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.
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