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Scheiner's Halo: Cubic Ice or Polycrystalline Hexagonal Ice?
Abstract
A new explanation is proposed for the rare Scheiner's halo, observed in
the sky at an angle of 28° from the sun or moon. The existing
explanation invokes the presence in the atmosphere of the cubic form of
ice, ice Ic. However, extensive laboratory work has not demonstrated
that ice Ic can form under conditions found in the atmosphere. We point
out an alternative, that polycrystals of ice Ih (the ordinary hexagonal
polymorph), in which specific orientation relations exist between
adjacent crystals, are another possible cause of Scheiner's halo.
Polycrystals with the appropriate orientation relation are not uncommon
in the atmosphere, but concentrations sufficient to produce optical
effects are expected to be rare. There appears to be no decisive
evidence to rule out either of these explanations.
... Starting with the observation of Scheiner's halo in 1629, claims were made about the occasional existence of cubic ice crystals in clouds, 1-3 e.g., in noctilucent mesospheric or polar stratospheric clouds. These claims are being debated since also polycrystals of hexagonal ice 4,5 or trigonal crystals may be of relevance in this context. 6 The higher vapor pressure and the lower thermal conductivity 7 of ice I c as compared to ice I h might be of importance in cloud freezing and persistent in-cloud supersaturations in cold cirrus. ...
... Here the indices c and h refer to the limiting cases of "cubic" or hexagonal stacking, respectively. The definition in Eq. (4) implies that X(T ) → 1 at small temperatures which, also in light of the above remarks, should not be taken to indicate that the "cubic" fraction is 1 but that it is at its (unknown) maximum. ...
Using various temperature-cycling protocols, the dynamics of ice I were studied via dielectric spec-troscopy and nuclear magnetic resonance relaxometry on protonated and deuterated samples obtained by heating high-density amorphous ices as well as crystalline ice XII. Previous structural studies of ice I established that at temperatures of about 230 K, the stacking disorder of the cubic/hexagonal oxygen lattice vanishes. The present dielectric and nuclear magnetic resonance investigations of spectral changes disclose that the memory of the existence of a precursor phase is preserved in the hydrogen matrix up to 270 K. This finding of hydrogen mobility lower than that of the undoped hexagonal ice near the melting point highlights the importance of dynamical investigations of the transitions between various ice phases and sheds new light on the dynamics in ice I in general. Published by AIP Publishing. https://doi.
... Halo is produced by sun-or moon-light interactng with atmospheric ice particles in the atmosphere, often seen as arcs around the sun or moon. 47 Scheiner's Halo is a rarely-observed and shortlived halo at B281 from the sun or the moon; 2 Whalley postulated its appearance to upper-atmosphere cubic ice (I c ), where NML temperatures prevail, noting that octahedral cubic-ice crystallites only form this halo via refraction through (111) and (% 1% 1% 1) faces. 2 However, ref. 48 suggests that a few specific orientations between adjacent crystallites of polycrystalline I h may explain Scheiner's Halo. Recent laboratory experiments confirm cubicice formation under upper-atmosphere-mimicking conditions. ...
... Recent laboratory experiments confirm cubicice formation under upper-atmosphere-mimicking conditions. 26 Here, in Fig. 1 and 4, adoption of a very loose octahedral shape, with the earlier-discussed conclusive evidence of the I c polymorph, bears only very tentative support, at best, for Whalley's reasoning and cannot be taken as significant; 2 the non-observation here of ref. 48 Are the electro-frozen crystallites stable upon applied-field removal? ...
