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Ice Ic” Werner F Extent and relevance of stacking disorder in “ice Ic” Werner F. Kuhsa,1, Christian Sippela,b, Andrzej Falentya, and Thomas C. Hansenb aGeoZentrumGöttingen Abteilung Kristallographie (GZG Abt. Kristallographie), Universität Göttingen, 37077 Göttingen, Germany; and bInstitut Laue-Langevin, 38000 Grenoble, France Edited by Russell J. Hemley, Carnegie Institution of Washington, Washington, DC, and approved November 15, 2012 (received for review June 16, 2012) “ ” “ ” A solid water phase commonly known as cubic ice or ice Ic is perfectly cubic ice Ic, as manifested in the diffraction pattern, in frequently encountered in various transitions between the solid, terms of stacking faults. Other authors took up the idea and liquid, and gaseous phases of the water substance. It may form, attempted to quantify the stacking disorder (7, 8). The most e.g., by water freezing or vapor deposition in the Earth’s atmo- general approach to stacking disorder so far has been proposed by sphere or in extraterrestrial environments, and plays a central role Hansen et al. (9, 10), who defined hexagonal (H) and cubic in various cryopreservation techniques; its formation is observed stacking (K) and considered interactions beyond next-nearest over a wide temperature range from about 120 K up to the melt- H-orK sequences. We shall discuss which interaction range ing point of ice. There was multiple and compelling evidence in the needs to be considered for a proper description of the various past that this phase is not truly cubic but composed of disordered forms of “ice Ic” encountered. cubic and hexagonal stacking sequences. The complexity of the König identified what he called cubic ice 70 y ago (11) by stacking disorder, however, appears to have been largely over- condensing water vapor to a cold support in the electron mi- looked in most of the literature. By analyzing neutron diffraction croscope. A phase with cubic diffraction signatures can also be data with our stacking-disorder model, we show that correlations formed by heating the amorphous water phase (e.g., refs. 12, 13) between next-nearest layers are clearly developed, leading to from water freezing in silica mesopores (e.g., ref. 14), freezing of marked deviations from a simple random stacking in almost all gels (15), aqueous ionic (16) or aqueous molecular solutions (17– investigated cases. We follow the evolution of the stacking disor- 19), from hyperquenched micrometer-sized water droplets (4), der as a function of time and temperature at conditions relevant to emulsified subcooled water (20), or by heating various high- atmospheric processes; a continuous transformation toward nor- pressure phases of ice recovered to ambient pressure (e.g., refs. PHYSICS mal hexagonal ice is observed. We establish a quantitative link 21, 22). “Ice Ic” may also be obtained by decomposing gas between the crystallite size established by diffraction and electron hydrates (23–26). Sample size (i.e., droplet- or pore size) plays an microscopic images of the material; the crystallite size evolves important role in many of these transitions; the formation of from several nanometers into the micrometer range with progres- “ice Ic” is favored in nanometer-sized confined geometry, where sive annealing. The crystallites are isometric with markedly rough it may take place directly from water up to temperatures close to surfaces parallel to the stacking direction, which has implications melting. All transitions starting from a solid water phase leading for atmospheric sciences. to “ice Ic” were found to be irreversible. Fig. 2 shows the main established routes for forming “ice Ic”. atmospheric ice | stacking faults | water frost | cirrus clouds | We are not aware of any unequivocal diffraction observations noctilucent clouds of ice Ih, forming by any of the pathways shown in Fig. 2, for temperatures below ∼190 K. Initially, stacking-disordered “ice Ic” t is generally assumed that there are two topologically different forms and anneals toward ice Ih at an increased rate as temperature Icrystalline ambient pressure forms of water ice. Diffraction rises. The unambiguous assignment of the degree of stacking dis- methods have played a crucial role for the identification of what order requires good-quality diffraction data. Differences with re- has been called cubic ice or ice Ic, as most of its physical prop- spect to ice Ih are small, in the range from 200 to 240 K, and easily erties are quite similar to the common hexagonal form of ice, ice unnoticed in lower-resolution, lower-quality data. Ih (1, 2). Indeed, the free-energy difference between ice Ih and There is general agreement, from diffraction as well as scan- “ ” ice Ic is quite small (3) and varies notably depending on the exact ning electron microscopy (SEM), that ice Ic