# Experimental characterisation and modelling of the fission products implantation at the fuel-cladding interface of high burnup PWR fuel rods

Cloé Schneider, Jerome Sercombe, Laurent Fayette, Karine Hanifi, Jérôme Favergeon, Sébastien Chevalier

► To cite this version:

Cloé Schneider, Jerome Sercombe, Laurent Fayette, Karine Hanifi, Jérôme Favergeon, et al. Ex-
perimental characterisation and modelling of the fission products implantation at the fuel-cladding
interface of high burnup PWR fuel rods. Journal of Nuclear Materials, 2025, 616, pp.156042.
10.1016/j.jnucmat.2025.156042. cea-05369801

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# Experimental characterisation and modelling of the fission products implantation at the fuel-cladding interface of high burnup PWR fuel rods

C. Schneider<sup>a,b,*</sup>, J. Sercombe<sup>a,●</sup>, L. Fayette<sup>a</sup>, K. Hanifi<sup>a,●</sup>, J. Favergeon<sup>c</sup>, S. Chevalier<sup>d</sup>

## HIGHLIGHTS

* Radial profiles of U, Zr and fission products at the fuel-cladding interface using EPMA.

* Reproduction of the ZrO₂-UO₂ interaction by a Fission Enhanced Diffusion model.

* Simulation of fission products implantation at the fuel-cladding interface.

* Simulation of zirconia circumvolutions' growth based on a coupled ballistic-geometric model.

## ARTICLE INFO

**Keywords:**

Fuel-cladding interface

Fission products

EPMA

Numerical simulation

Zirconia modelling

## ABSTRACT

During irradiation in light water reactors, numerous fission products (FPs) are produced by the fission reactions. At the periphery of the fuel, these elements implant by recoil in the cladding inner oxide layer (zirconia) located at the fuel-cladding interface (FCI). In the present study, two irradiated UO₂ fuel rods with high burnups (61.4 and 62.7 GWd/tU) have been analysed using EPMA. The aim of this work was to understand the mechanisms behind zirconia growth, FPs implantation at the FCI and their impact on the interface. In this objective, the measured elemental concentration profiles of U and Zr at the FCI is first compared to Fission Enhanced Diffusion (FED) models derived from out-of-pile experiments, showing good agreement. It is then shown that the implantation of metallic fission products (Nd, Mo, Pd, Ru) in the zirconia layer at the FCI can be described by a ballistic mechanism. Volatile fissions products, such as Xe, are found to affect differently the interface as they gather in bubbles. This explains the zirconia growth in form of protuberances called "circumvolutions" that are typically found in high burnup fuel rods. An analytical model describing zirconia swelling due to gaseous FP is proposed and compared successfully to measurements of zirconia thickness and circumvolution height.

## 1. Introduction

During irradiation in a light water reactor (LWR), contact between fuel UO₂ pellets and the Zr-based cladding leads to interaction between these materials. As a result, the inner wall of the cladding is not only oxidised by diffusion of oxygen from UO₂, but also exposed to irradiation by neutrons and fragments and fission products from the fuel periphery. This interaction is important for understanding the in-pile behaviour of the rods.

Early studies of the chemical interaction between the pellet and the fuel rod cladding frequently reported the presence of an intermediate

phase at the ZrO₂|UO₂ interface. In a 23 GWd/tU fuel sample from a boiling water reactor (BWR) [1] and in a 41 GWd/tU sample irradiated in a PWR [2], EPMA profiles have been acquired for the elements U, Zr, O and Cs at the ZrO₂|UO₂ interface and showed an enriched Zr-Cs-O region. For medium to high burnup samples (34 to 64.1 GWd/tU) irradiated in an experimental reactor (BR-3), a very thin layer of ZrO₂ bonded to a more or less dense layer of U-Zr-Cs was observed [3], sometimes with barium and possibly also containing a Pd-Te compound [4]. More recent studies show that this intermediate layer is in fact related to zirconia implanted with elements from the fission reactions [5–10].

<footnote><sup>a</sup> CEA, DES, IRESNE, DEC, Cadarache, F-13108 Saint-Paul-Lez-Durance Cedex, France</footnote>

<footnote><sup>b</sup> CEA, DES, ISAS, DRMP, Université Paris-Saclay, F-91191 Gif-sur-Yvette Cedex, France</footnote>

<footnote><sup>c</sup> Université de technologie de Compiègne, Roberval (Mécanique, énergie et électricité), Centre de recherche Royallieu - CS 60 319 - 60 203 Compiègne Cedex, France</footnote>

<footnote><sup>d</sup> ICB, UMR 6303 CNRS, Univ, Bourgogne Franche-Comté, 9 avenue Savary, 21078 Dijon, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: cloe.schneider@cea.fr (C. Schneider).</footnote>
Indeed, it has been observed that the internal zirconia is systemati-
cally implanted with fission products (FPs) on a depth of around 2 µm for
low burnup fuel and up to ten microns for high burnup fuel. Different
characterisation techniques have shown that the implanted elements are
the same as those observed in the fuel [7,9–16]. In particular, Xe [10,13,
15], Ba [13–15], Ce [12–14], Cs [10–14], I [10,11,15], Mo, Ru, Rh, Pd
[7,9,10,13,14,16], Tc and Te [9–11,16] have been found in the zirconia
layer. Lamontagne et al. [17] showed on a fuel rod irradiated 4 cycles in
a PWR that xenon had been implanted at a depth of 12 µm in the
zirconia.

In addition, the FPs concentration decreases gradually from the ZrO₂|UO₂ interface to the cladding. Lach et al. [8], who studied a TEM lamella extracted at the Zircaloy/UO₂ interface of a fuel irradiated in a BWR (burnup of 70 GWd/tU), also found, through EDS analysis, the presence of numerous FPs in solid solution and in the form of intermetallic precipitates (> 10 nm in diameter) implanted at the ZrO₂|UO₂ interface: Ru, Tc, Mo, Pd, Rh and Te. These elements were exclusively found in the first ~ 5 µm of zirconia in contact with the fuel, their concentration progressively decreasing with the distance from the ZrO₂|UO₂ interface. The same conclusion stems from the work of Liu et al. [7], who studied the pellet-cladding interface of a 73 GWd/tU irradiated rod (UO₂ fuel and Zr-Nb-O cladding), identifying the elements Mo, Tc, Ru, Rh and Pd by EDS.

