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NASA NTRS2000

The Structure of Ice Nanoclusters: Implications for Interstellar Ice Grains

Crystalline ice nanoclusters and thin-films of pure and impure water ice were deposited and studied in order to evaluate the extent to which surface-related effects control bulk properties. In pure water ice nanoclusters and thin-films of impure water ice, the cubic to hexagonal phase transformation occurs at lower temperatures than in thin-film deposits of pure water ice. In laboratory-grown crystalline ice nanoclusters, approx. 20 nm diameter, a significant proportion of water molecules exists in surface and near-surface environments which have an amorphous or nearly amorphous character. These disordered regions, which are highly reactive, serve to promote transformations or reactions which would otherwise be kinetically hindered. Likewise, dilute impurities such as methanol, sequestered to the surface of thin-films on crystallization, introduce defects into the ice network, thereby allowing sluggish structural transitions to proceed. These structural effects, which are surface phenomena, are believed to play an important role in promoting molecular reactions known to occur within interstellar ice grains in cold molecular clouds, where the first organic compounds are formed.

Delzeit, L.↗
NASA NTRS2000

From Interstellar PAHs and Ices to the Origin of Life

Tremendous strides have been made in our understanding of interstellar material over the past twenty years thanks to significant, parallel developments in observational astronomy and laboratory astrophysics. Twenty years ago the composition of interstellar dust was largely guessed at, the concept of ices in dense molecular clouds ignored, and the notion of large, abundant, gas phase, carbon rich molecules widespread throughout the interstellar medium (ISM) considered impossible. Today the composition of dust in the diffuse ISM is reasonably well constrained to micron-sized cold refractory materials comprised of amorphous and crystalline silicates mixed with an amorphous carbonaceous material containing aromatic structural units and short, branched aliphatic chains. In dense molecular clouds, the birthplace of stars and planets, these cold dust particles are coated with mixed molecular ices whose composition is very well constrained. Lastly, the signature of carbon-rich polycyclic aromatic hydrocarbons (PAHs), shockingly large molecules by earlier interstellar chemistry standards, is widespread throughout the Universe. The first part of this lecture will describe how infrared studies of interstellar space, combined with laboratory simulations, have revealed the composition of interstellar ices (the building blocks of comets) and the high abundance and nature of interstellar PAHs. The laboratory database has now enabled us to gain insight into the identities, concentrations, and physical state of many interstellar materials. Within a dense molecular cloud, and especially in the solar nebula during the star and planet formation stage, the materials frozen into interstellar/precometary ices are photoprocessed by ultraviolet light, producing more complex molecules. The remainder of the presentation will focus on the photochemical evolution of these materials and the possible role of these compounds on the early Earth. As these materials are thought to be the building blocks of comets and related to the carbonaceous components of micrometeorites, they are likely to have been important sources of complex organic materials on the early Earth and their composition may be related to the origin of life.

Allamandola, Louis J.↗
NASA NTRS2001

Grain Properties of Comet C/1995 O1 (Hale-Bopp) Deduced Through Computational Techniques

We present the computational analysis of the 7.6 - 13.2 micrometer infrared (IR) spectrophotometry (R approximately equal to 120) of comet C/1995 O1 (Hale-Bopp) in conjunction with concurrent observations which extend the spectral energy distribution from the near-infrared to far-infrared wavelengths. The observations include temporal epochs pre-perihelion, (1996 October UT and 1997 February UT), near perihelion (1997 April UT), and postperihelion (1997 June UT). Through the computational modeling of small amorphous carbon, and crystalline and amorphous silicate grains in Hale-Bopp's coma, we find that as the comet approached perihelion, the grain size distribution (the Hanner modified power law) steepened (N = 3.4 pre-perihelion, to N = 3.7 near and post-perihelion) along with an increase in the fractal porosity of larger (greater than 1 micrometer) grains. The peak of the grain size distribution remained constant (ap = 0.2 micrometer) at each epoch. We attribute the emergence of the 9.3 micrometer peak near perihelion to crystalline orthopyroxeno grains released from inside the nucleus. Crystalline silicates (olivine and orthopyroxene) make up about 30% (by mass) of the submicron sized (less than 1 micrometer) dust grains in Hale-Bopp's coma during each epoch.

