Resolving the Structure of Ti3C2Tx MXenes through Multilevel

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Resolving the Structure of Ti3C2Tx MXenes through Multilevel Structural Modeling of the Atomic Pair Distribution Function Hsiu-Wen Wang,*,† Michael Naguib,‡ Katharine Page,§ David J. Wesolowski,∥ and Yury Gogotsi⊥ †

Joint Institute for Neutron Sciences, ‡Materials Science and Technology Division, §Spallation Neutron Source, and ∥Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States ⊥ Department of Materials Science and Engineering, and A.J. Drexel Nanomaterials Institute, Drexel University, Philadelphia, Pennsylvania 19104, United States S Supporting Information *

ABSTRACT: MXenes are a recently discovered family of two-dimensional (2D) early transition metal carbides and carbonitrides, which have already shown many attractive properties and great promise in energy storage and many other applications. However, a complex surface chemistry and small coherence length have been obstacles in some applications of MXenes, also limiting the accuracy of predictions of their properties. In this study, we describe and benchmark a novel way of modeling layered materials with real interfaces (diverse surface functional groups and stacking order between the adjacent monolayers) against experimental data. The structures of three kinds of Ti3C2Tx MXenes (T stands for surface terminating species, including O, OH, and F) produced under different synthesis conditions were resolved for the first time using atomic pair distribution function obtained by high-quality neutron total scattering. The true nature of the material can be easily captured with the sensitivity of neutron scattering to the surface species of interest and the detailed “third-generation” structure model we present. The modeling approach leads to new understanding of MXene structural properties and can replace the currently used idealized models in predictions of a variety of physical, chemical, and functional properties of Ti3C2-based MXenes. The developed models can be employed to guide the design of new MXene materials with selected surface termination and controlled contact angle, catalytic, optical, electrochemical, and other properties. We suggest that the multilevel structural modeling should form the basis for a generalized methodology on modeling diffraction and pair distribution function data for 2D and layered materials.

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INTRODUCTION MXenes are the newest and fastest growing family of twodimensional (2D) materials, which already include 17 transition metal carbides and carbonitrides.1−4 They are usually fabricated from the layered ternary carbides and nitrides known as MAX phases through selective etching of the A layers (group 13 or 14 elements; Al, Si, Sn, etc.)5 without disrupting the integrity of M−X bonds in the parent MAX phase. The resulting materials have been named MXenes to illustrate the loss of the A atoms from the parent phase and to emphasize their 2D nature.1 The 2D sheets of MXenes have the general composition of Mn+1XnTx, where M is an early transition metal (Ti, V, Cr, Nb, Mo, etc.), X is C and/or N, Tx stands for surface terminating species (e.g., −OH, −O, or −F) introduced after © 2015 American Chemical Society

etching with aqueous hydrofluoric acid (HF) to remove the A layer, and n = 1, 2, or 3.6 Similar to the parent MAX phase, the M atoms in MXenes are arranged on the basis of hexagonal close packing (hcp) with the X atoms sitting in the octahedral interstices, forming the close packed Mn+1Xn sheets that are stabilized by the attachment of terminating species (T) bonded to the surface M atoms.4,7 The 2D morphology, intercalation ability,8−10 good electronic conductivity,11−13 and tunable surface terminations14−16 make MXenes promising for energy storage and other applications including Li-ion batReceived: November 2, 2015 Revised: December 4, 2015 Published: December 8, 2015 349

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Figure 1. Schematic DIFFEV/DISCUS/DShaper/KUPLOT refinement routine for building layered structures and incorporating the parameters used to build the structures into a refinement. Starting at top left and moving clockwise: DIFFEV generates initial trial parameters. There are 11 structural parameters within DISCUS, the module to build the atomistic structure and simulate a neutron total scattering pattern, while the convolution width is used in the DShaper module to approximate the shape function matching the model shape (layered hexagonal block). The KUPLOT module corrects for the missing shape information in the model data and compares the model to the fit. Information (goodness-of-fit) is sent back to the DIFFEV module to perform differential evolutionary algorithm.