An apparent mixing of U and Zr at the fuel-cladding interface (FCI) is also sometimes reported in the open literature. A (U, Zr)O₂ layer has been observed on a rod irradiated in a BWR at 42 GWd/tU [18,19], and the authors state that zirconia is not visible below a burnup of 30 GWd/tU. A (U, Zr)O₂-x layer was also observed using EPMA by Kim et al. at the FCI in fuel rods of burnups 35 and 53 GWd/tU [20]. In a sample irradiated in a BWR at 49 GWd/tU, Nogita et al. [21] even noticed a local UO₂ enrichment up to the Zr|ZrO₂ interface, which they were unable to explain. Recent studies show that the UO₂ lattice has a high tolerance to insert Zr atoms [22,23].

The mechanisms by which all these elements end up at this interface are still unclear, whether due to ballistic implantation and/or diffusion from the fuel [15,24]. The FPs effect on the growth of zirconia is also a point that needs to be clarified. Indeed, the ZrO₂|UO₂ interface is extremely disturbed at high burnup, with protuberances of zirconia (called “circumvolutions”) in the fuel of significant size (up to 10 µm) [5].

The aim of this work is to define the mechanisms behind: (i) the U-Zr (EPMA) profiles obtained at the FCI, (ii) the implantation of FPs in the zirconia layer at FCI and, (iii) the growth of zirconia into protuberances in the fuel. To this end, two high burnup samples were extensively characterised by EPMA to observe the distribution of U, Zr and FPs in the FCI. Modelling of U and Zr diffusion is then proposed, based on the work of Bérerd [25]. The ballistic implantation model of Minne [26] is then applied to the set of measured FPs. Finally, the potential contribution of FPs to the growth of zirconia into protuberances at high burnup is studied analytically by a coupled ballistic/geometric model. Conclusions are drawn on the importance of volatile FPs in zirconia versus metallic FPs.

## 2. Experimental characterisation of high burnup fuel samples

### 2.1. *Samples*

The spent nuclear fuel samples investigated in the present study come from two fuel rods irradiated in French PWRs, designated here by “BU61” and “BU63”. The BU61 sample was irradiated for five cycles, reaching a high burnup of 61.4 GWd/tU for the cross section examined. The BU63 sample was irradiated for four long cycles, reaching an average burnup of 62.7 GWd/tU for the cross section examined. The fuel rods are composed of a standard UO₂ fuel for BU61 and of a Chromia-doped UO₂ fuel for BU63, enriched at 4.95 wt % and 4.49 wt % ²³⁵U, respectively. The two rods have a Zr-based cladding: Zircaloy-4 and

M₅FRAMATOME, respectively. To prepare the cross-sections, each sample was cut and embedded under vacuum in a Bi-Sn alloy (57 %Bi, 43 %Sn) with a low melting point to ensure a good electrical conductivity. The surface was grinded with abrasive papers and polished with a series of diamond pastes down to 1 µm. The final polishing step was done with a colloidal solution of silica (0.02 µm). They were then cleaned with ethanol and ultrasonic cleaning. All samples preparation steps were conducted in hot cells at the LECA-STAR hot laboratory (CEA Cadarache, France).

### 2.2. EPMA

EPMA measurements were carried out on the shielded EPMA SX100-R (Cameca, Gennevilliers, France), located at the LECA-STAR Hot cell facility at CEA Cadarache. The measurements were carried out at 20 kV-200 nA, with a counting time per element and per point varying from 10 to 40 s (depending on the element analysed and its quantity) and a step size of 1 µm. All characterisations were realized at room temperature. Since the EPMA technique probes a pear-shaped volume of the order of 1 µm³, data are averaged over this volume. The spatial uncertainty is therefore around 1 µm. Concentration resolution is of the order of 0.1 wt %. Additional measurements on FPs (in particular, FIB-SEM tomography and S/TEM-EDS) were performed on BU61 sample, as detailed in reference [10].

### 2.3. *Experimental results*

For each sample, between 4 and 10 profiles were acquired and analysed (but for the sake of clarity, only a few profiles are shown here). The positioning of the profiles is given relatively to the Zr|ZrO₂ interface, taken as the origin.

Fig. 1 presents the radial profiles of the elements Zr, O, U and Pu measured at the FCI. From the Zr profiles, it is possible to define the average thickness of the zirconia layer, between 10 and 13 µm depending on the radial profile considered here in the BU61 and BU63 samples. Near the cladding ZrO₂ interface, an α-Zr(O) oxygen-enriched layer is visible in the cladding, characterised by increasing Zr and O contents. On about half of the zirconia layer thickness, the U concentration is increasing, similarly to the (U, Zr)O₂ layer previously observed by Kim et al. [20]. The Pu concentration profile is strongly related to that of U since it forms from U by capture of a neutron. It is however of importance since it is a fissile actinide that can contribute to the generation of other FPs in the FCI.

Fig. 2 presents the radial profiles of some FPs measured at the FCI. Mo, Ru and Pd are elements representative of the implantation of metallic FPs. Nd is a fission product that does not react with any other element and is non-volatile (i.e. not mobile), making it a good candidate among FPs to indicate the location of the fissioned U atoms. It is thus representative of the fission rate of U, and in particular, is used to determine the burnup of nuclear fuels. Cs is a volatile FP that is mobile and chemically reacts with other FPs within the fuel at high temperature. Xe is the most abundant inert gaseous FP and can be used to determine the distribution of gas bubbles at the FCI. It can be seen that, whatever the sample and the zone of the periphery probed, many fission products are implanted in the zirconia in non-negligible proportions.

