Polytypism in Hexagonal Tungsten Trioxide: Insights from Ab Initio

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C: Physical Processes in Nanomaterials and Nanostructures

Polytypism in Hexagonal Tungsten Trioxide: Insights from Ab Initio Molecular Dynamics Simulations Yonghyuk Lee, Taehun Lee, and Aloysius Soon J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b05595 • Publication Date (Web): 28 Aug 2018 Downloaded from http://pubs.acs.org on September 1, 2018

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The Journal of Physical Chemistry

Polytypism in Hexagonal Tungsten Trioxide: Insights from Ab Initio Molecular Dynamics Simulations Yonghyuk Lee,†,‡,¶ Taehun Lee,†,¶ and Aloysius Soon∗,† †Department of Materials Science and Engineering, Yonsei University, Seoul 03722, Republic of Korea ‡Department of Theoretical Chemistry, Technische Universität M¨ unchen, Lichtenbergstrasse 4, 85747 Garching, Germany ¶Contributed equally to this work E-mail: [email protected] Abstract Temperature-dependent microstructural evolution of hexagonal WO3 (h-WO3 ) polytypes is explored via ab initio molecular dynamics calculations within the densityfunctional theory framework. We present simulated finite temperature radial distribution function and X-ray diffraction patterns to re-interpret recent experimental pair distribution function analysis. This work clearly demonstrates that after a more careful analysis of the finite temperature structural properties of h-WO3 , an intermediate H1-like structure is predicted at higher temperatures, while the more stable H4 polytype (and not the experimentally suggested H2 polytype) is obtained nearer ambient temperatures. This is further corroborated by our electronic structure analysis which shows that the electronic band gap energy of the ambient temperature H4-like structure agrees much better with the experimentally reported band gap energies.

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Introduction The physiochemical properties of many functional metal oxides like tungsten trioxide, WO3 (including their charge states, electrical conductivity, and optical transitions, for instance) are known to be highly correlated to the intricate microscopic structure (i.e. atomic-scale description) of the (polymorphic) oxide phase in question, where both stoichiometry 1 and polymorphism/polytypism 2 can play a key role in their overall desired performance in e.g. catalytically photoactivated chemical reactions 3 and as effective hole transport materials. 4 However, often a lack of detailed knowledge in these complex structure-property relations hinder the accelerated progress that is very much desired in this area of technological development associated with high-performance devices. Unlike the well-studied ambient-stable monoclinic γ-phase of WO3 , 5 much less is known about its hexagonal phase (h-WO3 ) where many emerging useful properties 6,7 of this hexagonal polymorph can be exploited. The first crystalline form of h-WO3 was prepared by Gerand et al. in 1979 where a space group of P 6/mmm (denoted as H1) was assigned to h-WO3 via X-ray powder diffraction (XRD) analysis. 8 This was then challenged by Oi et al. in 1992 where they synthesized h-WO3 and proposed several possible space groups for their samples, namely P 63 /mcm (denoted as H2 or H3), P 63 cm (denoted as H4), or P 6c 2. 9 Given the limitation in the refinement of their XRD peaks, they tentatively concluded that the P 63 /mcm (i.e. the H2 or H3) is more likely to be the proposed space group symmetry adopted by their h-WO3 samples. 9 After a decade, in 2012, a first-principles density-functional theory (DFT) investigation was conducted by Kr¨ uger et al. to address the thermodynamic stability amongst the experimentally proposed polytypes, namely the H1, H2 (or H3), and H4 structures. 10 Within the semi-local approximation to the exchange-correlation (xc) functional and without considering finite temperature effects, they concluded that the H4 structure is the most energetically favoured phase (by 0.021 and 0.089 eV/formula unit (f.u.) when compared to H1 and H2, respectively), technically at T = 0 K. 10 2


