Revealing and Rationalizing the Rich Polytypism of Todorokite MnO2

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Revealing and Rationalizing the Rich Polytypism of Todorokite MnO Xiaobing Hu, Daniil A Kitchaev, Lijun Wu, Bingjie Zhang, Qingping Meng, Altug S. Poyraz, Amy C. Marschilok, Esther S. Takeuchi, Kenneth J. Takeuchi, Gerbrand Ceder, and Yimei Zhu

J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.8b02971 • Publication Date (Web): 07 May 2018 Downloaded from http://pubs.acs.org on May 7, 2018

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Journal of the American Chemical Society

Revealing and Rationalizing the Rich Polytypism of Todorokite MnO2 Xiaobing Hua,†, Daniil A. Kitchaevb,†, Lijun Wua, Bingjie Zhangc, Qingping Menga, Altug S. Poyrazd,#, Amy C. Marschilokc,d,e, Esther S. Takeuchic,d,e, Kenneth J. Takeuchic,e, Gerbrand Cederb,f,g, and Yimei Zhua,e,* a

Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, NY 11973, USA b c

Department of Materials Science and Engineering, MIT, Cambridge, MA, 02139, USA

Department of Chemistry, Stony Brook University, Stony Brook, NY 11794, USA

d

Energy Sciences Directorate, Brookhaven National Laboratory, Upton, NY 11973, USA

e

Department of Materials Science and Chemical Engineering, Stony Brook University, Stony Brook, NY 11794, USA f

Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

g

Department of Materials Science and Engineering, UC Berkeley, Berkeley, CA 94720, USA

† These authors contributed equally to this work. #

Current Address: Department of Chemistry and Biochemistry, Kennesaw State University,

Kennesaw, GA 30144 *Correspondence and requests for materials should be addressed to [email protected] (Yimei Zhu).

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ABSTRACT Polytypism, or stacking disorder, in crystals is an important structural aspect that can impact materials properties and hinder our understanding of the materials. One example of a polytypic system is todorokite MnO2, which has a unique structure among the transition metal oxides, with large ionic conductive channels formed by the metal-oxide framework that can be utilized for potential functionalization, from molecular/ion sieving to charge storage. In contrast to the perceived 3×3 tunneled structure, we reveal a coexistence of a diverse array of tunnel sizes in well-crystallized, chemically-homogeneous one-dimensional todorokite-MnO2. We explain the formation and persistence of this distribution of tunnel sizes thermochemically, demonstrating the stabilization of a range of coherent large-tunnel environments by the intercalation of partially solvated Mg2+ cations. Based on structural behavior of the system, compared to the common well-ordered alkalistabilized polymorphs of MnO2, we suggest generalizable principles determining the selectivity of structure selection by dopant incorporation.

1. INTRODUCTION The characterization of precise nanostructural features in transition metal oxides is an essential component to the understanding of emergent behavior of the materials. Polytypism in particular complicates this analysis as it introduces stacking disorder that is difficult to account for using traditional diffraction methods, and presents a challenge to the derivation of structureproperty relationships. One system, which we demonstrate here to be intrinsically polytypic, is todorokite MnO2. Todorokite minerals have unique manganese oxide structures with large


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tunnels that were first recognized in continental manganese ore deposits, deep-sea nodules and crusts.1,2 This tunnel feature allows todorokite to host various kinds of metallic ions (e.g. Ni, Co, Zn, Cu and Mg) within the nodules and is thereby regarded as a polymetallic source,3 drawing broad attention among mineralogists ever since its discovery. More recently, todorokite based structures have also found many functional applications in the field of catalysts,4-7 ion exchangers,8-10 molecular sieves11-14 and electrodes in rechargeable batteries.15-19 In particular, the todorokite structure is thought to be an ideal host material to accommodate the ionic diffusion of diverse cations17,20-22 such as Na+, Zn2+, and Mg2+, which are alternatives to Li for the design of next-generation advanced battery electrodes. However, natural todorokite minerals cannot be directly utilized because of numerous impurities typically found in the structure and porous crystallites, which has motivated the development of well-controlled syntheses of materials with the todorokite structure. Previous work on this topic12,23-26 has established the hydrothermal or refluxing syntheses for todorokite, yielding both pure and mixed platelet and rod morphologies.19,20,25-27 Although laboratory based synthesis of todorokite has been reported, the precise structure of this phase has not been truly resolved until now.27-30 The main difficulty in the characterization of todorokite lies in its generally poor crystallinity and lower spatial resolution of previously used characterization methods. The todorokite mineral is conjectured to exist as a 3×3 tunnel structure with a tunnel size of ～6.9 Å ×6.9 Å, constituted by triple chains of edge-sharing MnO6 octahedra27 (See Figure 1a schematic). The chemical formula can be approximated as AxMnO2 · yH2O, where A represents various metallic cations such as Mg2+ or Cu2+, and x and y are variables. However, structural disorder in this phase, and analogs with even larger tunnels, has been identified in both natural todorokites and synthesized Mg todorokite by means of lattice 3 ACS Paragon Plus Environment