Harker, David E.↗
NASA NTRS1997

Characteristics of Interstellar and Circumstellar Dust

This paper will review our current knowledge of circumstellar and interstellar dust from an astronomical point of view. About half of the interstellar dust volume consists of amorphous silicates. The remainder has to be made up of an carbonaceous component such as graphite, amorphous carbon (i.e., soot), Polycyclic Aromatic Hydrocarbon molecules (PAHs), and/or organic grain mantles (i.e., mixed polymers). The observational evidence for these components will be reviewed and their relative importance assessed. The emphasis will be on recent observations using the Infrared Space Observatory. Most of these dust components are formed in the outflows from stars in the late stages of their evolution (i.e., red giants, planetary nebulae, novae, supergiants, Wolf Rayet stars, and supernovae). Indeed, observation of such objects indicate an even richer spectrum of stardust components, including also SiC, MgS, and aluminates and crystalline silicates. These observations will be briefly discussed. The stardust budget of the galaxy will be reviewed and the relative importance of the various birth sites assessed. Finally, in recent years, isotopic composition studies have shown that some circumstellar and interstellar dust grains have been incorporated into solar system bodies such as planetary dust particles and meteorites without totally losing their identity. Among the components identified are SiC, graphite, diamonds, PAHs, aluminum oxides, as well as various trace element carbides. Studies of this kind have opened up a new window on the composition and structure of interstellar dust. These different sources of information on interstellar and circumstellar dust will be briefly contrasted.

Tielens, A. G. G. M.↗
NASA NTRS1997

The Carbon-Rich Dust Sequence: Infrared Spectral Classification of Carbon Stars

We have developed a classification system for the infrared spectral emission from carbon stars, using a sample of 96 bright carbon-rich variables associated with the asymptotic giant branch. In addition to the stellar contribution, most spectra include the 11.2 micron emission feature from SiC and either a smooth cool continuum from amorphous carbon or a secondary emission feature at 9.0 microns. We have identified a carbon-rich dust sequence along which the amorphous carbon component grows while the 9.0 micron feature declines in strength. Along this spectral sequence, the fraction of Miras increases, as does the period of variability, the mass-loss rate, and the thickness of the circumstellar shell. Thus the carbon-rich dust sequence appears to be an evolutionary sequence. One class of spectra shows a particularly strong 9.0 micron feature, Enhanced C/O ratio, and several other unusual properties that suggest a different sequence, perhaps related to J stars.

Solan, G. C.↗
NASA NTRS1998

Fifteen Years of Laboratory Astrophysics at Ames

Tremendous strides have been made in our understanding of interstellar material over the past fifteen years thanks to significant, parallel developments in two closely related areas: observational astronomy and laboratory astrophysics. Fifteen years ago the composition of interstellar dust was largely guessed at, the concept of ices in dense molecular clouds ignored, and the notion of large, abundant, gas phase, carbon-rich molecules widespread throughout the interstellar medium (ISM) considered impossible. Today the composition of dust in the diffuse ISM is reasonably well constrained to cold refractory materials comprised of amorphous and crystalline silicates mixed with an amorphous carbonaceous material containing aromatic structural units and short, branched aliphatic chains. In the dense ISM, these cold dust particles are coated with mixed-molecular ices whose compositions are very well known. Lastly, the signature of carbon-rich polycyclic aromatic hydrocarbons (PAHs), shockingly large molecules by early interstellar chemistry standards, is widespread throughout the ISM. This great progress has only been made possible by the close collaboration of laboratory experimentalists with observers and theoreticians, all with the goal of applying their skills to astrophysical problems of direct interest to NASA programs. Such highly interdisciplinary collaborations ensure fundamental, in depth coverage of the wide-ranging challenges posed by astrophysics. These challenges include designing astrophysically focused experiments and data analysis, tightly coupled with astrophysical searches spanning 2 orders of magnitude in wavelength, and detailed theoretical modeling. The impact of our laboratory has been particularly effective as there is constant cross-talk and feedback between quantum theorists; theoretical astrophysicists and chemists; experimental physicists; organic, physical and petroleum chemists; and infrared and UV/Vis astronomers. In this paper, two examples of the Ames Program will be given. We have been involved in identifying 9 out of the 14 interstellar pre-cometary ice species known, determined their abundances and the physical nature of the ice structure. Details on our ice work are given in the paper by Sandford et al. Our group is among the pioneers of the PAH model. We built the theoretical framework, participated in the observations and developed the experimental techniques needed to test the model. We demonstrated that the ubiquitous infrared emission spectrum associated with many interstellar objects can be matched by laboratory spectra of neutral and positively charged PAHs and that PAHs were excellent candidates for the diffuse interstellar band (DIB) carriers. See Salama et al. and Hudgins et al.

