Imperfections are not 0 K: free energy of point defects in crystals

Defects determine many important properties and applications of materials, ranging from doping in semiconductors, to conductivity in mixed ionic-electronic conductors used in batteries, to active sites in catalysts. The theoretical description of defect formation in crystals has evolved substantially over the past century. Advances in supercomputing hardware, and the integration of new computational techniques such as machine learning, provide an opportunity to model longer length and time-scales than previously possible. In this Tutorial Review, we cover the description of free energies for defect formation at finite temperatures, including configurational (structural, electronic, spin) and vibrational terms. We discuss challenges in accounting for metastable defect configurations, progress such as machine learning force fields and thermodynamic integration to directly access entropic contributions, and bottlenecks in going beyond the dilute limit of defect formation. Such developments are necessary to support a new era of accurate defect predictions in computational materials chemistry

Models of oxygen occupancy in lead phosphate apatite Pb10(PO4)6O

Lead phosphate apatite, the parent compound of the proposed room-temperature superconductor LK-99, features a [Pb10(PO4)6]II scaffold with a charge-compensating oxide ion. This O–II occupies a 4e site in the P63/m unit cell, with 25% probability on average. We model the occupancy of this site from substoichiometric (x = 0) to superstoichiometric (x = 4) regimes in Pb10(PO4)6Ox. Doping is predicted by adjusting the oxygen composition within the ⟨0001⟩ channel, with evidence for strong O–O correlation. This behavior introduces a sensitivity to the crystal growth and annealing conditions, with an opportunity for novel functionality to emerge