Rational Design Principles for Na- and Li-ion Carbon Anodes from Interlayer Spacing Control

Graphite, the standard commercial anode for Li-ion batteries, is thermodynamically incompatible with Na-ion batteries, leading researchers to search for alternative C-based structures (e.g., hard carbon, expanded graphite). In a simplified picture, the main idea of such search relies on identifying disordered C structures with a large interlayer spacing and distribution of local structural motifs (e.g., pores) with target electrochemical properties. Such exploration is typically done via trial-and-error experimentation, which often does not allow precise understanding of the role of interlayer distance and even Na/Li-ion intercalation in the electrochemical performance. Motivated by this, using density-functional theory and cluster expansion, we establish a structure-property relationship for Li- and Na-intercalation across a range of graphite interlayer spacings and stacking arrangements. We show that Na intercalation becomes thermodynamically possible in large concentrations above 4.21 {\AA} even without a change in interlayer spacing. Conversely, Li intercalation has a narrow optimal window, with maximum capacity (close to the commercial limit) at approximately 3.75 {\AA}, while larger spacings (e.g., 4.58 {\AA}) quickly reduce Li storage capacity. We also find that AA-stacked domains consistently offer stronger ion bonding and higher voltages than AB-stacked domains for both ions. Our results, thus, not only explain the role of metal ion intercalation in the electrochemical performance, but also clarify the fundamental design trade-offs for expanded C anodes, offering practical targets and interlayer distance ranges for the independent optimization of the next generation of negative electrodes for metal-ion batteries.