fringe imaging based on conventional transmission electron microscopy (TEM).23,31-35 The potential existence of these polytypic features complicates the common analysis of todorokite as a pure 3×3 tunnel structure, as well as the properties inferred on the basis of this simplified structural model. Structural disorder in natural todorokite minerals may be rationalized as arising from a variety of inhomogeneities, such as planar defects and intergrowths with other minerals, as well as the diversity of intercalated metallic ions occupying the tunnel.36 However, these rationalizations are not applicable to well-crystallized todorokites grown with a single cation species such as Mg2+ in the tunnel, raising the question of whether the polytypism persists in such laboratory-grown samples. Surprisingly, in similar minerals such as K+/Ag+ hollandites, one routinely finds pure 2×2 tunnels, while larger 2×5 tunnels exist within Rb0.27MnO2.37,38 We hypothesize that the source of the possible polytypism in todorokite lies in the structural selectivity of the mechanism by which intercalated metallic ions and crystalline water stabilize a crystal structure. Thus, in addition to understanding the polytypism of the Mn-O framework in todorokite, we aim to resolve the local geometry and associated energetics of the intercalated alkali-water complexes stabilizing the phase, the analysis of which was previously hindered by uncertainties in the underlying metal-oxide structural model.39,40 Revealing the underlying structural character and associated thermodynamic origin of synthetic todorokite is very fundamental to gaining a better understanding of both the geologic formation of todorokite nodules, the associated concentration process of alkaline and transition metal elements,41,42 and the unique materials properties offered by this porous structure.7,8,11,15,24 Herein, we report a detailed structural analysis of synthetic magnesium todorokite samples with a rod-like morphology using aberration corrected transmission electron microscopy (TEM). We 4 ACS Paragon Plus Environment

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show localized inhomogeneous nanostructural features within a single rod at the atomic scale, revealing that Mg todorokite is not a pure 3×3 tunnel structure but a family of polytypic structures of many different tunnel sizes. We rationalize the formation of such a polytypic structure by means of density functional theory (DFT) calculations, contrasting the driving force for the formation of the observed nanostructural features across tunnel sizes and configurations of partially solvated Mg2+-H2O complexes. Finally, we propose a general principle predicting the emergence of polytypic phases as a result of unconstrained structural degrees of freedom in the structure selection mechanism, such as a lack of constraint on tunnel size in todorokite MnO2 stabilized by the intercalation of Mg2+-H2O complexes. 2. EXPERIMENTS AND CALCULATIONS Synthesis of Todorokite. The synthesis of the todorokite material was adapted from a previous report.43 Briefly, sodium birnessite was prepared from MnSO4 • H2O, NaOH and an H2O2 solution. Mg-buserite was obtained by treatment of the sodium birnessite with the MgSO4 • H2O solution and isolation of the resultant solid. Todorokite type MgxMnO2 was prepared by hydrothermal treatment of Mg-buserite in 1M MgSO4 • H2O solution. Microstructural Characterizations. Todorokite nanorods for transmission electron microscopy (TEM) observations were prepared by suspending them in ethanol and then transferring to holey carbon-coated copper grids. Electron diffraction, transmission electron microscopy imaging, including atomic resolution high angle annular dark field (HAADF) imaging and electron energy loss spectroscopy (EELS) experiments were carried out using JEOL ARM 200CF with a coldfield emission gun and operated at 200 kV. The microscope was equipped with double spherical aberration correctors (CEOS GmbH) and GIF Quantum (Gatan, Inc.) with dual EELS system. EELS data were recorded in scanning TEM (STEM) mode with a convergence angle of 40 mrad



