research papers
Temperaturedependent _{2}O_{3}
study of the local structure and lattice dynamics in cubic Y^{a}Institute of Solid State Physics, University of Latvia, Kengaraga Street 8, Riga LV1063, Latvia, and ^{b}Institute for Applied Materials–Applied Materials Physics, Karlsruhe Institute of Technology, EggensteinLeopoldshafen, PO Box 3640, 76021 Karlsruhe, Germany
^{*}Correspondence email: janis.timoshenko@gmail.com
The local structure and lattice dynamics in cubic Y_{2}O_{3} were studied at the Y Kedge by Xray absorption spectroscopy in the temperature range from 300 to 1273 K. The temperature dependence of the extended Xray absorption fine structure was successfully interpreted using classical and a novel reverse Monte Carlo method, coupled with the evolutionary algorithm. The obtained results allowed the temperature dependence of the yttria atomic structure to be followed up to ∼6 Å and to validate two forcefield models.
Keywords: EXAFS; molecular dynamics; reverse Monte Carlo; evolutionary algorithm; yttria.
1. Introduction
Yttrium sesquioxide (yttria, Y_{2}O_{3}) is an important technological material, which is employed in pure, doped or nanosized forms. For instance, it is used as a phosphor in optical display and lighting applications (Igarashi et al., 2000; Schmechel et al., 2001; Capobianco et al., 2002), in rareearth ion doped lasers (Xu et al., 1997; Lu et al., 2001), for ethanol steam reforming in fuelcell applications (Sun et al., 2005) and in the production of ceramic materials (Wang et al., 2013). During the last decade Y_{2}O_{3} has attracted much attention since it was shown that mechanical properties and radiation resistance of steels can be improved by an addition of yttrium compounds during the manufacturing process leading to the formation of nanosized yttrium oxide within the steel matrix (Ukai & Fujiwara, 2002; Klueh et al., 2002; Schneibel et al., 2007). Such oxidedispersionstrengthened (ODS) steels are considered now as promising structural materials for concentrated solar power plants and jet engines, and, in particular, for fusion and fission nuclear reactors (Lindau et al., 2002).
The understanding and improving of ODS steel properties at the atomic scale represents a complicated task, whose solution requires the use of modern experimental and theoretical approaches. Among different experimental techniques, et al., 1981; Aksenov et al., 2006; Yano & Yachandra, 2009). Therefore its application to the case of ODS steels was naturally started during the last ten years (Degueldre et al., 2005; Pouchon et al., 2007; Béchade et al., 2012; He et al., 2012; Liu et al., 2014; Menut et al., 2015; Cintins et al., 2015). On the other hand, one expects that largescale (MD) (Hirata et al., 2011; Yashiro et al., 2012) and Monte Carlo (Alinger et al., 2007; Hin et al., 2009) simulations will contribute to the interpretation and prediction of experimental results. The reliability of these theoretical models is directly related to how well the interatomic interactions can be described in the steel matrix, within the oxide nanoparticles and between the nanoparticles and the matrix. This question can be addressed using the MDEXAFS method (Kuzmin & Evarestov, 2009), which allows validation of interatomic potentials by direct comparison of experimentally measured extended Xray absorption fine structure (EXAFS) with theoretically simulated ones. However, the accurate simulation of yttrium oxide nanoparticles, embedded in a steel matrix, or even of freestanding yttria particles is truly challenging, and therefore we have started from their bulk ancestor. Note also that for practical applications (e.g. for modelling of ODS materials) it is important to demonstrate that the chosen interatomic potentials are reliable over a broad temperature range and are able to reproduce the evolution of material local structure upon temperature increase. Therefore, in this study, we used data acquired in the temperature range from 300 to 1273 K.
is able to probe the local atomic structure and lattice dynamics in bulk and nanocrystalline materials around both concentrated and diluted elements (LeeCubic yttrium sesquioxide (cY_{2}O_{3}), known also as αY_{2}O_{3}, has complex crystallographic structure and belongs to the with Z = 16 (Fig. 1). Its lattice parameter is equal to a_{0} = 10.604 Å at T = 300 K (Bonnet et al., 1975) [the range of values reported in the literature is 10.6021–10.6042 Å (Carlson, 1990)]. There are two nonequivalent yttrium atoms Y1 and Y2 located at the Wyckoff positions 8b(0.25, 0.25, 0.25) and 24d(u, 0, 0.25) [u = −0.0326 at T = 300 K (Bonnet et al., 1975)], respectively, and the oxygen atoms occupy 48c(x, y, z) positions [x = 0.3911, y = 0.1519, z = 0.3806 at T = 300 K (Bonnet et al., 1975)]. As a result, Y1 atoms have regular octahedral coordination with six equivalent bond lengths R(Y1—O) = 2.89 Å, whereas Y2 atoms are located in distorted octahedral environment with three groups of slightly different distances R(Y2—O) = 2 × 2.24 Å, 2 × 2.27 Å and 2 × 2.33 Å.
