M Kamagaté

Aymen Amin Assadi

Tiangoua Kone

Sylvain Giraudet

Lacina Coulibaly

Khalil Hanna
email: khalil.hanna@ensc-rennes.fr

Mahamadou Kamagate

Use of laterite as a sustainable catalyst for removal of fluoroquinolone antibiotics from contaminated water

Keywords: Laterite, fluoroquinolone antibiotics, sorption, oxidation, stability, UVA irradiation

Use of laterite as a sustainable catalyst for removal of fluoroquinolone antibiotics from contaminated water

Introduction

Fenton reaction based on generation of highly reactive oxygen species (ROS) has attracted continuous attention during the past decades, and is considered as a powerful oxidative method for the treatment of persistent organic pollutants [START_REF] Anipsitakis | Radical generation by the interaction of transition metals with common oxidants[END_REF][START_REF] Pignatello | Advanced oxidation processes for organic contaminant destruction based on the Fenton reaction and related chemistry[END_REF]. In homogeneous Fenton process, dissolved iron and H2O2 are used to produce ROS [START_REF] Anipsitakis | Radical generation by the interaction of transition metals with common oxidants[END_REF][START_REF] Pignatello | Advanced oxidation processes for organic contaminant destruction based on the Fenton reaction and related chemistry[END_REF]). In heterogeneous system, iron oxy-hydroxides, iron bearing minerals and/or iron immobilized diverse supports are generally used to promote the Fenton reaction (Lin and Gurol 1998;[START_REF] Kwan | Rates of hydroxyl radical generation and organic compounds oxidation in mineral-catalyzed Fenton-like systems[END_REF][START_REF] Matta | Fenton-like oxidation of 2, 4, 6-trinitrotoluene using different iron minerals[END_REF][START_REF] Gonzalez-Olmos | Fe-zeolites as catalysts for chemical oxidation of MTBE in water with H2O2[END_REF][START_REF] Guo | S-doped α-Fe2O3 as a highly active heterogeneous Fenton-like catalyst towards the degradation of acid orange 7 and phenol[END_REF][START_REF] Ghauch | Degradation of aqueous carbamazepine in ultrasonic/Fe0/H2O2 systems[END_REF][START_REF] Gonzalez-Olmos | Fe-zeolites as heterogeneous catalysts in solar Fenton-like reactions at neutral pH[END_REF]Wang et al. 2015;[START_REF] Lan | Heterogeneous photo-Fenton degradation of acid red B over Fe2O3 supported on activated carbon fiber[END_REF]. The latter process offers many advantages over its homogeneous counterpart, such as no sludge formation, operation at near neutral pH, easy separation/recovery of catalyst, etc. [START_REF] Martínez | Iron species incorporated over different silica supports for the heterogeneous photo-Fenton oxidation of phenol[END_REF][START_REF] Gonzalez-Olmos | Fe-zeolites as catalysts for chemical oxidation of MTBE in water with H2O2[END_REF][START_REF] Guo | S-doped α-Fe2O3 as a highly active heterogeneous Fenton-like catalyst towards the degradation of acid orange 7 and phenol[END_REF][START_REF] Herney-Ramirez | Heterogeneous photo-Fenton oxidation with pillared clay-based catalysts for wastewater treatment: A review[END_REF][START_REF] Gonzalez-Olmos | Fe-zeolites as heterogeneous catalysts in solar Fenton-like reactions at neutral pH[END_REF][START_REF] Minella | Photo-Fenton oxidation of phenol with magnetite as iron source[END_REF]. Because the decomposition rate of organic contaminants in heterogeneous system is slower than in classic homogeneous Fenton reaction, different ways have been developed to enhance the oxidation efficiency while keeping the benefits of heterogeneous system. Among these processes, the photo-assisted Fenton reaction using light energy can accelerate the reaction rate by decomposing H2O2 into most powerful oxidizing species, and by reducing Fe III to Fe II and/or converting Fe III back to Fe II after the reaction [START_REF] Martínez | Iron species incorporated over different silica supports for the heterogeneous photo-Fenton oxidation of phenol[END_REF][START_REF] Herney-Ramirez | Heterogeneous photo-Fenton oxidation with pillared clay-based catalysts for wastewater treatment: A review[END_REF][START_REF] Gonzalez-Olmos | Fe-zeolites as heterogeneous catalysts in solar Fenton-like reactions at neutral pH[END_REF][START_REF] Minella | Photo-Fenton oxidation of phenol with magnetite as iron source[END_REF].

Different synthetic materials have been used as a catalyst in heterogeneous Fenton processes, e.g. iron oxides [START_REF] Matta | Fenton-like oxidation of 2, 4, 6-trinitrotoluene using different iron minerals[END_REF][START_REF] Minella | Photo-Fenton oxidation of phenol with magnetite as iron source[END_REF]Wang et al. 2015), zeolite [START_REF] Gonzalez-Olmos | Fe-zeolites as catalysts for chemical oxidation of MTBE in water with H2O2[END_REF][START_REF] Gonzalez-Olmos | Fe-zeolites as heterogeneous catalysts in solar Fenton-like reactions at neutral pH[END_REF], clay [START_REF] Bohu | Degradation studies of ciprofloxacin on a pillared iron catalyst[END_REF][START_REF] Herney-Ramirez | Heterogeneous photo-Fenton oxidation with pillared clay-based catalysts for wastewater treatment: A review[END_REF], and modified iron-carbon [START_REF] Lan | Heterogeneous photo-Fenton degradation of acid red B over Fe2O3 supported on activated carbon fiber[END_REF]. However, the use of these materials for high-scale applications in water and wastewater treatment may be limited due to their low effectiveness and/or high costs [START_REF] Garrido-Ramirez | Clays and oxide minerals as catalysts and nanocatalysts in Fenton-like reactions-A review[END_REF][START_REF] Litter | Advanced Oxidation Technologies: Sustainable Solutions for Environmental Treatments[END_REF]. Indeed, the high cost of supported or composite catalysts leads the researchers to propose a cheaper alternative, particularly in the developing countries.

Laterite soil is abundant in some parts of the earth including Africa. Although some studies were dedicated to the use of laterite in Fenton reactions [START_REF] Karale | Catalytic use of laterite iron for degradation of 2 aminopyridine using advanced oxidation processes[END_REF][START_REF] Khataee | Iron rich laterite soil with mesoporous structure for heterogeneous Fenton-like degradation of an azo dye under visible light[END_REF], much remains to be learned on the sorption/oxidation activity of this mineral surface and its catalytic stability. In addition, the binding and transformation mechanisms of organic compounds interacted with laterite surfaces remain unclear.

This work aims to develop an effective heterogeneous Fenton process based on the use of a natural catalyst and light source in order to effectively remove emerging contaminants from contaminated water. FLU, an antimicrobial agent belonging to the second generation of synthetic quinolones and frequently used in veterinary medicine [START_REF] Gothwal | Antibiotic Pollution in the Environment: A Review[END_REF], is selected here as a model of emerging pharmaceutical compounds. Due to its continuous release into the environment and its persistence, 2.5-50 ng L -1 [START_REF] Pozo | Efficient approach for the reliable quantification and confirmation of antibiotics in water using on-line solid-phase extraction liquid chromatography/tandem mass spectrometry[END_REF][START_REF] Tamtam | Occurrence and fate of antibiotics in the Seine River in various hydrological conditions[END_REF]) and 6.9 µg kg -1 [START_REF] Tamtam | Assessing the fate of antibiotic contaminants in metal contaminated soils four years after cessation of long-term waste water irrigation[END_REF]) of FLU residues have been detected in aquatic environments and in the soil, respectively. To the best of our knowledge, the removal of fluoroquinolone antibiotics using laterite soil as sorbent/catalyst was rarely investigated. Here, the FLU removal was investigated at two pH values (pH 3 as an acidic pH to ensure a high solubility of iron and pH 6.5, closer to near-neutral conditions of real effluents) and with and without UVA irradiation. The influence of laterite loading and initial concentrations of FLU and oxidant (H2O2) on the removal efficiency rate was also investigated.

Higher concentrations of FLU than those encountered in real contaminated effluents were used in order to test the removal capacity of laterite in heavily loaded contaminated waters, e.g. multi-components contaminated water. Effect of co-occurring antibiotic on the FLU degradation was also evaluated using norfloxacin (NOR), a fluoroquinolone antibiotic, which can be co-found with FLU in affected environments [START_REF] Tamtam | Occurrence and fate of antibiotics in the Seine River in various hydrological conditions[END_REF]. The Langmuir and Langmuir-Hinshelwood models were used to describe the surface interactions with FLU in the absence and the presence of oxidant (H2O2), respectively. Moreover, possible deactivation of surface sites as well as the catalytic stability of laterite were assessed by conducting sequential oxidation cycles, TOC measurements and solid characterization.

Experimental

Materials

Flumequine (99% purity), norfloxacin (99% purity), hydrogen peroxide (35% w/w), 1,10phenanthroline (>99% purity), sodium acetate (>99% purity), ferrous ammonium sulfate hexahydrate ((NH4)2Fe(SO4)2•6H2O), 2-propanol (C3H8O), and chloroform (CHCl3) were provided from Sigma-Aldrich. Solutions were prepared with high-purity water obtained from a Millipore Milli-Q system.

Laterite soil characterization

Laterite soil was collected from Sinématialy town (9°34'60" N and 5°22'60" W) in the north of Ivory Coast. The sample was grinded and passed through 250 µm sieve. The obtained fraction was washed several times with pure water, and then dried at 50 °C.

In order to determine the crystal structure of natural mineral, sample of laterite (≤ 250 µm) was analyzed by X-ray powder diffraction (XRD). The XRD data were collected with a D8 Bruker diffractometer, equipped with a monochromator and a position-sensitive detector. The XRD peaks (Fig. S1) were attributed to quartz, goethite, hematite, kaolinite and gibbsite.

