Yulia Arinicheva
email: y.arinicheva@fz-juelich.de

Clémence Gausse

Stefan Neumeier

Felix Brandt

Konstantin Rozov

Stephanie Szenknect

Nicolas Dacheux

Dirk Bosbach

Guido Deissmann

Clemence Gausse

Stéphanie Szenknect

Influence of temperature on the dissolution kinetics of synthetic LaPO4-monazite in acidic media between 50 and 130 °C

Keywords: monazite, nuclear waste form, dissolution kinetics, temperature dependence

établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Disposal of high-level radioactive wastes in deep geological repositories in stable geological formations is generally considered as the safest and most sustainable solution for the management of these wastes, providing for a high-level of passive post-closure safety (IAEA, 2004; Council of the European Union, 2011; [START_REF] Ahn | Geological repository systems for safe disposal of spent nuclear fuels and radioactive waste[END_REF]. The long-term containment and isolation of the wastes from the biosphere is generally ensured by a complementary and redundant system of engineered barriers including waste forms, waste containers, and backfill materials, in combination with a suitable repository host rock acting as geological barrier. In geological disposal facilities in crystalline or clay rocks the waste packages are generally expected to come into contact with groundwater in the long term, after resaturation of the repository. Even in repositories in salt rocks, the presence of water cannot be completely ruled out for less probable scenarios, for example, an early failure of shaft seals and plugs. After failure of the waste containers due to aqueous corrosion, radionuclides can be released from the degrading waste forms into the near-field water and subsequently migrate into the geo-/biosphere via the water pathway.

Thus insight into the aqueous durability of nuclear waste forms and the radionuclide source term are essential prerequisites for the long-term safety assessment of an underground repository, requiring a mechanistic understanding of the dissolution processes. The long-term performance of the waste forms in a deep geological repository and their aqueous durability are controlled to a varying degree by thermodynamics and reaction kinetics and can be affected by the near-field hydro-(geo)chemistry and the hydrodynamic regime. Geochemical conditions affecting waste form durability comprise in particular pH and redox conditions as well as ionic strength and composition of the near-field water as well as the temperature at the time of canister failure.

The dissolution rates of minerals or waste forms are often described by empirical formulations based on Transition State Theory (TST) and considering contributions from different factors. According to TST the dissolution rate r of a phase i can be written in simplified form as:

(1),

where k 0 is an intrinsic rate constant, A s is the reactive surface area, E a is the apparent activation energy of dissolution, RT is the product of the gas constant and the absolute temperature, a(H + ) n is the hydronium ion activity in solution with the reaction order n, the product term comprises the activity and reaction order of all ions in solution catalysing or inhibiting the dissolution reaction and f(G r ) describes the deviation from thermodynamic equilibrium (e.g. [START_REF] Lasaga | Fundamental approaches in describing mineral dissolution and precipitation rates[END_REF].

For several decades, a number of polyphase ceramics (e.g. SYNROC) and single-phase ceramic matrices have intensively been discussed as potential waste forms for the disposition of special actinide bearing nuclear waste streams, such as separated plutonium from civilian sources unsuitable for further use, surplus weapons plutonium, or minor actinides (MA: Np, Am, Cm) separated in advanced partitioning schemes (e.g. [START_REF] Ringwood | Immobilisation of high level nuclear reactor wastes in SYNROC[END_REF][START_REF] Donald | Review: the immobilisation of high level radioactive wastes using glasses and ceramics[END_REF][START_REF] Ewing | Ceramic matrices for plutonium disposition[END_REF][START_REF] Ewing | Ceramic matrices for plutonium disposition[END_REF][START_REF] Ewing | Actinides and radiation effects: impact on the back-end of the nuclear fuel cycle[END_REF][START_REF] Lumpkin | Ceramic waste forms for actinides[END_REF][START_REF] Weber | Materials science of high-level nuclear waste immobilization[END_REF][START_REF] Deissmann | Durability of potential plutonium wasteforms under repository conditions[END_REF][START_REF] Donald | Waste immobilization in glass and ceramic based hosts: Radioactive, toxic and hazardous Wastes[END_REF]. Besides ceramics based on zircon (ZrSiO 4 ) or zirconia (ZrO 2 ), titanate-and/or zirconate-based oxides (e.g. with zirconolite (CaZrTi 2 O 7 ) or pyrochlore (Ln 2 (Ti,Zr,Hf) 2 O 7 ) structure), various phosphate-based materials, such as Ln-orthophosphates (LnPO 4 ) with monazite or xenotime structure, thorium-phosphate-diphosphates (Th 4 (PO 4 ) 4 P 2 O 7 ), or britholites ((Ca,Ln) 5 ((PO 4 ),(SiO 4 )) 3 (OH,F)) have been extensively discussed for this purpose [START_REF] Boatner | Monazite[END_REF][START_REF] Ewing | Phosphates as nuclear waste forms[END_REF][START_REF] Dacheux | Immobilisation of actinides in phosphate matrices[END_REF]Terra et al., 2006a,b;[START_REF] Bregiroux | Solid-state synthesis of monazite-type compounds containing tetravalent elements[END_REF][START_REF] Oelkers | Phosphates and nuclear waste storage[END_REF][START_REF] Terra | Preparation of optimized uranium and thorium bearing brabantite or monazite/brabantite solid solutions[END_REF][START_REF] Vance | Actinide valences in xenotime and monazite[END_REF][START_REF] Mesbah | Incorporation of thorium in the zircon structure type through the Th 1-x Er x (SiO 4 ) 1-x (PO 4 ) x thorite-xenotime solid solution[END_REF]Neumeier et al., 2017a;[START_REF] Schlenz | Phosphates as safe containers for radionuclides[END_REF]. In particular phosphate ceramics with monazite structure (LnPO 4 , Ln = La to Gd) are deemed as promising waste matrices for actinide immobilisation, due to their outstanding properties, such as structural flexibility for actinide incorporation, high resilience against radiation-induced amorphisation, and high chemical durability [START_REF] Boatner | Monazite[END_REF][START_REF] Ewing | Phosphates as nuclear waste forms[END_REF][START_REF] Oelkers | Phosphates and nuclear waste storage[END_REF][START_REF] Clavier | Crystal chemistry of the monazite structure[END_REF][START_REF] Dacheux | Versatile monazite: resolving geological records and solving challenges in materials science. Monazite as a promising long-term radioactive waste matrix: benefits of high-structural flexibility and chemical durability[END_REF][START_REF] Schlenz | Monazite as a suitable actinide waste form[END_REF]Neumeier et al., 2017a). Ln-orthophosphates with monazite structure are monoclinic (space group P2 1 /n, Z = 4), consisting of chains of alternating and edge-sharing PO 4 tetrahedra and LnO 9 polyhedra that are aligned parallel to the c-axis [START_REF] Ni | Crystal chemistry of the monazite and xenotime structure[END_REF][START_REF] Boatner | Synthesis, structure and properties of monazite, pretulite and xenotime[END_REF]. Due to the rather large and irregular LnO 9 polyhedra exhibiting differing Ln-O bond-lengths, monazites can easily incorporate a large variety of cations including actinides [START_REF] Clavier | Crystal chemistry of the monazite structure[END_REF].

Several studies were carried out on the dissolution kinetics of natural monazite [START_REF] Oelkers | An experimental study of the dissolution stoichiometry and rates of a natural monazite as a function of temperature from 50 to 230 o C and pH from 1.5 to 10[END_REF] or synthetic lanthanide orthophosphates with monazite structure [START_REF] Terra | Preparation and characterization of lanthanum-gadolinium monazites as ceramics for radioactive waste storage[END_REF][START_REF] Brandt | Conditioning of minor actinides in lanthanum monazite ceramics: A surrogate study with Europium[END_REF][START_REF] Teng | Hot-pressure sintering, microstructure and chemical durability of Ce 0.5 Eu 0.5 PO 4 monazite ceramics[END_REF][START_REF] Arinicheva | Dissolution kinetics of synthetic LaPO 4 -monazite in acidic media[END_REF]. These investigations revealed that the steady state dissolution rates of monazite-type materials are several orders of magnitude lower compared to borosilicate glasses at corresponding conditions [START_REF] Weber | Materials science of high-level nuclear waste immobilization[END_REF]). However, so far only few studies were dedicated to the temperature dependence of the dissolution kinetics of monazite-type materials. [START_REF] Oelkers | An experimental study of the dissolution stoichiometry and rates of a natural monazite as a function of temperature from 50 to 230 o C and pH from 1.5 to 10[END_REF] studied the dissolution kinetics of natural monazite from Manangotry, Madagascar, as a function of temperature from 50 to 230°C at pH 2. [START_REF] Terra | Preparation and characterization of lanthanum-gadolinium monazites as ceramics for radioactive waste storage[END_REF] determined the apparent activation energy of the dissolution of synthetic GdPO 4 with monazite structure from the normalised dissolution rates measured at room temperature and 90°C under more acidic conditions (pH = 1). The dissolution rates of monazite as function of pH follow a trend common for many minerals, with a minimum at near neutral pH, and increasing both with decreasing pH under acidic conditions, and with increasing pH at basic conditions (e.g. [START_REF] Oelkers | An experimental study of the dissolution stoichiometry and rates of a natural monazite as a function of temperature from 50 to 230 o C and pH from 1.5 to 10[END_REF]). Therefore, the dissolution rates, determined in acidic media to reach elemental concentrations in solution above the detection limit of available analytical techniques to obtain measurable rates, can then be extrapolated to near neutral conditions, characteristic for a given nuclear repository.. [START_REF] Gausse | Determination of the solubility of rhabdophanes[END_REF] demonstrated that in aqueous environments at temperatures below about 90°C, the hydrous Ln-orthophosphate rhabdophane (LnPO 4 •0.667H 2 O) is more stable than the corresponding monazite-type phase. Therefore it is presumed that rhabdophane could occur as a potential neo-formed phase on the surface of monazite waste forms in contact with groundwater in a repository after failure of the waste container, potentially controlling also the release of actinide elements from the waste form (cf. du Fou de [START_REF] Du Fou De Kerdaniel | Actinide solubility-controlling phases during the dissolution of phosphate ceramics[END_REF][START_REF] Mesbah | Monoclinic form of the rhabdophane compounds[END_REF]2017;[START_REF] Gausse | Determination of the solubility of rhabdophanes[END_REF]Neumeier et al., 2017a[START_REF] Arinicheva | Dissolution kinetics of synthetic LaPO 4 -monazite in acidic media[END_REF]).

