A Study of Stacking Faults and Superlattice Ordering in Some Li-Rich Layered Transition Metal Oxide Positive Electrode Materials

Li-rich layered transition metal oxides such as Li[Li 0.2 Ni 0.2 Mn 0.6 ]O 2 have in-plane ordering between the excess Li atoms and the transition metal (TM) atoms in the transition metal layer. The √ 3a × √ 3a superlattice in the TM layer causes superlattice Bragg peaks in their X-ray diffraction patterns. This article describes the relation between the metal composition of the materials, stacking faults and superlattice ordering. The XRD patterns were ﬁtted with a program called FAULTS, which treats the effect of stacking faults on the superlattice peak shapes. The superlattice peak positions of Li[Li 1/3-2x/3 Ni x Mn 2/3-x/3 ]O 2 materials changed monotonically with Ni content (x), as did the positions of the main diffraction peaks of the base structure. This proves that the superlatices peaks originate from the Li[Li 1/3-2x/3 Ni x Mn 2/3-x/3 ]O 2 solid solution and are not caused by any domains of second phase such as Li 2 MnO 3 . Fitting the XRD patterns with FAULTS revealed that the stacking fault probability increased monotonically with Ni content. ©

Li-rich positive electrode materials (e.g. Li 1.2 Ni 0.13 Mn 0.54 Co 0.13 O 2 ) are potential candidates for high energy density Li-ion batteries. [1][2][3] They are capable of delivering reversible specific capacities up to 250 mAh/g 4,5 at an average discharge potential of ∼3.5 V vs Li metal. 6 Understanding the structure of Li-rich materials is essential to improve their properties and performance. Li-rich materials are layered transition metal (TM) oxides comprised of alternating layers of metal atoms (Li or TM) and oxygen atoms. 7 Compared to non-Li-rich layered transition metal oxides such as LiCoO 2 , the Li/TM ratio is greater than 1 for Li-rich layered transition metal oxides and usually Li atoms occupy the TM layer in addition to the Li layer. 8 Li 2 MnO 3 is a typical example of such a material in which 1 4 of the Li atoms occupy sites in the TM layer.
Li-rich layered transition metal oxides can be defined as O3 structures with A-B-C-A-B-C stacking but the arrangement of the atoms in the TM layer is different from that in other layered materials. 9 The presence of Li + ions with large ionic radii (0.74 Å) and small sized Mn 4+ ions (0.54 Å) in the TM layer causes an in-plane ordering resulting in a √ 3a × √ 3a superstructure or superlattice 10 and changes the symmetry from R-3m to C2/m. The superlattice ordering in the TM layer results in superstructure Bragg peaks in the range of ∼ 20 • to 35 • (Cu K α ). 9 11 Their work has clearly shown that overlithiation (Li in the TM layer) is required for superstucture reflections. Characterization techniques such as solid-state NMR 12 and EXAFS 13 have also been used to study the superlattice ordering.
Stacking disorder of the TM layers along the c axis or "stacking faults" strongly affects the shape of the superlattice peaks in the diffraction patterns. Boulienau et al. have demonstrated the existence of stacking faults in the structure of Li 2 MnO 3 using high resolution transmission electron microscopy. 14 In their XRD patterns of Li 2 MnO 3 , the broadening of some selective superlattice peaks was attributed to stacking faults. The extent of superlattice peak broadening increases with increasing probability of stacking faults.
In a separate study, Boulineau et al. have simulated the XRD pattern of Li 2 MnO 3 with varying stacking fault probabilities using a program called DiffaX. 15  Different stacking sequences of the TM layers along the c axis in Li 2 MnO 3 that generate different space groups have been proposed previously. Breger 18 and Meng 9 et al. have explained two different ways of stacking -A1-B1-C1 corresponding to C2/m and A1-B1-C2 corresponding to P3 1 12 space groups. Based on these two stacking sequences, they have simulated the XRD patterns of Li 2 MnO 3 using DiFFaX and found that the C2/m stacking scheme was better for estimating the stacking fault probabilities. According to Meng et al., the stacking sequences that generate the P3 1 12 space group are due to an abnormality in the C2/m sequence. Riou et al. have proposed an A1-B1-C2-A2-B3-C1 stacking sequence to explain the structure of Li 2 MnO 3 in terms of a C2/c space group. 19 Overall, any random stacking sequence is possible owing to the negligible energy difference between the sequences. In this work, stacking faults were selected randomly with varying probabilities.
Stacking faults in Li-rich layered transition metal oxides are affected by the synthesis temperature. 20 Several researchers have already reported that Li 2 MnO 3 synthesized at low temperature has high probability of stacking faults. 21 In particular, Boulineau et al. have suggested that synthesizing an ideal Li 2 MnO 3 with the absence of stacking faults is impossible. 15 It would be useful to understand the effect of metal composition on the stacking faults. Here, the composition of the TM layer (presence of ions such as Ni 2+ ) was studied as a factor that affects the probability of stacking faults. The focus of this article is to study the effect of metal composition on the superlattice ordering and stacking faults in Li[Li 1/3-2x/3 Ni x Mn 2/3-x/3 ]O 2 materials.

