Ab initio molecular dynamics simulations of negative thermal expansion in ScF3: the effect of the supercell size
AAb initio molecular dynamics simulations of negativethermal expansion in ScF : The effect of the supercellsize D. Bocharov a , M. Krack b , Yu. Rafalskij a , A. Kuzmin a , J. Purans a a Institute of Solid State Physics, University of Latvia, Kengaraga Street 8, LV-1063Riga, Latvia b Paul Scherrer Institute, Forschungsstrasse 111, CH-5232 Villigen PSI, Switzerland
Abstract
Scandium fluoride (ScF ) belongs to a class of negative thermal expansion(NTE) materials. It shows a strong lattice contraction up to about 1000 Kswitching to expansion at higher temperatures. Here the NTE effect in ScF is studied in the temperature range from 300 K to 1600 K using ab initiomolecular dynamics (AIMD) simulations in the isothermal-isobaric (NpT)ensemble. The temperature dependence of the lattice constant, inter-atomicSc–F–Sc bond angle distributions and the Sc–F and Sc–Sc radial distribu-tion functions is obtained as a function of supercell size from 2 a × a × a to 5 a × a × a where a is the lattice parameter of ScF . A comparison withthe experimental Sc K-edge EXAFS data at 600 K is used to validate theaccuracy of the AIMD simulations. Our results suggest that the AIMD cal-culations are able to reproduce qualitatively the NTE effect in ScF , howevera supercell size larger than 2 a × a × a should be used to account accurately ∗ Corresponding author
Email address: [email protected] (D. Bocharov)
URL: (D. Bocharov)
Preprint submitted to Computational Materials Science 25th February 2020 a r X i v : . [ c ond - m a t . m t r l - s c i ] F e b or dynamic disorder. The origin of the NTE in ScF is explained by theinterplay between expansion and rotation of ScF octahedra. Keywords:
ScF , Negative thermal expansion, Ab initio moleculardynamics, EXAFS, CP2K 2 . Introduction Materials with negative thermal expansion (NTE), contracting upon heat-ing, are not only of great interest from a fundamental physics point of view,but have also a high industrial importance [1, 2, 3]. Composites containingNTE components can possess zero thermal expansion, making them suitablefor high-precision devices, like space telescope mirrors, teeth fillings, sub-strates in microelectronics, fuel cells, thermoelectric converters and for manyother applications [4].During the last decade, fluorides of various metals, including ScF , haveattracted attention as a new class of materials with NTE [5]. ScF is a pecu-liar compound, which has simple ReO -type cubic structure and surprisinglystrong NTE effect appearing as a decrease of the lattice constant over a widerange of temperatures from 10 K to 1100 K, while the positive expansion ofthe lattice occurs at higher temperatures [6]. This makes ScF an excellentstudy subject for a deeper understanding of the NTE phenomenon. Notethat the NTE of pure ScF can be affected by reducing crystallites size [7, 8]or by substituting the scandium atoms with yttrium [9], titanium [10], iron[11, 12, 13], gallium [11] or aluminium [12, 14] atoms.The NTE effect is often explained based on the vibrational mechanismin terms of the so-called rigid unit modes (RUMs) model [3, 15, 16], whichinvolves coupled vibrations of the ScF octahedra. When two neighbouringrigid ScF octahedra librate in opposite directions, the distance betweenthe scandium atoms located at their centres decreases leading to the latticecontraction.The rigidity of ScF octahedra and coupling of their relative motion are3etermined by the strength of the Sc–F chemical bonding. Therefore, theaccurate description of the NTE effect should account for the interactionbetween the lattice, phonons and electrons. This challenging problem can beaddressed using the method of molecular dynamics (MD), which provides anatural way to include thermal disorder in simulations [17]. Moreover, theuse of ab initio molecular dynamics (AIMD), being computationally muchmore demanding than classical MD [18], allows one to account explicitly forchemical bonding and its anisotropy, which are most likely important for theinterpretation of the NTE effect.Until now the AIMD method was used to study the NTE of ScF in [19,20]. Both works employed ab initio Born-Oppenheimer molecular dynamicsimplemented in the VASP code [21] based on a plane wave basis set.In [19] the AIMD simulations were performed to study anharmonic effectsin the temperature range between 7 K and 750 K for a 3 a × a × a ( a is thelattice parameter) supercell containing 108 atoms. Based on the analysis ofthe MD trajectories, it was concluded that the motion of fluorine atoms islargely uncorrelated and strongly anisotropic in the direction orthogonal tothe Sc–F–Sc bonds. No attempt was made by Li et al. [19] to reproduce theNTE behaviour of ScF .The NTE effect was studied using AIMD simulations by Lazar et al. [20]employing the isothermal-isobaric (NpT) ensemble with a small 2 a × a × a supercell containing only 32 atoms. The simulations were performed in thetemperature range between 200 K and 1400 K. The experimental behaviourof the lattice constant a was reproduced after its normalization relative tothe value calculated at 200 K. These simulations also predicted that the ScF was explained by an interplay between the linear thermal expansion ofthe Sc–F bonds and a decrease of the average Sc–F–Sc bond angles due tooctahedra tilting motion [20].Though the AIMD method is a powerful tool to describe the NTE inScF , its accuracy is limited by several issues.It was demonstrated recently [22], that the AIMD simulations based onthe Newtons equations of motion underestimate the magnitude of the NTEin the entire temperature range due to a neglect of the zero point (quantum)atomic motion. The problem is particularly evident at low temperaturesbelow 500 K [22].Another issue, which is the topic of the present study, is related to the sizeof the supercell used in the simulations. To describe the librational motionof ScF octahedra, one needs at least eight octahedra placed in a simulationbox consisting of 2 × × [20].However, one can expect that such small supercell will strongly influence thelattice dynamics, in particular, long wavelength phonons, and, as a result,the correlation effects in the atomic motion will be overestimated. SinceAIMD simulations are computationally expensive, the choice of the supercellsize is critical.Note that the results of AIMD simulations can be validated by directcomparison with the results provided by experimental methods sensitive toboth average structure and disorder such as the pair distribution function(PDF) analysis [23] or the extended X-ray absorption fine structure (EX-AFS) spectroscopy [24]. EXAFS, being also sensitive to high-order correla-5ion functions, provides a unique possibility to probe the local structure andlattice dynamics of materials. It was successfully used by us previously tovalidate MD simulations for different materials such as SrTiO [25], ReO [26], ZnO [27], UO [28] and Cu N [29].In this study, we employ AIMD simulations to reproduce the NTE ef-fect in ScF and investigated the influence of the supercell size on the localstructure and dynamics. In particular, we will demonstrate that the use ofthe smallest supercell (2 a × a × a ) fails to describe thermal disorder ac-curately leading to a broadening of the inter-octahedral Sc–F–Sc bond angledistribution and of the peaks in the radial distribution function starting fromthe third coordination shell of scandium. At the same time, the details ofthe lattice dynamics due to the NTE effect are well reproduced for largersupercells, starting from 4 a × a × a . The explanation of the NTE effect inScF is discussed based on the AIMD results.