Therefore we systematically studied the dissolution kinetics of LaPO 4 with the monazite structure in dynamic dissolution experiments at far from equilibrium conditions in the temperature range between 50 and 130°C in 0.01M HNO 3 to gain a deeper insight into the mechanism governing the dissolution process within the stability fields of the two different La-orthophosphate phases. The relation between the stability of La-monazite and the potentially neoformed La-rhabdophane in the dissolution experiments was investigated within the present work in the temperature range of interest by thermodynamic modelling using the Gibbs energy minimisation (GEM) approach. The aim of the present study was to quantify the temperature dependency of the dissolution rates of La-monazite and gain insight into the mechanisms governing the dissolution process within the stability fields of the different Lnorthophosphate phases.

Materials and methods

Sample preparation

LaPO 4 precursor powders were prepared hydrothermally using a slight modification of the methods described by [START_REF] Messamy | Wet-chemical synthesis of doped colloidal nanomaterials particles and fibers of LaPO 4 :Eu, LaPO 4 :Ce, and LaPO 4 :Ce[END_REF] and [START_REF] Gausse | Determination of the solubility of rhabdophanes[END_REF]. A 3M La-nitrate solution was prepared by dissolving La(NO 3 ) 3 •6H 2 O (99.99%, Alfa Aesar, p.a.) in deionised water.

Subsequently a H 3 PO 4 solution (14.6M, Merck, p.a.) was added. This reaction mixture was transferred into Teflon beakers that were placed in a stainless steel autoclave (Parr Instruments) and hydrothermally treated at 200±2°C for 2 h. The synthesised powders were washed several times with deionised water, dried at 90°C, and calcined at 600°C for 2 h to remove water of crystallisation. After grinding in an agate mortar, the calcined powders were pelletised by uniaxial pressing at 445 MPa pressure and sintered at 1450°C for 5 h. The pellets were coarsely crushed and sieved in order to obtain the particle size fraction of 100 to 180 μm. These powders were additionally washed several times with deionised water in an ultrasound bath to remove finer particles from the materials surface.

Sample characterisation

The density of the sintered pellets was measured using Archimedes principle with water as immersion liquid at ambient temperature. The specific surface area of the powder samples of the particle size fraction 100 to 180 μm was determined via 5-point N 2 -BET measurements using a Quantachrome Autosorb instrument. The crystal structure of the samples was confirmed by powder X-ray diffraction using a Bruker D4 Endeavor with a θ-2θ-geometry configured with a Cu-K α target (λ = 1.54184 Å) and set to a power level of 50 kV and 30 mA.

In addition, the microstructure of the samples and phase purity/composition were studied by scanning electron microscopy (SEM) using a FEI Quanta 200 FEG scanning electron microscope equipped with Genesis energy dispersive X-ray spectroscopy (EDS) system. The SEM measurements were carried out in a low-vacuum mode at 0.4 to 0.6 mbar using acceleration potentials ranging between 7 and 20 kV.

Dissolution experiments

Dynamic dissolution experiments were performed using two different experimental setups depending on the temperature conditions. A single pass flow through (SPFT) experimental set-up adapted from [START_REF] Dacheux | Kinetics of dissolution of thorium and uranium doped britholite ceramics[END_REF] and [START_REF] Neeway | Dissolution mechanism of the SON68 reference nuclear waste glass: New data in dynamic system in silica saturation conditions[END_REF], and used in recent studies by [START_REF] Brandt | Conditioning of minor actinides in lanthanum monazite ceramics: A surrogate study with Europium[END_REF] was used for dissolution tests at 50, 60, and 80°C, respectively.

The setup consists of a perfluoroalkoxy polymer (PFA) reactor (Savillex) with a total volume of 50 mL placed inside a thermostatic oil bath, and a peristaltic pump, passing the inlet solution through the reactor. All experiments were carried out using 0.01M HNO 3 (Merck, Suprapur ® ) and employing 0.8 g of monazite powder. A flow rate between 0.18 and 0.7 mL min -1 was set and monitored by weighing the outflowing solution mass before sampling. The outlet solution was sampled regularly. Samples of the outlet solution were filtered using Anatop 25 plus filters with a pore size of 0.02 mm. To avoid sorption effects, the filters were saturated with outlet solution before sampling. The samples were acidified by adding 1 vol% HNO 3 (14.3 M, Merck, Suprapur ® ). The La-concentrations in the filtered and acidified samples were determined by ICP-MS using an ICP-MS ELAN 6100 DRC (PerkinElmer SCISX) instrument.

Moreover, experiments to temperatures up to 130°C were conducted in a hydrothermal mixed flow setup using a reactor system similar to the one used by [START_REF] Oelkers | An experimental study of the dissolution stoichiometry and rates of a natural monazite as a function of temperature from 50 to 230 o C and pH from 1.5 to 10[END_REF] and described in detail by [START_REF] Finkeldei | Dissolution of ZrO 2 based pyrochlores in the acid pH range: A macroscopic and electron microscopy study[END_REF]. The experimental setup consisted of a pressurised titanium reactor (Parr Instruments) with a total volume of 50 mL, equipped with a pressure gauge, an externally driven stirring system and a thermocouple. The acidic inlet solution was passed into the reactor by a high pressure liquid chromatography pump. The outflow of the reactor was regulated by a computer controlled pressure valve and was filtered through a Ti-cylinder frit with a pore size of 2 µm and an in-line Ti-filter with 0.5 µm pore size to avoid the loss of fines. At the start of a dissolution experiment, about 0.8 g of the LaPO 4 powder and 35 mL of 0.01 N HNO 3 (Merck) were placed into the reactor, which was pressurised with He and heated up to the desired temperature. During the experiment the reactor was continuously stirred at a low stirring rate of 100 rpm. The pressure was kept constant by pumping fresh solution into the reactor at pump rates of 0.5 to 0.6 mL min -1 and continuously releasing solution through the pressure valve. Samples were taken, filtered and analysed in the same way as for the experiments in the SPFT experimental setup with the PFA reactors.

Normalised steady state monazite dissolution rates (rmon) were calculated from the outlet solution concentrations of La (C (La) ) using the following equation:

(2), where F equals the fluid flow rate, (La) is the stoichiometric factor representing the mass fraction of La in LaPO 4 , and AS represents the total surface area of the powder present in the reactor at the start of the experiment.

Thermodynamic modelling

The preferential stability of anhydrous and hydrated La-orthophosphate phases in the temperature range from 25 to 95°C was addressed using a thermodynamic modelling approach to support the interpretation of the dissolution experiments. The modelling was performed using the GEM-Selektor software ver. 3.3. (Kulik et al., 2012). In GEM-Selektor, the phase equilibrium is found via direct minimisation of the total Gibbs energy of the system defined by its bulk elemental composition, temperature, pressure and standard Gibbs energy per mole of all chemical species. The chemical thermodynamic database implemented in GEM-Selektor based on SUPCRT92 [START_REF] Johnson | SUPCRT92: A software package for calculating the standard molal thermodynamic properties of minerals, gases, aqueous species, and reactions from 1 to 5000 bar and 0 to 1000[END_REF]) and the PSI/NAGRA Chemical Thermodynamic Database 12/07 [START_REF] Thoenen | The PSI/Nagra Chemical Thermodynamic Database 12/07[END_REF] was extended to include data for the relevant solid phases (cf. Table 1). Thermodynamic properties of LaPO 4 -monazite were taken from [START_REF] Tardy | Relationships among Gibbs free energies and enthalpies of formation of phosphates, oxides and aqueous ions[END_REF], [START_REF] Popa | High-temperature heat capacities of EuPO 4 and SmPO 4 synthetic monazites[END_REF] and Neumeier et al. (2017b), respectively, and added to the GEM thermodynamic database; for La-rhabdophane [START_REF] Gausse | Determination of the solubility of rhabdophanes[END_REF] were employed. For the thermodynamic modelling an input recipe reflecting the experimental conditions in the dissolution experiments was used by adding 20 g La-monazite to 1 kg 0.01 molar HNO 3 solution (i.e. solid to liquid ratio 1:50). Both La-rhabdophane and La-monazite were specified as possible stable phases under these conditions.

