Icarus 207 (2010) 314–319
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Icarus
journal homepage: www.elsevier.com/locate/icarus
Radiation-induced amorphization of crystalline ice
M. Famá *, M.J. Loeffler, U. Raut, R.A. Baragiola
Laboratory for Atomic and Surface Physics, University of Virginia, 351 McCormick Road, P.O. Box 400238, Charlottesville, VA 22904-4238, USA
a r t i c l e
i n f o
Article history:
Received 19 June 2009
Revised 24 October 2009
Accepted 2 November 2009
Available online 10 November 2009
Keywords:
Ices, IR spectroscopy
Infrared observations
Kuiper belt
Satellites, Surfaces
a b s t r a c t
We study radiation-induced amorphization of crystalline ice, analyzing the results of three decades of
experiments with a variety of projectiles, irradiation energy, and ice temperature, finding a similar trend
of increasing resistance of amorphization with temperature and inconsistencies in results from different
laboratories. We discuss the temperature dependence of amorphization in terms of the ‘thermal spike’
model. We then discuss the common use of the 1.65 lm infrared absorption band of water as a measure
of degree of crystallinity, an increasingly common procedure to analyze remote sensing data of astronomical icy bodies. The discussion is based on new, high quality near-infrared reflectance absorption
spectra measured between 1.4 and 2.2 lm for amorphous and crystalline ices irradiated with 225 keV
protons at 80 K. We found that, after irradiation with 1015 protons cm2, crystalline ice films thinner than
the ion range become fully amorphous, and that the infrared absorption spectra show no significant
changes upon further irradiation. The complete amorphization suggests that crystalline ice observed in
the outer Solar System, including trans-neptunian objects, may results from heat from internal sources
or from the impact of icy meteorites or comets.
Ó 2009 Elsevier Inc. All rights reserved.
1. Introduction
Crystalline ice has been identified on the surface of most of the
jovian, saturnian and uranian satellites (see Grundy et al. (1999)
and references therein), on Pluto’s satellite Charon (Brown and
Calvin, 2000), and on the surface of the trans-neptunian objects
(TNO) Quaoar (Jewitt and Luu, 2004), and 2003 EL61 (Merlin
et al., 2007). Its presence has been inferred from the near infrared
(NIR) spectrum of light reflected from the Sun, using the absorption
band at 1.65 lm, which is particularly sharp in crystalline ice
(Grundy and Schmitt, 1998). The sensitivity of the shape of this
band to temperature has been used, not only as an indicator of
the presence of the crystalline phase, but also to measure the surface temperature (Grundy et al., 1999; Fink and Larson, 1975; Cook
et al., 2007; Merlin et al., 2007). The presence of crystalline ice contrasts the expectations based on laboratory measurements. Due to
the low maximum surface temperatures of these objects in the
outer Solar System, less than 100 K for the saturnian satellites
(some regions of the south pole of Enceladus are at temperatures
higher than 100 K) and less than 50 K for TNOs (Jewitt and Luu,
2004), one expects that, if the ice is accreted from the vapor, it
would be amorphous in the absence of heating by high energy me-
* Corresponding author. Address: Department of Materials Science & Engineering, University of Virginia, 395 McCormick Road, P.O. Box 400745, Charlottesville,
VA 22904-474, USA. Fax: +1 434 924 1353.
E-mail addresses: [email protected] (M. Famá), [email protected] (M.J.
Loeffler), [email protected] (U. Raut), [email protected] (R.A. Baragiola).
0019-1035/$ - see front matter Ó 2009 Elsevier Inc. All rights reserved.
doi:10.1016/j.icarus.2009.11.001
teor impacts or episodic, internal heat sources. Such amorphous ice
would crystallize in a few minutes above 135 K but in more than
107 years at 80 K (Jenniskens and Blake, 1996; Baragiola, 2003).
However, exposure to space radiation: solar UV photons and ions,
cosmic rays or energetic charged particles trapped by the planetary
magnetic fields (Jurac et al., 1995), would eventually destroy crystallinity, since such energetic radiation is known to amorphize
crystalline ice in the laboratory (Golecki and Jaccard, 1978; Lepault
et al., 1983; Dubochet and Lepault, 1984; Heide, 1984; Strazzulla
et al., 1992; Moore and Hudson, 1992; Kouchi and Kuroda, 1990;
Leto and Baratta, 2003; Leto et al., 2005; Baragiola et al., 2005;
Mastrapa and Brown, 2006).
