Insights into the interfacial speciation of Ni in the corrosion layer of high burnup Zircaloy-2 cladding: A combined XRD, XAS, and LFDFT study

This work reports atomic-scale experimental and modeling studies of the zirconium oxide microstructure formed at the metal-oxide (M/O) interface, and the crystallography as well as the redox chemistry of alloying element nickel in the corrosion layer found on a serviced boiling water reactor Zircaloy-2 fuel rod cladding. Complying with radioprotection aspects a small-sized sample with only limited radioactivity, taken from a very high burnup (~ 79 MWd/kgU) cladding tube material, was prepared for the investigation using synchrotron-based X-ray microprobe techniques such as X-ray fluorescence ( μ XRF), X-ray diffraction ( μ XRD) and X-ray absorption spectroscopy ( μ XAS). The patterns of Ni K-edge XAS of solute Ni, probed at several location within the corrosion layer, have been recorded and analyzed. Close to the metal-oxide interface both the allotropic forms of zirconium oxide, monoclinic and tetragonal phases, have been identified by XRD analyses. XAS results of the barrier layer at the metal-oxide interface reveal that the oxides contain Ni atoms as divalent cations located in the proximity of oxygen vacancies. Near the M/O interface regions, all oxidized nickel atoms have a Ni 2 + homogeneous distribution and no trace or even evidence of any metallic Ni is found in the oxide matrix. The experimental results, also supported by first-principles ligand field DFT calculations, are interpreted in term of energetics, stability, chemical and structural specificity of divalent Ni ions in zirconium oxide microstructure. The present investigation on the basis of a combined experimental and theoretical approach shows that the oxidized nickel ions being situated in the neighborhood of oxygen defects is influential on the hydrogen evolution reaction including the hydrogen intake behavior accompanied with the oxidation reaction in irradiated Zircaloy-2.


Introduction
In boiling water reactors (BWR), Zircaloy-2 is used as the fuel cladding tubes and other core components structural material for in-reactor nuclear applications. The principle alloying elements in commercially used Zircaloy-2 are Sn, Fe, Cr, Ni etc. added at low concentrations primarily to improve the oxidation characteristics of reactor grade zirconium metal [1,2]. For the long-term use of the fuel rods, however, some of the main limiting factors are corrosion, uptake and diffusion of hydrogen as well as hydride formation in the cladding. It is well known that Zircaloy-2 cladding in BWR exhibits a higher hydrogen pickup fraction [3] compared to Zircaloy-4 (in pressurized water reactors, PWR), and the most significant microstructural difference between these two materials is that Zircaloy-2 contains Ni, Fe and Cr while Zircaloy-4 is Ni-free. In addition, all these transition metals (Fe, Cr and Ni) have a very limited solubility in the host metal for alloying with zirconium. As a result, they always tend to precipitate with matrix Zr atoms as intermetallic compounds forming second phase precipitates (SPP) in the sub-micron scale. Although many factors determine corrosion and hydrogen ingression in fuel rods, it is well established that the alloying elements including SPP's composition and size distribution influence both the corrosion rate and hydrogen absorption properties of Zircaloy-2. When the SPP size reaches below a critical size primarily due to irradiation induced SPP dissolution process, both corrosion resistance and hydriding performance are known to deteriorate [4].
According to the ASTM (American Society for Testing and Materials) specifications, the maximum concentration level of allowable transition metal impurities of Cr, Fe and Ni in reactor-grade Zircaloy-2 material are in the range of (0.05-0.15), (0.07-0.2), (0.03-0.08) [all in weight percent with remaining Zr in balance], respectively. Although the total content of these elements is much less than one weight percent and mostly they are contained in the second phase Zr(Fe,Cr) 2 and Zr 2 (Fe,Ni) precipitates in Zircaloy-2, the concentration of these alloying elements dissolved in the α-Zr matrix is extremely low. This is, however, not the case for neutron-irradiated materials. Previous research on the characterization of SPP in irradiated Zircaloy-2 by transmission electron microscopy (TEM) as well as atom probe tomography (APT) has demonstrated that the additive elements are redistributed in the alloy matrix after prolonged neutron irradiation and SPP dissolution. It has been also confirmed that neutron irradiation increases the dissolved concentrations of Fe, Cr and Ni in Zircaloy-2 [5] because of the dissolution of the precipitates. The principal importance is the alloying element Ni as it is prone to oxidation and demonstrates the highest sensitivity and specificity for hydrogen adsorption [6], although being at an experimentally limiting detectable concentration as low as 0.03 wt% in Zircaloy-2. Thus, the use of high brilliance synchrotron radiation for trace elements detection in order to characterize atomic scale microstructure of zirconium alloys in a non-destructive way is of utmost interest.
The present study was undertaken to determine structural specificity and chemical state of Ni atoms located in the outer oxide layer of a very high burnup Zircaloy-2 fuel rod cladding, and to investigate the apparent influence of nickel on the hydrogen absorption process into the metal of the irradiated fuel rod. The results are associated with the micro-beam synchrotron radiation based X-ray diffraction (XRD) quantification of tetragonal and monoclinic zirconia phases in the corrosion layer, and nickel K-edge X-ray absorption spectroscopy (XAS) characterization of solute Ni in the oxide matrix revealing the microcrystalline properties as well as the local atomic environment of Ni in zirconia microstructures. The work is relevant since it is regularly postulated that nickel is detrimental alloying addition in Zircaloy and responsible for the enhanced hydrogen pick-up fraction of BWR claddings. The present study also complements one of our recent work [7] carried out on the characterization of corrosion layers of intermediate burnup Zircaloy-2 materials describing the impact of nickel ions on the overall hydrogen evolution reaction in the alloy. Since experimental results cannot be separated from theoretical developments, a part of this work comprises computational modeling and first-principles ligand field Density Functional Theory (LFDFT) calculations for the nickel atoms embedded zirconia phases that is essential in understanding the interaction of nickel ions with the neighboring host-matrix atoms.

Material and methods
The material analyzed is commercial Zircaloy-2 developed by Westinghouse Electric Company. The fuel rod was irradiated over a nine-cycle period in a BWR plant ["Kernkraftwerk Leibstadt" (KKL)] in Switzerland. In this study, the oxide layer of a small-defueled corroded ring-segment, prepared from a mid-elevation of 2040 mm of the fuel rod, has been examined using synchrotron radiation. The main characteristics of the mother rod and the segment of interest are presented in Table 1.
For the investigation of any reactor-exposed material using a largescale synchrotron facility, sample preparation is a very crucial step. Of outmost importance is to comply with radioprotection aspects at the synchrotron laboratory that is more satisfied when only a tiny amount of radioactive material is brought at the beamline. In addition, a uniform sample thickness of sufficient surface quality is required for standard XRD and XAS work. A focused ion beam (FIB) instrument (Zeiss NVision 40 dual-beam microscope) was therefore used to create a thin window with defined dimension and good surface quality on a relatively small size Zircaloy-2 specimen prepared by cutting out an arc segment from the larger ring-segment. Fig. 1 shows a SEM micrograph of the FIBprocessed Zircaloy-2 sample (75 µm X 300 µm window) studied using monochromatic synchrotron radiation. The multistep samplepreparation method for high burnup cladding materials using FIBmilling procedure has been reported in two previous publications [7,8]. We may also note here that presence of periodically repeated cracks, eventually lateral cracks running parallel to the metal/oxide interface, have been observed in the oxide layer of FIB-ed window of the sample. For this reason, great care [7] has been taken to acquire micro-beam XAS spectra from crack free locations within the oxide matrix of the sample.

Synchrotron measurements
In order to determine the phases present in the oxide matrix and spatially resolved chemical speciation of nickel in the corrosion layer, synchrotron radiation based XRD and XAS experiments were performed at the Micro-XAS (X05LA) beamline of the Swiss Light Source (SLS) facility. At the sample location the X-ray beam was focused on a 1 µm × 1 µm spot size and all measurements were performed at room temperature. The incident X-ray intensity was monitored with an ultrathin Si-diode, and the emitted characteristic X-ray fluorescence (XRF) was detected by a Peltier cooled energy dispersive solid-state Si detector, positioned at a small take-off angle (grazing-exit geometry) to analyze only the near-surface area of the sample. The photon energy calibration of the Si(111) crystal pair based monochromator has been done by analyzing a Ni metallic foil (threshold K-edge energy 8333 eV for Ni). The diffraction pattern of the oxide layer was studied using the transmission Laue method in scanning mode. A Pilatus photon-counting area detector was positioned at about 70 mm behind the sample to collect the diffraction patterns.