(LaPO 4 •0.667H 2 O) data from

Table 1

Thermodynamic data for La-monazite (LaPO 4 ) and La-rhabdophane (LaPO 4 •0.667H 2 O) used for GEMS modelling. Coefficients a, b and c refer to the polynomial coefficients describing the temperature dependence of the heat-capacity C p according to C [START_REF] Tardy | Relationships among Gibbs free energies and enthalpies of formation of phosphates, oxides and aqueous ions[END_REF] and [START_REF] Popa | High-temperature heat capacities of EuPO 4 and SmPO 4 synthetic monazites[END_REF]

p = a + b•10 -3 T -c•10 -6 T -2 . ΔG f ° (kJ mol -1 ) ΔH f ° (kJ mol -1 ) S° (J mol -1 K -1 ) a b•10 3 c•10

Results and discussion

Sample characterisation

The X-ray diffraction (XRD) pattern of the synthesised and sintered LaPO 4 powder is depicted in Fig. 1. According to XRD, single-phase LaPO 4 -monazite of high crystallinity was obtained after the sintering step. The EDX analyses performed on sintered pellets revealed that, within the error of the applied analytical method, the synthesised La-monazite is

Dissolution kinetics

The La-concentrations obtained in the dynamic dissolution experiments at temperatures between 50 and 130°C are provided in Tables S1 andS2 in the supplemental information. In particular in experiments performed at temperatures below 90°C, the dissolution experiments followed the typical trend of dynamic dissolution experiments as frequently described in the literature (e.g. Oelkers andPoitrasson, 2002, Brandt et al., 2003;[START_REF] Horlait | Multiparametric study of Th 1-x Ln x O 2-x/2 mixed oxides dissolution in nitric acid media[END_REF][START_REF] Finkeldei | Synthesis and dissolution kinetics of zirconia based ceramics[END_REF]2014). In the initial stages of the experiments, higher dissolution rates were observed that decrease with time until a steady state, i.e. a constant rate with time, was reached. Steady state dissolution rates were approached within one week for all temperatures. The higher initial dissolution rates are generally thought to be due to dissolution of fine particles adhering to the materials surface and/or dissolution at highly reactive surface sites created during the crushing of the pellets (e.g. [START_REF] Chou | Study of weathering of albite at room-temperature and pressure with a fluidized-bed reactor[END_REF][START_REF] Knauss | Muscovite dissolution kinetics as a function of pH and time at 70°C[END_REF][START_REF] Wehrli | Monte Carlo simulations of surface morphologies during mineral dissolution[END_REF][START_REF] Casey | Leaching of mineral and glass surfaces during dissolution[END_REF][START_REF] Oelkers | An experimental study of the dissolution stoichiometry and rates of a natural monazite as a function of temperature from 50 to 230 o C and pH from 1.5 to 10[END_REF][START_REF] Horlait | Multiparametric study of Th 1-x Ln x O 2-x/2 mixed oxides dissolution in nitric acid media[END_REF]. An alternative explanation for the enhanced initial dissolution rates proposed by [START_REF] Luettge | A stochastic treatment of crystal dissolution kinetics[END_REF] is related to changes of the dominating dissolution mechanism e.g., from dissolution at grain boundaries to the dissolution on steps, kinks and etch pits on grain surfaces.

The steady state dissolution rates of the LaPO 4 monazite powders are summarised in Table 2. Within the temperature interval from 50 to 130°C, the normalised dissolution rates increased by roughly one order of magnitude from 3.210 -5 to 2.510 -4 g•m -2 •d -1 . The dissolution rates obtained using the two different experimental setups at the same temperatures are in a good agreement.

Table 2

Normalised dissolution rates of LaPO 4 in 0.01M HNO 3 at different temperatures using two

different experimental setups. T r mon (g•m -2 •d -1 ) r mon (g•m -2 •d -1 ) °C
PFA-reactor / SPFT Ti-reactor / mixed flow 50 3.2010 -5 ± 210 -7 60 4.6010 -5 ± 310 -7 3.610 -5 ± 310 -6 80 8.510 -5 ± 910 -6 1.20010 -4 ± 210 -7 90 1.810 -4 ± 510 -5 a 2.2010 -4 ± 410 -6 110 2.010 -4 ± 210 -5 130 2.510 -4 ± 110 -5 a data from [START_REF] Brandt | Conditioning of minor actinides in lanthanum monazite ceramics: A surrogate study with Europium[END_REF] The normalised dissolution rates of LaPO 4 obtained in our study correspond rather well to data derived for various other natural or synthetic monazites. [START_REF] Oelkers | An experimental study of the dissolution stoichiometry and rates of a natural monazite as a function of temperature from 50 to 230 o C and pH from 1.5 to 10[END_REF] determined dissolution rates of 9.310 -6 and 2.210 -5 g m -2 d -1 for natural Ce-monazite from Manangotry, Madagascar, under dynamic conditions at 50 and 70°C at pH 2, respectively. [START_REF] Terra | Preparation and characterization of lanthanum-gadolinium monazites as ceramics for radioactive waste storage[END_REF] measured dissolution rates of synthetic GdPO 4 with monazite structure of 3.810 -4 to 5.910 -4 g m -2 d -1 at 90°C at pH 1. Slightly higher dissolution rates of 1.710 -3 g m -2 d -1 were obtained by [START_REF] Brandt | Conditioning of minor actinides in lanthanum monazite ceramics: A surrogate study with Europium[END_REF] for synthetic Eu-monazite at 90°C and pH 2 in SPFT experiments. In this study, within the solid-solution series LaPO 4 -EuPO 4 , a minimum of the dissolution rate (5.810 -5 g m -2 d -1 ) was observed at an EuPO 4 mole fraction of 0.2. [START_REF] Teng | Hot-pressure sintering, microstructure and chemical durability of Ce 0.5 Eu 0.5 PO 4 monazite ceramics[END_REF] investigated the dissolution behaviour of synthetic Ce 0.5 Eu 0.5 PO 4 with monazite structure at 90°C in deionised water. They found normalised elementary release rates of Ce and Eu below 410 -5 and 210 -4 g m -2 d -1 , respectively, after 21d. [START_REF] Veilly | Comparative behavior of britholites and monazite-brabantite solid solutions during dissolution tests: a combined experimental and DFT approach[END_REF] determined the dissolution kinetics of Th-cheralite (CaTh(PO 4 ) 2 ), a monoclinic monazite type phase with similar lattice parameters compared to LaPO 4 , in dynamic dissolution experiments at 90 C and pH 1, reporting a Th-based dissolution rate of 2.210 -5 g m -2 d -1 .

Based on the dissolution rates obtained at constant pH and at far from equilibrium conditions, the apparent activation energy of the dissolution process can be determined according to the Arrhenius' law, where:

(3), with the activation energy E a , the gas constant R, and the absolute temperature T. Using a simple mathematical transformation equation (3) takes the form:

(4), where A is the pre-exponential factor of the Arrhenius equation. In the Arrhenius plot (Fig. 3) two different linear trends can be observed for the temperature dependence of the dissolution rates of LaPO 4 under acidic conditions, suggesting changes in the rate limiting step in the overall dissolution mechanism. From the slopes of the regression lines, apparent activation energies of 44 ± 5 and 7.5 ± 4.3 kJ mol -1 were determined for the temperature ranges 50 to 90°C and 90 to 130°C, respectively. The open triangle corresponds to the dissolution rate from [START_REF] Brandt | Conditioning of minor actinides in lanthanum monazite ceramics: A surrogate study with Europium[END_REF].

These values of apparent activation energies allow for an evaluation of the mechanisms of the overall dissolution reactions. According to literature, the apparent activation energy of surface-reaction controlled dissolution (E a from 40 to 140 kJ mol -1 ) is distinctively higher than for transport-controlled dissolution (E a less than 20 kJ mol -1 ) (cf. [START_REF] Locker | The kinetics of dissolution of II-VI semiconductor compounds in nonoxidizing acids[END_REF][START_REF] Lasaga | Rate laws of chemical eeactions[END_REF][START_REF] Lasaga | Chemical kinetics of water-rock interactions[END_REF][START_REF] Deng | Effect of pH on the reductive dissolution rates of iron(III) hydroxide by ascorbate[END_REF][START_REF] Langmuir | Aqueous environmental geochemistry[END_REF]. This suggests that the dissolution of the LaPO 4 ceramics proceeds via a surface-reaction controlled mechanism at temperatures below 90°C and via a transport-controlled dissolution mechanism at higher temperatures. Similar results revealing two different mechanisms for the dissolution of Lnorthophosphate ceramics depending on temperature were obtained by [START_REF] Gausse | Synthèse et dissolution de matrices phosphatées de structure monazitique[END_REF] in dynamic dissolution experiments. In this study apparent activation energies of 79 ± 8 kJ mol -1 (T: 25 to 40°C) and 13 ± 1 kJ mol -1 (T: 40 to 90°C) for the dissolution of LaPO 4 were determined [START_REF] Gausse | Synthèse et dissolution de matrices phosphatées de structure monazitique[END_REF], suggesting similarly a surface-reaction controlled dissolution mechanism at lower temperatures and a transport controlled dissolution mechanism at elevated temperature. The higher apparent E a determined in the temperature range 25 to 40 °C by [START_REF] Gausse | Synthèse et dissolution de matrices phosphatées de structure monazitique[END_REF] and the different temperature ranges for the two prevailing dissolution mechanisms observed by [START_REF] Gausse | Synthèse et dissolution de matrices phosphatées de structure monazitique[END_REF] in comparison to our work, might be due to the less acidic conditions in our experiments (cHNO3 =0.1 [START_REF] Gausse | Synthèse et dissolution de matrices phosphatées de structure monazitique[END_REF] vs. cHNO3 = 0.01 M (this work)), and the fact that only two data points were used for the determination of E a .

Different dissolution mechanisms as function of temperature have been also reported previously with respect to the leaching kinetics of brannerite (nominally UTi 2 O 6 ) ores [START_REF] Born | Processing of wolframite-cassiterite concentrate for brannerite removal[END_REF][START_REF] Gogoleva | The leaching kinetics of brannerite ore in sulfate solutions with iron(III)[END_REF]. In the low temperature range from 15 to 35°C, an apparent activation energy of 50.5 kJ•mol -1 was determined, typically for surface-reaction controlled dissolution mechanisms. Between 35 and 90°C, a decrease of the apparent activation energy down to 30.3 kJ•mol -1 was reported. [START_REF] Gogoleva | The leaching kinetics of brannerite ore in sulfate solutions with iron(III)[END_REF] assigned this value to a mix of two mechanisms, i.e. surface-reaction and product layer diffusion. [START_REF] Terra | Preparation and characterization of lanthanum-gadolinium monazites as ceramics for radioactive waste storage[END_REF] evaluated an apparent activation energy of 39 to 45 kJ mol -1 for the dissolution of synthetic GdPO 4 with monazite structure from the values of the normalised dissolution rates at 90°C and room temperature, in line with our value for LaPO 4 below 90°C.

