Abstract
Solid state materials with crystalline order have been wellknown and characterized for almost a century while the description of disordered materials still bears significant challenges. Among these are the atomic shortrange order and electronic properties of amorphous transition metal oxides [aTMOs], that have emerged as novel multifunctional materials due to their optical switching properties and highcapacity to intercalate alkali metal ions at low voltages. For decades, research on aTMOs has dealt with technological optimization. However, it remains challenging to unveil their intricate atomic shortrange order. Currently, no systematic and broadly applicable methods exist to assess atomicsize structure, and since electronic localization is structuredependent, still there are not wellestablished optical and electronic mechanisms for modelling the properties of aTMOs. We present stateoftheart systematic procedures involving theory and experiment in a selfconsistent computational framework to unveil the atomic shortrange order and its role for the electronic properties. The scheme is applied to amorphous tungsten trioxide aWO_{3}, which is the most studied electrochromic aTMO in spite of its unidentified atomicsize structure. Our approach provides a onetoone matching of experimental data and corresponding model structure from which electronic properties can be directly calculated in agreement with the electronic transitions observed in the XANES spectra.
Introduction
Amorphous transition metal oxides [aTMOs] are key components in optoelectronics, sensors, photoelectrochemical conversion, energy/data storage and emerging water splitting applications, where extensive research on their technological optimization has been performed^{1}. However, unveiling their intricate atomic shortrange order and the underlying electronic properties is challenging because no systematic and wellestablished methods exist to achieve such tasks. Structural analysis of amorphous materials by Xray/neutron pair distribution function [PDF], requires precise data corrections and complex data analysis depending on the diffraction geometry. For disordered materials exhibiting large multiplescattering phenomena such as complex oxides and perovskite materials it has been shown that the PDF is unreliable to recover the statistics of manybody correlations in the nearest coordination shells, thus, underestimating the distribution of atomic coordination^{2}. Standard Xrayabsorption spectroscopy [XASfitting], is applied to small atomic clusters without periodic boundary conditions to optimize structural parameters; DebyeWaller factors σ ^{2}, and relative weights of scatteringpaths^{3}. However, XASfitting merely provides average values of structural parameters, but not the full 3Dstructure of the system. The absence of shortrange order leads to a distribution of interatomic distances, bondangles and atomic coordinations^{4}, which cannot be wellresolved by standard XASfitting. As stated by Anderson, Mott and Cohen et al.^{5,6,7}, disorder induces electron localization near the energygap edges, yielding bandtails of occupied and unoccupied localized states extended into the mobility gap. However, due to the difficulty in determining local disorder, there is still no wellestablished electronic localization mechanisms for aTMOs. Unveiling atomic shortrange order is thus crucial to understand optical and electronic processes in aTMOs and would also be of vital importance in nanoparticle systems where the highsurfacetobulk ratio results in lower crystallinity arising from structural reconstruction and surface disorder^{8, 9}.
Here we present a stateoftheart systematic computational procedure based on XAS experiments to assess the atomic shortrange order and electronic properties of aTMOs. The scheme is applied to aWO_{3}, the leading electrochromic aTMO for application in energyefficient “smart windows”. This technology offers unique optical switching functionalities through cyclic inter/deintercalation of alkali metal ions [Li^{+}]^{10, 11}. There are so far no comprehensive studies assessing the atomic shortrange order of aWO_{3}, in spite that such knowledge can aid to tune and enhance functionalities. Although molecular dynamics [MD] has been used to assess atomic shortrange order in aWO_{3}. However, several structural artifacts have been reported and simulated structures were also unable to fit the experimental data^{12, 13}. In the present scheme, the atomic shortrange order of aWO_{3} is instead extracted from reverse Monte Carlo [RMC] simulation of the experimental extended Xrayabsorption fine structure [EXAFS] spectra. This RMCEXAFS approach overcomes the main drawbacks of standard EXAFSfitting since it provides optimized 3Dstructures and related parameters. The inclusion of multiplescattering terms yields an explicit treatment of threebody correlations^{2, 3}. The effects of static disorder due to the fluctuation of interatomic distances, atomic coordinations and bondangles are intrinsically considered by summing over a large ensemble of atomic configurations from which the ensemble averaged EXAFS spectrum is simulated. This scheme provides a onetoone matching of experimental data and the corresponding model structure, from which the electronic properties can be calculated in agreement with the measured Xrayabsorption nearedge structure [XANES] spectra. From RMCEXAFS simulations we show that the disordered structure of aWO_{3} comprises mainly cornersharing and a small proportion of edgesharing distorted WO_{6,5,4}unitblocks, while the O atoms hold nearly twofold coordination with W atoms. The distribution of WO_{6,5,4} polyhedra leads to the formation of spacious channels that could simplify chargeion injection/diffusion and provide enough free volume for ion storage, which could reduce activation energies and electrode volume variation during ion insertion/extraction. This result supports the fact that the disordered structure of aWO_{3} enhances its electrochromic performance when comparing with its crystalline counterparts, as has been assumed in previous studies^{10}. Electronic properties in aWO_{3} show that the valence band [VB] comprises mainly O[2p] states, while the conduction band [CB] consists mostly of W[5d] states. Disorderinduced localization of electronic states occurs at the O[2p] VB and W[5d] CB tailstates but the density of states [DoS] unveiled a band gap of ≈3.12 eV without defectinduced ingap states. This suggests that aWO_{3} to a great extent retains the electronic structure of its crystalline counterparts. However, from the W[5d(t _{2g }; e _{ g })] bands derived from the WL _{3} edge XANES spectra a crystal field splitting Δd ≈ 4.0 ± 0.2 eV was found, being it lower than that of crystalline WO_{3}.