Elucidating water-to-ice freezing, especially in ''No Man's Land'' (150 K o T o 235 K), is fundamentally important (e.g., predicting upper-troposphere cirrus-cloud formation)-and elusive. An oft-neglected aspect of tropospheric ice-crystallite formation lies in inevitably-present electric fields' role. Exploring nucleation in No Man's Land is technically demanding, owing to rapid nucleation rates, to mention nothing of difficulties of applying relevant electric fields thereto. Here, we tackle these intriguing open questions, via non-equilibrium molecular-dynamics simulations of sub-microsecond formation of rhombus-shaped ice I c nano-crystallites from aggressively-quenched supercooled water nano-droplets in the gas phase, in external static electric fields. We explore droplets' nano-confined geometries and the entropic-ordering agent of external electric fields as a means of realising cubic-ice formation, especially with very few stacking faults and defects.
... Both of these phases contain identical layers of hydrogen-bonded water molecules, only differing in their stacking sequences (3). The first detection of naturally occurring cubic ice was made by Scheiner in 1629 who discovered ice I c in the atmosphere by detecting halos (4). Increasing experimental evidence shows that most cubic ice crystals are in fact stacking disordered ice (ice I sd ) as they contain small segments of ice I h as a result of the random occurring stacking faults (5). ...
Premelting of ice, a quasi-liquid layer (QLL) at the surface below the melting temperature, was first postulated by Michael Faraday 160 y ago. Since then, it has been extensively studied theoretically and experimentally through many techniques. Existing work has been performed predominantly on hexagonal ice, at conditions close to the triple point. Whether the same phenomenon can persist at much lower pressure and temperature, where stacking disordered ice sublimates directly into water vapor, remains unclear. Herein, we report direct observations of surface premelting on ice nanocrystals below the sublimation temperature using transmission electron microscopy (TEM). Similar to what has been reported on hexagonal ice, a QLL is found at the solid-vapor interface. It preferentially decorates certain facets, and its thickness increases as the phase transition temperature is approached. In situ TEM reveals strong diffusion of the QLL, while electron energy loss spectroscopy confirms its amorphous nature. More significantly, the premelting observed in this work is thought to be related to the metastable low-density ultraviscous water, instead of ambient liquid water as in the case of hexagonal ice. This opens a route to understand premelting and grassy liquid state, far away from the normal water triple point.
... In particular, at large undercoolings the Ic form appears to have lower activation energy; i.e., the formation of Ic can be considered a manifestation of Ostwald's step rule. Evidence for Ic in the atmosphere has been claimed from halo observations (Riikonen et al., 2000;Whalley, 1983) but remains inconclusive (Weinheimer and Knight, 1987). However, laboratory observations suggest that, for atmospheric pressures, Ic is crystallized at temperatures below 200-210 K (Kuhs et al., 2004;. ...
From the frontiers of research on ice dynamics in its broadest sense, this review surveys the structures of ice, the patterns or morphologies it may assume, and the physical and chemical processes in which it is involved. Open questions in the various fields of ice research in nature are highlighted, ranging from terrestrial and oceanic ice on Earth, to ice in the atmosphere, to ice on other Solar System bodies and in interstellar space.
... The 28°halo is a very rare halo that has been reported a few times in literature [12]. Cubic ice [16] and polycrystalline crystals [17] have been suggested as possible explanations. A 28°halo can also be created by randomly oriented crystal with ð 2 0 2 3Þ faces in a tetrahedron habit. ...
This article focuses on the 1997 Lascar halo display, during which very unusual arcs and halos were documented. Photographs have been analyzed with the aid of a specific image processing method developed by us. Using crystals of hexagonal ice with exotic ( 2 0 2 ¯ 3 ) Miller index faces, it is possible to simulate all the features of the display with constant crystal populations and oriented crystals in plate orientation. The simulations perform better than the cubic ice explanation. The existence of ( 2 0 2 ¯ 3 ) crystal faces is supported by a 1998 South Pole halo display.