In contrast, [START_REF] Oelkers | An experimental study of the dissolution stoichiometry and rates of a natural monazite as a function of temperature from 50 to 230 o C and pH from 1.5 to 10[END_REF] determined the apparent activation energy associated with the dissolution of natural Ce-monazite from Manangotry, Madagaskar, to be 41.8 ± 12.6 kJ mol -1 in the entire temperature range from 50 to 230°C at pH = 2, without observing any change in the E a value. However, [START_REF] Oelkers | An experimental study of the dissolution stoichiometry and rates of a natural monazite as a function of temperature from 50 to 230 o C and pH from 1.5 to 10[END_REF] [START_REF] Oelkers | An experimental study of the dissolution stoichiometry and rates of a natural monazite as a function of temperature from 50 to 230 o C and pH from 1.5 to 10[END_REF].

Thermodynamic modelling

In Fig. 4, the results of the thermodynamic modelling of the dissolution of LaPO 4monazite in an acidic aqueous solution (0.01M HNO 3 ) at various temperatures are shown. The calculated La concentrations in solution depict the retrograde solubility of Ln-orthophosphates (cf. [START_REF] Poitrasson | Experimental determination of synthetic NdPO 4 monazite end-member solubility in water from 21°C to 300°C: implications for rare earth element mobility in crustal fluids[END_REF][START_REF] Cetiner | The aqueous geochemistry of the rare earth elements. Part XIV. The solubility of rare earth element phosphates from 23 to 150[END_REF] with La-concentrations decreasing from about 3.7•10 -5 mol L -1 to about 1.5•10 -5 mol L -1 in the temperature interval from 30 to 97°C.

Moreover, the thermodynamic calculations with GEM-Selektor revealed that La-rhabdophane is the thermodynamically stable phase in this temperature range. Scoping calculations at higher temperatures indicate that above about 102°C (375 K) La-monazite is the thermodynamically favoured La-orthophosphate phase (cf. Fig. 4). This is consistent with the experimental findings of du Fou de [START_REF] Du Fou De Kerdaniel | Actinide solubility-controlling phases during the dissolution of phosphate ceramics[END_REF], who observed in synthesis from oversaturation conditions, the formation of La-monazite at and above 373 K, whereas at temperatures below 363 K, La-rhabdophane occurred. In contrast, [START_REF] Cetiner | The aqueous geochemistry of the rare earth elements. Part XIV. The solubility of rare earth element phosphates from 23 to 150[END_REF] concluded from PXRD data that the solid phase used in experiments to determine the solubility product of LaPO 4 from under-saturation at 23°C and 50°C had the monazite structure before and after the experiment. However, this can probably be explained by the very low amount of neoformed rhabdophane during the dissolution experiment, which cannot be evidenced by PXRD (cf. [START_REF] Gausse | Synthèse et dissolution de matrices phosphatées de structure monazitique[END_REF].

Conclusions

The temperature dependence of the dissolution kinetics of sintered La-phosphate ceramics with monazite structure was studied, to gain a more detailed insight into the mechanisms governing the dissolution of monazite-type ceramics proposed as nuclear waste forms for actinide immobilisation. Pure single-phase La-monazite was obtained from precursors synthesised via a hydrothermal route after calcination and sintering. The dissolution kinetics of sintered La-phosphate powders were studied in dynamic dissolution experiments in the temperature range from 50 to 130°C under acidic conditions (0.01M HNO 3 ). The overall dissolution rates at far from equilibrium conditions increased by roughly one order of magnitude from 3.2×10 -5 to 2.5×10 -4 g m -2 d -1 in this temperature interval. The dissolution rates are in a similar range as those reported from dynamic experiments with natural and synthetic monazite in the literature. In the Arrhenius plot, two different temperature regions were observed, in which the normalised dissolution rates of LaPO 4 show a distinctively different dependence on temperature, indicating two different mechanisms of dissolution:

surface-controlled dissolution at lower temperature (T = 50 -90°C; E a = 44 kJ•mol -1 ) and transport-controlled dissolution at higher temperature (T = 90 -130°C; E a = 7.5 kJ•mol -1 ).

Complementary thermodynamic modelling reflecting the experimental conditions in the dissolution experiments demonstrated that La-rhabdophane (LaPO 4 ·0.667H 2 O) is the thermodynamically favoured phosphate phase in aqueous environments below about 100°C, whereas at higher temperatures La-monazite is the thermodynamically stable Laorthophosphate. Based on these results, it is proposed that the dissolution rates and activation energy reported here for temperatures below 90°C refer not directly to the dissolution of Lamonazite but to the formation and dissolution of a thin layer of La-rhabdophane formed at the monazite surface, including potentially a hydration step. Hence, rhabdophane-type phases might control the dissolution kinetics of Ln-orthophosphate-based ceramic waste forms under conditions relevant to geological disposal. Taking into account the dependency of the temperature of the rhabdophane-monazite transition on the cation radius described by du Fou de [START_REF] Du Fou De Kerdaniel | Actinide solubility-controlling phases during the dissolution of phosphate ceramics[END_REF], the transition temperature for An III -bearing La-monazite waste forms (An III = Pu III , Am III , Cm III ) would be higher than the temperature calculated here for the pure La-phosphate-system. Thus for an An-bearing La-monazite waste form generally the dissolution behaviour of the rhabdophane phase is the relevant issue under repository conditions.

Acknowledgement

The research leading to these results received financial support from the German Federal Ministry of Education and Research (BMBF) within the collaborative research project "Conditioning" (grant 02NUK021A).

Fig. 1 .Fig. 2 .

 12 Fig. 1. XRD-pattern of sintered LaPO 4 powder showing the presence of single-phase Lamonazite (Reference data monoclinic LaPO 4 , COD ID 9001647).

Fig. 3 .

 3 Fig. 3. Arrhenius plot of the dissolution rates of LaPO 4 as function of reciprocal temperature.

  studied natural monazite samples with very complex elemental composition, containing both, various lanthanide (Ce, La, Nd) and actinide (Th, U) cations, as well as SiO 4 3-and PO 4 3-anions. Du Fou de Kerdaniel et al. (2007) demonstrated the influence of the chemical composition of the Ln-orthophosphates on the temperature range of stability of rhabdophane-type compounds phases, which might explain the absence of two different dissolution mechanisms in the experiments of

Fig. 4 .

 4 Fig. 4. La-concentrations in equilibrium with a solid La-orthophosphate phase in 0.01M HNO 3 calculated with GEM-Selektor and estimated predominance fields of La-rhabdophane and La-monazite as function of temperature.


S Szenknect

S Finkeldei

F Brandt

J Ravaux

M Odorico

R Podor

J Lautru

N Dacheux

D Bosbach

Monitoring the microstructural evolution of Nd 2 Zr 2 O 7 pyrochlore during dissolution at 90°C in 4 M HCl: implications regarding the

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Several ceramics were considered as potential nuclear waste form for the specific conditioning of plutonium or fission products (1)(2)(3). The main advantage of single-phase ceramics is their capability to serve as tailor-made waste forms for the specific conditioning of radionuclides (4) , [START_REF] Anderson | Ceramics for the immobilization of plutonium and americium: Current progress of R&D of the VG Khlopin Radium Institute[END_REF]. For many ceramic systems, natural analogues have confirmed the suitability to immobilize radionuclides for several million years [START_REF] Ewing | [END_REF](7)(8). Besides monazite (9)(10)[START_REF] Boatner | Monazite for radwaste solidification[END_REF][START_REF] Oelkers | [END_REF](13)(14)(15), apatite (16)(17), thorium phosphate diphosphate (18)(19)(20), perovskite (21)[START_REF] Hartmann | Fabrication and properties of technetium-bearing pyrochlores and perovskites as potential waste forms[END_REF], and zirconolite (21,[START_REF] Deschanels | [END_REF], a particular interest was dedicated to pyrochlore (24)(25). Due to their high aqueous durability (26)(27)[START_REF] Finkeldei | Pyrochlore as nuclear waste form: actinide uptake and chemical stability[END_REF](29), chemical flexibility and radiation tolerance (8,30), zirconate pyrochlores with the general chemical composition A 2 B 2 O 7 seem to be highly promising candidates for the immobilization of plutonium (25,(31)(32).

The pyrochlore crystal structure can be derived from the fluorite structure type via the defect fluorite structure [START_REF] Finkeldei | Pyrochlore as nuclear waste form: actinide uptake and chemical stability[END_REF]. Randomly removing 1/8 th of the oxygen introduces vacancies into the fluorite structure which leads to the defect fluorite crystal structure. The introduction of anionic vacancies, reduces the mean coordination number of the cations from eight to seven. The defect fluorite crystallises in the Fm m space group. Removing oxygen atoms from well-defined lattice positions leads to the presence of two different cationic positions, A (yellow) and B (blue) (Figure 1re 1). This leads to the general pyrochlore formula A 2 B 2 X 6 Y. The A cation is eightfold coordinated in a scalenohedron shape by six X anions and two Y anions arranged. Due to the absence of 1/8 th of the oxygen the B cation is only sixfold coordinated by X anions in a trigonal antiprism. These two coordination polyhedra types are joined along edges to form the pyrochlore crystal structure. The pyrochlore crystallises in the Fd m space group. As a result of the higher ordering of the pyrochlore structure compared to the defect fluorite structure, the lattice parameter a for the pyrochlore is twice the parameter a of the defect fluorite structure (33). The A and B positions of stoichiometric pyrochlores are each occupied by only one cationic species. Pyrochlores with more than one cation type at the A and/or B position will be referred to as non-stoichiometric pyrochlores in this work.

