Identification and Structural Decomposition of Hidden Defect Configurations: A Case Study of Charged Oxygen Divacancies in HfO$_2$

Abstract

Extensive configurational searches have revealed hidden defect structures in crystalline compounds, yet how their local bonding arrangements modify the surrounding atomic environment remains less well understood. We examine this question in hafnium oxide (HfO$_2$), which hosts energetically competing monoclinic (M), tetragonal (T), and polar orthorhombic (PO) polymorphs. For the $c$-axis oxygen-divacancy complex ($T_c$), a local-distortion search with density-functional theory (DFT) relaxation under tetragonal-lattice confinement identifies a hidden family of low-energy configurations ($T_c^{*}$). For the fully charged complex ($2\mathrm{V}_{\mathrm{O}}^{2+}$), structural decomposition using Smooth Overlap of Atomic Positions (SOAP) descriptors reveals mixed M-, T-, and PO-like character, supported by independent analyses of Hf coordination and bond geometry. The idealized $T_c$ reference connects barrierlessly to the lowest-energy mixed-motif $T_c^{*}$ configuration, lowering the energy by $18.4$ meV/f.u. within the confined landscape. After releasing the lattice constraint, we compare transformation pathways to M and PO using solid-state nudged elastic band calculations with cell-relaxed endpoints. The respective barriers increase from $6.9$ and $10.1$ meV/f.u. for the idealized reference to $26.9$ and $15.3$ meV/f.u. for the $T_c^{*}$-derived structure. The larger increase for M makes PO, rather than M, the lower-barrier branch. This case study shows how structural decomposition connects hidden defect configurations with changes in the surrounding atomic environment and kinetic branching between competing polymorphs.