Supporting Information For:

Transcription

1 Supporting Information For: Structure Solution of Metal-Oxide Li Battery Cathodes from Simulated Annealing and Lithium NMR Spectroscopy Kristopher J. Harris, Jamie M. Foster, Matteo Z. Tessaro, Meng Jiang, Xingyi Yang, Yan Wu, Bartosz Protas, and Gillian R. Goward * Simulated Annealing Methodology. The SA algorithm is initialized with a random structure of the desired stoichiometry, and trial iterations are generated by swapping two randomly chosen TM sites. The probability, P, of accepting the swap is governed by the typical SA protocol. That is, the probability is controlled by the energy change produced by a tentative swap, ΔE, and a temperature parameter, T, according to the Metropolis equation:! = 1!! 0 Eq. S2 exp[!!/!]!! > 0 We note that it is only necessary to sum over 6 neighboring oxygen atoms at the pre- and post-swap configurations of the two sites to evaluate ΔE. This simplicity becomes clear if the total energy is considered from the perspective of the TMs. Each TM site participates in the local-charge-balance equation of 6 oxygen atoms: 3 in the plane above and 3 in the plane below; see Figure 1(c). The energy associated with a specific TM site is therefore given by a sum over the six neighboring oxygen atoms whose energies are defined by Equation 1. The concept of local charge balance is depicted graphically in Figure S1, where the six E i equations involve the three TM sites in each of the triangular tiles (as shown, these fit together to form a hexagon). Figure S1. View of a section of the sheet-like structure of the Li[Ni x Mn x Co 1-2x O 2 ] phases highlighting the local environments that are relevant to a single TM atom (at the center of the figure). The 6 oxygen-coordination triangular tiles that each TM is involved in are depicted with purple triangles.

2 For each material, the model structure size was increased until convergence was obtained. Simulations with >10 4 atoms produced model NMR spectra that were indistinguishable on the scales of interest, and were therefore judged large enough to accurately capture the statistics of the physical samples. Simulation results were only considered at points of thermal equilibrium, i.e., at points where the average energy stabilized and remained essentially constant over thousands of iterations. The number of iterations needed to reach this equilibrium was strongly dependent on the phase under consideration and the temperature parameter for which equilibrium was sought. However, for all temperatures with structures of size 10 4 atoms, 10 9 iterations were sufficient for the simulations to reach this type of steady state. For a single core on a standard desktop computer a simulation of this nature can be done within a few days.

3 Figure S2. 7 Li NMR spectra and simulations for Li[Ni 0.02 Mn 0.02 Co 0.96 O 2 ]. The data is that from Figure 3, but shown such that the smaller features are more easily seen, while the central peak (under grey box) is much too large to see on this scale. Peak assignments agree with those of Zeng et. al, 1 namely: (a) Mn in the 1 st shell and Ni in the 2 nd shell (b) [Mn in the 1 st ] or [Mn and Ni in the 1 st ] (c) Ni in the 2 nd (d) Mn in the 2 nd (e) Ni in the 1 st and Mn in the 2 nd. We note that peak-a and peak-e report the Mn/Ni pairing, and are used to determine the most accurate T parameter (which acts to break such pairs, and reduce these peaks). The optimum value for T is 1.55, as there is too much intensity in peak-a at lower T values, and too little intensity in peak-a and peak-e at higher T values (with essentially zero intensity in both under fully random, T = conditions). There is slightly more intensity in peak-d and the left side of peak-b in the experimental spectrum than in any simulation (n.b. including at T = when no Mn/Ni ions pair). These two peaks correspond to Mn ions isolated from any Ni, and the slight experimental excess intensity is attributed to a very small excess of Mn over Ni in the starting material (given the difficulty of obtaining exact equivalence by weight for the very small dopant quantity).

4 Figure S3. 7 Li NMR spectra and simulations for Li[Ni 0.1 Mn 0.1 Co 0.8 O 2 ]. The data is that from Figure 4, but shown such that the smaller features are more easily seen, while the central peak (vertically clipped at the ~) is too large to be seen entirely on this scale. The important discontinuities (peaks and shoulders) of the lineshape (labelled a to g) are all well represented in the T = 1.58 simulation. However, above or below this value for the T parameter the lineshape has inaccurate features: (i) the peak-b region is incorrectly split into multiple peaks in both T = 1.24 and T = simulations (ii) the ratio of peak-d to peak-e is inaccurate [too low for = 1.24 and too high for T = simulations]. Furthermore, in the T = simulation, peak-g of the experimental spectrum is completely absent and the peak-c region is inaccurately portrayed as multiple peaks. Therefore, the structure generated by the T = 1.58 simulation is the optimum model.

