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For a color version of this figure, see www.iste.co.uk/monconduit/batteries.zip

P3-type Na_xCoO₂ can also be obtained as a Na deficient (0.5 ≤ x < 1) and low-temperature phase by a solid state reaction (Fouassier et al. 1973). In the P3-type layered structure, alkali metal ions occupy prismatic sites in the interslab space between MO₂ slabs stacking with AB BC CA array of oxygen packing along the c-axis and the number of MO₂ slabs is three in the hexagonal unit cell with space group of R3m. The P3 type is generally formed by electrochemical Na extraction from O3-type accompanied by the gliding of MO₂ slabs without breaking the M-O bonds. P3-type materials are often observed as Na-deficient intermediate phases transform from O3-type ones by Na extraction. Compared to the P3-type phase, the P2-type (β-RbScO₂-type) phase is recognized as a high-temperature one, and P2-type (γ-)Na_xCoO₂ is actually obtained by heating at a higher temperature than that for P’3-Na_xCoO₂ (Fouassier et al. 1973). The phase transition from P3- to P2-type phase is accompanied by breaking Co-O bonds by heating at high temperature and does not occur in a Na (de)intercalation reaction at room temperature. In the P2-type structure, alkali metal ions occupy prismatic sites in interslab space between MO₂ slabs stacking with an AB BA array of oxygen packing along the c-axis and the number of MO₂ slabs is two in the hexagonal unit cell with space group of P6₃/mmc. The P2-type phase can electrochemically transform into an O2-type phase by the gliding of MO₂ slabs without breaking the M-O bonds (Lu and Dahn 2001a) as explained in detail in section 1.2.3.

      The average valence of transition metals in O3-NaMO₂ (M = Ti, V, Cr, Mn, Fe, Co, Ni) and P2-Na_2/3MO₂ (M = V, Mn, Co) is +3 and +3.33, respectively. Tetravalent or higher valent metals are necessary for the crystallization of P2-type materials, and only V, Mn and Co oxides have been reported as single 3d transition metal P2 systems so far due to difficulty in formation of trivalent Ti and tetravalent Cr, Fe and Ni under ambient air or oxygen pressure. In contrast to the single 3d transition metal P2 system, multiple transition metal P2 systems can be stabilized by combining divalent Ni, trivalent Cr and Fe, tetravalent Ti and Mn. Moreover, monovalent alkali metal ions, pentavalent Bi and Sb, and hexavalent Te are also includable for stabilization of O3- and P2-type layered oxides. These transition metal elements dominate the charge/discharge capacity and redox potential of O3-NaMO₂ and P2-Na_2/3MO₂ in Na cells as well as the structural changes accompanied by Na-extraction/insertion with the formation of Na/vacancy and charge orderings (or formation of dimers or trimers of transition metals).

1.2.2. Structural changes of O3-NaMO₂ by Na extraction

      Most O3-type materials generally transform in the O3 → P3 → O3 (→ O1) sequence by gliding of the MO₂ slab during Na extraction during the charging process (Kaufman and Van der Ven 2019) as shown in Figures 1.5 and 1.6(a). Note that O1-type CoO₂ was reported to be obtained via electrochemical Li extraction from LiCoO₂ in a Li cell (Amatucci et al. 1996). However, defect-free O1-type MO₂ including O1-CoO₂ has not been reported so far, although some literature reports defective O1-type MO₂ having migrated transition metal ions into the interslab spacing after Na extraction from NaMO₂ (Mariyappan et al. 2018b; Wang et al. 2019b). Non-hexagonal structures of O’3- and P’3-type phases are also formed in the compositional regions surrounding those of non-distorted O3- and P3-type phases. Furthermore, Na⁺/vacancy orderings in the interslab spacing are often observed for x = 2/3, 1/2 and 1/3 in Na_xMO₂ (Figure 1.6(b)), leading to voltage jumps in the charge-discharge profiles (Zandbergen et al. 2004; Toumar et al. 2015; Kaufman and Van der Ven 2019).

      Figure 1.5. Schematic illustrations of crystal structures reported for partly desodiated O3- and O’3-type Na_xMO₂. For a color version of this figure, see www.iste.co.uk/monconduit/batteries.zip

      Figure 1.6. (a) Calculated formation energies versus composition for Na_xCoO₂ configurations on the local convex hull of each host structure (top). Calculated zerotemperature equilibrium voltage curve (black) compared to experiment from Kubota et al. (2016) (gray) (bottom). (b) P3 ground-state orderings ζ and ∆, with Na shown in blue (top). O3 orderings with Na in yellow on the local convex hull of O3 for x = 1/3 and 1/2 in Na_xCoO₂ (bottom). Asterisks indicate that the ordering is above the global hull. Reprinted with permission from Kaufman and Van der Ven (2019). Copyright 2019, American Physical Society. For a color version of this figure, see www.iste.co.uk/monconduit/batteries.zip

1.2.3. Structural changes of P2-Na_xMO₂ by Na extraction

      Figure 1.7. Schematic illustrations of (a) P2-type and two choices of O2-type structures and (b) ideal O2 in choice 1 and a structural model with random stacking of O_f-e and O_e-f layers as completely desodiated [Ni,Mn]O₂ (left) and ideal OP4-type and a structural model with random stacking of P_P2 and O_O2 layers with simultaneous random stacking of O_f-e and O_e-f layers (right). Reprinted with permission from Kubota et al. (2018b) Copyright 2018, Wiley-VCH. (c) Na⁺/vacancy ordering observed for P2-Na_2/3CoO₂ and P′2-Na_1/2CoO₂. For a color version of this figure, see www.iste.co.uk/monconduit/batteries.zip

P2-type materials generally transform in the P2 → O2 sequence by gliding MO₂ slabs during Na extraction during the charging process (Lu and Dahn 2001a; Berthelot et al. 2011). However, the phase transition is not strictly accurate and is more complicated in the actual reaction. According to the literature (Lu and Dahn 2001a), O2-type phase contains stacking faults between two different O2-type stackings (Figure 1.7(a)). The two choices of slab-gliding, (1/3, 2/3, 0) and (2/3, 1/3, 0) vectors for the slab with BA oxygen-stacking in the P2-type AB BA stacking, form two types of O2-type structures possessing different oxygen stacking manners of AB CB and AB AC, respectively. Furthermore, the two O2-type stacking phases coexists with the P2-type one in the specific voltage plateau region at ~4.2 V. Our group proposed formation of the two different O2 types stacking and staking faults as a P2-O2 intergrowth structure for Na_2/3-xNi_1/4Mn_2/3Cu_1/12O₂ instead of the ideal OP4-type one (Figure 1.7(b)) with simulated synchrotron X-ray diffraction (XRD) patterns using DIFFaX software (Treacy et al. 1991; Kubota et al. 2017). Similar to O3 type, P2-type materials also have Na⁺/vacancy orderings in the interslab spacing typically for x = 2/3 and 1/2 in Na_xMO₂, as shown in Figure 1.7(c) (Hinuma et al. 2008; Berthelot et al. 2011; Lee et al. 2013).

      These phase transitions were usually confirmed by ex situ and in situ/operando XRD and transmission electron microscopy (TEM) measurements. The phase

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