The structural parameters do not change significantly below room temperature down to 77 K (Faucher & Pannetier, 1980). However, the lattice parameter of cY_{2}O_{3} increases nonlinearly up to 2512 ± 25 K, where a into the fluoritetype structure (space group ) occurs, followed by melting at 2705 ± 25 K (Swamy et al., 1999).
The lattice dynamics of cY_{2}O_{3} have been studied experimentally and theoretically. Bose et al. (2011) performed neutron measurements of the phonon and lattice dynamic calculations using firstprinciples density functional theory and forcefield interatomic potential model.
Classical MD simulations of cY_{2}O_{3} were reported in several papers (Bose et al., 2011; Álvarez et al., 1999; Belonoshko et al., 2001; Lau & Dunlap, 2011), and the results obtained in the two most recent studies (Bose et al., 2011; Lau & Dunlap, 2011) will be considered further.
In this study we employed two advanced methods: (i) MDEXAFS (Kuzmin & Evarestov, 2009) and (ii) the novel reverse Monte Carlo/evolutionary algorithm approach (RMC/EAEXAFS) (Timoshenko et al., 2014a) for the interpretation of temperaturedependent Y Kedge in cY_{2}O_{3}. First, we used the MDEXAFS method (Kuzmin & Evarestov, 2009) to validate the quality of the most recent forcefield models based on pair potentials (Bose et al., 2011; Lau & Dunlap, 2011). Next, to analyze the validity of the chosen forcefield models quantitatively, we compared the threedimensional structure models, obtained in the MD calculations, with those constructed directly from the experimental data via the RMC/EAEXAFS approach (Timoshenko et al., 2012, 2014a). Such combined approach allows one to analyze in detail the nearestneighbour interactions, and to follow their evolution upon temperature increase.
Note that both MDEXAFS and RMC/EAEXAFS approaches were successfully employed by us recently to a number of crystalline materials such as SrTiO_{3} (Kuzmin & Evarestov, 2009), ReO_{3} (Timoshenko et al., 2012, 2013, 2014a; Kalinko et al., 2009), LaCoO_{3} (Kuzmin et al., 2011), Ge (Timoshenko et al., 2011, 2012), NiO (Anspoks et al., 2012), H_{x}ReO_{3} (Timoshenko et al., 2014a), ZnO (Timoshenko et al., 2014b,c) and various tungstates (Kalinko & Kuzmin, 2013; Timoshenko et al., 2014d, 2015).
2. Experimental and data analysis
Xray absorption spectra of cubic Y_{2}O_{3} (99.99%, SigmaAldrich) were recorded at the Y Kedge (17038 eV) in transmission mode at the ELETTRA (Trieste, Italy) bendingmagnet beamline (Di Cicco et al., 2009). The storage ring operated in the topup multibunch mode at the energy E = 2 GeV and current I = 310 mA. The synchrotron radiation was monochromated using a Si(111) doublecrystal monochromator, and its intensity before and after the sample was measured by two ionization chambers. Yttrium metallic foil (99%, GoodFellow) was used for energy calibration. Polycrystalline cY_{2}O_{3} powder was mixed with boron nitride and pressed into pellets. The sample thickness was optimized to obtain the absorption Y Kedge jump value ≃ 1. The sample temperature was controlled using the l'AquilaCamerino glass furnace (Di Cicco et al., 2009) for hightemperature measurements in the range from 300 to 1273 K.