teries,3,8,14,17−20 hybrid cells,21−23 electrochemical capacitors,9,11,24,25 sensors,26,27 and actuators.28 MXenes have also shown great potential for use in water purification systems29−31 and as support for catalysts.32,33 Knowledge on both surface structure (e.g., how surfaces are terminated) and interlayer interactions (e.g., what holds the structure in place and how individual sheets are stacked to form multilayer MXenes) is, thus, a crucial first step to understanding and controlling the properties of MXenes and their many applications. Since the first reports of MXenes1 modeling and simulation were used extensively to understand MXene structure, to predict properties, and to identify applications. Heretofore, most of our understanding of MXene systems is based on ideally assumed structures that were not fully resolved experimentally. The first-generation theoretical models of MXenes did not account for surface termination.34,35 Secondgeneration models assumed uniform coverage of MXene surfaces with certain functional groups (pure −O, −OH, or −F terminations) and showed a strong effect of termination on MXenes’ thermodynamic stability,36 electronic properties,15,16 intercalation mechanisms, and energy storage capacity.14,20 Experimental observations to support such model-derived properties have not kept pace, since they require special treatments to achieve single/pure surface termination on the MXene anticipated in all the modeling studies, while the assynthesized MXene surfaces display a mixture of terminations. Very little effort has been dedicated to understanding the complex surface chemistry of MXenes, and only a limited number of experimental results can be found. These efforts have been limited to powder X-ray diffraction (XRD),1−4,11 high-resolution transmission electron microscopy (TEM),1,2,12,37,38 and X-ray atomic pair distribution function (PDF)7 analysis. None of the characterization techniques pursued to date is sensitive to hydrogen present in the MXene terminations, which is critical for understanding surface and interlayer nature in this new class of materials. Several neutron total scattering results for nanomaterials,39−41 including our

work on the structure of hydrated SnO2 nanoparticles,41 have demonstrated the sensitivity of PDF analyses for probing ligand and light species at the surface of oxide and metal nanoparticles. In complex materials like MXenes with (i) nanocrystalline nature in the Mn+1Xn sheets, (ii) short-range ordering of surface structure, and (iii) stacking disorder between the adjacent monolayers typical of 2D materials, the characteristics responsible for macroscopic phenomena are often missed by Bragg diffraction and pose a special set of challenges to crystallographic modeling. Indeed, the use of the PDF method has provided extensive insight into these crystallographically challenging materials. However, the structural characterization so far based on X-ray total scattering and PDF analysis was completed using a “small-box (unit-cell) modeling” scheme,7 which is in general too simple to capture the inherent complexity of MXenes. For instance, the nonperiodic distribution of adsorbed termination species is only defined/ refined as a site-occupancy as in the traditional Rietveld refinement, and the interlayer stacking is constrained to a fixed configuration with infinite repetitions.7 Development of a versatile and robust modeling capability for complex materials lies at the heart of many fundamental materials science problems (see Cliffe et al.,42 Billinge,43 Playford et al.,44 and references therein). Layered systems with diverse termination species, such as MXenes, require atomistic and coarse-grained combinations to achieve the simulation of how the terminated sheets self-assemble and stack as a function of surface chemistry. The atomic-scale recognition of the surface structure and the nature of multilayer stacking in Ti3C2Tx MXene have been recently disclosed by Wang et al.37 and Karlsson et al.38 using scanning TEM. The adsorbed termination species are reported to be randomly distributed on the surface of the Ti3C2Tx sheet with no specific spatial correlations among the −O and −F groups, with preferred locations at the vacant sites between the surface Ti atoms, right above the central Ti atoms in the Ti3C2 sheet.37 This configuration is consistent with the second350

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Chemistry of Materials generation of density functional theory (DFT) models,36 yielding the energetically most favorable surface structure. Furthermore, intercalation of different cations (Al or Na) can further lead to horizontal sliding of the Ti3C2Tx sheets. Wang et al.’s experimental observations37 ensure the need of advanced modeling beyond the small-box routine. Here we report new results from high-quality neutron total scattering measurements for Ti3C2Tx MXenes and demonstrate a multilevel structural refinement method (Figure 1) to benchmark a flexible and robust modeling capability for our material studies. In this communication, the so-called multilevel modeling has both atomistic and coarse-grained features for different levels of structural details. It considers the 2D periodicity of the bare Ti3C2 sheets, and the random/ nonperiodic distribution of terminal species attached on both sides of the bare Ti3C2 sheets, which as a whole represents the functionalized Ti3C2Tx nanosheet with finite lateral dimension and thickness. Two high-level structural parameters (i.e., not each atom), the spacing and the horizontal shifting between the adjacent two nanosheets, fully describe the stacking disorder observed in MXenes. Together, a set of structural parameters accounting for different levels of detail is refined and fit against the experimental neutron PDF data. The combination of neutron total scattering and multilevel refinement methods allows us to build a novel third-generation model of MXene, ensuring real distributions of diverse surface functional groups and monolayer stacking sequences in variously prepared materials.

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An energy dispersive X-ray spectroscopy (EDX) system attached to a Zeiss Merlin VP (Carl Zeiss Microscopy GmbH, Oberkochen, Germany) scanning electron microscope (SEM) was used to estimate the average atomic ratio of O/F in all the MXene samples (HF10, HF48, and HF48-NH4OH), and the ratios are reported in Table 1.