Figure 1. Anionic coordination polyhedra of a pyrochlore with the cations A (yellow), B (blue), the vacancies (grey squares), oxygen anion at the X position (red) and further oxygen ions at the Y position (light grey) [START_REF] Finkeldei | Pyrochlore as nuclear waste form: actinide uptake and chemical stability[END_REF].

The pyrochlore structure-type can accommodate a variety of A and B-site cations with valences from +II to +VI as long as reasonable ionic sizes and appropriate charge compensators are available [START_REF] Ewing | [END_REF](34)(35)(36). In the framework of the nuclear waste management, pyrochlores with trivalent A sites and tetravalent B sites are of particular interest, because they can accommodate radionuclides with the oxidation states +III and +IV (25). ZrO 2 based pyrochlores were studied due to their high radiation tolerance. In contrast to the titanates, the zirconates undergo a phase transition from the pyrochlore to the defect fluorite structure as a consequence of radiation damage. A recent study discovered this mechanism to occur via a weberite structure on the local scale (37).

As a potential radwaste matrix, the chemical durability of these materials is a key property. HCl as a dissolution medium to observe the microstructural evolution of the pellet for shorter dissolution time without reaching saturation of the solution relative to baddeleyite, even so the dissolution of the sample would be complete. Thus, under the conditions chosen in this study, the evolution of the microstructural properties of the Nd 2 Zr 2 O 7 ceramic was caused by the dissolution in a pure kinetic regime.

ESEM was used to evidence the evolution of the microstructure of the pyrochlore pellet at a submicron scale. Then, grazing incidence X-ray scattering was used to examine structural and microstructural modifications of the solid near the surface. By varying the incident angle, it was possible to collect reflectivity curves (below the critical angle for total reflexion) and diffraction patterns as a function of X-rays penetration depths. GI-XRR gives access to physical properties of the solid surface, as electron density and roughness of the entire sample. Whereas grazing incidence X-Ray Diffraction (GI-XRD) was used to study the structural stability of the pyrochlore material during dissolution. In addition, AFM was used to monitor changes of the solid surface topography. These complementary results were combined in order to gain a thorough understanding of the dissolution mechanism and to evaluate the chemical durability of the probed material.

Experimental

Preparation of Nd 2 Zr 2 O 7 pyrochlore pellets

A Nd 2 Zr 2 O 7 pellet was prepared from a powder obtained by a wet chemistry route. Details about the precipitation and a similar pellet fabrication are given in Finkeldei et al. (29). Two pellets were prepared in parallel, one for the dissolution experiment and a second for the characterization (called afterwards reference sample). After a precompaction step at 50 kN by uniaxial pressing at room temperature, both pellets were transferred into an uniaxial hot press at 1450 °C and 3.9 kN in inert atmosphere. A subsequent resintering step was applied at 1100 °C to remove the oxygen deficit. The pellet was polished with a diamond paste of 1 µm size. Via the Archimedes' method, a pellet density of 99.5% calculated density was measured. The pyrochlore crystal structure was probed via X-ray diffraction between 10-90° 2 using a D4 diffractometer (-2 geometry) from Bruker AXS GmbH.

Dissolution experiments

The dissolution experiments were performed in closed PTFE containers using static conditions.

They were carried out in 25 mL of 4 M HCl (prepared with 37% HCl of analytical grade from Sigma-Aldrich). These conditions were chosen on the basis of a multiparametric study of the kinetics of dissolution of Nd 2 Zr 2 O 7 (29,39). These conditions prevent the precipitation of any neoformed phases at the surface of the sample, thus allow to study the dissolution far from equilibrium, in a pure kinetic regime. Moreover, the impact of the acidity of HCl solutions was demonstrated previously and a higher acidity led to an increase of the dissolution rate that allows observing microstructural and structural evolution of the solid/liquid interface at dissolution times compatible with laboratory time scale experiments. The dissolution reactor was placed in an aluminium block regulated at 90 °C.

The dissolution experiments lasted about 2500 hours during which the pellet was regularly removed from the solution, washed three times with 50 mL of deionized water (18.2 M.cm) to stop dissolution, and gently dried on an absorbing towel. The surface of the pellet was then characterized by GI-XRR, GI-XRD, ESEM and AFM. After the examination the pellet was again placed in the reaction container into fresh and preheated leachate.

Characterizations of the evolving interface

GI-XRR: acquisition and data treatment

GI-XRR measurements were performed using a Bruker D8 Advance diffractometer equipped with a motorized reflectivity stage that allows vertical translation of the sample. The complete primary optics setup for XRR analysis was composed of a Cu K 1,2 (= 1.54184 Å) source, a Göbel mirror, a motorised divergence slit, a fixed 0.2 mm slit, an automatic absorber, a fixed 0.2 mm slit after the absorber, and 2.5° Sollers slits. The data were collected with a Lynxeye detector in point mode.

Standard -2 scans were collected with a step size of 0.005° and a counting time of 7 s. The resolution of this setup was estimated to 0.01°. The background was determined for each XRR measurement using the off specular scan method (56) starting at 2 = 1° with () = 0.5° and subtracting from the collected intensity. Geometric correction in the region of the plateau of total external reflection was performed according to Salah et al. (56). Corrected intensities, I (cps) were normalized to the incident intensity, I 0 (cps). Reflectivity curves showed the evolution of the logarithm of the normalized intensity, R = I/I 0 versus the wave vector transfer, q (Å -1 ):

[1]

The experimental GI-XRR curves were calculated using the matrix formalism implemented in the reflex20 software [START_REF] Daillant | X-ray and Neutron Reflectivity: Principles and Applications[END_REF][START_REF] Gibaud | Specular reflectivity from smooth and rough surfaces[END_REF]. Using reflex20, only two parameters were fitted to the experimental reflectivity curves: electron density,  e (e -Å -3 ) and roughness,  (Å) of the substrate. Electron density of the substrate is linked to the critical wave vector transfer, q c at which the plateau of total external reflection exhibits a strong dip: [2] where r e = 2.85 10 -15 m is the classical radius of the electron.

The fitted value of the electron density was used to determine the global porosity  of the solid surface, since: [3] in which  e,s (e -Å -3 ) is the calculated electron density of the solid. Electron density and mass density  s (g Å -3 ) are linked through: [4] where x j is the mole ratio of element j in the solid, Z j (e -) is the atomic number, M j (g mol -1 ) the molar mass and N A (mol -1 ) is the Avogadro's number.

GI-XRD: acquisition and data treatment

GI-XRD measurements were performed using the same apparatus as for the GI-XRR measurements. GI-XRD patterns were collected between 10 and 63° with a 0.02° step width for a total counting time of 15 hours in the reflection geometry. The angular domain was limited at higher angles by the beam knife-edge that equipped the reflectivity stage. The incident angle,  i , was fixed to a value ranging from 0.2° to 1°. By increasing the incident angle, it was possible to scan a layer of increasing thickness at the surface of the material. The penetration depth, z (Å) of X-rays (E = 8.048 keV) as a function of  i is linked to the material absorption coefficient,  and the critical angle for total reflexion,  c as follows ( 59): [START_REF] Anderson | Ceramics for the immobilization of plutonium and americium: Current progress of R&D of the VG Khlopin Radium Institute[END_REF] For a compound material, the absorption term  depends on the material linear absorption coefficient,  (cm -1 ), which is obtained from the sum of the absorption cross sections of the constituting atoms by: with [START_REF] Ewing | [END_REF] with  j (cm² g -1 ), the total atomic absorption cross section derived from CXRO X-ray Data Booklet [START_REF] Thompson | CXRO X-ray Data Booklet[END_REF]. As the density of the solid at the surface decreased during the dissolution experiments, the penetration depth of X-rays as a function of  i was also recalculated according to equations ( 2) -( 4).

The quality of the PXRD patterns collected under grazing incidence was not sufficient to perform Rietveld refinement. Only qualitative observations were made in order to identify the structural evolution during the dissolution. However, some pitfalls must be avoided. According to Simeone et al. [START_REF] Simeone | [END_REF] the measured centroid of the Bragg peaks exhibited a shift from its theoretical value as a function of  i . They demonstrated for Gd doped ceria, that this shift from the expected 2 hkl angle can reach 0.15° for  i = 1° to 0.35° for  i = 0.2°, but is relatively constant over the angular domain considered. Thus, only patterns recorded using the same incident angle were compared.

ESEM and EDX: acquisition and data treatment

The microstructural evolution of the pellet surface was monitored in operando by ESEM. The sample was disposed on the flat stainless steel sample holder without any preparation except rinsing with deionized water to avoid the presence of HCl vapour in the SEM chamber and to stop the dissolution. ESEM micrographs were recorded with a FEI Quanta 200 environmental scanning electron microscope under water pressure ranging from 250 to 400 Pa. To clean the atmosphere in the SEM, five cycles of water vapour filling between 400 and 1000 Pa were achieved. Mainly two different regions of interest were identified at the surface of the pellet and observed at several times during the dissolution experiment. ESEM micrographs of these two regions were recorded at different magnifications. Micrographs recorded at low magnification were used to evaluate the increase of the porosity. Thus, the surface area of the analysed regions reached 12 µm × 12 µm, whereas the resolution allowed the visualisation of intra and inter-granular pores. The low magnification images were processed and binarised with ImageJ 1.45m software [START_REF] Ferreira | ImageJ User Guide[END_REF]. The 2D porosity was then extracted from such analysis by calculating the ratio between the surface area of the pores (black pixels) and the total surface area of the investigated domain. High magnification images were used to visualize opening of the grain boundaries and the triple junctions as the resolution of the ESEM device under environmental conditions at high magnification reached few nanometers.