and a collection angle of 90 mrad. The energy resolution of EELS measurement was around 0.45 eV, as determined from the full-width at half-maximum of the zero-loss peak. All background signals in the EELS spectra were subtracted using a power law fitting method. The energy positions of Mn-L2,3 were determined by fitting the EELS profile with a combined Gaussian and Lorentz function. The white line ratio of L3/L2 was calculated using the Pearson method with double step functions44. The atomic resolution HAADF image simulations were carried out using our home-made computer codes based on the multi-slice method with frozen phonon approximation.45 Calculations. To investigate the origin of the tunnel structures obtained from the Mg2+containing precursor aqueous solution, we evaluate the thermodynamics of MgxMnO2 · yH2O using density functional theory (DFT) calculations. Following the previously reported analysis of phase selection among alkali–containing MnO2 phases,46 we consider structures derived from various MnO2 structural frameworks, with Mg2+ and H2O occupying interstitial sites. We refer to the MnO2 frameworks following the MnO2 polymorph naming convention,46 where β-MnO2 is the ground state rutile-type structure, α is the hollandite-type structure, λ is the spinel-type structure, and τ refers to the family of todorokite-type p×3 tunnel structures. Specifically, we refer to any structure with a p×3 tunnel framework as belonging to the τ (p×3) phase. We exclude other common MnO2 phases as they are not stable in the presence of the Mg2+ ions.46 Within each of these frameworks, we obtain a set of low-energy MgxMnO2·yH2O configurations, which yield the relative free energy of the various MnO2 phases and thereby, their stability. We rely on the Vienna Ab-Initio Simulation Package (VASP)47 for all DFT calculations, using the projector-augmented wave method,48 a reciprocal-space discretization of 25 K points per Å−1, and the strongly-constrained and appropriately-normed (SCAN) exchange-correlation functional49 following our earlier report that SCAN leads to accurate structure stabilization in the 6 ACS Paragon Plus Environment

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MnO2 space.50 In all cases, we ensure that our calculations are converged to 10−7 eV/atom on total energy, and 0.02 eV/Å−1 on interatomic forces. For each phase, we choose a representative antiferromagnetic configuration for the Mn sublattice following previously reported magnetic orderings.50 While alternative magnetic orderings have been recently reported,51 we did not find the energy differences due to these orderings to be sufficient to affect the results reported here. To enumerate MgxMnO2 · yH2O configurations, we first find low-energy MgxMnO2 (0≤x≤0.5) orderings within each phase, and then identify the lowest energy MgxMnO2 · yH2O (0≤y≤1.0) configuration for each of these orderings, analogously to the procedure described previously for other MnO2 phases.46 We identify MgxMnO2 configurations by enumerating electrostatically-favorable Mg-vacancy configurations on interstitial sites, assigning the Mn-O framework of the relaxed structure to the various MnO2 phases through a distortion-tolerant affine map implemented as the Structure Matcher module in the pymatgen package.52 We then generate hydrated MgxMnO2 · yH2O configurations by distributing H2O molecules within the crystal structure, ensuring that all oxygens lie at least 2.5 Å from each other.46 This procedure yields a representative set of structures across all hydrated and non-hydrated compositions, and provides a sufficiently accurate representation of the low-energy states of all phases. Finally, we approximate the Gibbs free energy of each phase as a function of composition and hydration in order to determine their relative stability. We define the reference state of water by equating the enthalpy of water vapor to that of a computed isolated water molecule, and use the experimental enthalpy of condensation and relevant entropies to obtain the chemical potential of liquid water compatible with our calculation scheme: , ≈ + ∆,→ −

, . To obtain the finite-temperature free energies for all phases based on the computed T=0

K enthalpies, we account for the entropy of any intercalated water by assuming that water in the MnO2 structure is ice-like, such that the entropy of intercalated water is approximately the same



as that of ice. We neglect all other sources of entropy as strong alkali-vacancy orderings suppress the effects of configurational entropy, and vibrational entropy does not contribute significantly to " the relative stability of MnO2 phases:46 ∆∙! ≈ ∙! − [$1 − 2'()* + 2'+*,.. + /, , 0≤x≤0.5.

3. RESULTS AND DISCUSSION 3.1 Crystallographic Account of the Todorokite Structure We first reveal the structural features of todorokite. As shown in the literature,21,53 all MnO2-based tunnel materials prepared by a hydrothermal method contain significant amounts of intercalated cations and crystalline water. However, to simplify the analysis, here we only consider the structure unit of the pure MnO2 framework. For the todorokite structure with a 3×3 tunnel, detailed crystallographic data is listed in the Table S1. Along the [010] direction, we can visualize the 3×3 tunnel with the size of ～6.9 Å ×6.9 Å, as shown in Figure 1a. According to the stacking features, the distance along the a lattice vector can be described as 2∆1 + 3∆2 as indicated, where ∆2 (～2.45 Å) indicates the projected distance of a single MnO6 octahedron in the [100] direction and 2∆1 (～2.46 Å) indicates the projected distance of neighboring cornerconnected MnO6 octahedra in the [100] direction. All MnO2-based tunnel structures are comprised of MnO6 octahedra with different polyhedral configurations. Neglecting the possible distortion of these octahedra, once the Mn location is fixed, the positions of O atoms are determined. To illustrate these atomic configurations, we highlight the Mn atoms with different colors based on their coordinates along the [010] tunnel direction. As shown in Figure 1b, the blue dots denote Mn atoms with the fractional coordinates of y=0, 1 along the [010] direction; while the green dots denote Mn atoms with the fractional coordinates of y=1/2 along the [010] direction. Extending the atomic configuration of the 3×3 tunnel, we can construct a series of 8 ACS Paragon Plus Environment

