Regular Article

Isotopic effects in structural properties of graphene

Instituto de Ciencia de Materiales de Madrid, Consejo Superior de Investigaciones Científicas (CSIC), Campus de Cantoblanco, 28049 Madrid, Spain

^a e-mail: ch@icmm.csic.es

Received: 28 April 2020
Received in final form: 23 June 2020
Published online: 3 August 2020

Abstract

Isotopic effects are relevant to understand several properties of solids, and have been thoroughly analyzed along the years. These effects may depend on the dimensionality of the considered solid. Here we assess their magnitude for structural properties of graphene, a paradigmatic two-dimensional material. We use path-integral molecular dynamics simulations, a well-suited technique to quantify the influence of nuclear quantum effects on equilibrium variables, especially in cases where anharmonic effects are important. Emphasis is put on interatomic distances and mean-square displacements, as well as on the in-plane area of the graphene layer. At low temperature, the relative difference in C–C distance for ¹³C and ¹⁴C, with respect to ¹²C, is found to be − 2.5 and − 4.6 × 10⁻⁴, respectively, larger than in three-dimensional carbon-based materials such as diamond. For the in-plane area, the relative changes amount to − 3.9 and − 6.9 × 10⁻⁴. The magnitude of anharmonicity in the lattice vibrations is estimated by comparing the internal energy and atomic vibrational amplitudes with those derived from a harmonic approximation.