Allamandola, L. J.↗
NASA NTRS2001

Annealing of Silicate Dust by Nebular Shocks at 10 AU

Silicate dust grains in the interstellar medium are known to be mostly amorphous, yet crystalline silicate grains have been observed in many long-period comets and in protoplanetary disks. Annealing of amorphous silicate grains into crystalline grains requires temperatures greater than or approximately equal to 1000 K, but exposure of dust grains in comets to such high temperatures is apparently incompatible with the generally low temperatures experienced by comets. This has led to the proposal of models in which dust grains were thermally processed near the protoSun, then underwent considerable radial transport until they reached the gas giant planet region where the long-period comets originated. We hypothesize instead that silicate dust grains were annealed in situ, by shock waves triggered by gravitational instabilities. We assume a shock speed of 5 km/s, a plausible value for shocks driven by gravitational instabilities. We calculate the peak temperatures of pyroxene grains under conditions typical in protoplanetary disks at 5-10 AU. We show that in situ annealing of micron-sized dust grains can occur, obviating the need for large-scale radial transport.

Harker, David E.↗
NASA NTRS2002

The Exobiological Role of Interstellar Polycyclic Aromatic Hydrocarbons and Ices

Tremendous strides have been made in our understanding of interstellar material over the past twenty years thanks to significant, parallel developments in observational astronomy and laboratory astrophysics. Before this time, the composition of interstellar dust was largely guessed-at, the presence of ices in interstellar clouds ignored, and the notion that large, gas phase, carbon rich molecules might be abundant and widespread throughout the interstellar medium (ISM) considered impossible. Today, the composition of dust in the ISM is reasonably well constrained to micron-sized cold refractory materials comprised of amorphous and crystalline silicates mixed with an amorphous carbonaceous material containing aromatic structural units and short, branched aliphatic chains. Shrouded within the protective confines of cold, opaque molecular clouds--the birthplace of stars and planets--these cold dust particles secrete mantles of mixed molecular ices whose compositions are also well constrained. Finally, amidst the molecular inventory of these ice mantles are likely to be found polycyclic aromatic hydrocarbons (PAHs), shockingly large molecules by the standards of interstellar chemistry, the telltale infrared spectral signature of which is now recognized throughout the Universe. In the first part of this talk, we will review the spectroscopic evidence that forms the basis for the currently accepted abundance and ubiquity of PANs in the ISM. We will then look at a few specific examples which illustrate how experimental and theoretical data can be applied to interpret the interstellar spectra and track how the PAN population evolves as it passes from its formation site in the circumstellar outflows of dying stars, through the various phases of the ISM, and into forn~iing planetary systems. Nevertheless, despite the fact that PANs likely represent the single largest molecular reservoir of organic carbon in evolving planetary systems, they are not what would be considered "biogenic" molecules. Although interesting from a chemical and astrophysical standpoint, in the absence of a mechanism by which this population can be dislodged from the precipitous thermodynamic well afforded by their extensive aromatic networks, they are of little Astrobiological significance. Consequently, for the remainder of the talk, we will consider the photochemical evolution of PANS under conditions similar to those found in the ISM and in proto-planetary systems with an eye toward means by which this rich repository of pre-biotic organic "ore" might be converted into materials of greater importance to Astrobiology.

Hudgins, Douglas M.↗
NASA NTRS2003

Diaplectic Glass Content in Experimentally Shock-loaded Quartz Determined by X-Ray Powder Diffraction

Quartz is the most common mineral of terrestrial crustal rocks and thus a widespread indicator for impact cratering and associated shock metamorphism. Planar deformation features (PDFs) are among the most prominent and diagnostic shock features in quartz and they represent thin lamellae of glass that formed via solid-state transformations. This socalled 'diaplectic' glass becomes pervasive at higher pressures and results in optically isotropic and X-ray-amorphous phases that resemble texturally the original quartz grains (without evidence of melt flow). In the past, it has been shown that the amount of this amorphous material in experimentally shock-loaded quartz correlates with peak shock pressure. Both reports derive the glass content from density measurements of individual crystals employing the equation X(%) = (rho(sub x) - rho(sub 0))/(rho(sub x) - rho(sub gl)), where x and 0 stands for X-ray and average (optical) density, respectively. The density of glass, rho(sub gl), was adopted as 2.2 g/cu cm. Though the same procedures had been applied, the resulting glass content differs significantly among the above studies. In the present study, we are using a new approach based solely on the integral intensity of a single, carefully selected reflection in the XRD pattern, and we will compare our data to those reported in the literature.

