Visualizing defect energetics.

Defect energetics impact most thermal, electrical and ionic transport phenomena in crystalline compounds. The key to chemically controlling these properties through defect engineering is understanding the stability of (a) the defect and (b) the compound itself relative to competing phases at other compositions in the system. The stability of a compound is already widely understood in the community using intuitive diagrams of formation enthalpy (ΔH) vs. composition, in which the stable phases form the 'convex-hull'. In this work, we re-write the expression of defect formation enthalpy (ΔH) in terms of the ΔH of the compound and its defective structure. We show that ΔH for a point defect can be simply visualized as intercepts in a two-dimensional convex-hull plot regardless of the number of components in the system and choice of chemical conditions. By plotting ΔH of the compound and its defects all together, this visualization scheme directly links defect energetics to the compositional phase stability of the compound. Hence, we simplify application level defect thermodynamics within a widely used visual tool understandable from basic materials science knowledge. Our work will be beneficial to a wide community of experimental chemists seeking to build an intuition for appropriate choice of chemical conditions for defect engineering.