  Graphite is the most widely used and among the most widely-studied anode
materials for lithium-ion batteries. With increasing demands on lithium
batteries to operate at lower temperatures and higher currents, it is crucial
to understand lithium intercalation in graphite due to issues associated with
lithium plating. Lithium intercalation into graphite has been extensively
studied theoretically using density functional theory (DFT) calculations,
complemented by experimental studies through X-ray diffraction, spectroscopy,
optical imaging and other techniques. In this work, we present a first
principles based model using DFT calculations, employing the BEEF-vdW as the
exchange correlation functional, and Ising model to determine the phase
transformations and subsequently, the thermodynamic intercalation potential
diagram. We explore a configurational phase space of about 1 billion structures
by accurately determining the important interactions for the Ising model. The
BEEF-vdW exchange correlation functional employed accurately captures a range
of interactions including vdW, covalent and ionic interactions. We incorporate
phonon contributions at finite temperatures and configurational entropy to get
high accuracy in free energy and potentials. We utilize the built-in error
estimation capabilities of the BEEF-vdW exchange correlation functional and to
develop a methodological framework for determining the uncertainty associated
with DFT calculated phase diagrams and intercalation potentials. The framework
also determines the confidence of each predicted stable phase. The confidence
value of a phase can help us to identify regions of solid solutions and phase
transformations accurately.