Quantitative microanalyses were performed using a Bruker SDD 5010 EDX analyzer coupled with the ESEM at three different acceleration voltages (5, 15 and 30 kV). The samples were neither goldnor carbon-coated in order to limit the absorption of the X-rays emitted during the electron-matter interaction, mainly at low voltage. As the samples are insulating, the analyses were performed under low-vacuum conditions (50 Pa of H 2 O). To perform these analyses in the best conditions, a dedicated Gaseous Analytical Detector (GAD) provided by FEI Company was used. The final aperture of this detector is located very close to the sample surface in order to improve the accuracy and spatial resolution of the X-ray analysis. Measurements of standards and samples were performed using the same configuration and counting time (120 seconds). The standard materials that were used are pure ZrO 2 and NdPO 4 . The mass of oxygen was determined by stoichiometry considering Zr(IV) and Nd(III).

For each acceleration voltage, five to ten analyses were performed on the pyrochlore sample after 2739 h of dissolution (end of experiment) and on the Nd 2 Zr 2 O 7 sample of reference. This reference sample came from the same batch of synthesis than the dissolved sample and was sintered following the same protocol. Monte-Carlo simulations of the trajectories of electrons in the sample were performed using the Casino v3.3 software [START_REF] Demers | [END_REF]. Images of the simulated trajectories are gathered in the Figure S1 of the supplementary material, as well as the X-rays emission profiles from Nd (MV and LIII) and Zr (LIII).

AFM: acquisition and images analysis

AFM images were recorded in tapping mode in air using a commercial Multimode8 (Bruker)

apparatus. The free amplitude A 0 , varied from 1 to 1.5 Volt and the amplitude point was set around 1.2 V. Probes with nominal spring constants k = 40 N m -1 were used (RTESP, nominal tip radius 8 nm, resonance frequency around 300 kHz, Bruker). All images were taken at scan rates lower than 1 Hz. AFM images were flattened and analyzed using the Nanoscope 5 Analysis software (Bruker).

Results and Discussion

Monitoring of the microstructural evolution

A series of images of the solid surface during dissolution in 4 M HCl solution at 90 °C recorded with ESEM are depicted in Figure 2. This region of interest was selected because it was representative of the sample microstructure. The selected region appeared to be well densified. The grain size was in the range from 0.5 to 2 µm. At intermediate magnification, the alteration of the surface appeared to be heterogeneous. Grain pull-out was observed after only 20 hours in the dissolution medium. This process occurred at different locations in the investigated surface area of the pellet for the entire duration of the experiments (for example this phenomenon is underlined by a green circle in Figure 2, 613 h). The opening of the grain boundaries (examples are indicated by blue arrows in Figure 2) and triple junctions was suspected early and became obvious after 84 hours of dissolution. The dissolution of grain boundaries occurred all over the investigated surface area of the pellet leading to additional grains pull-outs. One area of a detached grain on Figure 2 (red box, 39 h) was additionally observed at the highest magnification. The shape of the pore created by the detachment of a grain did not evolve. The comparison with the image obtained after 84 hours of dissolution showed that new sites get activated for dissolution, especially the opening of triple junctions (examples are indicated by white arrows in Figure 2) and the digging of corrosion pits within the grains was observed (indicated by yellow arrows in Figure 2). This behaviour was also noticed at various locations at the surface of the altered pellet. ESEM images at the highest magnification presented in Figure 3, show also more clearly the modifications of single grains topography. After 613 hours of dissolution, the surface of some grains seems to change, as indicated by an orange circle, Figure 3). However, this process may have occurred earlier, as illustrated by the ESEM micrographs recorded after 62 hours presented in Figure ESEM observations were in reasonably good agreement with the results obtained by VSI, considering that "flat pores" referred to altered grains (orange circle in Figure 3), whereas "plateaus" corresponded to unaltered grains.

ESEM micrographs recorded at the highest magnification (Figure 3) also unambiguously evidenced that the material dissolution was located within grain boundaries. Obviously, the grain boundaries and triple junctions constitute preferential dissolution zones, thus confirming several observations made on other ceramic materials (49,(63)(64). The weaker chemical durability of grain boundaries could be either caused by a different chemical composition than the bulk (65-67), or by a degraded crystalline order, even an amorphous state, as the junction between two crystals of different orientations led to a high concentration of defects, especially for high misorientation angle (63). For pyrochlore, the opening of the grain boundaries was first hardly detectable by ESEM, and only at the highest magnification. The ESEM images presented in Figure 3 show that the intragranular distance generally did not exceed 2 nm, except at some locations after 2739 h of dissolution where it could reach 10 to 16 nm. The complete dissolution of the grain boundaries was clearly evidenced by the subsequent detachment of grains, the resulting pores due to the detached grains did not evolve further. This mechanism is described in the literature as chemo-mechanical corrosion of polycrystalline material. AFM images of the pellet surface were performed before and after 2739 hours of dissolution in 4

M HCl solution at 90 °C in order to better evaluate the topographic changes. Prior to dissolution, the root-mean square roughness, Rq was determined by AFM for several randomly selected areas of 4 µm² at the surface of the same pellet and reached 1.15 ± 0.05 nm, with a maximum height value of 27 nm corresponding to the presence of polishing marks (images not shown). Figure 4 shows the surface of the pellet observed after 2739 hours of dissolution under the optical microscope (Figure 4- Rq was determined with AFM for a selected region in area 1 (Figure 4-b) and reached 1.90 ± 0.02 nm, a value slightly higher than the initial one. This result indicates that the topography of the grains that are still present at the surface at the end of the dissolution experiment did not strongly evolve during the dissolution. A 1 µm² AFM image recorded in the area 1 (red square, Figure 4-b) is presented in Figure 5-a and 5-b with the corresponding depth profiles (Figure 5-c). These profiles were compared to one depth profile recorded at the sample surface prior to dissolution. The topography of the surface of the grains (red depth profile) did not differ significantly from the initial one, indicating that these surfaces present a remarkable low reactivity. The presence of remaining polishing marks at the surface of the grains strengthened the conclusion. However, due to the absence of a reference surface, the dissolution of the surface of the grains by normal retreat was not totally excluded. The grain boundaries were hardly detectable by AFM measurements and could be easily mixed with the polishing marks. Only one grain boundary can be identified in the blue profile Figure 5-c, which was also visible for the green profile. The formation of large holes was also evidenced (blue profiles) whose dimensions were characteristic of the grain size. The depth of these large holes can vary due to the abrasion of the grains during the polishing of the sample surface. In the area investigated by AFM, remarkable grain retreat was not detected. We assumed that the most reactive grains that could present such dissolution patterns could have been released in solution after 2739 hours of dissolution due to the intense chemo-mechanical corrosion process, thus only the less reactive grains were still present at the solid surface when AFM images were recorded. The evolution of surface porosity and roughness of the surface of the pyrochlore pellet was suggested by ESEM images in Figure 2 and Figure 3. However ESEM, as all microscopic techniques, provides local information. From this point of view, XRR is a complementary technique, as the characteristic length of the microstructural details that can be detected in the direction normal to the surface is almost the wavelength of the X-ray source, whereas the surface area of the probed region is that of the sample. Thus, it gives access to a 2D-characterization of the solid/solution interface properties. The XRR curves monitored during dissolution of Nd 2 Zr 2 O 7 pyrochlore in 4 M HCl solution at 90 °C are presented in Figure 6-a. All curves show a single critical angle and a rather smooth subsequent decrease of the reflected signal. Regardless the dissolution time, neither second critical angle, nor oscillations that would be associated to the presence of a surface layer of contrasted electron density or a secondary phase precipitated at the surface of the pyrochlore pellet were observed in these curves. The alteration of the pellet surface gave rise to a decrease of the critical angle, related to the decrease of the electron density at the surface. The data were fitted with a model accounting for the evolution of the electron density and roughness of the surface of the sample. The evolution of the two parameters fitted on XRR curves during dissolution in 4 M HCl at 90 °C is presented in Figure 6-b. The roughness of the surface of the sample did not change significantly for the entire duration of the dissolution experiment. The fitted values ranged between 1.5 and 2.2 nm, which is in very good agreement with values determined with AFM before and at the end of the experiment for the less reactive assemblages of grains. The electron density of the surface of the sample was found to decrease strongly during the dissolution, but after 1916 hours the evolution slowed down. It is noteworthy, that the value of the electron density determined for 1916 hours of dissolution was clearly out of this trend (Figure 6-b). It is not excluded that a strong microstructural change occurred at the solid/solution interface surface at this time, probably linked with an intense release of grains in the dissolution medium. Thus, the results recorded after 1916 hours using grazing incidence X-rays would not correspond exactly to the same solid surface as before.

The porosity, , was obtained from equation [3], in which  e is the fitted electron density of the sample (deduced from the fitted value of the critical angle) and  e,s is the value calculated from the crystallographic data. The evolution of the calculated porosity of the altered surface compared to the estimation made by ESEM micrographs analyses is shown in Figure 7. The porosity calculated from the electron density determined by XRR increased strongly from 0.02 to 0.32. The same trend was observed by ESEM but to a lower extent. The increase of the porosity calculated from low magnification ESEM micrographs was mainly due to the grain detachments. The decrease of the electron density determined by GI-XRR could be related to the opening and digging of the grain boundaries and triple junctions and to the formation of nanometric etch pits. At low magnification, the resolution of ESEM is not sufficient to take these phenomena into account, which explains the discrepancy between both estimations of the porosity. It is also noteworthy, that the increase of the porosity determined by GI-XRR slowed down after 1916 hours of dissolution. Such behaviour could be also related to the presence at this stage of the dissolution, of mostly non-reactive grains at the solid surface that were still reflecting X-rays, whereas the most reactive grains were already released in the dissolution medium.