Table 1. Description of Structural and Nonstructural Parameters Defined in the Multilevel Modelinga multilevel modeling (13 variables) 11 structural parameters (1) a* (Å) (2) c′ (Å)

(3) a−b dim. (Å) (4) −OH fraction (5) Ti: Uiso (Å2) (6) (7) (8) (9)

C: Uiso (Å2) O/F: Uiso (Å2) H: Uiso (Å2) s (Å)

(10) σ

pseudo-P63/mmc a*(=b*) lattice param pseudo-P63/mmc c′ lattice parameter, equivalent to the thickness of a single Ti3C2Tx nanosheet size in the a−b plane dimension population of −OH terminating group Debye−Waller thermal displacement

spacing between the adjacent two nanosheets Gaussian distribution σ for shifting away from (±1/3, ±2/3, z) stacking sequence

(11) c dir. (Å)

size along the stacking c direction

2 nonstructural parameters (12) scale factor (13) convo width (Å)

(1) a (Å) (2) c (Å) ≈ c* = 2 × (c′+s)

(3) spdimeter (Å) (4) OH scale factor (5, 6) Ti: U11&U33 (Å2) (7, 8) C: U11&U33 (Å2) (9) O/F: Uiso (Å2) (10) H: Uiso (Å2) (not applicable) (11) Ti (z)

(12) C (z) (13) O/F (z) (14) H (z) (cannot be separated from spdiameter) 1 nonstructural parameter

EXPERIMENTAL SECTION

Ti3C2Tx MXene Synthesis and Basic Characterization. The precursor of MXenes used in this work, Ti3AlC2, was synthesized by heating a mixture of Ti2AlC (95%, KANTHAL) with TiC (2 μm, 99.5%, Alfa Aesar), with an atomic ratio 1:1, at a heating rate of 10 °C/min until 1350 °C, and then soaked at that temperature for 2 h before cooling down to room temperature. The heating and cooling cycle was carried out under a continuous flow of argon. The resulting material was pulverized into powder using a TiN-coated milling bit, and only particles less than 38 μm in size were used for the synthesis of MXene. The latter was synthesized by soaking the Ti3AlC2 powders in hydrofluoric acid, HF, with different concentrations (48% HF for HF48 sample, and 10% HF for HF10 sample) for 24 h at room temperature; a magnetic stirrer was used during the course of the reaction. The ratio of Ti3AlC2 weight to the volume of the solution was 1 g of Ti3AlC2 per 10 mL of solution in the case of 48% HF, and 1 g per 20 mL in the case of 10% HF. After the reaction time, the solutions with the powders were transferred to centrifuging vials and centrifuged at 3500 rpm for 30 min. Then, the supernatant was decanted, and fresh deionized water was added to the settled powder, which was shaken and then centrifuged again. This was repeated until the pH of the decanted liquid exceeded 4. Then the settled powders were removed from the centrifuging vials using DI water and filtered using a vacuum-assisted filtration device. After filtration of all the liquid, the samples were kept on the filter with the vacuum suction running for 18 h to facilitate drying at room temperature. The HF48-NH4OH sample was synthesized by stirring powders of the HF48 sample in an aqueous ammonium hydroxide, NH4OH, solution (28−30% NH3 basis, Sigma-Aldrich) at room temperature with a ratio of 1 g Ti3C2Tx to 10 mL of NH4OH solution. After 18 h of stirring, the solution containing the powder was centrifuged (3500 rpm, for 30 min) to separate solution from the powders. Then, the settled powder was transferred from the vial to the vacuum filtration device using DI water, and vacuum-filtered for 18 h in air, after filtering all the liquids. The air-dried powder was then annealed inside a vacuum furnace at 110 °C for 18 h to ensure removal of any water or ammonium compounds from in-between the MXene layers.

small-box modeling (15 variables) 14 structural parameters

overall intensity scaling factor for the finite shape correction in DShaper

(15) scale factor (cannot be separated from spdiameter)

