Ground-state phase diagram of Na_xCoO₂: correlation of Na ordering with CoO₂stacking sequences

Abstract

We have proposed a Hamiltonian that takes into account both Na-Na interactions and coupling between Na ions and CoO(2) layers. By a combination of the Monte Carlo and first-principles approaches, all the possible stacking sequences of CoO(2) layers together with the Na ordering have been obtained. In particular, an infinite series of ground states of Na ordering has been predicted in P3-Na(x)CoO(2). We have obtained the ground-state phase diagram with the variation of Na concentration, which explains well the complex variation of the CoO(2) stacking sequences. Our calculations show that the ordering of Na ions to minimize the Coulomb interaction is the main cause of the variation of the CoO(2) stacking sequences.

Review—Manganese-Based P2-Type Transition Metal Oxides as Sodium-Ion Battery Cathode Materials

“…63 The global instability index, a measure of the valence violations for the whole material, was plotted as a function of x, for O3-and P2-Na x CoO 2 and was found to be in good agreement with the formation energies obtained by Wang et al for these phases (shown in Figure 7a). 64 This study highlights the importance of lattice strains in explaining the highly unstable Na x MO 2 phases obtained at low Na content. 63 Challenges for Mn 3+ /Mn 4+ systems.-Manganese-based sodium-ion battery cathode materials fulfill the requirements for low cost, sustainable, and environmentally friendly energy storage technologies.…”

“…The balance between all of these interactions is highly sensitive to sodium content, and various cationic distributions are observed for each composition along the electrochemical cycle. 67 64 This study used a combination of ab initio Density functional Theory (DFT) calculations within the Generalized Gradient Approximation (GGA) and Monte Carlo simulations to determine the ground state Na + ion/vacancy arrangements, as a function of x, for a variety of structural polytypes (O1, O2, O3, P2, and P3). The resulting 0 K phase stability diagram and the formation energies obtained for the lowest energy Na + ion/vacancy ordered arrangements, plotted as a function of x, are presented in Figure 7a.…”

“…Meng et al obtained a global energy minimum for the P2 phase for x = 0.75, 129 while Wang et al found a global energy minimum at ca. 0.33, 64 presumably due to the different sizes of the supercells used, hence the different Na + ion/vacancy arrangements explored in the two studies (and the different level of theory). On the other hand, an experimental study by Lei et al explored the Na x CoO 2 synthesis phase diagram.…”

Vacancy Ordering in O3 -Type Layered Metal Oxide Sodium-Ion Battery Cathodes

“…The trial set consists of structures that commonly occur as ground-state orderings on the triangular lattice, such as those determined by Kaburagi and Kanamori [28] to be ground states with up to third-neighbor interactions, as well as the possible ground states for O3-NaCoO 2 found by Wang, Ding, and Ni [22]. In addition, potential structures are generated at Na concentrations of 1=4, 1=3, 1=2, 2=3, and 3=4.…”

“…Such Na-vacancy ordering occurs through clear first-order transitions in single TM compounds and therefore can be best studied in these systems. Though some work has been done on predicting alkali ion ordering in several Li-ion and Na-ion systems [21][22][23][24][25], this has been undertaken for the entire intercalation range in only a very few cases and with little comparison between similar systems.…”