Within the zirconia layer, the measured FP distribution is not the same from one element to another (Fig. 2). All the FP profiles, except that of Xe, show a decreasing trend when going from the fuel to the cladding. The Nd concentration profile at the FCI is the only smooth profile (Fig. 2.e), similar to those of Fig. 1. The Mo, Ru and Pd concentration profiles show slight peaks near the ZrO₂|UO₂ interface (Fig. 2.a, b and c), that are probably associated to local heterogeneities, i.e., the formation of precipitates. The Cs concentration profile across the layer is more homogeneous (Fig. 2.d), reflecting the volatile nature of this FP at high temperature. The Xe concentration profiles differ significantly from those of the others FPs and is characterised by a
<figure><img src="image_4.png" /><figcaption>Fig. 1. Weight concentration profiles at the FCI for (a) Zr, (b) U, (c) O and (d) Pu. Section burnups are given, as well as the corresponding maximum thicknesses of zirconia.</figcaption></figure>

sudden loss of signal at approximately the middle of the zirconia layer after a pronounced peak (Fig. 2.f). The signal remains low in UO₂, as generally found in the high burnup structure (HBS) of high burnup fuels when characterised by EPMA [27]. This result is an experimental artefact related to the micrometric size of the bubbles in the HBS that leads to a significant loss of the gas during sample preparation. The difference between the measured Xe contents in UO₂ and ZrO₂ might be explained by the smaller size of gas bubbles in ZrO₂ [10] (that reduces gas released during sample preparation), and improves characterisation by EPMA.

Superposition of the concentration profiles of U and Zr with SEM images of the FCI, as shown in Fig. 3, gives a better idea of the intimate interlocking of the oxidised cladding and fuel material. The O, Zr and U concentration profiles show what appears to be a 2 to 5 µm thick ZrO₂ | UO₂ interaction zone (Fig. 3.b). EPMA measurements through a circumvolution (Fig. 3.a) highlight the complexity of the interweaving of zirconia and UO₂ when the FCI is not flat. Thanks to the SEM images, it is clear that the oxide layer thickness is actually comprised between 4.5 and 13 µm. In this case, it is difficult to conclude if the apparent (U, Zr)O₂ layer results from the intimate mixing of the materials or if the signal is related to the presence of UO₂ below the circumvolution in the out-of-plane direction.

Similarly, superposition of the Xe concentration profiles with the same SEM images (Fig. 4) gives additional clues on the origin of the Xe loss starting from the middle of the zirconia layer. By comparison to Fig. 3, it can be seen that the Xe profile decreases significantly as the U concentration increases, which might again stems from the different size of the gas bubbles in the two materials [10], resulting in a significant gas loss in UO₂ during sample preparation, and not in the ZrO₂ layer.

## 3. Modelling

### 3.1. Modelling of diffusion at the FCI

As discussed in Section 2, the EPMA profiles of U and Zr of Fig. 1 seem to indicate a diffusion mechanism at the interface between the zirconia and the fuel. For the modelling of this phenomenon at the ZrO₂ |

UO₂ interface, it is proposed here to rely on the work of Bérerd [25], where the diffusion of U in zirconia was studied in out-of-pile experiments. In these experiments, the samples consisted of a titanium support covered by a 0.3 µm thick uranium oxide layer enriched at 98 %²³⁵U, itself covered by a 3 µm thick zirconia foil. The samples have been irradiated at 480°C in the Institut Laue Langevin (ILL) high flux reactor in Grenoble, generating a fission products flux of approximately 10¹¹ ions.cm⁻².s⁻¹. For more details on this work, see references [25,28–31]. The measured U concentration profiles in the zirconia foil were fitted using the solution of the diffusion equation in a semi-infinite plane:

$$c_U(x, t) = c_U^0 \text{erfc}\left(\frac{x}{2\sqrt{D_U t}}\right) \qquad (1)$$

with $c_U^0$ the atomic concentration of U in UO₂ at the interface with zirconia (in at.at⁻¹), x the distance from the ZrO₂ | UO₂ interface (in cm), $D_U$ the diffusion coefficient of U in zirconia (in cm².s⁻¹), and t the time (in second). Bérerd obtained a diffusion coefficient of 10⁻¹⁵ cm².s⁻¹ for a fission products flux of 10¹¹ ions.cm⁻².s⁻¹. He also showed that this order of magnitude was consistent with the measurements of Matzke [32] of the diffusion coefficients of U in UO₂ where the following relation was established between the diffusion coefficient $D_U$ (in cm².s⁻¹) and the fission rate $\tau$ (in fission.cm⁻³.s⁻¹):

$$D_U = A \cdot \tau \qquad (2)$$

with $A = 1.3 \times 10^{-29}$ cm.fission⁻¹. Bérerd also performed thermal diffusion experiments where pre-oxidised zirconium samples were implanted with ²³⁸U²⁺ ions and then annealed at 800°C during 23h. No uranium diffusion was detected during the experiments, showing the prevalence of U Fission Enhanced Diffusion (FED) in zirconia.

The FED model can be applied to the two samples characterised in this work. The following quantities are required: the average fission rate in the sample and the duration of pellet-clad contact. Both quantities can be obtained by a simulation with the fuel performance code ALCYONE [33], where the neutron-based model PRODHEL, is available. The calculated evolution of the average fission rate in the sample BU63 is
<figure><img src="image_5.png" /><figcaption>Fig. 2. Weight concentration profiles of various FPs at the FCI: (a) Mo, (b) Ru, (c) Pd, (d) Cs, (e) Nd, (f) Xe. Section burnups are given, as well as the corresponding maximum thicknesses of zirconia.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 3. Weight concentration profiles of the elements U, Zr and O superimposed on electronic images of the zones analysed: at the level of circumvolutions in sample (a) BU61 – zone 3 (SEM ESB image) and (b) BU63 – zone 4 (SEM SE image). The white arrows mark the path of the EPMA beam.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>Fig. 4. Xe weight concentration profiles superimposed on electronic images of the analysed zones: a) at circumvolutions in samples (a) BU61 – zone 3 (SEM ESB image) and (b) BU63 – zone 4 (SEM SE image). The white arrows mark the path of the EPMA beam.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 5. Evolution of the calculated average fission rate of the sample BU63 as a function of time during the four irradiation cycles.</figcaption></figure>

plotted in Fig. 5 as a function of time. The time-averaged fission rate during the four irradiation cycles is close to 10¹³ fissions·cm⁻³·s⁻¹. The diffusion coefficient, given by Eq. (2), is therefore equal to 1.3 × 10⁻¹⁶ cm²·s⁻¹. The closing of the pellet-clad gap is estimated by ALCYONE to take place at the beginning of the second irradiation cycle, after approximately 500 days of irradiation. The pellet-clad gap remains closed during the four last cycles, meaning that FED of U takes place during approximately 1200 days.

