Article

Cite This: J. Am. Chem. Soc. XXXX, XXX, XXX−XXX pubs.acs.org/JACS

Revealing and Rationalizing the Rich Polytypism of Todorokite MnO2 † ∇ ‡ ∇ † § † 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*, , † Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, United States ‡ Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States § Department of Chemistry, Stony Brook University, Stony Brook, New York 11794, United States ∥ Energy Sciences Directorate, Brookhaven National Laboratory, Upton, New York 11973, United States ⊥ Department of Materials Science and Chemical Engineering, Stony Brook University, Stony Brook, New York 11794, United States # Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States ^Department of Materials Science and Engineering, University of California at Berkeley, Berkeley, California 94720, United States

*S Supporting Information

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 alkali-stabilized polymorphs of MnO2, we suggest generalizable principles determining the selectivity of structure selection by dopant incorporation.

− 1. INTRODUCTION accommodate the ionic diffusion of diverse cations17,20 22 such + 2+ 2+ The characterization of precise nanostructural features in as Na ,Zn , and Mg , which are alternatives to Li for the transition-metal oxides is an essential component to the design of next-generation advanced battery electrodes. understanding of emergent behavior of the materials. However, natural todorokite minerals cannot be directly Polytypism, in particular, complicates this analysis as it utilized because of numerous impurities typically found in the introduces stacking disorder that is difficult to account for structure and porous crystallites, which has motivated the ff development of well-controlled syntheses of materials with the using traditional di raction methods and presents a challenge 12,23−26 − todorokite structure. Previous work on this topic has to the derivation of structure property relationships. One fl system, which we demonstrate here to be intrinsically polytypic, established the hydrothermal or re uxing syntheses for − todorokite, yielding both pure and mixed platelet and rod is todorokite MnO2. Todorokite minerals have unique 19,20,25−27 manganese oxide structures with large tunnels that were first morphologies. recognized in continental manganese ore deposits, deep-sea Although laboratory-based synthesis of todorokite has been 1,2 reported, the precise structure of this phase has not been truly nodules, and crusts. This tunnel feature allows todorokite to 27−30 ffi host various kinds of metallic ions (e.g., Ni, Co, Zn, Cu, and resolved until now. The main di culty in the character- Mg) within the nodules and is thus regarded as a polymetallic ization of todorokite lies in its generally poor crystallinity and source,3 drawing broad attention among mineralogists ever lower spatial resolution of previously used characterization methods. The todorokite mineral is conjectured to exist as a 3 since its discovery. More recently, todorokite-based structures × ∼ × have also found many functional applications in the field of 3 tunnel structure with a tunnel size of 6.9 6.9 Å, − − − catalysts,4 7 ion exchangers,8 10 molecular sieves,11 14 and − electrodes in rechargeable batteries.15 19 In particular, the Received: March 16, 2018 todorokite structure is thought to be an ideal host material to Published: May 7, 2018

© XXXX American Chemical Society A DOI: 10.1021/jacs.8b02971 J. Am. Chem. Soc. XXXX, XXX, XXX−XXX Journal of the American Chemical Society Article