Thus, inferring the origin and evolution of the ice phase from
the reflectance spectrum of astrophysical bodies is complex since
the current phase of ice depends not only on surface conditions
during deposition, but also on the temperature history, and the
radiation environment. To untangle this complexity, more laboratory studies are needed that allow predictions in a variety of conditions. Here, we concentrate on radiation-induced amorphization
of crystalline ice showing that, even though it has been studied for
almost three decades, it is partially understood, with discrepancies
between different laboratories.
The techniques used to detect the amorphous content of
irradiated ice include as channeling in Rutherford backscattering
(RBS-c), electron diffraction (ED) and infrared spectroscopy (IR)
(Golecki and Jaccard, 1978; Lepault et al., 1983; Dubochet and Lepault, 1984; Heide, 1984; Strazzulla et al., 1992; Moore and Hudson,
1992; Kouchi and Kuroda, 1990; Leto and Baratta, 2003; Leto et al.,
315
M. Famá et al. / Icarus 207 (2010) 314–319
2005; Baragiola et al., 2005; Mastrapa and Brown, 2006). The RBS-c
technique measures disorder of the O sub-lattice in single crystals,
which includes displacements from the regular positions and misaligned micro-crystallites. ED measures crystallinity within the
coherence length while IR spectra of a given ice sample can be interpreted as a linear superposition of spectra of amorphous and crystalline regions, in the absence of porosity (Teolis et al., 2007). All these
techniques show that amorphization as a function of irradiation
dose D (energy deposited per molecule) follows an exponential
behavior:
/A ¼ /Amax ð1 exp½KDÞ
ð1Þ
where /A is the fraction of amorphized ice, /Amax is its maximum
value, and K is a fitting parameter (when D = K1 the fraction of
amorphous ice reaches a 63.2% of the maximum value) that was
found to depend strongly on temperature. The dose, an average
over the irradiation depth, is given by D = hFSei, where Se = N1
dE/dx is the stopping cross section, N the molecular density and
dE/dx is the linear energy transfer of the projectile in the solid.
The deposited energy must be corrected for reflected projectiles
and ejected secondary particles, but this correction is usually negligible. The maximum amorphous fraction /Amax is obtained for saturation doses (KD 1). While most experiments yielded full
amorphization, /Amax ¼ 1, others reported only partially amorphized ice at high fluences (for example, /Amax 60% with 3 keV
He ions at 77 K) (Strazzulla et al., 1992; Moore and Hudson, 1992).
We present first an analysis of these previous reports pointing
out apparent inconsistencies. We then describe a theoretical
approximation valid for high energy densities produced by ion impact, based on the thermal spike model, which can help explain the
temperature dependence of the variable K and might clarify some
of the differences between experiments. Finally, we present our
experiments of the amorphization of crystalline ice irradiated with
225 keV protons and a methodology to extract the amorphous fraction of ice from near-infrared spectra.
Fig. 1. K1 (see Eq. (1)) vs. temperature from previous reports: h 100 keV H+
(Golecki and Jaccard, 1978); s 3 keV He+, 4 1.5 keV H+ (Strazzulla et al., 1992); }
30 keV H+, / 30 keV He+, j 60 keV Ar+ (Leto and Baratta, 2003); . 200 keV H+ (Leto
et al., 2005); d 100 keV Ar+ (Baragiola et al., 2005); 100 keV e (Lepault et al.,
1983); 100 keV e (Heide, 1984); > 10.2 eV photons (Leto and Baratta, 2003). For
electrons, K1 diverges above 70 K (dotted line).
with Eq. (1), using /Amax ¼ 1 which yielded K1 from 1 to
>700 eV/mol between 13 and 77 K. Re-analyzing the data allowing
/Amax to vary, we find that K1 is more than one order of magnitude
smaller above 66 K. The data of Kouchi and Kuroda (1990) obtained
with Lyman-a UV radiation (10.2 eV) is not shown because of
unphysical low amorphization fluences (Jenniskens and Blake,
1996) which may be due to problems with their experimental
technique (Baragiola, 2003). Baragiola et al. (2005) found unusually low amorphization fluences for ice at 70 K using 100 keV Ar+,
for which the fraction of energy loss into elastic displacement collisions is 43%, the largest in Table 1. Finally, Mastrapa and Brown
(2006) observed full amorphization for a sample deposited at
40 K, crystallized at 160 K and cooled back to 40 K for irradiation,
but not for a sample deposited at 50 K, crystallized at 160 K, cooled
back at 50 K and then irradiated. It is difficult to obtain the values
for K1 from this report since the results are represented as the ratio between two IR bands, and they could be affected differently by
ion irradiation.