Specimen localization and XRF mapping
It may be noted that alloying elements in low concentration in Zircaloy-2, like 0.18 wt% Fe, 0.11 wt% Cr and 0.05 wt% Ni, provide high counting statistics of the fluorescence peaks when excited using synchrotron light. The result is shown in Fig. 2. For example, an XRF spectrum of the Zircaloy-2 sample, excited by an incident energy of 8.4 keV and collected in about 90 s, is depicted in Fig. 2a. As can be seen on the figure, all three alloying elements (Cr, Fe and Ni) in Zircaloy-2 are easily identifiable in the energy range between 5 and 8 keV. The highest intensity peak at 8.4 keV, originating from elastic scattering events, indicates the energy of the incident X-ray photons. Note also that additional XRF peaks of light elements can be observed in Fig. 2a. The intense peak at 2.958 keV results from the atmospheric argon present in ambient air. The other K-shell peak at 3.692 keV originates from the Ca impurity present in the adhesive Kapton film attached on the sample holder. The spurious Si peak at 1.740 keV comes from the detector crystal.
Using a microfocused beam at the fixed X-ray energy of 8.4 keV, we scanned an area over the oxide layer with 1-μm step-size and generated the 2D element map of nickel atoms. The sampling time for each data point was 2 s. An example of the nickel intensity map for a 30 µm × 100 µm area, imaged in the neighborhood of the FIB-processed window (see Fig. 1), is illustrated in Fig. 2b. It might be mentioned here that the nickel signal intensities in the 2D image ( Fig. 2b) are not absolute values, and our central purpose was to map the spatial distribution of nickel in the corrosion layer for conducting spatially resolved XRD and XAS measurements. The μXRF map of Fig. 2b clearly show an oxide layer formed on the cladding and underlying a CRUD (Corrosion Residual Unidentified Deposit) layer. The average oxide thickness, estimated from the μXRF map, is about 50 µm in the probed regions of the specimen. Although not quantified in this study, a pixel dependent and local color-contrast based detail image analysis reveals that the oxide layer at the metal-oxide (M/O) interface has a moderate degree of unevenness in the micron scale. The probing regions of the specimen for XRD and Ni XAS measurement were identified from the nickel distribution map shown in Fig. 2b. As the interface properties of the oxide layer are decisive for the hydrogen evolution in the metal, the metal-oxide interface area has been probed selectively and in details.

XRD, XAS data collection and reduction
With a motorized sample manipulator to regulate the incident beam position on the sample to 1 µm or even better, microbeam XRF and XRD experiments were carried out by scanning the sample across the focused synchrotron light. Measurements were conducted at several regions, both near the oxide/metal interface (as indicated in Fig. 2b) and in the bulk of the oxide layers. The acquired datasets were processed using XRDUA [9] and/or Fit2D [10] software package. From single spot consecutive Laue images measured at a given location, average 2D diffraction images were generated and analyzed. The 2D images were then radially integrated and transformed into 1D plots (intensity vs. 2θ). The diffracted intensities have been obtained by so-called cake integration. All Bragg peaks in the XRD spectra were indexed on the basis of known crystallographic structures for zirconia polymorphs reported in open literatures.
The mapping mode in μXRD has permitted identification, localization and assessment of the degree of crystallinity, and quantification of the relative volume fractions of t-ZrO 2 and m-ZrO 2 phases with micrometer-scale spatial resolution. The 2D μXRD map of integrated t-ZrO 2 intensity was collected using a focused X-ray microbeam (1 µm × 1 µm), and this involved recording of about 2000 two-dimensional Laue images (40 µm × 50 µm examined area; 1 µm step size, 1 s exposure). The 2D XRD patterns were integrated and analyzed using the XRDUA software in a batch-wise processing mode. To perform a quantitative study XRD curves were analyzed by iterative Rietveld refinement [11].
For each m-ZrO 2 and/or t-ZrO 2 structure, both the lattice parameters and the internal coordinates of the atomic sites within the unit cell have been optimized. Before starting the refinement, a Pseudo-Voigt function was selected to describe the background removed spectral line shape of an XRD pattern in obtaining the best fit and data analysis. The structural models for the unit cell indexing and refinement of m-ZrO 2 (space group P2 1 /c) and t-ZrO 2 (space group P4 2 /nmc) phases have been taken from the ICSD Database (FIZ Karlsruhe, Germany [12]).
In order to obtain Ni K-edge XAS spectra, the locations of the probing regions on the sample were identified using the nickel intensity distribution map, as presented in Fig. 2b, investigating the evolution of crystallography as well as redox chemistry of nickel in the corrosion layer. To achieve this purpose, XAS spectra were recorded at different locations of the Zircaloy-2 sample. A total of at least 8 energy scans were collected from each selected location and combined in order to obtain EXAFS (Extended X-ray Absorption Fine Structure) data with good signal to noise ratio. For each scan all channels were inspected individually and glitches (produced by the single crystal monochromator) were removed from the spectrum prior to averaging. The computer program Demeter [13] was used to correct the background and processing of the XAS data and EXAFS analyses. The spectra were background subtracted using the cubic polynomials spline fit method to the experimental data. Fig. 3 presents one of the selected spectra recorded at the metal side of the metal-oxide interface, and other spectra acquired at four distinct locations within the oxide matrix. That are, one at the oxide side close to the M/O interface, two at the intermediate regions of the oxide matrix and one at the outer region in the oxide layer near the oxide-water interface. The results in Fig. 3 illustrate that high-quality XAS data is achievable from an adequately designed synchrotron based experiment to find the trace element nickel in the corrosion layer of a high burnup Zircaloy-2 cladding specimen.
For reliable determination of the chemical properties of Ni throughout the corrosion layer, the XANES (X-ray Absorption Near Edge Structure) part of all spectra in Fig. 3 have been analyzed in detail. The energy shifts of the Ni K-edge, relative to the excitation energy of Ni measured from a metallic reference foil, were determined by the first inflection point at the edge position of the XANES spectra. The local atomic environment around nickel ions contained in the zirconia crystallites is examined by analyzing the EXAFS part of the XAS spectra presented in Fig. 3. The procedure is standard as follows. After background subtraction and normalization to an edge jump height 1.0, the EXAFS oscillation of all coordination shells or χ(k) were extracted from the measured absorption spectra. The k 2 -weighted χ(k) spectra were then Fourier transformed (FT) from momentum space (k) space to real space (R). During the data reduction, a Hanning window function was chosen over the desired χ(k) range to reduce the termination ripples at the end points of the Fourier transform.
Qualitative and quantitative analyses of the FT peaks to obtain EXAFS structural parameters on Ni was accomplished by using the leastsquares curve fitting methods. All fits used the site-selective and four free parameters: average interatomic distance, R, average coordination number, CN, the Debye-Waller (DW) term, σ 2 , and an energy correction parameter, ΔE 0, which were numerically evaluated from XAS data. In modeling experimental data, theoretical EXAFS amplitudes and phase functions of Ni coordination shells were calculated applying FEFF9 [14] for a nickel dopant incorporated into the host ZrO 2 monoclinic crystallites being the main oxide phase in the corrosion layer.
First, the EXAFS signals were modeled using a conventional multicomponent approach involving a set of single-scattering FEFF paths. Considering the major difficulty and thus limitation in EXAFS multishell data analyses, we also attempted an alternative fit method, where the first peak in the RDF (Radial Distribution Function) spectrum was isolated by Fourier filtering for structural determination by EXAFS curve fittings.

Computational DFT+U methodology and LFDFT model
In order to study the incorporation behavior, dopant solubility and interaction of Ni ions with the zirconia matrix, we have performed detailed electronic structure calculations, based upon Density Functional Theory (DFT), for a Ni-doped m-ZrO 2 system. These calculations have been carried out by means of the Vienna Ab initio Simulation Package (VASP) [15] and the Amsterdam Density Functional (ADF) code [16]. The equilibrium geometric structures, energetics and electronic structures of three zirconia allotropes (monoclinic, tetragonal and cubic phases) have been reported in the literature to date [17,18]. In a recent publication, we have described the effects of nickel doping on the phase stability and modifications of the electronic band structure in Ni-doped m-ZrO 2 crystallite [7]. This study was undertaken to analyze Ni K-edge XANES profile, together with theoretical investigations using DFT to explore the influence of nickel doping on the electronic structure of monoclinic ZrO 2 (both Ni free and Ni bearing). In the calculations, a 3 × 3 × 3 supercell model structure of m-ZrO 2 (space group P2 1 /c) containing 324 atoms (Zr 108 O 216 ) was considered. The model for Ni-doped ZrO 2 was realized by replacing a Zr 4+ host cation by a Ni 2+ ion in a 3 × 3 × 3 supercell leading to the chemical formula Zr 107 NiO 215 made up of an O-vacancy located within the first coordination sphere of the Ni atom. Electronic structure analyses showed that doping of Ni contribute to slight lowering the bandgap of m-ZrO 2 by the presence of Ni-3d impurity states on the upper edge of the valence band and bottom of conduction band. The theoretically determined Ni speciation by DFT has led to considerable insight into the Ni-O structures and changes in bond length required to accommodate a given bonding arrangement.