Using Eq. (1), the U concentration profile can be calculated after 1200 days of FED in zirconia. By assuming that Zr diffusion in UO₂ proceeds with similar kinetics than U diffusion, Eq. (1) can be applied to Zr to estimate the Zr concentration profile after 1200 days as well.

The U concentration in the fuel and the Zr concentration in zirconia are determined using Eq. (3):

$$c_i = \frac{1}{M_{tot}} \sum_i x_i M_i \quad (3)$$

For one mole of the element i (U or Zr) at the moment of the EPMA characterisation: cᵢ the elemental concentration in the matrix (g·g⁻¹), xᵢ the fraction of the nuclide i, Mᵢ the molar mass of the nuclide i, and Mₜot the total molar mass (matrix and elements).

Elemental concentrations are calculated using the CEA simulation code for the fuels and structures evolution under irradiation in French

PWR, called “CESAR” [34]. Based on the CESAR v.5.3 results, at the end of the irradiation in PWR, the application of Eq. (3) to the sample BU61 gives:

- U concentration:

$$c_U^0 = 0.81 \text{ g·g}^{-1}_{\text{irr.UO2}}$$

- Zr concentration:

$$c_{Zr}^0 = 0.74 \text{ g·g}^{-1}_{\text{ZrO}_2}$$

Note that the concentration for U in UO₂ takes into account the FPs created during irradiation. The concentration of Zr in ZrO₂ does not account for the recoil of the FPs in the oxide, but considers the Zr isotopes (induced by the neutron activation of the cladding).

Thus, the calculated U and Zr concentration profiles are compared in Fig. 6 to the measured EPMA profiles in the BU61 and BU63 samples, showing an excellent agreement with the measurement, in particular in what concerns the radial extension of the FED at the length of the ZrO₂| UO₂ interface layer (between 8 and 12 µm).
<figure><img src="image_9.png" /><figcaption>Fig. 6. Comparison of the U and Zr simulated profiles with results acquired by EPMA at the ZrO₂/UAO₂ interface of (a) sample BU61 and (b) sample BU63.</figcaption></figure>

A slight difference between the simulated U profiles and the exper-
imental data can be observed. First, the important burnup at the sam-
ple's periphery alters the composition of the fuel. In addition, the EPMA
efficiency is not always 100 %, and some fraction of element may not be

counted. In particular in the present study, some signal is lost during
data acquisition due to the heterogeneity of the interface materials, and
it is not possible to achieve 100 wt % by EPMA technique. Therefore,
EPMA analysis shows that the zirconia here is composed of 28 wt % O

<figure><img src="image_10.png" /><figcaption>Fig. 7. Average thickness evolution of the internal corrosion layer as a function of MOX and UO2-Zy4 fuel rod burnup, according to the measurements gathered by Desgranges [36]. At burnups below 40 GWd/tU, the zirconia layer was discontinuous and the measurements refer to locations where zirconia islets were found.</figcaption></figure>
and 70 wt % Zr, and the UO₂ is composed of 11 wt % O and 76 wt % U.

Nevertheless, the application of Eq. (1) shows that the diffusion of U within zirconia can be reasonably estimated from the out-of-pile measurements of Bérerd.

## 3.2. Modelling of fission products recoil and implantation in zirconia

Fig. 2 shows that the FPs found in the cladding are implanted in the zirconia oxide layer and not in the non-oxidised metal material. The FPs are generated by the fission reactions that take place at the pellet periphery and can be implanted in the cladding when the pellet-clad gap becomes less than the recoil distance (close to 8–10 µm). As soon as the gap is closed (even partially), oxidation of zirconium by the oxygen of the pellet takes place. Since the oxidation reaction is anionic, the oxidation front moves towards the inside of the cladding. As the zirconia layer continues to expand (growing in the metal) to reach 10–12 µm, the FPs are finally found in zirconia. Measurements of zirconia thickness in fuel rods irradiated up to 70 GWd/tU show two phases after the closing of the pellet-clad gap (Fig. 7). First, an apparent rapid growth of disconnected zirconia islets, 4 to 8 µm thick. Second, a slow increase of the zirconia islets until forming a continuous and wavy layer 10 to 12 µm thick (for samples analysed from [35]).

To simplify the modelling of FPs implantation in zirconia and derive analytical solutions, it was decided to ignore the complex time evolution of the zirconia layer, assuming an instantaneous implantation of FPs at the end of irradiation. Although the process is of course progressive, the fast evolution of the thickness of the zirconia layer (4–8 µm) as soon as the pellet-clad contact, the recoil distance of the same other of magnitude than the zirconia thickness and the slow evolution of zirconia after the initial pellet-clad contact, makes this hypothesis not inconsistent.

J.-B. Minne [26] established models describing FPs recoil in UO₂ and FPs implantation in zirconia after closing of the pellet-cladding gap. To do this, he neglected the curvature of the ZrO₂|UO₂ interface and considered the pellet and zirconia as two semi-infinite media. The FPs trajectory in the fuel and the zirconia was furthermore assumed linear with no change of direction. The FP recoil model in UO₂ is based on the textbook of Olander [37]. Details of the calculations can be found in reference [26]. The concentration of a given fission product in UO₂ after recoil $c^{recoil}$ (at m·m⁻³) is given by:

$$c^{\text{recoil}}(r) = \frac{1}{2\delta_{\text{UO}_2}} \int_{r-\delta_{\text{UO}_2}}^{R} c^{\text{created}}(x) \, dx \quad (4)$$

With $c^{created}$ the concentration of the fission product created from fission (at m·m⁻³), r the radial position in the fuel pellet (m), R the fuel pellet external radius (m) and $\delta_{UO_2}$ the recoil distance in UO₂ (m). Note that the FP creation radial profile is non-linear which explains the integral.

The FP implantation model in zirconia follows the work of Fregonese et al. [38] for iodine implantation by recoil in the cladding. In the model, a fission product created in the pellet at a position $x_p$ of the ZrO₂|UO₂ interface leaves the pellet with an energy $E_i$ and with an angle $\theta$ and settles in zirconia at a position $x_i$ of the interface (Fig. 8).