Results and Discussion
Atomic shortrange order of aWO_{3}
As a starting point, standard nonlinear leastsquares fitting [STF] of the experimental EXAFS spectrum, \({k}^{3}\chi (k)\), was implemented to obtain preliminary average values for interatomic distances, atomic coordination and σ ^{2} parameters [see Methods]. Results from standard fitting \({k}^{3}\chi {(k)}_{{\rm{STF}}}\) displayed in Fig. 1a, show that structural disorder around the photoabsorbing W atoms reduces the oscillation amplitude in the \({k}^{3}\chi (k)\) spectrum at high k, thus, main structural features can be identified in the interval Δk ≈ 2–10 Å^{−1}. Since the STF approach does not provide any 3Dstructure of aWO_{3}, the experimental \({k}^{3}\chi (k)\) spectrum was compared against the abinitio MDEXAFS, \({k}^{3}\chi {(k)}_{{\rm{MD}}}\) function, calculated directly from MD structural trajectories of aWO_{3}. To this end, energetically preconverged abinitio MD structural trajectories of aWO_{3} comprising W = 64 and O = 192 atoms into cubic cells [V ≈ 4400 Å^{3}, ρ ≈ 5.27 g/cm^{3}] were analyzed, and their associated \({k}^{3}\chi {(k)}_{{\rm{MD}}}\) functions were extracted by abinitio selfconsistent realspace full multiplescattering [FMS]^{14} into the muffintin approximation [see Methods]. The structural averaging over twelve MD trajectories of aWO_{3} leads to a main \({k}^{3}\chi {(k)}_{{\rm{MD}}}\) function properly reproducing the phase, shape, and damping of the oscillations of the experimental \({k}^{3}\chi (k)\) spectrum. However, spectral features at k ≈ 4.8 Å^{−1} and k ≈ 9.2 Å^{−1} are not wellresolved in the abinitio FMS calculated \({k}^{3}\chi {(k)}_{{\rm{MD}}}\) function [Fig. 1a]. Next, in order to correct for those spectral discrepancies and to accurately reproduce the atomic shortrange order of aWO_{3}, those abinitio MD structural trajectories were fitted to the experimental \({k}^{3}\chi (k)\) spectrum through RMCEXAFS simulations [see Methods]^{15}. To incorporate the important multiplescattering processes yielding explicit treatment of threebody correlations, and effects of static disorder due to the fluctuation of interatomic distances, atomic coordination and bondangles, the following scattering paths between the photoabsorbing and scattering \(\overline{){\rm{\Theta }}};\overline{){\rm{\Phi }}}=\) ; atoms were used; (i) singlescattering , (ii) triplescattering , (iii) double and (iv) triplescattering in nearly collinear chains with the photoabsorber at the end of the chain ; [scatteringangles ≈0°–30°], (v) double triangular scatteringpath with the photoabsorber at the middle [scatteringangle≈20°–180°], (vi) doublescattering in triangularpaths with scatterers at the 1st and 2nd shells around the photoabsorber [scatteringangles ; ≈0°–40°], (vii) triplescattering in collinear chain with scatterers at the 1st shell around the photoabsorber [scatteringangles ≈10°–180°]. The contribution of each of those scatteringpaths to the RMCEXAFS simulated \({k}^{3}\chi {(k)}_{{\rm{RMC}}}\) spectrum is specified according to ref. 2
where ijn are serial numbers of atoms, ξ the pathtype (i)–(vii), θ is a parametrization angle for (k, θ), R _{eff} is the effective pathlength, the pathlegs, (k, θ) is the EXAFS amplitude and (k, θ) the phaseshift, λ is the mean free path for the photoabsorber atoms. The amplitude (k, θ) and phaseshift (k, θ), for single and multiplescattering paths were selfconsistently calculated by abinitio FMS considering atoms up to R ≈ 7 Å from the photoabsorbing atoms according to
where (k, θ), \({{\rm{\Lambda }}}_{{\rm{red}}}(k)\), 2Δ(k) and \({\rm{\Phi }}(k,\theta )\) denote the amplitude magnitude, reduction factor, kdependent phase correction and phase^{2}. From a first RMCEXAFS run, the structural averaged \({k}^{3}\chi {(k)}_{{\rm{RMC}}}\) spectrum [Δk ≈ 2–10 Å^{−1}], is calculated as a sum of the (k) contributions from the different single and multiplescattering paths (i)–(vii), according to
Results of spectral fitting from the RMCEXAFS simulated spectrum, \({k}^{3}\chi {(k)}_{{\rm{RMC}}}\), is in excellent agreement with the experimental \({k}^{3}\chi (k)\) spectrum [Fig. 1a], and as also outlined above, include multiplescattering events. After convergence, a minimum residual of ≈1–5 × 10^{−3} is attained, which confirms that the RMCEXAFS refinements correctly reflect the atomic shortrange order of aWO_{3}. Thermal damping of the RMCEXAFS signal associated to the structural disorder σ ^{2}, is given by the statistical averaging of \({k}^{3}\chi {(k)}_{{\rm{RMC}}}\) signals obtained by summing over the ensemble of atomic configurations^{3}. The FourierTransform of the experimental \({k}^{3}\chi (k)\) spectrum into the realspace FT\({k}^{3}\chi (k)\) and its corresponding wavelet transform [WT; 2Dcontour plot] are shown in Fig. 1b [phaseuncorrected, Real and Im components at the bottom]. The main peak in the FT\({k}^{3}\chi (k)\) spectrum at R ≈ 1.3 Å with k ≈ 5.6 Å^{−1} in the WT, is associated to singlescattering by neighboring O atoms in the first coordination shell [WO]. The peak in FT\({k}^{3}\chi (k)\) at R ≈ 2.7 Å with k ≈ 4.1 Å^{−1} in the WT, is due to multiplescattering contributions in the first shell. The peak in FT\({k}^{3}\chi (k)\) at R ≈ 3.4 Å with k ≈ 6.4 Å^{−1} in the WT, emerges from the contribution from mixed single and multiplescattering by W and distant O atoms at the second coordination shell. Results from standard nonlinear leastsquares fitting FT\({{k}^{3}\chi (k)}_{{\rm{STF}}}\) of the experimental FT\({k}^{3}\chi (k)\) spectrum in Fig. 1b, leads to the structural parameters shown in Table 1. A direct comparison with the abinitio FMS calculated FT\({{k}^{3}\chi (k)}_{{\rm{MD}}}\) function obtained from MD structural trajectories of aWO_{3}, shows that the FT\({{k}^{3}\chi (k)}_{{\rm{MD}}}\) signal reproduces the realspace position of the first coordination shell WO, but the spectral features in the range R ≈ 1.7–6.0 Å are not wellresolved [Fig. 1b]. The interatomic bond distances in FT\({{k}^{3}\chi (k)}_{{\rm{MD}}}\) are close to the experimental data, but the relative intensities of the peaks in FT\({{k}^{3}\chi (k)}_{{\rm{MD}}}\) are lower than those of the experimental FT\({k}^{3}\chi (k)\) spectrum. Thus, main atomic coordination in abinitio MD structures of aWO_{3} [N _{WO} = 5.38 ± 0.13, N _{WW} = 4.53 ± 0.24], are lower than those obtained from the experimental FT\({k}^{3}\chi (k)\) spectrum [N _{WO} = 5.80 ± 0.10, N _{WW} = 5.30 ± 0.10]. Note that STF optimizes the relative weights of scatteringpaths, σ ^{2} factors and the amplitude reduction factor \({S}_{0}^{2}\) to provide average values of atomic coordination [N _{WO}, N _{WW}]. To the contrary, atomic coordinations [N _{WO}, N _{WW}] computed directly from abinitio MD structures of aWO_{3} correspond to the average over a large ensemble of configurations with different scatteringpaths, σ ^{2} and \({S}_{0}^{2}\) factors. Since the \({S}_{0}^{2}\) factor entering equation (2) is completely correlated with N _{WO}, N _{WW} ^{16}, a small variation in \({S}_{0}^{2}\) could lead to large variation in N _{WO}, N _{WW}. Thus, differences between the experimental \({k}^{3}\chi (k)\), FT\({k}^{3}\chi (k)\) and abinitio FMS computed \({k}^{3}\chi {(k)}_{{\rm{MD}}}\), FT\({{k}^{3}\chi (k)}_{{\rm{MD}}}\) spectra could possibly be ascribed to structural correlations with the \({S}_{0}^{2}\) factor and approximations on the muffintin radii for the potential of the photoabsorbing W atoms^{14, 16, 17}.