a

For an easy comparison between the multilevel and small-box modeling methods, parameters in the multilevel modeling are grouped by their corresponding fit variables in the small-box modeling. Fixed parameters: Qdamp, Qbroad, and O/F ratio-EDX (O/F ratio was obtained by averaging EDX results from SEM samples at low magnification; HF10 = 1.4, HF48 = 0.85, and HF48-NH4OH = 1.15). Sample crystallinity and purity of the sample were checked with XRD measurements (Cu Kα radiation, PANalytical Empyrean diffractometer). MXene sample powders were mounted in a 0.2 mm-deep cavity mount, and XRD measurements were made under ambient conditions at 2θ angle ranging from 5° to 90°. Results from XRD measurements are shown in Figure 2A. Neutron Total Scattering. Data were collected on the NOMAD beamline at the Spallation Neutron Source, Oak Ridge National Laboratory, as described by Neuefeind et al.45 Three MXene powder samples (HF10, HF48, and HF48-NH4OH) were loaded into a 2 mm quartz capillary sealed with fiber glass wool and a plastic stopper. Each sample was measured for ∼2 h at room temperature (∼22 °C). The observed intensities were normalized by scattering from a vanadium rod (corrected for absorption and multiple scattering), and background scattering from the empty container and instrument was subtracted. The beamline’s autoreduction software45 was used for data reduction, and no absolute normalization is performed; i.e., the measured total scattering structure factor S(Q) is not scaled to the corresponding sample compositions. This only influences the overall signal intensity and is taken into account during the modeling via a scaling factor. The experimental PDF was obtained by a Fourier transform of S(Q) up to a Qmax of 25 Å−1. Inelastic incoherent effects 351

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Figure 2. (A) Cu Kα X-ray, (B) neutron, and (C) synchrotron X-ray diffraction patterns for three MXenes studied, illustrating different scattering sensitivity and Q resolution of these sources. The vertical dashed lines are (002), (004), and (006) reflections.

Figure 3. Comparison between (A) neutron and (B) synchrotron X-ray PDFs of the three MXenes studied. resulting from hydrogen comprise a small portion of the sampledependent background, and were corrected prior to Fourier transformation. The treatment of hydrogen background follows the method of nonlinear least-squares fitting to a pseudo-Voigt function. All experimental PDFs were first analyzed using the software package PDFgui46 for small-box modeling and then with the multilevel modeling scheme (the fit r-range is 0.7−70 Å). Instrument resolution parameters, Qdamp = 0.017 66 Å−1 and Qbroad = 0.019 18 Å−1, were determined with Ni powder (99.99%, Sigma-Aldrich) measured under similar conditions and are incorporated into the modeling. Results from neutron total scattering measurements and the corresponding PDFs are shown in Figures 2B and 3A, respectively. X-ray Total Scattering. Synchrotron X-ray total scattering data were collected at the 11-ID-B beamline at the Advanced Photon Source (APS) at Argonne National Laboratory, utilizing a beam size of 500 μm × 500 μm, a photon energy of 58.65 keV (λ = 0.2114 Å), and a total measurement time of 10 min per sample. Samples were loaded into polyimide capillaries and measured in transmission mode at room temperature using a PerkinElmer amorphous silicon image plate detector.47 Data for an empty polyimide container and a Ni powder standard were also collected. The program Fit2D48 was used to calibrate the sample to detector distance (172.8 mm) and detector alignment with data from a CeO2 powder standard. Raw scattering data was integrated into Q-space spectra, applying a mask and polarization correction during integration. The normalized total scattering patterns, S(Q)’s, were produced in PDFgetX249 by

subtracting polyimide container scattering, utilizing the appropriate sample composition, and applying standard corrections for the area detector setup.47 Pair distribution function patterns, G(r), were calculated via Fourier transformation of the total scattering data utilizing a Qmax of 23.5 Å−1. The Ni data set was fit in PDFgui46 between r = 1 and 50 Å to refine the instrument resolution parameters, Qdamp = 0.038 Å−1 and Qbroad = 0.021 Å−1. Results from X-ray total scattering measurements and the corresponding PDFs are shown in Figures 2C and 3B, respectively.

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RESULTS AND MODELING Neutron PDFs of Ti3C2Tx MXenes. With the sample composition of Ti3C2(OH,O,F)x and the negative value of neutron coherent scattering lengths for Ti and H atoms, the measured structure factor S(Q), intensity of the (hkl) reflections, and the corresponding PDFs are quite different from those observed by X-ray scattering. Figures 2 and 3 illustrate different structural and elemental sensitivities of these two sources. In general, the (00l) reflections are better determined with X-ray scattering (sets of (002), (004), and (006) reflections are marked by vertical dashed lines in Figure 2). However, the presence of termination species (in particular OH) is better resolved with neutron scattering, especially when data are Fourier transformed and displayed in real space 352