This FP therefore travels a total distance $\delta$ in UO₂ and ZrO₂ while losing energy, until it reaches the threshold energy for displacement, of the order of 40 eV. This recoil distance is obviously the most difficult to determine, since it depends on the nature of the FP, on the initial position of the FP ($x_i$, $x_p$), on the angle $\theta$ and on its path through the two materials, UO₂ and ZrO₂. Minne used the SRIM code to evaluate the distance covered in ZrO₂ as a function of the distance covered in UO₂. An example of SRIM calculation results for Mo is given in Fig. 9.

The concentration of a given FP in zirconia at a distance $x_i$ from the UO₂|ZrO₂ interface can be expressed as follows:

<figure><img src="image_11.png" /><figcaption>Fig. 8. Schematic representation of the fission product implantation at the FCI, adapted from [26].</figcaption></figure>

$$c^{\text{implanted}}(x_i) = \int_{0}^{x_{\text{pmax}}} \frac{c^{\text{created}}(x)}{2\delta} \, dx \quad (5)$$

where $x_{pmax}$ is the maximum recoil distance in the pellet leading to FP implantation in zirconia perpendicularly to the interface ($\theta = 0$). It depends on the position in zirconia $x_i$. The calculation of the integrals Eq. (4) and Eq. (5) is not straightforward. To derive an analytical solution, one needs a refined calculation of the FP creation radial profile near the pellet periphery. A mesh size of 1 µm is used in the last 10 µm of the fuel pellet. The average concentration of FP in the last 10 µm is then used to get an analytical estimation of FP recoil in UO₂ and FP implantation in ZrO₂. For the latter, the relation shown in Fig. 8, based on SRIM calculations, is used. Fig. 10 shows the calculated evolution of Mo concentration at the pellet periphery and in zirconia, according to Eqs. (4) and 5, compared with the creation profile (from calculations with PRODHEL). The recoil distance in UO₂ used here is 8 µm and also corresponds to the distances measured by SEM [10].

These calculations can be compared to the EPMA profiles of Mo presented in Fig. 2. The same equations can be applied to other FPs and results compared to EPMA profiles, as shown in Fig. 11. Note that the SRIM calculations for Mo have been used for the other FPs. From Fig. 11, it can be seen that the curves obtained are globally in good agreement with the measurements, particularly in the zirconia. The non-linear evolution in zirconia is due to the non-linear relation between the recoil distances in zirconia and UO₂, as shown in Fig. 9. The radial profiles of Nd, Mo and Pd are very close to the measurements, while more scatter can be seen for Cs. This difference may be due to the more volatile nature of Cs, some of which may have been released during irradiation or lost during sample preparation.

Fig. 12 presents the same comparison for Xe. The model gives a good estimation of the Xe distribution in the zirconia layer (outside the circumvolutions) but does not fit with the measured quantity of Xe in the fuel. This can be explained by the loss of gas due to the piercing of the large bubbles found in the HBS of the fuel during the polishing of the sample (hence the difference, as with Cs, Fig. 11). The Xe measured by EPMA in the fuel pellet corresponds mainly to the Xe dissolved in the matrix and precipitated in nanobubbles [10].

## 3.3. Modelling of circumvolutions' growth

The formation of zirconia circumvolutions at the FCI is a complex phenomenon that is still far from being explained. However, it appears to be correlated with the constrained growth of the zirconia. In fact, the zirconia layer is compressed in the radial and circumferential directions
<figure><img src="image_12.png" /><figcaption>**Fig. 9.** Recoil distance of Mo in zirconia as a function of the recoil distance previously covered in UO₂, adapted from the SRIM calculations presented in reference [26].</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>**Fig. 10.** Calculated radial profiles of Mo concentration from fission reactions (creation) and after recoil and implantation (recoil implantation), superimposed with an SEM image of the FCI of the sample BU63.</figcaption></figure>

due to the restricted space at the FCI. Despite this, the circumvolutions sometimes reach large dimensions (height of up to 20 µm at high burnup) with a predominantly spherical shape. Fig. 13 illustrates the sphericity of the circumvolutions by showing a SEM image of zirconia circumvolutions at the FCI of a 64 GWd/tU fuel sample, after chemical removal of the fuel.

The question remains of which mechanism drives the growth of the circumvolutions? There seem to be two possible explanations:

* The diffusion of oxygen through the zirconia already formed and the oxidation of zirconium at the Zr|ZrO₂ interface is known to induce a significant volume expansion (Pilling-Bedworth ratio of 1.56 [26]). This expansion could be entirely transferred to the ZrO₂|UO₂ interface, assuming that the HBS at the periphery of the fuel is sufficiently flexible to accommodate zirconia growth. The expansion of the zirconia layer is in fact strongly constrained in the circumferential direction by the underlying metal, forcing the “outer” interface of the zirconia (ZrO₂|UO₂) to “grow” in the fuel, i.e. to deform the zirconia layer in the radial direction. The spherical shape of the circumvolutions is however difficult to explain from the diffusion in volume of oxygen in the zirconia layer.

* FPs implantation in zirconia may contribute to the expansion of the layer by increasing its volume in proportion to the content of implanted FPs. The presence of numerous metallic precipitates in the circumvolutions and of fission gas bubbles support this view [10]. As shown in Fig. 13, the ZrO₂|UO₂ interface at high burnup is characterised by numerous circumvolutions that present a close to spherical shape. The spherical shape is the most stable geometry in case of a volume increase related to isotropic swelling. FPs implantation could therefore explain the volume increase of the zirconia layer and the apparent sphericity of the circumvolutions. This mechanism is therefore studied in more details in the next paragraphs.

In order to model zirconia circumvolutions' growth, it is necessary to define the initial geometry of the FCI. According to Ciszak et al. [5], zirconia is known to present three different configurations during irradiation, see Fig. 14: (i) first, it is found as disconnected islets along the pellet circumference, (ii) a continuous layer is then formed with a wavy interface, (iii) the wavy interface leads to the development of protuberances (circumvolutions) that present a strong bond with the fuel material. How the disconnected islets lead to a continuous layer is still not well understood, as protuberances can sometimes be found at
<figure><img src="image_14.png" /><figcaption>Fig. 11. Comparison of the FPs implantation model and experimental results for some elements at the FCI of sample BU61: (a) Nd, (b) Mo, (c) Pd and (d) Cs.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>Fig. 12. Comparison of the Xe implantation model and experimental results at the FCI of sample BU61.</figcaption></figure>

relatively low burnup [39]. It is possible that the wavy interface without large protuberances is the consequence of the formation of islets in the initial stage of the FCI.

