Ge(110) c(8×10) reconstructions stabilized by vibrations

• Ab initio DFT calculations reveal novel Ge(110) c(8 × 10) structures related with adatom clusters and surface vacancies. • Vibrational entropy must be included to reconcile DFT-derived surface free energies with experimental observations. • The unit cell of Ge(110) c(8 × 10) unit cell contains surface divacancies , in addition to the pentamers visible in STM images. • These divacancies play a crucial role in phase transitions on Ge(110). Determining the atomic structure of a surface is essential for reliable simulations and in-depth exploration of chemical and atomic-scale physical processes. Using Ge(110) c(8 × 10) as a case study, this work employs Density Functional Theory (DFT) calculations to examine the role of vibrational entropy in surface reconstruction stability. The Ge(110) c(8 × 10) unit cell consists of interstitial-based pentamers (Universal Building Block model, UBB) interspersed with regions appearing in STM images as unreconstructed. DFT calculations predict that adding more pentamers lowers the surface energy, contradicting experimental findings. This discrepancy is resolved when vibrational entropy is accounted for and surface divacancies are introduced in addition to the UBB pentamers. These divacancies are similar to those proposed earlier in the Tetramer-Heptagonal and Tetragonal Ring (THTR) reconstruction model. The nearest neighbors of the vacancy sites are rebonded as on monatomic step edges. The differences in the vibrational entropy contributed by pentamers, divacancies, and unreconstructed surface stabilize Ge(110) c(8 × 10) reconstructions with the pentamer density observed experimentally. The presence of divacancies is conceptually consistent with the presence of monatomic steps in Ge(110) “16×2″, the most stable reconstruction of this surface.