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A couple of years later, with the advent of more sophisticated techniques in synthesis and characterization methods, state-of-the-art in situ experiments using synchrotron X-rays were carried out to probe the microstructure of h-WO3 in real time by analyzing the pair distribution function (PDF). 11 It was reported that the H1 structure formed from ammonium metatungstate precursor solution is the thermodynamic product, while the kinetic product (H2 structure) may be obtained in the flow reactor using the same precursor due to a lack of adequate time to reorganize the WO6 octahedrons into the ordered H1 structure. 11 Consequently, this is not in agreement with the theoretical results of Kr¨ uger et al. 10 where admittedly finite temperature effects were not considered. In this work, using DFT-based ab initio molecular dynamics (aiMD) calculations as implemented in the Vienna Ab Initio Simulation Package (VASP) code, 12,13 we will demonstrate the temperature-dependent microstructural evolution of h-WO3 in real time via firstprinciples simulated temperature-time evolving radial distribution function (RDF) and XRD patterns. With comparison to the latest available experiments, 11 we will show how finitetemperature DFT results can reconcile and guide the interpretation of experiments, and addressing the wide range of the electronic band gap energies reported in experiments.

Computational Methods Density-functional theory calculations are performed using the projector augmented wave (PAW) 14 method as implemented in VASP code. 12,13 The 5p, 5d, and 6s states of W, and the 2s and 2p states of O are explicitly considered as the valence states, with the PAW approach. The self-consistent van der Waals xc functional (optB88) is used to compute the energetics and structural parameters (including molecular and lattice dynamics calculations), while the hybrid DFT xc functional due to Heyd, Scuseria, and Ernzerhof (HSE06) 15,16 is used to determine the electronic band structure. The kinetic cutoff energy for the expansion of the planewave basis used in this work is set to 500 eV. The Brillouin-zone integrations are

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sampled with the uniform reciprocal distance of 0.2 ˚ A−1 , yielding k-grids of 5 × 5 × 9 for H1 and 5 × 5 × 5 for H2 and H4, respectively. Ab initio molecular dynamics (ai MD) calculations are performed at constant volume with different starting geometries of WO3 polytypes. For each polytype, the starting structure is obtained from the DFT-computed structural parameters of H1, H2, and H4 with densities of 6.251, 6.237, and 6.212 g/cm3 , respectively. The canonical (NVT ) ensemble (which is commonly used for solid phase ai MD simulations 17–19 ) is chosen due to the small volumetric thermal expansion coefficients (∼ 10−5 K−1 ) of H1, H2, and H4 (see Figure S2 in Supporting Information) which are determined by fitting the energy–volume data to the Debye model. 20,21 The Nosé-Hoover thermostat is used to control the temperature modulation, 22 with a Nosé-mass parameter corresponding to the period of ∼ 48 timesteps (2 fs per time step). It is ensured that the temperature as well as the total energy of extended system based on the Nosé-Hoover thermostat are well converged with respect to time evolvement (see Figures S6 and S7). A (2 × 2 × 2) supercell of the DFT-optimized H4 phase (192 atoms) is adopted as an initial atomic configuration and corresponding lattice constants of simulated supercell are presented in Table S1. For this supercell, the Brillouin zone is folded to the Γ-point, and it is tested to a total-energy convergence of 0.01 eV/atom. The initial structure is randomized at 1000 K for 10 ps, and then, it is further annealed at 600 K for 20 ps for direct comparison with experiments. 11,23 The resulting structure is quenched to 300 K over 20 ps with a cooling rate of 15 K/ps. We take the additional 500 timesteps at the final quenched structure in 300 K in order to get more representative geometries at the temperature. Therefore, the total ai MD simulation consists of 25500 timesteps (51 ps). The same is done and tested for with the fully relaxed H1 (using a (2 × 2 × 4) supercell) and H2 structure (up to the annealing process for comparison).