The RMCEXAFS refinement Fourier transformed into the realspace FT\({{k}^{3}\chi (k)}_{{\rm{RMC}}}\) of the WO and WW coordination shells in the experimental FT\({k}^{3}\chi (k)\) spectrum was calculated according to
Spectral fitting from RMCEXAFS refined FT\({{k}^{3}\chi (k)}_{{\rm{RMC}}}\) to the experimental FT\({k}^{3}\chi (k)\) spectra reproduces the realspace position of the first [WO] and second coordination shells [WW], and the multiplescattering contributions observed in the experimental spectra. These results confirm that the atomic shortrange order of aWO_{3}, can be properly extracted through RMCEXAFS simulations based on abinitio FMS approaches [Fig. 1b, Real and Im components at the bottom]. Table 1 summarizes the main interatomic bonddistances, atomic coordination and σ ^{2} factors, obtained from nonlinear leastsquares spectral fitting of the measured \({k}^{3}\chi (k)\), FT\({k}^{3}\chi (k)\) spectra, and those calculated directly from the RMCEXAFS optimized structures of aWO_{3}. The data show an excellent agreement to each other, which confirms that averaging over nonequivalent WO_{ x } atomicenvironments yields accurate reproduction of the \({k}^{3}\chi (k)\), FT\({k}^{3}\chi (k)\) spectra and correlated structural parameters of aWO_{3}. The σ ^{2} factors in Table 1 reflect the attenuation of \({k}^{3}\chi (k)\) and FT\({k}^{3}\chi (k)\) due to the meansquare static disorder in the distribution of interatomic bonddistances and ionic displacements^{3}. Thus, the calculated values for σ ^{2} correspond to the degree of disorder in aWO_{3}, which is mainly manifested in the shortening of interatomic bonddistances [WO, WW, OO], and in the lowering of the atomic coordination [N _{WO}, N _{OW}, N _{WW}, N _{OO}], with respect to crystalline phases of WO_{3}.
To more quantitatively assess the atomic shortrange order of our RMCEXAFS optimized structure of aWO_{3} we analyze the local bonding and coordination around the W and O atoms. The RMCEXAFS optimized structures of aWO_{3} comprise mainly cornersharing distorted WO_{6,5,4} units and a small proportion of edgesharing WO_{6,5,4} unitblocks [Fig. 2a–d]. Distribution of atomic coordination [at a WO bondlength cutoff of ≈2.8 Å], shows that W atoms hold mainly octahedra [N _{WO} = 6, ≈76%], under coordinated pentahedra [N _{WO} = 5, ≈22%], and tetrahedra [N _{WO} = 4, ≈2%] locally bonding with neighbouring O atoms [Fig. 2e]. This results in a main atomic coordination N _{WO} ≈ 5.74 ± 0.12 in the first WO shell, in agreement with the main value N _{WO} ≈ 5.8 ± 0.1 obtained from leastsquares fitting of the \({k}^{3}\chi (k)\) and FT\({k}^{3}\chi (k)\) spectra. The O atoms hold nearly twofold coordination with W atoms, N _{OW} ≈ 1.91 ± 0.10 [Fig. 2e]. The edgesharing [OWO] and cornersharing [WOW] bondangle distributions show peaks at 94°, 161° and at 105°, 150° [Fig. 2f]. After refinements, all the RMCEXAFS optimized structures of aWO_{3} attained a similar atomicbonding distribution and displayed small variation in the atomic coordination and bondangle distributions. This is of course, due to the use of preconverged MD trajectories, and the structural constraints applied in simulations, which force the input structures to achieve a similar atomic shortrange order to properly fit the \({k}^{3}\chi (k)\) and FT\({k}^{3}\chi (k)\) spectra [see Methods]. Interatomic bondlengths were almost the same. Some structures displayed overcoordinated WO_{7}units at larger WO bondlength cutoff [≈3.12 Å]. However, atomic coordinations N _{WO} = 5,6 dominates accurately the structural characteristics of the EXAFS spectra of aWO_{3}. Here the reported structural correlations and physical quantities correspond to the average over twelve RMCEXAFS optimized structures of aWO_{3}.
To compare our results with Xray and neutron diffraction experiments, the atomic shortrange order of our RMCEXAFS optimized structures of aWO_{3} was further analyzed in terms of the structure factor S(Q), defined according to
where b _{ j } is the Xray/neutron scattering length, R _{ j } the position of the atom j, and N the number of atoms. The Xray \({\boldsymbol{S}}{({\boldsymbol{Q}})}_{{\rm{X}}}\), neutron \({\boldsymbol{S}}{({\boldsymbol{Q}})}_{{\rm{N}}}\) structure factors and their associated reduced structure function Q[S(Q)−1], exhibit interference maxima around scattering wavevector magnitudes in the interval ΔQ ≈ 1.5–8.2 Å^{−1}. Beyond that range the oscillation amplitude in \({\boldsymbol{S}}{({\boldsymbol{Q}})}_{{\rm{X}}}\) and \({\boldsymbol{S}}{({\boldsymbol{Q}})}_{{\rm{N}}}\) is damped out due to the structural disorder [Fig. 3a,b]. \({\boldsymbol{S}}{({\boldsymbol{Q}})}_{{\rm{X}}}\) and \({\boldsymbol{S}}{({\boldsymbol{Q}})}_{{\rm{N}}}\) exhibit distinct interference patterns caused by different scattering processes. The scattering due to W atoms contributes more to \({\boldsymbol{S}}{({\boldsymbol{Q}})}_{{\rm{X}}}\) than that from O atoms, because Xrays interact mainly with the electron cloud surrounding the atoms [Zdependent]. Contrary, the scattering due to O atoms contributes more to \({\boldsymbol{S}}{({\boldsymbol{Q}})}_{{\rm{N}}}\) than that of W atoms, because neutrons interact with the atomic nucleus. These distinct features, the relative amplitude, peak position and the lineshape in our calculated \({\boldsymbol{S}}{({\boldsymbol{Q}})}_{{\rm{X}}}\), \({\boldsymbol{S}}{({\boldsymbol{Q}})}_{{\rm{N}}}\) and Q[S(Q)−1] patterns agree with previous data reported for stoichiometric Wbased oxides from Xray, electrons and neutron diffraction experiments^{18,19,20,21,22}, and show a qualitative similarity to data for substoichiometric W oxide^{23}.