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Chemistry of Materials (Figure 3). Distinctly, neutron PDFs of the three Ti3C2Tx MXene samples contain both positive and negative signals (Figure 3A), depending on the types of atom−atom pair correlations, e.g., negative peaks for O−H and Ti−C/O/F and positive peaks for Ti−Ti, C−C, and Ti−H. The 0.97(3) Å peak is the O−H distance for OH terminating species, and the 2.13(2) Å peak is the direct bonding distance of Ti−C/O/F within the Ti3C2Tx sheet. The third peak at 3.04(2) Å corresponds primarily to the Ti−Ti and C−C distances, which is the distance for the in-plane hcp lattice dimension a, which equals b, if the presence of termination species were ignored. Note that this peak is broad and slightly asymmetric, resulting from the fact that the terminating species also contribute certain indirect bonding pairs to this r range, including in-plane O/F−O/F and Ti−H pairs, and out-of-plane Ti−H, H−H, and O/F−H pairs. The latter bonding pairs occur when the two adjacent sheets are within close distance and the terminating species from the two opposite surfaces create effective bonding interactions. As compared with X-ray PDFs (Figure 3B), the 3.04(2) Å peak is more narrow in width owing to less elemental sensitivities to the presence of terminating species. Among the three MXenes, HF10 has more ordered crystalline structures than the other two samples, as is indicated by the sharp (00l) and (hkl) reflections (Figure 2) and persistence of strong PDF peaks at both short- and long-r regions (Figure 3). At r > ∼45 Å, the disappearance of long-r correlations in HF48 and HF48-NH4OH samples suggests the disorder in their structure, which can be caused by (i) smaller coherent lateral dimension of Ti3C2Tx sheets, (ii) more Ti−C bonding defects, and (iii) higher degrees of interlayer stacking disorder as compared to the HF10 sample. The concentration of HF solution used during the synthesis thus appears to affect the overall crystallinity and defects/ordering in the resultant MXenes. Small-Box Structural Modeling and Refinement. To further interpret neutron PDF data, small-box modeling was first applied to the experimental data, using a two-phase model, the P63/mmc Ti3C2Tx structure + an independent OH pair, designed to account for the OH peak observed at 0.97(3) Å, and Ti3C2Tx structure observed at r > 2 Å. Structural parameters for P63/mmc Ti3C2Tx were adopted from the previously reported X-ray PDF analysis by Shi et al.7 as a starting point. During the fit, the overall intensity scale factor, the unit cell, the z-coordinate of Ti, C, and O/F, and the thermal displacement (Uiso or Uij, i, j = 1, 2, 3) for Ti, C, and O/F in the Ti3C2Tx phase (all constrained by the P63/mmc space group) were varied. The O/F site-occupancy ratio was assigned a value determined from EDX analysis and was fixed in the refinement. A spherical envelope function, involving the shape damping parameter (spdiameter), was also included in order to model the nanocrystalline nature of the Ti3C2Tx MXenes. The model for the independent OH pair is a 4 Å cubic box with an OH group sitting at each corner of a primitive cell. During the fit, a cutoff value (stepcut = 2 Å) was kept fixed to avoid periodic boundary contributions from this phase, and only the scale factor, z-coordinate of H, and the isotopic Uiso for H were refined. After several refinement cycles, a suitable fit was obtained, and results are shown in Figure 4 and reported in Table S1 (in the Supporting Information). The structure results for HF48 and HF48-NH4OH MXenes are similar to those reported by Shi et al.,7 providing indications of decreased order in these two MXenes relative to HF10 MXene, as expected by preliminary inspection of the data.

Figure 4. Neutron PDF fits using small-box (a single least-squares fit) and multilevel modeling (population-averaged results) approaches. The gray circle is the observed PDFs, and the black dashed and solid orange curves show the calculated PDFs based on each model. The differences between the observed and model data are given in solid black (for small-box modeling) and orange (for multilevel modeling) lines shown at the bottom.

Multilevel Structural Modeling and Refinement. Additional structure details of interest include stacking sequence/ disorder, surface species identity, distribution, and interactions, all properties to which the neutron PDF data are sensitive. A set 353

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the weak long r-range correlations as is seen by the large unfit residual signals (Figure 4). The large U33 for Ti and C along the stacking c direction and large Uiso for O/F (Table S1) also suggest that the small-box approach is less physically representative of the system. This is due in large part to the fact that such a crystallographically constrained model is incapable of separating the consequences of horizontal shifting of stacked sheets from the effects of interlayer spacing and/or in-plane c lattice deformation. Furthermore, the introduced OH phase (used to account for the observed OH peak) in the smallbox modeling is unable to account for the formation of hydrogen bonds (e.g., OH···O and OH···F) and any high-r distance correlations involving H atoms, in particular when the two adjacent sheets are closely spaced. In the multilevel structural modeling, certain structural variations can be explored individually, providing high-fidelity tests on the defined variables, especially when the correlations between parameters are uncertain. To demonstrate such utility, systematic sensitivity analyses were performed by varying parameters one by one while keeping all others unchanged. Selected examples are shown in Figure 5 for five closely related structural parameters: (1) the horizontal shifting, (2) spacing between sheets, (3) in-plane a−b lattice deformation, (4) inplane c′ lattice deformation, and (5) −OH fraction. It can be seen from Figure 5 that the sensitivity for determining the spacing and in-plane a−b lattice deformation (Figure 5B,C) is higher than that for resolving the amount of horizontal shifting and in-plane c′ lattice deformation (Figure 5A,D). The amounts of the −OH terminating group contained in the model vary certain peak intensities up to the high-r region (Figure 5E), and this can overlap with the scaling factor effects. One can thus predict that the high-sensitivity parameters (e.g., the spacing and in-plane a−b lattice deformation) will converge at faster rates than low-sensitivity ones. The minimum and maximum bound for each refined variable based on prior knowledge and/ or guided by complementary characterizations are thus very important in constraining the physical meaning of the resultant structures.