However, the most abundant phases in our sample are quartz, goethite and hematite, which is in agreement with a previous work [START_REF] Coulibaly | Fourier transform infra-red (FTIR) spectroscopy investigation, dose effect, kinetics and adsorption capacity of phosphate from aqueous solution onto laterite and sandstone[END_REF]. Consistently, the TEM-EDX indicated a composition of Fe, Al and O (i.e. under oxide forms), together with two major elements Ca and Mg (Fig. S1). More details are given in the supporting information. To determine the metal contents in laterite, elements were analyzed using an inductively coupled plasma atomic emission spectrometer (ICP-AES, Jobin-Yvon JY 70 Type HORIBA) after acid digestion of the sample (Table S1). Potentiometric titrations of the laterite were conducted in thermostated double walled pyrex cell at 293 K in 0.001, 0.01 and 0.1 M NaCl solutions. The pH value of the suspensions was adjusted and kept constant with titrant solutions (HCl or NaOH) at pH 3 or 6.5. The B.E.T. specific surface area and the Point Zero Charge (PZC) of laterite soil were 23 ± 1 m 2 g -1 and 6.5 ± 0.3, respectively.

Photoreactor and photodegradation experiments

All experiments were performed in a 500 mL capacity batch photoreactor (made of borosilicate glass) at room temperature (20 ± 2 °C). The reactor was designed in a column shaped in 34 cm high and 3.8 cm diameter. This setup has an enclosed chamber comprising a reactor; an UVA lamp 24 W (Philips PL-L) placed in the center of the glass cell emitting in a wavelength region 320-400 nm with emission peak centered at λmax = 360 nm, yielding a irradiation intensity of 16 mW cm -2 as detected with a UVA Radiometer (VLX-3W equipped with a sensor CX 365, ALYS Technologies, Switzerland). The solution with catalyst was continuously stirred with a magnetic bar at 180 rpm. The pH of the sample solution was measured by means of VWR instruments 6000 pH-meter. Monitoring of suspension temperature indicated no significant fluctuation (20 ± 2 °C) along the experiment. The UVvisible spectrum of FLU is shown in Figure S2.

Two different experiments were conducted at room temperature. In a first experiment, the suspension of FLU and laterite was stirred in the dark for 4 h to reach the adsorption equilibrium without UVA irradiation and oxidant (H2O2). In the second test, FLU, oxidant, and laterite were mixed simultaneously under UVA irradiation. In both experiments, 500 mL of a FLU solution of known concentration were prepared and the appropriate amount of catalyst was added. In order to keep it constant, the pH of the solution was adjusted by HCl and NaOH (0.1 M). Then, the required volume of H2O2 (35% w/w) was added to the solution.

At time intervals, 5 mL of the solution were collected and analyzed.

Aqueous organic compound concentrations were determined using a high performance liquid chromatography (Waters 600 Controller) equipped with a reversed-phase C18 column (250 mm×4.6 mm i.d., 5 μm) and UV detector (Waters 2489). The detector was set to 246 nm for FLU and 277 nm for NOR. The mobile phase was mixture of acetonitrile/water (20/80 v/v) containing 0.1% formic acid. The flow rate was set at 1 mL min -1 in isocratic mode. Total Organic Carbon (TOC) was determined using a TOC-meter (Shimadzu TOC-VCSH) using 10 mL of solution. Total dissolved iron concentrations were measured by the 1,10phenantrholine method at 510 nm [START_REF] Tamura | Spectrophotometric determination of iron (II) with 1,10-phenanthroline in the presence of large amounts of iron(III)[END_REF]. All these experiments were repeated 2 times and showed a good reproducibility with a standard deviation of 3%.

Results and discussion

Preliminary characterization of removal capacity of the investigated laterite

To characterize the sorption capacity of laterite, adsorption isotherms were determined at two pH values (3 and 6.5) (Fig. 1). Preliminary kinetic batch experiments conducted over 24 h showed that equilibrium was achieved within 4 h of reaction time. The experimental isotherm data were best fitted to the equation of Langmuir through linear regression (r² = 0.99). The linear form of the Langmuir equation is given by:

e e q C = e m m a C q q K 1 1 + (1)
where qm (µmol m -2 ) is Langmuir maximum sorbed amount and Ka (L µmol -1 ) is the Langmuir isotherm constant. The progressive saturation of the surface sites shows that the adsorption followed the Langmuir assumption with a maximum adsorption capacity of 1.40 µmol m -2 at pH 3 and 1.19 µmol m -2 at pH 6.5. As typically encountered for anionic ligands, FLU adsorption was greatest under acidic to circumneutral pH, and lowest under alkaline conditions (See Fig. S3 for distribution of FLU species at various pH values). The Ka values estimated from Langmuir model are 1.95 L µmol -1 at pH 3 and 0.37 L µmol -1 at pH 6.5.

The removal of FLU was then evaluated under different oxidation systems in presence and in absence of laterite (Fig. 2). The heterogeneous process (i.e. UVA/H2O2/Laterite) showed the best removal performance at both pH values, 77% and 62% of removal at pH 3 and 6.5, respectively. In both experiments, the direct photolysis is less than 12%. To account for the sorption on laterite, desorption tests (adding NaOH to have pH 11) were performed and total amounts of FLU in aqueous phase were plotted against time (Fig. 2). The amounts of degraded FLU lied at 56% at pH 3, and 43% at pH 6.5 and after 420 min of reaction time. It is worth noting that pre-equilibration of FLU with laterite suspension for 4 h in the dark before irradiation did not significantly change the kinetics behavior (Fig. S4). TOC measurements over 540 min confirmed the oxidative degradation in UVA/H2O2/Laterite system, whereas 45% and 33% of mineralization was achieved at pH 3 and 6.5, respectively. As explained below, optimization of experimental parameters improved the FLU degradation up to 94%, and mineralization up to 72%.

The higher degradation performance at pH 3 may result from (i) changes in surface interactions between FLU and laterite as more adsorption was observed at pH 3, (ii) high formation rate of radical species at acidic pH [START_REF] Buxton | Critical review of rateconstants for reactions of hydrated electrons, hydrogen atoms and hydroxylradicals . OH/O .-) in aqueous solution[END_REF]) and/or (iii) possible leaching of Fe from laterite surfaces contributing to a homogeneous Fenton reaction. The latter was excluded since the amount of iron leaching was found very low (< 6 µg.L -1 ) even if it is relatively higher at acidic pH than at pH 6.5 (Fig. S5). The possible release of trace elements such as Cr, Cu, Co, Ni and Zn was also checked by ICP/AES, which indicated that these elements were under quantification limits under our experimental conditions.

We note an increase of FLU degradation in UVA/H2O2/Laterite compared to UVA/H2O2 system. This improvement could be attributed to the higher generation of active species, e.g.

hydroxyl radicals and iron ferrous (Fe II ) [START_REF] Martínez | Iron species incorporated over different silica supports for the heterogeneous photo-Fenton oxidation of phenol[END_REF][START_REF] Gonzalez-Olmos | Fe-zeolites as heterogeneous catalysts in solar Fenton-like reactions at neutral pH[END_REF][START_REF] Minella | Photo-Fenton oxidation of phenol with magnetite as iron source[END_REF]. First, direct photolysis of H2O2 under UVA irradiation may generate highly oxidizing species (i.e. • OH radicals). Moreover, the UVA irradiation may also enhance the heterogeneous Fenton activity on the surface, by promoting the photo-assisted reduction of Fe III to Fe II , which subsequently reacts with H2O2 generating • OH radicals. Therefore, addition of H2O2 led to an acceleration of reaction rate, as compared to the UVA/Laterite system, further confirming the synergetic effect of laterite and H2O2.

Optimization of operating conditions

The influences of H2O2 concentration, laterite dosage and initial concentration on the removal of FLU were investigated at pH 3 and 6.5. The experiments, which were repeated 2 times, showed a good reproducibility with a 5% of averaged standard deviation.

Effect of H2O2 concentration

Removal kinetics of FLU were determined at a wide range of H2O2 concentration (1 -9 mmol L -1 ) and two pH values (3 and 6.5). The degradation of organic compounds by HO . is typically described as a second-order reaction [1-6]:

(2)

where [HO . ] is steady-state concentration of hydroxyl radical, [FLU] is concentration of FLU in water, k is the second-order rate constant, and t is the reaction time. By assuming that HO

. ] ][ [ ] [ . HO FLU k dt FLU d - =
instantaneous concentration is constant, the kinetics of degradation of FLU in water can be described according to the pseudo-first-order equation as given below:

(3) where kapp is the pseudo-first-order apparent rate constant (min -1 ). kapp (min -1 ) obtained by linear regression of ln (Ct/Co) versus time t, was plotted against H2O2 concentration. The kapp constants were higher at pH 3 than pH 6.5. Since the degradation of FLU solution is directly related to the concentration of hydrogen peroxide and formation of radicals, the removal kinetic of FLU was enhanced when the H2O2 concentration increased from 1 to 4 mmol L -1 . However, a decrease in kapp was observed at higher H2O2 concentrations (Fig. 3), thereby suggesting scavenging effects of radicals by hydrogen peroxide (kH2O2/HO . = 2.7 x10 7 M -1 s -1 ) [START_REF] Mechakra | Use of natural iron oxide as heterogeneous catalyst in photo-Fenton-like oxidation of chlorophenylurea herbicide in aqueous solution: Reaction monitoring and degradation pathways[END_REF]) and/or recombination of radicals [START_REF] Buxton | Critical review of rateconstants for reactions of hydrated electrons, hydrogen atoms and hydroxylradicals . OH/O .-) in aqueous solution[END_REF][START_REF] Litter | Advanced Oxidation Technologies: Sustainable Solutions for Environmental Treatments[END_REF]. At much higher H2O2 concentration, there is a competitive reaction between FLU and H2O2 towards the reaction with ROS.

Effect of laterite dosage

The pseudo-first-order apparent rate constants (kapp (min -1 )) were determined as previously explained, and plotted against laterite loading (0.5 to 4 g L -1 ) in Figure 4. As for previous experiments, the observed pseudo-first order rate constant firstly increased with laterite loading increasing and then reduced. This phenomenon can be explained by screening effects occurring at high loading of solid in aqueous suspension, as previously reported for heterogeneous photo-Fenton reactions [START_REF] Bohu | Degradation studies of ciprofloxacin on a pillared iron catalyst[END_REF][START_REF] Mechakra | Use of natural iron oxide as heterogeneous catalyst in photo-Fenton-like oxidation of chlorophenylurea herbicide in aqueous solution: Reaction monitoring and degradation pathways[END_REF]). In addition, the generated radicals can be scavenged by metal oxide surfaces (koxide/HO . = 8 x 10 11 (g mL -1 ) - 1 s -1 ) [START_REF] Miller | Mechanistic studies of surface catalyzed H2O2 decomposition and contaminant degradation in the presence of sand[END_REF].