Those structural characteristics are more clearly observed in the total Xray \(g{({\bf{R}})}_{{\rm{X}}}\) and neutron \(g{({\bf{R}})}_{{\rm{N}}}\) PDF defined according to
where c _{ α }, c _{ β } are the concentrations of α, β atoms [c _{ α,β } = N _{ α,β }/N], b _{ α }, b _{ β } denotes the Xray/neutron scattering length of species α, β, and \({g}_{\alpha \beta }({\bf{R}})\) denotes the partial PDF according to
with \(d\langle {n}_{\alpha \beta }({\bf{R}})\rangle \) the ensemble average number of β atoms in a shell d R at a distance R of an α atom. Here ρ is the number density and \({g}_{\alpha \beta }({\bf{R}})\) is the probability to find a β atom at a distance R from an α atom. The calculated \(g{({\bf{R}})}_{{\rm{X}}}\) exhibits two peaks at R ≈ 1.85 Å, R ≈ 3.7 Å, associated to the first [WO], [WW] coordination shells, respectively. The first [OO] shell at R ≈ 2.75 Å is also resolved in \(g{({\bf{R}})}_{{\rm{X}}}\), but it exhibits lower intensity [Fig. 3c]. Contrary, \(g{({\bf{R}})}_{{\rm{N}}}\) shows two peaks at R ≈ 1.85 Å, R ≈ 2.75 Å, associated to the first [WO], [OO] coordination shells, but the [WW] shell at R ≈ 3.7 Å, is not wellresolved in \(g{({\bf{R}})}_{{\rm{N}}}\) [Fig. 3d]. In Fig. 3e–g, maxima in the partials g _{WO} \({({\bf{R}})}_{{\rm{X}}}\) [at R ≈ 1.85, R ≈ 3.58, R ≈ 4.36 Å], in g _{OO}(R)_{X} [at R ≈ 2.75, R ≈ 3.90, R ≈ 5.26 Å], and in g _{WW}(R)_{X} [at R ≈ 3.7, R ≈ 4.96, R ≈ 5.6 Å], relate to the 1st, 2nd and 3rd coordination shells [WO, OO, WW], respectively. Note that the main atomic coordinations [N _{WO}, N _{OW}, N _{WW}, N _{OO}] as a function of R, and calculated according to
at the first minimum of g _{WO}(R)_{X}, g _{WW}(R)_{X}, g _{OO}(R)_{X}, in Fig. 3e–g agree with the main values N _{WO} ≈ 5.8 ± 0.1 and N _{WW} ≈ 5.3 ± 0.1, obtained by leastsquares fitting of the \({k}^{3}\chi (k)\) and FT\({k}^{3}\chi (k)\) spectra [Table 1]. The low intensity shoulder at the left side of g _{WW}(R)_{X} is due to WW pairs with bondlength R ≈ 3.1 Å, in neighboring edgesharing WO_{ x } structural units [inset Fig. 3f]. Those short WW bonds induce small polaron formation upon insertion of oxygenvacancies [O _{ v }], or alkali metal impurity ions [Li^{+}] and chargebalancing electrons^{10, 24}. It has been suggested that electrochromism in aWO_{3} arises from the optical absorption due to small polaron hopping associated to the formation of W^{5+} states due to transfer of electrons from O _{ v }sites and inserted Li^{+} species^{10, 24}. Short WW bonds have been previously reported for ion exchange and sputtered aWO_{3} solid thin film oxides^{18, 20}.
The RMCEXAFS simulations on aWO_{3} not only fit the experimental \({k}^{3}\chi (k)\) and FT\({k}^{3}\chi (k)\) spectra, but also the calculated Xray D(R) = 4πρ R · g(R) function [Fig. 3h], accurately reproduces the relative amplitude, peak position and the lineshape of earlier D(R)’s reported from electron and Xray diffraction experiments^{13, 18,19,20,21,22}. Especially, the peak at R ≈ 7.3 Å in the D(R) of the RMCEXAFS optimized structures of aWO_{3} accurately reproduces the formation of WO_{6} sixmembered rings [Fig. 3i], in agreement with experimental data^{18, 21, 22}. Particularly, the distribution of distorted WO_{ x } octahedraunits in the structure of aWO_{3} leads to the formation of distorted WO_{ x }like chains analogous to those found in the Magnéli phases W_{ x }O_{ z } ^{25}, and a wide distribution of WO_{4,5,6,7}membered rings comprising distinct WO_{ x } units with large free volume forming spacious channels as shown in Fig. 3i. Analogous channels have been reported for hexagonal hWO_{3} and nanostructured WO_{3} systems, which have WO_{6}three and sixmembered rings forming trigonal cavities with hexagonal and fourcoordinated square channels^{26, 27}. Those local structures provides large available sites for cation intercalation and superior charge densities, simplifying chargeion injection/diffusion and providing enough free volume for ion storage, which reduce activation energies and electrode volume variation during ion insertion/extraction. These results support the fact that the disordered structure of aWO_{3} enhances its electrochromic performance when comparing with its crystalline counterparts, as has been assumed in previous technical studies^{10}. Formation of different distorted WO_{ x }like chains and WO_{4,5,6,7}membered rings comprising distinct WO_{ x } units suggest that the atomic shortrange order of aWO_{3} should consist of a mixture of the different symmetries existing in the polymorphs and Magnéli phases of WO_{3}, rather than comprising a single hexagonal or distorted ReO_{3}octahedra phase, as suggested previously^{13, 18, 22}. This would also explain why aWO_{3} turns into a mixture of the monoclinic, hexagonal and triclinic phases of crystalline WO_{3} upon heating^{28}. Difficulties with the assignment of a single phase to aWO_{3}, arises because previous structural models were deduced by hand from direct comparison of the D(R)’s of crystalline and aWO_{3}. Thus, such model results are unrealistic since they do not take into account the contribution of distinct atomic environments to the total D(R) of aWO_{3}. Structural characterizations of aWO_{3} in terms of crystalline phases are ambiguous because the monoclinic/hexagonal WO_{3}, and the W_{ x }O_{ z }like Magnéli phases exhibit very analogous D(R) functions^{23}. Because of the localstructural reconstruction at nonequivalent atomic environments, amorphous materials should display a distribution of interatomic distances, and lower average atomic coordination. Here, energetically and structurally preconverged MD structural trajectories of aWO_{3} were used. This ensures that effects of static disorder due to the fluctuation of interatomic distances, atomic coordination and bondangles, were intrinsically taken into account in the simulations. Multiplescattering processes were included by selfconsistent calculations considering atoms beyond the first coordination shell. Thus, preconverged amplitudes and phaseshifts for different scattering processes around the photoabsorbing W atoms, allow the explicit treatment of threebody correlations. The use of bonddistance and coordination constraints prevent the aWO_{3} simulated structures getting away from the atomic shortrange order defined in the measured \({k}^{3}\chi (k)\) and FT\({k}^{3}\chi (k)\) spectra. Thus, since the structure was optimized at each atomic displacement, until it reached an accurate onetoone matching with the experimental \({k}^{3}\chi (k)\) and FT\({k}^{3}\chi (k)\) spectra, we expect our RMCEXAFSbased simulation to properly describe the atomic shortrange order of aWO_{3}.
Electronic properties of aWO_{3}
We now use the RMCEXAFS optimized structures of aWO_{3} to assess the correlations between atomic shortrange order and the electronic properties by detailed calculations of the electronic structure by hybrid density functional theory [DFT]^{29}, and electronic transitions associated to the XANES spectra by abinitio finite difference methods [FDM]^{30} [see Methods]. Figure 4a displays the total and projected DoS of aWO_{3}. The VB comprises mostly O[2p] states while the CB consists mainly of W[5d] states. This suggests that aWO_{3} to a great extent conserves the electronic structure defined in its crystalline counterparts. From the RMCEXAFS optimized structures of aWO_{3} a band gap of ≈3.12 eV without defectinduced ingap states in the DoS was consistently calculated. Increasing the HF exchange in the hybrid HSE06 functional yielded a band gap lowering of ≈0.8 eV. Note that the lack of periodicity in aWO_{3} yields an illdefined kvector, thus, the electronic energy band gap is merely given by the KohnSham eigenvalue difference between highest occupied [HOMO] and lowest unoccupied [LUMO] states. When going from crystalline WO_{3} [band gap ≈ 2.8 eV^{31}], to aWO_{3} [band gap ≈ 3.12 eV], a band gap widening of ≈0.32 eV is found. This electronic energy band gap is in good agreement with our experimental optical band gap of \(\hslash {\omega }_{g}\) ≈ 3.2 ± 0.07 eV, previously reported for sputtered aWO_{3} thinfilm oxides from optical UVvisNIR spectroscopy^{24}. To describe the disorderinduced localization of electronic states at the VB and CB tailsstates the inverse participation ratio [IPR; \(I({\psi }_{\eta ,l})\)], which allows to distinguish between localized and delocalized states, was calculated according to
where \({\psi }_{\eta ,l}({{\bf{R}}}_{i})\) denotes the eigenstate projection of a state \(\eta \) for the atom at a distance R _{ i }, and angular momentum l. N is the total number of atoms in the cell. For an ideally localized state, only one atomic site contributes all the charge [\(I({\psi }_{\eta ,l})\) = 1]. For a uniformly delocalized state, the charge contribution per site is uniform and equal to 1/N [\(I({\psi }_{\eta ,l})\approx \mathrm{1/}N\)]. Thus, large \(I({\psi }_{\eta ,l})\) values correspond to localized states, and low \(I({\psi }_{\eta ,l})\) to delocalized states^{32}.