The experimental Y Kedge spectra were extracted using the conventional procedure (Aksenov et al., 2006; Kuzmin, 1995) and are shown together with their Fourier transforms (FTs) in Fig. 2. The position of the photoelectron energy origin E_{0} was set at 17050 eV to be in agreement with the theoretical one obtained by the FEFF8 code (Ankudinov et al., 1998). The first peak in the FT at ∼1.7 Å is due to the contribution of the first coordination shell (six closest oxygen atoms) around the absorbing yttrium atom, whereas the second peak, at 3.5 Å, having a doublepeak shape at room temperature, originates mainly due to the second and third coordination shells formed by yttrium atoms. Note that six Y atoms in the second coordination shell are located at about 3.5 Å from the absorbing yttrium atom, and their YO_{6} octahedra share a common edge with that of the absorbing yttrium; the distance between six Y atoms in the third coordination shell and the absorbing yttrium atom is about 4.0 Å, and their YO_{6} octahedra are connected through a common vertex (Fig. 1).
3. simulations
Classical GULP code (Gale, 1996; Gale & Rohl, 2003) in the canonical (NVT) ensemble with periodic boundary conditions. The simulation box had a size of a 2a_{0}×2a_{0}×2a_{0} including 640 atoms. The starting configuration was set to the mean crystallographic cY_{2}O_{3} structure (Bonnet et al., 1975). A Nosé–Hoover thermostat (Hoover, 1985) was used to maintain the required average temperature during each simulation. Newton's equations of motion were integrated using the Verlet leapfrog algorithm (Hockney, 1970) with a time step of 0.5 fs. The equilibration and production times were 20 ps each. The simulations were performed at temperatures in the range from 297 K to 1273 K, corresponding to that of the experiments. A set of 4000 atomic configurations were accumulated during each production run, and the Y Kedge spectra were calculated for two nonequivalent yttrium atoms (Y1 and Y2) in each MD configuration using the ab initio realspace multiplescattering FEFF8 code (Ankudinov et al., 1998; Rehr & Albers, 2000). Finally, the configurationaveraged Y Kedge spectra were obtained (Kuzmin & Evarestov, 2009) and used for direct comparison with the experimental ones.
simulations were performed using theThe multiplescattering contributions were accounted up to the seventh order. Note, however, that the influence of such contributions for investigated material is quite small. The calculation of the cluster potential was performed only once for the mean crystallographic cY_{2}O_{3} structure (Bonnet et al., 1975), thus neglecting its small variation due to thermal disorder. The complex exchangecorrelation Hedin–Lundqvist potential and default values of muffintin radii [R_{mt}(Y) = 1.57 Å and R_{mt}(O) = 1.06 Å], as provided within the FEFF8 code (Ankudinov et al., 1998), were employed.
Two forcefield models (Bose et al., 2011; Lau & Dunlap, 2011), based on the rigidion Buckingham potential, were used in the MD simulations to describe interactions in cY_{2}O_{3} (Table 1),
The Coulomb interactions were described using the effective ion charges q(Y) = +2.4 and q(O) = −1.6 in the first model (Model 1) (Bose et al., 2011), whereas the formal ion charges [q(Y) = +3 and q(O) = −2] were assumed in the second model (Model 2) (Lau & Dunlap, 2011).

Several properties of cY_{2}O_{3} such as the lattice parameter, bulk modulus (B_{0}) and elastic constants (C_{11}, C_{12} and C_{44}) were calculated using two forcefield models (Bose et al., 2011; Lau & Dunlap, 2011) and are compared with the available experimental data (Faucher & Pannetier, 1980; Palko et al., 2001) in Table 2. As one can see, both models reproduce the experimental values equally well.
The experimental Y Kedge and configurationaveraged MDEXAFS spectra, calculated using two models, and their Fourier transforms are compared in Fig. 3 for the two extreme temperatures (300 and 1273 K). The first model (Model 1) gives an overall good agreement with experimental data, except for some small discrepancy in the FT peaks amplitude at 300 K due to the underestimation of the YO_{6} octahedra distortion in the model. The second model (Model 2) fails significantly at 300 K in the description of peaks located between 1 and 4 Å in the FT, and the discrepancy remains for the first shell at 1273 K. In fact, the difference at 300 K for Model 2 is also well observed in kspace.
To analyze the validity of Model 1 in more detail and to validate the temperaturedependencies of interactions within different nearestneighbour pairs separately, we compared the threedimensional structure model, obtained in the MD simulations, with that constructed directly from the experimental Y Kedge data using the reverse Monte Carlo approach.