Skala, R.↗
NASA NTRS2003

Elastic Properties of Films of Water and Noble Gases Condensed at Low Temperatures

We have shown that there are extensive similarities between the quench-condensed noble gas films and those of amorphous water ice. In particular, both can be quite soft upon deposition and can stiffen considerably when annealed. Furthermore, this stiffening follows a logarithmic time dependence for all substances. The temperature dependence of these behaviors scales with the triple point. The results shown here show a strong thickness dependence, which has implications for any study of mechanical properties of films on substrates. The temperature dependence of the stiffening and the stiffening rate have now been characterized for the noble gases, and these observations provide a roadmap for new experiments on amorphous water ice.

Pohl, Robert O.↗
NASA NTRS2002

Disappearance of 19P/Borrelly's Silicate Feature in 2001 Apparition Is Attributed to Increase in Grain Size

We report on observations and analysis of HIFOGS 10 microns spectrophotometry of short period comet 19P/Borrelly on 2003 October 13, 15 UT at the NASA IRTF. 19P/Borrelly is one of two short period comets, comet 4PIFaye being the other, to have a silicate feature detected. During Borrelly s perihelion passage in 1994 December, a silicate feature was present with a flux-to-continuum ratio of 0.25. Two apparitions later in 2003 October, the silicate feature is absent. Thermal emission modeling using amorphous olivine and amorphous carbon shows that a slight increase in grain size accounts for the disappearance of the silicate feature. Analysis of 19P/Borrelly suggests grain size, and not the absence of olivine minerals, may be responsible for the absence of silicate features in most short period comets. 19P/Borrelly is one of the more active short period comets. However, short period comets as a family are less active than long period comets. Short period comets probably originated in the Kuiper Belt and suffered collisions while in residence in the outer solar system. Upon evolution into orbits that take them through the inner solar system, the surfaces of short period comets are exposed to sunlight through their many perihelion passages. This is in contrast to long period comets which probably originated near Jupiter and were expelled to the Oort cloud where they have existed and been exposed to cosmic ray processing. By studying the grain properties in short period comets and comparing to long period comets, we compare the effects on the grain populations of different parent body evolution histories. Upcoming opportunities to study short and long period comets will be advertised.

Wooden, D. H.↗
NASA NTRS2003

X-ray Polarimetry with an Active-Matrix Pixel Proportional Counter

We report the first results from an X-ray polarimeter with a micropattern gas proportional counter using an amorphous silicon active matrix readout. With 100% polarized X-rays at 4.5 keV, we obtain a modulation factor of 0.33+/- 0.03, confirming previous reports of the high polarization sensitivity of a finely segmented pixel proportional counter. The detector described here has a geometry suitable for the focal plane of an astronomical X-ray telescope. Amorphous silicon readout technology will enable additional extensions and improvements.

Black, J. K.↗
NASA NTRS2003

Laboratory Simulation of Space Weathering: ESR Measurements of Nanophase Metallic Iron in Laser-irradiated Olivine and Pyroxene Samples

S-type asteroids are believed to be parent bodies of ordinary chondrites. Although both S-type asteroids and ordinary chondrites contain the same mineral assemblage, mainly olivine and pyroxene, the reflectance spectra of the asteroids exhibit more overall depletion (darkening) and reddening, and more weakening of absorption bands relative to the meteorites. This spectral mismatch is explained by space weathering process, where high-velocity dust particle impacts should change the optical properties of the uppermost regolith surface of asteroids. In order to simulate the space weathering, we irradiated nanosecond pulse laser beam onto pellet samples of olivine (8.97wt% FeO) and pyroxene (enstatite: 9.88wt% FeO, hypersthene: 16.70wt%). We got spectral changes in our samples similar to that by space weathering on asteroids and confirmed nanophase alpha-metallic iron particles, which were theoretically predicted, not only on olivine but also on pyroxene samples by Transmission Electron Microscopy (TEM). Nanophase metallic iron particles were widely scattered throughout the amorphous rims developed along the olivine grains, whereas they were embedded in aggregates of amorphous in enstatite samples. Recently, we also measured laser-irradiated samples by ESR (Electron Spin Resonance). Strong ESR signals, characteristic to nanophase iron particles, are observed on irradiated olivine samples. In this paper, we report the quantities of nanophase metallic iron particles in pyroxene samples by ESR observations in addition to olivine samples.

