  The thermodynamics of point defects is crucial for determining the functional
properties of materials. Defect stability is typically assessed using
grand-canonical defect formation energy, which requires deducing the
equilibrium chemical potential or Fermi level. This process is complicated by
the interplay of chemical potential and Fermi level and their dependence on
composition and temperature. The grand-canonical formation energy is added to
the bulk Gibbs energy, creating a defect-centric framework where each new
defect state needs a distinct Gibbs energy formulation. The CALPHAD method
offers a more flexible alternative by integrating defect energies into the
total Gibbs energy model, allowing easier extrapolation to complex
compositions. CALPHAD unifies the analysis of chemically and electronically
driven defects using chemical composition as the primary variable. However, the
Compound Energy Formalism (CEF) used in CALPHAD has limitations, such as a lack
of clear connections between defect formation energies and Gibbs energy
parameters and an exponential increase in complexity with added chemical or
charge variations. We present the theoretical derivation of the Defect Energy
Formalism (DEF), which overcomes CEF limitations by establishing explicit
relationships between absolute defect energies - independent of chemical
potential and Fermi level - and the Gibbs energy parameters of defective
compounds. This results in a first-principles model for dilute defects,
eliminating the need for model fitting to experimental or simulation data. DEF
reduces the complexity of CEF by applying the superposition of absolute defect
energies, making it feasible for modeling multi-component and chemically
complex compounds. This paper presents a formal derivation of DEF and offers
guidelines for its application, promising more accurate and efficient
thermodynamic modeling of defective materials.
