a Mediterranean burnt area amended with sewage sludge and greenwaste compost. Kermes oak is one of the most important shrub species in the Mediterranean basin, where it covers more than 2 Mha and accounts generally for 60-70% of the total litter [START_REF] Can ˜ellas | Litter fall and nutrient turnover in Kermes oak (Quercus coccifera L.) shrublands in Valencia (eastern Spain)[END_REF].

Our objectives were to (i) determine the effects of compost amendment on kermes oak leaf litter colonization by bacteria and fungi, (ii) offset the drastic Mediterranean climatic conditions (e.g. drought) against the potential improvement of soil fertility by compost, (iii) provide comprehensive data on leaf litter breakdown in terrestrial Mediterranean ecosystems by separately quantifying fungal and bacterial biomass.

Material and methods

Study site and experimental design

The experiment was carried over 6000 m 2 on the plateau of Arbois (Southern Provence, France; 5818 0 6 00 E-43829 0 10 00 N in WSG-84 Geodetic system) at 240 m above sea level and under Mediterranean climatic conditions (Fig. 1). The soil was a siltyclayey chalky rendzina, with a high percentage of stones (77%) and a low average depth (24 cm). The last fire occurred in June 1995 and the site was colonised by typical Mediterranean sclerophyllous vegetation, with 70% total cover; Q. coccifera L. and Brachypodium retusum Pers. being the two dominant species. This natural vegetation belongs to the holm oak (Quercus ilex L.) succession series.

Compost was surface applied in January 2002. The experimental design was a complete randomised block of twelve plots of 500 m 2 . Four plots did not receive any compost (D0 = control), four received 50 t ha À1 (D50), and four 100 t ha À1 (D100). The compost was produced by a local company (Biotechna, Ensue `s, Southern Provence) and is certified conform to the French norm on composts made with materials of water treatment origin (NF U 44-095, 2002). This compost was made with greenwastes (1/3 volume), pine barks (1/3 volume), and local municipal sewage sludge (1/3 volume). The mixture was composted for 30 days (windrows submitted to forced ventilation, Beltsville method) at 75 8C to kill pathogenic microorganisms and decompose phytotoxic substances, and then sieved (<20-mm mesh) to remove large bark pieces and stored in windrows. The windrows were mixed several times over the next 6 months to promote organic matter humification. The final compost met the French legal standards for pathogenic microorganisms, organic trace elements and heavy metals (order of the 08/01/1998 on sewage sludge use in agriculture). Soil and compost characteristics are shown in Table 1.

Field procedures

Humiferous episolum was sampled nine times superficially from June 2002 to October 2003, and 2mm sieved. The fraction >2 mm was classed as litter

fraction (O-h >2

). Chemical analyses were performed on this coarse mixed litter. Each analysed sample was a mix of three samples randomly collected on each plot. Kermes oak entire leaf litter, on which leaf litter breakdown is the most efficient [START_REF] Toutain | Les litie `res: sie `ge de syste `mes interactifs et moteurs de ces interactions[END_REF], was separated from the O-h >2 samples to determine microbial biomass. Green leaves were also collected on three bushes per plot to analyse N and P concentrations, at maximum Q. coccifera litterfall in late May (2002 and2003) (Can ˜ellas and San Miguel, 1998).

Laboratory procedures

Fungal colonization of litter was estimated using the ergosterol concentration, taking advantage of its recent improvement. Ergosterol is a fungal indicator that offers an efficient measure of living fungal biomass [START_REF] Gessner | Extraction and quantification of ergosterol as a mesure of fungal biomass in leaf litter[END_REF][START_REF] Gessner | Use of solid phase extraction to determine ergosterol concentrations in plant tissue colonized by fungi[END_REF][START_REF] Cortet | Increasing species and trophic diversity of mesofaune affects fungal biomass, mesofaune structure community and organic matter decomposition processes[END_REF]. Fifty milligrams of leaf litter were roughly crushed and lyophilized. Ergosterol was extracted from leaf litter by 30 min refluxing in alcohol base [START_REF] Gessner | Extraction and quantification of ergosterol as a mesure of fungal biomass in leaf litter[END_REF] and purified by solid-phase extraction [START_REF] Gessner | Use of solid phase extraction to determine ergosterol concentrations in plant tissue colonized by fungi[END_REF]. Final purification and quantification of ergosterol was achieved by high performance liquid chromatography (HPLC; HP series 1050 chromatograph). The system was run with HPLC-grade methanol at a flow rate of 1.5 ml min À1 . Ergosterol eluted after 9 min and was detected at 282 nm; peak identity was checked on the basis of retention times of commercial ergosterol (Fluka 1 ; >98% purity).

Bacterial colonization was determined by counting numbers of bacteria following the general protocol of [START_REF] Porter | The use of DAPI for identifying and counting aquatic microflora[END_REF] modified by [START_REF] Schallenberg | Solutions to problems in enumerating sediment bacteria by direct counts[END_REF]. Samples of fresh litter were stored in 2% formalin before analysis. Bacteria were detached from entire leaves by 2 min probe sonication, according to [START_REF] Buesing | Comparison of detachment procedures for direct counts of bacteria associated with sediment particles, plant litter and epiphytic biofilms[END_REF]. Then, 4 0 ,6-diamidino-2phenylindole (DAPI) at a concentration of 5 mg l À1 [START_REF] Baldy | Bacteria, fungi and the breakdown of leaf litter in a large river[END_REF] was added for DNA staining. Finally, numbers of bacteria were counted by epifluorescence microscopy.

Soil, compost (<4 mm) and O-h >2 chemistry (total N, total and exchangeable P, total Cu and Zn) were determined using standard procedures [START_REF] Afnor | Qualite ´des sols[END_REF]. Exchangeable P was measured by the Olsen method [START_REF] Olsen | Estimation of available phosphorus in soils by extraction with sodium bicarbonate[END_REF]. Humidity of Q. coccifera leaf litter was measured by oven drying samples at 60 8C during 3 days.

Green leaves of Q. coccifera were washed with demineralised water, oven dried at 40 8C and crushed (2 mm mesh) in a trace metal free grinder (FOSS TECATOR Sample Mill 1093 Cyclotec). Foliar N concentration was determined according to [START_REF] Masson | Simultaneous analysis of nitrogen, potassium, calcium and magnesium in digested plant samples by ion chromatography[END_REF], modified. Samples (250 mg) were digested in H 2 SO 4 and H 2 O 2 at 400 8C during 3 h (Bioblock Scientific Digestion Unit 10401). Then, the solutions were diluted 500 times, filtered at 0.45 mm and analysed by ion chromatography (Dionex DX120). The eluent used was 26 mmol l À1 methan sulfonic acid. Foliar P concentration was measured by atomic absorption spectrometry (VARIAN VISTA Radial) after digestion in aqua regia.

