Producing desired ice faces

The ability to prepare single-crystal faces has become central to developing and testing models for chemistry at interfaces, spectacularly demonstrated by heterogeneous catalysis and nanoscience. This ability has been hampered for hexagonal ice, I_h––a fundamental hydrogen-bonded surface––due to two characteristics of ice: ice does not readily cleave along a crystal lattice plane and properties of ice grown on a substrate can differ significantly from those of neat ice. This work describes laboratory-based methods both to determine the I_h crystal lattice orientation relative to a surface and to use that orientation to prepare any desired face. The work builds on previous results attaining nearly 100% yield of high-quality, single-crystal boules. With these methods, researchers can prepare authentic, single-crystal ice surfaces for numerous studies including uptake measurements, surface reactivity, and catalytic activity of this ubiquitous, fundamental solid.Studies of model, single-crystal surfaces have revolutionized understanding of a vast array of heterogeneous catalysts and nanoparticles ranging from pure metals to alloys to semiconductors. Applying the single-crystal surface strategy to ice––arguably one of the most fundamental and ubiquitous hydrogen-bonded interfaces––has been limited due to challenges associated with surface generation. As a result, questions about molecular-level dynamics, surface binding site patterns, and the molecular-level structure remain unanswered (1). Several strategies have been adopted for studying ice: (i) Depositing solid water on a metal or ionic substrate that matches the oxygen lattice (2, 3). However, ice on a substrate often has distinctly different properties from those of neat ice; indeed, such ice can even be hydrophobic (4, 5)! (ii) Uptake measurements often use a Knudsen cell with vapor-deposited ice on a substrate (6) or compacted, finely divided, artificial snow (7) to arrive at a molecular-level picture for gas–particle interaction despite the irregular, highly variable surfaces used. (iii) Small crystallites can be well characterized but, as highlighted by Libbrecht and Rickerby (8), results can be clouded by competition from nearby crystallites; small faces compete with adjacent faces. In addition, crystallites are perturbed by the supporting surface. It is therefore desirable to prepare macroscopic samples with known faces.Interactions at ice surfaces have a particularly profound effect on climate. For example, correlational studies suggest that rain formation depends on ice particles in clouds (9), but not all ice-containing clouds yield rain. It is thought that variation in supersaturation and the mechanism for gathering water molecules by ice particles profoundly affects precipitation. Discrepancies between experiment and theory are often rationalized as a result of irregular shapes, inelastic scattering, or differing binding sites leaving large uncertainties for climate models (10). More reproducible, well-characterized surfaces of I_h––the most stable form of ice at ambient pressure––are needed to bring clarity.Ice is unusual in that the macroscopic sample does not reveal the crystal lattice orientation. Neighboring grain lattice orientation is a critical issue in the ice-core and glaciology communities (11). Hence, previous work (12–14) focused on determining grain orientation with respect to the grain boundary. The most quantitative of these are the two methods of Matsuda (12). The first uses etch pits measuring lengths inside the pit. Large uncertainties in length measurements result in large uncertainties in lattice axis orientation angles; this is not a major issue for grain growth studies but is a serious problem for generating targeted faces. The second method measures only the azimuths, thus incompletely determining orientation. Both methods break down if the optic axis is near-parallel to the surface, and neither provides the tools required to accurately orient a macroscopic sample to generate a targeted face. Lattice orientation could be determined with X-ray methods (15, 16) provided such determination includes a connection to the macroscopic sample. For wide-spread use, a laboratory-based method is preferable. This work describes two methods to fill this important need. The first uses pit perimeter ratio measurements; because the perimeter is sharp, accuracy is greatly improved. The second method locates the optic axis via cross-polarizers (11, 17), then precisely determines the hexagonal orientation via etching. Closed-form, analytical formulas are derived relating lattice orientation to the macroscopic sample. These orientation formulas feed into rotation matrices generating additional analytical formulas enabling precise cutting of any targeted face. The result is illustrated by cutting each of the three major ice faces. These techniques provide researchers with the tools needed to prepare neat ice surfaces.This work specifically describes face preparation from cylindrical boules (18); however, the method is easily adapted to any macroscopic, single-crystal geometry. Due to nearly equal energy faces, ice takes on the shape of the confining container. The near-energy match is demonstrated by growth in the modified Bridgeman apparatus (19). Nucleation occurs on a polycrystalline seed; single-crystal growth is achieved due to competitive growth among the multiple ice–water interfaces (18). Careful thermal management maintains near-equilibrium conditions yielding a large single crystal, but the crystal orientation is not a priori known. [Note: ice seeded by a floating crystal tends to have the optic axis perpendicular to the growth direction but single-crystal yield is low, ~10% (20).] Close energy match among the faces also means that ice does not readily cleave along any lattice plane (21). Thus, successful face preparation for any ice sample begins with characterization of the lattice orientation.