Defect Thermodynamics in Nonstoichiometric Alluaudite-Based Polyanionic Materials for Na-Ion Batteries

Sodium iron sulfate in the form of alluaudite Na_2+2xFe_2-x(SO₄)₃ (or NFSx) has emerged as one of the most promising cathodes for Na-ion batteries due to its highest Fe^2+/3+ redox potential, low cost, sustainability, and high rate capability. Unlike most of the other cathodes, NFSx generally crystalizes in its nonstoichiometric form with partial Na substitution for Fe sites and contains a small amount of impurities. However, profound explanations behind this inherent behavior including others, like phase stability, configurational structure, and defect formation are still ambiguous. We therefore performed first-principles calculations combined with a random swapping method to determine the minimum energy configurations of NFSx (with x = 0, 0.25, and 0.5) and find a correlation between the Na distribution pattern and energetics in which the site preference for Na⁺ ion is in a sequence of Na4 > Na1 > Na2 > Na3. Our result points out that the nonstoichiometry cannot be properly described under the framework of primitive structures. Moreover, we investigated phase stability diagrams and defect formations based on thermodynamic criteria. Our predicted phase diagrams can explain the inevitable impurity precipitation, which can be reduced as x diminishes. Defect formation analysis indicates an unlikely formation of channel blockage and identifies the dominant formation of Fe_Na + V_Na and Na_i + Na_Fe complexes. While the former can become spontaneous in a Na-deficient environment, the latter occurs mainly in NFS0 and accommodates the presence of nonstoichiometry.