Monitoring the structural evolution at the solid/solution interface

GI-XRD is one of the most appropriate methods to evidence dynamic structural changes at the surface of crystallized materials (68). GI-XRD patterns with  i = 1° were recorded regularly during the dissolution of the pellet. The recorded patterns are presented in Figure 8. The GI-XRD patterns present all the characteristic reflexes of the pyrochlore structure without any additional reflex regardless of the dissolution time. This result confirmed the absence of a crystallized neo-formed phase as it was expected under the conditions used. In addition, the superstructural reflections characteristic of the higher ordering of a pyrochlore phase compared to a defect fluorite phase were maintained. The diffracted intensity under grazing incidence was too low to allow for Rietveld refinement of the patterns, even after long counting times (almost 15 hours per pattern). Here, only qualitative evidence can be derived from these results. To avoid misinterpretation, only the patterns recorded with the same incident angle were compared. Qualitatively, an increase of the Bragg position could be associated with a decrease of the cell volume. In the stoichiometric pyrochlore structure (Fd m space group), Nd 3+ occupies the A cationic position and is coordinated by eight oxygen atoms, whereas Zr is coordinated by six oxygen atoms (33,36). The ionic radius of Nd 3+ in this environment reaches 1.109 Å, whereas it equals 0.72 Å for Zr 4+ (69). A pyrochlore solid solution formation can be obtained in the range of 20.4 -36.7 mol. % the proportion of non-reactive grains presenting a similar composition than before dissolution was increasing, which explains that the GI-XRD patterns get closer to the initial one. This observation (i.e.

 i =1°
the decrease in the (2 hkl ) shift at late dissolution times) led to the conclusion that the remaining grains at the surface of the pellet, which were the less reactive grains from a microstructural point of view were also less affected by the structural changes evidenced by GI-XRD.

The magnitude of the shift (2 hkl ), was more pronounced at the lowest incident angle, corresponding to the lowest X-rays penetration depth. Figure 11 represents the evolution of the penetration depth of the X-ray beam at the most intense Bragg reflection angle (2 222  29°) for several incident angles. For  i = 0.2°, the penetration depth increased from 50 nm to 70 nm during the dissolution experiment. In this layer, (2 222 ) reached + 0.7° for 1916 hours of dissolution (Figure 10). Thus, the evolution of the unit cell parameter was more pronounced at the solid/solution interface and might be linked with the dissolution mechanism.

Towards the dissolution scenario

The combination of the present results allows establishing a possible dissolution scenario that is illustrated in Figure 13. The evolution of the microstructure revealed a heterogeneous spatial distribution of dissolution rates. The specificity of grain boundaries and triple junctions compared to the durable bulk material was evidenced by high resolution ESEM images. This behaviour of the pyrochlore material is illustrated in Figure 13 for t ≤ 1916 h by large red arrows. As a result of the grain boundaries dissolution, grains detachment was observed early in the dissolution, and could lead at longer dissolution times to the complete disintegration of the pellet microstructure. The release of the grains in the dissolution medium revealed fresh surfaces of grains, which can offer new sites for the progress of the dissolution process. This step in the dissolution scenario is illustrated in Figure 13 for t ≤ 2739 h. The alteration of the surface of grains is not totally excluded, as textural modifications were observed by ESEM after 613 hours of dissolution (Figure 3 3). This process however did not concern all the grains at the solid/liquid interface, as some of the grains were found to be mostly non-reactive, as shown by AFM images. This alteration process was not correlated to a strong increase of the roughness (R q ) of the grains, which was found to be almost constant by GI-XRR and consistent with the AFM measurements. These techniques however, provided data relative to the less reactive grains. In Figure 13, it can be seen that for long dissolution times, as a consequence of the grain detachment mechanism, the reflective surface is mostly composed of less reactive grains (in blue slashes), which can explain the constant value obtained for the roughness by GI-XRR.

Another consequence of the grain detachment, the opening of grain boundaries and triple junctions is a strong increase of the porosity of the solid/solution interface as evidenced by GI-XRR and low magnification ESEM micrographs. This increase of the porosity, thus of the surface area of the solid/solution interface could also lead to an increase of the macroscopic dissolution rate during a transient step, before the dissolution of all the grain boundaries. An evolution of the crystal structure was also evidenced by GI-XRD, especially at low incident angles. This evolution occurred early during the dissolution and is temporally correlated to the decrease of the electron density determined by GI-XRR, the appearance of textural patterns on ESEM images recorded in BSE mode and to an incongruent dissolution step with a preferential release of Nd 3+ in solution (29). This structural changes could affect preferentially the most reactive grains (represented by a green to blue colour gradient, Figure 13) that are also likely to detach from the pellet. A preferential Nd dissolution would lead to a Zr enriched layer at the solid/solution interface.

This non-stoichiometric pyrochlore layer presents a smaller cell volume than the stoichiometric pyrochlore as expected by the evaluation of effective cationic radius on the A site position. Finkeldei et al. (29) observed also a strong decrease of the Nd-release rate with time leading to a congruent or close to congruent dissolution. Therefore the Zr-release from the non-stoichiometric pyrochlore layer may dominate this steady state rate. Finally, such structural rearrangement of the solid/solution interface could act as a passivating layer, regarding to the Nd 3+ release. This last stage of the dissolution scenario is however difficult to observe using surface characterization techniques as the most reactive grains are mainly released in the dissolution medium by chemo-mechanical corrosion.

Conclusions

By combining several techniques, it was possible to evaluate the microstructural and structural changes occurring at the solid/solution interface at a Nd 2 Zr 2 O 7 pyrochlore sintered pellet placed in an acidic dissolution medium. The dissolution occurs heterogeneously at the surface with a complex interplay of several dissolution rate contributors. The most important process observed is the chemo-mechanical corrosion of the pyrochlore as a consequence of the preferential grain boundaries dissolution. Parallel to the grain detachments, the dissolution of the grain boundaries, the opening of triple junctions and the digging of corrosion pits occurred, which led to an increase of the porosity of the surface and of the reactive surface area. The alteration of the surface of some grains leading to the formation of dissolution patterns evidenced by ESEM was also suspected. This process was however hardly visible for long dissolution times, due to the release in solution of the most reactive grains that present such dissolution patterns. The different behaviour of the grains could be attributed to different crystallographic orientations. A detailed study of the dissolution rates of the oriented surfaces of the grains using EBSD would allow for a more detailed analysis.

An evolution of the crystal structure at the solid/solution interface was also evidenced by GI-XRD, which could correspond to a transition from the stoichiometric to the non-stoichiometric pyrochlore structure. This evolution was inferred to the dissolution mechanism as a consequence of Nd and Zr occupancy of non-equivalent cationic positions in the pyrochlore structure. This structural rearrangement is temporally correlated to the increase of the porosity, the appearance of textural patterns for some of the grains, and to an incongruent dissolution step with a preferential release of Nd 3+ in solution that was evidenced at the macroscopic scale (29).

The results obtained in this work show that the study of the microstructural evolution during the dissolution of ceramic material is necessary and must be coupled with the synthesis and densification steps in order to be able to elaborate a durable matrix for the conditioning of actinides. Regarding the chemical durability of the pyrochlore as a conditioning matrix for plutonium or fission products, this work demonstrates the impact of the microstructure, which is mostly controlled by the choice of the synthesis route and sintering step. By increasing the grain size, and thus by decreasing the density of grain boundaries, it should be possible to improve the chemical durability of the ceramic by limiting the detachment of the grains, the increase of the reactive surface area and the subsequent disintegration of the microstructure. However, due to the expected He built-up as a consequence of radionuclide embedding, a certain number of pores is necessary to avoid the formation of cracks within the ceramic. Therefore, a suitable compromise between the different requirements of a potential waste form matrix needs to be made. In the future, the establishment of a sintering map would be helpful to be able to control the densification rate, thus the remaining porosity, as well as the grain size of the pyrochlore pellet.

  Monitoring the microstructural evolution of Nd2Zr2O7 pyrochlore during dissolution at 90 °C in 4 M HCl: Implications regarding the evaluation of the chemical durability Stephanie Szenknect, S. Finkeldei, F. Brandt, J. Ravaux, Michaël Odorico, Renaud Podor, J. Lautru, N. Dacheux, D. Bosbach To cite this version: Stephanie Szenknect, S. Finkeldei, F. Brandt, J. Ravaux, Michaël Odorico, et al.. Monitoring the microstructural evolution of Nd2Zr2O7 pyrochlore during dissolution at 90 °C in 4 M HCl: Implications regarding the evaluation of the chemical durability. Journal of Nuclear Materials, 2017, 496, pp.97-108. 10.1016/j.jnucmat.2017.09.029. hal-02048799

