Extent and relevance of stacking disorder in "ice I(c)"

Abstract

A solid water phase commonly known as "cubic ice" or "ice I(c)" is frequently encountered in various transitions between the solid, liquid, and gaseous phases of the water substance. It may form, e.g., by water freezing or vapor deposition in the Earth's atmosphere or in extraterrestrial environments, and plays a central role in various cryopreservation techniques; its formation is observed over a wide temperature range from about 120 K up to the melting point of ice. There was multiple and compelling evidence in the past that this phase is not truly cubic but composed of disordered cubic and hexagonal stacking sequences. The complexity of the stacking disorder, however, appears to have been largely overlooked in most of the literature. By analyzing neutron diffraction data with our stacking-disorder model, we show that correlations between next-nearest layers are clearly developed, leading to marked deviations from a simple random stacking in almost all investigated cases. We follow the evolution of the stacking disorder as a function of time and temperature at conditions relevant to atmospheric processes; a continuous transformation toward normal hexagonal ice is observed. We establish a quantitative link between the crystallite size established by diffraction and electron microscopic images of the material; the crystallite size evolves from several nanometers into the micrometer range with progressive annealing. The crystallites are isometric with markedly rough surfaces parallel to the stacking direction, which has implications for atmospheric sciences.

Fig. 1.

(Left) Sequences of cubic (Upper) and hexagonal (Lower) stacking corresponding to the fault-free structures of ice I_c and ice I_h, respectively, in a ball-and-stick model; only the oxygen atoms are shown, which are connected by H bonds. The midpoints of the H bonds along the vertical stacking direction correspond to the topological A, B, and C layers of the stacking as indicated. Note that there is a horizontal mirror plane at the A and B locations in the case of ice I_h and an inversion center (on the arrows) at all locations A, B, and C in the case of ice I_c. Considering the local symmetries, one can define hexagonal H- and cubic K sequences with either a local mirror plane or a plane containing local inversion centers, respectively: any layer neighbored by two different layers, e.g., ABC, defines a K sequence; any layer surrounded by two identical layers, e.g., ABA, defines an H sequence. (Right) Example of a stacking-disordered arrangement of A, B, and C layers. Pairs of H-bonded water molecules along the stacking direction form a layer and possess either a local mirror symmetry (H stacking, green atoms, also represented as plane) or a local inversion center (K stacking, red atoms, also represented as arrows).

Fig. 2.

Main established routes of forming “ice I_c”.

Fig. 3.

Evolution of cubicity as a function of time for annealing of vapor-deposited frost at temperatures of 175, 180, 185, and 190 K. Compared with 175 K, a clear acceleration of the loss of cubic sequences is seen at 180 K, speeding up even more at 185 K, whereas a smaller further change is seen at 190 K.

Fig. 4.

SEM micrographs showing the hierarchic microstructure of vapor-deposited water frost. (Left) Micrometer-sized spherules consisting of smaller units, which themselves consist of more or less isometric nanoparticles (Right); their sizes correspond to the crystallite size established by analyzing diffraction data of the same sample.

Fig. 5.

SEM micrographs of single crystallites of “ice I_c” formed by decomposition of CO₂ hydrates via a sudden depressurization to gas pressure well below the hydrate stability. Formation conditions: (A) 167.7 K and 6 mbar, (B, C) 175 K and 6 mbar, (D) 195 K and 6 mbar, (E, F) 220 K and 900 mbar. Scale bar: 5 μm. All crystallites have a pseudohexagonal shape and have kinks (some indicated by white arrows) on the prismatic faces. Whereas at the lowest temperatures kinks are frequent and the prismatic planes quite rough, at the highest temperatures larger portions of the prismatic planes are free of kinks.