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Results and Discussion All polytypes of h-WO3 (namely, H1, H2, and H4) comprise of corner-sharing WO6 octahedrons (see Figure 1). In the case of H1, a perfect WO6 octahedron is assumed. For H2 and H4, the central metal atom in the WO6 octahedron are slightly displaced, as captured by the quadratic elongation index, ⟨λ⟩ 24–26 (cf. Equation S1; Ideal polyhedrons will take on a value of 1.0) where ⟨λ⟩ = 1.000, 1.016, and 1.017 for H1, H2, and H4, respectively. This results in a different number of W-O bond lengths for both H2 and H4 and their values are listed in Table 1. For H2, the central W atom is displaced in ab-plane, while the H4 includes an additional displacement in the c-direction (as indicated by the small arrows in Figures 1b and 1c). For both polytypes, their overall symmetry is lower than in the case for H1, and this accounts for the doubling of their unit cells in the c-direction. We note that the inter-octahedral distortions amongst the polytypes are minute, varying less than 2 ◦ for the angle between the vertex O atoms in adjacent WO6 octahedrons. To identify structural properties of the distorted h-WO3 phase prepared by Oi et al., 9 various structural models with possible space groups are investigated theoretically and experimentally. 10,11 In this work, the structural model with the proposed space group P 6c 2 has been neglected due to a lack of accessible structural parameters from literature. Using the optB88 xc functional, 27,28 we have computed the optimized lattice parameters Table 1: Bond distances are given in ˚ A between the central tungsten to the surrounding oxygens, dW−Oa , dW−Ob of H1, H2, and H4. Ob and Oa are the oxygen atoms in basal plane and axial plane, respectively.

h-WO3

d W−Ob

d W−Oa

H1 H2 H4

1.922 1.809, 2.093 1.826, 2.053

1.918 1.913 1.809, 2.073

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Figure 1: (Color online) Top- (left panel) and side-views (right panel) of the atomic structures of h-WO3 polytypes: (a) H1, (b) H2, and (c) H4. Tungsten and oxygen atoms are depicted as gray and red spheres, respectively. Yellow boxes are used to indicate the bulk unit cell. for the all polytypes and listed their values in Table 2. In our ground state DFT calculations, the difference in the lattice parameters a0 and c0 of H1 and H4 are less than 0.1 %, and that for a0 and c0 when comparing H1 and H2 are 0.67 and −1.30 %, respectively. In agreement with the previous theoretical work of Kr¨ uger et al., 10 we find the same ordering of energetic stability (both without finite temperature effects), i.e. at T = 0 K, where H4 is the most stable followed by H2 and then H1 being the least stable energetically (see Table 2). However, the difference in the enthalpy of formation between H2 and H4 is less than 0.01 eV per WO3 formula unit (albeit within the error bar of DFT), and therefore H2 and H4 phases may be energetically competitive. The same tendency is captured by all xc functionals considered in this work: local (LDA), semilocal (PBE and optB88), and hybrid (HSE06) functionals (see Tables S2, S3, and S4). Now, referring to the most recent experimental characterization of h-WO3 , 11 the authors have studied these minute (but non-negligible) structural changes in h-WO3 by conducting in situ synchrotron X-ray PDF measurements. The authors in this paper 11 have commented

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˚) and the enthalpy of forTable 2: Space group, structural parameters (a0 and c0 , given in A f mation, E (expressed in eV per formula unit (f.u.)) of crystalline h-WO3 (for the polytypes H1, H2, and H4) calculated using the vdW-corrected semi-local optB88 xc-functional.