of versatile tools for creating discrete Ti3C2Tx nanosheets and building layered MXene structure is therefore called for. We employed the DIFFUSE Software Suite50,51 and DShaper52 approach to perform whole (nonperiodic/multilevel) structure refinements. The refinement includes creating populations of layered structures based on parameter sets (also known as populations) generated within a differential evolutionary algorithm, and comparing the calculated data sets against the collected data between refinement steps. Much of the functionality of the software suite is described by Neder and Proffen.51 Examples utilizing the DShaper programs can be found in Olds et al.52 for approximation of the so-called “shapefunction” in any finite-sized atomistic modeling. Figure 1 outlines the workflow of the method. Starting at top left and moving clockwise, DIFFEV generates initial trial parameter sets, and there are 11 structural parameters (Table 1) used within DISCUS, the module to build the atomistic structure and simulate PDF data. These variables have a more direct physical meaning than those used in the small-box modeling, and are essential for achieving simulation of terminated layer structures, the details of which are described in the Supporting Information text. The KUPLOT module corrects for instruments effects and the finite nature of information collected in Q space to the model data. Comparison between the model data and the observed one is then performed. The quality of fitting is evaluated by a goodness-of-fit indicator (Rw) and is sent back to the DIFFEV module, a generic evolutionary refinement program, to generate new sets of trial parameters. All algorithms are population-based; i.e., sufficiently large populations/parameter sets are created and evolved simultaneously on the basis of the differential evolutionary algorithm implemented in DIFFEV. There are a total of 13 variables in a given population (11 structural parameters + 2 nonstructural factors for the scaling and shape-function correction), and there are a total of 90 different populations generated within each refinement cycle. A general consideration is the size of the populations: populations that are too small tend to be dominated by a few individuals, leading to stagnation and poor sampling of the parameter spaces, while populations that are too large slow down the convergence toward the optimal parameter set.51 Once started, the refinement is an automatic loop, and the iteration is terminated when no further improvements are observed. The final fit and the optimal structural model are thus population-averaged, yielding a meaningful result. Advantage of Multilevel Structural Modeling. Figure 4 compares the optimum fits derived from the two approaches, and Table S1 summarizes the refined variables based on each method. We emphasize here that results for the multilevel modeling given in Figure 4 and Table S1 are averaged over 90 similar structures/simulations generated in the last refinement step, as compared to a single least-squares fit out of the smallbox modeling. For the more ordered HF10 sample the Rw values achieved with the two approaches are similar. However, a substantial improvement was obtained for the less ordered HF48 and HF48-NH4OH samples. Interestingly, although the degrees of freedom in each model (13 vs 15 variables in the multilevel and small-box modeling, respectively) and the Rw values are similar between the two approaches, we found that the c lattice parameter is difficult to converge via the small-box method and has to be constrained to the expected value based on XRD d(00l) reflections in order to obtain a reasonable fit. Additionally, the small-box modeling is not capable of capturing

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DISCUSSION As shown in Table S1, the derived stoichiometric compositions indicate that the O/F ratio varies between the samples. In agreement with the O/F ratio obtained from EDX results, HF10 has the highest O/F ratio of 1.4(1), HF48-NH4OH has O/F ratio of 1.1(3), and the highest F content was found in the HF48 that has O/F of 0.8(1). The increase of the O/F ratio in MXene upon treatment with hydroxides was reported before,10,24,30 and it was predicted to be due to replacement of F by OH. The fact that there are no significant differences in the structure between the HF48 and HF48-NH4OH samples (Table S1) suggests that the changes observed between the HF10 and HF48 are not just simply due to a lower F content in the HF10 compared to HF48, since the HF48-NH4OH has less F compared to HF48 (Table S1). The use of 10% HF to synthesize Ti3C2Tx was reported first by Ying et al.,29 and XRD was used to characterize the structure. They found that the (002) peak of Ti3C2Tx shifts from 2θ of 9.136° to 6.545° (corresponding to c lattice parameters of 19.34 and 26.99 Å, respectively) by switching from 50% HF to 10% HF. While the c lattice parameter for the 50% HF is comparable to what we observed for HF48, the c value for the 10% HF is much larger than we observed for HF10 (Table 1, c* in the multilevel modeling or c in the small-box modeling). However, we noticed 354