Inspired by the pioneer work of the nineteenth century photographer, William Nicholson Jennings, we studied quantitatively how realistic painted lightnings are. In order to answer this question, we examined 100 paintings and 400 photographs of lightnings. We used our software package to process and evaluate the morphology of lightnings. Three morphological parameters of the main lightning branch were analysed: (i) number of branches Nb, (ii) relative length r, and (iii) number of local maxima (peaks) Np of the turning angle distribution. We concluded: (i) Painted lightnings differ from real ones in Nb and Np. (ii) The r-values of painted and real lightnings vary in the same range. (iii) 67 and 22% of the studied painted and real lightnings were non-bifurcating (Nb = 1, meaning only the main branch), the maximum of Nb of painted and real lightnings is 11 and 51, respectively, and painted bifurcating lightnings possess mostly 2-4 branches, while real lightnings have mostly 2-10 branches. To understand these findings, we performed two psychophysical experiments with 10 test persons, whose task was to guess Nb on photographs of real lightnings which were flashed for short time periods Δt = 0.5, 0.75 and 1 s (characteristic to lightnings) on a monitor. We obtained that (i) test persons can estimate the number of lightning branches quite correctly if Nb ≤ 11. (ii) If Nb > 11, its value is strongly underestimated with exponentially increasing difference between the real and estimated numbers. (iii) The estimation is independent of the flashing period Δt of lightning photos/pictures. (iv) The estimation is more accurate, if skeletonized lightning pictures are flashed, rather than real lightning photos. These findings explain why artists usually illustrate lightnings with branches not larger than 11.
Ice crystals in the atmosphere nucleate from supercooled liquid water and grow by vapor uptake. The structure of the ice polymorph grown has strong impact on the morphology and light scattering of the ice crystals, modulates the amount of water vapor in ice clouds, and can impact the molecular uptake and reactivity of atmospheric aerosols. Experiments and molecular simulations indicate that ice nucleated and grown from deeply supercooled liquid water is metastable stacking disordered ice. The ice polymorph grown from vapor has not yet been determined. Here we use large-scale molecular simulations to determine the structure of ice that grows as a result of uptake of water vapor in the temperature range relevant to cirrus and mixed-phase clouds, elucidate the molecular mechanism of the formation of ice at the vapor interface, and compute the free energy difference between cubic and hexagonal ice interfaces with vapor. We find that vapor deposition results in growth of stacking disordered ice only under conditions of extreme supersaturation, for which a non-equilibrium liquid layer completely wets the surface of ice. Such extreme conditions have been used to produce stacking disordered frost ice in experiments and may be plausible in the summer polar mesosphere. Growth of ice from vapor at moderate supersaturations in the temperature range relevant to cirrus and mixed-phase clouds, from 200 to 260 K, produces exclusively the stable hexagonal ice polymorph. Cubic ice is disfavored with respect to hexagonal ice not only by a small penalty in the bulk free energy (3.6 ± 1.5 J mol-1 at 260 K), but also by a large free energy penalty at the ice-vapor interface (89.7 ± 12.8 J mol-1 at 260 K). The latter originates in higher vibrational entropy of the hexagonal-terminated ice-vapor interface. We predict that the free energy penalty against the cubic ice interface should decrease strongly with temperature, resulting in some degree of stacking disorder in ice grown from vapor in the tropical tropopause layer, and in polar stratospheric and noctilucent clouds. Our findings support and explain the evolution of the morphology of ice crystals from hexagonal to trigonal symmetry with decreasing temperature, as reported by experiments and in-situ measurements in clouds. We conclude that selective growth of the elusive cubic ice polymorph by manipulation of the interfacial properties can likely be achieved at the ice-liquid interface, but not at the ice-vapor interface.