Aside from an atomistic modeling study of Ni 2+ doping effect on the phase stability as well as modifications of the electronic band structure in Ni-doped m-ZrO 2 crystallite, it is also important to assess the model's capability in representing the experimental results and validation of the predictive model structure of consideration. The present work is framed for ligand field multiplet calculations using the results of the VASP simulation obtained previously for Ni-doped m-ZrO 2 crystal [7].
The LFDFT calculations performed in this work pertain primarily to model the measured Ni K-edge XANES spectra, that relate to the electron transition by the promotion of core Ni 1 s electrons to the valance Ni 4p component in 3d-4p hybridized orbitals. In the first step, the total electronic energy per unit cell of Ni-doped m-ZrO 2 in the optimal spatial structure and lowest energy configuration has been computed using Hubbard-rooted DFT+U method [19], as described in Ref. [7]. The model of the optical properties due to the nickel 1 s 2 3d 8 →1 s 1 3d 8 4p 1 and 1 s 2 3d 8 →1 s 1 3d 9 transitions, relating to electric dipole and quadrupole transitions, respectively, have been tackled by means of electronic structure calculations within the framework of LFDFT methodology. Using the formalism of the ligand field theory, important spectroscopic parameters such as Slater-Condon parameters, spin-orbit interaction parameters and parameters required to construct the ligand field potential are obtained by DFT calculations. As we explain below, this allows us to compute the energies of all multiplet levels associated with open-shell 1 s 1 3d 8 4p 1 and 1s 1 3d 9 electron configurations of the divalent nickel ion in Ni-doped m-ZrO 2 crystallite. Accordingly, the oscillator strengths of the electric-dipole allowed 1 s 2 3d 8 →1 s 1 3d 8 4p 1 involving 4p virtual orbitals in the excitation process, which represent the Ni K-edge XANES, have been calculated. Finally, the scope of LFDFT is extended accounting multiplet splitting and ligand field effects of 1 s core-electron excitations for the evaluation of the intensities of the Ni K-edge absorption spectrum, followed by quantum theoretical calculations of the XANES profile using the LFDFT methodology.
In order to determine multiplet energies an effective ligand field Hamiltonian (H) has been set-up to incorporate possible configuration interactions of three open shells multi-electron systems within 1s, 3d and 4p orbitals. By diagonalizing the Hamiltonian H, we have obtained the many-electron energy levels, also called multiplet energy levels that characterize the electronic fine structure of the Ni 2+ ion in the monoclinic zirconia host lattice.
The effective Hamiltonian (H), proper to describe the electric-dipole allowed 1 s 2 3d 8 → 1 s 1 3d 8 4p 1 transition of divalent nickel ions, can be constructed by the combination of the following four terms as: Here, H ER stands for the inter-electron repulsion Hamiltonian. The second (H SO ) and third (H LF ) terms represent the spin-orbit coupling Hamiltonian and the ligand field Hamiltonian, respectively. The term H CT (also known as configuration-average energy correction term) denotes a Hamiltonian that combines all the relevant energy terms involving the zeroth order inter-electron electrostatic repulsion, the electronic kinetic energy component and the electron-nuclear interaction for the system having 1 s 1 3d 8 4p 1 and 1 s 2 3d 8 electron configurations.
The matrix elements of inter-electron repulsion term in Eq. (1) can be represented in terms of Slater-Condon parameters F and G. In the expanded form, relevant to describe 1s → 4p transitions for Ni 2+ ion, it is given by: where f and g denote the angular factors in parameters F and G, respectively. In Eq. (2) parameters are defined to account for both Coulomb and exchange interactions effects using two-electron Slater-Condon integrals F and G, respectively.
The spin-orbit part of the effective Hamiltonian in Eq. (1) to describe the influence of spin-orbit coupling on excited states of 1s, 3d and 4p nonequivalent electrons can be written as: where ξ nl (r i ) denotes an effective one-electron spin-orbit coupling constants for the electron i in the nl atomic shell, and the summation index i runs over all electrons in the atom. The l.s term represent spinorbit interaction. In Eq. (1), the ligand field splitting term, symbolized by H LF , accounts for chemical effects that ogygen ligand ions exert on the electronic structure. We have used the Wyboume's tensor operators, related to the standard Wybourne's spherical tensor operators C acting on the 1s, 3d and 4p orbitals, for extracting crystal field parameters, B, in the Wybourne's convention. The corresponding Hamiltonian matrix is: The spherical harmonics representation, (C (k) q ) in Eq. (4), of the ligand field potential may be technically limited by the symmetry constraint. Therefore, the ligand field matrices are mostly constructed on the basis of spherical harmonics functions and using B q k (Wybourne parameters) where B q k parameters act as one-electron parameters in front of spherical harmonic operators C (k) q as in Eq. (4). The last term H CT in Eq. (1) describes the atomic-like body preserving the spherical symmetry. Generalizing this term for the case of Ni 2+ complexes involving three open shells 1s, 3d and 4p electrons, the Hamiltonian model can be represented as: where h p and h s are one-electron energies, respectively, originating from the 4p 1 and 1s 1 electron configurations of the free Ni 2+ ion. The Δ 0 parameter in the H CT equation refers to the energy gap between the ground and excited electronic states in the absence of ligand field interaction. The terms F 0 and B 0 0 in Eq. (5) denote the zeroth-order interelectronic repulsion interaction and Wybourne-normalized crystal field parameters, respectively.
Though not elaborated here, the standard mathematical formulation for purposes of numerical calculation of the multiplet energy levels applying LFDFT algorithm can be accessed via the open literature [20,21]. Briefly, the computational procedure adopted in the present study can be outlined as follows: (i) the local atom structure around Ni in doped m-ZrO 2 (stoichiometric) has been defined via structural optimizations in terms of total DFT energies. After defining the computational geometry, a molecular orbital model involving a single Ni(II) ion in hexa-coordinated ligand environment has been considered, utilizing the LFDFT approach; (ii) the matrix elements of all the entities of the effective Hamiltonian in Eq. (1) are expressed as function of Slater determinant using LFDFT algorithm, which involve evaluation of the expectation values of a four component Hamiltonian matrix; (iii) the matrix elements of inter-electron repulsion (H ER ) in Eq. (2) are obtained using Coulomb-repulsion integrals (F) and exchange integrals (G). The integrals are computed in the framework of first-order perturbation theory and central-field approximation according to Slater. For the calculations, we used the calculated radial functions (R 1 s , R 3d and R 4p ) of the Kohn-Sham orbitals for Ni 2+ ion configuration in m-ZrO 2 ; (iv) the calculation of spin-orbit matrix elements (H SO ) is based on the Zeroth Order Regular Approximation (ZORA) approximation to the Dirac equation, and this implementation is available in the ADF code. Accordingly, the spin-orbit coupling constants, ξ 1 s , ξ 3d , and ξ 4p , with angular coefficients (d s , d d and d p ) in Eq. (3), have been calculated using the radial functions R 1 s , R 3d and R 4p , respectively; (v) the B parameters in Eqs. (4) and (5) are determined (following the Wybourne parametrization scheme of LFDFT) using the molecular orbital energy and the associated eigenfunctions of 1 s, 3d and 4p Kohn-Sham orbitals; (vi) the energy gap term, Δ 0 , in Eq. (5) has been calculated as the energy shift between the multiplet states of the 1s 1 3d 8 4p 1 and 1s 2 3d 8 electron configurations;. (vi) using all these optimized parameters, finally, we have performed multiplet calculations of the energies by taking the corresponding 1 s 2 3d 8 and 1 s 1 3d 8 4p 1 electronic configurations for the oxidized nickel ions, naturally of greatest interest in this study.
