Journal
PHYSICAL REVIEW B
Volume 87, Issue 9, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.87.094112
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Funding
- NSF through the Cornell Center for Materials Research [DMR-1120296]
- CAREER award [DMR-1056587]
- Texas Advanced Computing Center [TG-DMR050028N]
- Direct For Mathematical & Physical Scien
- Division Of Materials Research [1056587] Funding Source: National Science Foundation
- Division Of Materials Research
- Direct For Mathematical & Physical Scien [1542776] Funding Source: National Science Foundation
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Ripples in graphene can occur due to strain or thermal fluctuations and stabilize the two-dimensional material. Molecular dynamics simulations show that thermally induced ripples in graphene lead to angular deviations of the surface normal that agree with previous electron diffraction experiments [J. C. Meyer et al., Nature (London) 446, 60 (2007)]. We discover scaling relationships for the average angular deviations as a function of size of the graphene sheet L and averaging radius R. The average angle scales as exp{-c(R/L)(alpha)} with a scaling exponent alpha = 1 for single layer, 5/4 for bilayer, and 5/3 for trilayer graphene, respectively. We show how these angular deviations depend on temperature, strain, and layer numbers. The scaling relations can provide guidance to the optimization of properties that are sensitive to out-of-plane distortions. DOI: 10.1103/PhysRevB.87.094112
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