Experimental
Mixed transition metal carbonate precursors (example: Ni(II) 0.3 Mn(II) 0.7 CO 3 ) were synthesized through co-precipitation. The reaction was started with an aqueous solution of 0.1 M NH 4 OH in a continuously stirred tank reactor (CSTR). NH 4 OH was used as a source of NH 3 ligand for TM coordination to facilitate the formation of spherical particles. 22,23 The temperature of the reaction was held at 60 • C and the pH was maintained at 8 by adding appropriate amounts of acid (H 2 SO 4 ) or base (NaOH). A 2M aqueous solution of the mixed TM sulfate solutions and an equimolar solution of sodium carbonate (Na 2 CO 3 ) were pumped at a desired flow rate. After the completion of the reaction, the resulting suspension was collected and washed several (5) times with distilled water. Then it was filtered and the resulting product (Ni x Mn 1-x CO 3 ) was dried in an oven at 100-120 • C in air for ∼12 h. The Li[Li 1/3-2x/3 Ni x Mn 2/3-x/3 ]O 2 compounds were synthesized by adding stoichiometric amounts of Ni x Mn 1-x CO 3 precursors and Li 2 CO 3 . A 5 wt% excess of Li 2 CO 3 was added to compensate for Li loss in the high temperature sintering process. The reactants were weighed accurately, mixed, ground well using a mortar and pestle and calcined in air at 900 • C to yield the product. The heating and cooling profiles were followed as reported in reference. 8 The elemental composition of the synthesized materials was obtained using inductively coupled plasma optical emission spectroscopy (ICP-OES).
A powder X-ray diffraction (XRD) pattern for each sample was collected using a Siemens D5000 diffractometer equipped with a copper target X-ray tube and a diffracted beam monochromator. The program "FAULTS" was used for the stacking faults calculation 24 as well as to fit the XRD data. The program FAULTS considers the layered arrangements of the structure and fits the structure based on a recursive algorithm/method 25 as explained by Treacy et al. Parameters corresponding to unit cell dimensions, the peak shape, scale factor and the stacking faults probability were refined.

