Nuclear quantum effects on the thermal expansion coefficient of hexagonal boron nitride monolayer

This work examines the importance of vibrational delocalization on a basic thermomechanical property of a hexagonal boron nitride monolayer, namely its thermal expansion coefficient (TEC). Using a recently parametrized bond-order potential of the Tersoff type, the TEC was theoretically obtained from the thermal variations of the lattice parameter a(T) calculated using three different methods: (i) the quasiharmonic approximation; (ii) its anharmonic improvement based on self-consistent phonons; (iii) fully anharmonic Monte Carlo simulations possibly enhanced within the path-integral framework to account for nuclear quantum effects. The results obtained with the three methods are generally consistent with one another and with other recently published data, and indicate that the TEC is negative at least up to ca. 700 K, quantum mechanical effects leading to a significant expansion by about 50% relative to the classical result. Comparison with experimental data on bulk hexagonal BN suggests significant differences, which originate from possible inaccuracies in the model that tend to underestimate the lattice parameter itself, and most likely from the 2D nature of the monolayer and the key contribution of out-of-plane modes. The effects of isotopic purity in the natural abundances of boron are found to be insignificant.