The interactions of same-row oxygen vacancies on rutile TiO$_2$(110)

摘要

Based on a dipolar-elastic model for oxygen vacancies on rutile (110), weevaluated analytically the overall energy of a periodic array of two vacanciesand extracted the interaction parameters from total-energy density functionaltheory (DFT) calculations. Our calculations show that the dipole model holdsfor next-nearest neighbor vacancies and beyond. The elastic-dipolar interactionvanishes for adjacent vacancies, but they still experience an electrostaticrepulsion. The proposed interaction model predicts a vacancy separationdistribution that agrees well with that determined in our ultra-high vacuumscanning tunneling microscopy experiments, and provides a perspective forunderstanding earlier DFT reports.