The \(I({\psi }_{\eta ,l})\) function based on the electron density obtained from the hybrid DFT calculation is shown at the bottom of Fig. 4a. For RMCEXAFS refined aWO_{3}, \(I({\psi }_{\eta ,l})\) exhibits high values at the VB and CB edges, suggesting electronic localization of the O[2p] VB and W[5d] CB tail states. The VB tailstates shows slightly more localization than those electronic orbitals at the CB tail states. The mobility band gap defined as the energy gap between extended VB and CB states, is estimated to be ≈3.22 eV. The extent of localization of the VB and CB tail states in aWO_{3} depends on the charge density contribution due to the atomic shortrange order of distinct WO_{ x }units. Figures 4b,c display the electronic charge density contribution arising from localized O[2p] VB and W[5d] CB tail states [denoted \(\varphi \); \(\vartheta \) in Fig. 4a]. Fully delocalized Blochlike VB and CB states [denoted \(\nu \); \(\phi \)], are also shown in Fig. 4d,e. Localized VB tail states arise from O[2p]like charge density contributions due to single and twocoordinated O atoms holding short bonds with the W atoms [≈1.72–1.76 Å]. Localized CB tail states arise from W[5d]like charge density contributions due to undercoordinated WO_{4,5}units, and to a minor extent to formally sixfoldcoordinated W atoms that are largely displaced from the center of the WO_{6}octahedra. Unpaired electrons from the singlecoordinated O ions could yield localized acceptorslike dangling bonds at the VB tail edge. Overcoordinated W atoms could yield localized donorlike electronic states at the CB tailedge. Therefore, the VB and CB edges are strongly dependent on the type of ligands and on the atomic shortrange order around the O and W sites in the first and second coordination shells.
Figure 5a,b display the experimental and abinitio FDMRMC computed WL _{3}edge XANES spectra of aWO_{3}. The normalized spectra exhibit a strong and broad whiteline absorption maximum above the absorption edgeenergy centered at ≈10210.8 eV. The relative intensity, energy position, line shape and the electronic transitions in the experimental spectrum are well reproduced by the FDMXANES function calculated from the RMCEXAFS optimized structures of aWO_{3}. According to the dipole selection rules, the absorption WL _{3}edge is due to allowed electronic dipole transitions of the photoelectron from the initial W[2p _{3/2}] orbitals to the final unoccupied hybridized W[5d]O[2p] CB states. Thus, from the projected DoS it is qualitatively observed that the WL _{3}edge XANES spectrum of aWO_{3} follows the distribution of W[5d] and O[2p] CB orbitals [Fig. 5c]. The second derivative, \({d}^{2}\mu (E)/{d}^{2}E\), of the measured WL _{3}edge XANES spectrum [bottom Figs. 5a,b] exhibits lower and higher energy minima at ≈10208.9 eV and at ≈10212.9 eV, due to the splitting of the W[5d] orbitals into the W[t _{2g }] and W[e _{ g }] bands by the crystal field of the surrounding O atoms. In the calculated \({d}^{2}\mu (E)/{d}^{2}E\) of the WL _{3}edge FDMXANES spectra the minima associated to the W[t _{2g }] and W[e _{ g }] bands are located at ≈10209.2 eV and ≈10213.2 eV, respectively. The W[e _{ g }] orbitals tend to be smeared out, broadened and shifted by ≈0.3 eV, relative to the experimental spectrum. From the relative energy separation of the W[t _{2g }] and W[e _{ g }] bands, the crystal field splitting is found to be Δd ≈ E(e _{ g }) − E(t _{2g }) ≈ 4.0 ± 0.2 eV, being lower than that of crystalline WO_{3} ^{33}. Considering that the W[e _{ g }] orbitals point toward neighboring O[2p] orbitals, then this weaker crystalfield splitting Δd could be ascribed to the local structural disorder in the first and second coordination shells along with the contribution of undercoordinated W and O atoms [N _{WO} ≈ 5.74 ± 0.12, N _{OW} ≈ 1.91 ± 0.03].
Since the electronic correlations due to the interaction between the corehole and the excited electron are small at the OKedge, the projected DoS, which reflects the electronic ground state, provides a consistent interpretation of the OKedge XANES spectra of aWO_{3}. Figure 5d shows the abinitio FDM calculated OKedge XANES spectrum of aWO_{3} as calculated from the RMCEXAFS optimized structures. The calculated OKedge FDMXANES spectrum properly reproduces the relative intensity, energy position and shape of earlier reported spectra for aWO_{3} ^{34}. In the framework of the dipole selection rules, the spectrum is due to electronic transitions from the O[1s] corelevel into the unoccupied O[2p] orbitals. Due to the electronic hybridization between the W[5d] and O[2p] orbitals, the OKedge also provides the features of the density of W[5d] states. The OKedge XANES spectrum in Fig. 5d shows a main peak at γ ≈ 530.2 eV. From the projected DoS in Fig. 5e, it is noted that this peak reflects the O[2p] states in the t _{2g } CB due to unoccupied W[5d] and O[2p] orbitals. It has been argued that the relative intensity and width of the γ peak is determined by the number of O[2p] empty states, and by the width of the W[5d][t _{2g }] band, respectively. This depends on the contribution of nonequivalent O atoms in the first coordination shell [WO]^{34}. The peak at τ ≈ 535.7 eV emerges from W[5d] [e _{ g }]O[2p] hybridization while the peak ζ ≈ 542.8 eV is due to W[6sp]O[2p] interactions. The relative intensity of the τζpeaks depends on the atomic shortrange order of the WO_{ x }units present in the structure of aWO_{3}, and thus, the ζpeak exhibits lower intensity when comparing with crystalline WO_{3} ^{34}. The CB states of the O projected DoS in Fig. 5e, suggests that the OKedge XANES spectrum of aWO_{3}, which gives the unoccupied final states located above the Fermi level, emerges mainly from contributions due to the W[5d]O[2p] hybridized states. The W[s, p] states do not contribute significantly to the absorption at low energies, but they contribute to the ζpeak, and also contribute in some extent to the broad feature at ε ≈ 565.1 eV, observed in the OKedge XANES spectrum of aWO_{3}.