Among the several questions that arise from these results, some
are particularly relevant from our point of view: what is the physical meaning for the dependence of K1 with temperature? Why
was full amorphization observed at saturation fluences in some
experiments and not in others? In addition, why is it not possible
to amorphize crystalline ice with electrons above 70 K? In this
2. Previous studies
The results of previous experiments are summarized in Table 1
and Fig. 1. Specific comments are needed to explain some of the
values in the table. To obtain values of D we resorted to stopping
power (dE/dx) tables (stopping powers for electrons and positrons
ICRU Report 37; International Commission on Radiation Units and
Measurements, Bethesda, Maryland, USA, 1984; Ziegler et al.,
2008). To derive K1 from the results of Heide (1984) we assumed
/A = 0.99, since total dose values given in this reference are for
complete amorphization. Moore and Hudson (1992) fit their data
Table 1
Summary of data on amorphization of ice by particles.
Particle
+
H
e
e
He+
H+
H+
Ly-a
H+
He+
Ar+
Ly-a
H+
Ar+
H+
H+
a
Assumed.
Energy (keV)
T (K)
K1 (eV/mol)
/Amax
Tmax
Method
References
100
100
100
3
1.5
700
82–133
20–70
8–60
10–100
4.5–300
4–10
0.5–17
1.6–9
1.0
1.0
1.0
0.95–0.27
70
70
Channeling
ED
ED
IR: 3 lm
Golecki and Jaccard (1978)
Lepault et al. (1983) and Dubochet and Lepault (1984)
Heide (1984)
Strazzulla et al. (1992)
13–77
10 to >70
16
1–700
1.0a
70
Moore and Hudson (1992)
Kouchi and Kuroda (1990)
Leto and Baratta (2003)
Leto et al. (2005)
Baragiola et al. (2005)
Mastrapa and Brown (2006)
This work
30
30
60
200
100
800
225
90
70
9–100
80
0.7–1.7
1.0
IR: 20–100 lm
ED
IR: 3 lm
5.6
0.7
1.0
1.0
61.0
1.0
NIR: 1.65 lm
IR: 3 lm
IR: 1.65 lm
IR: 1.65 lm
4
316
M. Famá et al. / Icarus 207 (2010) 314–319
regard, we note that the ice could be crystallized by heating from
the radiation source, enabled by the low thermal conductivity of
ice. This effect will be more important at higher substrate temperature but cannot be appraised from the literature in the absence of
detailed description of experimental setups.
Since the density of energy deposition is very different for different excitation sources (ions, electrons, Lyman-a photons) it is
perhaps surprising that K1 shows similar temperature dependence. Below we will confine our discussion to ion irradiation for
which there exists a model (thermal spike) that can be applied.
First, we analyze the temperature dependence of K1.
K 1 ¼
T 0 ¼ T 0 þ wðT m T 0 Þ
g dE=dx
eqcðT m T 0 Þ
ð6Þ
where 0 < w < 1. We model the specific heat by a function c(T)
c¼
A¼
ð5Þ
This equation predicts that K1 should decrease with increasing
temperature, but this is opposite to the experimental results
shown by Fig. 1. A reasonable explanation for such inconsistency
is that the specific heat, neglected in Szenes’ treatment, plays a crucial role. We need to evaluate the specific heat at a temperature T0
between T0 and Tm:
3. Thermal spike model
The basic idea of the thermal spike model for amorphization is
that the energy deposited by a projectile in a small region can
abruptly heat the solid to the liquid and gaseous state (thermal
spike) from which extremely fast cooling rates lead to a disordered
solid. The thermal spike model, as discussed, for instance, by
Szenes (1995), is valid for ions and electrons with dE/dx high enough to produce a continuous ionization track. This implies a stopping power of 10 eV/Å or larger, given that the energy to form an
ion pair in water is 30 eV (Srdoč et al., 1995) and the interatomic
spacing is 3 Å. Among the projectiles in Table 1, only protons near
100 keV and 100 keV Ar+ have dE/dx in the required range.