Ice crystals in cirrus frequently exhibit the shape of a bullet rosette composed of multiple bullets that radiate from a junction center. The authors studied the sensitivity of the scattering phase formation of a bullet rosette to its geometrical characteristics: the shape, aspect ratio, and spatial orientation. In doing so, they defined first an idealized bullet rosette according to the current knowledge of the crystalline structure and nucleation process of bullet rosettes. The scattering phase formation of a bullet rosette varies with its shape, and the lateral and backward scattering tends to increase with the number of bullets/bullet rosettes. Although the shape of a bullet rosette with 3D random orientation does not greatly affect the general feature of normalized scattering phase functions, its geometrical shape still remains an important factor for scattering and microphysical properties of cirrus. -from Authors
The discrete-dipole approximation is used to study the problem of light scattering by homogeneous rectangular particles. The structure of the discrete-dipole approximation is investigated, and the matrix formed by this approximation is identified to be a symmetric, block-Toeplitz matrix. Special properties of block-Toeplitz arrays are explored, and an efficient algorithm to solve the dipole scattering problem is provided. Timings for conjugate gradient, Linpack, and block-Toeplitz solvers are given; the results indicate the advantages of the block-Toeplitz algorithm. A practical test of the algorithm was performed on a system of 1400 dipoles, which corresponds to direct inversion of an 8400 × 8400 real matrix. A short discussion of the limitations of the discrete-dipole approximation is provided, and some results for cubes and parallelepipeds are given. We briefly consider how the algorithm may be improved further.
Cubic ice (Ic) is a metastable form of ice with very similar physical
properties but different crystal symmetry than normal, hexagonal ice
(Ih). Below 200 K, water preferentially nucleates to Ic, then transforms
to the more stable Ih in minutes to days. As a metastable phase, Ic will
necessarily have a higher vapor pressure than Ih. A cloud parcel model
shows that nucleation to Ic, conversion to Ih, and the vapor pressure
differential together produce larger ice crystals that can more
effectively dehydrate air. The modelled effect is largest at 180 to 200
K, just the range most important for the tropical tropopause and polar
stratospheric clouds. The cloud model also produces a wider size
distribution when Ic is included, in agreement with observations.
An ice crystal halo display that contains several previously unknown halo phenomena was observed in Northern Chile. Analysis of computer simulations of the halos demonstrates that most of the new halo arcs in the display can be explained by the presence of airborne and preferentially oriented crystals of cubic ice. These observations therefore provide evidence of the existence of the cubic phase of ice in the Earth’s atmosphere.
Clusters are produced in a free jet expansion of water vapor. Keeping constant the nozzle diameter (d=0.4 mm) and temperature (T=430 K), an increase in inlet vapor pressure from 1 to 5 bar produces an increase in mean cluster size from several tens to several thousands of molecules per cluster. An electron diffraction analysis provides information about the cluster structure and dynamics. A direct observation of diffraction patterns shows that the largest clusters exhibit mainly a crystalline structure, namely, diamond cubic which is the metastable phase of bulk solid water, whereas the smallest ones are amorphous. In order to elucidate the local order in the latter, a comparison is made between the experimental curves and the diffraction functions calculated for various noncrystalline models. The best agreement is obtained with a model which presents distorted rings of three to six H2O molecules, constructed by cooling a liquid water droplet through a molecular dynamics calculation. In particular, this means that the regular dodecahedral structure often referred to in mass spectroscopy is not a realistic model for neutral clusters.
The polymorphic varieties of water ice are important rock-forming minerals in the outer Solar System. The Voyager 1 and 2 missions have shown that most of the ice moons of Jupiter and Saturn have had some form of tectonic or internal activity. Understanding of the tectonics and building reasonable models of the interior of these planets depend on our knowledge of the Theological properties and viscosity of high-pressure and low-temperature forms of ice.
Refraction of sunlight at the angle of minimum deviation between octahedral faces of crystals of ice Ic in the upper atmosphere could produce a halo around the sun or the moon at 27.46 degrees . Crystals of hexagonal ice having low-index faces cannot produce a halo of this radius. It is therefore suggested that Scheiner's halo, which has been reported at least four times since 1629 at 28 degrees from the sun, is due to ice Ic. If this is correct, it is apparently the first evidence that ice Ic occurs naturally and that liquid water can freeze to ice Ic.