2. Ab initio molecular dynamics
Understanding of the NTE effect in ScF requires detailed and accurateknowledge of its temperature-dependent structure and lattice dynamics. Thisinformation is obtained in the present study using the AIMD simulations.Our simulations were based on Kohn–Sham density functional theory(DFT) [30] and were performed in the isothermalisobaric (NpT) ensemble atseven different temperatures (300 K, 400 K, 600 K, 800 K, 1000 K, 1300K and 1600 K) using the CP2K code [31]. The CP2K code employs alocalized basis set of Gaussian-type orbital functions for the description ofthe Kohn-Sham matrix within the framework of the Gaussian Plane Waves6
300 600 900 1200 15003.983.994.004.014.024.034.04 L a tt i ce c on s t a n t ( Å ) Temperature (K)
Diffraction
VASP
Figure 1: Comparison of the temperature dependences of the lattice constant of ScF calculated in this work for 2 a × a × a (open asterisks), 3 a × a × a (open squares),5 a × a × a (open circles) supercell using CP2K code, calculated in [20] for 2 a × a × a supercell by VASP code (solid diamonds) and experimental data from [6] (solid triangles). method [31, 32]. A cutoff of 600 Rydberg is used for the auxiliary basis set ofplane waves to expand the electronic density. Sc and F atoms are describedby scalar-relativistic norm-conserving Goedecker-Teter-Hutter pseudopoten-tials [33, 34, 35] are employed for including 11 ([Ne] 3 s p s d ) and 7([He] 2 s p ) valence electrons, respectively. Calculation were performed atthe Gamma point only using MOLOPT basis sets [36] optimized for thesepseudopotentials. By performing DFT calculations at T = 0 K we foundthat the PBEsol functional gives the value of the lattice constant ( a = 4.027˚A) closer to the experimental one ( a = 4.026 ˚A [6]) than the PBE functional[37] ( a = 4.065 ˚A), which can be important for proper description of the7 Sc-F Sc-Sc
NPT AIMD 600K
ScF RD F G ( R ) ( a t o m s / Å ) Distance R (Å)
Sc-F Sc-Sc
NPT AIMD 600K
ScF RD F G ( R ) ( a t o m s / Å ) Distance R (Å)
Sc-F Sc-Sc
NPT AIMD 600K
ScF RD F G ( R ) ( a t o m s / Å ) Distance R (Å) a ×2 a ×2 a a ×3 a ×3 a Figure 2: Radial distribution functions (RDFs) G ( R ) for the Sc–F and Sc–Sc atom pairsat T = 600 K calculated from the AIMD simulations for 2 a × a × a , 3 a × a × a and4 a × a × a supercell sizes. The models of the 2 a × a × a and 3 a × a × a supercellsare also shown. NTE effect. Therefore, the PBEsol exchange-correlation functional [38] wasused in all AIMD calculations.ScF model system of increasing size ranging from 2 a × a × a to 5 a × a × a primitive unit cells containing 32–500 atoms (8–125 unit cells with 4atoms per unit cell) were employed in the AIMD simulations. After therm-alisation MD run of about 15 ps, an AIMD production run of 50 ps wasperformed for the 3 a × a × a to 5 a × a × a supercells and 100 ps for8
200 -150 -100 -50 0 50 100 150 2000.000.010.02
NPT AIMD 600K
ScF N u m b e r o f c on f i gu r a t i on s ( a . u ) ΔT (°C) Δ Figure 3: Instantaneous distribution of temperature for supercells of different sizes at T = 600 K. the 2 a × a × a supercell. The required temperature was maintained dur-ing the sampling run using the CSVR (Canonical Sampling through VelocityRescaling) thermostat of Bussi et al. [39]. The MD time step of 0.5 fs wasused in all simulations. The values of the lattice parameter a are reportedin Fig. 1: they were calculated by averaging over all atomic configurationsobtained during the production run.The obtained from MD simulations sets of atomic coordinates were usedto calculate the radial distribution functions (RDFs) G ( R ) for the Sc–F andSc–Sc atomic pairs and are reported in Fig. 2. The RDF G ( R ) is defined asa number of atoms (Sc or F) located within a distance of R and R + dR ( dR = 0.01 ˚A) away from the scandium atom.9ig. 3 shows instantaneous distribution of temperatures during the pro-duction run for supercells of different sizes at T = 600 K. The temperaturefluctuation is in the range of about ±
100 K from the target one for two largest(4 a × a × a and 5 a × a × a ) supercells. The temperature fluctuation rangebecomes broader for the 3 a × a × a supercell exceeding 100 K and is twicelarger for the 2 a × a × a supercell. The growing broading of the temperaturedistribution for shrinking supercells is caused by the decreasing number ofdegrees of freedom (DOF) for smaller model systems containing less atoms.A massive thermostatting by employing a thermostat for each DOF was onlyapplied during the thermalisation period whereas just one global thermostatwas coupled to the actual model system during the sampling period in orderto minimise any bias from the interaction with the thermostat. Fig. 3 showsthat a narrow temperature distribution can be obtained even with a mildthermostatting if a sufficiently large model system is chosen which will even-tually ensure physically more meaningful results compared to a small modelsystem requiring massive thermostatting.