) exp( ] [ ] [ 0 t k FLU FLU app t - =
It is interesting to note that the optimal laterite loading of FLU removal is around 1 g L -1 regardless of the tested pH (kapp = 6.4 x10 -3 ± 0.0003 min -1 and 4.6 x10 -3 ± 0.0003 min -1 at pH 3 and pH 6.5, respectively).

Effect of initial flumequine concentration

The pseudo first-order rate constants (kapp) at various initial concentrations of FLU were determined with the optimum conditions for laterite loading and oxidant concentration (Fig. 5). There is a decrease of kapp from 1.87x10 -2 ± 0.0003 to 6.2 x10 -3 ± 0.0003 min -1 at pH 3 and from 9.4x10 -3 ± 0.0003 to 4.1 x10 -3 ± 0.0003 min -1 at pH 6.5 when FLU concentration increased from 19 to 77 µmol L -1 . This expected phenomenon can be explained by the competition of species (here FLU and H2O2) with each other for interactions with a fixed number of active sites on solid surfaces. At higher FLU concentration, adsorption may occupy a greater number of Fe III -sites, which become unavailable to generate Fe II upon irradiation and/or interact with H2O2. This is consistent with previous works where photon absorption by catalyst or photo-assisted reduction of surface sites to trigger the oxidation reaction is considered as the rate-limiting step [START_REF] Avetta | Activation of persulfate by irradiated magnetite: implications for the degradation of phenol under heterogeneous photo-Fenton-like conditions[END_REF]. Furthermore, higher FLU concentrations may lead to a decrease of photons entering into solution thereby lowering the performance of photo-assisted Fenton reaction, as previously reported [START_REF] Rivas | Modelling of the operation of raceway pond reactors for micropollutant removal by solar photo-Fenton as a function of photon absorption[END_REF].

The Langmuir-Hinshelwood model that is widely used in heterogeneous catalysis was tested here [START_REF] Turchi | Photocatalytic degradation of organic water contaminants: Mechanisms involving hydroxyl radical attack[END_REF]) to describe the oxidation process at the oxide surface. This Langmuir-Hinshelwood model can be expressed as:

0 int 1 C K K k k s s app + = (4)
and linear expression :

s app K k k C k int int 0 1 1 + = ( 5
)
where kapp is the initial pseudo-first-order rate constant (min -1 ), kint is the intrinsic reaction rate constant (µmol L -1 min -1 ), and Ks is the adsorption constant of FLU over laterite surfaces (L µmol -1 ). The linear correlations (r² = 0.99) between 1/kapp and Co are good at both pH (3 and 6.5), indicating that surface reactions of FLU including sorption and oxidation played a key role in determining the rate of the whole reaction. The values of kint and Ks obtained are 0.51 µmol L -1 min -1 and 0.12 L µmol -1 at pH 3 and 0.33 µmol L -1 min -1 and 0.06 L µmol -1 at pH 6.5. The Ks values estimated from L-H model are lower than the constants determined in the absence of oxidant by Langmuir model (1.95 L µmol -1 at pH 3 and 0.37 L µmol -1 at pH 6.5), underscoring competition effects between species at laterite surfaces.

Implication of radical species in the degradation process

Different ROS may be formed during heterogeneous photo-Fenton reaction such as • OH and/or HO2 • /O2 •- (Martínez et al. 2005;[START_REF] Xue | Adsorption and oxidation of PCP on the surface of magnetite: Kinetic experiments and spectroscopic investigations[END_REF]. In order to better understand the process involved in the degradation of FLU, 2-propanol was used as scavenger as it can react with • OH radical with relatively high reaction rate constant (k = 1.9 × 10 9 M -1 s -1 ). Chloroform was also used as the scavenger of HO2 • /O2 • -radical due to its relatively high reaction rate constant with hydrated electron (k = 3.0 × 10 10 M -1 s -1 ) and relatively low reaction rate constant with • OH radical (k = 7.4 × 10 6 M -1 s -1 ) [START_REF] Anbar | A Compilation of Specific Bimolecular Rate Constants for the Reactions of Hydrated Electrons, Hydrogen Atoms and Hydroxyl Radicals with Inorganic and Organic Compounds in Aqueous Solution[END_REF]. Because the pKa of HO2 • /O2 •-is 4.8, the hydroperoxide anion HO2 • is the predominant form at pH 3 while the superoxide anion O2 •-is preponderant at pH 6.5 [START_REF] Bielski | Reactivity of HO2 • /O2 •-Radicals in Aqueous Solution[END_REF].

First, 10 mmol L -1 of 2-propanol fully inhibited the FLU degradation (only oxidation is considered here as the total FLU concentration was plotted versus time, Fig. S6), suggesting that the • OH radical was by far the dominant species in the FLU degradation at pH 3. At pH 6.5, 2-propanol did not fully stopped the FLU degradation, while the effect of chloroform is more pronounced than at pH 3, suggesting that hydroxyl radicals still predominantly degrade FLU, but to a lower extent.

In the presence of 10 mmol L -1 of chloroform, the percentage of removed FLU fell down from 50% in the absence of chloroform to around 37% at pH 6.5, suggesting that O2 •-radicals may play a role in FLU degradation (Fig. S6). O2 •-can promote the formation of • OH through the reduction of Fe III to Fe II [START_REF] Bielski | Reactivity of HO2 • /O2 •-Radicals in Aqueous Solution[END_REF]Lin and Gurol 1998):

≡Fe III + O2 •- ≡Fe II + O2 k = 1.2 x10 6 M -1 s -1 (6)
Nevertheless, the use of 2-propanol at both tested pH led to relatively high inhibition of degradation, confirming that the oxidation of FLU is mainly due to • OH radicals.

Effect of co-occurring antibiotic on the FLU degradation

The influence of presence of co-solute on the degradation efficiency of FLU was evaluated with the optimum conditions for laterite loading and oxidant concentration and at two pH values (3 and 6.5). The photo-assisted degradations of FLU ([k FLU, •OH] = 8.26 x10 9 M -1 s -1 at pH 7 [START_REF] Santoke | Free-radicals-Induced oxidative and reductive degradation of fluoroquinolone pharmaceuticals: Kinetic studies and degradation mechanism[END_REF])) and NOR ([k NOR, •OH] = 6.18 x10 9 M -1 s -1 at pH 7 [START_REF] An | Mechanistic considerations for the advanced oxidation treatment of fluoroquinolone pharmaceutical compounds using TiO2 heterogeneous catalysis[END_REF]))

were evaluated in separate system (FLU or NOR) and binary system (an equimolar mixture of FLU and NOR) (Fig. 6).

Firstly, the degradation of each compound in the mixture decreased with respect to the single system, probably due to competition of compounds for reaction with hydroxyl radicals.

As an attempt to better understand the competition effect, the percentage of the hydroxyl radical ( • OH) reacted with FLU can be estimated using the following equation (Huang et al.

2013):

R Flu = (7) , H2O2] are the second-order rate constants between • OH and FLU, NOR and hydrogen peroxide. k •OH, H2O2= 2.7x10 7 M -1 s -1 [START_REF] Buxton | Critical review of rateconstants for reactions of hydrated electrons, hydrogen atoms and hydroxylradicals . OH/O .-) in aqueous solution[END_REF]).

k • OH, Flu [Flu]o k • OH, Flu [Flu]o + k • OH, Nor [Nor]o + k • OH, H2 O2 [H2O2]o Where [k • OH, FLU], [k • OH, NOR] and [k •OH
[FLU]o, [NOR]o and [H2O2]o were their initial concentrations. The same equation can be used to determine the percentage of the hydroxyl radical ( • OH) reacted with NOR, by replacing

[FLU]0 by [NOR]0 in the numerator of eq. 12. Since the reaction rate constants of FLU ([k FLU,

•OH] = 8.26 x10 9 M -1 s -1 ) [START_REF] Santoke | Free-radicals-Induced oxidative and reductive degradation of fluoroquinolone pharmaceuticals: Kinetic studies and degradation mechanism[END_REF]) and of NOR ([k NOR, •OH] = 6.18 x 10 9 M -1 s - 1 ) [START_REF] An | Mechanistic considerations for the advanced oxidation treatment of fluoroquinolone pharmaceutical compounds using TiO2 heterogeneous catalysis[END_REF] with the hydroxyl radical are relatively close, 41% and 31% of • OH reacted with FLU and NOR, respectively. It is worth noting that these reaction rate constants were determined at pH buffered to 7 (i.e. pKa1 <pH< pKa2 for NOR where the zwitterionic form is the predominant species, and pH > pKa for FLU where the anionic form is predominant), which is different from the working pH value (6.5 ± 0.1) in the present study. Nevertheless, we can conclude that the degradation of each compound (FLU or NOR) is not considerably affected by the presence of the other, underscoring potential benefits of the investigated process in the treatment of multi-components contaminated systems.

Stability and reusability of laterite

The reusability of catalyst is a critical parameter, from an economical point of view, for its usage in large scale reactors [START_REF] Nidheesh | Heterogeneous Fenton catalysts for the abatement of organic pollutants from aqueous solution: a review[END_REF]. The reusability of laterite has been evaluated in successive oxidation cycles, with the above-mentioned optimum conditions and at two pH conditions (Fig. 7). At the end of the oxidation process, the solid is easily removed from the reactor, washed with ultra-pure water, and dried at 50°C overnight, and then used for next experiment. The degradation using the recovered catalyst showed a slight difference with the first oxidation cycle, suggesting that the catalytic activity kept constant after five cycles of oxidation reaction. The removal rates of FLU were about 6.4 x10 -3 min -1 at pH 3 and 4.4 x10 -

The excellent stability of UVA/H2O2/Laterite system was then confirmed through TOC measurements at the end of each oxidation cycle. 72 ± 4% of mineralization was achieved at pH 3 and 50 ± 4% at pH 6.5, and this value remains constant even after 5 oxidation cycles.

The dissolved iron concentration measurements showed a very low release of Fe from laterite surfaces (less than 2 wt.% of total Fe initially present in laterite). In addition, XRD diffractogram recorded at the end of oxidation reaction was found to be quite similar with that recorded before reaction (Fig. S1). The excellent stability of the catalytic activity could be, therefore, attributed to the very low iron leaching during oxidation cycles and to the structural stability of the solid.

