SUPPLEMENENTARY INFORMATION for

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1 SUPPLEMENENTARY INFORMATION for Resolving the Structure of Ti 3 C 2 T x MXenes through Multilevel Structural Modeling of the Atomic Pair Distribution Function Hsiu-Wen Wang, *, Michael Naguib, Katharine Page, David J. Wesolowski, 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 1. Supporting Information Text: Parameters defined in Multilevel Structural Modeling Multilevel structural modeling provides simple steps for building layered structures and incorporating the parameters used to build the structures into a refinement. DIFFEV/DISCUS/DShaper/KUPLOT Software Suite 1-3 is utilized. The initial guessed structure is based on the small-box refinement result, as well as TEM 4,5 and DFT 6 models. There are eleven structural parameters used within DISCUS, the module to build the atomistic structure and simulate PDF data: (1,2) pseudo-hexagonal a*(=b*) and c lattice parameter, (3) the a-b plane dimension, (4) population of -OH terminating group, (5-8) Debye-Waller thermal displacement (U iso ) for Ti, C, H, and O/F, (9,10) the spacing (s) and the distribution of horizontal shifting ( ) between the adjacent two nanosheets, and (11) dimension along the stacking c direction. Parameters (1-8) are used to construct discrete Ti 3 C 2 T x nanosheets. The -O/OH/F groups are assumed to be at the energetically favorable surface sites in accordance with the TEM and DFT observations, 4-6 as described in the introduction section of the main text. We also assume the entire surface sites are occupied by any one of the three terminating species with no spatial correlations defined, i.e., a random occupation among the -O/OH/F groups is applied. Note that since the number of available surface sites is known and the total O/F ratio is a fixed value based on EDX analysis, only one variable (named as -OH fraction) is required to define the

2 relative amount of -O, -F and -OH species. Furthermore, besides the thermal displacement for each atom type, thermal vibrations are considered in order to displace atoms from their idealized positions according to the corresponding isotropic Debye-Waller factor, U iso. Soft bonding constrains and repulsions are applied to the O-H and H-H pair-pair correlations, respectively, via simplistic pair-wise (Lennard-Jones type) potential and are relaxed through a Monte Carlo algorithm to minimize the model s energy. Accordingly, each constructed Ti 3 C 2 T x nanosheet is slightly different from the other in terms of the distribution of termination species and relaxation of individual atoms. Parameters (9-11) stack constructed Ti 3 C 2 T x nanosheets into layered MXene structures following a sequence of ABAB, where A and B stands for the adjacent two nanosheets. The created shifts are Gaussian distributed ( = standard deviation), and are centered at (+1/3, +2/3, z) position for the ABAB shifting. The dimension along the c direction defines the total number of stacked sheets. The averaged interlayer spacing (d) based on the pseudo-p6 3 /mmc unit-cell definition is thus the sum of c and s (i.e., d = c +s). The former defines the thickness of a single Ti 3 C 2 T x nanosheet (c ), and the latter defines the distance between the two adjacent nanosheets (s). Twice this value (2d) is the pseudo-p6 3 /mmc c* unit lattice and it is comparable to the P6 3 /mmc c unit lattice in the parent Ti 3 AlC 2 MAX phase and the small-box structural model for Ti 3 C 2 T x MXene. In addition to the eleven structural parameters, the two nonstructural parameters are considered: (12) the overall intensity scale factor to scale the model to the calculated PDF data, and (13) the size of the convolution width used to generate the finite shape correction in DShaper (for the layered hexagonal block). The KUPLOT module corrects for the missing shape information in the model data and compares the model data with the observed one. The quality of fitting is evaluated by a goodness-of-fit indicator (R w ) and is sent back to the DIFFEV module, a generic evolutionary refinement program, to generate new sets of trial parameters. Since all algorithms are population based, sufficiently large populations/parameter sets (there are 13 variables in a given population and there are total of 90 different populations) are created and evolved simultaneously based on the differential evolutionary algorithm implemented in DIFFEV. Different parameter combinations are thus investigated simultaneously (i.e., implicit parallelism) through different regions of the parameter space, particularly advantageous for the solution of problems with many degrees of freedom.