Results and Discussion
Li 2 MnO 3 .-Li 2 MnO 3 serves as an ideal model for describing superlattice ordering and stacking faults. Figure 1 shows the structure of Li 2 MnO 3 in which the boundaries of both the monoclinic (C2/m) and hexagonal unit cells (R-3m) have been indicated to highlight the correlation between their atomic arrangements. The unit cells have been slightly tilted and the oxygen atoms are not drawn to scale (smaller) for clear visualization. Equation 1 shows the relation between the monoclinic unit cell and the hexagonal unit cell.
The stacking faults in Li 2 MnO 3 (as well for Li[Li 1/3-2x/3 Ni x Mn 2/3-x/3 ]O 2 ) arise from the stacking disorder of the TM layer along the c axis. The top panel of Figure 2 shows a triangular lattice plane, labeled as A1, corresponding to the TM layer of Li 2 MnO 3 . The plane A1 is formed by 1/3 Li (green balls) and 2/3 Mn atoms (pink balls) and it is easy to identify the ordering in the TM layer. The top panel of Figure 2 shows a 2-D hexagonal unit cell of the plane A1.
Referring to the hexagonal 3-D unit cell of Li 2 MnO 3 shown in Figure 1, the very bottom TM layer is considered to be A1 (the starting layer). Since Li 2 MnO 3 can be considered as an O3 structure, the TM layer shifts 3 times within one hexagonal 3-D unit cell. With reference to A1, the stacking of the next TM plane follows a (1/3, 1/3, 1/3) translation in fractional atomic coordinates in accordance with the O3 structure. As a result, the next TM plane, labeled B1, is placed on top of A1. The plane B1 has been constructed by atoms designated by triangles in Figure 2. A subsequent (1/3, 1/3, 1/3) translation from B1 results in a TM layer called C1, in which the atoms are designated as stars in Figure 2. The bottom left and right panels of Figure 2 show the A1 to B1 and B1 to C1 translations, respectively. The A1 to B1 and B1 to C1 translations can be easily understood by following the 2-D hexagonal unit cells in the bottom right panel of Figure 2. If the TM layer stacking perfectly follows the trend A1-B1-C1-A1-B1-C1. . . , then there are no stacking faults in the structure. The origin of the stacking faults of these layered Li-rich materials arises only from stacking mistakes in the TM layers whereas the oxygen layers are always in their ideal positions and are not involved in the stacking disorder along the c-axis. In other layered materials, the entire MO 2 slab may be involved in stacking disorder, but that is not the case here.
The XRD pattern of such an ideal structure of Li 2 MnO 3 with zero stacking faults was simulated using FAULTS. The program FAULTS considers the whole structure under investigation as series of layers stacked in a defined sequence and calculates the diffraction pattern based on first principles. 25 Figure 3 shows the XRD pattern of Li 2 MnO 3 with 0% stacking faults obtained from a FAULTS simulation that considers only the A1-B1-C1-A1-B1-C1 stacking of the TM layers. The simulation was made using the unit cell parameters of Li 2 MnO 3 reported by Boulineau et al. 14 All the peaks in the simulated XRD patterns can be indexed using a C2/m space group. Figure 3 shows that the superlattice peaks (indicated by the red boxes) are as sharp as the other peaks.
The stacking of TM layers in real samples of Li 2 MnO 3 as well as for Li[Li 1/3-2x/3 Ni x Mn 2/3-x/3 ]O 2 involves stacking disorder along the caxis. In addition to the (1/3, 1/3, 1/3) translation, two other translations are possible: (2/3, 0, 1/3) and (0, 2/3, 1/3), which can create two more triangular lattice planes. For example, the next stacking layer above A1 could be B2 or B3. Figure 4 shows the A1 to B2 and A1 to B3 translations. Thus a total of 9 triangular lattice plane variants, A1, B1, C1, A2, B2, C2, A3, B3 and C3 can be involved in the TM layer stacking sequence. In a structure with stacking faults, the TM layer stacking does not follow the ordered A1-B1-C1. . . sequence. Instead, a disordered stacking sequence occurs, which involves all the 9 triangular lattice plane variants in various probabilities.  Figure S1 shows the simulated XRD patterns of Li 2 MnO 3 with varying stacking fault probabilities. As the stacking fault probability increases from 0% to 100%, the broadening of the superlattice peaks increases simultaneously. At the same time, the increase in stacking fault probability does not have any effect on the other Bragg peaks. Figure S2 shows the simulated XRD patterns of Li 2 MnO 3 with varying stacking fault probabilities but only in the range between 20 • to 35 • . The superlattice peaks of the structure with 0% stacking faults have a clear 3-D peak signature but they gradually change to a 2-D type peak for the structure with 100% stacking faults. Thus the extent of broadening of the superlattice peaks should be taken as a direct measure of the probability of stacking faults.
The occurrence of stacking faults in two samples of Li 2 MnO 3 were analyzed -one made at 1100 • C (LM1100) and other at 900 • C (LM900). Figure 5 shows the XRD patterns of both LM1100 and LM900 and the inset shows the comparison of their superlattice peaks

Translation Vectors
Translation Probabilities simulation, by contrast to fitting, underestimated the probability of stacking faults in their methods.