Conclusion

We have notably demonstrated that laterite can be effectively used for the removal of flumequine under UVA irradiation and at two pH values 3 and 6.5. The photo-assisted Fenton oxidation using laterite as iron source is dependent on H2O2 dose, laterite loading and initial concentration of FLU. The degradation rate firstly increased with the dosage of H2O2 or with laterite loading, reached an optimum value and then decreased. The occurrence of these optimums values could be explained by the parasite's scavenging reactions and/or lightscreening effects. The apparent heterogeneous reaction rate is dominated by the rate of intrinsic surface chemical reactions including sorption and light-induced reduction of Fe III , which are crucial to enhance the oxidation reaction. The laterite-promoted degradation of FLU is not dramatically affected by the presence of NOR, which can be co-found in affected environmental systems. The laterite can be re-used for several oxidation cycles without structural changes or deactivation of surface sites. This environmentally friendly remediation technology may appear as a promising way for water treatment in developing countries, using a low cost natural catalyst and solar light for the removal of fluoroquinolone antibiotics from multi-contaminated waters.

Capture Figures

Fig. 1 .

 1 Fig.1. Adsorption isotherms of flumequine (FLU) on laterite at pH 3 and 6.5: [FLU]o = 19 -77 µmol.L -1 ; [Laterite] = 1 g L -1 . Solid lines represent the Langmuir model.

Fig. 2 .

 2 Fig.2. Kinetics of flumequine (FLU) removal for various oxidation processes at pH 3 and pH 6.5: [FLU]o = 77 µmol L -1 ; [H2O2] = 1 mmol L -1 ; [Laterite] = 1g L -1 ; [FLU]aq = aqueous (residual) concentration of flumequine. [FLU]tot = total concentration of flumequine representing both aqueous (residual) concentration and adsorbed concentration obtained after desorption. Solid lines represent the pseudo-first order model.

Fig. 3 .Fig. 4 .

 34 Fig.3. Effect of H2O2 concentration on flumequine (FLU) removal by heterogeneous photo-Fenton process at pH 3 and pH 6.5: [FLU]o = 77 µmol L -1 ; [Laterite] = 1g L -1 ; UVA irradiation; reaction time = 420 min.Fig.4. Effect of laterite dosage on flumequine (FLU) removal by heterogeneous photo-Fenton process at pH 3 and pH 6.5: [FLU]o = 77 µmol L -1 ; UVA irradiation; [H2O2] = 4 mmol L -1 ; reaction time = 420 min.

Fig. 5 .

 5 Fig.5. kinetic rate constants of flumequine (FLU) versus initial concentration of flumequine in heterogeneous photo-Fenton processes at pH 3 and pH 6.5: [FLU]o = 19-77 µmol L -1 ;[laterite] = 1g L -1 ; [H2O2] = 4 mmol L -1 ; UVA irradiation ; reaction time = 420 min.

Fig. 6 .

 6 Fig.6. Total concentration of flumequine (FLU) and norfloxacin (NOR) degraded versus time in single and binary systems in the heterogeneous photo-Fenton process at two pH values (3 and 6.5): [FLU]o = [NOR]o = 19 µmol L -1 ; [laterite] = 1 g L -1 ; [H2O2] = 4 mmol L -1 ; UVA irradiation; reaction time = 300 min.

Fig. 7 .

 7 Fig.7. Reusability cycles of laterite in the heterogeneous photo-Fenton process at pH 3 and pH 6.5: [FLU]o = 77 µmol L -1 ; [laterite] = 1 g L -1 ; [H2O2] = 4 mmol L -1 ; UVA irradiation; reaction time = 420 min. Solid line represents pseudo-first order kinetic model.

  Fig.1

min -1 at pH 6.5, whereas percentage efficiencies lied at 94 ± 2% and 70 ± 2%, respectively.

Acknowledgements

This work was supported by a bilateral governmental program, Ivory Cost (Contract C2D) and Campus France. We gratefully acknowledge Dr. M. Pasturel (Rennes University) for XRD analysis and Dr. S. Rtimi (EPFL, Lausanne) for TEM analysis.

Appendix A. Supplementary data

Supplementary data associated with this article can be found, in the online version.


K Thirunavukkuarasu

G Radtke

Z Lu

M Lazzeri

P C M Christianen

M V Ballottin

H A Dabkowska

B D Gaulin

D Smirnov

M Jaime

A Saúl

Magnetoelastic interactions in SrCu 2 (BO 3 ) 2 studied by Raman scattering experiments and first principles calculations

Keywords: Shastry-Sutherland, High Magnetic Fields, Frustration, Pantograph mode, Quantum magnetism, Quasi two-dimensional

come

Magnetoelastic interactions in SrCu2(BO3)2 studied by

Raman scattering experiments and first principles calculations

I. INTRODUCTION

SrCu 2 (BO 3 ) 2 is a Mott-Hubbard insulator that hosts an orthogonal spin-dimer system, with a tetragonal unit cell that accommodates spin S = 1/2 Cu 2+ dimers arranged in copper-oxygen-boron planes separated by strontium spacer layers as shown in Fig. I. SrCu 2 (BO 3 ) 2 is also a physical realization of the twodimensional Shastry-Sutherland model proposed more than four decades ago [1]. Here, oxygen-mediated magnetic super exchange results in an inter-dimer J ′ to intradimer J exchange constant ratio J ′ /J ≃ 0.63, that leads to an exact spin-singlet ground state, close to a critical point at J ′ /J ≃ 0.68 marking a transition to an intermediate plaquette phase [2]. The combination of geometrical frustration, tunable exchange interactions that are sensitive to the CuOCu angle, and proximity to the critical point make this a fascinating compound, very rich in magnetic phases that have been predicted and observed to be stabilized with tuning parameters such * andres.saul@cnrs.fr as temperature, external magnetic fields, applied pressures, and disorder induced by minute chemical substitutions as attested by more that two decades of exciting research and results [3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Indeed, it is known from extensive earlier work that, when in the low temperature spin-dimer ground state, applied magnetic fields, external pressure, and temperature have similar effects on the lattice properties and physics of SrCu 2 (BO 3 ) 2 . This, due to all three control parameters ultimately being responsible for the suppression of the spin-gapped state, makes SrCu 2 (BO 3 ) 2 a unique system for the numerous practical routes available to tune exotic states such as spin stripe phases, spin supersolids, plaquettes, and quantum spin liquids, just to mention a few.

Work by Radtke and collaborators [10] first identified and quantitatively demonstrated that an optically-active lattice mode coined the pantograph mode is behind the strong spin-lattice coupling in SrCu 2 (BO 3 ) 2 amplifying the influence of minute lattice parameter variations via the CuOCu bond angle and resulting in an altered Cu 2+ -Cu 2+ exchange interaction that effectively stabilizes spin stripes and magnetization plateaus. Further work by Bettler et al. [18] has shown that the pantograph mode, which surprisingly softens with lowering temperatures, hardens under applied pressure to the point of changing its temperature dependence entirely with an external pressure of 27.5 kbar. These results are intriguing, because in more standard magnetic systems' lattice modes often freeze and harden upon reducing the temperature.

Raman spectroscopy has been successfully used to probe lattice and spin degrees of freedom in SrCu 2 (BO 3 ) 2 [18][19][20][21][22][START_REF] Gozar | Frontiers in Magnetic Materials[END_REF][START_REF] Gozar | [END_REF][25] including a recent study of low-energy magnetic excitations at high magnetic fields up to 27 T [26]. For further understanding the role of the lattice on stabilizing magnetic structures and exotic spin states, here we expand the range of magneto-Raman studies and trace the behavior of magnetic-field-dependent phonon modes up to 45 T. We use density functional theory to successfully compute the observed field-dependent Raman modes, classifying them into two types: pantograph and non-pantograph modes, and show that while the former are unusual, the later display enhanced but more conventional temperature dependence. We also show that their field dependence correlates with their respective temperature dependencies, e.g. modes that are hardened with increasing temperature also harden with applied magnetic fields and modes that become softer with temperature also soften with applied fields and are, likely, going to be important in field-(or pressure) induced states. The detailed evolution of the mode energies in magnetic fields mimic the changes observed in dilatometry and magnetization, displaying anomalies at plateaus. Last but not least, we observe via dilatometry, that the coefficient of thermal expansion appear to vanish at magnetic fields in the proximity of the closing of the spin gap, a feature not entirely understood at the moment.

II. EXPERIMENTAL DETAILS

High-quality single crystals of incongruently melting SrCu 2 (BO 3 ) 2 were grown by the optical floating zone technique in an image furnace using self-flux. Selected single crystals were oriented and characterized by x-ray diffraction and by neutron scattering using highly enriched 11 B as described elsewhere, see Dabkowska et al. [27].

Raman spectroscopic experiments at high magnetic fields were performed using three different magnet systems. Two of the experimental facilities are the 45 T hybrid magnet and 31 T resistive magnet at the National High Magnetic Field Laboratory (NHMFL) in Tallahassee, USA. The third Raman facility coupled to a 30 T resistive magnet is stationed at High Field Magnet Laboratory (HFML) in Nijmegen, Netherlands. The crystals were mounted in a custom-built fiber-based (NHMFL) or a direct-optics (HFML) probe inserted in a cryostat with helium exchange gas. Scattered light was collected in back-scattering geometry from the ab plane of the SrCu 2 (BO 3 ) 2 crystal with the magnetic field applied along the c-axis (Faraday geometry) using a 532 nm laser excitation focused to a (2-4) µm-diameter spot with incident power of about 100 µW to minimize sample heating. The Raman spectra were analyzed by a monochromator (NHMFL: SP2750 Princeton Instruments, 1800 g/mm grating; HFML: (Horiba FHR1000, 1200 g/mm grating) and recorded by a liquid-nitrogen-cooled CCD (PyLoN 100BR, Princeton Instruments) with a spectral resolution of about 1 cm -1 . The magneto-Raman measurements were carried at lowest stable temperature of about 2 K. The temperature-dependent and polarizationresolved Raman spectra were collected using a direct beam optics setup (HFML).

High-field magnetostriction and thermal expansion measurements were performed using an optical fiber Bragg grating (FBG) technique in the NHMFL 45 T hybrid magnet at pumped 4 He temperatures [28]. Axial dilatometry data ∆c/c(T, B), were obtained as a function of the temperature and magnetic field to 45 T applied along the crystallographic c-axis. The data were obtained with a swept wavelength laser interrogator by Micron Optics®, yielding a resolution ∆L/L = 3 × 10 -8 .