In the model proposed hereafter, the development of a single islet at the FCI, assumed representative of the wavy interface will be studied. The islet can be represented by a spherical cap of radius R and of height h, as shown in Fig. 15, such that its volume V and outer surface S are defined by:

$$V = \left(R - \frac{h}{3}\right)\pi h^2 \qquad (6)$$

$$S = 2\pi R h \qquad (7)$$

The growth of the islet is assumed to be driven by the FP implantation that takes place during irradiation. The FPs can be found in different

state in zirconia and their contribution to the volume increase of islets depends on it. FPs can be dissolved in the matrix or form solid precipitates or gather in bubbles when gaseous [40]. Here, the contribution of dissolved FPs to zirconia swelling will be neglected, as their contribution is relatively small [41–43]. To simplify the modelling of FP implantation, a constant flow of FPs $\phi$ from the fuel to the zirconia is considered and calculated as follows [37]:

$$\phi = \frac{1}{4}(2\tau)\delta \qquad (8)$$

with $\phi$ the flux in at.µm$^{-2}$.s$^{-1}$, $\tau$ the fission rate at the FCI (fissions.µm$^{-3}$.s$^{-1}$) and $\delta$ the recoil distance (µm). The factor 2 accounts for the generation of approximately 2 FPs per fission. The quantity of FPs atoms $Q_{FPs}$ implanted in the zirconia islet during a time interval $\Delta t$ depends on the
<figure><img src="image_16.png" /><figcaption>Fig. 13. SEM image of zirconia circumvolutions on the cladding inner wall after removal of the fuel on a 64 GWd/tU sample [5].</figcaption></figure>

flux of FPs $\phi$ and on the outer surface S of the islet, such that:

$$Q_{FPs} = \phi \Delta t S \qquad (9)$$

The volume increase of the islet due to the quantity of metallic and gaseous FPs implanted during a time interval $\Delta t$ is equal to:

$$\Delta V = (V_{solid}^{at}f_{solid} + V_{gas}^{at}f_{gas})Q_{FPs} \qquad (10)$$

With $f_{solid}$ and $f_{gas}$, the fractions of FPs implanted as solid precipitates and in gas form, respectively. In the same way, $V_{solid}^{at}$ and $V_{gas}^{at}$ are the

atomic volumes of the FPs implanted as solid precipitates and in gas form respectively. The height increase of the islet $\Delta h$ is then calculated by solving the following equation Eq. (11) relating the updated volume of the islet to its updated height and assuming the islet radius remains constant:

$$V + \Delta V = \frac{3R - h - \Delta h}{3} \pi (h + \Delta h)^2 \qquad (11)$$

In Eq. (11), V and h are the volume and the height of the islet at the beginning of the time step. This equation is solved numerically or can be solved analytically by neglecting the terms in $\Delta h^3$, see appendix A.

First, only the FPs found as solid precipitates are considered, as they are the most numerous ($f_{solid} \sim 0.84$ meaning that 84 % of the FPs implanted in zirconia by fission recoil are found as solid precipitates). An initial islet of zirconia with a radius of 4 µm and a thickness of 2 µm is considered, consistent with experimental observations (Fig. 15.a). The fission rate at the exact FCI is approximately equal to twice the pellet average value calculated in Section 3.1: $\tau = 2.10^{13}$ fissions.cm$^{-3}$.s$^{-1}$. The recoil distance is derived from the SRIM calculation of Mo recoil and implantation in zirconia of Section 3.2 (Fig. 9), with a value of 9 µm. The atomic volume of Mo is taken here as the reference for solid FPs, leading to $V_{solid}^{at} = 1.5 \times 10^{-11}$ µm$^3$. The evolution of the height of the islet resulting from solid FPs implantation is plotted in Fig. 16 as a function of time (dotted line). Fig. 16 shows a very small increase of the height of the islet with solid FPs implantation after 1200 days of irradiation (<0.2 µm).

The same calculation is then performed with the gaseous FPs ($f_{gas} \sim 0.16$). As Xe is the most abundant gaseous FP, it is taken as the reference for the calculations. It is furthermore assumed that all the

<figure><img src="image_17.png" /><figcaption>Fig. 14. Schematic representation of the evolution of the FCI with burnup, adapted from [5].</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>Fig. 15. (a) SEM (SE) image at the FCI of sample BU61, and (b) schematic representation of the zirconia islet used to model the wavy zirconia interface (as framed in red in the SEM image).</figcaption></figure>
<figure><img src="image_19.png" /><figcaption>**Fig. 16.** Evolution at 400°C of the calculated height of the simulated islet with implantation of FPs metal precipitates (dotted line) and gaseous FPs (solid line).</figcaption></figure>

gaseous FPs are contained in bubbles in equilibrium with the internal pressure of the rod (~ 5 MPa) and at the temperature of the FCI, estimated at 400°C. The density of Xe at this temperature and at this pressure can be estimated from the Van der Waals equation (see Appendix B), leading an atomic volume $V_{gas}^{at} = 1.9 \times 10^{-9} \text{ µm}^3$. The evolution of the height of the islet resulting from gaseous FPs is plotted in Fig. 16 as a function of time (solid line). In <1200 days, the height of the islet reaches nearly 8 µm, showing that the implantation of gaseous FPs in zirconia by recoil might explain the formation of spherical circumvolutions at the FCI. The fast increase of the zirconia islet height is due to the increase of its external surface in contact with the fuel that in turn leads to an increase of the quantity of FPs implanted during a given time step. It is therefore a purely geometrical effect that explains the growth of the islets into spherical circumvolutions in <1200 days. Although the model proposed here gives a simplified representation of FP implantation in a spherical cap, it seems that the contribution of gaseous FPs can explains the particular shape of the FCI in high burnup fuels. It should also be pointed out that this is possible thanks to the high porosity of the HBS that provides the free space needed for the growth of the circumvolutions.