The multiplet energy levels are eigenvalues of Eq. (1). The oscillator strength (I) in electric-dipole and electric-quadrupole approximations can be calculated using the following: where e and m e are the charge and mass of the electron, respectively. In the right-hand side of Eqs. (6) and (7), the quantum states are represented as bra-ket pairs in Dirac notation. The terms < 1s 1 3d 8 4p 1 , Γ i | and < 1s 1 3d 9 , Γ i | symbolize all manifolds of the multiplet levels belonging to excited electrons in the final states. The corresponding term for the ground state electronic configuration is |3d 8 , Γ 0 > . The notation d α in Eq. (6) denotes the dipole operator for absorption with αpolarized light.
In this equation, E 0 and E i are the energy for the ground state and excited electronic configurations, respectively, and the values are taken from the output list of the LFDFT calculations. Likewise, M ab represents the electric-quadrupole moment operator. Here the subscripts a and b are used to denote the polarization of X-ray light. The delta function (δ) in Eqs. (6) and (7) takes care of the energy conservation, where the notation hν stands for the energy of the absorbed photon. Eqs. (6) and (7) are used for the computation of the oscillator strengths for permitted dipole 1s 2 3d 8 →1s 1 3d 8 4p 1 and quadrupole 1s 2 3d 8 →1s 1 3d 9 transitions, where strength of transitions is directly related to the dipole (or quadrupole) matrix elements. In these calculations, the matrix elements of d α (or M ab ) are distributed over all manifold of the multiplet states arising from the ground 1s 2 3d 8 and excited 1s 1 3d 8 4p 1 (or 1s 1 3d 9 ) configurations of Ni 2+ in their chemical environment, as calculated using LFDFT Hamiltonian (Eq. (1)). Consequently, the numerical intensity values are scaled to unity to facilitate comparisons among contributions from all possible electronic configurations in the system. Further discussion on those scattering operators in deriving the intensity at the Ni K-edge is beyond the scope of this work. For completeness, let us also mention that the theoretical Ni K-edge absorption spectrum has been made by broadening the oscillator strengths and accounting the physical contribution (i.e., multiplet dependent core-hole lifetime energy, Γ i ) as well as the instrumental energy resolution to the XANES spectral shape, as will be shown later.
First-principles XANES calculation by evaluating multiplet absorption oscillator strengths needs a careful treatment of the theoretical intensity data for an estimation of true line shapes and widths, and their comparison with experimental results. As already mentioned, the theoretical Ni K-edge XANES has been calculated using Eqs. (6) and (7). The absolute line intensity of all possible dipole and quadrupole transitions have been convoluted with a Lorentzian function. This Lorentzian broadening effect is taken to account the finite lifetime of the core-hole. In the present work, absolute intensities of all possible transitions of the multiplets have been convoluted by a Lorentz line shape with a broadening parameter, Γ (the half-width at half maximum of the Lorentz function). Subsequently, a model arctangent function is also constructed to mimic the absorption jump at the edge step.
To simulate the experimental Ni K-edge XANES, the Lorentzian curves were centered at each calculated multiplet energy over the whole energy region. To represent the continuum absorption spectrum the inflection point of the arctangent curve was set at the threshold excitation energy measured from the experimental XANES curve. A quantitative analysis of experimental XANES data using line shape fittings was done applying standard fitting procedures. In the fits, the Γ parameter and the amplitude of the arctangent function were optimized until the resulting spectrum and the measured spectrum showed a fairly good agreement with all spectral features being reproduced accurately. As the calculations did not reproduce the absolute energy positions for the calculated multiplets, it was necessary to shift simply the computed XANES spectrum to the higher energy for an easy comparison with the experiment. We used the white line feature of the experimental data for this alignment and overlap with the theoretical spectrum.

Results and discussion
The Ni distribution analysis via μXRF has allowed the identification of the zirconium oxide layer and underlying metallic-part of Zircaloy-2 for spatially resolved micro-beam XRD and XAS studies. The image shown in Fig. 2b evidences the location of the thick oxide layer formed, the Zircaloy-2 metal matrix, and the metal-oxide interface region as also sketched in the map. The regions covering the metal-oxide interface and the CRUD deposits on the cladding surface are also indicated in Fig. 2b.
The signature of a ridge-like structure running from top left to bottom left of the Ni elemental mapping image, as appears in light-to-dark yellow color-coded regions, corresponds to one of the two-side walls zone of the FIB-processed window in the sample. It is important to note that relative increases of Ni signals occur in this area due to sample thickness variation effects. However, the rest of the Ni map within the metal and/or zirconium oxide corrosion layer seems to indicate a fairly homogeneous distribution of Ni over the scanned area.
In general, the alloying element nickel in Zircaloy-2 forms intermetallic precipitates [usually of bct-Zr 2 (Fe,Ni) type] containing most of this alloying element, and the concentration of dissolved Ni in the bare α-Zr matrix is very low. However, when dissolution of precipitates occurs in reactors, the bonded Ni atoms originally in the precipitates are dispersed into and retained in the α-Zr matrix. The Ni distribution analysis via μXRF of 79 MWd/kgU burnup Zircaloy-2 in Fig. 2b shows that the microstructure continually has evolved. Almost all Ni-bearing precipitates have disappeared completely in the metal matrix and in the oxide overlayers. We may note in this regard the results of two previous studies [22,23] using APT and TEM to elucidate SPP characteristics in Zircaloy-2 material under investigation. The TEM images have revealed irregular shaped ultrafine SPP still present in the material and Fe-Ni(Cr) clusters can be detected by APT, but none have been detected in our micro beam synchrotron experiments due to their very limited sizes (≤ 50 nm), sporadic distributions and drastically reduced number density (~ 1 ×10 19 m − 3 ) on irradiated Zircaloy-2 irradiated up to nine annual cycles in a BWR core. Let us also mention that present work concerns redox chemistry and speciation studies of Ni when in solute form in the oxide layer. Consequently, the evaluation of nanostructured and remnant SPP for hydrogen pick-up properties of Zircaloy-2 is beyond the scope of this paper.

Analysis of XRD data
In Fig. 4a, a typical single-spot 2D μXRD image (inset) and the corresponding XRD pattern are displayed for experimental data collected from a selected-area near the metal/oxide interface at the sample stage (see Fig. 2b). The XRD spectrum in Fig. 4a show two strong peaks at 2θ values of 27 • and 30 • arising from the (− 111) m and (111) m reflections, respectively, of the monoclinic ZrO 2 phase, and a weak XRD signal contribution at 2θ = 29 • for the tetragonal zirconia. The observed tetragonal peak corresponds to the (101) t Bragg planes. Besides, small intensity peaks due to the diffraction of {200} family m-ZrO 2 planes can also be seen in Fig. 4a. In order to quantify the diffraction information, the data measured in the diffraction angle range 2θ = 26-31 • have been analyzed in detail. The two-dimensional μXRD map of integrated (101) t intensity has also enabled to examine the local distributions of the crystalline t-ZrO 2 phase in the corrosion layer of the sample. From the respective (− 111) m , (111) m and (101) t peak intensity values, the volume fractions of the tetragonal phase, at selected locations on the map with high t-ZrO 2 content, have been determined by using Gravie's and Nicholson's formula [24]. A μXRD map, essentially reflecting the t-ZrO 2 phase distribution observed for the entire 40 µm × 50 µm mapped-area in the sample, is shown in Fig. 4b.
In our results, the Rietveld refinements resulted in very good fits between the observed and calculated line patterns for the dominant (− 111) m and (111) m monoclinic peaks. However, in view of the significant fall-off in the (101) t tetragonal peak intensity, it exhibits the diffraction line that is consistently broader than those of the monoclinic phase, observed for the entire mapped area in the sample (Fig. 4b).
Within the µXRD mapped oxide layer, it is also noted that there is some local variability in the (101) t peak-intensity distributions due to the close proximity and overlapped position in µm of each microbeamanalyzed spot, and slight differences in the measured lattice parameters with respect to those of the reference t-ZrO 2 unit cell.
The spatial mapping of the crystalline t-ZrO 2 phase, depicted in Fig. 4b, shows that there is a noticeable amount of tetragonal zirconia present at or near the oxide/metal interface regions, and a sudden decrease of the tetragonal content at some critical distance of about 10-12 µm from the metal-oxide interface. Another notable feature is that the t-ZrO 2 distribution is anisotropic in the lateral direction and features a two-layer type heterogeneous structure at the interfacial oxide region. On the whole oxide scale of 50 µm thickness, the distribution of the t-ZrO 2 phase is non-uniform and exhibits some sort of cyclic periodicity in the oxide layer grown in the BWR reactor during nine annual cycles of irradiation.