5 Figure S4. 7 Li NMR spectra and simulations for Li[Ni 1/3 Mn 1/3 Co 1/3 O 2 ]. The data is that from Figure 5, but shown larger and with the experimental spectrum overlain for comparison. Simulations produced at low values of the T parameter demonstrate much more ordered than the experimental results. Those produced at very high T values contain too much disorder and produce simulated NMR lineshapes that extend well outside the experimental one. The simulated spectrum at the optimum value of T = 1.55 however, is an excellent match with the experiment, particularly given the hundredfold local environments present.

6 Statistical Analysis of Li[Ni 1/3 Mn 1/3 Co 1/3 O 2 ]. Further insight into the structure can be obtained through comparison to the [ 3! 3]R30 -type [1,2] phase. For a given TM in this hypothetical structure, the six metals in its 1 st and 3 rd coordination shells are composed by 3 of each of the other types of TMs, Figure S2. The second shell, however, is entirely composed of 6 homonuclear metals. This configuration is shown clearly in the left side of Table S1, where the 1 st and 3 rd shells have zero populations on the shaded diagonals with 3 atoms of each type as the off-diagonal entries. The 2 nd shell is described with only diagonal entries, as each metal type is surrounded by 6 of the same metals in this shell. Calculations for the average populations of each type of metal in the best-match, T = 1.55, simulation of Li[Ni 1/3 Mn 1/3 Co 1/3 O 2 ] are also included in Table S1. There, it can be observed that in the 1 st and 3 rd shells, the diagonal entries (homonuclear pairings) are smaller than the off-diagonal ones, while it is the diagonal entries that are larger for the 2 nd shell. This is exactly the behavior of the [ 3! 3]R30 phase, with some blurring due to disorder. Of note is the fact that the statistics are closer to the hypothetical [ 3! 3]R30 phase for the Ni and Mn pairings than for Co, which follows from the fact that there is no penalty for Co-Co interactions in the Hamiltonian. Furthermore, the statistics are closest to those of the [ 3! 3]R30 phase in the 1 st shell, and follow less closely as the shells get farther out. The NMR/annealing-derived structure can therefore be described as a disordered version of the [ 3! 3]R30 -type phase. Figure S5. Section of a TM layer from a theoretical [ 3! 3]R30 -type [1,2] structure of Li[Ni 1/3 Mn 1/3 Co 1/3 O 2 ]. Each color refers arbitrarily to one of the three TMs, which alternate metal-1, metal-2, metal-3 in all directions, creating threefold symmetry at each TM site.

7 Table S1. Average local environments in the simulated Li[Ni 1/3 Mn 1/3 Co 1/3 O 2 ] structure at T = For each atom, the average population in the six sites of its 1 st, 2 nd, and 3 rd coordination shells are reported. These 1 st, 2 nd, and 3 rd shells are defined as the nearest and second-nearest M-M positions within a TM sheet (at ca. 2.86, 4.95, and 5.72 A ). [ 3 x 3]R30 -type NMR/Annealing Structure Center 1 st Shell # of TM Type: 1 st Shell # of TM Type: Atom Ni Co Mn Ni Co Mn Ni Co Mn Center 2 nd Shell # of TM Type: Atom Ni Co Mn Ni Co Mn Ni Co Mn Center 3 rd Shell # of TM Type: Atom Ni Co Mn Ni Co Mn Ni Co Mn Comparison to Diffraction Data. The determined structure of Li[Ni 1/3 Mn 1/3 Co 1/3 O 2 ] is also in reasonable agreement with reported pair-distribution function, PDF, data. [1] The comparison between the pairing frequencies calculated for the best-match structure predicted here versus that derived from a diffraction experiment [1] is provided in Table S2. The agreement between the two sets of numbers is excellent, particularly given that it is often difficult to obtain a unique fit of PDF data. This challenge is exacerbated in NMC because the neutron scattering lengths of the elements are a mixture of positive (Co, Ni, O) and negative (Li, Mn) values, which makes a unique fit difficult to ascertain. The fact that the structure determined here agrees with experimental data that was not employed in the fitting procedure provides an encouraging further corroboration of the method. Moreover, the NMR/annealing method produces not only this average numerical description of the structure, but also the complete structural diagram.

8 Table S2. Values of pair-counting frequencies for Li[Ni 1/3 Mn 1/3 Co 1/3 O 2 ] structure at T = 1.55 simulations versus literature values. [1] The frequency of each type of metal pairing is presented as a fraction of the total number of metal-metal pairings at that distance. See Table S1 caption for definition of The 1 st /2 nd coordination shells. Pair 1 st Shell 1 st Shell 2 nd Shell 2 nd Shell Type This work (%) Literature 3 (%) This work (%) Literature 3 (%) Co-Co Mn-Co Ni-Co Ni-Ni Mn-Mn Ni-Mn Bibliography [1] D. Zeng, J. Cabana, J. Bréger, W. Yoon, C. P. Grey, Chem. Mater. 2007, 19, [2] Y. Koyama, N. Yabuuchi, I. Tanaka, H. Adachi, J. Electrochem. Soc. 2004, 151, A1545.