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polytypic structures of p×3 denoted by the τ (p×3) phase, with different tunnel sizes, such as τ (5×3) and τ (1×3) polymorphs possessing the tunnel sizes of ～11.5 Å ×6.9 Å and ～2.3 Å ×6.9 Å, respectively as shown in Figure 1c and 1d. The only structural difference between the τ (p×3) families is the octahedral configuration in the [100] direction. For τ (1×3), τ (3×3) and τ (5×3) structure, there are one, three and five edge sharing MnO6 octahedron/octahedra, respectively, along the [100] direction. Here, we note that single p×3 fragments can construct the crystallographic lattice when p is an odd integer. When p is an even integer, single p×3 fragments cannot be regarded as a crystallographic lattice owing to the absence of the translation periodicity in [100] direction and the unit cell length along the [100] direction needs to be doubled in order to keep the translation periodicity. Alternatively, intergrowth of p1×3 and p2×3 fragments, where p1 and p2 are two even integers, can also maintain the translation periodicity, such as the intergrowth of 2×3 and 4×3 fragments, labeled as τ (2×3+4×3) phase and shown in Figure 1e, with two types of tunnel size of ～4.6 Å ×6.9 Å and ～9.2 Å ×6.9 Å. Generally speaking, we can unify the lattice features of τ (p×3) families based on the monoclinic lattice of τ (3×3). The lattice parameters of the τ (p×3) family can be described as ap≈2∆1+p*∆2, b≈2.85 Å, c≈9.8 Å, β≈94.5°, where p is odd integer indicating the number of octahedra in the [100] direction and β is the intersection angle between lattice vectors a and c. For a lattice constituted by the intergrowth of p1×3 and p2×3 fragments, where p1 and p2 are both even numbers, the lattice parameters can be described as ap≈2∆1+(p1+p2+1)*∆2, b≈2.85 Å, c≈9.8 Å, β≈94.5°. 3.2 Atomic Scale Imaging of the Structural Intergrowth Figure S1 TEM bright field image and Figure 2a low-magnification HAADF image show the morphological features of synthesized Mg todorokite nanorods. The rods generally are a few microns in length and 20-100 nm in width, oriented crystallographically along the [010] and [100] 9 ACS Paragon Plus Environment


directions, respectively. In Figure 2b, the blue and green arrows in the electron diffraction patterns (EDPs) taken along the [001] direction mark the (020) and (400) reflections corresponding to lattice distances of 1.45 Å and 2.45 Å for the τ (3×3) structure. The pronounced streaking of the diffuse scattering along the (100)* direction indicates a structural disorder in the [100] direction within a single rod. To reveal the structural disorder, high resolution HAADF images were acquired and are shown in Figure 2c. Two types of contrast are clearly visible. The bright stripes running across the [010] direction represent the high density of Mn along the projected direction. The integrated line scan intensities based on Figure 2c are plotted in Figure 2d, showing that the distance between two neighboring bright stripes is non-uniform. Six types of lattice spacing are identified and labeled as d1 (4.9 Å), d2 (7.4 Å), d3 (9.8 Å), d4 (12.3 Å), d5 (14.7 Å) and d6 (17.2 Å). The distribution of these spacings is shown in Figure 2e, indicating d3, d4 and d5 are the most frequently observed lattice distances in this system. Lattice fringe measurements of polytypic structures33,34 have serious limitations because it is impossible to account for the possible lattice translation along the [100] direction. Similarly, although Figure 2c shows the variation in distance between neighboring stripes, it is not possible to identify the detailed structural features due to the lower spatial resolution. In Figure 3 we show atomically resolved HAADF images to illustrate the inhomogeneous structural nature within the rod. The characteristic feature within the τ (p×3) phase is the variation of the numbers of MnO6 octahedra in the [100] direction. Thus, the different structural features shown in Figure 3a and 3b can be labeled as by ap correspondingly to a p×3 tunnel. As shown in Figure 3a and 3b atomic resolution images, the τ (p×3) structures, where p is an even number, cannot be regarded as a true unit cell because of a lack of translational periodicity. Thus, we should only regard them as structural fragments. Besides the commonly recognized τ (3×3) tunnel structure, the τ (1×3)