The observed variations of the tetragonal phase distributions with oxide thickness in Fig. 4b are qualitatively consistent with many experimental results reported in the literature [25][26][27][28]. According to literature, a continuous phase transformation of the metastable tetragonal phase to the stable monoclinic structure occurs during the oxidation process of Zircaloy, which is directly linked to the transition behavior of the oxidation kinetics of the alloy. The oxide layers grow up to the transition point (so-called pre-transition period), and involve successive cycle of pre-transition corrosion periods following the periodicity of the oxidation kinetics as the oxide thickens [29]. Many experimental results have shown that the consequence of the formation of tetragonal phase at the metal/oxide interface region is accumulation of local compressive stresses in the oxide, which is induced by the volumetric expansion when Zr is oxidized to ZrO 2 (Pilling-Bedworth ratio is 1.56) at the interface. The existence of a stress gradient in the grown oxide film enables the high density tetragonal phase to transform to a less dense monoclinic ZrO 2 at some distance from the interface accompanied by the development of micron size cracks and porosity. The observed periodic pattern in the evolution of t-ZrO 2 content within the oxide thickness (Fig. 4b) is related to the cyclic growth of the oxide layers during corrosion following the oxidation kinetics periodicity, consistent with prior reports in the literature [30]. It is however not the purpose of this report to go further into details of these formation conditions. The issue of stabilization of the tetragonal phase and the main factors affecting the phase stability in Zircaloy materials have been reported in the published literature [31,32].
In order to offer a general idea about the amount of tetragonal zirconia phase fraction present in the oxide layer, quantitative information is obtained by analyzing a selected set of 2D Laue images because the μXRD data on a per pixel basis could be used as part of the map and every map pixel contains an independent XRD frame. For this purpose, areas of elevated t-ZrO 2 intensities on the map (Fig. 4b) were preferred for XRD Rietveld analyses.
The volume fractions of tetragonal oxide were determined using the Gravie-Nicholson relation [24] and amount to a range of 12-16% near the oxide/metal interface. The tetragonal fraction away from the M/O interface varied between ~ 5% and ~ 8%. The decline in the proportion of tetragonal zirconia away from the interface means that a part of tetragonal phase has transformed to monoclinic phase during the corrosion process with growth of outer oxides. Because it was not possible to account texture effects [33] while performing the structural Rietveld refinements, which would require specific corrections since the measured intensities of the (− 111) m , (111) m and (101) t lines are far from those of the isotropic m-ZrO 2 and/or t-ZrO 2 phases, the obtained tetragonal phase fractions are not absolute values. We plan to carry out additional studies focusing on the crystallographic structures of the preand post-transition oxides formed, stress characteristics that is sensitive to the grain size of the oxide near the M/O interface, and texture as well as orientation of the oxide grains in the corrosion layer of the sample under investigation. These results will be reported in a future publication.
We also mention here that the present study is focused to obtain the atomic scale structural information on the microstructure of zirconium oxide formed by oxidation of the very high burnup Zircaloy-2 cladding where the alloying element Ni has been incorporated into the growing oxide layers comprising a mixture of m-ZrO 2 and t-ZrO 2 phases. As discussed above, the apparent volume fractions of the tetragonal phase ranged from approximately 5-15% (over the entire oxide layer) in which the estimated phase volume-fractions are not corrected for the oxide texture and/or any crystallographic anisotropy effects. In this report, the concentration distribution and spatial variation of t-ZrO 2 content within the oxide matrix are highlighted, rather than its absolute value. Since the amount of tetragonal phase formed is much lower relative to the main monoclinic phase oxide, its EXAFS contribution to the measured Ni K-edge XAS spectra can be considered negligible.

Analysis of Ni K-edge XAS data
In Fig. 3 we have shown the evolution of the normalized Ni K-edge XAS spectra from the M/O interface to the outer part (water side) of the oxide region in the sample. For comparison, the absorption spectrum acquired at the metal side near the M/O interface is also presented in Fig. 3. We first used the XANES part of the experimental data to identify the chemical state of Ni in the sample. The quantitative XANES spectra (see inset in  oxide-like white line feature at 8350 eV above the absorption edge, and give rise to the same results in terms of XANES shape as well as the main edge energy position. The edge position (E 0 ) of these oxide spectra, determined by taking the centroid position on the first derivative XANES data, is located at 8345.5 eV. This energy value is 12.5 eV higher compared to the measured absorption edge energy of 8333 eV for Ni atoms present at the metal side of the M/O interface.
In general, a shift toward higher energies can be attributed to an increased oxidation state of nickel atoms. The energies at which the absorption edges occur for oxidized nickel atoms, measured at three different spot locations near the M/O interface, represent a characteristic Ni 2+ ionic environment. This fact is interpreted by comparing Ni Kedge XANES spectrum from a reference NiO (the E 0 position of 8345.2 eV, data not shown) sample. The characteristic XANES features in the oxide spectra of the interfacial region in Fig. 3 also show close resemblance to those observed on the XANES spectra of NiO model compound or NiO x thin films reported in the literature [34]. However, it is noted that the Ni spectrum measured at about 25 µm from the M/O interface (location 4 in Fig. 2b) has a slightly higher edge-energy (E 0 ) position of 8346.2 eV, and the XANES spectral features exhibit a pronounced increase in the white line intensity peaking at 8351.2 eV. In this XANES spectrum, the peak energy of the white line is shifted towards the high energy side by 1.2 eV relative to the spectra acquired near the M/O interface regions. These results indicate that nickel at the outer oxide regions has an effective oxidation state larger than 2 + that observed at the M/O interface regions. This is what has been also seen in previous studies for reactor exposed Zircaloy-2 materials that nickel is mainly divalent near the M/O interface, and the valence of Ni is slightly higher (~ 2.3) at distant locations within the oxide matrix [35]. It is perhaps worth mentioning here that the presence of Ni(II) hydroxide (such as the Ni(OH) 2 phase) in the outer part of corroded nickel electrodes has been reported in the open literature [36]. The Ni K-edge XANES and EXAFS results of Ni(OH) 2 samples have revealed a pre-edge feature from the 1 s → 3d forbidden transitions due to mixing of local orbitals and octahedral symmetry breaking of Ni coordination in Ni(OH) 2 [37]. However, we do not observe any signature of a pre-edge peak in our measured XANES data (spectrum 4 in Fig. 3). It will be shown later in this section that any consideration about the possible octahedral coordination environment for oxidized Ni atoms located in the outer oxide region does not support our EXAFS analysis results. Therefore, we exclude the presence of any Ni containing hydroxide species in the oxide layer of the analyzed sample. It should be also mentioned that the interpretation of a XANES for determining oxidation state(s) is often not as straightforward and may require more detail analyses such as any variation related to nickel coordination environment, which influences both the XANES edge energy and absorbance intensity. In the following, we present a comprehensive EXAFS analysis to characterize the nickel speciation (the local atomic environment around Ni ions, bonding configurations of Ni-O and Ni-Zr interactions, and the cation-specific atomic scale defect structures) in order to ascertain the potential role of nickel in the hydrogen transport process through the oxide film into the metal side of Zircaloy-2.
In order to extract structural information, the quantitative EXAFS curve-fitting analysis was applied following the procedure as summarized in the experimental section. For all spectra, the Fourier transform have been performed in the k-range 3-10 Å − 1 . In Fig. 5 the resulting RDF curves are shown. The crystallographic data of m-ZrO 2 and results of the EXAFS structural refinements are summarized in Table 2.
It is obvious that the RDF spectra in Fig. 5 show mainly two major peaks between 1 and 3.5 Å. Also note that spectral features are quite noisy for more distant coordination shells. The strong first peak at around 1.5 Å originates from the first coordination shell of nickel atoms and refers to oxygen neighbors in the ZrO 2 lattice. This peak contains no contribution from any Ni-Ni or Ni-Zr pairs. The second peak in the RDF, located around 2.5 Å, is sensitive to the immediate neighborhood of the central nickel atoms beyond the first-shell of oxygen neighbors, and corresponds to Ni-metal (Ni,Zr) correlation. This second peak, shown up between 2 Å and 3 Å, also contains contribution from multiple scattering effects. Other higher-order and distant Ni-O(Ni,Zr) peaks in the higher R region are very weak and not clearly resolved in the RDF spectrum.