h-WO3

Space group

H1 H2 H4

P 6/mmm P 63 /mcm P 63 cm

a0

c0

Ef

7.46 3.84 −9.31 7.51 7.58 −9.40 7.46 7.72 −9.41

that the long-range order (from 5.5 to 20 ˚ A) found in their h-WO3 samples synthesized under hydrothermal condition agrees well with their simulated H1 PDF data, based on a local atomic structural model. However, referring to their short-range PDF data, they observed two distinct peaks at 1.87 and 2.22 ˚ A which clearly disagree with their simulated H1 PDF plot. Instead, they argued that the origin of these two peaks agree much better with the simulated H2 PDF data they presented 11 which calls into question: What is the actual ground-state polytype of h-WO3 ? Is the H4 polytype observed as predicted by theory? Before invoking finite temperature effects in h-WO3 , we turn to our DFT-optimized H1, H2, and H4 h-WO3 and their simulated RDF plots (cf. Equation S2), yielding identical results to the PDF (at T = 0 K, with the corresponding simulated XRD plots) in Figure 2. As seen in Figure 2a, given that the W-O bond lengths in H1 are identical, a single peak near 1.92 ˚ A is observed, while distinct (multiple) peaks near 2 ˚ A for H2 and H4 are seen (in Figures 2b and 2c, respectively), corroborating well with the degree of metal off-center displacements found in both H2 and H4. Specifically, H2 is found to have one dW−Oa at 1.91 ˚ A and two different dW−Ob at 1.81 and 2.09 ˚ A, and hence yielding three peaks near 2˚ A (in Figure 2b). Likewise, additional c-direction displacement of the central W atom in H4 produces two groupings of broadened peaks – about 1.82 and 2.06 ˚ A (in Figure 2c). Interestingly, these two peaks coincide with the experimentally reported values of 1.87 and 2.22 ˚ A, hinting that the experimental h-WO3 may well be the H4 instead, which we will

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Figure 2: (Color online) Calculated radial distribution functions (RDF), g(r) of (a) H1, (b) H2, and (c) H4 phases as a function of distances, r given in ˚ A unit. The corresponding X-ray diffraction (XRD) patterns (in the range from approximately 20 to 30 ◦ ) are shown in the inserts. demonstrate below. Here, we note that this comparison of the simulated RDF based on H1, H2, and H4 (i.e. structurally optimized at T = 0 K) is not complete as finite temperature effects are not considered explicitly and may be important. In most experiments, h-WO3 samples have been prepared at fairly high temperatures (see Table S5). Thus, to include temperature effects, we have conducted first-principles DFT aiMD calculations, within the N V T ensemble with the Nosé-Hoover thermostat to vary the temperature. From our DFT aiMD trajectories, we provide complementary temperaturetime evolving RDF data to compare and understand the experimental PDF results from Reference 11. As shown in Figure 3a, starting from the ideal H4 structure, we randomize the initial structure at a temperature of 1000 K for 10 ps, followed by an annealing process for another 20 ps at a constant temperature of 600 K (similar to the reported temperatures in experiment 11 ). Lastly, for yet another 20 ps, we now apply a cooling rate of 15 K/ps to mimic a quenching process from 600 to 300 K (ambient temperature). In addition, an extra 500 timesteps are taken using the final quenched structure as a starting geometry to generate more representative structures at T = 300 K. Upon analyzing our simulated RDF data, surprisingly we find that regardless of our initial starting polytype geometry (with different densities of 6.251, 6.237, and 6.212 g/cm3 8


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Figure 3: (Color online) Temperature-time evolution of (a) the simulated RDF (left column) and the associated partial RDF of O-W (right column) and (b) the simulated XRD patterns, based on DFT-aiMD. The starting H4 h-WO3 structures are first randomized at 1000 K, followed by an annealing process at 600 K and then quenched from 600 to 300 K (at 15 K/ps) while keeping the last 1 ps at 300 K. Atomic structures from the last 500 steps of each DFTaiMD process are taken and averaged to generate the line plots shown above the temperaturetime evolution plots for each process. The experimental PDF data 11 is extracted from r = 1.5 ˚ A to r = 2.5 ˚ A (with an interval of r = 0.02 ˚ A) to make a direct comparison with our quenched structure (300 K) shown in the insert of first-row and second-column of (a). We note that starting from both the DFT-optimized H1 and H2 structures produce identical averaged RDF and XRD plots (as shown in Figure S4). for the H1, H2, and H4 phases, respectively; see Figure S4), we always end up with the thermodynamically stable H4-like structure under ambient conditions (with an averaged ⟨λ⟩ value of 1.021 from a Gaussian fit; See Figure S5). This transition is tractable by following 9