4. Reverse Monte Carlo simulations
The reverse Monte Carlo (RMC) method (McGreevy & Pusztai, 1988; Timoshenko et al., 2012) allows one to construct a structure model of the material based on the available experimental data (EXAFS in our case) only and does not require knowledge of interatomic potentials, which is a crucial point in MD simulations. Additionally, the RMC method can be applied to study the materials also at cryogenic temperatures, where the classical MD approach fails due to the neglect of quantum effects. On the other hand, the extraction of dynamical information (interatomic forces, frequencies of atomic oscillations) from the results of the RMC process is not straightforward. Therefore, both approaches, MD and RMC, complement each other.
Recently we have proposed an enhanced RMC approach for the analysis of et al., 2014a,d). As in the conventional RMC method, the threedimensional structure model of a material is optimized in the RMC/EA scheme via the consequent proposal of random changes of atomic coordinates, and the agreement between the experimental and configurationaveraged spectra, calculated for the proposed structure model, is used as the only criterium for the acceptance or rejection of the proposed move. This configurationaveraged spectrum is obtained from ab initio multiplescattering calculations performed using the FEFF8 code (Ankudinov et al., 1998). Implementation of the evolutionary algorithm in the conventional RMC scheme significantly improves the convergence of the simulations: in this case we use not just one but several (32 in this study) structure models of the material simultaneously. The information exchange between the simulated structure models allows us to find the solution (i.e. the average atomic configuration that gives the best possible description of experimental data) much faster (Timoshenko et al., 2014a).
data from crystalline materials, based on the use of the evolutionary algorithm (EA). The combined RMC/EA scheme allows us to perform accurate analysis of data from distant coordination shells, taking into account static and thermal disorder as well as multiplescattering effects, and can be applied even for complex materials with low symmetry (TimoshenkoSince we are interested in simulating the effect of thermal disorder in crystalline Y_{2}O_{3}, the random displacements of atoms at each RMC iteration were constrained to be smaller than 0.4 Å around their equilibrium positions, known from diffraction experiments (Bonnet et al., 1975; Faucher & Pannetier, 1980). As a result, the average atomic structure provided by our RMC simulations corresponds to the crystallographic one and the positions of atoms are distributed around the Wyckoff ones. This allowed us to follow thermal disorder effects separately around both inequivalent Y1 and Y2 atoms.
As in our MD simulations, the model of crystalline yttria in RMC/EAEXAFS analysis is constructed as an infinite crystal employing periodic boundary conditions for the 2a_{0} ×2a_{0} ×2a_{0} unit cells of cubic Y_{2}O_{3}. The value of the lattice parameter a_{0} = 10.607 Å was fixed at the experimental value for crystalline yttria obtained from a neutron powder diffraction experiment (Faucher & Pannetier, 1980). The Y Kedge spectra were calculated for both nonequivalent yttrium positions (Y1 and Y2) separately, and then added together with weights of 1/4 and 3/4, which correspond to the ratio of Y1 and Y2 atoms in cubic Y_{2}O_{3} structure, to obtain the total configurationaveraged spectrum. The latter was used for the comparison with the experimental data. The calculations were performed using the same scattering paths and cluster potential as for the MD simulations. The experimental and calculated Y Kedge spectra at each iteration were compared using the Morlet wavelet transform (WT) (Muñoz et al., 2003; Funke et al., 2005; Timoshenko & Kuzmin, 2009) in the kspace range from 3.5 to 14.5 Å^{−1} and in the Rspace range from 1.0 to 6.9 Å. This allowed us to account for the features of spectra in k and R spaces simultaneously.
composed ofAt each temperature a good agreement between the experimental and calculated Y Kedge spectra (Figs. 4 and 5) was achieved after several thousands of RMC/EA iterations. As one can see, RMC/EA modelling, unlike the MD approach, allowed us to obtain a very good description of all features of in k and R spaces at all temperatures. The final atomic configurations then were used to estimate the structure parameters of interest, and to compare them with those obtained in our MD simulations. The final set of atomic coordinates was also used to evaluate the importance of a contribution from the multiplescattering (MS) effects to the total spectrum (Fig. 4). As one can see, the MS contribution in cubic Y_{2}O_{3} is quite small but not negligible over the whole krange. Moreover, an account of the MS effects is important to correctly describe the FT peaks at ∼3.7 Å and 6 Å: here the main MS contributions come from the octahedral environment around the absorbing yttrium atoms in the first (oxygen) and second (yttrium) coordination shells, respectively.