3. Validation of AIMD simulations
Temperature-dependent AIMD simulations provide information on theaverage structure, reported in Fig. 1 in terms of the ScF lattice parameter,and on the dynamical (time-dependent) structure, which can be describedby distribution functions. The latter can be experimentally probed by X-rayor neutron total scattering experiments [8, 40] or by EXAFS spectroscopy[41].The results of AIMD simulations were validated in the present study10 T=600 K
Expt. AIMD
AIMD NPT 5x5x5
Sc K-edge in ScF FT ( k ) k ( Å - ) Distance R (Å)
T=600 K
Expt. AIMD EX A F S ( k ) k ( Å - ) Wavenumber k (Å -1 ) AIMD NPT 5x5x5
Sc K-edge in ScF -3-2-10123 T=600 K
Expt. AIMD EX A F S ( k ) k ( Å - ) AIMD NPT 4x4x4
Sc K-edge in ScF -2-1012 T=600 K
Expt. AIMD
AIMD NPT 4x4x4
Sc K-edge in ScF FT ( k ) k ( Å - ) -2-1012 T=600 K
Expt. AIMD
AIMD NPT 2x2x2
Sc K-edge in ScF FT ( k ) k ( Å - ) -3-2-101234 T=600 K
Expt. AIMD EX A F S ( k ) k ( Å - ) AIMD NPT 2x2x2
Sc K-edge in ScF -3-2-10123 T=600 K
Expt. AIMD EX A F S ( k ) k ( Å - ) AIMD NPT 3x3x3
Sc K-edge in ScF -2-1012 T=600 K
Expt. AIMD
AIMD NPT 3x3x3
Sc K-edge in ScF FT ( k ) k ( Å - ) Figure 4: Experimental (black solid line) and calculated (blue dashed line) Sc K-edgeEXAFS χ ( k ) k and their Fourier transforms (modulus and imaginary parts are presented)at T = 600 K for different supercell sizes. using the experimental Sc K-edge EXAFS data from [41, 42], obtained at T = 600 K to minimize the influence of zero point quantum effects [22]. Setsof atomic configurations obtained in AIMD NpT simulations were used tocalculate configuration-averaged EXAFS spectra χ ( k ) ( k is the photoelectronwavenumber) following the approach described previously [25, 27].The Sc K-edge EXAFS spectrum for each configuration was calculatedusing the real-space multiple-scattering FEFF9.64 code [43, 44]. First, the11cattering potential and partial phase shifts of Sc and F atoms were obtainedwithin the muffin-tin (MT) approximation (15% overlap of the nearest MT-spheres, R MT (Sc)=1.31 ˚A and R MT (F)=1.01 ˚A) for the cluster of 8.0 ˚A ra-dius, constructed using the crystallographic ScF structure [6] and centeredat the absorbing Sc atom. The cluster potential was fixed during all simula-tions, thus we neglected its small variations due to thermal vibrations. Themultiple-scattering contributions were accounted up to the 6th order to guar-antee the convergence of the total EXAFS in the k -space range of interest.The photoelectron inelastic losses were accounted within the one-plasmonapproximation using the complex exchange-correlation Hedin-Lundqvist po-tential [45]. The value of the amplitude reduction factor S was set to 1.0[24, 44].The configuration-averaged Sc K -edge EXAFS χ ( k ) k spectra of ScF and their Fourier transforms (FTs) at T = 600 K are shown in Fig. 4 forseveral supercell sizes. The Fourier transforms were calculated using the10% Gaussian window function and were not corrected for the backscatteringphase shift of atoms, therefore the positions of all peaks are displaced tosmaller distances relative to their crystallographic values. The significantlyworse agreement between the experimental and calculated spectra for the2 a × a × a supercell is obvious.