The energy deposition is due to elastic and inelastic collisions
with atoms or molecules of the target and, therefore, the particle
loses part of its energy, which is absorbed and eventually dispersed
as heat through the material. The energy deposition processes include ionization and excitation of atoms/molecules, which may
lead to dissociation and recombination of molecules, production
of defects, sputtering, and structural changes. The transformation
of incident energy to heat is not complete since particles (electrons, photons, ions) can be ejected from the solid and, more
importantly, since some of the energy remains in lattice defects
or dissociation products. A fraction of this stored energy may be released by recombination of defects or of radicals but at a much
longer timescale than the spike.
In Szenes’ model, the spike, which is not at thermodynamic
equilibrium, is approximated by a temperature rise above the bulk
temperature T0, that depends on time t and distance r to the ion
trajectory, and which decays quickly after impact (1014 K s1).
The energy deposited per unit length in a cylindrical track of cross
sectional area A0 is dE/dx, the projectile stopping power. A fraction
g < 1 of this deposited energy transforms into heat and can eventually change the phase of the material. In this model, there is a
threshold stopping power for amorphization, dE/dxth = A0
qc (Tm T0)g1, when the maximum spike temperature equals
Tm, the melting temperature. In this equation, q is the density
and c a specific heat that is taken to be constant. The hot track expands and cools with time; the central region exceeding Tm reaches
a maximum cross section area A that can be approximated by:
S eqcðT m T 0 Þ
¼
A
Ng
1
cLow
þ
1
1
cHigh
ð7Þ
where cLow = a0N3; cHigh = a1 + a2T with a0 = 0.0034 J mol1 K4,
a1 = 4 J mol1 K1 and a2 = 0.12388 J mol1 K2, after fitting to
experimental data (Giauque and Stout, 1936; Flubacher et al.,
1960; Handa and Klug, 1988) and neglecting the latent heat in
phase changes. This heuristic expression has the right limits of
the specific heat at low and high temperatures. Introducing the specific heat into Szenes model, we obtain g K1 shown in Fig. 2 for different values of the variable w in Eq. (6). To get agreement with the
temperature trend in Fig. 1 we have to assume that g is quite small
(between 0.01 and 0.08). This may be reasonable for electronic energy deposition due to the small electron–phonon coupling. In contrast, in nuclear collisions that occur with 100 keV Ar+, a large
fraction of the energy loss goes to displacements (approximately
60%), as verified by TRIM. Comparison of H and Ar data suggests
that g is four times larger for Ar. We note that A for elastic collisions
is an average transverse area of the collision cascade, rather than a
track radius.
Another important difference between Eqs. (1) and (4) is that
the model predicts full amorphization for saturation fluences. It
is important to realize that, at least two experimental factors
may contribute to a measured /Amax < 1: an analysis area larger
than the irradiation area, and target ice films of thickness larger
than or comparable to the ion range.
4. Experimental methods
The experiments were performed in a cryopumped ultrahigh
vacuum chamber, with base pressure of 1 1010 Torr, which
is connected to a 300 kV mass-analyzed ion-accelerator. Crystal-
ð2Þ
from which the radius of the amorphous track can be obtained.
The amorphization rate is given by:
duA
¼ Að1 uA Þ
dF
ð3Þ
with solution:
uA ðFÞ ¼ 1 expðAFÞ
ð4Þ
Comparing Eqs. (1) and (4) and considering that the dose in energy per molecule is D = F S, the fluence F times the stopping
power cross section S = N1dE/dx:
Fig. 2. The product g K1 from Eqs. (5)–(7). The temperature dependence for low w
values appears as an effect of the specific heat of ice. The parameter labeling each
curve is w used in Eq. (6).
M. Famá et al. / Icarus 207 (2010) 314–319
line and amorphous films of high purity water ice were vapor
deposited from a micro-capillary array doser onto a cooled goldcoated quartz-crystal microbalance (Sack and Baragiola, 1993),
which has a sensitivity of 0.04 ML (1 ML = 1015 water molecules cm2). The crystalline film was deposited at 150 K and cooled
to 80 K to avoid thermal re-crystallization during irradiation. The
amorphous ice films were grown at 50 and 100 K; both cases show
similar IR spectra. The amorphous ice grown at 100 K was also
cooled down to 80 K before irradiation. In all cases, the column
density of the ice films was 9.3 1018 molecules cm2, which is
smaller than the range of the 225 keV protons. The irradiations
were done at fluxes less than 1012 protons cm2 s1.
