Thermodynamic Guidelines for Maximum Solubility

When attempting to synthesize a doped compound, it is natural to prepare nominal compositions that emulate changes due to the expected defect. In systems with three or more components, simply forming multiphase samples along these intended compositions does not necessarily ensure achieving the actual maximum solubility of the added component. With several examples, we show cases where the solubility limit was mistakenly underestimated. The study of the true maximum solubility in such complex materials can be quite intensive and can benefit from simplifying initial assessments, which are guided by thermodynamics. Using defect thermodynamics, we summarize in simple graphical guidelines how the maximum dopant solubility caused by neutral and charged defects can be identified using the stoichiometry of the impurity phases in equilibrium. These predictive guidelines─applicable to systems regardless of number of elements involved─justify why the intuitive nominal (or intended) compositions should yield maximum solubility due to the expected defect but only if (a) the nominal composition is accurate (no inadvertent loss of a component) and (b) the oppositely charged defects that are more sensitive to chemical conditions form in relatively smaller amounts. In a real system where the nominal composition is not perfectly accurate, observing impurity phases whose stoichiometries are consistent with the guidelines (for the expected defect) is necessary to establish the true maximum solubility limit.