4. Discussion
The temperature dependence of the lattice constant of ScF , determ-ined from NpT AIMD simulations, are compared with the experimental dataobtained by diffraction measurements in Fig. 1. The AIMD simulations per-12 Sc -F Sc -F Sc -F NPT AIMD 600K
ScF RD F G ( R ) S c - F ( a t o m s / Å ) Distance R (Å)
Sc-Sc NPT AIMD 600K
ScF RD F G ( R ) S c - S c ( a t o m s / Å ) Distance R (Å)
Sc-Sc Figure 5: Radial distribution functions (RDFs) G ( R ) for the Sc–F and Sc–Sc atom pairsat T = 600 K calculated from the AIMD simulations for different supercell sizes. formed in this study for 2 a × a × a , 3 a × a × a and 5 a × a × a supercellsand by Lazar et al. for a 2 a × a × a supercell reproduce qualitatively thenegative thermal expansion effect in scandium fluoride up to 1000 K as wellas positive expansion at higher temperatures. The quantitative values of thecalculated lattice constant a are close to the experimental diffraction values[6] with a deviation being less than ± a × a × a supercell. This effect is caused by theoverestimated amplitude of the librational motion of ScF octahedra and is13learly observed in the Sc–F–Sc bond angle distribution function (BADF)discussed below.Further we will discuss the results obtained at T = 600 K as a represent-ative case.Radial distribution functions (RDFs) G ( R ) for the Sc–F and Sc–Sc atompairs at T = 600 K calculated in the range of R = 0–14 ˚A for the supercellsizes from 2 a × a × a to 4 a × a × a are shown in Fig. 2. As one can see,for the smallest supercell sizes, sharp peaks in the Sc–Sc RDF (indicated byarrows in Fig. 2) are observed due to periodic boundary conditions (PBC)employed in the simulations. For the 2 a × a × a supercell with a size of2 a = 8.054 ˚A, the three peaks are due to PBC along < > , < > and < > crystallographic directions. For the 3 a × a × a supercell with asize of 3 a = 12.081 ˚A, only one sharp peak due to the PBC along < > is observed in the R -range till 14 ˚A. Similar effects should appear also in theSc–F RDFs, however, they are much less visible due to an overlap betweenclosely located shells.An enlarged view of the RDFs in the range of the first five coordinationshells of scandium is shown in Fig. 5. The reduction of the supercell sizeclearly leads to an increase of the peak widths and to a distortion of thepeak shape for the smallest supercell. At the same time, the asymmetricshape of the first (Sc–F ) and second (Sc–Sc ) shell peaks is close for allsupercells, explaining the success of the 2 a × a × a supercell model in adescription of the NTE lattice behaviour in [20].The atomic coordinates obtained in the AIMD simulations were used tocalculate the inter-octahedral Sc–F–Sc BADF and the average value of the14
20 130 140 150 160 170 1800.000.020.040.06
NPT AIMD 600K
ScF BAD F S c - F - S c ( d e g r ee - ) Angle (degree)
Figure 6: The inter-octahedral Sc–F–Sc bond angle distribution function (BADF) at T =600 K for NpT ensemble and 2 a × a × a to 5 a × a × a supercell sizes. The averagevalues of the Sc–F–Sc bond angle for each BADF are given in brackets. Sc–F–Sc angle, which are reported in Fig. 6. Note that in cubic ScF thecrystallographic angle between the average positions of atoms in the Sc–F–Scchains is equal to 180 ◦ . However, the value of the average Sc–F–Sc angle willbe always smaller when calculated from mean distances due to vibrations offluorine atoms perpendicular to the direction of the ScFSc chains [46, 47].As one can see, the Sc–F–Sc BADF for the 2 a × a × a supercell deviatessignificantly from the others being broader and giving the average value ofthe Sc–F–Sc angle by about ∼ ◦ smaller. This means that the simulationsusing the smallest supercell should fail in describing dynamical behaviour ofScF and, in fact, result in the underestimated absolute values of the latticeparameter (Fig. 1).The effect of dynamic disorder can be illustrated using the comparison ofthe experimental and calculated Sc K-edge EXAFS spectra and their Fourier15ransforms (FTs) shown in Fig. 4 for the four supercell sizes at T = 600 K.Thermal disorder is responsible for