27 constituted by triple chains of edge-sharing MnO6 octahedra formation of todorokite nodules, the associated concentration (see Figure 1a schematic). The chemical formula can be process of alkaline and transition metal elements,41,42 and the unique materials properties offered by this porous struc- ture.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 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 fi 2+− con gurations of partially solvated Mg 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 2+− Figure 1. Tunnel features of the τ (p × 3) todorokite family. (a, b) todorokite MnO2 stabilized by the intercalation of Mg H2O Schematics of the 3 × 3 tunnel structure viewed along the [010] complexes. Δ Δ direction. 1 and 2 indicate the projected distance of neighboring Mn columns along the [100] direction. (c, d) Schematics of the 5 × 3 2. EXPERIMENTS AND CALCULATIONS and 1 × 3 tunnel structure, respectively. (e) Structure schematic for the intergrowth of the 2 × 3 and 4 × 3 tunnels. The atomic fractional Synthesis of Todorokite. The synthesis of the todorokite material was adapted from a previous report.43 Briefly, sodium birnessite was coordinates of Mn along the [010] tunnel direction are indicated. The · − lattice vectors a, c and their intersection angle β of different tunnel prepared from MnSO4 H2O, NaOH, and an H2O2 solution. Mg buserite was obtained by treatment of the sodium birnessite with the structures are marked. · MgSO4 H2O solution and isolation of the resultant solid. Todorokite- type MgxMnO2 was prepared by hydrothermal treatment of Mg- · · buserite in 1 M MgSO4 H2O solution. approximated as AxMnO2 yH2O, where A represents various metallic cations such as Mg2+ or Cu2+ and x and y are variables. Microstructural Characterizations. Todorokite nanorods for transmission electron microscopy (TEM) observations were prepared However, structural disorder in this phase and analogues with fi by suspending them in ethanol and then transferring to holey carbon- even larger tunnels have been identi ed in both natural coated copper grids. Electron diffraction and transmission electron todorokites and synthesized Mg todorokite by means of lattice microscopy imaging, including atomic resolution high angle annular fringe imaging based on conventional transmission electron fi − dark eld (HAADF) imaging and electron energy loss spectroscopy microscopy (TEM).23,31 35 The potential existence of these (EELS) experiments were carried out using JEOL ARM 200CF with a polytypic features complicates the common analysis of cold-field emission gun and operated at 200 kV. The microscope was todorokite as a pure 3 × 3 tunnel structure as well as the equipped with double-spherical aberration correctors (CEOS GmbH) properties inferred on the basis of this simplified structural and GIF Quantum (Gatan, Inc.) with a dual EELS system. EELS data model. were recorded in scanning TEM (STEM) mode with a convergence angle of 40 mrad and a collection angle of 90 mrad. The energy Structural disorder in natural todorokite minerals may be resolution of EELS measurement was around 0.45 eV, as determined rationalized as arising from a variety of inhomogeneities, such from the full-width at half-maximum of the zero-loss peak. All as planar defects and intergrowths with other minerals, as well background signals in the EELS spectra were subtracted using a power fi as the diversity of intercalated metallic ions occupying the law tting method. The energy positions of Mn_-L2,3 were determined tunnel.36 However, these rationalizations are not applicable to by fitting the EELS profile with a combined Gaussian and Lorentz well-crystallized todorokites grown with a single cation species function. The white line ratio of L3/L2 was calculated using the 44 such as Mg2+ in the tunnel, raising the question of whether the Pearson method with double step functions. The atomic resolution polytypism persists in such laboratory-grown samples. Surpris- HAADF image simulations were carried out using our homemade ingly, in similar minerals such as K+/Ag+ hollandites, one computer codes based on the multislice method with frozen phonon approximation.45 routinely finds pure 2 × 2 tunnels, while larger 2 × 5 tunnels 37,38 Calculations. To investigate the origin of the tunnel structures exist within Rb0.27MnO2. We hypothesize that the source of obtained from the Mg2+-containing precursor aqueous solution, we · the possible polytypism in todorokite lies in the structural evaluated the thermodynamics of MgxMnO2 yH2O using density selectivity of the mechanism by which intercalated metallic ions functional theory (DFT) calculations. Following the previously − and crystalline water stabilize a crystal structure. Thus, in reported analysis of phase selection among alkali containing MnO2 46 addition to understanding the polytypism of the Mn−O phases, we consider structures derived from various MnO2 structural 2+ framework in todorokite, we aim to resolve the local geometry frameworks, with Mg and H2O occupying interstitial sites. We refer − to the MnO2 frameworks following the MnO2 polymorph naming and associated energetics of the intercalated alkali water 46 β complexes stabilizing the phase, the analysis of which was convention, where -MnO2 is the ground-state rutile-type structure, α is the hollandite-type structure, λ is the spinel-type structure, and τ previously hindered by uncertainties in the underlying metal− × 39,40 refers to the family of todorokite-type p 3 tunnel structures. oxide structural model. Specifically, we refer to any structure with a p × 3 tunnel framework as τ × Revealing the underlying structural character and associated belonging to the (p 3) phase. We exclude other common MnO2 thermodynamic origin of synthetic todorokite is very phases as they are not stable in the presence of the Mg2+ ions.46 Within · fundamental to gaining a better understanding of the geologic each of these frameworks, we obtain a set of low-energy MgxMnO2