  Froma thermodynamic point of view Jafar et al.(38) demonstrated the stability of uranium-substituted Gd 2 Zr 2 O 7 through high-temperature calorimetry experiments under reducing and oxidizing conditions. From a kinetic point of view, the dissolution of synthetic ZrO 2 based pyrochlores was studied recently by Finkeldei et al.[START_REF] Finkeldei | Pyrochlore as nuclear waste form: actinide uptake and chemical stability[END_REF](29)39). The influence of pH and temperature on the normalized dissolution rate was determined through dynamic dissolution experiments. A preferential release of Nd was observed during the early stage of dissolution. At steady state, the dissolution became congruent, and the normalized dissolution rates were found to be low and typically in the range of 4×10 -7 to 3×10 -6 g m -² d -1 at 90 °C and [H 3 O + ]= 0.1 M. As noted by other authors(40)(41), both chemical and physical properties of the solid surface can affect the dissolution mechanism.Measurements of macroscopic dissolution rates were thus complemented by studies of the surface after reaction by means of techniques such as atomic force microscopy (AFM)(42)(43)(44)(45)(46)(47)(48), environmental scanning electron microscopy (ESEM)(29,49), grazing incidence X-ray Reflectivity (GI-XRR) (50-52), and light optical microscopy methods, mainly vertical scanning interferometry (VSI)(53)(54)(55). Applying these techniques provides the possibility to track the microstructural evolution of the solid/solution interface, to identify preferential dissolution zones and even to determine local dissolution rates. These approaches however, are mostly dedicated to the study of single crystals cleaved surface.Focused on the solid/solution interface, this work thus presents a new approach to study the dissolution kinetics for Nd 2 Zr 2 O 7 ceramics in 4 M HCl solution at 90°C. The choice of the dissolution medium was based on several considerations. First, Finkeldei et al.[START_REF] Finkeldei | Pyrochlore as nuclear waste form: actinide uptake and chemical stability[END_REF]29) determined the impact of the proton activity on the dissolution rate and demonstrated that stoichiometric pyrochlores are highly durable materials, especially at near neutral pH. As it is virtually impossible to evidence any evolution of the properties of stoichiometric pyrochlores at the timescale of laboratory experiments under conditions strictly representative of a repository site, a conservative assumption is that acidic conditions enhance the dissolution rate and thus, decrease the time necessary to observe the impact of the dissolution mechanism on the material. Second, geochemical modelling performed by Finkeldei et al.[START_REF] Finkeldei | Pyrochlore as nuclear waste form: actinide uptake and chemical stability[END_REF]29) showed that for static experiments in 0.1 M HCl solution, the dissolution of Nd 2 Zr 2 O 7 could led to solutions oversaturated relative to baddeleyite. It was thus decided to use 4 M

Figure 2 .

 2 Figure 2. ESEM observations in SE mode of one selected region of interest of the Nd 2 Zr 2 O 7 sample surface during its dissolution in 4 M HCl at 90 °C. This series of images (at intermediate magnification) was used to estimate the evolution of the 2D-porosity. The green circle highlights the grain detachment. The red area indicates the position of the images monitored at the highest magnification. Blue, yellow and white arrows indicate respectively locations where the opening of the grain boundaries, the digging of the corrosion pits and the opening of the triple junctions can be seen.

3 .

 3 In the ESEM image recorded after 2739 hours of dissolution, it appears that some of the grains still present the same topography as prior to dissolution. Thus the surface of some grains contributed to the overall dissolution rate, whereas other grains remained the same as prior to the dissolution experiment. VSI experiments performed on the same type of ceramic pellet support the results observed by ESEM. Indeed, Fischer et al.(55) observed the formation of "flat pores" already after the short reaction period of 40 h in 4 M HCl solution at 90°C. Then, the occurrence of flat pores was increasing as well as the retreat depth that reached 60 to 115 nm after 420 hours of dissolution. VSI also showed the existence of "plateaus", which are attributed to the existence of less reactive grains.

Figure 3 .

 3 Figure 3. ESEM images in SE mode at high magnification. White arrows indicate the opening of triple junctions, yellow arrows underline corrosion pits formation or digging, orange circles highlight the grain surface alteration, blue arrows indicate the opening of the grain boundaries.

  a) and AFM (Figure4-b and 4-c). After 2739 hours of dissolution, the solid/solution interface was strongly modified by grains pull-out. However, the initial surface was partially still present and appeared as white zones under the optical microscope (area 1 in Figure4-a), whereas black zones corresponded to large holes created by the detachment and release of grains (area 2 in Figure4-a).

Figure 4 .

 4 Figure 4. (a): Image of the solid surface after 2739 hours of dissolution in 4 M HCl solution at 90 °C obtained by coupling an optic microscope with the AFM, and showing the location of the two regions investigated by AFM in a larger field of view of the pellet. (b) and (c): AFM images of the surface of the pyrochlore pellet after 2739 hours of dissolution in 4 M HCl solution at 90 °C . The white square in Figure 4-b represents the selected zone for the measurement of root-mean square roughness, Rq. The red square indicates the location of the 1 µm² image presented Figure 5.

Figure 5 .

 5 Figure 5. AFM image of 1 µm 2 of surface area recorded in the white area (zone 1, Figure 4-b) after 2739 h of dissolution. (a): 3D reconstruction of the depth image, (b): corresponding depth image. (c): The depth profiles (green, blue and red) are compared with a profile representative of the initial surface (black).

Figure 6 .

 6 Figure 6. (a): Experimental (symbols) and simulated (lines) XRR curves obtained during the dissolution of a Nd 2 Zr 2 O 7 pyrochlore pellet in 4 M HCl at 90 °C. (b): Evolution of the electron density and roughness of the solid/solution interface during dissolution in 4 M HCl at 90 °C, determined by XRR.

Figure 7 .

 7 Figure 7. Evolution of the relative porosity of the solid surface during dissolution in HCl 4 M, 90 °C, determined either by XRR (red dots, secondary axis) or by ESEM images analyses (black squares).

Figure 8 .

 8 Figure 8. Grazing-incidence X-ray diffraction patterns collected at a Nd 2 Zr 2 O 7 pyrochlore sintered pellet during dissolution in 4 M HCl at 90 °C for an incident angle of 1°. * Bragg position associated to Nd 2 Zr 2 O 7 pyrochlore (JCPDS #01-078-1617).

Figure 9 -

 9 a, 9-b and 9-c represent the evolution during dissolution of the position of the most intense Bragg reflection (2 222 = 28.948°) collected at respectively  i = 0.2°, 0.4° and 1°. Interestingly, the centroid of the Bragg peak shifted towards higher theta values during the first 1186 hours of dissolution. From 1186 hours to 1916 hours the centroid of the Bragg peaks stabilized, then a decrease of the centroids position in theta values was observed and finally it approached its initial position after 2709 hours of dissolution. The shape of the Bragg peaks was also evolving during dissolution. One can note the appearance of a shoulder for the  222 reflection after 1916 hours of dissolution especially for  i = 0.2° and 0.4° (Figure 9-a and 9-b).

Figure 9 .Figure 10 (

 910 Figure 9. Evolution of the normalized most intense Bragg reflection (222) collected at a Nd 2 Zr 2 O 7 pyrochlore sintered pellet during the dissolution in 4 M HCl at 90 °C for several incident angles: (a)  i = 0.2°, (b)  i = 0.4°, and (c)  i = 1°.The evolution of the centroid of the Bragg peaks for the  222 reflection at  i = 0.2° is illustrated in

Figure 10 .

 10 Figure 10. Evolution during the dissolution of the centroid of the Bragg peaks for the most intense Bragg reflection (222) collected at a Nd 2 Zr 2 O 7 pyrochlore sintered pellet during the dissolution in 4 M HCl at 90 °C at  i = 0.2°.

Nd 2 O 3 (

 23 [START_REF] Finkeldei | Pyrochlore as nuclear waste form: actinide uptake and chemical stability[END_REF]. The structural changes of a stoichiometric pyrochlore to the non-stoichiometric pyrochlores as consequence of mixed Nd and Zr occupancy of the A or B site is described with the help of the antisite cation exchange model. In case of the stoichiometric composition Nd 2 Zr 2 O 7 , the number of eight fold coordinated (neodymium) and six fold coordinated (zirconium) cations for the A and B position are equal. For non-stoichiometric compositions (Nd,Zr) 2 Zr 2 O 7+x , Zr is in excess compared to Nd. Within the antisite model, Zr cations in excess are assumed to occupy the A position. The substitution of Nd by Zr is accompanied by a change of the coordination number for these Zr 4+ cations from six to eight, which is the typical coordination number of the A position. The ionic radius of Zr 4+ in this environment reaches 0.84 Å. Thus, in that model the effective radius of the cations in the A site decreases linearly with the neodymium depletion. This structural rearrangement could explain the first part of the evolution observed in Figure10. The increase in the (2 hkl ) observed before 1100 hours of dissolution could correspond qualitatively to the decrease of the cell volume caused by the partial substitution of Nd 3+ by Zr 4+ in the A site. The second part of the curve depicted in Figure10(i.e. the decrease in the (2 hkl ) shift) could be explained by the release in solutions of the most reactive grains at the surface of the pellet due to the chemo-mechanical corrosion process. Following this assumption, at the later stage of the dissolution (after 1916 hours)

Figure 11 .Figure 12 .

 1112 Figure 11. Evolution of the penetration depth of the X-ray beam at the most intense Bragg reflection angle (2 222 = 29°) for several incident angles. The penetration depth was calculated using equation[START_REF] Anderson | Ceramics for the immobilization of plutonium and americium: Current progress of R&D of the VG Khlopin Radium Institute[END_REF].

Figure 12 .

 12 Figure 12. Variation of the chemical composition (Nd and Zr atomic %) with depth in Nd 2 Zr 2 O 7 pyrochlore after 2739 h of dissolution and in the reference sample. Depth corresponds to the thickness of material emitting 99 % of X-rays collected by X-EDS (simulations are shown in Figure S1 of the supplementary material).

Figure 13 .

 13 Figure 13. Schematic representation of the dissolution scenario proposed based on ESEM, GI-XRR, GI-XRD and AFM results at a Nd 2 Zr 2 O 7 pyrochlore pellet surface during dissolution in 4 M HCl solution at 90 °C (not to scale). Green arrows represent the reflection of X-rays on the surface of the grains.

Acknowledgements

S.F. wants to thank A. Bukaemskiy for the help during the ceramic fabrication. S.S. thanks B.

Corso for the technical support during the use of diffractometers.