Kurahashi, E.↗
NASA NTRS2003

A Critical Examination of Relative Concentrations of Volume-correlated and Surface-correlated Submicron Globules of Pure Fe-0 in Lunar Soils

Impacts on lunar soils produce melt and vapor in an approximate proportion of 7:1. The melt scavenges soil grains of diverse size, quenches and forms agglutinates, thereby converting surface correlated components of soil grains as volume correlated components; simultaneously, parts of the vapor may condense or escape. Cumulative small impacts increase the maturity of the soils, increase the abundance of agglutinates, and increase the concentration of vapor condensated material. Since the discovery of vapor deposited crystalline Fe-0 in vugs of regolith breccias and the theoretical anticipation of amorphous vapor deposits of diverse composition coating lunar soils grains, empirical evidence is gathering in support of such deposits, now commonly called vapor deposited patina (VDP). In addition, submicron globules of Fe-0 are seen to be ubiquitous in VDP. The amorphous VDP lowers the albedo of lunar soils, affects magnetic properties of soils, changes the slopes of uv-vis-ir reflectance spectra, and potentially also alters the gamma and x-ray spectra of lunar soils, compromising compositional inferences from remote sensing.

Basu, A.↗
NASA NTRS2003

Determining the Biogenicity of Microfossils in the Apex Chert, Western Australia, Using Transmission Electron Microscopy

For over a decade, the oldest evidence for life on this planet has been microfossils in the 3.5 Ga Apex Chert in Western Australia. Recently, the biogenicity of these carbon-rich structures has been called into question through reanalysis of the local geology and reinterpretation of the original thin sections. Although initially described as a stratiform, bedded chert of siliceous clasts, the unit is now thought to be a brecciated hydrothermal vein chert. The high temperatures of a hydrothermal environment would probably have detrimental effects to early non-hyperthermophilic life, compared to that of a shallow sea. Conversely, a hydrothermal origin would suggest that if the microfossils were valid, they might have been hyperthermophilic. Apex Chert controversy. The Apex Chert microfossils were originally described as septate filaments composed of kerogen similar in morphology to Proterozoic and modern cyanobacteria. However new thin section analysis shows that these carbonaceous structures are not simple filaments. Many of the original microfossils are branched and have variable thickness when the plane of focus is changed. Hydrothermal alteration of organic remains has also been suggested for the creation of these strange morphologies. Another point of contention lies with the nature of the carbon material in these proposed microfossils. Kerogen is structurally amorphous, but transforms into well-ordered graphite under high pressures and temperatures. Raman spectrometry of the carbonaceous material in the proposed microfossils has been interpreted both as partially graphitized kerogen and amorphous graphite. However, these results are inconclusive, since Raman spectrometry cannot adequately discriminate between kerogen and disordered graphite. There are also opposing views for the origin of the carbon in the Apex Chert. The carbon would be biogenic if the proposed microfossils are indeed the remains of former living organisms. However, an inorganic Fischer- Tropsch-type synthesis is also a possible explanation for the formation of large-aggregate carbonaceous particles and could also account for the depletion of (13)C observed.

DeGregorio, B. T.↗
NASA NTRS1998

Silicate Mineralogy of the Dust in the Inner Coma of Comet C/1995 01 (Hale-Bopp) Pre- and Post-Perihelion