III. COMPUTATION DETAILS

Density functional theory (DFT) calculations have been carried out using the pseudopotential plane-wave method as implemented in the Quantum Espresso suite of codes [29]. The self consistent electronic structure and the phonon modes and Raman spectra have been calculated using the PWscf and PHonon codes respectively. In our calculations, we used optimized norm-conserving Vanderbilt (ONCV) pseudopotentials and the PBE functional [30] with a plane-wave and charge-density cutoff of 80 Ry and 320 Ry, respectively. We included an on-site Hubbard U eff on the Cu atoms using the simplified method developed by Cococcioni and de Gironcoli [31] with a U eff = 10.3 eV. The phonon band-structure has been computed using the phonopy [32] code with a 2x2x2 super-cell. concerns the B-O bonds and in particular the out of plane movement of the B atoms on the top of the band. Finally, the modes below 450 cm -1 involve the Cu-O bonds while the low energy modes below 100 cm -1 are mostly localized on the Sr atoms.

Parallel-and cross-polarized, (aa) and (bb), zero-field Raman spectra measured at 7 K are shown in Fig. 3(a). In the measured frequency range, our measurements are consistent with the previous studies [20,[START_REF] Gozar | Frontiers in Magnetic Materials[END_REF]. In Fig. 3(b) we show the calculated spectra. There is an overall good agreement between the spectra apart from a stretch of 7% of the theoretical frequencies, which is state-of-the- art when comparing experimental and theoretical Raman spectra. In Fig. 3(a) we have labeled with their energy (200, 385, 450, and 478 cm -1 ) the four experimental modes involving the Cu-O bonds, i.e., below 480 cm -1 in the experimental spectra. In Fig. 3(b), we have used the same labels for the theoretical modes despite that their calculated frequencies are slightly different (189, 340, 415, and 434 cm -1 ). The relative experimental intensities are fairly well reproduced by the theoretical calculations with the exception of the intensity of the mode at 200 cm -1 .

B. Temperature dependence

Raman spectra from the ab plane of SrCu 2 (BO 3 ) 2 were measured as a function of temperature in the range from 295 K to 2 K. To examine the Raman data, we fitted the relevant Raman peaks with Lorentzians and plot the extracted peak positions in Fig. 4(a). Typically for phonons in crystalline solids, the phonon frequencies are almost constant below cryogenic temperatures and exhibit a red shift with increasing temperature due to the combined effects of anharmonic phonon-phonon interaction and thermal expansion. We found that all measured SrCu 2 (BO 3 ) 2 phonon modes that do not involve the Cu-O bonds, exhibit such usual temperature dependence in the whole measured temperature range. The phonon modes involving the Cu-O bonds behave quite differently at low temperatures showing spectacular deviations below 15 K. As summarized in Fig. 4(a), the frequencies of the phonons at 385 cm -1 and 478 cm -1 show quick upturn while the modes at 200 cm -1 and 450 cm -1 change in the opposite direction. Similar temperature dependence for phonons at 200 cm -1 and 385 cm -1 has been recently reported [26]. with temperature. In (a), the lines are exponential fits to the experimental points that extrapolate to zero at zero temperature. They must be considered as guides to the eye.

Our DFT calculations allowed us to analyze the four modes showing anomalous temperature dependence (see Fig. 5). The mode at 200 cm -1 with the strongest .

temperature dependence is indeed the pantograph mode [2,10,18]. As can be seen, in this mode there is a rigid movement of the CuBO 3 groups. The Cu-Cu intra-dimer distance oscillates and the O-O distance also oscillates but in anti-phase. As a consequence these displacements involve a modification of the CuOCu super-exchange angle [10]. The mode at 450 cm -1 also shifts to higher energies when increasing temperature (see Fig. 4(a)).

The four BO 3 groups around the Cu dimers move almost rigidly, but now the Cu atoms move in the opposite direction with respect to the BO 3 group and their relative displacement is smaller. The relative displacement of the Cu and O atoms also involves a modification of the CuOCu super-exchange angle. This appears as a signature for the modes whose energies soften with decreasing temperature. In contrast, as can be seen in Fig. 5, the modes at 385 and 478 cm -1 whose frequencies rise when decreasing temperature do not involve a significant modification of the CuOCu super-exchange angle. In particular in the 478 cm -1 mode, the Cu and O displacements can be seen as an almost angle-preserving homothetic transformation of the Cu 2 O 2 plaquette (see Fig. 5). In the 385 cm -1 mode, the only moving atoms are the oxygens of the BO 3 groups that collectively rotate around the B atom.

C. Magnetic field dependence

The four strongest modes involving the Cu-O bonds (200, 385, 450, and 478 cm -1 ) that exhibit significant temperature dependence also show significant response to the external magnetic field. Figure 6(a) shows the magnetic-field dependence of their energies at 2 K and magnetic fields up to 45 T. Figures 6(c) and(d) show waterfall plots with the evolution of the 200 cm -1 pantograph mode with the applied magnetic field in the range 24 -44 T.

The overall change of the phonon modes with increasing magnetic field is similar to the shifts observed for increasing temperature. The energy of phonons at 200 cm -1 and 450 cm -1 shift to higher energies with increasing magnetic field while the energy of phonons at 385 cm -1 and 478 cm -1 lower their energies.

The observation of magnetic field induced response similar to temperature dependence suggests that the same magneto-elastic interactions are at play. The thermal excitations involves the same physical mechanisms as that of the magnetic excitations.

For the pantograph phonon modes at 200 cm -1 and 450 cm -1 the modification with temperature and magnetic field of the superexchange paths can be the mechanism at the origin of the observed hardening. When increasing temperature or applying a magnetic field, the spins localized in some Cu dimers would orient parallel to each other. As the interaction is AFM, the system would try to decrease the superexchange angle in order to decrease the interaction. The slight decrease of the angle is obtained by shortening the Cu-Cu distance [10] which leads to the hardening of the pantograph phonon modes [2].

Similar conclusions about the common origin of the temperature and magnetic field dependence can be drawn by comparing the macroscopic deformation of the lattice parameter measured in magnetostriction experiments [8,10] as shown in Figures 6(b) and 7 and the corresponding deformation measured versus temperature in neutron scattering experiments [33].

We now discuss possible origins of magnetic-field sensitivity of non-pantograph phonon modes. As mentioned above these modes do no not involve a significant modification of the super-exchange angle. In the 478 cm -1 mode, the Cu and O displacements concern an almost angle-preserving homothetic transformation of the Cu 2 O 2 plaquette and in the 385 cm -1 mode, the oxygens of the BO 3 rotate around the B atom.(see Fig. 5). The symmetry of their movement does not affect the intra-dimer interaction J but it does modify the second neighbor interaction J', which depends on the longer effective exchange path Cu-O-B-O-Cu. In particular, the homothetic transformation of the 478 cm -1 mode modifies both interactions J' connecting one Cu atom to a perpendicular dimer in a similar in-phase manner, while the rotation of the BO 3 groups of the 385 mode, breaks the symmetry of the two J' interactions breaking the frustration of the ground state. This is probably the rea-son explaining the enhanced temperature and magnetic field dependence for this last mode.

The energies of four phonon modes involving the Cu-O bonds vary monotonically with the magnetic field up to about 27 T. Around 20 T a change of slope is visible on the 200 cm -1 mode that can be associated with the closing of the spin gap in this system [8]. At higher fields, however, in addition to the phonon energy shifts, several anomalies were observed in the phonon energy as function of magnetic field. These anomalies are seen most clearly in the field dependence of the strongest pantograph mode at 200 cm -1 featuring the largest overall response to magnetic field and temperature (see Fig. 6(a)). There are two kinks observed around ≃ 28 T and ≃ 39 T (also detected in 450 cm -1 and 478 cm -1 modes) that coincide with the kinks or plateaus observed in the magnetostriction measurements as shown in Figures 6(b) and7. There is also a more subtle anomaly manifesting as a change of slope at ≃ 34 -35 T similar to that detected in c-axis magnetostriction.

The magnetostriction ∆c/c B and thermal expansion ∆c/c vs T were measured at constant temperatures between 1.7 K and 14 K on the same crystal used for Raman experiment. From these experiments, it can be seen in Fig. 7 that the c-axis lattice parameter expands with fields monotonically, consistent with earlier results obtained in pulsed magnetic fields [8], and displays clearly seen plateaus corresponding to M/M s = 1/4 and 1/3. Thermal expansion shown in Fig. 7 (top-left inset) was obtained that shows a large anomaly at the ordering temperature for the M/M s = 1/3 stripe phase. Combined magnetostriction, thermal expansion and Raman scattering data was used to build the phase diagram displayed in Fig. 7 7 (bottom-right inset). Note that only lines above T = 1.5K are displayed due to the base temperature of our 4He fridge. The data amount to supporting true bulk thermodynamic states for the stripe phases in SrCu 2 (BO 3 ) 2 . Additionally, a curious phenomenon is seen in the magnetostriction curves, which appear to cross in the region of transition between M/Ms = 1/5 and 2/9 stripe phases [8], suggesting an unusual vanishing and a change of sign of the coefficient of thermal expansion. Such change of sign has been seen in systems that display a divergence of the Gruneissen parameter (defined as the coefficient of thermal expansion α divided by the specific heat C(T ) at zero temperature) in the proximity of a quantum critical point (see Weickert et al. [34]). A full investigation requires access to lower temperatures and complementary measurements of the specific heat C(T ), and is currently under course.

V. DISCUSSION

We have shown the results of expanding the range of magnetic fields in a magneto-Raman experiment to follow the magnetic-field dependence of phonon modes involving Cu-O bonds of SrCu 2 (BO 3 ) 2 to magnetic fields high enough to reach the magnetic superstructures at M/M s = 1/8, 1/4, and 1/3 that can shed light on the role of the lattice stabilizing magnetic structures and exotic spin states. We use density functional theory to successfully model and compute the energies of these modes, classifying them into two types: pantograph (200 cm -1 and 450 cm -1 ) and non-pantograph (385 cm -1 and 478 cm -1 ) modes. These four phonon modes exhibit unusual shifts at low temperatures below approximately 15 K while other phonons energies remain unaffected.