Finally, we remark that our scheme could offer a consistent route to experimentally and theoretically unveil the atomic shortrange order of aTMOs, and how local disorder affects their underlying electronic properties. The approach provides a onetoone matching of experimental data and corresponding model structure from which electronic properties can be directly calculated in agreement with the electronic transitions giving rise to the XANES spectrum of aTMOs.
Methods
Thinfilm oxide deposition and Xrayabsorption spectroscopy [XAS] experiments
In this study we used aWO_{3} thin film oxides [thickness 600 ± 20 nm, density ρ ≈ 5.27 g/cm^{3}] deposited by reactive DC magnetron sputtering, with an O/W ratio of 3.00 ± 0.04 as determined by Rutherford Backscattering Spectrometry [RBS], and previously reported^{24}. Xrayabsorption nearedge structure [XANES], and extended Xrayabsorption fine structure [EXAFS] spectra at the WL _{3}edge of aWO_{3} thinfilms oxides were collected using a passivated implanted planar silicon [PIPS] detector in fluorescence mode at beamline I811MAXlab synchrotron source, Lund, Sweden^{35}. The beam was focused using a Si[111] doublecrystal monochromator. A total of ten EXAFS spectra, \({k}^{3}\chi (k)\), were extracted from standard data reduction, absorption edge energy calibration, and background subtraction, as implemented in ATHENA^{36}. Those spectra were averaged to a total \({k}^{3}\chi (k)\) spectrum in the range Δk ≈ 2–10 Å^{−1}, and then Fourier transformed into the realspace FT\({k}^{3}\chi (k)\) in the interval ΔR ≈ 0–6 Å. Standard nonlinear leastsquares EXAFSfitting was implemented to previously obtain main values for interatomic distances, coordination numbers and σ ^{2} factors. To this end, atomic clusters of aWO_{3} generated by ATOMS^{36}, were fitted to the experimental \({k}^{3}\chi (k)\) [Δk ≈ 2–10 Å^{−1}], and FT\({k}^{3}\chi (k)\) [ΔR ≈ 0–6 Å] spectra by ARTEMIS^{36}. Amplitude and phase shift for single [WO, WW] and multiple scattering [WOO, WWO, WOWO] paths, were calculated selfconsistently by the abinitio FMS FEFF8.4 code^{14}. Fitting was carried out by allowing small variations in the interatomic distances and atomic coordination, while the σ ^{2} factors and the threshold energy shift ΔE _{0} were treated as free parameters.
Abinitio molecular dynamics MD simulations and FMS calculations of EXAFS spectra
In order to generate energetically and structurally preconverged 3Dmodels of aWO_{3} for further RMCEXAFS refinements, abinitio MD simulations, as implemented in VASP^{29}, were carried out to extract snapshots of structural trajectories of aWO_{3}. To this end, a cubic cell comprising W = 64 and O = 192 atoms [V ≈ 4400 Å^{3}, ρ ≈ 5.27 g/cm^{3}], rescaled from the crystalline symmetry of monoclinic WO_{3} [space group P121/n1; ICSD 14332], was used as input structure. Amorphization was carried out by melting the cubic cell by heating it up to 5000 K [WO_{3} melting point 1743 K]. The MD was equilibrated in the liquid state for 2 ps, and then, allowed to evolve for 2 ps, using 1 fs time steps at constant energy as a microcanonical ensemble. Twelve MD snapshots were selected and quenched down to 300 K, to simulate aWO_{3}. Reaching a steadystate condition upon 10^{4} ionic steps ensures that the MD was energetically and structurally relaxed. The PerdewBurkeErnzerhof [PBE]^{37} exchangecorrelation potential was used with a plane wave cutoff energy of 700 eV, and atomic positions were optimized by a force convergence criterion of 0.01 eV/Å. We used these energetically and structurally preconverged MD structural trajectories of aWO_{3} because they resemble more closely the experimental EXAFS spectrum, being computationally more efficient for RMCEXAFS optimization. To assess the reliability of the MD structural trajectories of aWO_{3}, MDEXAFS functions \({k}^{3}\chi {(k)}_{{\rm{MD}}}\) were computed by abinitio FMS and compared against the measured \({k}^{3}\chi (k)\) spectra. The complex exchangecorrelation HedinLundqvist selfenergy potential was used. The scattering potentials were computed in the muffintin approximation and muffintins were overlapped to 1.15 to reduce effects due to potential discontinuities using FEFF8.4^{14}. An amplitude reduction factor \({S}_{0}^{2}\approx 0.90(2)\) was estimated from the overlap integral by selfconsistent calculations of the cluster potential. The thermal damping of the MDEXAFS signals due to the structural disorder σ ^{2}, is given by the statistical averaging of \({k}^{3}\chi {(k)}_{{\rm{MD}}}\) signals obtained by summing over the ensemble of twelve MD trajectories. Single WL _{3}edge \({k}^{3}\chi {(k)}_{{\rm{MD}}}\) functions were computed for each photoabsorbing W atom inside clusters of radii R = 7 Å, and then averaged to a total \({k}^{3}\chi {(k)}_{{\rm{MD}}}\) and Fourier transformed to a total FT\({{k}^{3}\chi (k)}_{{\rm{MD}}}\) function.
Reverse Monte Carlo simulations RMCEXAFS
To simulate the atomic shortrange order of aWO_{3}, the twelve MD structural trajectories of aWO_{3} were fitted to the experimental \({k}^{3}\chi (k)\) [Δk ≈ 2–10 Å^{−1}] and FT\({k}^{3}\chi (k)\) [ΔR ≈ 0–6 Å] spectra by RMCEXAFS simulations, as implemented in RMCProfile^{15}. From the prior EXAFS analysis by ARTEMIS, the threshold energy shift was fixed to ΔE _{0} ≈ 6.84 eV and \({S}_{0}^{2}\approx 0.92(4)\). From EXAFS fitting by ARTEMIS, atoms were constrained to move into cutoff distances WO ≈ 1.4–2.8 Å, OO ≈ 2.2–3.3 Å, WW ≈ 2.8–4.2 Å. This avoids the atoms getting too close, and the breaking of WO bonds. Average coordination constraints were set and their weighting was gradually reduced at each RMCEXAFS cycle. This leads to mean coordination constraints N _{WO} ≈ 4–6 and N _{WW} ≈ 4–6, which were found to be the most suitable steadystate conditions to decrease the residual and reach spectral convergence. Hence, we are using structural constraints to avoid the exploration of configurations far from the already energetically and structurally preconverged structures. RMCEXAFS structures of aWO_{3} were then optimized allowing a 3–5% of atoms to undergo displacements of ≈0.08 Å, at every RMCEXAFS cycle. Each atomic movement is evaluated according to the degree of consistency \({\Re }^{2}\) between the experimental and the refined spectraldatapoints. Thus, if the atomic movement increases the consistency \({\Re }^{2}\) it is accepted. If instead, it lowers the consistency \({\Re }^{2}\) it is accepted with probability \(\wp \) = \({e}^{({\Re }_{0}^{2}{\Re }_{1}^{2})\mathrm{/2}}\). When the experimental and refined datapoints are statistically the same then the value of \({\Re }^{2}\) is less than the number of degrees of freedom^{38}. Total \({k}^{3}\chi {(k)}_{{\rm{RMC}}}\) and FT\({{k}^{3}\chi (k)}_{{\rm{RMC}}}\) functions; equal to the averaged single spectrum of each photoabsorbing W atom were recalculated at each RMCEXAFS cycle. Reaching of convergence to a minimum residual of ≈1–5 × 10^{−3} was attained by running ≈8 × 10^{5} RMCEXAFS cycles. After refinements, all twelve RMCEXAFS optimized structures of aWO_{3} attained similar atomicbonding distributions and displayed small variation in the atomic coordination and bondangle distributions. This is of course, due to the use of already preconverged MD trajectories and structural constraints applied in simulations, which force the input structures to achieve similar structural order to fit the EXAFS spectra. Here the reported structural correlations and physical quantities correspond to the average over those twelve RMCEXAFS optimized structures.