Statistical analyses

Two-way ANOVAs combined with Tukey tests [START_REF] Zar | Biostatistical Analysis[END_REF] were used to make comparisons of the different parameters (ergosterol, bacterial numbers, litter and green leaves chemistry) according to the two studied factors (sampling date and compost rate). Previously, normality and homocedaticity were verified by Shapiro-Wilks and Bartlett tests, respectively [START_REF] Zar | Biostatistical Analysis[END_REF]. Data were ln-transformed when test assumptions were not met (i.e. bacterial numbers). To relate microbial biomass and chemical characteristics of leaf litter, linear regressions were performed. Significant level was considered to be 95%. The software Statgraphics plus (version 2.1: Statistical Graphics Corporation # , Copyright 1994-1996) and Minitab (release 13 for Windows, 2000, Minitab Inc., USA) were used.

Results

Q. coccifera green leaves at maximal litterfall and coarse mixed litter (O-h >2 )

N and P concentrations in green leaves increased significantly after compost amendment (Table 2, Fig. 2). There was no difference between the two compost rates for P, whereas N concentration in green leaves was higher in D100 than D50 for both years (2002,2003). Moreover, N concentration in green leaves increased significantly from May 2002 to May 2003, respectively, 5 months and 1.5 years after compost amendment (Table 2, Fig. 2). P concentration in green leaves decreased significantly from 2002 to 2003 (Table 2, Fig. 2).

Compost amendment significantly increased the following physical and chemical parameters of O-h >2 (Table 2): O-h >2 humidity (Fig. 3), exchangeable P (Fig. 3), total N (0.92, 1.58, and 1.67% DM, for D0, D50 and D100, respectively, means of the nine Results of the comparison are given by an exponent letter: values that do not differ at the 0.05 level are noted with the same letter (a < b < c). D0: control plots; D50: plots amended with 50 t ha À1 of compost and D100: plots amended with 100 t ha À1 of compost. sampling dates), total Cu (8.75, 75.4 and 69.8 ppm DM, means of the 2 sampling years), and total Zn (50.9, 137.6 and 139.4 ppm DM, means of the 2 sampling years). However, there was no significant difference between the two compost rates (D50 and D100) for these parameters.

Sampling year had also a significant effect on Oh >2 . Total N and exchangeable P concentrations in Oh >2 had similar dynamics to N and P in green leaves from 2002 to 2003 (Table 2). Moreover, N and P concentrations in O-h >2 green leaves were positively correlated with concentrations in green leaves (R = 0.45, p = 0.026 and R = 0.64, p = 0.004, respectively, for N and P). Total N in O-h >2 increased from 1.3% DM in 2002 (mean of the three treatments) to 1.5% DM in 2003, whereas exchangeable P decreased from 859 ppm DM in 2002 (mean of the three treatments) to 309 ppm DM in 2003 (Fig. 3). Total P in O-h >2 remained similar (Table 2) from 1 year (2002, 0.08% DM) to another (2003, 0.09% DM).

Humidity of O-h >2 was lowest during the summer 2003 (Fig. 3). Spring, summer, and autumn 2003 were exceptionally dry (Fig. 1), and as a consequence, October 2003 values were found to be similar to summer 2002 values.

Microbial biomass of kermes oak leaf litter

Compost amendment had a significant effect on leaf litter colonization by fungi, whereas it did not affect bacterial numbers (Fig. 4, Table 3). Compost at highest rate decreased overall the ergosterol concentration in Q. coccifera leaf litter compared to control (159 and 194 mg g À1 DM in D100 and D0, respectively, mean over the studied period). Ergosterol concentration for D50 rate (189 mg g À1 DM, mean Results of the comparison are given by an exponent letter: values that do not differ at the 0.05 level are noted with the same letter (a < b < c). D0: control plots; D50: plots amended with 50 t ha À1 of compost and D100: plots amended with 100 t ha À1 of compost.

over the studied period) was similar to control. Moreover, ergosterol was negatively correlated to exchangeable phosphorus in O-h >2 . However, neither bacterial number nor ergosterol are correlated to total P, N, Cu or Zn concentrations (Table 4).

Both ergosterol concentration and bacterial number of leaf litter varied significantly according to sampling date within a year. The lowest values corresponded to summers (June and July, both years), when drought is maximum under Mediterranean climatic conditions (Fig. 1). In addition, both bacterial and fungal colonisation were positively correlated with O-h >2 humidity, particularly ergosterol (Table 4). As O-h >2 humidity (month n) is positively correlated (R = 0.76, p = 0.03) to precipitation (month n-1), the highest ergosterol values corresponded to the highest rainfall of the month before.

Discussion

Microbial biomass of kermes oak leaf litter

Compost amendment significantly decreased kermes oak leaf litter fungal colonization at 100 t ha À1 rate whereas it had no effect on bacterial colonization. This shows the importance of studying separately fungi and bacteria in order to determine precisely the response of microbial communities after compost amendment. In our study, the two groups of microorganisms exhibited

Table 4 Matrix of Pearson correlation analysis between ergosterol, numbers of bacteria and O

-h >2 parameters Ergosterol Bacterial numbers O-h >2 humidity R = 0.44 *** R = 0.25 * O-h >2 exchangeable P R = À0.31 * R = À0.13 O-h >2 total P R = À0.21 R = À0.02 O-h >2 total N R = À0.16 R = 0.04 O-h >2 total Cu R = À0.39 R = À0.05 O-h >2 total Zn R = À0.38 R = À0
.001 * Significant (0.05 < p < 0.01). *** Highly significant ( p < 0.001). different reactions. The decrease in ergosterol concentrations found within D100 amended plots differs from numerous studies which have found enhancing effects of organic amendments on soil microbial biomass [START_REF] Albiach | Microbial biomass concentration and enzymatic activities after the application of organic amendments to a horticultural soil[END_REF][START_REF] Kunito | Copper and Zinc fractions affecting microorganisms in long-term sludge-amended soils[END_REF][START_REF] Ros | Soil microbial activity after restoration of a semiarid soil by organic amendments[END_REF]. However, the ergosterol concentrations observed on Q. coccifera leaf litter of D100 plots remained similar to those of the rare studies that have attempted to quantify separately bacterial and fungal colonization of Mediterranean litter or soil [START_REF] Barajas-Aceves | Effect of polluants on the ergosterol concentration as indicator of fungal biomass[END_REF][START_REF] Cortet | Increasing species and trophic diversity of mesofaune affects fungal biomass, mesofaune structure community and organic matter decomposition processes[END_REF].