B DOI: 10.1021/jacs.8b02971 J. Am. Chem. Soc. XXXX, XXX, XXX−XXX Journal of the American Chemical Society Article

Figure 2. Microstructural features of a Mg todorokite nanorod. (a) Low-magnification HAADF image of the general morphology of Mg todorokite nanorods. (b) [001] EDPs obtained from single nanorod 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).

fi ffi yH2O con gurations that yield the relative free energy of the various hydrated and nonhydrated compositions and provides a su ciently MnO2 phases and, thus, their stability. accurate representation of the low-energy states of all phases. We rely on the Vienna Ab-Initio Simulation Package (VASP)47 for Finally, we approximate the Gibbs free energy of each phase as a all DFT calculations, using the projector-augmented wave method,48 a function of composition and hydration in order to determine their reciprocal-space discretization of 25 K points per Å−1, and the strongly relative stability. We define the reference state of water by equating the constrained and appropriately normed (SCAN) exchange-correlation enthalpy of water vapor to that of a computed isolated water molecule functional49 following our previous report that SCAN leads to accurate and use the experimental enthalpy of condensation and relevant 50 structure stabilization in the MnO2 space. In all cases, we ensure that entropies to obtain the chemical potential of liquid water compatible −7 μDFT ≈ DFT Δ exp − our calculations are converged to 10 eV/atom on total energy and with our calculation scheme: H2O,l EH2O molecule + HH2O,v→l −1 exp fi 0.02 eV/Å on interatomic forces. For each phase, we choose a TSH2O,l. To obtain the nite-temperature free energies for all phases representative antiferromagnetic configuration for the Mn sublattice based on the computed T = 0 K enthalpies, we account for the entropy 50 following previously reported magnetic orderings. While alternative of any intercalated water by assuming that water in the MnO2 structure magnetic orderings have been recently reported,51 we did not find the is ice-like, such that the entropy of intercalated water is approximately energy differences due to these orderings to be sufficient to affect the the same as that of ice. We neglect all other sources of entropy as results reported here. strong alkali-vacancy orderings suppress the effects of configurational To enumerate Mg MnO ·yH O configurations, we first find low- entropy, and vibrational entropy does not contribute significantly to x 2 2 46 Δ f ≈ energy Mg MnO (0 ≤ x ≤ 0.5) orderings within each phase and then the relative stability of MnO2 phases: GMgxMnO2·yH2O x 2 DFT DFT DFT DFT · ≤ ≤ E · −[(1 − 2x)Eβ‑ +2xEλ‑ + yμ ,0≤ x ≤ identify the lowest energy MgxMnO2 yH2O(0 y 1.0) MgxMnO2 yH2O MnO2 Mg0.5MnO2 H2O,l configuration for each of these orderings, analogously to the procedure 0.5. 46 described previously for other MnO2 phases. We identify MgxMnO2 configurations by enumerating electrostatically favorable Mg-vacancy 3. RESULTS AND DISCUSSION fi − con gurations on interstitial sites, assigning the Mn O framework of 3.1. Crystallographic Account of the Todorokite the relaxed structure to the various MnO2 phases through a distortion- ffi Structure. We first reveal the structural features of todorokite. tolerant a ne map implemented as the Structure Matcher module in 21,53 52 · As shown in the literature, all MnO -based tunnel materials the pymatgen package. We then generate hydrated MgxMnO2 yH2O 2 fi fi con gurations by distributing H2O molecules within the crystal prepared by a hydrothermal method contain signi cant structure, ensuring that all oxygens lie at least 2.5 Å from each other.46 amounts of intercalated cations and crystalline water. However, This procedure yields a representative set of structures across all to simplify the analysis, here we only consider the structure unit