We show that all four modes are affected by the external magnetic field (applied along c axes) consistently with their respective temperature dependencies, e.g., pantograph modes that are hardened with increasing temperature also harden with applied magnetic fields and non-pantograph modes that become softer with temperature also soften with applied fields and are, likely, going to be important in field-(or pressure) induced states. We compare their field dependence against static physical properties (magnetization and magnetostriction). The detailed evolution of the mode energies in magnetic fields mimics the changes observed in dilatometry and magnetization to 45 T, displaying anomalies at plateaus. In particular, the field dependence of the strongest pantograph 200 cm -1 mode and c-axis magnetostriction exhibit a striking resemblance with kinks at M/M s = 1/8 and 1/3 and slope change at M/M s = 1/4. These strong magnetoelastic couplings revealed under temperature and magnetic field allow the use of combined dilatometry and Raman data to build a (B vs T) phase diagram (see inset in fig. 7) in good agreement with available data in the literature.

FIG. 1 .

 1 FIG. 1. Atomic structure of SrCu2(BO3)2 (a) along the [100] direction and (b) along the [001] direction. Sr atoms are in yellow, O in red, B in green, and Cu in blue. The buckling of the [CuBO3] -layers along the [001] direction is visible in (a). The orthogonal Cu dimers have been highlighted in magenta in (b). Atomic structures were drawn with VESTA [17].

  FIG. 2. Phonon band structure and projected density of states of SrCu2(BO3)2.

FIG. 3 .

 3 FIG. 3. Comparison of the (a) experimental spectra of SrCu2(BO3)2 measured at 7 K and (b) theoretical Raman spectra for two polarizations. The energy of the theoretical spectra has been stretched by 7%. The four intense experimental phonon modes involving Cu-O bonds whose schematic representation are shown in Fig. 5 are labeled in the spectra (see text).

FIG. 4 .

 4 FIG. 4. (a) Evolution of the energy of four Raman modes of SrCu2(BO3)2 at B=0 with temperature and (b) waterfall plot showing the evolution of the energy of the peak at 200 cm -1with temperature. In (a), the lines are exponential fits to the experimental points that extrapolate to zero at zero temperature. They must be considered as guides to the eye.

FIG. 5 .

 5 FIG. 5. Schematic representation of the phonon modes of SrCu2(BO3)2 with strongest temperature and magnetic field dependence. The lengths of the arrows are proportional to the atomic displacements. Phonon mode visualizations were drawn with VESTA [17]. Displacement diagrams labeled 200 cm -1 and 450 cm -1 show Cu and O atom motion consistent with the pantograph modes, while 385 cm -1 and 478 cm -1 are non-pantograph..

FIG. 6 .

 6 FIG. 6. (a) Evolution of the energy of four Raman modes of SrCu2(BO3)2 with applied magnetic fields up to 45 T. The arrows point to the anomalies detected in 200 cm -1 mode coinciding with M/Ms = 1/8, 1/4, and 1/3 phases. The energy of the modes was obtained from Lorentzian fit of the average spectrum over multiple spectra obtained at each magnetic field step. The error bars were obtained from the data deviation at each spectrum in the group. (b) Magnetostriction of SrCu2(BO3)2 along a and c crystallographic axes measured at magnetic fields up to 45 T. Adapted from Ref.[10]. (c) and (d) Evolution of the 200 cm -1 pantograph phonon mode with respect to increasing magnetic fields in the range 24 -44 T. The data points are shown as open circles and the solid lines are the Lorentzian fit of the data.

FIG. 7 .

 7 FIG. 7. Main panel: c-axis magnetostriction measured to 45T at different temperatures between 1.7K and 5.4K. Inset (a): Thermal expansion ∆c/c (left y-axis) and coefficient of thermal expansion α (right y-axis) vs temperature measured at constant magnetic field B = 45T, showing a sharp phase transition at 5.2K. Inset (b): B, T phase diagram from magnetostriction ∆c/c vs field (black and red symbols), thermal expansion ∆c/c vs temperature (blue symbol), and magneto-Raman measurements (open circles). Note that only lines above T = 1.5K are displayed due to the base temperature of our 4He fridge.

ACKNOWLEDGMENTS

ZL and DS acknowledge support from the US Department of Energy (DE-FG02-07ER46451) for magneto-Raman measurements performed at the NHMFL, which is supported by NSF through NSF/DMR-1644779 and the State of Florida. M. J. acknowledges support by DOE Office of Science BES project "Science at 100 Tesla". BDG acknowledges support from NSERC (Canada). This work was supported by HFML-RU/NWO-I, member of the European Magnetic Field Laboratory (EMFL).


Mathilde Briard
email: mathilde.briard@inh.fr

Valerie Le Clerc

Anita Suel

Identification of duplicates for the optimization of carrot collection management

Keywords: AFLP, Bulked DNA, Genetic resources, Rationalisation, Redundant accessions

published or not. The documents may come

Introduction

Plant genetic resources collection managers have to develop strategies for characterisation, conservation and use of genetic resources. They need to evaluate the extent and distribution of genetic diversity in species of interest and to determine the proportion of duplicate accessions (redundancy) in their collections. The identification of putative duplicates is becoming a priority for genebank managers, as highlighted by the increasing number of studies on this topic. Indeed, as emphasised by [START_REF] Ford-Lloyd | Molecular markers and the management of genetic resources in seed genbanks: a case study of rice[END_REF], the identification of redundant accessions allows curators to focus effort on characterisation, evaluation and regeneration of unique genetic material.

A few years ago, the identification of duplicate accessions was done exclusively on the documentation of the accessions and on morphological characters if the information was available. Since the advent of PCR-based techniques, molecular markers have been used successfully for the identification of redundant material. RAPD and AFLP markers have proved their efficiency for this kind of analysis in different species such as rice [START_REF] Virk | The identification of putative duplicate accessions within a rice germplasm collection using RAPD analysis[END_REF][START_REF] Verma | Random amplified polymorphic DNA analysis of Indian scented basmati rice (Oryza sativa L.) germplasm for identification of variability and duplicate accessions, if any[END_REF], wheat [START_REF] Cao | Genetic diversity within spelta and macha wheats based on RAPD analysis[END_REF], sweet potato [START_REF] Zhang | Identifying duplicates in sweet potato (Ipomea batatas (L.) Lam) cultivars using RAPD[END_REF] and Solanum (del [START_REF] Rio | RAPD markers efficiently distinguish heterogenous populations of wild potato (Solanum)[END_REF][START_REF] Mcgregor | Analysis of the wild potato germplasm of the series Acaulia with AFLPs: implications for ex situ conservation[END_REF]. [START_REF] Virk | The identification of putative duplicate accessions within a rice germplasm collection using RAPD analysis[END_REF] proposed two strategies where putative duplicates were first selected on the basis of the passport data. The first procedure proposed the morphological characterisation followed by molecular characterisation for accessions not distinguished on a morphological basis. In the second procedure, no morphological evaluation was done, but a preliminary molecular analysis was performed with a small number of markers followed, if necessary, by a full molecular study on samples that could not be initially discriminated. Accessions that could not be distinguished after the two analyses were declared as duplicates. Whatever the strategy employed, the crucial question is to determine the threshold required to declare that two accessions are duplicates or not. Some users rely, for this final decision, on a specific number of markers or a combination of informative primers. For example, [START_REF] Virk | The identification of putative duplicate accessions within a rice germplasm collection using RAPD analysis[END_REF] within their rice germplasm collection designated accessions as duplicates if no variation was found across 100 RAPD markers. [START_REF] Negash | AFLP analysis of enset clonal diversity in south and southwestern Ethiopia for conservation[END_REF] declared enset clones, belonging to Musaceae family, as duplicates based on the identity of 104 AFLP fragments generated by four primer pairs. However, looking for the identity of such a set of markers within allogamous plants would be unreasonable. Indeed, due to their reproductive biology, residual heterozygosity exists even in inbred lines, such as hybrid parental lines. Curators are generally not in charge of very advanced cultivars, but of open-pollinated varieties, landraces or wild populations. Therefore, the elaboration of a strategy for the identification of duplicates within allogamous species, including an adapted threshold appears to be of great importance. Carrot [Daucus carota ssp. sativus (Hoffm.) Arcangeli] is an allogamous species. Preliminary studies have shown that a residual heterozygoty exists in cultivars, and depending on the variety, intravarietal dissimilarity values are between 17 and 31% for open-pollinated varieties, around 10% for hybrids and 3-5% for stabilised parental lines (Le Clerc 2001;[START_REF] Clerc | Influence of number and map distribution of AFLP markers on similarity estimates in carrot[END_REF].

Within the context of the European GENRES (Genetic Resources) Carrot project (GENRES CT-99-105) on the management and availability of carrot genetic resources, the partners decided to evaluate molecular markers as a complementary tool to morphological markers for developing a strategy of identification of carrot duplicate accessions [START_REF] Astley | The future of European carrot: a programme to conserve, characterise, evaluate and collect carrot and wild relatives[END_REF]. Taking into account the putative duplicate accessions maintained in the European genebanks, the group of 'Jaune du Doubs' accessions was selected as a model for this analysis.

Materials and methods

Plant material

'Jaune du Doubs' is an old variety with a yellow conical root approximately 18-20 cm in length, and mainly used as a fodder carrot. On the basis of passport data and information provided by curators, accessions with the same name, synonyms and/or yellow rooted forms were selected for the experiment. Twenty-one presumed duplicates of 'Jaune du Doubs' from the European collections were obtained for morphological and molecular analyses. For convenience, accessions were named by a code (Table 1).

Morphological characterisation

In July 2001, two replications of four linear meters per accession were sown in the field with 100 seeds/m. After visual examination of both replications and according to UPOV and IPGRI recommendations, an average score on a 1-9 scale was given to each accession for each morphological character. In late September, three foliar characters (foliage leaf dissection, width crown, anthocyanin in petiole) were scored. In November, 11 root characters such as length, diameter, shoulder shape and pigmentation were scored. All data were compiled with Excel software and registered in the European database (European Carrot/Daucus Inventory-ECDI-available at http://www.hri.ac.uk/ gru/). As a result, accessions were declared morphologically distinguished if, according to the procedure used by the Plant Variety Rights Office, they presented at least one clearly distinctive character.

Molecular analysis

DNA extraction procedure Root slices of previously morphologically characterised accessions were freezedried and ground to powder in a mortar with liquid nitrogen. Extraction followed the protocol described by Briard et al. (2000a).

To investigate the effect of bulk composition on the amplification of rare bands, some extractions and amplifications were done on bulks and compared to individual profiles. Bulks consisted of five individuals of an accession. For this purpose, root powder of five individuals was pooled in equal proportions before extraction. This was repeated and applied to five different accessions.