Conversely, litter humidity highly improved Q. coccifera leaf litter colonization. Q. coccifera leaf litter moisture was positively correlated both to ergosterol concentrations and bacterial numbers, and fungi were more affected than bacteria. Thus, microbial colonization was lowest during dry months (June and July) in both years, and 2003 values were lower than 2002 values due to exceptional drought. This is in accordance with previous works, such as [START_REF] Papatheodorou | The effects of large-and small-scale differences in soil temperature and moisture on bacterial functionnal diversity and the community of bacterivorous nematodes[END_REF] who reported seasonal patterns for bacterial richness in soil. Likewise, [START_REF] Criquet | Annual variations of phenoloxidase activities in an evergreen oak litter: influence of certain biotic and abiotic factors[END_REF] and [START_REF] Barajas-Aceves | Effect of polluants on the ergosterol concentration as indicator of fungal biomass[END_REF] found that fungal biomass reaches maximum values under humidity conditions in Mediterranean areas.

Q. coccifera green leaves at maximal litterfall and coarse mixed litter (O-h >2 )

The compost significantly increased the moisture of Q. coccifera leaf litter in amended plots. This result is in contradiction with the depreciating effect of the compost on fungal colonization. Thus, some changes induced by compost amendment may have had strong enough decreasing effects on fungal colonization of kermes oak leaf litter to annul the increasing moisture effect, even if drought is one of the major limiting factors in Mediterranean areas.

Total N concentration significantly increased in amended plots (D50 and D100) in kermes oak green leaves and in O-h >2 . These two parameters are positively correlated (R = 0.45), which suggests that the N increase in green leaves is involved in the O-h >2 total N enrichment. This species generally provides 60-70% of the total litter in garrigue ecosystems [START_REF] Can ˜ellas | Litter fall and nutrient turnover in Kermes oak (Quercus coccifera L.) shrublands in Valencia (eastern Spain)[END_REF]. As nitrogen is frequently a limiting nutrient in Mediterranean ecosystems [START_REF] Archibold | Mediterranean ecosystems[END_REF], an increase in O-h >2 amended plots improves microbial biomass [START_REF] Berg | Fungal biomass and nitrogen in decomposing scots pine needle litter[END_REF]. Moreover, the N enrichment of Q. coccifera litter may decrease its C/N ratio, as well as its polyphenol concentration, leading to an easier breakdown [START_REF] Gosz | Biological factors influencing nutrient supply in forest soils[END_REF]. However, in our experiment, no significant positive correlation was found between microbial colonization of kermes oak litter and total N concentration in O-h >2 . In contrast to the literature, we observed the highest depletion of fungal biomass when total N in O-h >2 was the highest: 2 years after amendment (2003), in D100. Therefore, it is very likely that N accumulates in O-h >2 consequently to fungal biomass decrease in D100 plots.

The reduction of fungal colonization at D100 could be the result of a decrease in another limiting factor in Mediterranean ecosystems [START_REF] Archibold | Mediterranean ecosystems[END_REF]: P is mostly unavailable, because it is associated with calcium in inorganic forms on calcareous soils [START_REF] Khanna | Soil characteristics influencing nutrient supply in forest soils[END_REF]. [START_REF] Thirukkumaran | Microbial activity, nutrient dynamics and litter decomposition in a Canadian Rocky Mountain pine forest as affected by N and P fertilizers[END_REF] reported that microbial variables were unaffected by N addition, whereas an increase of substrate induced respiration (SIR) was found with P fertilization. In addition, [START_REF] Kwabiah | Response of soil microbial biomass dynamics to quality of plant materials with emphasis on P availability[END_REF] found that phosphorus is the most important quality factor affecting microbial biomass. But, this explanation is not confirmed by our results. Compost amendment led to a marked increase in exchangeable P in O-h >2 , as a result of an increase in P concentration in Q. coccifera green leaves (R = 0.64). However, exchangeable P in O-h >2 was negatively correlated to fungal colonization (R = À0.31).

In our study, compost amendment induced significant increases in O-h >2 total copper and zinc concentrations. As heavy metals are known to affect growth, morphology and metabolism of microorganisms in soils [START_REF] Dai | Influence of heavy metals on C and N mineralisation and microbial biomass in Zn-, Pb-, Cu-, and Cdcontaminated soils[END_REF], Cu and Zn increases could have decreased the fungal colonization of leaf litter collected on plots amended with 100 t ha À1 . However, neither bacterial numbers, nor ergosterol content of leaf litter were correlated to Cu and Zn total concentrations. On the one hand, total heavy metal concentrations do not reflect exactly their biological effects and available concentrations in the soil have to be taken into account. On the other hand, Cu accumulates more in plant roots [START_REF] Van Den Driessche | Nutrient storage, retranslocation and relationship of stress to nutrition[END_REF] than in shoots. Thus, the Q. coccifera leaf litter may have been slightly contaminated by this element, explaining the absence of Cu effect on microbial colonization. However, Zn (as Cd, Hg and Ni) is a metal reported to be toxic to microorganisms at lower levels than other metals [START_REF] Kabata-Pendias | Trace Elements in Soils and Plants[END_REF]. Moreover, this element is considered to be readily soluble relative to the other heavy metals in soils [START_REF] Kabata-Pendias | Trace Elements in Soils and Plants[END_REF]. Thus, Zn in available form could have reduced fungal colonization of Q. coccifera leaf litter in D100. However, bacteria are known to be less resistant to heavy metals than fungi [START_REF] Dai | Influence of heavy metals on C and N mineralisation and microbial biomass in Zn-, Pb-, Cu-, and Cdcontaminated soils[END_REF] and are not affected by compost amendment in our study. Therefore, the hypothetical negative effect of Zn on fungal colonization of kermes oak litter must be put in perspective. Moreover, it is not easy to predict microbial consequences of soil pollution without determining microbial diversity changes under heavy metal contamination, according to species relative sensibility [START_REF] Dai | Influence of heavy metals on C and N mineralisation and microbial biomass in Zn-, Pb-, Cu-, and Cdcontaminated soils[END_REF].