3 2. Supporting Information Table: Refinement Summary Table S1. Summary of refined parameters based on the multilevel and small-box modeling methods for neutron PDFs. For an easy comparison between the two approaches, structural parameters in the multilevel modeling are grouped by their corresponding fit variables in the small-box modeling. Derived stoichiometric coefficients for each sample are given in the unit formula of Ti 3 C 2 [O x1 (OH) x2 F x3 ]. The e.s.d. values are in parentheses. Multilevel PDF modeling (13 variables) Small-box PDF modeling (15 variables) MXenes: HF10 HF48 HF48-NH 4 OH MXenes: HF10 HF48 HF48-NH 4 OH R w a 0.196(1) 0.178(2) 0.194(5) R w a scale factor 0.052(3) 0.044(5) 0.055(8) scale factor 0.129(2) 0.099(1) 0.102(3) a* (Å) (2) 3.050(1) 3.042(1) a (Å) (4) 3.046(4) 3.040(1) c* = 2 (c +s) (Å) b 19.12(1) 19.57(8) 19.41(6) c (Å) b 19.15(1) 19.57(8) 19.38(9) -OH fraction 0.52(3) 0.42(7) 0.32(8) OH scale factor 0.012(3) 0.011(5) 0.017(4) O/F ratio-edx c O/F ratio-edx c Ti: U iso (Å 2 ) (1) 0.005(1) 0.005(1) Ti: U 11 (Å 2 ) 0.003(1) 0.003(5) 0.003(1) Ti: U 33 (Å 2 ) 0.008(3) 0.011(8) 0.009(5) C: U iso (Å 2 ) (2) 0.004(1) 0.004(1) C: U 11 (Å 2 ) 0.004(1) 0.004(4) 0.004(1) C: U 33 (Å 2 ) 0.024(3) 0.033(8) 0.026(6) O/F: U iso (Å 2 ) (3) 0.007(3) 0.005(2) O/F: U iso (Å 2 ) 0.015(1) 0.016(8) 0.019(2) H: U iso (Å 2 ) 0.014(5) 0.013(7) 0.014(8) H: U iso (Å 2 ) 0.02(1) 0.02(1) 0.02(1) size: a-b dim. (Å) 95(2) 76(9) 81(11) size: c dir. (Å) 25(2) 29(9) 22(9) spdimeter (Å) 82(2) 46(6) 50(2) convo. width (Å) 6(1) 6(2) 6(2) Ti (z) 0.127(1) 0.124(4) 0.128(1) : Gaussian C (z) 0.061(1) 0.063(4) 0.061(1) distribution sigma 0.2(1) 0.6(2) 0.5(2) O/F (z) 0.191(1) 0.180(3) 0.187(1) for shifting H (z) 0.245(7) 0.245(8) 0.259(5) Derived stoichiometric coefficients for the unit formula of Ti 3 C 2 [O x1 (OH) x2 F x3 ], where x1 + x2 + x3 = ~2.0 x1: O 0.13(1) 0.1(1) 0.4(1) x1: O x2: OH 1.04(6) 0.8(1) 0.6(2) x2: OH cannot be determined. x3: F 0.83(5) 1.1(2) 0.9(2) x3: F a. R w = weighted residual value. The weighting factor is the inverse of observed intensity at each data point. b. The c lattice parameters determined based on sets of d(002), d(004), and d(006) reflections by Cu-Kα and synchrotron radiation XRD are: HF10 = 19.15(3) Å, HF48 = 19.6(2) Å, and HF48-NH 4 OH = 19.4(5) Å. c. The O/F ratio was obtained by averaging EDX results from SEM sample at low magnification.

4 3. Supporting Information Figure: Structural representation for the dry HF48-NH 4 OH MXene A B c* b* a* s a* c C MXene HF48-NH 4 OH: Ti 3 C 2 [O 0.4(1) (OH) 0.6(2) F 0.9(2) ] Figure S1. Structural representation of HF48-NH 4 OH MXene. 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. Plot A is viewed along the crystallographic c* axis (i.e., the stacking direction). Plot B shows top view (the a*-b* surface) of a single isolated sheet, illustrating random occupation of -O/OH/F groups. Plot C highlights 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 length of 1.5 Å and 2.3 Å.

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