Vibrational-Entropy-Driven Compensation Mechanism on the Rutile TiO_{2} (111) Polar Surface

Polar surfaces, known for their unique electronic and chemical properties, play vital roles in catalysis and electronics, yet their atomic structures remain difficult to resolve due to intrinsic instability often mitigated by surface reconstruction. However, the role of entropy, particularly vibrational entropy, in stabilizing such reconstructions is not well understood. Herein, we combine in situ atomic-resolution spherical aberration-corrected scanning transmission electron microscopy, density-functional theory calculations, and a differential evolution algorithm for global structural search to resolve the (1×1) reconstructed structure of the classical polar rutile TiO_{2}(111) surface. Crucially, we demonstrate that this reconstruction is predominantly stabilized by vibrational entropy at high temperatures. These findings not only highlight the importance of vibrational entropy in surface reconstructions but also advance our understanding of compensation mechanisms on polar surfaces by highlighting entropy as a critical stabilizing factor.