For each accession, extraction was realised on 4-8 bulks of five individuals to assess the genetic distance within and between accessions.

An additional set of 7 bulks was extracted for the accession 'Ta´borska´Zluta (DAU 110/88)' in order to provide true replicates, named TZA and TZB.

AFLP and ISSR amplification AFLP electrophoresis and silver staining procedures were carried out as described by Briard et al. (2000a). Twelve primer combinations were used for the amplification (Table 2). Polyacrylamide gels were dried overnight at room temperature. To test the AFLP reproducibility of each primer and to allow the comparison of AFLP profiles between gels, 4-5 bulks were systematically reamplified at least twice.

ISSR amplifications were realised with three primers (Table 2) chosen because they generated clear profiles with multiple polymorphic bands on Table 2. Sequence of the three selective nucleotides for the primers Eco/Mse and sequences of the ISSR primers.

Primer

Sequence

P1 AAG/CAG P2 AGG/CTC P3 ACT/CAG P4 ACT/CAA P5 AAG/CTC P7 ACA/CTT P8 AAG/CAA P9 AAG/CTT P14 AGC/CAT P17 AGG/CAT P20 AGG/CTA P21 ACT/CAC ISSR5* VHVCTCTCTCTCTCTCTCT ISSR8us GAACAAACAAACAAACA ISSR9* HVHTCTCTCTCTCTCTCTC *V = G, A, C; H = A, T, C.
numerous carrot accessions (Le Clerc 2001). DNA amplification reactions were performed in a volume of 12.5 ll containing 2.5 ll of diluted DNA (approximately 1 ng/ll), 2 mM of each dNTP (Eurogentec), 2 mM MgCl2 (Perkin Elmer), 0.5 lM of a single primer, 0.75 unit of AmpliTaq DNA polymerase (Perkin Elmer). Amplifications were realised on a MJ research PTC-100 thermocycler using the following program: 5 min at 94 °C, 40 cycles of (30 s at 94 °C, 45 s at 50 °C, 2 min at 72 °C) with a final 7 min extension at 72 °C. Amplification products were electrophoresed on 2% agarose gels for 5 h at 100 V and detected by staining with ethidium bromide.

Gel scoring and data analysis

Only non-ambiguous and polymorphic bands were scored as present (1) or absent (0). Pair-wise genetic distances between the bulks of one accession and between accessions were calculated according to the coefficient of [START_REF] Sokal | A statistical method for evaluating systematic relationships[END_REF]. In addition to double presence, this index also takes into account the double absence of a marker between two individuals as recommended for intraspecific analyses (Briard et al. 2000b). For each accession, the intravarietal distance value (IAD) was obtained from the mean of the distances calculated for each pair of bulks belonging to one accession. The intervarietal distance value (IED) between two accessions was the mean of the distances calculated between all the bulks of one accession and all the bulks of the other accession. IEDm, for one accession, is the mean of its IED values with all the other accessions. A Neighbor joining dendrogram based on similarity coefficients was constructed using the Darwin 4.1 software [START_REF] Perrier | Analyse de la diversite´ge´ne´tique: mesures de dissimilarite´et repre´sentations arbore´es[END_REF]).

To assess the reliability of cultivar identification, the assignment calculator (http://www.biology.ualberta.ca/jbrzusto/alpha/Doh.html) developed by [START_REF] Paetkau | Microsatellite analysis of population structure in Canadian polar bears[END_REF] was used. It allows assigning a bulk to the accession in which it has the greatest possibility of occurrence. The likelihood of the bulk's multilocus genotype occurring in each accession were computed. As explained on the web site, a matrix A was obtained. Each data of the matrix is a measure of how much more likely genotypes of bulks sampled in accession X are in accession X rather than in accession Y.

Results

Based on the morphological characterisation of the minimum descriptors established by the European partners, eight accessions were distinguishable and therefore, it was not necessary to make further investigations with molecular markers to declare them as original material. The other 13 accessions were subjected to the molecular analysis.

Efficiency of bulk sample to assess carrot genetic diversity and assignment calculation

For the five accessions analysed, all the major bands found in each individual profile were also amplified in the bulks of five individuals (Figure 1). Some faint bands present in one individual were sometimes absent from the bulk profile, but they were not taken into account. The amplification profiles obtained on five individual plants and on the bulks of five individuals gave exactly the same results in terms of marker analysis. Reproducibility between the two bulks of the same five individuals was absolute whereas larger bulks were not enough reliable and fail sometimes to amplify all the major bands found in each individual profile.

Figure 1. AFLP profiles obtained on five individuals (lanes 1-5) of the accession Gelbe Lobbericher (GL) and two bulks of the same five individuals (lanes B) after silver staining. Primer pair P20 was used for this analysis.

Estimation of the genetic distances within and between accessions

Three AFLP primer pairs (P7, P8 and P17) did not give sufficiently reliable polymorphic markers and were discarded. With nine primer pairs, 75 polymorphic markers were generated. The three ISSR primers revealed a very poor polymorphism (1 or 2 polymorphic markers per primer).

The intravarietal distance values, varied from 10 to 31%, whereas the intervarietal distance values ranged from 12 to 55% (Table 3). For each accession, distance was lower within the accession than between accessions except for TZB -the IED distance between TZA and TZB was 12%, whereas the IAD distance of TZB was 15%.

Mean genetic distances, IEDm, varied from 37% for the accessions GW and WB to 50% for the accession Z.

On the dendrogram (Figure 2), bulks of the accessions TZA and TZB, which were representing true duplicates, clustered in a single group. All the bulks of one accession clustered in one separate group except for five accessions. Accessions JOD, WB and LGS presented one bulk separated from the others, whereas accessions LOB and JL were dispersed, presenting bulks on different clusters.

The likelihood values computed for each accession with the assignment calculator were comprised between 31.01 and À0.82. (Table 4). The accessions TZ and Z presented the highest values whereas the lowest value was observed between JD and LGS (2.99). Finally, TZA bulks have no more chance to belong to TZA than to TZB and reciprocally for TZB. LGS 10.89 7.17 6.74 8.81 15.81 23.49 9.76 5.02 26.11 30.34 5.28 9.85 8.83 JOD 7.88 3.82 3.17 5.41 13.84 20.03 7.78 4.07 20.32 22.95 3.06 6.20 5.72 JL 5.46 8.16 5.43 7.50 6.84 14.12 7.72 9.28 15.97 18.56 7.89 5.96 5.94 LOB 11.06 7.51 4.63 11.35 9.55 19.47 6.55 9.47 15.27 17.25 7.42 6.22 6.75 Each value is a measure of how much more likely genotypes of bulks sampled in accession X are in accession X rather than in accession Y.

Discussion

Several molecular techniques have been used successfully to analyse carrot species variability [START_REF] Grzebelus | The use of RAPD markers for genotype identification of carrot lines and F1 hybrids[END_REF][START_REF] Grzebelus | Comparison of RAPD and AFLP techniques used for the evaluation of genetic diversity of carrot breeding materials[END_REF][START_REF] Shim | Genetic structure in cultivated and wild carrots (Daucus carota L.) revealed by AFLP analysis[END_REF]. According to our previous studies, AFLP and ISSR appear to be the most appropriate techniques for studying carrot. On average, these techniques have generated 9 and 15 polymorphic markers per primer or primer combination, respectively (Le [START_REF] Clerc | Carrot genetic substructure evaluation: comparison of the efficiency of mapped molecular markers and randomly chosen markers[END_REF][START_REF] Clerc | Influence of number and map distribution of AFLP markers on similarity estimates in carrot[END_REF][START_REF] Briard | A comparative study on the use of ISSR, Microsatellites and RAPD markers for varietal identification of carrot genotypes[END_REF]). In the present study, the very low number of markers detected with the ISSR technique and the relatively low number of AFLP markers per combination suggested that the material was genetically closely related.

Efficiency of bulk sample to assess carrot genetic diversity

Usefulness of DNA bulks to evaluate the extent and distribution of genetic diversity in species was already tested [START_REF] Dubreuil | Evaluation of DNA pooled sampling strategy for estimating the RFLP diversity of maize populations[END_REF][START_REF] Gilbert | Developing an appropriate strategy to assess genetic variability in plant germplasm collections[END_REF][START_REF] Van Treuren | Efficiency of reduced primer selectivity and bulked DNA analysis for the rapid detection of AFLP polymorphisms in a range of crop species[END_REF]. The main question, when using bulks for such analyses, concerns the representation of those bulks versus individuals and therefore, the optimal bulk size. As highlighted by [START_REF] Gilbert | Developing an appropriate strategy to assess genetic variability in plant germplasm collections[END_REF] and [START_REF] Van Treuren | Efficiency of reduced primer selectivity and bulked DNA analysis for the rapid detection of AFLP polymorphisms in a range of crop species[END_REF], some bands present in few individuals of large bulks might not always be amplified in the pool sample leading to a bias in the estimation of genetic similarity. However, as suggested by del [START_REF] Rio | RAPD markers efficiently distinguish heterogenous populations of wild potato (Solanum)[END_REF], using large bulks is not inevitably a problem, on the contrary, it might be a way to minimise sampling error. Indeed, only significant differences between accessions based on differences in major bands would be taken into account [START_REF] Bamberg | Comparison of reputed duplicate populations in the Russian and US potato genebanks using RAPD markers[END_REF]). In the present analysis, we proposed to base the identification of redundant accessions on the comparison of genetic distances within and between accessions. Therefore, the use of large bulks with 20 individuals or more was not justified. Moreover, in a previous study, we tested different sizes of bulk ranging from 5 to 20 individuals (data not published). The bulks of five individuals seemed fully representative of all the individuals constituting the DNA bulks, which was not the case for the bulks with more individuals. The present analysis of the five individual bulks of five accessions confirmed the reliability of this bulk size. All the rare markers, present in only one of the constitutive individuals, were efficiently represented in the bulks.

Working on Lupin, [START_REF] Gilbert | Developing an appropriate strategy to assess genetic variability in plant germplasm collections[END_REF] concluded that 2-3 bulks of five genotypes should be enough to assess the genetic distances within and between accessions. For carrot, we showed in a previous study (results to be published) that the optimal number of individuals to analyse per accession depends on the level of genetic homogeneity, ranging from 5 to 35 individuals for, respectively, the identification of inbred lines to heterogeneous populations. Therefore, in the present study, investigating OP varieties (see sample status in Table 1), we decided, when possible, to analyse seven bulks of five individuals in order to reach 35 individuals per accession.