Figure 4: Calculated HSE06 electronic band structures of (a) H1, (b) H2, and (c) H4. Here, the valence band maximum (VBM) energy is set to 0 eV. Note that the c unit lattice parameters of H2 and H4 are twice that of H1, and thus their reciprocal spaces are folded accordingly. (d) The high-symmetry k-points Γ, M, K, and Γ labelled in (b) and (c) are identical to the high-symmetry k-points A, L, H, and A in (a). the RDF peaks near 2 ˚ A (more clearly shown in the partial O-W RDF plot in Figure 3a) where a very broad peak with a shoulder is first observed during the randomization process at 1000 K. The shoulder peak starts to split off from the broaden peak during the annealing process (at 600 K), and finally form two clear sharp narrower peaks – ∼ 1.8 (with higher intensity) and ∼ 2.1 ˚ A upon quenching as shown in the insert of Figure 3a. These two peaks reflect the local coordination of the O-W bonds in the distorted octahedron in the H4 polytype, which would otherwise be not present in either H1 or H2. The two peaks are observable from annealing to the quenching process at 600 and 300 K, and likely due to thermal motion, a certain degree of broadening in these peaks might be expected when compared to those peaks found for H4 at T = 0 K. Referring back to the recent in situ synchrotron X-ray PDF measurements by Saha et al., 11 we question and argue that the synthesized product which clearly shows two localized peaks around 2 ˚ A in their experimental PDF is more likely to be the thermodynamic H4 polytype, rather than their assigned H2 structure. With regards to the earlier theoretical work by Kr¨ uger et al., 10 we now demonstrate that our DFT aiMD calculations further validate previous DFT calculations and with the consideration of finite temperature effects, the predicted room-temperature ground-state of h-WO3 is indeed the H4 polytype phase. 10


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We will also briefly report simulated temperature-time dependent XRD data from our DFT aiMD calculations. Previous XRD experiments 23,29–34 have proposed that the asprepared h-WO3 phases possess two space groups – P 6/mmm and P 63 /mcm (as listed in Table S5). However, from the reported experimental XRD spectra in References 23,29–34, it seems difficult to distinguish peaks especially between 20 and 30 ◦ , likely due to the limited resolution of the experiments. In spite of this, here we provide complementary theoretical XRD simulation and analysis to show additional evidence for the H4 h-WO3 to exist near ambient temperatures, as opposed to the H1 structure. In Figure 3b, using the structures calculated from DFT aiMD trajectories, we calculate and simulate the XRD peaks as a function of temperature and time (in the similar fashion to our RDF data described above). Here, referring to the inserts in Figure 2, a distinctive (2¯11) peak is only observed in H2 and H4 at ∼ 26.2 ◦ where it is clearly absent in the XRD plot for H1. Albeit, the XRD plots of H2 and H4 look identical and it is not easy to distinguish between them. However, in H2, the (002) and (102) peaks are found to be located closer to the (2¯10) and (200) peaks, respectively, when compared to that of H4. Unlike what is found through the RDF analysis, simulated XRD plots in the second-row of Figure 3b show the existence of H1-like structures during the annealing process at 600 K. The (2¯11) peak has not been observed during the annealing process, and thus hinting that the phase at relatively high temperatures may structurally resemble H1. It seems very plausible for an intermediate H1-like structure to be present/trapped at high temperatures (600 ∼ 1000 K), and then forming the more stable H4-like structure nearer ambient temperatures. In the similar argument for our simulated RDF data, our computed XRD pattern in Figure 3b (and Figure S3) supports and corroborates that the H4 structure is the ambient h-WO3 , irregardless of our starting polytype geometry. This is confirmed by the emergence of the (2¯11) peak in the middle of quenching process (as indicated by the small white arrow in Figure 3b), which is absent during the randomization and annealing processes (i.e. an intermediate H1-like structure at high temperatures).

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Table 3: Electronic band gap energies, Eg in eV of H1, H2, and H4 h-WO3 (computed using the hybrid HSE06 xc-functional at T = 0 K) are shown. We have also randomly selected 5 h-WO3 structures from the quenched MD trajectories at T = 300 K and calculated their electronic band gap energies with the standard deviation. The range of experimentally measured band gap energies 30,33–38 is also included for comparison (Details of these experiments can be found in Table S5).

h-WO3

Eg (eV)

H1 (T = 0 K, DFT) H2 (T = 0 K, DFT) H4 (T = 0 K, DFT) Quenched (T = 300 K, aiMD) Experiments