C DOI: 10.1021/jacs.8b02971 J. Am. Chem. Soc. XXXX, XXX, XXX−XXX Journal of the American Chemical Society Article of the pure MnO2 framework. For the todorokite structure with disorder in the [100] direction within a single rod. To reveal a 3 × 3 tunnel, detailed crystallographic data are listed in Table the structural disorder, high-resolution HAADF images were S1. Along the [010] direction, we can visualize the 3 × 3 tunnel acquired and are shown in Figure 2c. Two types of contrast are with the size of ∼6.9 × 6.9 Å, as shown in Figure 1a. According clearly visible. The bright stripes running across the [010] to the stacking features, the distance along the a lattice vector direction represent the high density of Mn along the projected Δ Δ Δ ∼ can be described as 2 1 +3 2 as indicated, where 2 ( 2.45 direction. The integrated line scan intensities based on Figure Å) indicates the projected distance of a single MnO6 2c are plotted in Figure 2d, showing that the distance between Δ ∼ octahedron in the [100] direction and 2 1 ( 2.46 Å) indicates two neighboring bright stripes is nonuniform. Six types of fi the projected distance of neighboring corner-connected MnO6 lattice spacing are identi ed and labeled as d1 (4.9 Å), d2 (7.4 octahedra in the [100] direction. All MnO2-based tunnel Å), d3 (9.8 Å), d4 (12.3 Å), d5 (14.7 Å), and d6 (17.2 Å). The ff structures are composed of MnO6 octahedra with di erent distribution of these spacings is shown in Figure 2e, indicating polyhedral configurations. Neglecting the possible distortion of d3, d4, and d5 are the most frequently observed lattice distances these octahedra, once the Mn location is fixed, the positions of in this system. O atoms are determined. To illustrate these atomic Lattice fringe measurements of polytypic structures33,34 have configurations, we highlight the Mn atoms with different colors serious limitations because it is impossible to account for the based on their coordinates along the [010] tunnel direction. As possible lattice translation along the [100] direction. Similarly, shown in Figure 1b, the blue dots denote Mn atoms with the although Figure 2c shows the variation in distance between fractional coordinates of y = 0, 1 along the [010] direction, neighboring stripes, it is not possible to identify the detailed while the green dots denote Mn atoms with the fractional structural features due to the lower spatial resolution. In Figure coordinates of y = 1/2 along the [010] direction. Extending the 3, we show atomically resolved HAADF images to illustrate the atomic configuration of the 3 × 3 tunnel, we can construct a series of 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 × 6.9 Å and ∼2.3 × 6.9 Å, respectively, as shown in Figure 1c,d. The only structural difference between the τ (p × 3) families is the octahedral configuration in the [100] direction. For the τ (1 × 3), τ (3 × 3), and τ (5 × 3) structures, there are one, three, and fi ve 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 × Figure 3. Atomic configurations of the polytypic features of Mg 3 fragments, labeled as τ (2 × 3+4× 3) phase and shown in todorokite. (a, b) Atomic resolution HAADF images viewed along the Figure 1e, with two types of tunnel size of ∼4.6 × 6.9 Å and [001] direction revealing characteristic polytypic features within a ∼9.2 × 6.9 Å. Generally speaking, we can unify the lattice 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 features of τ (p × 3) families based on the monoclinic lattice of × τ × τ × τ × 3), and (5 3) are embedded in the experimental images, (3 3). The lattice parameters of the (p 3) family can be showing good agreement. ≈ Δ *Δ ≈ ≈ β ≈ ° described as ap 2 1+p 2, b 2.85 Å, c 9.8 Å, 94.5 , where p is odd integer indicating the number of octahedra in the [100] direction and β is the intersection angle between inhomogeneous structural nature within the rod. The character- lattice vectors a and c. For a lattice constituted by the istic feature within the τ (p × 3) phase is the variation of the × × intergrowth of p1 3 and p2 3 fragments, where p1 and p2 are numbers of MnO6 octahedra in the [100] direction. Thus, the both even numbers, the lattice parameters can be described as different structural features shown in Figure 3a,b can be labeled ≈ Δ *Δ ≈ ≈ β ≈ ° × ap 2 1 +(p1 + p2 +1) 2, b 2.85 Å, c 9.8 Å, 94.5 . as by ap correspondingly to a p 3 tunnel. As shown in the 3.2. Atomic-Scale Imaging of the Structural Inter- atomic resolution images of Figure 3a,b, the τ (p × 3) growth. Figure S1 (TEM bright field image) and Figure 2a structures, where p is an even number, cannot be regarded as a (low-magnification HAADF image) show the morphological true unit cell because of a lack of translational periodicity. Thus, features of synthesized Mg todorokite nanorods. The rods we should only regard them as structural fragments. Besides the generally are a few microns in length and 20−100 nm in width, commonly recognized τ (3 × 3) tunnel structure, the τ (1 × 3) oriented crystallographically along the [010] and [100] and τ (5 × 3) tunnel structures can be also identified, which directions, respectively. In Figure 2b, the blue and green can coexist with each other. In addition, intergrowth of the ff × × arrows in the electron-di raction patterns (EDPs) taken along structural fragments, such as 2 3 (labeled as a2) and 4 3 fl the [001] direction mark the (020) and (400) re ections (labeled as a4), have also been observed as shown in Figure 3b, corresponding to lattice distances of 1.45 Å and 2.45 Å for the τ which is identified as a τ (2 × 3+2× 3) phase yielding a long × ff (3 3) structure. The pronounced streaking of the di use periodicity labeled as a7. Similarly, intergrowth of other * × × scattering along the (100) direction indicates a structural structural fragments 4 3 (labeled as a4) and 6 3 (labeled

