A new and promising P2‐type layered oxide, Na5/6[Li1/4Mn3/4]O2 is prepared using a solid‐state method. Detailed crystal structures of the sample are analyzed by synchrotron X‐ray diffraction combined with high‐resolution neutron diffraction. P2‐type Na5/6[Li1/4Mn3/4]O2 consists of two MeO2 layers with partial in‐plane √3a × √3a‐type Li/Mn ordering. Na/Li ion‐exchange in a molten salt results in a phase transition accompanied with glide of [Li1/4Mn3/4]O2 layers without the destruction of in‐plane cation ordering. P2‐type Na5/6[Li1/4Mn3/4]O2 translates into an O2‐type layered structure with staking faults as the result of ion‐exchange. Electrode performance of P2‐type Na5/6[Li1/4Mn3/4]O2 and O2‐type Lix[Li1/4Mn3/4]O2 is examined and compared in Na and Li cells, respectively. Both samples show large reversible capacity, ca. 200 mA h g−1, after charge to high voltage regardless of the difference in charge carriers. Structural analysis suggests that in‐plane structural rearrangements, presumably associated with partial oxygen loss, occur in both samples after charge to a high‐voltage region. Such structural activation process significantly influences electrode performance of the P2/O2‐type phases, similar to O3‐type Li2MnO3‐based materials. Crystal structures, phase‐transition mechanisms, and the possibility of the P2/O2‐type phases as high‐capacity and long‐cycle‐life electrode materials with the multi‐functionality for both rechargeable Li/Na batteries are discussed in detail.

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Z-Rietveld is a program suite for Rietveld analysis and the Pawley method; it was developed for analyses of powder diffraction data in the Materials and Life Science Facility of the Japan Proton Accelerator Research Complex. Improvements have been made to the nonlinear least-squares algorithms of Z-Rietveld so that it can deal with singular matrices and intensity non-negativity constraints. Owing to these improvements, Z-Rietveld successfully executes the Pawley method without requiring any constraints on the integrated intensities, even in the case of severely or exactly overlapping peaks. In this paper, details of these improvements are presented and their advantages discussed. A new approach to estimate the number of independent reflections contained in a powder pattern is introduced, and the concept of good reflections proposed by Sivia [J. Appl. Cryst. (2000), 33, 1295-1301] is shown to be explained by the presence of intensity non-negativity constraints, not the intensity linear constraints. research papers J. Appl. Cryst. (2012). 45, 299-308 R. Oishi-Tomiyasu et al. Application of matrix decomposition in Z-Rietveld 305 Figure 3 Complementary cumulative distribution function of the chi-squared distribution f ðx; NÞ.