In Fig. 5 it can be also seen that the three RDF curves (as labeled 1-3 according to the probed spots shown in Fig. 2b), measured near the M/O interface, have similar line shapes and equivalent intensities, indicating no significant changes in the local environment around Ni at the M/O interface regions. With regards to the EXAFS RDF around Ni measured at the outer part of the oxide layer (RDF 4 in Fig. 5), the FT peakamplitudes are found to be notably higher than previously indicated although their positions appear to be nearly unchanged. In addition, a third-neighbor feature at around 5 Å can also be observed in the RDF curve obtained for this EXAFS data set. Far from the metal-oxide interface, the increase of the FT amplitude and appearance of a third shell of scatters can be considered as that resulting from an increment of average coordination numbers in the consecutive crystallographic shells representing nickel coordination spheres belonging to an ordered structural environment, i.e. to the crystallinity of zirconia microstructure. Moving closer to the metal-oxide interface regions, a qualitative shape change of the RDF curves and reduction of the FT-peak intensities could be assigned to the presence of structural disorder in the interfacial oxides (relative to well-ordered crystalline phase of ZrO 2 ), which gives rise to a distorted coordination environment of Ni atoms, thus having a lower contribution (from nearest neighbors backscattering atoms) to the EXAFS signals. It should also be mentioned that existence of zirconium suboxides at the M/O interface regions and/or the lattice defects present in the oxide films contribute to the damping of the EXAFS signal.
It is important to remark that the FT-EXAFS spectra (Fig. 5), associated with the four probing locations in the zirconia corrosion layer, are related to the same structural parameters (R, CN, ΔE 0 , σ 2 ), and each individual RDF pattern is an independent measurement of the related structural observables. Also, the XAS spectra are normalized to the contribution per nickel atom. This effectively means that comparisons of the Ni structural environments between two different locations within the oxide matrix can be made, regardless the nickel content present in the corrosion layer. In analyzing the FT data in Fig. 5 the theoretical EXAFS scattering amplitudes and phase shifts functions have been taken from the FEFF program [14] output files. The cation substitution method has been used to characterize the local environment of Ni in m-ZrO 2 structure.  Fig. 2b. Note that the FT-EXAFS spectra are not phase corrected. The experimental FT-spectra are shown in filled circles and the solid lines give the best-fitted spectra. For clarity, the spectra are vertically shifted along the y-axis. See main text for details.
To model the Ni site, it was also necessary to consider the simple case of a single-shell analysis using the FEFF paths data of the oxygen or zirconium shells. It may be noted that the first and second coordination spheres of a central Zr atom in monoclinic zirconia contain a large numbers of coordination shells (see Table 2). The first coordination sphere is formed by seven oxygen atoms with a distribution of metal--oxygen distances between 2.04 and 2.26 Å. The second coordination sphere comprises successive seven zirconium atoms in the radial distance range from 3.35 to 3.59 Å. Therefore, using the model bond lengths of all paths generated in the FEFF calculation, it was impossible to derive the structural parameters (R, CN, ΔE 0 , σ 2 ) by conventional curve-fitting methods.
We have thus carried out the curve-fitting analyses using one single scattering FEFF path (of the first coordination sphere) involving O backscattering at a distance of 2.16 Å (the mean distance of the first seven Ni-O pairs, see Table 2). Likewise, the second FT peak in Fig. 5 has been modeled using a single scattering FEFF path with a bond distance of 3.47 Å, which is the same as the mean distance of the first seven Ni-Zr pairs in Table 2. Based on the approach outlined in the previous section, the experimental data were analyzed through shell-by-shell fittings in two steps with the desire to gain a better understanding of the Ni environment in the zirconium oxide layer. First, a single shell fit for the first coordination sphere of Ni and O atoms was done by varying three EXAFS parameters (R, σ 2 , ΔE 0 ) for determining the Ni-O interatomic distance (R), the Debye-Waller factor (σ 2 ), and the energy correction parameter (ΔE 0 ), while the coordination number (CN) was kept fixed to its crystallographic value. The fit range in R-space was 0.7-2.0 Å (see Fig. 5). At the second step, initial fits of higher shells were performed in the R-range 2.0-3.5 Å in which both R and σ 2 varied simultaneously, CN fixed as seven-coordinated as the known coordination of zirconium in m-ZrO 2 ( Table 2), and ΔE 0 constrained to the best-fit value derived from fitting first coordination Ni-O shell. Note here that this procedure has led to limit number of free variables in curve fitting analyses as required in the standard approach, and also reduces the correlation related effects between R and ΔE 0 parameters used for fitting the data. Once an approximate distance (R) and the Debye-Waller factor (σ 2 ) for the second nearest Zr neighbors were known, we carried out another fit in which the energy correction term (ΔE 0 ) was refined while the R and σ 2 parameters were kept fixed to the values determined from the above approach. Finally, a combined fit for the first two coordination shells (Ni-O and Ni-Zr) was performed using the assumed coordination number parameters (CN) together with resultant bestfit parameters (R, σ 2 , ΔE 0 ) obtained in the two previous steps, and was allowed to freely float during optimization. The EXAFS ℜ-factor was used to judge the fit quality with an acceptable standard of less than 20%.
In Table 2 we report the best-fit values of the structural parameters obtained from fitting of the EXAFS data. The quantitative structural parameters extracted from the FT-EXAFS spectra measured near the M/ O interface regions at locations labeled as (1), (2) and (3) are very similar. The analyses of the obtained set of Ni-O distances evidence the location of solute nickel in the zirconium oxide microstructure, and definitively indicate that central Ni atoms are undercoordinated with neighboring O atoms (with respect to seven fold oxygen coordination for the first-shell of Zr-O pairs in monoclinic zirconia phase). The average Ni-O bond distance at the metal-oxide interface is 1.96 Å with an average coordination number of 2.5. With regards to the RDF around Ni measured at the outer part of the oxide layer (spectrum 4 in Fig. 5), we obtained the Ni-O interatomic distance R = 1.96 ± 0.01 Å and the coordination number CN = 3.6 ± 0.3. Thus, it can be inferred from these experimental results that oxygen vacancies are sited preferentially adjacent to solute nickel ions in the oxide layer formed during corrosion of Zircaloy-2 cladding. At the same time, we also find that the average Ni-O radial distances, obtained by EXAFS analysis at multiple locations within the oxide area, are sufficiently shorter (about 0.2 Å, see Table 2) than the mean distance of the first seven Zr-O pairs in the idealized m-ZrO 2 structure. Table 2 also gives structural information associated with the Ni-Zr interactions, derived for the second coordination shell around nickel ions. Because of the very low concentration of solute nickel in Zicaloy-2, here in our model it is assumed that Ni-Ni pairs of a second coordination sphere do not give an EXAFS contribution to Ni K-edge data, so that, in the distance range of 2-3.5 Å, only the metal Zr element in the base ZrO 2 matrix contributes to the experimental signal.
The results of the Ni-Zr shell EXAFS analysis in Fig. 5 point to the fact that the fitted curves do not accord well with the experimental curves. In all the FT-EXAFS spectra, the Ni-Zr nearest-neighbor distribution is not reproduced with a corresponding single-scattering shell FEFF path. The determined bond lengths at four different locations in the oxide layer are 3.34, 3.37, 3.48 3.52 Å. From these values, one derives an average of 3.43 Å, close to the crystallographic Zr-Zr distance in m-ZrO 2 (see Table 2). However, the resulting coordination number of nickel for this shell, which was assigned to the Zr in seven-fold coordinated sites in all Table 2 Crystallographic data of m-ZrO 2 together with structural parameters extracted from EXAFS fit results. CN, R and σ 2 imply coordination number, radial distance and Debye-Waller factor, respectively. The estimated errors in R is about ±0.02 Å and approximately ±10-15% in CN and σ 2 . For details see text.