We recall that vapor deposited films are porous. For this reason,
our films are initially not fully compact, q 0.82 g cm3 (Westley
et al., 1998) vs. 0.94 g cm3 for compact ice (Narten et al., 1976).
The near-infrared reflectance spectra were measured at 2 cm1
resolution, using unpolarized light (tungsten halogen lamp) at
35° incidence angle, using an InGaAs detector. The spectra are converted to units of optical depth, ln(R/R0), derived from the ratio
between the reflectance of the sample R to that of the bare gold
mirror R0. We obtained the amorphous fraction by fitting the spectra in the near infrared to a combination of spectra for the pure
amorphous and crystalline phases.
5. Results and discussion
5.1. Freshly deposited ices
Fig. 3 shows the optical depth in the near-infrared region for
crystalline and amorphous ices deposited at 100 and 150 K but
measured at 80 K. The figure also shows the IR absorption spectrum for amorphous ice deposited at 50 K and taken at 80 K. We
concentrate our analysis on the 1.65 lm band, of its diagnostic value in the remote sensing of planetary ices. This band is an overtone of the stretching mode (Sceats and Rice, 1979) which, by
involving collective motion (Sceats and Rice, 1979; Buch and Devlin, 1999), is sharpest for the crystalline phase.
Our spectra taken at 80 K show that the absorption band at
1.65 lm is intense and narrow in the crystalline phase, as seen previously (Mastrapa and Brown, 2006; Schmitt et al., 1998). The band
is still present in amorphous ice, but it is broadened and blueshifted 10 nm (the precise peak position of this band in Fig. 4 is
317
Fig. 4. Optical depth for the near infrared absorption of crystalline and amorphous
ice at 80 K irradiated with 225 keV protons up to a fluence of 3.8 1015 protons cm2. After subtracting a baseline, the spectra were displaced vertically for
clarity.
1.653 lm and 1.643 lm for crystalline and amorphous ice respectively). This is in agreement with the observations of Mastrapa and
Brown (2006). These results differ from the measurements of Leto
et al. (2005), who observed a temperature-dependent 1.65 lm
band for crystalline ice films grown at 150 K but could not detect
the band for amorphous ice at the growth temperature of 16 K.
5.2. Irradiations
The energy deposited by the projectiles along the penetration
depth is constant within 15%, as evaluated using the TRIM code
(Ziegler et al., 2008) for a 3 lm film. Fig. 4 shows the effect of
ion irradiation on the near infrared absorption bands between
1.4 and 1.8 lm. For crystalline ice, the 1.65 lm band decreases
and broadens with irradiation fluence, saturating at fluences higher than 3.8 1015 protons cm2. For amorphous ice, ion irradiation
only causes a slight change in the infrared band, which is likely
caused by the compaction during irradiation (Raut et al., 2008).
Most importantly, both samples show the same spectra when they
are fully irradiated.
5.3. Data analysis
One method to estimate the crystalline and amorphous concentrations with irradiation fluence consists in assuming that the IR
spectrum f of every partially irradiated sample results from the linear addition of equivalent crystalline and amorphous terms
(Strazzulla et al., 1992),
f ¼ /C f C þ /A f A
Fig. 3. Optical depth in the near-infrared region for crystalline and amorphous ices
at 80 K. Deposition temperatures were 150 and 100 K for crystalline and amorphous
ices respectively (solid lines). The dotted line corresponds to a sample of
amorphous ice grown at 50 K and also measured at 80 K. The spectra are baseline
subtracted.
ð8Þ
where /C and /A are the fractions of crystalline and amorphous
phases (/A = 1 /C), and fC and fA are the IR spectra for fully crystalline and fully amorphous ices respectively. We applied this method
to the entire near-infrared spectra range (1.4–2.3 lm), shown in
Fig. 5 left, obtaining an excellent match in all cases.
Another method that has been reported consists in measuring
the band area for the 1.65 lm band (Fig. 5 right) vs. irradiation
dose. However, irradiation causes the band shape to change such
that the minimum band area actually occurs before the ice is completely amorphized. Fig. 6 shows results from both methods.
