Stabilization mechanism of tetragonal structure in hydrothermal synthesized BaTiO$_3$ nanocrystal

Higher OH concentration is identified in tetragonal barium titanate (BaTiO$_3$) nanorods synthesized by a hydrothermal method with 10 vol% ethylene glycol solvent [Inada, M. $et$ $al$. $Ceram.$ $Int.$ $2015$, $41$, 5581-5587]. This is apparently inconsistent with the known fact that higher OH concentration in the conventional hydrothermal synthesis makes pseudo-cubic BaTiO$_3$ nanocrystals more stable than the tetragonal one. To understand where and how the introduced OH anions are located and behave in the nanocrystals, we applied $ab$ $initio$ analysis to several possible microscopic geometries of OH locations, confirming the relative stability of the tetragonal distortion over the pseudo-cubic one due to the preference of trans-type configurations of OH anions. We also performed FTIR and XRD analysis, all being in consistent with the microscopic picture established by the $ab$ $initio$ geometrical optimizations.