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Layered Li(Ni,Mn,Co,)O$_2$ (NMC) presents an intriguing ternary alloy designspace for optimization as a cathode material in Li-ion batteries. Recently, thehigh cost and resource limitations of Co have added a new design constraint andhigh Ni-containing NMC alloys have gained enormous attention despite possibleperformance trade-offs. It is not fully understood if this material space is adisordered solid solution at room temperature and any arbitrary combination canbe used or if there exist distinct transition metal orderings to whichmeta-stable solid solutions will decay during cycling and affect performance.Here, we present a high fidelity computational search of the ternary phasediagram with an emphasis on high-Ni, and thus low Co, containing compositionalphases to understand the room temperature stability of the ordered anddisordered solid solution phases. This is done through the use of densityfunctional theory training data fed into a reduced order model Hamiltonian thataccounts for effective electronic and spin interactions of neighboringtransition metal atoms at various lengths in a background of fixed compositionand position lithium and oxygen atoms. This model can then be solved to includefinite temperature thermodynamics into a convex hull analysis to understand theregions of ordered and disordered solid solution as well the transition metalorderings within the ordered region of the phase diagram. We find that for themajority of transition metal compositions of the layered material, specificallymedium to high-Ni content, prefer transition metal ordering and predict thecollection of preferred compositions in the ordered region.

Towards Ultra Low Cobalt Cathodes: A High Fidelity Computational Phase Search of Layered Li-Ni-Mn-Co Oxides