The fit in Fig. 6, using Eq. (6), results in rA = 56 ± 6 Å2 close to
the value of 66 Å2 for the area of compaction of microporous amorphous ice (Raut et al., 2008). This similarity suggests a similar
318
M. Famá et al. / Icarus 207 (2010) 314–319
Fig. 5. Left:
unirradiated and fully irradiated crystalline ice; ––– partially irradiated. ———— Fit using Eq. (8). Right: optical depth of the 1.65 lm band after baseline
subtraction. The partially irradiated sample is found to be 66% amorphous.
In Jupiter’s magnetosphere, amorphization will be dominated
by ions of around 100 keV. The energy distribution falls rapidly
above this value (Cooper et al., 2001) and energies below 10 keV
do not contribute much to amorphization due to the small penetration and track radii. Using the same procedure as Raut et al. (2008)
we obtain, for an order of magnitude estimate:
s1 hrA Ui
Fig. 6. (d) Fraction of amorphous phase vs. irradiation fluence of 225 keV protons.
The solid line shows that amorphization of crystalline ice induced by ion irradiation
varies exponentially with fluence. (s) 1–1.65 lm band area (normalized to zero
fluence) vs. irradiation fluence.
underlying process: the production of a transient liquid track by
each ion that cools very fast, leading to amorphization if the ice
was crystalline or to the compaction if the amorphous ice was
microporous. Converting the experimental amorphization cross
section into the variable K1 gives 4 ± 0.4 eV/mol which satisfactorily compares with previous results shown in Fig. 1. In contrast
with some previous reports in the literature, we find that crystalline ice fully amorphizes at 80 K when irradiated with energetic
ions.
6. Astrophysical implications
Raut et al. (2008) developed a model to calculate the compaction time s of nanoporous ice due to ionizing radiation based on
their laboratory results. The model was applied to cosmic ray impact in the interstellar medium, resulting in
s1 ¼ 38f
ð9Þ
where f is the ionization rate of interstellar H2 in the medium.
Using known ionization rates, yields s 30 ± 20 Myr. This time
should also hold for amorphization of crystalline ice, since the
track radius is very similar, as stated above.
ð10Þ
where rA is the amorphization cross section, U the ion flux and
hrAUi an average, over the ion type and energy distribution. Using
rA 5 1015 cm2 and U = 104–107 cm2 s1 from Ganymede’s
equator to Europa, we obtain amorphization times in the range
0.6–600 years. This time will be larger for the satellites of Saturn,
where the magnetosphere has lower fluxes. For trans-neptunian objects (TNO), the main ion fluxes are the weak solar wind (which can
only amorphize a small fraction of the optical depth, and cosmic
rays). Hence, our estimate for those objects is tens of millions of
years, somewhat larger than for interstellar grains due to the reduction of cosmic ray fluxes by the interplanetary magnetic field. In the
absence of internal heat sources, crystalline ice in TNOs is likely
formed in impacts of meteorites or comets, which cause the surface
ice to liquefy and then cool slowly into crystalline ice. Such cometary impacts need to be only more frequent than 107/year to explain the observation of crystalline ice in those objects.
7. Conclusions
In this work, we analyzed the extant measurements of amorphization of crystalline ice by different irradiation sources, pointing
out similarities and discrepancies between different results. The
amount of energy deposited per molecule required for amorphization is found to increase with temperature within a broad band for
different projectiles. This behavior is explained, using a thermal
spike model, to result from the variation of the specific heat of
ice with temperature. We presented an improved analysis of the
1.65 lm absorption band to obtain more reliable crystalline/amorphous ratios, useful to interpret remote sensing data of ices in the
outer Solar System. Using this method, we analyzed our experiments on irradiation of crystalline ice by 225 keV protons finding
that, at high fluences, the films become completely amorphous.
The results show the fluence dependence for amorphization is in
agreement with previous reports. Although the model applies only
to ion impact, the idea should be applicable to the hot spots occurring in spurs induced by electrons and in photoabsorption.
M. Famá et al. / Icarus 207 (2010) 314–319
These results and conclusions re-open the question about the
origin and presence of crystalline ice in astrophysical bodies at
low temperatures that are constantly exposed to energetic charged
particles and photons.
Acknowledgment
This work was funded by NASA Outer Planet Research Program.
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