the EXAFS amplitude damping at high- k values [24] and, consequently, leads to a reduction of the peaks amplitude inthe FTs. The first peak at 1.6 ˚A in FT corresponds purely to the first shellcontribution due to 6 fluorine atoms (F ). The second peak at 3.5 ˚A hascomplex origin due to the interference between the second (Sc ) and third(F ) coordination shells plus the so-called multiple-scattering contributionsgenerated within the Sc–F–Sc atomic chains, which are sensitive to the Sc–F –Sc bond angle variation. The last peak at 5.4 ˚A is mainly due to thefourth (Sc ) and fifth (F ) coordination shells. As one can see, the AIMDsimulations reproduce well the experimental EXAFS data for all supercellsizes except the smallest one, for which the amplitude of all three peaks inFT is systematically smaller than in the experiment. This result correlateswell with the behaviour of RDFs in Fig. 5. It is interesting to note thatin spite of the Sc–Sc RDF is close for all supercells, the sensitivity of theFT peak at 3.5 ˚A to the Sc–F –Sc bond angle gives origin of its reducedamplitude for the 2 a × a × a supercell.The NTE mechanism in ScF can be understood from our AIMD simu-lations by considering the temperature variation of the lattice parameter a and interatomic distances R (Sc–F ) and R (Sc–Sc ) (Fig. 7(a)) and relatedvariation of the average Sc–F–Sc bonding angle (Fig. 7(b)). For ease ofcomparison, the values of a and R (Sc–Sc ) are divided by two. Note thatthermal vibrations of scandium atoms in the direction orthogonal to the crys-tallographic axes are responsible for the difference between the values of a and R (Sc–Sc ) [47]. 16
00 600 900 1200 15002.002.022.042.062.08 D i s t a n ce ( Å ) Temperature (K) R (Sc-F ) R (Sc-Sc )/2 a /2 (a)
300 600 900 1200 1500150155160165170 (b) A ng l e S c - F - S c ( ) Temperature (K)
Figure 7: (a) Temperature dependence of the lattice parameter a (circles) and interatomicdistances R (Sc–F ) (squares) and R (Sc–Sc ) (diamonds) in ScF calculated by AIMDfor the 2 a × a × a (solid symbols) and 5 a × a × a (open symbols) supercells. (b)Temperature dependence of the average bonding Sc–F-Sc angle in ScF calculated byAIMD for the 2 a × a × a (solid circles) and 5 a × a × a (open circles) supercells. Linesare guides for the eye. An increase of temperature affects strongly the Sc–F bond, which elong-ates almost linearly by about 0.05 ˚A in the temperature range of 300–1600K. This trend is close in both supercell models and is in good agreement withthe analysis of the experimental EXAFS data published in [40, 47] and theresults of previous AIMD simulations from [20]. Such behaviour indicatesthat the ScF octahedra do not behave as rigid units and expand signific-antly upon heating. The behaviour of the Sc–F bonds contrasts strongly17ith that of the Sc–Sc interatomic distances suggesting much larger amp-litude of thermal vibrations for fluorine atoms in the direction orthogonal tothe Sc–F–Sc linkage. This fact is well evidenced by temperature variationof the average Sc–F–Sc bonding angle in Fig. 7(b), which decreases uponheating meaning stronger rotations of ScF octahedra.One should note that the R (Sc–Sc ) next-nearest-neighbour distance be-haves in a slightly different way for small and large supercells. It alwaysexpands (by about 0.02 ˚A) for the 2 a × a × a supercell in the temperaturerange of 300–1600 K, whereas it has a shallow minimum at 400 K and ex-pands by only 0.01 ˚A up to 1600 K for the 5 a × a × a supercell. Also thedifference between R (Sc–F ) and R (Sc–Sc )/2 distances is larger for smallersupercell, indicating stronger rotations of ScF octahedra as is also evidencedin the Sc–F–Sc BADFs in Fig. 6.Thus, while the NTE effect in ScF is reproduced using all supercellmodels and can be explained by the interplay between expansion and rotationof ScF octahedra, the small supercell overestimates the contraction of thelattice and vibrational amplitudes of atoms. This fact is responsible for theworse agreement between the experimental and simulated Sc K-edge EXAFSspectra in Fig. 4 for the smallest 2 a × a × a supercell.