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and τ (5×3) tunnel structures can be also identified, which can coexist with each other. In addition, intergrowth of the structural fragments, such as 2×3 (labeled as a2) and 4×3 (labeled as a4) have also been observed as shown in Figure 3b, which is identified as a τ (2×3+2×3) phase yielding a long periodicity labeled as a7. Similarly, intergrowth of other structural fragments 4×3 (labeled as a4) and 6×3 (labeled as a6) can result in an even larger periodicity, for instance a11 as shown in Figure 3b. The oval shape of the atom columns within the bright strips result from the slight misalignment of the Mn atoms along the projected [001] direction. Image simulations overlaid in Figure 3a and 3b are based on the τ (1×3), τ (3×3), τ (5×3) and τ (2×3+4×3) tunnel structures and agree well with the experimental observations. In order to reveal the chemical features at a higher spatial resolution, spectroscopy imaging analyses were performed along the line indicated in Figure 4a HAADF image. The averaged EELS features of O-K and Mn-L2,3 edge are shown in Figure 4b. The variation for the positions of the Mn-L2, Mn-L3 peaks and white line ratio of L3/L2 along the line indicated in Figure 4a are extracted and shown in Figure 4c. It is found that there is no evident variation for the positions of both Mn-L2 and Mn-L3 edges. The white line ratio of L3/L2 also reveals no evident variations. In addition, the integrated spectrums corresponding to different tunnel structures are further compared in Figure S2. It is again found that there is no evident variation in Mn-L2,3 positions and white line ratio of L3/L2 across different tunnel structures. These indicators demonstrate that there is no significant variation in Mn chemistry and oxidation state across different p×3 tunnel structures.54 Thus, polytypic features in todorokite are likely not related to chemical inhomogeneity or variation in the oxidation state of Mn. 3.3 Thermochemical Origin of Polytypism



It is well-established that todorokite forms from aqueous Mg2+-containing solutions.23,55 As alkali ions and hydration have been recently discussed as thermodynamic structure-directing agents in MnO2 frameworks,46 we have investigated the role of Mg2+ in driving the formation of the τ-MnO2 family of tunnel structures. We computationally enumerated Mg-vacancy configurations within the τ (3×3), τ (1×3), τ (2×3+4×3), and τ (5×3) phases across MgxMnO2 and MgxMnO2 · yH2O (0≤x≤0.5 and 0≤y≤1.0) compositions to reveal the preferred geometry of Mg dopants within these structures. We define possible Mg sites as the vertices and edge midpoints of a Voronoi decomposition of the structure,56 filtered by minimum bond length, and ensure that high-symmetry tunnel center, edge, and corner sites are included in the set of candidate sites, among others. We find that in all cases Mg2+ prefers to occupy sites at the corner of the MnO2 tunnel. As can be seen in Figure 5a for the example of the traditional τ (3×3) structure, these sites provide the maximal coordination of Mg2+ by lattice oxygen. When H2O is present, as for example in the Mg0.166MnO2 · 0.5H2O structure shown in Figure 5a, the oxygen from the water molecule orients towards the Mg2+, further increasing its coordination, approaching the typical 6-fold coordination environment found in octahedral Mg-O complexes. Stable Mg2+ ions in our computed structures are either 5- or 6- fold coordinated, with 1 to 3 water molecules in the first coordination shell. This result is at odds with the picture of Mg0.12MnO2· 0.658H2O todorokite proposed previously,40 which placed Mg2+ in the tunnel center site. However, this earlier refinement was highly uncertain in its chemical identification due to the lack of characterization of the intrinsically polytypic features within todorokite and the similar x-ray scattering potential of Mg and O. Our analysis suggests that instead, the tunnel center is much more likely to be occupied by a water molecule.