Hybrid density functional theory [DFT]
Electronic properties of the RMCEXAFS optimized structures of aWO_{3} were studied by abinitio hybrid DFT^{39} and used to assess electronic transitions from the W[2p _{3/2}] and O[1s] orbitals to unoccupied hybridized W[5d]O[2p] and single O[2p] CB orbitals. Structural relaxation was done using the PBE^{37} exchangecorrelation potential into the electron projectoraugmented wave [PAW] method^{40}, as implemented in VASP^{29}. A maximal force criterion convergence of 0.01 eV/Å was used and an energy cutoff of 700 eV was used to expand the KohnSham orbitals in the plane wave basis set. A 1 × 1 × 1 MonkhorstPack mesh^{41} centered at the \({\rm{\Gamma }}\)point was used for ksampling and the nonlocal range separated screened hybrid functional HSE06 [10% HF; 90% PBE; \(\omega \) = 0.2 Å^{−1}]^{42} was used.
Abinitio calculations of RMCXANES spectra
Abinitio calculations of the XANES spectra for RMCEXAFS optimized structures of aWO_{3} were carried out in order to assess the electronic transitions associated to unoccupied states in aWO_{3}. The WL _{3} and OK edge RMCXANES spectra were calculated selfconsistently by abinitio FDM, as implemented in the nearedge structure FDMNES code^{30}. The full potential FDM method does not approximate the potential’s form, providing a precise description of occupied and unoccupied electronic states. The energy dependent exchangecorrelation potentials by HedinLundqvist and Von Barth were used and evaluated using relativistic DFT. Electronic correlations and spinorbit coupling were approached by FockDirac schemes. Single WL _{3} and OK edge XANES signals were calculated on grids of 7 Å centered at each photoabsorbing W or O atom and then averaged to a total FDMRMCXANES function.
References
 1.
Wu, J., Cao, J., Han, W.Q., Janotti, A. & Kim, H.C. Functional metal oxide nanostructures. 3–358 (SpringerVerlag, New York, USA, 2012).
 2.
Neméth, K. et al. Efficient simultaneous reverse Monte Carlo modeling of pairdistribution functions and extended xrayabsorption fine structure spectra of crystalline disordered materials. J. Chem. Phys. 136, 074105110, doi:10.1063/1.3684547 (2012).
 3.
Krayzman, V. et al. A combined fit of total scattering and extended Xray absorption fine structure data for local structure determination in crystalline materials. J. Appl. Crystallogr. 42, 867–877, doi:10.1107/S0021889809023541 (2009).
 4.
Massobrio, C., Du, J., Bernasconi, M. & Salmon, P. S. Molecular dynamics simulations of disordered materials. 417–419 (Springer, Switzerland, 2015).
 5.
Anderson, P. W. Model for the electronic structure of amorphous semiconductors. Phys. Rev. Lett. 34, 953–955, doi:10.1103/PhysRevLett.34.953 (1975).
 6.
Mott, N. Electrons in glass. Rev. Mod. Phys. 50, 203–208, doi:10.1103/RevModPhys.50.203 (1978).
 7.
Cohen, M. H., Fritzsche, H. & Ovshinsky, S. R. Simple band model for amorphous semiconducting alloys. Phys. Rev. Lett. 22, 1065–1068, doi:10.1103/PhysRevLett.22.1065 (1969).
 8.
Santos, L. et al. Electrochemical devices: Structure and morphologic influence of WO_{3} nanoparticles on the electrochromic performance of dualphase aWO_{3}/WO_{3} inkjet printed films. Adv. Electron. Mater. 1, 1400002110, doi:10.1002/aelm.201400002 (2015).
 9.
Dalavi, D. S. et al. Efficient electrochromic performance of nanoparticulate WO_{3} thin films. J. Mater. Chem. C 1, 3722–3728, doi:10.1039/c3tc30378k (2013).
 10.
Monk, P. M. S., Mortimer, R. J. & Rosseinky, D. R. Electrochromism and electrochromic devices. 125–190 (Cambridge University Press, New York, USA, 2007).
 11.
Triana, C. A. & Niklasson, G. A. Electrochromic properties of Li^{+}intercalated amorphous tungsten (aWO_{3−x }) and titanium (aTiO_{2−x }) oxide thin films. J. Phys: Conf. Series. 559, 01200415, doi:10.1088/17426596/559/1/012004 (2014).
 12.
de Wijs, G. A. & de Groot, R. A. Structure and electronic properties of amorphous WO_{3}. Phys. Rev. B. 60, 16463–16473, doi:10.1103/PhysRevB.60.16463 (1999).
 13.
Lugovskaya, L. A., Aleshina, L. A., Kalibaeva, G. M. & Fofanov, A. D. Xray study and structure simulation of amorphous tungsten oxide. Acta Cryst, B 58, 576–586, doi:10.1107/S0108768102006833 (2002).
 14.
Ankudinov, A. L., Ravel, B., Rehr, J. J. & Conradson, S. D. Realspace multiplescattering calculation and interpretation of xrayabsorption nearedge structure. Phys. Rev. B. 58, 7565–7576, doi:10.1103/PhysRevB.58.7565 (1998).
 15.
Tucker, M. G., Keen, D. A., Dove, M. T., Goodwin, A. L. & Hui, Q. RMCProfile: reverse Monte Carlo for polycrystalline materials. J. Phys.: Condens. Matter. 19, 3352181–16 (2007).
 16.
Newville, M. Fundamental of XAFS. Rev. Mineral. Geochem. 78, 33–74, doi:10.2138/rmg.2014.78.2 (2014).
 17.
Triana, C. A., Araujo, C. M., Ahuja, R., Niklasson, G. A. & Edvinsson, T. Electronic transitions induced by shortrange structural order in amorphous TiO_{2}. Phys. Rev. B. 94, 16512919, doi:10.1103/PhysRevB.94.165129 (2016).
 18.
Nanba, T., Nishiyama, Y. & Yasui, I. Structural study of amorphous WO_{3} thin films prepared by the ion exchange method. J. Mater. Res. 6, 1324–1333, doi:10.1557/JMR.1991.1324 (1991).
 19.
Bets, V. et al. Studies of tungsten oxide electrochromic thin films and polycrystals by the EXAFS method. Nucl. Instr. and Meth. A. 261, 175–177, doi:10.1016/01689002(87)905936 (1987).
 20.
Nanba, T. et al. Characterization of amorphous tungsten trioxide thin films prepared by rf magnetron sputtering method. J. NonCrystalline Solids. 178, 233–237, doi:10.1016/00223093(94)902909 (1994).
 21.