5. Conclusions
The ab initio molecular dynamics (AIMD) simulations performed withinthe isothermalisobaric (NpT) ensemble as presented in this study are ableto reproduce the negative thermal expansion of ScF up to ∼ is explained by theinterplay between expansion and rotation of ScF octahedra.At the same time, the simulations based on the smallest supercell (2 a × a × a ) fail to describe thermal disorder accurately, leading to an overes-timated broadening of the inter-octahedral Sc–F–Sc bond angle distributionand of the outer coordination shells (starting from the third) in the radialdistribution functions of scandium.The results obtained by the AIMD simulations were validated using theMD-EXAFS approach based on the ab initio multiple-scattering theory. Acomparison between the calculated and experimental Sc K-edge EXAFS spec-tra at T = 600 K suggests that a supercell larger than 2 a × a × a shouldbe employed to obtain good agreement, and the best results are achieved fora supercell of at least 4 a × a × a . Thus, we demonstrated that the resultsof the AIMD simulations are sensitive to the size of the supercell, and theexperimental EXAFS spectra can be used to distinguish between differenttheoretical models. Acknowledgements
The calculations were performed on the Paul Scherrer Institute clusterMerlin4, HPC resources of the Swiss National Supercomputing Centre (CSCS)in Lugano as well as at the Latvian SuperCluster (LASC). The authors grate-fully acknowledge staff of the Swiss National Supercomputing Centre (CSCS)during the project ID s628 realization.The authors sincerely thank S. Ali, A. Kalinko, and F. Rocca for providingexperimental EXAFS data, as well as M. Isupova, V. Kashcheyevs, and A. I.19opov for stimulating discussions. Financial support provided by project No.1.1.1.2/VIAA/l/16/147 (1.1.1.2/16/I/001) under the activity “Post-doctoralresearch aid” realized at the Institute of Solid State Physics, University ofLatvia is greatly acknowledged by D.B. A.K and J.P. would like to thankthe support of the Latvian Council of Science project No. lzp-2018/2-0353.Authors have no conflict of interest to declare.
Data availability
The raw/processed data required to reproduce these findings cannot beshared at this time as the data also forms part of an ongoing study.CRediT authorship contribution statement
D. Bocharov : Conceptualization, Data curation, Formal analysis, Fund-ing acquisition, Investigation, Methodology, Project administration, Resources,Validation, Visualization, Writing - original draft, Writing - review & edit-ing.
M. Krack : Conceptualization, Data curation, Formal analysis, Invest-igation, Methodology, Resources, Software, Supervision, Writing - review& editing.
Yu. Rafalskij : Data curation, Formal analysis, Investigation,Software, Validation, Visualization.
A. Kuzmin : Conceptualization, Datacuration, Formal analysis, Investigation, Methodology, Resources, Software,Supervision, Validation, Visualization, Writing - review & editing.
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