Thus, fungal biomass was decreased at D100 rate despite an increase of humidity, N and P concentrations of O-h >2 after compost amendment. We hypothesize that amendment led to a redistribution of fungi from O-h >2 to O-h <2 . The compost used in this study contained 57% of sewage sludge (<2 mm fraction), which presents a higher decomposability (rich in low-molecular dissolved organic carbon and in salts, [START_REF] Agassi | Percolation and leachate composition in a disturbed soil layer mulched with sewage biosolids[END_REF] than O-h >2 (containing leaves, rich in inhibiting molecules as polyphenols, especially in the Mediterranean region, [START_REF] Gershenzon | Changes in the level of plant secondary metabolites production under water and nutrient stress[END_REF]. This would induce an accumulation of O-h >2 litter and could explain the total N increase that occurred in O-h >2 of D100 amended plots from 2002 to 2003. Likewise, [START_REF] Borken | Application of compost in spruce forest: effects on soil respiration, basal respiration and microbial biomass[END_REF] showed that compost could induce some redistribution of microbes from one fraction to another. They noted that after compost application, microbial biomass decreased in the organic horizons (O-h >2 and O-h <2 ), whereas it increased in the mineral soil, the latter being enriched by nutrients released from organic horizon.

Conclusion

In conclusion, compost at D100 induced significant decrease in colonization of Q. coccifera leaf litter by fungi, especially the second year after amendment. Compost had no significant effect on litter colonization by bacteria. Furthermore, compost at D100 increased O-h >2 humidity, as well as N and P concentrations, which should have improved the decomposition of O-h >2 OM. Compost Zn enrichment could be responsible for the observed fungal biomass decrease, but it should have affected bacteria as well. Thus, we hypothesize a redistribution of fungi from refractory components of O-h >2 to easily decomposable O-h <2 . This could be responsible for leaf litter N accumulation in O-h >2 . Therefore, it would be of great interest to study the microbial colonization of Oh <2 and mineral soil.

Fig. 1 .

 1 Fig. 1. Mean air temperature and precipitation from June 2002 to May 2003 (Me ´te ´o France).

Fig. 2 .

 2 Fig. 2. N and P foliar concentrations in green Quercus coccifera leaves at maximum litterfall (late May 2002 and 2003). Bars denote S.E. (N = 4). D0: control plots; D50: plots amended with 50 t ha À1 of compost and D100: plots amended with 100 t ha À1 of compost. Results of the comparison are given by a letter: values that do not differ at the 0.05 level are noted with the same letter (a < b < c).

Fig. 3 .

 3 Fig. 3. Exchangeable P concentration (in ppm of dry mass) and humidity (in % of dry mass) in the O-h >2 from June 2002 to October 2003. Bars denote S.E. (N = 4). D0: control plots; D50: plots amended with 50 t ha À1 of compost and D100: plots amended with 100 t ha À1 of compost.

Fig. 4 .

 4 Fig. 4. Dynamics of ergosterol concentrations (in mg of ergosterol per gram of dry mass) and bacterial numbers (per gram of dry mass) associated with leaf litter of Quercus coccifera decomposing in control plots (D0), plots amended with 50 t ha À1 (D50) and plots amended with 100 t ha À1 (D100) of compost. Bars denote S.E. (N = 4).

Table 1

 1

	Soil (0-24 cm: maximal depth; N = 12) and compost (N = 3) physico-chemical characteristics
	Parameter	Soil		Compost
		Mean (S.E.)	Allowed French limit value before	Mean (S.E.)	Allowed French limit
			sewage sludge amendment		value (08/01/1998)
	pH H 2 O	7.34 (0.008)		7.7 (0.05)
	Humidity (% FM)			4.8 (0.29)
	CEC (meq. 100 g À1 )	23.12 (0.31)
	Total calcareous (% DM)	4.17 (0.13)
	OM (% DM)	7.58 (0.12)		46.8 (2.74)
	Total N (% DM)	0.36 (0.005)		2.03 (0.03)
	C/N	12.42 (0.09)		13.4 (0.78)
	Total P (% DM)	0.037 (0.001)		3.24 (0.03)
	Exchangeable P (mg kg À1 DM)	23.3 (0.35)		2514.8 (7.82)
	Copper (mg kg À1 DM)	19.8 (0.14)	100	144.1 (0.84)	1000
	Zinc (mg kg À1 DM)	78.2 (0.24)	300	265.0 (5.49)	3000
	Cadmium (mg kg À1 DM)	0.31 (0.002)	2	0.8 (0.0)	15
	Chrome (mg kg À1 DM)	67.3 (0.33)	150	27.1 (0.65)	1000
	Mercury (mg kg À1 DM)	0.06 (0.001)	1	0.86 (0.06)	10
	Nickel (mg kg À1 DM)	45.3 (0.17)	50	16.5 (0.23)	200
	Lead (mg kg À1 DM)	43.1 (0.26)	100	57.3 (2.53)	800

DM: dry mass; FM: fresh mass.

Table 2

 2 Results of two-way ANOVA on N and P foliar concentrations in green leaves of Quercus coccifera at maximal litterfall (late May) and on O-h >2 parameters (only statistically significant results are reported)

	Parameter	Factor	F	p	Tukey's test
	Q. coccifera N concentration in green	Year	4.88	0.0403	May02 a , May03 b
	leaves at maximal litterfall	Rate	23.55	<0.001	D0 a , D50 b , D100 c
	Q.coccifera P concentration in green	Year	8.66	0.0123	May02 a , May03 b
	leaves at maximal litterfall	Rate	4.13	0.0433	D0 a , D50 ab , D100 b
	Q. coccifera litter humidity	Date	145.43	<0.001	June02 bc , July02 d , Oct02 e , Dec02 f ,
					Mar03 e , Apr03 d , June03 ab , July03 a , Oct03 c ,
		Rate	10.8	<0.001	D0 a , D50 b , D100 b
	O-h >2 exchangeable P	Year	53.77	<0.001	2002 b , 2003 a
		Rate	115.46	<0.001	D0 a , D50 b , D100 b
	O-h >2 total P	Year	0.54	0.464	2002 a , 2003 a
		Rate	117.6	<0.001	D0 a , D50 b , D100 b
	O-h >2 total N	Year	30.06	<0.001	2002 a , 2003 b
		Rate	202.2	<0.001	D0 a , D50 b , D100 b
	O-h >2 total Cu	Year	46.08	<0.001	Mar02 a , Mar03 b
		Rate	58.52	<0.001	D0 a , D50 b , D100 b
	O-h >2 total Zn	Date	31.53	<0.001	Mar02 a , Mar03 b
		Rate	20.69	<0.001	D0 a , D50 b , D100 b

