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Striped, honeycomb, and twisted moire patterns in surface adsorption systems with highly degenerate commensurate ground states

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journal contribution
posted on 2017-12-08, 16:10 authored by Ken R. Elder, C.V. Achim, E. Granato, S.C. Ying, Tapio Ala-NissilaTapio Ala-Nissila
Atomistically thin adsorbate layers on surfaces with a lattice mismatch display complex spatial patterns and ordering due to strain-driven self-organization. In this work, a general formalism to model such ultrathin adsorption layers that properly takes into account the competition between strain and adhesion energy of the layers is presented. The model is based on the amplitude expansion of the two-dimensional phase field crystal (PFC) model, which retains atomistic length scales but allows relaxation of the layers at diffusive time scales. The specific systems considered here include cases where both the film and the adsorption potential can have either honeycomb (H) or triangular (T) symmetry. These systems include the so-called (1 × 1), (√3 × √3) R30∘, (2 × 2), (√7 × √7) R19.1∘, and other higher order states that can contain a multitude of degenerate commensurate ground states. The relevant phase diagrams for many combinations of the H and T systems are mapped out as a function of adhesion strength and misfit strain. The coarsening patterns in some of these systems is also examined. The predictions are in good agreement with existing experimental data for selected strained ultrathin adsorption layers.


K.R.E. acknowledges financial support from the National Science Foundation under Grant No. DMR-1506634, and from the Aalto Science Institute. C.V.A. acknowledges financial support from CRHIAM-FONDAP-CONICYT Project No. 15130015. E.G. acknowledges support from CNPq (Conselho Nacional de Desenvolvimento Cientifico e Tecnologico) in Brazil. S.C.Y. acknowledges support from the Brazilian Initiative funded by the Watson Institute of Brown University. T.A-N. has been supported in part by the Academy of Finland through its Centres of Excellence Programme (2012–2017) under Project No. 251748. We acknowledge the computational resources provided by the Aalto Science-IT project and the CSC IT Center for Science, Finland.



  • Science


  • Mathematical Sciences

Published in

Physical Review B






195439 - 195439


ELDER, K.R. ... et al, 2017. Striped, honeycomb, and twisted moire patterns in surface adsorption systems with highly degenerate commensurate ground states. Physical Review B, 96 (19), Article no. 195439.


© American Physical Society


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This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

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This paper was published in the journal Physical Review B and the definitive published version is available at https://doi.org/10.1103/PhysRevB.96.195439.






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