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While Mg2+ appears to strongly prefer the tunnel corner site, this site occupancy does not uniquely constrain the remaining Mn-O framework. In general, the hydrated Mg2+ ions occupying tunnel corner sites must be sufficiently separated from each other to avoid steric repulsion, but they do not directly interact with the Mn-O framework outside of the tunnel corner, leaving the overall tunnel size unconstrained. Consequently, a range of tunnel sizes exhibit the same behavior with partially hydrated Mg2+ occupying tunnel corner sites, such as in the τ (5×3) structure shown in Figure 5b. Similar behavior can even be observed in the smaller 2×2 tunnel found in the α-MnO2 phase, although the strong electrostatic repulsion between adjacent Mg2+ ultimately destabilizes this smaller-tunnel phase.46 The favorable Mg2+-O coordination afforded by the tunnel corner site and hydration significantly stabilizes the Mg2+-intercalated τ-MnO2 structure. The formation energies of these phases with respect to the β-MnO2 and λ-MgMn2O4 endpoint phases shown in Figure 5c reveal that while the τ-MgxMnO2 phases have high formation energies for all tunnel sizes, τMgxMnO2 · yH2O have much lower formation energies, and in the case of τ (3×3), are thermodynamically stable with respect to β-MnO2, λ-MgMn2O4 and water at 200 ℃. Thus, while Mg2+ alone does not favor any type of τ (p×3) tunnel structure, Mg2+ with H2O does stabilize these todorokite-like MnO2 frameworks. One implication of this stabilization mechanism is that structures with tunnels of different sizes should have a different Mg composition, as the number of tunnel corner sites per MnO2 decreases with tunnel size. In contrast, our EELS results do not indicate any evident variations in Mn oxidation state across tunnel sizes, implying that the tunnels are most likely homogeneous in their composition. The explanation of this apparent discrepancy is that in larger tunnels, Mg sites are farther apart and better screened by water, reducing the repulsion between adjacent Mg and allowing for a higher equilibrium occupancy 13 ACS Paragon Plus Environment


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per interstitial site, counteracting the decrease in the total number of sites. These counterbalancing effects lead to similar equilibrium Mg2+ content across a range of tunnel sizes, as can be qualitatively seen in Figure 5c. In concert, these results suggest that the formation of the

τ-MnO2 phase

by

hydrothermal

growth

from

a

Mg2+-containing

solution

is

thermodynamically controlled and indeed driven by the compatibility of this phase and the Mg2+H2O complex. The impact of the partially-solvated Mg2+-H2O complex in stabilizing the τ-MnO2 family of structures suggests a plausible explanation for the diversity of tunnel sizes observed experimentally. This large, partially-solvated complex stabilizes the local Mn-O environment corresponding to a tunnel corner driving the formation of relatively large tunnel sizes found in the τ (3×3), τ (1×3), τ (2×3+4×3) and τ (5×3) structures. Accordingly, all these phases have relatively low free energies of formation as shown in Figure 5c, where the similar energy of all these phases indicates that the interaction between adjacent Mg2+-H2O complexes is wellscreened and weak. While we find the τ (3×3) phase to be lowest in free energy, the nucleation of this phase does not exclude the coherent formation of domains corresponding to the other lowenergy τ-MnO2 structures. While the total energy of such a non-equilibrium domain in a macroscopic particle or rod is high, at the nucleation stage these diverse domains may be expected entropically. Of course, an alternative explanation for the experimental results is that we simply have not been able to resolve the configuration of the more complex, low-symmetry τ (2×3+4×3) and τ (5×3) structures as well as that of the τ (3×3), as the structural relaxation of the hydrated configurations in particular are fairly uncertain and prone to errors due to numerous local-minima in energy. Nonetheless, despite the uncertainty in the relative energies of the hydrated τ (p×3) structures, we may still conclude that the various τ-MnO2 phases are stabilized


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by the partially-solvated Mg2+-H2O complex without forming any bonding environments that would strongly prefer a particular tunnel size. Thus, the todorokite-like structure formed experimentally is unequivocally thermodynamically favored by the co-intercalation of Mg2+ and H2O, with disorder in tunnel sizes arising as a consequence of the diversity of Mn-O frameworks which accommodate the stable Mg2+-H2O bonding environment. A stark contrast to the lack of structure-selecting constraints and resulting polytypism in the todorokite family of structures is the unique 2×2 tunnel size observed in hollandite MnO2.51 The origin of this difference lies in the geometry of stabilizing alkali intercalants in the MnO2 tunnel, and their effectiveness at constraining degrees of freedom in the structure.46 Polytypism of the τ (p×3) family arises from the fact that the partially solvated Mg2+ cation that stabilizes this tunnel occupies the tunnel corner site and only interacts strongly with the Mn-O framework immediately adjacent to this single tunnel corner. The lack of strong bonds spanning the width of the tunnel leaves the total tunnel size unconstrained, and results in a range of large tunnel sizes close in energy to each other. In contrast, the 2×2 tunnel seen in the hollandite structure is generally not stabilized by cations occupying corner sites, and instead is found with larger cations such as K+ in the tunnel center site. These cations interact strongly with all sides of the Mn-O tunnel and thus constrain its size. The unique stable cation site in hollandite thus suppresses polytypism and promotes the formation of a single type of local environment. Generalizing from this observation, we speculate that among intercalation-stabilized phases, the structural selectivity provided by a stabilizing cation is directly proportional to the fraction of structural degrees of freedom constrained by the cations’ local bonding environment. 4. CONCLUSIONS