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Chemistry of Materials

completely, the c lattice parameter dropped dramatically. It is worth noting that the decrease of the c lattice parameter upon drying was found to be irreversible. Thus, it is most likely that the XRD pattern reported by Ying et al.29 for 10% HF sample was recorded while it was still wet after washing and contained water or aqueous solution between the MXene layers, as shown previously for other MXenes.4 The reason behind the larger c lattice parameter for the HF10 compared to the HF48 in the wet state is not clear at the moment. The structural representation for the dry HF10 and HF48 MXenes is illustrated in Figure 6, and for the HF48-NH4OH MXene, the structural representation is provided in Figure S1 (in the Supporting Information). We found that besides the slight difference in the c lattice parameters the structural features for HF48 and HF48-NH4OH obtained from the modeling are quite similar to each other, and hence only the HF10 and HF48 samples are discussed below. For both MXenes studied, each structure shown in Figure 6 is just one (out of 90) of the final structure population, but the other 89 structures are similar to each other with small variations. The differential evolutionary algorithm implemented here demonstrates a great advantage over a single least-squares fitting, since the experimental data are collected from an ensemble average of sample powders exposed to the neutron beam, and properties, such as stacking disorder and coherent domain sizes, can be better characterized via population-based approaches. Figure 6A,D provides the side view comparisons between the two MXenes. The difference in the pseudo-P63/ mmc c* unit lattice (Figure 6A,D, Table S1) is essentially caused by the spacing (s) between the adjacent two Ti3C2Tx nanosheets, where the s value in HF48 (2.55(4) Å) is ∼0.34 Å larger than s in HF10 (2.21(1) Å). This subtle difference also impacts the stacking disorder, where the distribution sigma (σ) for horizontal shifting is much larger in HF48 than in HF10 (Table S1). As shown in Figure 6A,D, the stacking sequence is better ordered in HF10 than in HF48. Each nanosheet in HF10 tends to be at (±1/3, ±2/3, z) relative positions, following closely the strict definition of ABAB stacking, while more random lateral shifts are observed for HF48. Our modeling result also agrees with the XRD observations (Figure 2A), where HF10 displays sharper (00l) reflections than HF48. Neutron total scattering and PDF analysis provide sensitivity to light atom species and are uniquely capable of capturing H atom interactions at MXene interfaces. The chemistry of terminating species mediates interlayer interactions and influences the characteristics of MXenes, including the nature of stacking faults, the interlayer spacing (s), and ultimately the bonding interactions between layers. In particular, the (±1/3, ±2/3, z) stacking sequence seems to facilitate the bond formation between layers more effectively than a random stacking sequence. In HF10, the offsets of adjacent layers by (±1/3, ±2/3) eliminate the chance of the same termination species facing each other directly from the two surfaces, resulting in a small interlayer spacing and strong interlayer attractions. When layers are stacked more randomly or without strict lateral offsets, as in HF48, there is a greater chance of having the same termination species facing each other and creating repulsion that weakens interlayer attractions and pushes layers apart. Also, a larger number of F terminations in HF48 increases the probability of a F atom on one surface facing another F atom on the opposite surface, leading to a greater disorder. Layer−layer interactions and interlayer bonding formation, thus, consist of at least two kinds, (i)

Figure 5. Systematic sensitivity tests for five closely related structural parameters, performed by varying parameters one by one while keeping all others unchanged.

that the HF10 sample had a large c lattice parameter during drying right after washing, but once it has been dried 355

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Figure 6. Structural representation of (A−C) HF10 and (D−F) HF48 MXenes. The Ti, C, O, F, and H are in blue, black, red, green, and pink spheres, respectively. Hydrogen bonds are as black/white dashed lines for O···H and F···H. All other bonds are as solid lines. Plots A and D are viewed along the crystallographic c* axis (i.e., the stacking direction). Plots B and E are top view (the a*−b* surface) of a single isolated sheet, illustrating random occupation of −O/OH/F groups. Plots C and F highlight the formation of interlayer hydrogen bonds (attractive force) and repulsive interactions when alike terminating atoms are facing each other. All hydrogen bonds shown in the plot are with the lengths of ≥1.5 Å and ≤2.3 Å. This describes moderate hydrogen bonding interactions according to Jeffrey (1997)60 and Wang et al. (2014).61 XYZ structure file can be provided upon request.