Nanba, T. & Yasui, I. Xray diffraction study of microstructure of amorphous tungsten trioxide films prepared by electron beam vacuum evaporation. J. Solid. State. Chem. 83, 304–315, doi:10.1016/00224596(89)901801 (1989).
 22.
Zeller, H. R. & Beyeler, H. U. Electrochromism and local order in amorphous WO_{3}. Appl. Phys. 13, 231–237, doi:10.1007/BF00882886 (1977).
 23.
Ankele, J., Mayer, J., Lamparter, P. & Steeb, S. Evaluation of the Structure of Amorphous Tungsten Oxide W_{28}O_{72} by the Combination of Electron, XRay and NeutronDiffraction (ThreeBeam Experiment). Z. Naturforsch. 61a, 189–196, doi:10.1515/zna20063412 (2006).
 24.
Triana, C. A. & Niklasson, G. A. Electrochromism and smallpolaron hopping in oxygen deficient and lithium intercalated amorphous tungsten oxide films. J. Appl. Phys. 118, 02490119, doi:10.1063/1.4926488 (2015).
 25.
Migas, D. B., Shaposhnikov, V. L. & Borisenko, V. E. Tungsten oxides. II. The metallic nature of Magnéli phases. J. Appl. Phys. 108, 09371416, doi:10.1063/1.3505689 (2010).
 26.
Gerand, B., Nowogrocki, G., Guenot, J. & Figlarz, M. Structural study of a new hexagonal form of tungsten trioxide. J. Solid State Chem. 29, 429–434, doi:10.1016/00224596(79)901993 (1979).
 27.
Zheng, H. et al. Nanostructured Tungsten Oxide  Properties, Synthesis, and Applications. Adv. Funct. Mater. 21, 2175–2196, doi:10.1002/adfm.v21.12 (2011).
 28.
Ramana, C. V., Utsunomiya, S., Ewing, R. C., Julien, C. M. & Becker, U. Structural stability and phase transitions in WO_{3} thin films. J. Phys. Chem. B. 110, 10430–10435, doi:10.1021/jp056664i (2006).
 29.
Kresse, G. & Furthmuller, J. Efficient iterative schemes for ab initio totalenergy calculations using a planewave basis set. Phys. Rev. B 54, 11169–11186, doi:10.1103/PhysRevB.54.11169 (1996).
 30.
Bunau, O. & Joly, Y. Selfconsistent aspects of xray absorption calculations. J. Phys.: Condens. Matter. 21, 345501111 (2009).
 31.
Wang, F., Valentin, C. D. & Pacchioni, G. Electronic and structural properties of WO_{3}: A systematic hybrid DFT study. J. Phys. Chem. C. 115(16), 8345–8353, doi:10.1021/jp201057m (2011).
 32.
Abtew, T. A. & Drabold, D. A. Ab initio models of amorphous Si_{1−x }Ge_{ x }:H. Phys. Rev. B. 75, 04520119, doi:10.1103/PhysRevB.75.045201 (2007).
 33.
Yamazoe, S., Hitomi, Y., Shishido, T. & Tanaka, T. XAFS study of tungsten L _{1} and L _{3}edges: Structural analysis of WO_{3} species loaded on TiO_{2} as a catalyst for photooxidation of NH_{3}. J. Phys. Chem. C. 112, 6869–6879, doi:10.1021/jp711250f (2008).
 34.
Purans, J., Kuzmin, A., Parent, P. & Laffon, C. Xray absorption study of the electronic structure of tungsten and molybdenum oxides on the O Kedge. Electrochem. Acta 46, 1973–1976, doi:10.1016/S00134686(01)00370X (2001).
 35.
Carlson, S., Clausen, M., Gridneva, L., Sommarin, B. & Svensson, C. XAFS experiments at beamline I811, MAXlab synchrotron source, Sweden. J. Synchrotron. Rad. 13, 359–364, doi:10.1107/S0909049506025611 (2006).
 36.
Ravel, B. & Newville, M. ATHENA, ARTEMIS, HEPHAESTUS: data analysis for Xray absorption spectroscopy using IFEFFIT. J. Synchrotron. Rad. 12, 537–541, doi:10.1107/S0909049505012719 (2005).
 37.
Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868, doi:10.1103/PhysRevLett.77.3865 (1996).
 38.
McGreevy, R. L. & Pusztai, L. Reverse Monte Carlo Simulation: A New Technique for the Determination of Disordered Structures. Molecular Simulation. 1, 359–367, doi:10.1080/08927028808080958 (1988).
 39.
Kohn, W. & Sham, L. J. Selfconsistent equations including exchange and correlation effects. Phys. Rev. 140, 1133–1138, doi:10.1103/PhysRev.140.A1133 (1965).
 40.
Bloch, P. E. Projector augmentedwave method. Phys. Rev. B. 50, 17953–17979, doi:10.1103/PhysRevB.50.17953 (1994).
 41.
Monkhorst, H. J. & Pack, J. D. Special points for Brillouinzone integrations. Phys. Rev. B. 13, 5188–5192, doi:10.1103/PhysRevB.13.5188 (1976).
 42.
Paier, J. et al. Screened hybrid density functionals applied to solids. J. Chem. Phys. 124, 154709113, doi:10.1063/1.2187006 (2006).
Acknowledgements
This work has been supported by the Swedish Research Council. Computational facilities were provided by the Swedish National Infrastructure for Computing [SNIC] at PDC Center for High Performance Computing and National Supercomputer Center at Linkping University [Triolith]. Experimental work was carried out at beamline I811, MAXlab synchrotron radiation source, Lund University, Sweden. Funding for the beamline I811 project was kindly provided by The Swedish Research Council and The Knut & Alice Wallenbergs Stiftelse.
Author information
Affiliations
Contributions
C.A.T. deposited thin film oxides, performed the EXAFSXANES experiments, carried out the MD, RMC, EXAFSXANES simulations, and implemented abinitio DFT calculations. C.A.T. G.A.N. and T.E. initiated this research project and contributed to the design of experiments and simulations. C.M.A. and R.A. supervised the MD, RMC, EXAFSXANES and DFT simulations. All authors were involved in analysing and reviewing the manuscript.
Corresponding author
Correspondence to C. A. Triana.
Ethics declarations
Competing Interests
The authors declare that they have no competing interests.
Additional information
Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Triana, C.A., Araujo, C.M., Ahuja, R. et al. Disentangling the intricate atomic shortrange order and electronic properties in amorphous transition metal oxides. Sci Rep 7, 2044 (2017). https://doi.org/10.1038/s41598017011512
Received:
Accepted:
Published:
Further reading

The effects of dilute concentrations of substitutional Re or Os on the thermodynamics and kinetics of oxygen in tungsten
Physica B: Condensed Matter (2020)

Soft Templating and Disorder in an Applied 1D Cobalt Coordination Polymer Electrocatalyst
Matter (2019)

Pathways towards true catalysts: computational modelling and structural transformations of Znpolyoxotungstates
Dalton Transactions (2019)

Advanced approach to the local structure reconstruction and theory validation on the example of the W L3edge extended xray absorption fine structure of tungsten
Modelling and Simulation in Materials Science and Engineering (2018)

Electrochromic materials and devices for energy efficiency and human comfort in buildings: A critical review
Electrochimica Acta (2018)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.