Table 3

 3 Results of two-way ANOVA on ergosterol concentration and bacterial numbers associated with kermes oak leaf litter

	Parameter	Factor	F	p	Tukey's test
	Ergosterol	Date	10.55	<0.001	June02 bc , July02 b , Oct02 de , Dec02 f , Mar03 ef
		Rate	5.54	0.0056	Apr03 bcd , June03 cde , July03 a , Oct03 de
		Date  rate	1.2	0.2845	D0 a , D50 a , D100 b
	Number of bacteria	Date	4.52	0.0002	June02 ab , July02 a , Oct02 bcd , Dec02 abc , Mar03 cd
		Rate	0.9	0.4096	Apr03 d , June03 ab , July03 a , Oct03 ab
		Date  rate	0.98	0.4852	D0 a , D50 a , D100 a

https://payment.sips-atos.com/cgis-payment/prod/callresource?rsc=creditcard 1/1

https://payment.sips-atos.com/cgis-payment/prod/callresource?rsc=creditcard

Acknowledgements

This research was supported by the Conseil Ge ´ne ´ral des Bouches-du-Rho ˆne, the ADEME (Agence De l'Environnement et de la Maı ˆtrise de l'Energie) and the Agence de l'Eau Rho ˆne-Me ´diterrane ´e-Corse. We thanks the two reviewers for their interesting remarks, and Mr. Michael Paul for English improvement.


Aurélie Mahalatchimy

Emmanuelle Rial-Sebbag

Eurostemcells-Legal update Regulation of stem cell research in France

I-Research on human stem cells A) Current legal position

In the French legal system, two pieces of legislation must be respected when a research is performed on human stem cells. First, the rules regarding research on human participants must be fulfilled (a written protocol must be submitted including the information document and the consent form). Second, specific rules apply to collection of human material (including the biobanking activity).

According to article L1121-1 of the French Public Health Code1 , three categories of research are considered to involve the human person: -Interventional study (clinical trial) -Interventional study (clinical trial) with minimal risk study -Non-interventional study (clinical trial)

In case Human Stem Cells are considered to be to be part of a research involving the human person, and if the cells are used by an institution for its scientific purposes (case 1) or when an institution wants to preserve and prepare human tissues and cells, organs, blood and blood components or derivatives products in order to give them up to another institution for research purposes (case 2), the only opinion of a local Research Ethics Committee ("Comité de Protection des Personnes", CPP) must be seek. It will assess the quality of the information to research participants and if provided the informed consent for biobanking, the obtaining of informed consent and its modalities, the scientific and ethical relevance of the project. The French National Agency for the Safety of Medicines and Health Products (ANSM) should be informed of these research activities if they are conducted on the same site as therapeutic activities. In the latter case, The French National Agency for the Safety of Medicines and Health Products (ANSM) can request the suspension or the prohibition of the research activities for health safety reasons (Article L1243-3 of the French Public Health Code2 )

In case Human Stem Cells are not considered to be to be part of a research involving the human person (for the biobanking activities, re-used of human cells), French law distinguishes activities for which a preceding declaration is required and activities that need to be authorised by the French Ministry of Research, and by the Health Regional Agency if the research institution is also a health establishment (providing care, therapeutic activities). For more information, please see: https://appliweb.dgri.education.fr/appli_web/codecoh/IdentCodec.jsp (French)

In both case, an authorisation from the French National Agency for the Safety of Medicines and Health Products (ANSM) has to be obtained for interventional studies. Moreover, the French National Agency for the Safety of Medicines and Health Products (ANSM) has to be informed in case of other studies (interventional study with minimal risk and non-interventional study) (Article L1121-4 of the French Public Health Code3 ). For more information, please see: http://ansm.sante.fr/Activites/Essaiscliniques/Recherches-impliquant-la-personne-humaine-RIPH/(offset)/ (French)

B) Ethical and regulatory oversight

Local Ethics Committee ("Comité de Protection des Personnes") for ethical approval of the research project.

French National Agency for the Safety of Medicines and Health Products (ANSM)4 for authorization of interventional studies and to be informed in case of other studies (interventional study with minimal risk and non-interventional study) French Ministry of Research5 and Health Regional Agency ("Agence Régionale de Santé")6 :

-To be jointly sent the preceding declaration of research if the research institution is also a health establishment (providing care, therapeutic activities). -Can be opposed to the activities -Can suspend or prohibit these activities at any time -To jointly deliver the required authorization if the research institution is also a health establishment (providing care, therapeutic

II-Research on human embryonic stem cells A) Current legal position

After almost 20 years of prohibition and prohibition with exceptions, the 2011 law on bioethics as amended in 2013 authorises research on human embryos and embryonic stem cells under specific conditions:

-The scientific relevance of the research is established -The research, whatever fundamental or applied, has a medical purpose -In accordance with the current scientific knowledge, the research cannot be conducted without these human embryos or embryonic stem cells -The research project complies with ethical principles for research on embryos and embryonic stem cells

Embryos used for research must come from the assisted reproduction process (IVF), and should no more be part of a parental project. Previous written informed consent must be obtained from the donors' couple, and should be renewed after three months. It is revocable at any time without reasons.

Research projects that meet these criteria can be authorised by the French Biomedicine Agency ("Agence de la Biomédicine").

B) Ethical and regulatory oversight

The French Biomedicine Agency ("Agence de la Biomédicine")7 delivers authorisation of research on human embryos and embryonic stem cells.

III-

Selected bibliography A) Laws, regulations, guidelines

  Law on Bioethics, LOI n° 2011-814 du 7 juillet 2011 relative à la bioéthique https://www.legifrance.gouv.fr/affichTexte.do?cidTexte=JORFTEXT0000243231 02&categorieLien=id Law strengthening health safety for medicines and health products, LOI n° 2011-2012 du 29 décembre 2011 relative au renforcement de la sécurité sanitaire du

https://www.legifrance.gouv.fr/affichCodeArticle.do;jsessionid=62D39AE001EEB74CFB7C5D5 A2A517ECA.tpdila19v_2?idArticle=LEGIARTI000032722870&cidTexte=LEGITEXT00000607266 5&categorieLien=id&dateTexte=

https://www.legifrance.gouv.fr/affichCodeArticle.do;jsessionid=97E7418CD65AEBB9B0BDBA0 9B73D57EC.tpdila19v_2?idArticle=LEGIARTI000025449694&cidTexte=LEGITEXT00000607266 5&categorieLien=id&dateTexte=

https://www.legifrance.gouv.fr/affichCodeArticle.do?cidTexte=LEGITEXT000006072665&idArt icle=LEGIARTI000006685833&dateTexte=&categorieLien=cid

http://ansm.sante.fr/

http://www.enseignementsup-recherche.gouv.fr/

https://www.ars.sante.fr/

https://www.agence-biomedecine.fr/


M Bella

C Rivero

S Blayac

H Basti

M C Record

P Boulet

Oleylamine-assisted solvothermal synthesis of copper antimony sulfide nanocrystals: morphology and phase control

We report a one-pot synthesis of copper antimony sulfide nanocrystals by a facile and easily scalable route using a surfactant assisted solvothermal method. Phase-pure and quasi-monodisperse Cu 3 SbS 4 nanocrystals have successfully been synthetized by adjusting the sulfur to copper molar ratio as well as the surfactant to solvent volumetric ratio. Nanocrystals morphology and chemical composition are characterized. As synthetized and purified nanocrystals are formulated into a colloidal suspension in order to fabricate copper antimony sulfide films. Morphological, electrical and optical characterizations of famatinite films are conducted. The electrical resistivity of the as deposited films is comprised between 10 Ω.cm and 48 Ω.cm. The optical gap is found to be indirect with a value of 0.82 eV.