D DOI: 10.1021/jacs.8b02971 J. Am. Chem. Soc. XXXX, XXX, XXX−XXX Journal of the American Chemical Society Article

Figure 4. Chemical characterization of Mg todorokite. (a) High magnification HAADF image indicates the region used for line-scan EELS analyses. fi − − − − (b) The averaged EELS pro les 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. 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,b 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. 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 the 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 spectra corresponding to different tunnel structures are further compared in Figure S2.It − Figure 5. Underlying cause of polytypism in Mg todorokite. The is again found that there is no evident variation in the Mn L2,3 2+− positions and white line ratio of L /L across different tunnel partially desolvated Mg H2O complex occupies tunnel corner sites, 3 2 stabilizing not only the (a) traditional 3 × 3 tunnel todorokite structures. These indicators demonstrate that there is no τ fi structure but also a range of other -MnO2 structures such as the (b) 5 signi cant variation in Mn chemistry and oxidation state across × 3 tunnel structure. (c) Relative Gibbs free energies of formation of different p × 3 tunnel structures.54 Thus, polytypic features in τ ° · the -MnO2 phases at 200 C across the MgxMnO2 yH2O composition β α λ todorokite are likely not related to chemical inhomogeneity or space with respect to the low-energy , , and -MgxMnO2 phases. For variation in the oxidation state of Mn. each value of x, the solid lines denote the formation energy of the 3.3. Thermochemical Origin of Polytypism. It is well- nonhydrated MgxMnO2 structure, while the dashed lines denote the 2+ · established that todorokite forms from aqueous Mg - expected formation energy for the most stable MgxMnO2 yH2O containing solutions.23,55 As alkali ions and hydration have structure, where the hydration level (y value) for the most stable ≈ − fi been recently discussed as thermodynamic structure-directing structures typically lies near y 0.75 x, although the speci c value 46 varies by tunnel size (see Supporting Information for detailed agents in MnO2 frameworks, we have investigated the role of × 2+ τ structural data). The Gibbs free energy of the p 3 tunnel structures Mg in driving the formation of the -MnO2 family of tunnel 2+ with either Mg or H2O intercalation is consistently higher than that structures. We computationally enumerated Mg-vacancy − − fi τ × τ × τ × of the other low-energy phases in the Mg MnO2 H2O energy space. con gurations within the (3 3), (1 3), (2 3+4 However, the cointercalated τ-Mg MnO ·yH O structures have much × τ × · x 2 2 3), and (5 3) phases across MgxMnO2 and MgxMnO2 lower energies and are stable with respect to the β-MnO and λ- ≤ ≤ ≤ ≤ 2 yH2O(0 x 0.5 and 0 y 1.0) compositions to reveal the MgMn2O4 end point phases. preferred geometry of Mg dopants within these structures. We define possible Mg sites as the vertices and edge midpoints of a sites provide the maximal coordination of Mg2+ by lattice 56 fi Voronoi decomposition of the structure, ltered by minimum oxygen. When H2O is present, as, for example, in the · bond length, and ensure that high-symmetry tunnel center, Mg0.166MnO2 0.5H2O structure shown in Figure 5a, the oxygen edge, and corner sites are included in the set of candidate sites, from the water molecule orients toward the Mg2+, further among others. We find that in all cases Mg2+ prefers to occupy increasing its coordination, approaching the typical 6-fold − sites at the corner of the MnO2 tunnel. As can be seen in Figure coordination environment found in octahedral Mg O 5a for the example of the traditional τ (3 × 3) structure, these complexes. Stable Mg2+ ions in our computed structures are