crystallites are of formation conditions (4). This material is not a well-defined nanoscopic size upon formation. From diffraction peak broad- phase (1, 2) and is still not fully characterized. ening, typical sizes of 4–200 nm are deduced (e.g., refs. 6, 7), and ThestructureoficeIh can be considered as a regular there is some evidence that these small particles are isotropic [ABABAB]∞ stacking of hexagonal symmetry by centering a (10). The smallness of ice crystals and their isotropic nature are structural building block at the midpoint of a H bond along the likely to be at the base of cryopreservation methods for bi- hexagonal c axis. Correspondingly, ideal ice Ic forms a cubic ological tissue (e.g., ref. 27). In the following we establish [ABCABC]∞ stacking of such building blocks (consisting of two H- a quantitative link between crystallite sizes derived from cryo- bonded water molecules) centered at the midpoint of a H bond along SEM and diffraction. a cubic 111 direction; both stacking arrangements are shown in Fig. 1. The formation of ice in the Earth’s atmosphere takes place It was noticed early on that ice formed by condensing water predominantly at or in aerosol particles by either homogeneous vapor on a cold support was not pure cubic ice (5). A number of (28, 29) or heterogeneous nucleation (30). Laboratory experi- attempts were made to explain the origin of the hexagonal fea- ments have shown that aerosol droplets may form “ice Ic” at tures in the diffraction patterns and it was realized that there is a gradual transition from this defective ice Ic into well-crystal- lized ice Ih upon temperature increase. This transient phase has Author contributions: W.F.K. and T.C.H. designed research; W.F.K., C.S., A.F., and T.C.H. been given various names: cubic ice (sometimes so-called “cubic performed research; C.S., A.F., and T.C.H. analyzed data; and W.F.K. and C.S. wrote the paper. ice”)or“ice Ic” (respectively, “ice Ic”) are the most frequently The authors declare no conflict of interest. used. We shall use the term “ice Ic” in the following; the quotation marks reflect the observational fact that there are deviations from This article is a PNAS Direct Submission. cubic symmetry. The transition temperature range of “ice Ic” Freely available online through the PNAS open access option. differs, partly owing to differences in the sensitivity of the method 1To whom correspondence should be addressed. E-mail: [email protected]. used for detection (1, 4). A suggestion by Kuhs et al. (6) set the This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. correct entry point by explaining all deviations from a hypothetical 1073/pnas.1210331110/-/DCSupplemental. www.pnas.org/cgi/doi/10.1073/pnas.1210331110 PNAS Early Edition | 1of6 Downloaded by guest on September 25, 2021 B cubic [111] directions, thus forming multiple twins. It is unclear B how frequently this happens and to what extent cubic stacking H A sequences are formed directly from the vapor phase. Exper- A K imentally, it has been established that thin vapor-deposited B C K K films of ice anneal to “ice Ic” (36, 37). In the following, we B K H C present details of the microstructural evolution of vapor-de- posited ice at temperatures from 175 to 240 K over many A H B hours, i.e., at timescales relevant to the processes in the ’ K C Earth s atmosphere. A H A Results B H Time-Resolved Neutron Diffraction Study of “Ice Ic”. The crystallo- H C graphic details of “ice Ic” formed from the vapor phase or by A H K A isothermal decomposition of gas hydrates have been studied by B H neutron diffraction at the high-intensity two-axis diffractometer H B D20 (38) at the High-Flux Reactor of the Institut Laue-Langevin A Methods A in Grenoble, France ( ). The diffraction data obtained show clear signs of stacking disorder as well as diffraction broadening due to small crystallite Fig. 1. (Left) Sequences of cubic (Upper) and hexagonal (Lower) stacking sizes, both changing with time and temperature. The complex corresponding to the fault-free structures of ice Ic and ice Ih, respectively, in a ball-and-stick model; only the oxygen atoms are shown, which are con- diffraction patterns clearly cannot be explained by a simple nected by H bonds. The midpoints of the H bonds along the vertical stacking mixture of the pure ice Ic and ice Ih phases; they were analyzed direction correspond to the topological A, B, and C layers of the stacking as by means of a least-squares full-pattern profile refinement using indicated. Note that there is a horizontal mirror plane at the A and B loca- the stacking disorder model of some of us (9, 10). For a satis- tions in the case of ice Ih and an inversion center (on the arrows) at all factory description, interactions up to the next-nearest layer had locations A, B, and C in the case of ice Ic.
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