Introduction

The successful synthesis of colloidal semiconducting nanocrystals (NCs) ink is a prerequisite step toward large-scale fabrication of conformable active devices for energy applications such as thermoelectrics and photovoltaics. In effect, colloidal nanocrystals are most suitable for large-scale deposition techniques such as inkjet and screen printing, provided that a large volume of phase pure nanomaterials are obtained. The prerequisites for printing conductive or semiconductive nanomaterials are, essentially size control, stability of the colloidal dispersion, and high nanoparticle loading (20 to 80 wt%). Consequently large scale and reproducible nanoparticles production has to be ensured when choosing the synthesis technique.

Copper antimony sulfide (CAS) materials have attracted a lot of attention lately due to their promising thermoelectric and photovoltaic properties [1][2][3][4][5] . In addition, since CAS are constituted of cheap, available and abundant elements they are envisaged as sustainable materials for energy conversion applications. In spite of these remarkable properties, there are only a few investigations that have been driven on the synthesis of CAS NCs, in particular on the famatinite compound (Cu 3 SbS 4 ) [6][7][8][9][10] . The elaboration method used in [6][7][8][9] is the hot-injection one, which enables the synthesis of small batches of monodisperse nanocrystals of a few nanometers with precise phase control under controlled inert atmosphere. However, this method is hardly transferable for industrial, large-scale synthesis of phase pure monodisperse nanocrystals as it is necessary to precisely control the injection temperature as well as provide efficient mixing of the precursors in the hot solvent to yield homogeneous nucleation. An et al. have obtained large famatinite crystals and tetrahedrite NCs using a solvothermal approach 10 , which is an efficient route towards the large-scale production of nanomaterials. However, the particles morphology and size were not controlled, which is not suitable for the fabrication of inks. Homogeneous dispersions with functionalized nanocrystals are preferable as they can be more easily dispersed in the solvent. In this paper, we thus propose a new method for the synthesis of phase pure and monodisperse famatinite nanocrystals by a surfactant assisted solvothermal route. This method enables the synthesis of functionalized spherical CAS nanocrystals by a versatile solvothermal method which is a step towards facile synthesis of large-scale phase pure CAS NCs.

In this paper, the synthesis procedure for the obtention of phase pure, nearly monodisperse famatinite nanocrystals is described. Those nanocrystals morphology and chemical composition are then characterized via SEM, TEM techniques and EDX, XPS ones, respectively. Details on ink preparation and films fabrication methods are then given along with structural, optical and electrical characterization of CAS films.

Experimental section

Materials. Chemicals used for CAS nanoparticle synthesis were ethanol, distilled water, copper (II) chloride dihydrate (CuCl 2 2H 2 O > 99.99 %) from Acros Organics, elemental sulfur (99.998 %) and oleylamine (OLA technical grade, 70 %) from Sigma-Aldrich, antimony (III) chloride (SbCl3 ≥ 99.95 %) from Alfa Aesar, which was stored in a glovebox under N 2 atmosphere to avoid moisture. N-heptane (99 %), used for the preparation of the nanoparticle dispersion, was purchased from Sigma-Aldrich. All reagents were used as is without any further purification.

Synthesis and purification of Cu 3 SbS 4 NCs. The synthesis of Cu 3 SbS 4 relied on the preparation of two solutions, one containing copper (II) chloride and antimony (III) chloride dissolved in absolute alcohol with a Cu:Sb molar ratio of 1:1, and the other containing elemental sulfur dissolved in oleylamine which was thoroughly sonicated for 1h to obtain a clear solution. Both solutions were then mixed and stirred for a few minutes. The mixture was then loaded into a 50 mL Teflon-liner and carefully sealed to prevent leakage and impurities formation from the reaction with oxygen during the synthesis. The final solution volume represented 80 % of the reactor volume. The Teflon-liner was then inserted in a stainless steel autoclave, which was subsequently sealed and heated up to 150 °C and maintained at this temperature for 15h. The autoclave was then left to cool down to room temperature by natural convection. The synthetized nanoparticles were then isolated and washed with ethanol and centrifuged (Heraeus centrifuge from Thermo Scientific) at 4000 rpm for 5 minutes to remove the unreacted salts, reaction by-products and excess capping agent. The process was repeated until a clear supernatant was obtained. This step was followed by a final centrifugation after dispersion in 25 mL of n-heptane and the addition of 25 mL of ethanol, necessary to precipitate the nanoparticles. The powder was then finally isolated and dried in oven under vacuum at 50 °C for 2h.

Different volumetric ratios of oleylamine/ethanol (1:1, 1:2 and 1:3) and different sulfur to copper molar ratios (1:0.4 and 1:0.75) were investigated.

Ink preparation, film deposition. The 50 wt% nanoparticle solution was obtained by dispersing the nanoparticles in n-heptane. Films were deposited by spin-coating, at 2000 rpm for 20 s, on a quartz substrate cleaned beforehand in an ultra-sonic bath with acetone and isopropanol consecutively. The process was repeated several times to obtain micrometer thick layers.

Characterization

Nanocrystals. X-Ray diffraction (XRD) analyses were done on the isolated and purified powders using a Siemens D5000 (Bruker) diffractometer (Cu Kα radiation at 0.15418 nm). Scanning electron microscopy (SEM) images were recorded using a field-emission gun scanning electron microscope Ultra 55 from Zeiss. Energy-dispersive X-ray (EDX) analyses were performed using an EDAX X-ray detector from Oxford Instrument mounted on the scanning electron microscope. High resolution transmission electron microscopy (HRTEM) images were recorded with a Philips CM200 transmission electron microscope. The sample for TEM analyses was prepared by drop deposition of a 1 wt% suspension of CAS nanocrystals in n-heptane on a carbon-coated gold grid which was subsequently dried in air under atmospheric pressure and room temperature. X-ray photoelectron spectroscopy (XPS) analyses were conducted using an Axis Nova equipment.