E DOI: 10.1021/jacs.8b02971 J. Am. Chem. Soc. XXXX, XXX, XXX−XXX Journal of the American Chemical Society Article either 5- or 6- fold coordinated, with one to three water energy of all these phases indicates that the interaction between fi 2+− molecules in the rst coordination shell. This result is at odds adjacent Mg H2O complexes is well-screened and weak. · fi τ × with the picture of Mg0.12MnO2 0.658H2O todorokite proposed While we nd the (3 3) phase to be lowest in free energy, previously,40 which placed Mg2+ in the tunnel center site. the nucleation of this phase does not exclude the coherent However, this earlier refinement was highly uncertain in its formation of domains corresponding to the other low-energy τ- fi chemical identi cation due to the lack of characterization of the MnO2 structures. While the total energy of such a non- intrinsically polytypic features within todorokite and the similar equilibrium domain in a macroscopic particle or rod is high, at X-ray scattering potential of Mg and O. Our analysis suggests the nucleation stage these diverse domains may be expected that, instead, the tunnel center is much more likely to be entropically. Of course, an alternative explanation for the occupied by a water molecule. experimental results is that we simply have not been able to While Mg2+ appears to strongly prefer the tunnel corner site, resolve the configuration of the more complex, low-symmetry τ this site occupancy does not uniquely constrain the remaining (2 × 3+4× 3) and τ (5 × 3) structures as well as that of the τ Mn−O framework. In general, the hydrated Mg2+ ions (3 × 3), as the structural relaxation of the hydrated occupying tunnel corner sites must be sufficiently separated configurations in particular are fairly uncertain and prone to from each other to avoid steric repulsion, but they do not errors due to numerous local-minima in energy. Nonetheless, directly interact with the Mn−O framework outside of the despite the uncertainty in the relative energies of the hydrated τ tunnel corner, leaving the overall tunnel size unconstrained. (p × 3) structures, we may still conclude that the various τ- 2+− Consequently, a range of tunnel sizes exhibit the same behavior MnO2 phases are stabilized by the partially solvated Mg H2O with partially hydrated Mg2+ occupying tunnel corner sites, complex without forming any bonding environments that such as in the τ (5 × 3) structure shown in Figure 5b. Similar would strongly prefer a particular tunnel size. Thus, the behavior can even be observed in the smaller 2 × 2 tunnel todorokite-like structure formed experimentally is unequiv- α found in the -MnO2 phase, although the strong electrostatic ocally thermodynamically favored by the co-intercalation of 2+ 2+ repulsion between adjacent Mg ultimately destabilizes this Mg and H2O, with disorder in tunnel sizes arising as a smaller-tunnel phase.46 consequence of the diversity of Mn−O frameworks which 2+ 2+− The favorable Mg −O coordination afforded by the tunnel accommodate the stable Mg H2O bonding environment. corner site and hydration significantly stabilizes the Mg2+- A stark contrast to the lack of structure-selecting constraints τ intercalated -MnO2 structure. The formation energies of these and resulting polytypism in the todorokite family of structures β λ × 51 phases with respect to the -MnO2 and -MgMn2O4 end point is the unique 2 2 tunnel size observed in hollandite MnO2. phases shown in Figure 5c reveal that while the τ-Mg MnO The origin of this difference lies in the geometry of stabilizing x 2 ff phases have high formation energies for all tunnel sizes, τ- alkali intercalants in the MnO2 tunnel, and their e ectiveness at · 46 MgxMnO2 yH2O have much lower formation energies and, in constraining degrees of freedom in the structure. Polytypism the case of τ (3 × 3), are thermodynamically stable with respect of the τ (p × 3) family arises from the fact that the partially β λ ° 2+ to -MnO2, -MgMn2O4, and water at 200 C. Thus, while solvated Mg cation that stabilizes this tunnel occupies the Mg2+ alone does not favor any type of τ (p × 3) tunnel tunnel corner site and only interacts strongly with the Mn−O 2+ structure, Mg with H2O does stabilize these todorokite-like framework immediately adjacent to this single tunnel corner. MnO2 frameworks. One