Surface Energy and Surface Proton Order of IceIh

Abstract

Ice Ih is comprised of orientationally disordered water molecules giving rise to positional disorder of the hydrogen atoms in the hydrogen bonded network of the lattice. Here we arrive at a first principles determination of the surface energy of ice Ih and suggest that the surface of ice is significantly more proton ordered than the bulk. We predict that the proton order-disorder transition, which occurs in the bulk at $72 K, will not occur at the surface at any temperature below surface melting. An order parameter which defines the surface energy of ice Ih surfaces is also identified. DOI: 10.1103/PhysRevLett.101.155703 PACS numbers: 64.60.Cn, 68.47.Àb, 82.65.+r Ice Ih, the normal form of ice, is built from water molecules arranged on a tetrahedral lattice, subject to a set of rules known as the ice rules [1]. These rules allow for orientational disorder of the molecules, which is discussed in terms of the positional disorder of the hydrogen atoms, a phenomenon known as proton disorder. Under ambient pressures, ice Ih is the stable phase down to $72 K [2], below which a proton ordered (ferroelectric) phase known as ice XI becomes the ground state. In practice, the ordering transformation from ice Ih to the lowest total energy ice XI phase rarely happens since, as the temperature is lowered to the transition temperature, proton motion comes to a halt. This leaves the crystal out of equilibrium at below 72 K with residual entropy. Indeed, ice Ih is so resistant to transforming from ice Ih into ice XI that a dopant that accelerates proton rearrangement (KOH) is usually added to make it occur.Given the experimental difficulties in probing the ice Ih-XI transition, molecular simulations are very useful [3][4][5]. In particular, in a tour de force study, density functional theory (DFT) was combined with a framework based on graph invariants to simulate the bulk ice Ih-XI transition. A transition temperature of 98 K was predicted, within 30 K of the experimental transition [5]. This demonstrates that DFT is appropriate for tackling the subtle question of proton order and disorder in ice, something which cannot necessarily be said about the many empirical potentials that otherwise describe many parts of the phase diagram of water well [6].Unlike in bulk ice, the understanding of the energetics of proton order at the surface is in its infancy [7,8]. This is true despite widespread interest in ice surfaces at low temperatures, motivated mainly by their catalytic role in atmospheric chemistries such as ozone depletion (see, e.g., [9]). Indeed, the understanding is so incomplete that the value of the surface energy-one of the most important quantities of any material-is well-established neither experimentally nor theoretically and how it is influenced by proton order is not known. Here, in arriving at an ab initio determination of the surface energy of the (0001) (basal plane) of ice Ih, we demonstrate that the energetics of proton ordering differs significantly at the surface compared to the bulk. Indeed, the range of...

Electronic and nuclear quantum effects on the ice XI/ice Ih phase transition

“…DFT calculations correctly reproduce the lattice structure 16 , and give the cohesive energy of ferroelectric-ordered ice to be larger than either antiferroelectric-ordered or disordered ices 17,18 . That is, ferroelectric-ordered ice is the stable ground state.…”

“…In this paper we focus on the phase transition between proton ordered (ice XI) and proton disordered (ice Ih) hexagonal ice. This phase transition has been subject of a large number of experimental [4][5][6][7][8] and theoretical studies [9][10][11][12][13][14][15][16][17][18][19][20][21] . However, open questions remain about the mechanisms behind the phase transition and the importance of nuclear quantum effects in the temperature of the transition 22 .…”

Spin ice Thin Film: Surface Ordering, Emergent Square ice, and Strain Effects

“…Although often described as a liquid layer, its conductivity is orders of magnitude larger than that of bulk liquid water. This is admittedly a vastly more complex problem than our model spin ice [66][67][68]. However, on cleaving a surface off an ice crystal, one might expect polarization charge to be induced in an analogous manner.…”

First-Principles Framework to Compute Sum-Frequency Generation Vibrational Spectra of Semiconductors and Insulators

“…We sampled 8 proton disordered and 8 proton ordered surfaces (each slab had 2 surfaces). For proton ordered surfaces, we considered the Fletcher's striped phase, which was predicted to be one of the most stable phases of ice I h basal surfaces [24]. We computed the bulk contributions χ BQ eff and χ…”

“…[18][19][20][21][22][23]. To our knowledge our study represents the first comprehensive ab initio formulations of SFG spectra, as well as the first ab initio simulation of the SFG spectra of ice [18,24].…”