To assess genetic variability among Lupin accessions, [START_REF] Gilbert | Developing an appropriate strategy to assess genetic variability in plant germplasm collections[END_REF] used 2-3 pools of five genotypes by pooling DNA, i.e. DNA extractions were done on 10-15 individuals. In our case, plant material was pooled prior to DNA extraction reducing the number of extractions to seven per accession. This method limits cost: we performed a total of 80 DNA extractions and AFLP analyses instead of 400.

Estimation of genetic distances within and between accessions

In previous studies, to clearly assess genetic distances between accessions, we relied on a precise evaluation of genetic distance within accessions [START_REF] Briard | A comparative study on the use of ISSR, Microsatellites and RAPD markers for varietal identification of carrot genotypes[END_REF][START_REF] Clerc | Influence of number and map distribution of AFLP markers on similarity estimates in carrot[END_REF]. The more precise the analysis of each accession, the better the genetic distance estimation between them. Therefore, to determine an adapted threshold for the identification of carrot duplicates, we relied on the comparison between intravarietal and intervarietal genetic distances. We previously showed that 70 AFLP markers were sufficient to clearly identify related carrot accessions (Le [START_REF] Clerc | Influence of number and map distribution of AFLP markers on similarity estimates in carrot[END_REF]. Therefore, when using 9 AFLP primer combinations, which resulted in 75 markers to score, we reached optimal experimental requirements.

The true duplicates TZA and TZB presented the lowest intravarietal genetic distances with 10 and 15%, respectively and therefore were the most homogeneous samples. Intervarietal genetic distance between them (12%) was slightly lower than the TZB intravarietal genetic distance and, on the dendrogram, the bulks of the two replicates clustered together in one group. With the exception of these true duplicates that could not be distinguished, most of the other accessions were clearly identified presenting intravarietal values higher than intervarietal values. On the dendrogram, those accessions were clearly discriminated without ambiguity, the bulks of one accession being grouped together. Even if the accessions WB and JOD presented one bulk separated from the others, they were clearly differentiated from the other accessions. It could be explained by the possible presence of one off-type root (a root which is not characteristic to the accession's root type) in the isolated bulk. Accessions JL and LOB, which presented the highest intravarietal genetic distances (30 and 31%, respectively), were scattered among different clusters. In this case, we could question ourselves about the opportunity to conserve such heterogeneous accessions, probably originating from a mix of different accessions.

Finally one LGS bulk is on a common branch with one JD bulk. Even if the other bulks of these two accessions are not mixed together and the IAD values are smaller than the IED values, it probably indicates some degree of genetic relationship between the two accessions. It could be interesting to analyse separately the five individuals of the two related bulks in order to determine if all the individuals are related or if it is due to only one plant coming from the other accession. Such an experiment would answer the question, is it a real relationship or pollinic pollution?

To confirm that our relatively simple procedure of comparison between IAD and IED is reliable, we used a statistical test based on assignment calculations. This assignment test was already successfully used in several population studies [START_REF] Lougheed | A comparison of RAPD versus microsatellite DNA markers in population studies of the Massasauga Rattlesnake[END_REF][START_REF] Hansen | Assigning individual fish to populations using microsatellite DNA markers[END_REF]. [START_REF] Kubik | Genetic diversity in seven Perennial Ryegrass (Lolium perenne L.) cultivars based on SSR markers[END_REF] were able to distinguish seven perennial ryegrass cultivars by correctly assigning 210 individuals to their cultivar of origin. This method assumes Hardy-Weinberg equilibrium, no linkage disequilibrium among loci, and depends on the number of loci and genotypes sampled per cultivar. In the present case, accuracy is probably not optimal due to the low number of bulks sampled per cultivar. However, it confirms the fact that no accessions were duplicates except true duplicates and that JD and LGS accessions were probably relatively close to each other.

In conclusion, even with morphologically related material, we were able to declare that the 'Jaune du Doubs' accessions were not duplicates. Therefore, it seems reasonable to think that those root types, which are morphologically but not genetically identical, are probably resulting from a phenotypical convergence created by a selection pressure on the same root characters. Moreover, with this molecular approach, we highlighted the existence of original genetic material such as the accessions TZ and Z, originating from Russia and Persia, respectively. The morphological and the molecular approaches work as complementary tools. According to these results, we are now able to propose a general strategy for the identification of carrot duplicates. After morphological characterisation, if some accessions are still considered as putative duplicates, they should be submitted to molecular analysis as follows. Seven bulks of each accession should be analysed with at least 70 AFLP markers, with accessions declared as duplicates when one of their intravarietal genetic distances is higher than their intervarietal genetic distance. It is important to notice that there is no one absolute threshold because it will depend on the data set analysed.

Despite these convincing results, one could question the validity of a molecular approach, especially when working with small collections. It could seem more reasonable for the curator to stock a few grams of each accession, even if it means keeping all the accessions, rather than starting expensive molecular analysis. This argument could be true for orthodox seeds, whereas it should be reconsidered for recalcitrant seeds, for which conservation is much more expensive. Considerations about costs of regeneration and evaluation should also be taken into account. Indeed, regeneration is expensive, especially for allogamous species, which require a high number of plants under insect-proof cages. An evaluation such as the quantification of a chemical compound by HPLC is also more expensive and tedious than a molecular analysis. Therefore, even if the identification of duplicate accessions via molecular analysis does not lead to reduction in size of germplasm collections (if it is not expensive, duplicates may be kept as safety resources), it could help curators to give priorities for the regeneration or evaluation of unique material.

Table 1 .

 1 List of the 21 accessions analysed in the present study.

	Accession name	Institute code	Accession	Sample	Code	Number of
			number	status		bulk analysed
	Jaune du Doubs	FRAINH	313	5	JD	4
	Jaune obtuse du Doubs	GBRHRIGRU 9053	5	JOD	4
	Lopee	GBRHRIGRU 11289	5	L	5
	Long red	GBRHRIGRU 10246	3	LR	5
	Lobbericher	DEUGAT	K 8172/96	-	LOB	6
	Gelbe Wortel	GBRHRIGRU 11146	5	GW	6
	Ta´borska´Zluta	DEUGAT	DAU 110/88 -	TZA/TZB 7
	White belgian fodder carrot GBRHRIGRU 8112	5	WB	7
	Gelbe Lobbericher	GBRHRIGRU 3922	5	GL	7
	Lange gele stoppel	GBRHRIGRU 11286	5	LGS	7
	Fance	GBRHRIGRU 10235	3	F	7
	Jaune de Lobberidr	FRAINH	312	3	JL	7
	Zahedan	GBRHRIGRU 4012	5	Z	8
	D. carota subsp sativus	DEUGAT	DAU211/85 -	*
	Santene Skvirskaja	DEUGAT	DAU 74/97 -	*
	Juared	GBRHRIGRU 8140	5	*
	Cape Market	GBRHRIGRU 10301	5	*
	Fiumicino	GBRHRIGRU 6042	5	*
	Lennox	GBRHRIGRU 6527	5	*
	Yellow carrot No. 12	GBRHRIGRU 10524	-	*
	Jaune obtuse du Doubs	FRAINH	77	-	*

*Not retained for molecular analysis. Sample status: 3 = traditional cultivar/landrace; 5 = advanced cultivar OP; -= unknown.

Table 3 .

 3 Intravarietal distances (IAD, in grey), intervarietal distances (IED) and mean intervarietal distances (IEDm) calculated according to the Sokal and Michener coefficient. .45 24.96 26.70 7.86 7.21 10.68 12.47 F 8.96 15.03 9.95 14.38 14.61 13.44 14.26 21.99 24.14 14.14 13.24 8.41 9.91 Z 20.27 20.17 21.00 22.90 14.86 23.83 23.15 26.95 29.21 23.36 19.61 14.70 19.49 GL 14.16 8.93 6.88 16.78 13.27 24.17 9.36 19.53 22.37 9.10 10.19 10.20 7.87 JD 12.64 6.35 3.43 7.01 16.24 25.87 8.41 25.75 27.73 2.99 5.06 11.92 10.12 TZA 25.52 21.17 22.05 24.15 22.36 27.82 18.98 23.86 À0.82 26.75 20.73 17.19 15.65 TZB 29.04 23.99 23.73 26.11 25.03 29.98 21.87 26.24 0.79 29.93 23.18 20.33 18.08

		F GL GW JD JL JOD L LGS LOB LR TZA TZB WB Z IEDm
	F	2 5							43
	GL	41 22							39
	GW 43 33 20							37
	JD	45 35 30	20						39
	JL	40 36 36	40 30						40
	JOD 45 37 30	30 39 25						38
	L	4 3 4 4 3 4	3 1 4 2 3 3	2 0					4 0
	LGS 43 35 31	28 37 31	33 23					39
	LOB 39 39 39	42 34 38	39 39	31				40
	LR	36 40 37	39 40 36	34 36	36	19			40
	TZA 49 43 45	51 42 48	49 53	46	52 10			45
	TZB 50 44 45	52 43 49	50 53	46	52 12	15		46
	WB 39 33 30	30 35 32	35 33	37	33 48	49	27	37
	Z	43 52 47	55 51 52	52 51	45	48 52	53	51	24 50

Figure 2. Dendrogram of 13 carrot accessions (described in

Table 1) analysed with 75 AFLP markers and based on Neighbor Joining cluster analysis of Sokal and Michener's similarity matrix. Table 4. Matrix A computed with the assignment calculator. LR GW WB L F Z GL JD TZA TZB LGS JOD JL LOB LR 12.83 7.10 10.08 10.59 21.54 15.05 13.76 27.30 31.01 10.90 10.11 8.01 12.44 GW 13.38 5.24 9.89 16.55 21.20 9.10 7.35 21.45 24.55 6.74 6.63 10.87 9.01 WB 6.96 4.08 7.85 10.29 20.37 5.96 4.11 22.16 23.46 5.49 4.41 7.21 5.11 L 10.13 9.49 8.18 15.22 23.55 16.13 7

Acknowledgements

The authors thank all the European GENRES partners for providing seeds and particularly Dave Astley for revising the manuscript. This work was funded by the European Commission in the context of the 4 year CEC GENRES 105 carrot project (GENRES CT99-105).