Phase Diagrams for Systems with Low Free Energy Variation:  A Coupled Theory/Experiments Method Applied to Li-Graphite

Abstract

The paper presents a fast and efficient method to compute phase diagrams using first-principles methods and statistical physics coupled with experimental techniques. The method is applied to lithium intercalated graphite for which evidence of experimental anomalies have recently questioned the currently accepted stage II/stage I two-phase transformation in the 0.5 ≤ x ≤ 1.0 composition range. Our coupled experimental and theoretical analysis has led to a full determination of the Li x C6 phase diagram in this range of composition, revealing previously unknown phase transitions and the characterization of at least two new phases.

Li intercalation in graphite: A van der Waals density-functional study

“…6(b) followed by a coexistence of the stage 2 compounds LiC 32 and LiC 12 for 3/16 < x < 1/2 (green line), and finally a coexistence of the stage 2 compound LiC 12 and the stage 1 compound LiC 6 for 1/2 < x < 1 (blue line). Experimentally the stability and structures of the LiC 12 and LiC 6 compounds are well established [12][13][14][15]22]. Also quite consistently a stable phase with a composition around x ≈ 0.2 is observed, which we attribute to the √ 7× √ 7 dilute stage 2 structure.…”

“…This means that PBE-PBE yields Li x C 6 compounds where the Li concentration x is a simple monotonic function of the Li chemical potential, like in a simple lattice gas. This is clearly at variance with experiment, where phases with specific compositions are found to be thermodynamically stable [12][13][14][15]22].…”

“…[22] and treat the intermediate Li x C 6 compositions as alloys of occupied and unoccupied Li lattice sites. Positions above the centers of C 6 hexagons count as possible lattice sites for Li atoms, as in the structures of Fig.…”

“…Upon decreasing the Li content to x < 1/N , one then moves to the next equilibrium plateau between stage N + 1 and stage N phases. This simple model is under scrutiny * e.hazrati@science.ru.nl † g.dewijs@science.ru.nl ‡ g.h.l.a.brocks@utwente.nl though, as neutron diffraction experiments give evidence for the formation of phases with partially filled Li layers instead of fully completed higher-order stage N phases [14], and calculations suggest the relative stability of certain partially filled structures [22].…”

Diffusion of alkali metals in the first stage graphite intercalation compounds by vdW-DFT calculations

“…The Li-GIC system has been intensively studied for decades because of its use in rechargeable lithium ion batteries, [1][2][3][4][5][6][7][8] while Na-GICs are model materials for Na-ion battery anodes. [9][10][11][12][13] Interactions between sodium and graphite is also a key factor in the degradation of cathode lining in aluminium electrolysis cells.…”