Surface energy and surface proton order of the ice Ih basal and prism surfaces

Abstract

Density-functional theory (DFT) is used to examine the basal and prism surfacesof ice Ih. Similar surface energies are obtained for the two surfaces; however,in each case a strong dependence of the surface energy on surface protonorder is identified. This dependence, which can be as much as 50% of theabsolute surface energy, is significantly larger than the bulk dependence (<1%) on proton order, suggesting that the thermodynamic ground state of the ice surface willremain proton ordered well above the bulk order–disorder temperature of about 72 K. Onthe basal surface this suggestion is supported by Monte Carlo simulations withan empirical potential and solution of a 2D Ising model with nearest neighborinteractions taken from DFT. Order parameters that define the surface energyof each surface in terms of nearest neighbor interactions between dangling OHbonds (those which point out of the surface into vacuum) have been identified andare discussed. Overall, these results suggest that proton order–disorder effectshave a profound impact on the stability of ice surfaces and will most likely havean effect on ice surface reactivity as well as ice crystal growth and morphology.