implication of this stabilization The lack of strong bonds spanning the width of the tunnel mechanism is that structures with tunnels of different sizes leaves the total tunnel size unconstrained, and results in a range should have a different Mg composition, as the number of of large tunnel sizes close in energy to each other. In contrast, × tunnel corner sites per MnO2 decreases with tunnel size. In the 2 2 tunnel seen in the hollandite structure is generally not contrast, our EELS results do not indicate any evident stabilized by cations occupying corner sites and instead is found + variations in Mn oxidation state across tunnel sizes, implying with larger cations such as K in the tunnel center site. These that the tunnels are most likely homogeneous in their cations interact strongly with all sides of the Mn−O tunnel and composition. The explanation of this apparent discrepancy is thus constrain its size. The unique stable cation site in that in larger tunnels, Mg sites are farther apart and better hollandite thus suppresses polytypism and promotes the screened by water, reducing the repulsion between adjacent Mg formation of a single type of local environment. Generalizing and allowing for a higher equilibrium occupancy per interstitial from this observation, we speculate that among intercalation- site, counteracting the decrease in the total number of sites. stabilized phases, the structural selectivity provided by a These counterbalancing effects lead to similar equilibrium Mg2+ stabilizing cation is directly proportional to the fraction of content across a range of tunnel sizes, as can be qualitatively structural degrees of freedom constrained by the cations’ local seen in Figure 5c. In concert, these results suggest that the bonding environment. τ formation of the -MnO2 phase by hydrothermal growth from a Mg2+-containing solution is thermodynamically controlled and 4. CONCLUSIONS indeed driven by the compatibility of this phase and the Mg2+− Precisely understanding nanostructural features in materials is − H2O complex. essential to the rational assessment of the structure property 2+− The impact of the partially solvated Mg H2O complex in relationships. Through atomic resolution images and DFT τ 2+ stabilizing the -MnO2 family of structures suggests a plausible calculations, we have demonstrated that Mg -stabilized MnO2 explanation for the diversity of tunnel sizes observed todorokite should not be seen as a pure τ (3 × 3) tunnel experimentally. This large, partially solvated complex stabilizes structure but rather as a polytypic τ (p × 3) family, where p is the local Mn−O environment corresponding to a tunnel corner an integer generally less than or equal to 6, with 3 × 3, 4 × 3, driving the formation of relatively large tunnel sizes found in and 5 × 3 tunnels appearing most frequently. We rationalized the τ (3 × 3), τ (1 × 3), τ (2 × 3+4× 3), and τ (5 × 3) this intrinsic polytypism by the nonspecific stabilization of τ (p structures. Accordingly, all these phases have relatively low free × 3) structures by the coincorporation of Mg2+ and water into energies of formation as shown in Figure 5c, where the similar the MnO2 tunnels during hydrothermal synthesis. The

F DOI: 10.1021/jacs.8b02971 J. Am. Chem. Soc. XXXX, XXX, XXX−XXX Journal of the American Chemical Society Article resolution of the precise structural character of todorokite Energy Efficiency and Renewable Energy and located at the provides an opportunity for the precise evaluation of structure− National Renewable Energy Laboratory. property relationships in this phase, connecting the unique distribution of large tunnel sizes to functionality in catalysis, ■ REFERENCES charge storage, and molecular sieving. More generally, we (1)Chukhrov,F.V.;Gorshkov,A.I.;Rudnitskaya,E.S.; anticipate that the relationship we derived between constrained Beresovskaya, V. V.; Sivtsov, A. V. Clays Clay Miner. 1980, 28, 346− structural degrees of freedom and polytypism can be applied to 354. the structural features of synthetic todorokites based on Ni2+, (2) Post, J. E. Proc. Natl. Acad. Sci. U. S. A. 1999, 96, 3447−3454. − Co2+,Ca2+,Zn2+, and Cu2+ intercalation12,57,58 as well as other (3) Ostwald, J. 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H DOI: 10.1021/jacs.8b02971 J. Am. Chem. Soc. XXXX, XXX, XXX−XXX