Li[Li 1/3-2x/3 Ni x Mn 2/3-x/3 ]O 2 .-
The structural and electrochemical properties of materials from the Li[Li 1/3-2x/3 Ni x Mn 2/3-x/3 ]O 2 series were first reported by Lu et al. 26 Table II shows the ICP-OES composition of the studied Li[Li 1/3-2x/3 Ni x Mn 2/3-x/3 ]O 2 samples. The Ni content (x) increased from sample LM900 to LMN3, which has a composition close to LiNi 0.5 Mn 0.5 O 2 . Figure S3 shows the XRD patterns of the  The XRD pattern at the top represents sample LM900 whereas the one at bottom of the stack represents the sample LMN3. All the samples were O3 structures (α-NaFeO 2 ) and most of the diffraction peaks could be indexed using the R-3m space group except for the broad superlattice peaks between 20 • to 30 • . Figure S3 (right panel) shows an enlarged view of the (003) peaks (R-3m) that occur around 18.6 • . The (003) peak position shifted from higher to lower angle (black dotted line in Figure S3) as x (Ni content) increased from LM900 to LNM3 due to an increase in the fraction of larger Ni 2+ ions. The (003)   has been considered for peak position analysis. For samples LNM2 and LNM3, the intensities were scaled up slightly for the purpose of clarity. The (020) peak positions from sample LM900 to LNM3 shift from higher to lower scattering angle as the Ni content increases and has been indicated with a dashed line in Figure 7. The (020) peak peak shift with increased Ni content for the materials in the Li[Li 1/3-2x/3 Ni x Mn 2/3-x/3 ]O 2 series also suggests the solid solution behavior as expected from the (003) peak shift belonging to the non-superlattice reflections.
The position of the non-superlattice C2/m (33-1) peak (corresponds to the R-3m (110) peak) occurring around 65 • and the superlattice C2/m (020) peak occurring around 20 • were compared from samples LM900 to LMN3. The peak positions (2θ) were converted into dspacings using Bragg's law. Table III shows the 2θ positions of C2/m (020) and the C2/m (33-1) peak and Figure 8 shows a plot of their corresponding d-spacings. Figure 8 shows a linear relationship with an R 2 value equal to 0.998 and a slope of ∼0.4. This correlation clearly reiterates that the SL peaks belong to the solid solution between Li 2 MnO 3 and LiMO 2 (M = Ni, Mn and Co) and do not originate from any secondary phase. If Li 2 MnO 3 were a separate phase in the Li[Li 1/3-2x/3 Ni x Mn 2/3-x/3 ]O 2 series, then peaks corresponding to that phase would not have shifted with an increase in Ni content.
Superlattice peak broadening.-The cause of superlattice peak broadening in the diffraction patterns of Li-rich layered transition metal oxide materials has been a subject of debate. Believers in the composite 32 nature of these materials contend that nano-domains of Li 2 MnO 3 cause the broadened SL peaks. 33,34 On the other hand, believers in the solid solution argue that the SL peak broadening must be attributed to the stacking faults along the c axis. 15  In the earlier parts of this paper the superlattice peak broadening in Li 2 MnO 3 was attributed to stacking faults. In the same way, Li Ni 2+ ) and the small ions (Mn 4+ ) deviates from the ideal value (1:2) in Li 2 MnO 3 . The substitution of Ni 2+ in the TM layer will, therefore, likely affect the 2-D ordering between Li, Ni and Mn ions in the TM layers, which in turn can increase the probability of the stacking disorder along the c axis. Hence it is very likely to observe superlattice peak broadening in Li[Li 1/3-2x/3 Ni x Mn 2/3-x/3 ]O 2 materials. Figure 9 shows the FAULTS fitted XRD patterns of samples LM900 to LNM3 whereas Figure 10 shows only the superlattice region from 20 • to 28 • . The red points and the black solid lines represent the data points and the calculated patterns, respectively. As the concentration of Ni increases, the broadening of the SL peaks increased due to an increase in the stacking fault probability. Figure 11 shows the stacking fault probability plotted versus the Ni content. This plot clearly demonstrates how the presence of Ni 2+ ions in the TM layer influences the probability of stacking faults. For the sample LNM3, the superlattice peak broadening with change in the stacking faults probability is very subtle due to the very weak superlattice peaks. Hence the uncertainty of the stacking faults probability reported for LNM3 is higher.

Conclusions
The superlattice peak broadening in the XRD patterns of layered Li-rich transition metal oxides has been examined. First, by using a fitting program called FAULTS, which can take into account the existence of stacking faults, the XRD patterns of Li 2 MnO 3 were simulated and fitted. The fitting results revealed that the stacking disorder along the c axis (stacking faults) is the underlying reason for the superlattice peak broadening. Similarly, the XRD patterns of Li[Li 1/3-2x/3 Ni x Mn 2/3-x/3 ]O 2 materials were also examined. The superlattice peak positions of Li[Li 1/3-2x/3 Ni x Mn 2/3-x/3 ]O 2 materials changed monotonically with Ni content, as did the main peaks, demonstrating that the superlattice peaks originate from solid solutions and are not caused by any separate phase such as Li 2 MnO 3 in a composite.
FAULTS results on Li[Li 1/3-2x/3 Ni x Mn 2/3-x/3 ]O 2 materials showed that stacking fault probability increased with Ni content. Hence, it is believed that presence of aliovalent ions such as Ni 2+ in the TM layer can perturb the stacking order along the c-axis and thus the broadening of the superlattice peaks of Li[Li 1/3-2x/3 Ni x Mn 2/3-x/3 ]O 2 materials. It is expected that the presence of Co 3+ ions in the TM layer can also induce the stacking faults in the same way as Ni 2+ ions.