5. Discussion
To compare the structure models, obtained by MD and RMC/EA simulations, one can calculate the atomic radial distribution functions (RDFs) around both Y1 and Y2 (Fig. 6). Note that, while the distribution of atoms in the outer coordination shells of Y1 and Y2 differs significantly, the first three peaks of RDFs have close shapes and positions for both nonequivalent yttrium sites. We will limit our further discussion to these peaks only.
Comparison of RDFs for Y—O and Y—Y atom pairs at room temperature indicates that both RMC/EA and MD methods give close results. However, one can note that the width of the peaks in the RDF around Y1 is systematically narrower and, hence, the peaks are higher in the case of the MD results.
To make the comparison more quantitative and to follow temperaturedependent variations, we have extracted the mean square relative displacement (MSRD) factors, containing contributions from both static and thermal disorder, from the widths of RDF peaks: their temperaturedependencies for the first three coordination shells are shown in Fig. 7. The uncertainties of the RMC/EA results were estimated by repeating calculations several times with different sequences of pseudorandom numbers (Timoshenko et al., 2014a). Temperaturedependencies of the MSRDs, obtained from RMC/EA results, were best fitted using the correlated Einstein model (Sevillano et al., 1979) (solid lines in Fig. 7). Using the obtained value of the Einstein frequency , one can estimate the effective bondstrength constant = , where μ is the of the atomic pair. For the MD results, in turn, the corresponding effective bondstrength constants can be calculated simply from the slopes of the temperaturedependencies of the MSRD factors, since MSRD(T) = k_{B}T/κ (T is the absolute temperature and k_{B} is the Boltzmann's constant). Hence the obtained temperature dependencies of the MSRD factors can be used to validate the strength of interatomic interactions in the MD model. The values of κ obtained in the MD and RMC/EA simulations are compared in Table 3.

Note that our RMC/EA results suggest that the corresponding MSRD factors for the nearest neighbours of nonequivalent Y1 and Y2 atoms are close. For RMC/EA results we cannot discriminate between nonequivalent Y2—O bonds in the first coordination shell within the uncertainties of the analysis. We also do not observe any significant difference in the MSRD values for Y1—O and Y2—O pairs. Similarly, we do not detect any significant differences in the MSRD values for Y1—Y2 and Y2—Y2 pairs in the third coordination shell. For the Y—Y pairs in the second coordination shell, in turn, only minor difference in the static disorder contribution was observed.
From the results, summarized in Figs. 7(b)–7(d) and in Table 3, one can see that MSRD factors, obtained in the MD simulations and extracted from experimental data using RMC/EA methods, are close at room temperature, and the temperaturedependencies of MSRD factors for all three coordination shells of yttrium are also close. The estimated effective bondstrength constant values for the first coordination shell, obtained by MD and RMC/EA methods, agree well and are also close to that determined by infrared and Raman spectroscopies [103 N m^{−1} (Repelin et al., 1995) and 108 N m^{−1} (Ubaldini & Carnasciali, 2008)]. Thus one can conclude that the pairwise Y—O interactions are described with good accuracy in the used force fieldmodel (Model 1).
Similar conclusions can be drawn for the second and third coordination shells (Y—Y pairs), Figs. 7(c) and 7(d): results obtained by RMC/EA and MD methods are in reasonable agreement. In both cases the effective bondstrength constant for the third coordination shell is smaller by about 10–20% than that for the second coordination shell. Note that from the relatively large value of κ for the first coordination shell (Y—O pairs) one may conclude that YO_{6} octahedra are relatively rigid. Therefore the observed difference in the bond strengths for the Y—Y pairs in the second and third coordination shells may be attributed to their different connectivity to the absorbing yttrium atom: yttrium atoms in the second coordination shell are connected through two oxygen atoms of a common YO_{6} octahedra edge, whereas yttrium atoms in the third coordination shell are connected through a common YO_{6} octahedra vertex (Fig. 1).