# 4. Discussion

## 4.1. Diffusion phenomenon

In the present work, the Fission Enhanced Diffusion model of Bérerd [25], when applied to the experimental results, shows a good match with the EPMA profiles. This a priori demonstrates that, in spite of the low temperatures at the FCI, U and Zr migrate in $ZrO_2$ and $UO_2$, respectively. In the past, some authors have identified (U, Zr, O, fission products) compounds at the $ZrO_2|UO_2$ interface. As an example, Yagnik et al. identified a layer of U-Zr-Cs in 34 to 64.1 GWd/tU irradiated PWR fuel samples [3]. In BWR fuel rods irradiated at burnups from 35 to 53 GWd/tU, a (U, Zr)$O_{2-x}$ layer was observed by several research teams [18, 20, 44]. Nogita et al. [21] have mentioned observations of an $UO_2$-enriched area at the $Zr|ZrO_2$ interface that they could not explain. However, in recent works [7,10], some authors explain that these intermediate layers could actually be related to the fuel material under the surface of the studied samples. Indeed, zirconia growth forms protuberances that are interlocked with the fuel material leading to a three-dimensional mixed interface. This means that the interpretation of

EPMA results is complex. Observations of the surface of the radial cross-section of the fuel rod does not give indications on the morphology of the materials below the surface. In addition, the electron interaction volume of the EPMA beam is about $1 \text{ µm}^3$, which is significant compared to the oxide layer thickness (4.5 to 13 µm in the present work). Thermodynamic calculations of the O-U-Zr ternary phase diagram in PWR standard conditions (350°C and 155 bar), presented in Fig. 17, shows furthermore an indication that there is no stable (U, Zr, O)-phase in these conditions. Thus, it is possible that the U-Zr interaction layer identified by EPMA in this work and the U-Zr-FP compounds mentioned in the open literature are actually due to the presence of $UO_2$ grains with FPs below the $ZrO_2$ layer (in the depth, perpendicular to the surface, not visible with SEM).

Furthermore, finer analysis using more precise techniques than EPMA (STEM-EDS, Raman spectroscopy, µXRD...) and combining modelling [22,23], have shown that it is possible to insert Zr atoms into the crystallographic lattice of $UO_2$. This implies diffusion on the scale of the crystallographic cell (i.e. much smaller than the precision provided by EPMA). This lattice tolerance allows chemical bonding of zirconia and fuel.

## 4.2. Zirconia circumvolution's growth

In the modelling of circumvolution's growth of Section 3.3, it is assumed that the gas bubbles in zirconia are at equilibrium with the rod internal pressure (~ 5 MPa) and that the temperature of the FCI is 400°C. While the temperature level can be confirmed by a simulation with the fuel performance code ALCYONE, the pressure in the gas bubbles in zirconia is more difficult to assess. Advanced experimental techniques have been used in the last decade to estimate the pressure inside $UO_2$ HBS bubbles. EPMA combined to SIMS analyses of the gas concentration in the fuel rim and SEM image analyses for the porosity distribution were used to estimate the molar volume of Xe at room temperature in gas bubbles within the HBS of high burnup fuel samples [27] (of average burnup between 62 and 78 GWd/tU). The measured molar volume of Xe in the HBS bubbles was found in the range 90–100 $cm^3.mol^{-1}$. The pressure within the HBS bubbles at 650 K, calculated with the Van der Waals equation, reached 70–90 MPa, far above the rod internal pressure during nominal irradiation conditions and the equilibrium pressure of the bubble ($2\gamma/r$ with $\gamma = 0.41 (0.85–1.4 \times 10^{-4}(T–273))$ the surface tension [46] in J.m$^{-2}$
<figure><img src="image_20.png" /><figcaption>Fig. 17. O-U-Zr ternary phase diagram at 350°C and 155 bar (PWR conditions), using FactSage<fnref n="1" /> [45].</figcaption></figure>

and *r* the bubble radius in m). The diameter of the bubbles in the HBS of the studied samples was measured within 0.5 and 1.5 µm [47], leading to an equilibrium pressure at 650 K between 0.87 and 2.61 MPa. More recently, this estimation of the HBS bubbles' pressure has been reassessed [48] using Soave equation of state [49] for Xe-Kr, well adapted to the high pressures at hand, according to Cagna [50]. It was found that the HBS bubbles' pressure at room temperature is of the order of 8 MPa, consistent with a pressure of 70–90 MPa at 650 K. This order of magnitude was also confirmed by the analysis of single bubbles' molar volume, thanks to FIB-SEM 3D reconstruction of the bubbles's volume and SIMS measurements of the gas content of the independent bubbles [48]. Note that Soave and Van der Waals equations lead to close estimations of the molar volume (and hence of the atomic volume of Xe) when used at 5 MPa and 400°C (see Appendix B). Differences increase when the pressure increases.

Of course, these measurements cannot be applied as is to gas bubbles in zirconia. To the authors' knowledge, there is no data on the surface tension of gas bubbles in this material and no measurement of the molar volume of the gas in the bubbles within zirconia. However, the average equivalent diameter of the bubbles formed in zirconia has been recently estimated by FIB-SEM 3D reconstruction at around 0.2 µm [10]. This number is smaller than the equivalent diameter of bubbles in the HBS that often reaches or exceeds the µm (see for instance Table 1 of reference [48] where measurements from different authors are summarized). In consequence, the equilibrium pressure of gas bubbles in zirconia (due to surface tension) could be higher than in the HBS of the fuel. Using the surface tension available for UO₂ [46], one obtains an equilibrium pressure of 6.5 MPa at 700 K, not very far from the internal pressure of the rod. Because of the large expansion of zirconia protuberances into the HBS, it can be expected that gas bubbles in zirconia are at equilibrium since a significant reduction of the overpressure in the bubbles must take place during the formation of circumvolutions. With this equilibrium condition, the circumvolutions' growth model of Section 3.3 gives consistent estimates of the circumvolutions' height and volume after >1000 days in reactor. In addition, another parameter which was no taken into account here was the effect of the FPs on the ionic

conductivity of oxygen. Indeed, the FPs having a lower oxidation state than Zr⁴⁺ in zirconia can react with oxygen [40], leading to a non-stoichiometric oxide ZrO₂-x. This could increase the oxygen diffusivity through the zirconia layer, and then, participate in circumvolution growth. Nevertheless, additional experimental data are necessary to confirm this hypothesis.