Films. The electrical sheet resistance was measured using a 4-point probe equipment (Jandel). UV/VIS/NIR measurements were carried out with a spectrometer (UV 2600) from SHIMADZU.

Results and discussion

Solvothermal synthesis of CAS nanocrystals. In the synthesis procedure reported by An et al. 10 , copper (I) chloride and thiourea are used as copper and sulfur sources, respectively. In our procedure, described in the experimental section, copper (II) chloride is preferred as it can easily be dissolved in ethanol. In order to obtain functionalized nanocrystals with a controlled morphology, a hydrophobic ligand molecule is added during the synthesis. Oleylamine is chosen for its ability to act both as a surfactant as well as a reducing agent. Sulfur is used instead of thiourea as it can easily be dissolved in oleylamine and is less harmful. Two solutions are prepared, one containing metal salts dissolved completely in ethanol and the other is an homogeneous sulfur-oleylamine solution. Upon mixing the two initial solutions, a dark brown precipitate is immediately observed. SEM pictures and elemental mapping through energy dispersive X-ray spectroscopy (EDS) indicate that this precipitate is mainly composed of large sulfur particles, a small amount of Cu-Sb-S particles being also present (Fig. 1). The presence of large sulfur particles can be explained by the poor solubility of sulfur in ethanol. Nanocrystals (NCs) nucleation and growth is achieved by heating the heterogeneous mixture for 15 hours at 150 °C. Heating time has a direct influence on the NCs synthesis yield due to the slow reaction kinetic using sulfur in oleylamine [11][12] . Each batch produces around two grams of functionalized nanocrystals. Based on the amount of reacted copper, an estimated yield around 90% is achieved with a heating time of 15h.

NCs characterization. The influence of surfactant to solvent ratio on the product morphology is investigated. Two ratios have been selected for this study, namely 1:1 (batch-1.1) and 1:3 (batch-1.3) volumetric ratios of oleylamine/ethanol. Nanocrystals from batch-1.1 are found to be quasi-monodisperse (Fig. Increasing the proportion of oleylamine induces better control of nanoparticle size. This can be attributed to the fact that oleylamine serves as both a coordinating solvent and a surfactant. The -NH 2 group in oleylamine interacts with metal precursors and partakes in the nanoparticles formation. The ligand molecules bound to the nanoparticle surface not only control the growth of the particles during synthesis, but also prevent the aggregation of the nanoparticles. Specifically, lone pairs of electrons on the nitrogen atoms in the polar groups of oleylamine are donated to an sp hybrid orbital of the Cu 2p ions to form a Cu-N coordination allowing the ligand molecule to control the growth rate of the nanoparticle through the limitation of the diffusion rate of metal precursors at the surface of the nanoparticle. Moreover, during nanoparticles growth stage, the surfactant reduces the surface tension 13 and avoids agglomeration through repulsive force between particles due to steric exclusion. Besides, as mechanical stirring is not possible in the autoclave, effective mass transport is ensured by the solvent reflux as it is heated in a closed vessel and above its boiling point. The product from batch-1.1 was chosen for further characterization as it is highly homogeneous and the synthesis procedure yields reproducible results. Figure 3 shows SEM (Fig. The crystallographic structure of the synthetized powder was investigated by means of X-ray diffraction. All the diffraction peaks in the XRD pattern (Fig. 4.) can be attributed to the tetragonal structure of Cu 3 SbS 4 (JCPDS # 01-071-0555). The recorded diffractogram is in good agreement with that calculated from the crystallographic data of Cu 3 SbS 4 (space group , with a = 5.38500 Å and c = 10,75400 Å) and represented as vertical bars in Fig. 4. No diffraction peaks corresponding to other ternary or binary phases in the Cu -Sb -S system can be detected in the XRD pattern. This observation confirms that no other crystalline phase than famatinite (Cu 3 SbS 4 ) is obtained with the synthesis route employed in this work.

Fig. 4. XRD patterns of as prepared CAS nanocrystals synthetized with excess sulfur

When the sulfur to copper molar ratio equals 1:0.75, which corresponds to the Cu 3 SbS 4 stoichiometry, the synthesized product is a mix of famatinite (Cu 3 SbS 4 ) and tetraedrite (Cu 12 Sb 4 S 13 ) phases. The XRD pattern of this product is represented in Fig. 5. The XRD pattern calculated from the crystallographic data of Cu 12 Sb 4 S 13 (space group , a=10.327 Å) is represented as red vertical bars whereas the calculated XRD pattern of Cu 3 SbS 4 is represented in blue (Fig. 4). A Rietveld refinement has been performed to estimate the weight fraction of each crystalline component, which gives approximately 67 % of famatinite and 33 % of tetrahedrite. This study shows that, to obtain pure famatinite nanocrystals, sulfur excess is necessary in the initial mixing. In the XPS spectrum, the peaks corresponding to nitrogen and carbon account for the presence of organic compounds at the surface of the nanocrystals. The spectrum also indicates the presence of oxygen. Sulfur S 2p region in the XPS spectrum is given in Fig. 7. The low intensity peak centered at 168.8 eV indicates the presence of sulfates, which may account for the presence of oxygen in the sample. A quantitative analysis of the broad XPS spectrum indicates less than 1% sulfates in the analyzed area.

Quantitative analysis of atomic composition of the nanoparticles surface gives an excess sulfur and antimony content compared to the Cu 3 SbS 4 formula. The sulfur excess is partly attributed to the presence of sulfates at the nanocrystal surface. As sulfur and antimony have been added in excess prior to the synthesis, they may have been adsorbed on the surface of the nanoparticles.

Fig. 7. XPS S 2p spectrum of famatinite NCs

Ink preparation from functionalized NCs. After the purification process nanocrystals are found to be readily dispersible in non-polar solvents such as n-heptane and hexane. XPS spectrum of phase pure famatinite nanocrystals in which the peak at 399 eV can be assigned to the amine group [R-NH 2 ] (Fig. 8.) confirms the presence of oleylamine. The peak centered at 401.7 eV can be attributed to oxidized N groups.

Fig. 8. XPS N 1s core level spectrum from famatinite NCs analysis

No precipitate is observed in the 50 wt% dispersion after a few hours of storage. After a few days of shelf storage, sedimentation of nanoparticles can be observed. The homogeneity can be restored after a few minutes of ultra-sonication. One can explain this phenomenon by the fact that the bonds between the inorganic nanoparticle surface and an electron-donating end group of a ligand molecule, such as thiol [14][15] , amine or phosphine 16 , undergo dynamic binding and unbinding processes [17][18] . This yields to the important consequence that the ligand molecules can get off for instance by excessive washing, which might compromise the stability of the nanoparticles that might ultimately aggregate and precipitate over time.