The obtained results suggest that the first forcefield model (Model 1) is consistent with our experimental data. Therefore we can employ the results obtained in the MD simulation for detailed analysis of atomic displacements in Y_{2}O_{3}. The temperaturedependencies of isotropic meansquare displacement (MSD) factors for the Y and O atoms are shown in Fig. 7(a). The MSD and MSRD values for the i–j atom pair are related as MSRD_{ij} = , where φ is a dimensionless correlation parameter (Booth et al., 1995), which is equal to +1 for perfectly inphase atom motion, to 0 for completely independent motion, and to −1 for perfectly antiphase motion. For materials without phase transitions one can expect that the value of φ depends on temperature in the lowtemperature region, but reaches some saturation value at high temperatures. Using the results of our MD simulations for Model 1, we have found (Fig. 8) that the correlation parameter is φ = 0.55 at 50 K and decreases to φ = 0.40 at 1273 K for both first (Y1—O pairs) and second (Y1—Y2 pairs) coordination shells, indicating prevalent inphase motion of nearest neighbours in cY_{2}O_{3}. In the third (Y1—Y2 pairs) coordination shell the correlation φ ≃ 0.25 is small and remains constant at all temperatures within the simulation error.
The variation of MSRDs for nearest Y—O and Y—Y as a function of the interatomic distance was calculated at T = 300 K from a set of atomic coordinates obtained in the MD simulations for Model 1 and is shown in Fig. 8. The values of MSRD increase and reach the sum of the MSD values for distant shells at about 9–15 Å. Only in these distant shells can the motion of atoms be considered as uncorrelated with respect to the motion of the central atom, and, hence, the corresponding MSRD values can be used directly to find the MSD values. This finding indicates that the extraction of the MSD values from data only (using, for instance, the RMC/EA method) for crystalline yttria is, in principle, possible, but is challenging since it requires having highquality experimental data as well as performing the analysis of distant coordination shells (Sapelkin & Bayliss, 2002; Jeong et al., 2003).
6. Conclusions
Local atomic structure and lattice dynamics in cubic Y_{2}O_{3} were studied in the temperature range from 300 to 1273 K by Xray absorption spectroscopy. The experimental Y Kedge data were analysed by reverse Monte Carlo/evolutionary algorithm simulations and were also used to validate by the MDEXAFS method (Kuzmin & Evarestov, 2009) two forcefield models (Bose et al., 2011; Lau & Dunlap, 2011), which were employed in the classical simulations and are based on the Buckingham potential. We found that, while both forcefield models give close values of the lattice parameter, bulk modulus (B_{0}) and elastic constants (C_{11}, C_{12} and C_{44}) (Table 2) in rather good agreement with the available experimental data (Faucher & Pannetier, 1980; Palko et al., 2001), the second forcefield model (Model 2) from Lau & Dunlap (2011) fails to reproduce the temperaturedependence of the spectra. Thus the spectra provide additional information on the structure and dynamics of bulk cubic Y_{2}O_{3}, which allows one to discriminate such close theoretical models as shown by Bose et al. (2011) and Lau & Dunlap (2011).
The MD simulations performed using the forcefield model (Model 1) from Bose et al. (2011) give configurationaveraged spectra in rather good agreement with the experimental data at all temperatures, except for a small discrepancy in the broadening of the first and second coordination shells at 300 K. This discrepancy is due to the pairpotential model, which is not able to account properly for YO_{6} octahedra distortions in cubic Y_{2}O_{3}. Further, we compared the structure model, obtained in the MD simulations, with the one constructed directly from the experimental data using the RMC/EA approach and found that temperaturedependencies of the pairwise interactions at least for the first three coordination shells are reproduced rather well with the forcefield model (Model 1) developed by Bose et al. (2011).
We found that the difference in the local dynamics around nonequivalent Y1 and Y2 sites is not large. At the same time, our analysis suggests that there are significant differences in the
on the interaction of Y—Y pairs in the second and third coordination shells, despite the fact that corresponding interatomic distances are close.The results of the MD simulations also suggest a decrease of the correlation in atomic motion with increasing temperature for nearest atom pairs in the first and second coordination shells, whereas the correlation effects are smaller and remain constant in the third coordination shell. We also found from the MD simulations that the correlation in atomic motion decreases in distant coordination shells (above 9 Å), providing the possibility to estimate the values of MSD factors from
data directly, if accurate analysis of outer shell contributions would be possible.Acknowledgements
This work has been carried out within the framework of the EUROfusion consortium and has received funding from the Euratom research and training programme 2014–2018 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission. We gratefully acknowledge the assistance of the
beamline staff members during the experiment. The research leading to these results has received funding from the European Community's Seventh Framework Programme (FP7/2007–2013) under Grant agreement No. 312284.References
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