polar molecules, such as dimethyl sulfoxide (DMSO),55 and similar phenomena were also found in MXenes,8 in which multilayer MXene particles can be fully exfoliated into single layers. In MXenes, we postulate that the extent of interlayer hydrogen bonding depends not only on the orientation of the OH groups relative to the layers but also on the amount/ distribution of −OH versus −O versus −F species positioned on the opposite surface. Furthermore, van der Waals bonding between the O or F atoms on either side of the surface is another source of bonding interaction. These van der Waals forces should be comparable to the weak interlayer interactions found in pyrophyllite56−59 or talc56,59 (the 2:1 clay with neutralcharge layer structure and no interlayer cation), which lack surface hydroxyls, and the layers are held together purely by van der Waals forces. The similarity between neutral layer-charge clays and MXenes when phenomena such as intercalation and swelling are concerned is not surprising, owing to the fact that the atomic interactions between layers strongly depend on surface chemical moieties. Many interesting questions relating to MXene applications, such as how the spacing between two interacting surfaces affects intercalation processes, what the strength of interlayer interactions is, and how the surface free

hydrogen bonds between O/F atoms on the surface of one layer and OH groups on the opposing surface, and (ii) van der Waals forces between layers. Formation of hydrogen bonds across the layers is likely to be a primary force that holds the structure in place. Certainly, hydrogen bonds can be formed within the same surface (Figure 6B,E) or across the two surfaces (Figure 6C,F). The former is due to the small a (=b) unit lattice (∼3.05 Å), and the latter is due to the small interlayer spacing (2.21(1) Å in HF10 and 2.55(4) Å in HF48). Such hydrogen bonding interactions observed in the MXene system have similarities to those found in 1:1 clay minerals. In kaolinite (the 1:1 clay with neutral-charge layer structure and no interlayer cation), for instance, the layers are held together via interlayer hydrogen bonds, and the binding energy (function of the interlayer hydrogen-bong strength) is computed to be 32 kJ/mol per unit cell,53,54 which is high enough to prevent easy swelling or intercalation processes. Proton dynamics simulations also suggested that some surface hydroxyls in kaolinite continuously rotate between vertical (connecting adjacent layers) and horizontal (parallel to the layer) positions.53 Weakening of interlayer hydrogen bonds in kaolinite can only be achieved through intercalation with highly 356

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Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy. Research at the 11-ID-B beamline used resources of the Advanced Photon Source at Argonne National Laboratory, supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under contract no. DE-AC02-06CH11357. 11-ID-B data were collected as part of an APS Partner User Proposal granting access for NOMAD instrument studies. Materials synthesis efforts by M.N. were supported by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the U.S. Department of Energy. H.-W.W. and K.P. conducted neutron and X-ray measurements, and performed the modeling. D.J.W. and Y.G. supervised the research. All authors contributed to writing and revising the manuscript. Time spent by H.-W.W., D.J.W., and Y.G. was supported as part of the Fluid Interface Reactions, Structures and Transport (FIRST) Center, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences.

energy varies as a function of surface terminations and site defects in the layers, are however open questions at this time, and we hope to pursue them further in the near future. The neutron PDF studies presented in this work provide detailed structural information on MXenes where neither ions nor water molecules are involved as intercalated species. On the fundamental side, our findings for the third-generation model deepen the understanding of the true nature of MXene structure and can be used to compare/replace computationally idealized structures with pure −O, −OH, or −F terminations, enhancing the theoretical analyses used to quantify key property determining parameters. From a practical point of view, information gained from this study provides a knowledge base for the discovery of new materials and opens up a new territory of application developments, e.g., it can be employed to guide the design of new MXene materials with selected surface termination and controlled contact angle, catalytic, optical, electrochemical, and other properties.

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CONCLUSION A much improved (third-generation) atomistic model for 2D Ti3C2Tx, MXene, was resolved using atomic pair distribution function obtained by high-quality neutron total scattering, providing new information on light atom species at surfaces and interfaces. The combination of neutron total scattering and multilevel structural modeling provides an unprecedented level of structural detail for the three studied MXenes. These experimentally derived atomistic models can replace the currently used idealized models in predictions of a variety of physical, chemical, and applied properties of Ti3C2-based MXenes and can be adapted to study details of intercalation and other surface chemistry processes in the future. Additionally, the modeling method shown in this work for a disordered layered material demonstrates key advantages over the other popular modeling tools, including Rietveld-type small-box methods and reverse Monte Carlo methods. Both approaches are incapable of extracting/defining layer−layer correlations, which is an important parameter for characterizing structure− property relations in 2D materials, especially when phenomena such as intercalation and swelling are concerned. We suggest that the multilevel structural modeling should form the basis for a generalized methodology on modeling diffraction and PDF data for layered systems.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.5b04250. Additional details on multilevel modeling and tabulated report of neutron PDF refinements based on small-box and multilevel modeling approaches (PDF)

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Research at the NOMAD beamline at ORNL’s Spallation Neutron Source (SNS) was sponsored by the Scientific User 357

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