To overcome this issue, we added a dispersing agent, Solsperse® 9000 from Lubrizol, up to 1 wt% which was found to be benefic for the obtention of an homogeneous and stable dispersion (Fig. 9.).

Fig. 9. Famatinite NCs based dispersion

After a few weeks of storage, sedimentation is observed, the dispersion has thus to be sonicated before use. Increasing the amount of the dispersing agent induces better stability over time. However, the addition of more than 2 wt% of dispersing agent leads to highly resistive films after a deposition and drying step.

The prepared solution is found to be easily processable and is therefore used for the fabrication of CAS films for further characterization.

CAS films morphological study. According to the methodology described in the experimental section, CAS films have been deposited on quartz substrates. Homogeneously deposited films are obtained via dynamic spin coating. Fig. 10.-a shows a top view of the as deposited film and Fig. 10.-b shows a cross section of the same film. To obtain the cross section, the sample is etched via low ion polishing using an Ilion Gatan system. SEM images in Fig. 10 show a top and cross-section view of a spin-coated film on a glass substrate. The spin-coated film is found to be crack free and homogeneous with a thickness of 2 µm. We can observe an inhomogeneous layer formed on top of the CAS film. From EDS measurement, this layer corresponds to the deposition of glass, from the substrate, during the etching process. The spin coated film thickness is homogeneous.

CAS films electrical and optical characterization. Spin coated films are found to be conductive, albeit highly resistive with a sheet resistance around 240 kΩ/□ (ρ = 48 Ω.cm). Lower resistivities are achieved for drop deposited films, around 10 Ω.cm, despite the presence of micro cracks. The measured resistivity is higher than reported value of 0.249 Ω.cm for bulk famatinite 19 . The relatively high resistivity of the nanocrystals based films can be due to different factors such as nanoparticles cristallinity, high density grain boundaries and presence of organic compounds at some interfaces between nanocrystals (surfactant and dispersing agent). As our nanoparticles show good crystallinity similar to that of K. Ramasamy et al. 9 , the high resistivity is likely attributable to the two latter factors. Thicker layers deposition along with a sintering step may be useful to further reduce the electrical resistivity of the famatinite film. Optical characteristics of spin coated CAS films on glass substrates are then characterized through UV/VIS/NIR spectroscopy in the spectral range from 200 nm to 1400 nm. Optimal absorbance without saturation is obtained for 100 nm thick films (see Fig. 11). Where C is a constant of proportionality, h is Planck's constant, ν is the frequency of vibration, α is the absorption coefficient and n depends on band transitions. For a direct transition, n equals 2 and for an indirect one, n equals ½. Based on the UV/VIS spectrum, both (αhν) 2 and (αhν) 0.5 are plotted as a function of hν. Then, a fit of the linear portion of the curve and an extrapolation at α=0 is performed. For famatinite (batch-1.1), the extrapolated energy gap is found to be 0.82 eV with an indirect transition (Fig. 12). The plot of (αhν) 2 versus hν gives a higher energy gap of 1.5 eV for the direct transition. The calculated band gap is in the range of reported values for famatinite, from 0.46 eV to 1.2 eV 6,9,19,21,22 . The literature data is however ambiguous as both direct 19,21 and indirect band gap 9,22 are reported for Cu 3 SbS 4 .

Conclusion

Famatinite nanocrystals were synthetized by a surfactant assisted solvothermal method under mild and safe conditions as no toxic solvents and precursors were used. Nanocrystalline and phase-pure famatinite particles were obtained by carefully controlling the surfactant to solvent volumetric ratio as well as the sulfur to copper molar ratio and without the need of an inert atmosphere during the synthesis process. The structure of the synthetized Cu 3 SbS 4 nanocrystals was confirmed by XRD. For the synthesis, excess of sulfur in the molar ratio S:Cu was necessary to obtain the phase-pure famatinite, whereas the stoichiometric ratio 1:0.75 yielded a famatinite-tetraedrite mix of phases. The proposed method is easily scalable as compared to the hot-injection method partly because all the precursors are mixed before the reaction. A homogeneous and easily processable solution was obtained. Depending on the printing technique used to deposit the nanoparticle based solution, further formulation optimization can be done to adjust key parameters such as viscosity and nanoparticle size.

The prepared dispersion was used to fabricate homogeneous films. The electrical resistivity of the films could be reduced by increasing their thickness. Further studies on the impact of sintering on the electrical properties have to be conducted to evaluate the possibility to improve the electrical conductivity of famatinite films.

Fig. 1 .

 1 Analysis of the precipitate formed upon mixing the initial solutions (metal salts in ethanol and sulfur in oleylamine) (a) SEM picture and (b) EDS mapping (sulfur in red, antimony in blue and copper in green)

  2.-a) with an average size of 20 nm. Particles from batch-1.3 size dispersion is found to be highly polydisperse (Fig. 2.-b). (a) (b) Fig. 2. SEM images of the synthetized nanoparticles with different surfactant/solvent volumetric ratios: (a) 1:1 and (b) 1:3

3 .Fig. 3 .

 33 -a) and TEM (Fig. 3.-b) micrographs for batch-1.1 nanoparticles produced with a molar ratio S:Cu of 1:0.4. Nanoparticles average size is 20 nm. HR-TEM picture (Fig. 3.-b) shows a highly crystalline isolated nanocrystal. SEM (a) and TEM images (b) of as synthetized famatinite nanocrystals

Fig. 5 .Fig. 6 .

 56 Fig. 5. XRD pattern of as prepared CAS nanocrystals synthetized with a sulfur to copper molar ratio of 1:0.75

Fig. 10 .

 10 SEM images of (a) top and (b) crosssection views of the spin-coated layer

Fig. 11 .

 11 Fig. 11. UV/VIS/NIR absorption spectrum of famatinite NCs based 100 nm thick film

Fig. 12 .

 12 Fig. 12. Dependence of (a) (αhν) 0.5 and (b) (αhν) 2 on photon energy hν plot for famatinite NCs based 100 nm thick film

Acknowledgements

This work has been supported by an ANRT CIFRE grant. The authors would like to thank L. Beauvisage and L. Fares from STMicroelectronics Rousset (RCCAL laboratory) for their support on TEM characterizations as well as B. Bortolotti from STMicroelectronics Rousset (RCCAL laboratory) for the XPS analysis. The authors would also like to thank C. Chassigneux from MADIREL laboratory for the help with XRD analysis.