## 5. Conclusions

The aim of this work was to quantify and model the mechanisms behind the formation of the FCI and FPs implantation in the zirconia layer. To this end, two high burnup fuel samples have been extensively characterised by EPMA and SEM to provide radial profiles of U, Zr, Mo, Nd, Pd, Cs and Xe at the FCI. Modelling of the diffusion of U and Zr at the pellet-zirconia interface was based on the out-of-pile experiments of Bérerd [25] while the ballistic implantation models of Minne [26] were used to study the FPs distribution in both the rim of the fuel pellet and the zirconia layer. The peculiar growth of the zirconia layer at high burnup into a wavy layer with pronounced protuberances was then analysed by a coupled ballistic – geometric model. It was shown that these models could reproduce quantitatively most of the experimental observations:

(i) Bérerd's model reproduces well the U and Zr elemental profiles obtained at the fuel-cladding interface by EPMA, highlighting the existence of a potential Fission Enhanced Diffusion mechanism.

(ii) The implantation of metallic fission products (Nd, Pd, Mo) in the zirconia layer at the FCI can be described by a ballistic mechanism. The distribution of the gaseous fission products (Cs, Xe) is also well reproduced by the model for what concerns zirconia. The agreement is less good in the fuel pellet rim. This can be explained by the loss of gas due to the piercing of the large bubbles found in the HBS of the fuel during the polishing of the sample. The differences in gas content between zirconia and the HBS of the fuel are consistent with the smaller size of pores in

<footnote n="1">¹ FactSage calculations were carried out using the “pure substances database” (SGPS) maintained by Scientific Group Thermodata Europe (SGTE).</footnote>
zirconia (equivalent pore diameters of 0.2 and 1 µm, respectively).

(iii) The formation of spherical circumvolutions of large size at the FCI can be attributed to the recoil of gaseous fission products, such as Xe, that form bubbles in zirconia and leads to its expansion. Simple geometric considerations explain the exponential growth of these circumvolutions at some point, since the quantity of fission products implanted in a typical zirconia protuberance is proportional to its external surface. When an initial zirconia protuberance of diameter 8 µm and height 2 µm evolves into a spherical protuberance of diameter 8 µm, its external surface in contact with the fuel (where fission reactions take place) increases by a factor 4.

Future experimental work should be focused on the estimation of the pressure inside gas bubbles in zirconia circumvolutions, to confirm or infirm the hypothesis of an equilibrium with the fuel rod internal pressure used in the analytical model developed in this paper. This could be done by combining FIB-SEM 3D characterisations of the bubbles' volume and SIMS measurements of the bubbles' gas content, as recently shown for gas bubbles in the HBS of fuel samples [48]. The analytical models used and developed in this paper could easily be included in multi-dimensional simulations of the FCI, as already shown by Minne for the FED and the ballistic models [26]. This would provide some insight on the stresses generated in the fuel HBS by the expansion of the zirconia

layer.

### CRediT authorship contribution statement

C. Schneider: Writing – original draft, Formal analysis, Methodology, Writing – review & editing, Investigation. J. Sercombe: Validation, Formal analysis, Writing – original draft, Supervision. L. Fayette: Validation, Supervision. K. Hanifi: Methodology, Investigation. J. Favergeon: Validation, Supervision. S. Chevalier: Visualization, Validation.

### Declaration of competing interest

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

### Acknowledgements

The authors would like to thank EDF and FRAMATOME for their technical and financial support in the framework of the PhD thesis performed at the CEA Cadarache in which this work is included. They would also like to thank Dr. M. Rochedy for the thermodynamic calculations on FactSage.

## Appendix A

The height increases of the islet $\Delta h$ can be calculated by solving the following equation relating the updated volume of the islet to its updated height and assuming the islet radius remains constant:

$$V + \Delta V = \frac{3R - h - \Delta h}{3} \pi (h + \Delta h)^2$$

This third order equation can be solved numerically by the Newton-Raphson method. To obtain an analytical solution, the terms in $\Delta h^3$ can be neglecting, leading to the following second order equation:

$$3(R - h)dh^2 + 3h(2R - h)dh + 3Rh^2 - h^3 - \frac{3}{\pi}(V + dV) = 0$$

with the positive root of interest given by:

$$dh = \frac{-3h(2R - h) + \sqrt{9h^2(2R - h)^2 + 12(R - h)(3Rh^2 - h^3 - \frac{3}{\pi}(V + dV))}}{6(R - h)}$$

It was checked that the analytical solution led to negligible differences with the exact solution.

## Appendix B

The Van der Waals equation of state reads as follows:

$$P = \frac{RT}{(V_m - b)} - \frac{a}{V_m^2}$$

where $V_m$ is the molar volume in $m^3 \cdot mol^{-1}$, T is the temperature in K, R the gas constant (8.314 J \cdot mol$^{-1} \cdot K^{-1}$), a and b two parameters ($a = 0.425 \ m^6 \cdot Pa \cdot mol^{-1}$, $b = 5.11 \times 10^{-5} \ m^3 \cdot mol^{-1}$).

The Soave equation of state takes the following form [50]:

$$P = \frac{RT}{(V_m - b)} - \frac{a}{(V_m^2 + bV_m)}$$

with a and b two parameters given by:

$$a = a_0 \frac{R^2 T_c^2}{P_c} b = 0.0866 \frac{R T_c}{P_c}$$
where $T_c$ and $P_c$ are the critical temperature (K) and pressure (Pa), respectively. For Xe, $T_c = 289.7$ K and $P_c = 5.86 \times 10^6$ Pa. The parameter $a_0$ can be calculated as follows:

$$a_0 = 0.42748 \left(1 + f\left(1 - \sqrt{\frac{T}{T_c}}\right)\right)^2$$

With $f = 0.492$ for Xe.

From the Van der Waals and the Soave equations, the molar volume $V_m$ can be estimated for given temperature and pressure. The atomic volume of Xe is then calculated as follows:

$$V_{at}^{Xe} = \frac{V_m}{N_A}$$

With $N_A = 6.02 \times 10^{23}$ atoms.mol⁻¹ the Avogadro constant.

## Data availability

Data will be made available on request.

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