Absorbing atom Ni Spot location (see Fig. 2b experimental RDF, falls at a significantly smaller value close to 5.2 (an average value). Also, the DW factors evaluated at the metal-oxide interface and outer oxide region for this shell are very large as compared to that of m-ZrO 2 (~ 0.0036 Å 2 ) reported in the literature [38]. Larger σ 2 is typically the sign of a greater amount of local structural disorder in the oxide grains of corroded Zircaloy-2, which may reasonably be attributed to effects of neutrons irradiation on the growth of zirconia layers under the operating high temperature conditions of a BWR. For the three EXAFS spectra measured near the metal-oxide interface, σ 2 is almost constant ~ 0.0073 Å 2 which is slightly higher than that determined for the outer-part of the oxide layer (0.0068 Å 2 ). In addition, higher values of the EXAFS ℜ-factor, as obtained in the standard way [39] in Table 2, do not signify a moderately good fit of the FT-EXAFS especially for the Ni-Zr interaction peaks occurring at higher radial distances (see Fig. 5). Since the magnitude of EXAFS oscillation functions χ(k) is proportional to both CN and 1/σ of a Ni-O absorber-scatterer pair, this could explain the undercoordinated metal--metal distributions, and high values resulted for the DW factors of the Ni-Zr distance in the oxide sample because the two parameters are strongly correlated in the EXAFS equation. However, the fact that numbers of nickel neighbors of the second coordination shell are much smaller than expected to have a real structural meaning, may thus be considered as the consequence of an inadequate fitting procedure. It appears necessary to include additional Ni-Zr FEFF paths, which may represent a combination of all single scattering paths and several multiple scattering paths of similar lengths, in the analysis to obtain physically meaningful results of best-fit structural parameters. The knowledge of Ni speciation (including oxidation state) is essential for understanding its role on the accelerated hydrogen pickup property of Zircaloy-2, which enlightens the fundamental mechanisms driving hydrogen absorption in the alloy. It is evident from the above discussion, that an unrestricted and multi-shell EXAFS fitting procedure is unable to provide good results. Moreover, the resulting goodness-of-fit parameters (ℜ-factor values) in the range 12-17% (see Table 2) do not signify a moderately good fit of Ni K-edge data. As a remedy to this situation, we have analyzed only the first coordination Ni-O shell of the Ni(II) centers as the strongest EXAFS contribution usually comes from the first nearest neighbor shell surrounding the absorbing atom. After all, our primary interest here is the parameters R and CN, the distance and coordination number, respectively, of the Ni-O RDF, that parametrizes the speciation of dissolved nickel in the oxide layer and the nature and amount of distortion present around the Ni 2+ ions. For this reason, the frequency component of the FT-EXAFS data in Fig. 5, corresponding to the Ni-O shell alone in the radial range of 0.7-2.0 Å, has been backtransformed and best-fitted. In the fit procedure all structural parameters, R, CN, and σ, have been allowed to float freely to the best fit. The principal advantage of this approach is that a maximum of only 3 variable parameters are involved in the least-squares refinement, and the multiple scattering contributions in EXAFS data analysis become irrelevant.
The fitted curves together with the Fourier-filtered k-space EXAFS data are depicted in Fig. 6. The comparison of the experimental data and the simulated data shows a good agreement. The quantitative analyses, based on the fitting procedure, give direct information on average coordination number and interatomic distance of local Ni-O bonding configuration at the oxide layer of the irradiated Zircaloy-2 sample. The fitting results, derived from a single shell fitting, are also summarized in Table 2. The results clearly show that the dissolved Ni, located in the oxide grains near the metal/oxide interface region of the sample, is coordinated to approximately five O-atoms with the mean Ni-O distance 1.96 ± 0.03 Å. The deduced bond dispersion, σ 2 , for the Ni-O scattering path is about 72 × 10 − 4 Å 2 (represent the average value).
In the outer part of the oxide film (location 4 in Fig. 2b), the effective coordination number and the Ni-O bond length are quite similar (within the error margins) when compared with the corresponding Ni speciation in the first coordination shell of the interfacial zirconium oxide layer. On the other hand, the σ 2 value [52 × 10 − 4 Å 2 ] of the Ni-O bond at the outer oxide region is significantly smaller compared to those determined for the oxide formed at the immediate vicinity of the Zr-ZrO 2 interface. These results imply a large static disorder in the nickel bonding environment at the metal-oxide interface regions belonging to the crystalline structure of m-ZrO 2 phase. The general microstructural characteristics associated with zirconia nucleation and oxides formed on Zircaloy-2 during in-reactor corrosion, in both pre-transition oxide layers adjacent to metal-oxide interface and post-transition outer oxide films at different distances with respect to the oxide/metal interface, have been discussed in the literature [40]. There exists a variation in crystallinity and oxide crystallite size between zirconia located at the metal-oxide interface and bulk zirconia, both linked to their ultrafine grain characteristics in different stages of oxidation, observed for in-reactor grown corrosion layers. In addition, the impact of irradiation induced microstructural changes on oxidizing Zircaloy claddings in the reactor and/or an increasing deviation from the ideal ZrO 2 stoichiometry in the growing oxide following in-pile radiation exposure could be positive factors to promote intragranular lattice defects formation in the zirconium oxide microstructure.

Simulation of Ni K-edge XANES for Ni 2+ -doped m-ZrO 2
In this section, we present a generic framework that extracts electronic, chemical and structural information with the computational aids considering full multiplet effects of 1 s core-electron excitations in evaluating the intensities of Ni K-edge absorption spectrum for the Nidoped m-ZrO 2 of interest here. In order to clarify the electronic transitions involved, and identify those electronic states responsible for the XANES spectroscopic features, we have compared the Ni K-edge experimental spectrum with the computed one. This allows us to ascertain the divalent character of nickel ions in the oxide layer formed on Zircaloy-2 as found in the measured XANES spectra, and verify the validity of the structural model (cation substitution method to characterize the local environment of Ni in m-ZrO 2 structure) which has been used for the EXAFS fitting. In fact, a model is built directly from experimental data, thus demonstrating the ability of the ability LFDFT method that interprets the K-edge X-ray absorption features in the near edge region of a Ni 2+ impurity center in stoichiometric phase m-ZrO 2 . This development supports the interpretation of XANES experimental data and help in deducing fundamental properties of the nickel dopant, such as oxidation state, spin state as well as coordination geometry to better understand migration mechanisms of hydrogen in Zircaloy-2.
The output of the multiplet energy levels arising from nickel 1s 2 3d 8 , 1s 1 3d 9 and 1s 1 3d 8 4p 1 electron configurations in Ni 2+ -doped m-ZrO 2 is shown in Fig. 7. We have computed the corresponding oscillator strengths for 1s 2 3d 8 →1s 1 3d 8 4p 1 (electric dipole-allowed) and 1s 2 3d 8 →1s 1 3d 9 (electric quadrupole-allowed) transitions, and the resulting line spectra for the multi-electron eigenstates are presented in Fig. 7. According to the Hund's rule of maximum multiplicity, the lowest energy term of nickel with an electronic configuration 1 s 2 2 s 2 2p 6 3 s 2 3p 6 4 s 2 3d 8 is a 3 F term in spectroscopic notation. When the spin-orbit coupling interactions are included, the term symbol for the ground state of nickel is 3 F 4 . The results of our computations show that under the influence of the inter-electron repulsion, the ground-state electronic configuration 1s 2 3d 8 yields five spectral terms with singlet and triplet spin-multiplicities: 1 S, 3 P, 1D, 3 F and 1 G. For the excited 1s 1 3d 9 configuration, the final state generates two discrete bands corresponding to singlet 1D and triplet 3D multiplets. We next point out that for the excited 1s 1 3d 8 4p 1 configuration thirty-eight multiplet terms have been calculated with singlet, triplet and quintet spin multiplicities.
The numerical values of calculated muliplet energies and the corresponding spectral terms notation of all those atomic multiplet levels are not delineated in this presentation. These results in detail will be reported separately in a dedicated publication.
In Fig. 8, Ni K-edge experimental and calculated (using LFDFT methodology) XANES spectra are compared. The experimental spectrum was acquired from the interfacial oxide region of the analyzed Zircaloy-2 sample (see Fig. 2b). The agreement between best-fit calculation and observation is fairly good, indicating that the local model of a Ni 2+ impurity center in a m-ZrO 2 phase accounts reasonably well for the measured XANES.
Our full calculation, fitted to x-ray absorption data, yields Γ = 2.5 eV [i.e., the core-hole lifetime energy term in Eqs. (6) and (7)], which is roughly 1.7 times higher than that of the natural line width (1.45 eV) of Ni-1s core-electron excitations reported in the literature [41]. At this point let us mention that the linear combination modeling of the Ni 2+ spectrum in Fig. 8 utilizing a Voigt or a pseudo-Voigt convolution of Gaussian (to account experimental resolution ~ 1.5 eV) and Lorentzian (to account core-hole lifetime widths) including one arctangent line shape background component would have been perhaps better. Instead and for numerical convenience and to avoid models having too many fitting parameters, only Lorentzian convolution is performed in our simplified approach. Here we should mention that there are various peak shape functions ranging from Gaussian to pure Lorentzian, and/or the combination of Lorentz and Gauss functions giving the so-called Voigt functions that can be chosen to characterize the spectral lines of the electronic multiplets contributing to the Ni 2+ absorption spectrum in Fig. 8. For our purposes, fitting the XANES data by a linear combination of Voigt type functions, which combine a Lorentzian width related to the core-hole lifetime and a Gaussian width to account experimental resolution (~ 1.5 eV in our measurement), plus an arctangent function to provide the background absorption could have been more appropriate. However, to avoid numerical instability by analyzing too many variables or parameters of fitting models to the data, we instead used only Lorentzian convolution for both simplicity and numerical convenience. Nevertheless, using a simple cluster model consisting of a single Ni 2+ cation with six-fold coordinated oxygen ligands in a m-ZrO 2 host crystal, we are able to demonstrate important aspects of the ligand field multiplet calculations for a highly reliable description of the measured Ni K-edge absorption spectrum. It also shows an applicability of the LFDFT methodology to predict electronic and structural insights via ligand field transitions, a valuable tool for evaluating the speciation and redox state (s) of alloying elements in relation to Zr-alloy corrosion including the hydrogen intake behavior in the alloy.