Precisely understanding nanostructural features in materials is essential to the rational assessment of the structure-property relationships. Through atomic resolution images and DFT calculations, we have demonstrated that Mg2+-stabilized MnO2 todorokite should not be seen as a pure τ (3×3) tunnel structure but rather as a polytypic τ (p×3) family, where p is an integer generally less than or equal to 6, with 3×3, 4×3 and 5×3 tunnels appearing most frequently. We rationalized this intrinsic polytypism by the non-specific stabilization of τ (p×3) structures by the co-incorporation of Mg2+ and water into the MnO2 tunnels during hydrothermal synthesis. The resolution of the precise structural character of todorokite provides an opportunity for the precise evaluation of structure-property relationships in this phase, connecting the unique distribution of large tunnel sizes to functionality in catalysis, charge storage, and molecular sieving. More generally, we anticipate that the relationship we derived between constrained structural degrees of freedom and polytypism can be applied to the structural features of synthetic todorokites based on Ni2+, Co2+, Ca2+, Zn2+, and Cu2+ intercalation,12,57,58 as well as other transition metal oxide/sulfide phases59-62 which are stabilized by cation intercalation and hydration, such as prussian blue and its analogs.63-65


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SUPPLEMENTARY INFORMATION Included in the supplementary information are 1> the atomic configurations of the structural framework for τ (3×3) MnO2; 2> low magnification morphological features of synthesized Mg todorokite; 3> Chemical features for different tunnel structures; 4> Computed structures of hydrated τ (3×3), τ (2×3+4×3), and τ (5×3) at their most energetically favorable compositions. ACKNOWLEDGEMENTS The materials synthesis and bulk characterization, including the direct TEM experiments conducted by X.H. were supported as part of the Center for Mesoscale Transport Properties, an Energy Frontier Research Center supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, under award #DE-SC0012673. L.W., Q.M., Y.Z. and the TEM facility were supported by the U.S. Department of Energy, Office of Basic Energy Science, Division of Materials Science and Engineering, under Contract No. DE-SC0012704. D.A.K and G.C. acknowledge support for the computational analysis from the Center for Next-Generation of Materials by Design, an Energy Frontier Research Center funded by U.S. Department of Energy, Office of Basic Energy Science. The computational analysis was performed using computational resources provided by the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1548562, as well as computational resources sponsored by the Department of Energy’s Office of Energy Efficiency.



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Figure captions Figure 1. Tunnel features of the τ (p×3) todorokite family. (a, b) Schematics of the 3×3 tunnel structure viewed along the [010] direction. ∆1 and ∆2 indicate the projected distance of neighboring Mn columns along the [100] direction. (c, d) Schematics of the 5×3 and 1×3 tunnel structure respectively. (e) Structure schematic for the intergrowth of the 2×3 and 4×3 tunnels. The atomic fractional coordinates of Mn along the [010] tunnel direction are indicated. The lattice vectors a, c and their intersection angle β of different tunnel structures are marked. Figure 2. Microstructural features of a Mg todorokite nanorod. (a) Low-magnification HAADF image of the general morphology of magnesium todorokite nanorods. (b) [001] EDPs obtained from single nano-rod in (a). (c) HAADF lattice image obtained from [001] direction. (d) The corresponding intensity line scan integrated along vertical direction of (c) lattice image showing the inhomogeneous periodicity of the (100)p lattice distances. The arrow pairs indicate different planar periodicities. (e) Histogram showing the occurrence frequency of the different lattice periodicities within the rod shown in (c). Figure 3. Atomic configurations of the polytypic features of Mg todorokite. (a, b) Atomic resolution HAADF images viewed along the [001] direction revealing characteristic polytypic features within a single nanorod. Four simulated images viewed along [001] direction based on the tunnel structures of the τ (1×3), τ (3×3), τ (2×3+4×3), and τ (5×3) are embedded in the experimental images, showing good agreement. Figure 4. Chemical characterization of Mg todorokite. (a) High magnification HAADF image indicates the region used for line-scan EELS analyses. (b) The averaged EELS profiles for O-K and Mn-L2,3 edges. (c) Mn-L2, Mn-L3 peak positions and white line ratio of L3/L2 along the line indicate in (a) showing no evident changes of chemical state of Mn across different tunnel structures. Figure 5. Underlying cause of polytypism in Mg todorokite. The partially desolvated Mg2+-H2O complex occupies tunnel corner sites, stabilizing not only the (a) traditional 3×3 tunnel todorokite structure, but also a range of other τ-MnO2 structures such as the (b) 5×3 tunnel structure. (c) Relative Gibbs free energies of formation of the τ-MnO2 phases at 200 ℃ across the 20 ACS Paragon Plus Environment