1.60 2.12 2.90 2.69 ± 0.07 2.48 to 2.96

Having determined the temperature-time evolution of the polytype transition in h-WO3 , we now turn our attention to the electronic structure of the various h-WO3 polytypes. Using the more accurate hybrid DFT xc functional due HSE06, 15,16 we calculate the electronic band structures of H1, H2, H4, and the ambient temperature H4-like structure (as determined from randomly selecting 5 different structures from our quenched aiMD trajectories) and list the electronic band gap energies, Eg in Table 3. The experimental Eg (consolidated from Table S5) is also shown for comparison. From our HSE06 DFT calculations, H1 is determined to have an indirect band gap of 1.60 eV, while both H2 and H4 possess a direct band gap of 2.12 and 2.90 eV, respectively (with their detailed electronic band structures are plotted in Figure 4). This implies that, within the accuracy of the hybrid DFT xc approximation, a large band gap opening (of more than 1 eV) can be achieved simply by a polytypical change from the H1 to H4 structure by e.g. controlling the synthesis conditions. It may also be understood that the H1 → H4 transformation can result in an indirect → direct band gap transition. Our ambient temperature H4-like structure yields an averaged electronic band gap of 2.69 eV (with a standard deviation of 0.07 eV), agreeing very well with our calculated H4’s

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band gap as well as reported band gap energies from experiments. 30,33–38 The calculated band gap of the H4-like structure (2.69 eV) is much closer to that of the H4 phase (2.90 eV) when compared to those of H1 and H2. This lends a strong support, from an electronic structure point-of-view, that our ai MD simulated H4-like structures should be in close resemblance to the actual H4 phase. It is now evident that both theory and experiments can reconcile and agree that, after a careful analysis of both structural and electronic properties of h-WO3 , the H4 structure is indeed the ambient stable polytype of h-WO3 .

Summary In summary, using DFT-based aiMD calculations, we explore the temperature-dependent microstructural evolution of h-WO3 polytypes to address the dispute between previously reported experimental and theoretical studies. Using our simulated finite temperature RDF and XRD patterns, we conclusively show that an intermediate H1-like structure is predicted at higher temperatures, while the more stable H4-like structure is obtained nearer ambient temperatures. Our aiMD results challenge the validity of the experimentally suggested H2 polytype as the synthesized phase, while proposing a possible thermally-assisted H1 → H4 transformation in h-WO3 . Our hybrid DFT electronic band gap energy of ambient temperature H4-like structure agrees much better with experiments, lending further support to our finite temperature microstructural analysis from first-principles.

Acknowledgement We gratefully acknowledge support by Creative Materials Discovery Program through the National Research Foundation of Korea (NRF) funded by Ministry of Science and ICT (2018M3D1A1058536), as well as the National Research and Development Program of Ministry of Science and ICT (2017M3A7B4032124). Computational resources have been kindly provided by the KISTI Supercomputing Center (KSC-2017-C3-0059) and the Australian 13



National Computational Infrastructure (NCI). We thank Mr. Woosun Jang for helpful discussions in this work.

Supporting Information Available Structural parameters of ai MD simulated supercell; Structural parameters and the enthalpy of formation of H1, H2, and H4; Space groups and Eg calculated/measured via various approaches; Volumetric thermal expansion coefficient (α); Simulated X-ray diffraction (XRD) patterns of H1, H2, and H4, and randomized, annealed, and quenched structures; RDF and XRD plots at 600 and 1000 K with different starting geometries; ⟨λ⟩ population profile; Temperature and energy oscillations in the ai MD trajectory at T = 300, 600, 1000 K for 1 ps. This material is available free of charge via the Internet at http://pubs.acs.org/.

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Graphical TOC Entry

Temperature-time evolution of simulated radial distribution function, g(r) for h-WO3 polytypes from ab initio molecular dynamics calculations; An intermediate H1-like polytype is predicted at higher temperatures while the more stable H4 polytype is obtained nearer ambient temperatures.

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Polytypism in Hexagonal Tungsten Trioxide: Insights from Ab Initio

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