Impact of Ni and hydrogen pickup
The use of advanced spectroscopic experiments, optimized to determine the coordination environment and the redox speciation of nickel in the oxide layer formed on a serviced BWR Zircaloy-2 fuel rod, is vital to linking the chemical behavior of nickel to its potential role in hydrogen uptake behavior of Zircaloy-2. As a whole, our XANES results show a divalent nickel ions distribution in the zirconia layer near the oxide/metal interface, and its valence state is slightly higher (average value of about 2.3) at distant locations near the oxide-water interface. The LFDFT calculations for the Ni-doped m-ZrO 2 of interest here, also reproduce the structural information from the XANES experiment. Since charge balance must follow when a solute Ni atom, located in the cation site, is oxidized to a lower valance state than quadrivalent Zr ions in the zirconia matrix, structural disorder occurs inevitably resulting in the production of oxygen ion vacancies in defected Ni-doped m-ZrO 2 structures as demonstrated by EXAFS analyses. We also found that there is a strong propensity for the oxygen vacancies and Ni 2+ ions to form pairs.
Structural vacancies are one of the most common defects in Fig. 7. Calculated multiplet energy levels (in blue) arising from the excited 1s 1 3d 8 4p 1 (dipole allowed) and 1s 1 3d 9 (quadrupole allowed) electron configurations of Ni 2+ in a Ni-doped m-ZrO 2 crystallite. The corresponding oscillator strengths (i.e. calculated intensity values) of the nickel 1s core-electrons excitation (vertical lines shown in black) are also displayed in the plot. irradiated zirconia microstructure. Oxygen vacancies prefer to reside close to Ni 2+ ions due to its smaller ionic size (0.70 Å) compared to Zr 4+ (0.78 Å), thereby reducing their overall mobility [42]. Relevant here is the effective valence of a Ni ion in conjunction with an adjacent oxygen vacancy (V o ), possibly in oxide grain boundaries, pores or fine-scale cracks within the oxide close to the metal interface, where the Ni 2+ coordination is generic and displays an affinity to any hydrogen present locally. From a hydrogen ingress point of view, the experimental result obtained in this study is indeed significant in explaining the reactivity of the hydride ions (H -) towards hydride-proton recombination utilizing the Ni 2+ − V o pairs, and enhanced hydrogen permeation for being picked up into the Zircaloy-2 [7,[43][44][45]. The information provided by micro-beam XRF, XRD, XAS experiment and LFDFT calculation helps to understand the nickel effects on the oxidation of BWR Zircaloy-2 type material towards clarifying the hydrogen pickup mechanisms underlying, and development of new alloys with substantially improved corrosion properties as well as material performance during in-reactor lifetime. We shall also mention that analysis of autoclave corroded samples (i.e., non-irradiated oxides) will not be adequate in predicting the in-pile corrosion performance and hydrogen uptake behavior of most zirconium alloys. In the harsh environment of a reactor core, both the process of oxidation and hydrogen pick-up contents during aqueous corrosion of zirconium-based alloys are influenced by various parameters that do not otherwise contribute to the autoclave corrosion performance of the Zircaloys. To examine the extent of the effect of irradiation on the corrosion behavior and the hydrogen uptake activity in Zircaloy material, previous studies have compared inpile corrosion with un-irradiated autoclave corroded zircaloy samples. It has been consistently found that irradiation causes increase in both the oxide growth rate and the pickup rate of hydrogen in Zircaloy material. The results are ascribed to effect of thermal conditions (temperature and heat flux), radiolytic decomposition of the coolant (i.e., production of deleterious reaction products through radiolysis, such as H 2 O 2 , OH − , H + etc.), formation of electron− hole pairs by β and γ radiation, dissolution of SPP in the oxide as well as in the metal matrix, the presence of additional vacancies as a result of irradiation damage to the oxide matrix etc. Further discussion of these issues is beyond the scope of this paper, and can be found in [29,[46][47][48].

Summary and conclusion
The present report describes a combined experimental and theoretical investigation of the local atomic environment of solute Ni atoms located in the oxide layer that was formed on an in-reactor exposed nuclear fuel tube made from Zircaloy-2 material. The experiment was conducted using synchrotron radiation and the theoretical analysis was performed for experimental data using the ligand field multiplet theory approach. The analyzed sample was identified from a high burnup (about 79 MWd/kgU, an average value) spent fuel rod.
To comply with radioprotection aspects at the synchrotron laboratory, a small-sized sub-sample has been prepared by means of a FIB instrument for X-ray based characterization. A combined use of μmresolved XRF, XRD and XAS techniques has been applied to analyze the irradiated Zircaloy-2 material. The principal importance is the trace element nickel detection by means of high brilliance synchrotron microprobe, which is essential to determine its chemical speciation in a non-destructive way.
The Ni distribution analysis via μXRF has allowed to identify the oxide layers and unoxidized metallic regions of corroded Zircaloy-2, and to determine the location of the metal-oxide interface in the sample.
High spatial resolution μXRD mapping result reveals the presence of the major m-ZrO 2 and minor t-ZrO 2 crystalline phases in the oxide matrix. The trends in the distribution of the t-ZrO 2 content within the entire 50 µm oxide thickness almost mirror the oxidation kinetics periodicity, which corresponds to the cyclic nature of in-reactor corrosion of Zircaloy-2. Uncorrected volume fractions of tetragonal zirconia amounts to the range of 12-16% near the oxide/metal interface region, and vary between ~ 5% and ~ 8% at distant locations within the oxide thickness.
Spots of interest containing dissolved Ni at the bare-oxide regions have been chosen for μXAS measurements to determine the chemical speciation and oxidation state of Ni in the zirconium oxide microstructure. According to XANES data all Ni atoms, located in the vicinity of the metal/oxide interface, are stabilized in divalent oxidation state. At a distance of about 40 µm away from the interfacial oxide area, the valence of Ni reaches ~ 2.3 within the oxide matrix, and there is no trace or even evidence of any metallic Ni found in the corrosion layer. The EXAFS data analysis using a combined FEFF calculation of a Nidoped m-ZrO 2 model crystal reveals that the first neighbor Ni-O average bond distance is significantly shorter than that expected from the crystallographic data, evidences an under-coordinated environment of nickel centers, and suggests the tendency of solute Ni 2+ ions to bind preferentially with oxygen vacancies in the zirconia matrix. These findings are encouraging as they support theoretical predictions of hydrogen evolution reactions during the water-induced oxidation of zirconium alloys, and of the subsequent hydrogen uptake process following the transition metal associated hydride ions and protons recombination mechanism proposed in the literature. This occurs at Ni 2+ − V o sites located in hydroxylated grain boundaries of ZrO 2 , nanopore clusters and micro-cracks inside the oxide films close to the M/O interface where the overall hydrogen evolution reaction is energetically favored, and may thus act as preferential nucleation sites for hydride ions (H -) storage and also causing accelerated hydrogen uptake in Zircaloy-2.
To facilitate a comparison with experimental XANES and EXAFS results, and perhaps more importantly, to demonstrate the validity of the structural model adopted for quantitative analysis of the Ni K-edge absorption spectra (both XANES and EXAFS), we have also studied the substitutional doping behavior of divalent nickel cations in m-ZrO 2 using first-principles LFDFT calculations. In overall, a good agreement is seen between the theoretical XANES simulation and experimental findings. The results of this study from joint theoretical and experimental investigations on the chemical and structural specificity of Ni in zirconium oxide microstructure have strong implications for understanding the structural and electronic properties of the corrosion layer in Zircaloy-2 including the hydrogen intake behavior accompanied with the oxidation reaction in the alloy.
Bullemer and Viacheslav Kuksenko for supporting the handling of active material and sample preparation by FIB. Our sincere thanks go to the PSI-SLS management for providing beam-time through the accepted proposal, and to Camelia Borca (beam line scientist at the micro-XAS beam line) for providing technical support during the experimental data collection. We also thank Itai Panas (Chalmers University of Technology, Sweden) for helpful discussions.