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MgxMnO2 · yH2O composition space with respect to the low-energy β, α, and λ-MgxMnO2 phases. For each value of x, the solid lines denote the formation energy of the non-hydrated MgxMnO2 structure, while the dashed lines denote the expected formation energy for the most stable MgxMnO2 · yH2O structure, where the hydration level (y-value) for the most stable structures typically lies near y~0.75-x, although the specific value varies by tunnel size (see Supplementary Information for detailed structural data). The Gibbs free energy of the p×3 tunnel structures with either Mg2+ or H2O intercalation is consistently higher than that of the other low-energy phases in the Mg-MnO2-H2O energy space. However, the co-intercalated τ-MgxMnO2 · yH2O structures have much lower energies and are stable with respect to the β-MnO2 and λ-MgMn2O4 endpoint phases.



Figure 1. Tunnel features of the τ (p×3) todorokite family. (a, b) Schematics of the 3×3 tunnel structure viewed along the [010] direction. ∆1 and ∆2 indicate the projected distance of neighboring Mn columns along the [100] direction. (c, d) Schematics of the 5×3 and 1×3 tunnel structure respectively. (e) Structure schematic for the intergrowth of the 2×3 and 4×3 tunnels. The atomic fractional coordinates of Mn along the [010] tunnel direction are indicated. The lattice vectors a, c and their intersection angle β of different tunnel structures are marked. 176x124mm (300 x 300 DPI)

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Figure 2. Microstructural features of a Mg todorokite nanorod. (a) Low-magnification HAADF image of the general morphology of magnesium todorokite nanorods. (b) [001] EDPs obtained from single nano-rod in (a). (c) HAADF lattice image obtained from [001] direction. (d) The corresponding intensity line scan integrated along vertical direction of (c) lattice image showing the inhomogeneous periodicity of the (100)p lattice distances. The arrow pairs indicate different planar periodicities. (e) Histogram showing the occurrence frequency of the different lattice periodicities within the rod shown in (c). 148x128mm (300 x 300 DPI)



Figure 3. Atomic configurations of the polytypic features of Mg todorokite. (a, b) Atomic resolution HAADF images viewed along the [001] direction revealing characteristic polytypic features within a single nanorod. Four simulated images viewed along [001] direction based on the tunnel structures of the τ (1×3), τ (3×3), τ (2×3+4×3), and τ (5×3) are embedded in the experimental images, showing good agreement. 165x122mm (300 x 300 DPI)


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Figure 4. Chemical characterization of Mg todorokite. (a) High magnification HAADF image indicates the region used for line-scan EELS analyses. (b) The averaged EELS profiles for O-K and Mn-L2,3 edges. (c) MnL2, Mn-L3 peak positions and white line ratio of L3/L2 along the line indicate in (a) showing no evident changes of chemical state of Mn across different tunnel structures. 160x68mm (300 x 300 DPI)



Figure 5. Underlying cause of polytypism in Mg todorokite. The partially desolvated Mg2+-H2O complex occupies tunnel corner sites, stabilizing not only the (a) traditional 3×3 tunnel todorokite structure, but also a range of other τ-MnO2 structures such as the (b) 5×3 tunnel structure. (c) Relative Gibbs free energies of formation of the τ-MnO2 phases at 200 ℃ across the MgxMnO2 · yH2O composition space with respect to the low-energy β, α, and λ-MgxMnO2 phases. For each value of x, the solid lines denote the formation energy of the non-hydrated MgxMnO2 structure, while the dashed lines denote the expected formation energy for the most stable MgxMnO2 · yH2O structure, where the hydration level (y-value) for the most stable structures typically lies near y~0.75-x, although the specific value varies by tunnel size (see Supplementary Information for detailed structural data). The Gibbs free energy of the p×3 tunnel structures with either Mg2+ or H2O intercalation is consistently higher than that of the other low-energy phases in the Mg-MnO2H2O energy space. However, the co-intercalated τ-MgxMnO2 · yH2O structures have much lower energies and are stable with respect to the β-MnO2 and λ-MgMn2O4 endpoint phases. 175x137mm (300 x 300 DPI)


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Caption for TOC: Diverse polytypism in tunneled manganese oxide stabilized by hydrated alkali ions. 65x40mm (300 x 300 DPI)


Revealing and Rationalizing the Rich Polytypism of Todorokite MnO2

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