We present 7.6 - 13.3 microns infrared (IR) spectrophotometry (R approx. = 180 - 350) of the 10 microns silicate emission from dust in the inner coma (i.e., within a diameter of 3in.) of comet C/1995 O1 (Hale-Bopp) at four temporal epochs from 1996 October through 1997 June during Hale-Bopp s approach to, arrival at, and recession from perihelion. The HIFOGS spectra at large heliocentric distances exhibit strong emission peaks from 9.9 - 10.1 microns and at 11.2 microns. The HIFOGS spectra of Hale-Bopp taken 1996 October 07 - 14 UT are identical in shape to the ISO SWS spectrum at 2.8 AU obtained on 1996 October 06 UT. Magnesium-rich olivine was unambiguously identified due to presence of the expected 11.2 microns peak along with the matching far-IR 18 microns, 23 microns, and 33 microns peaks in the ISO SWS spectrum. In contrast, to large heliocentric distances, we find that the silicate feature at small heliocentric distances (tau(sub lambda) less than or = 1.7 AU) exhibits strong peaks at 9.3 microns, 9.9 - 10.1 microns, and 11.2 microns, and weak at 10.5 microns and 11.8 microns. We will show that the dramatic increase of the 9.3 microns and 10.0 microns peaks close to perihelion leads to the hypothesis that there are two crystalline grain components with significantly different temperatures. The hotter mineral species (including olivines) radiate over a large range of heliocentric distances at detectable leve!s. The cooler mineral species (pyroxenes) radiate on the Wien side of the blackbody, too faint to detect in the mid-infrared spectra, until close to the sun when this species radiates on the Reyleigh-Jeans tail and becomes apparent. Decomposition of the observed silicate emission features into mineral components through comparison of the height and shape of the silicate feature ("Flux/cont") derived from the cometary spectra, to optical extinctions (Qext) derived from laboratory measurements of terrestrial silicate minerals and interplanetary dust particles (IDPs) is successful for a combination of warm grains (consisting of olivines, amorphous olivines, amorphous pyroxenes, and layer-lattice silicates) and cool grains (crystalline pyroxenes).

Wooden, Diane H.↗
NASA NTRS2004

Organics on Fe-Silicate Grains: Potential Mimicry of Meteoritic Processes?

Currently, it is unknown what exact process or combination of processes produced organics that are found in meteorites or are detected in comets and nebulas. One particular process that forms organics involves Fischer-Tropsch type (FTT) reactions. Fischer-Tropsch type reactions produce hydrocarbons by hydrogenating carbon monoxide via catalytic reactions. The overall reaction is shown. The products of these reactions have been studied using natural catalysts and calculations of the efficiency of FTT synthesis in the Solar Nebula suggest that these types of reactions could make significant contributions to the composition of material near three AU. We use FTT synthesis to coat amorphous Fesilicate grains with organic material to simulate the chemistry in the early Solar Nebula. We used lab-synthesized amorphous Fe-silicate grains for the catalyst because they might better simulate the starting materials found in protostellar nebulas. A brief description of the synthesis of these grains is given in Experiments. This work is different from previous studies because we focus here on the carbonaceous material deposited on the grains. In our experiments, we roughly simulate a model of the nebular environment where grains are successively transported from hot to cold regions of the nebula. In other words, the starting cold regions of the nebula. In other words, the starting gases and FTT products are continuously circulated through the grains at high temperature with intervals of cooling. Overall, organics generated in this manner could represent the carbonaceous material incorporated into comets and meteorites. We present the analyses of the organics produced using pyrolysis gas chromatography mass spectrometry (GCMS) and compare the results with those organics found in the Murchison meteorite.

Johnson, N. M.↗
NASA NTRS2003

Effect of Viscosity on the Crystallization of Undercooled Liquids

There have been numerous studies of glasses indicating that low-gravity processing enhances glass formation. NASA PI s are investigating the effect of low-g processing on the nucleation and crystal growth rates. Dr. Ethridge is investigating a potential mechanism for glass crystallization involving shear thinning of liquids in 1-g. For shear thinning liquids, low-g (low convection) processing will enhance glass formation. The study of the viscosity of glass forming substances at low shear rates is important to understand these new crystallization mechanisms. The temperature dependence of the viscosity of undercooled liquids is also very important for NASA s containerless processing studies. In general, the viscosity of undercooled liquids is not known, yet knowledge of viscosity is required for crystallization calculations. Many researchers have used the Turnbull equation in error. Subsequent nucleation and crystallization calculations can be in error by many orders of magnitude. This demonstrates the requirement for better methods for interpolating and extrapolating the viscosity of undercooled liquids. This is also true for undercooled water. Since amorphous water ice is the predominant form of water in the universe, astrophysicists have modeled the crystallization of amorphous water ice with viscosity relations that may be in error by five orders-of-magnitude.

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