SCIENCE ADVANCES | RESEARCH ARTICLEMETALS

Pure iron grains are rare in the universe
Yuki Kimura,1* Kyoko K. Tanaka,1 Takaya Nozawa,2 Shinsuke Takeuchi,3 Yuko Inatomi3,4

INTRODUCTIONRESULTS

Most of the atoms in the interstellar medium exist in the gas phase. Only
about 1% of the total mass of the elements forms tiny solid particles
called grains. Despite their low abundance, these grains are significant
as building blocks of planetary systems (1), as substrates for the formation of molecules (2, 3), as energy transducers in interstellar and circumstellar environments (4, 5), and as key players in the efficient formationof stars (6, 7). The efficiency of these various contributions depends
strongly on the chemical composition, size, crystal structure, and geometry of the grains that are initially formed in gaseous outflows of evolvedstars and subsequently processed in interstellar environments. Therefore, to understand these characteristics of grains, it is necessary firstto clarify the compositions and quantities of grains formed in stellar
gas outflows.
Iron (Fe) is a key element for deciphering the overall composition
and amount of interstellar grains, because it is the most abundant refractory element in concurrence with magnesium and silicon in thecosmic abundance (8). Possible major components of Fe-rich grains
include metallic iron, iron oxide, or iron sulfide (9). Fe-bearing grains
are highly efficient catalysts for molecular formation (10). In addition,some Fe-bearing grains have high magnetic susceptibilities, and theresulting polarized thermal emissions and magnetic dipole emissions
might efficiently disturb the cosmic microwave background (11).
Therefore, the identification of the most common form of Fe is crucial
in understanding the evolution history of grains, the reprocessing ofelectromagnetic waves, and the chemistry in the universe.
Despite extensive astronomical observations and analyses of meteorites, insufficient amounts of Fe compounds, including iron oxides, sulfides, and carbides, have been detected to account for the expected
abundance of Fe in the universe (12–14), suggesting that most cosmic
Fe atoms exist as grains of the pure metal. Therefore, the feasibility of
the formation of metallic Fe grains in astronomical environments is an
important subject for study. Here, we perform a reproduction experiment for the condensation of Fe grains in a model microgravity system,to elucidate the likelihood of the formation of Fe grains.

Advantages of the microgravity experiment
Condensation of grains from the gas phase proceeds through the nucleation of stable small clusters and their subsequent growth. These processes are mainly controlled by two physical quantities: the sticking
probability with which gas-phase atoms attach onto clusters or grains
and the surface tension of small clusters. In most theoretical models ofgrain formation, the sticking probability has been assumed to be 1, andthe surface tension has been assumed to equal that of the corresponding
bulk material. However, this optimistic assumption regarding the
sticking probability may lead to an overestimation of the grain formation rate; furthermore, the surface tension of particles with sizes of lessthan a few nanometers must differ markedly from the corresponding
bulk value (15, 16). To determine the physical quantities involved in
the formation of Fe grains, we performed an ideal nucleation experiment in a microgravity environment of (6.2 ± 0.8) × 10−3 m s−2[(6.3 ± 0.8) × 10−4 G] (fig. S1) aboard the sounding rocket S-520-28.
An on-board in situ observation system composed of a nucleationchamber with a double-wavelength Mach-Zehnder–type laser interferometer and an image-recording system was adapted to conform to thesize and weight limitations of the rocket (Fig. 1 and fig. S2) (16, 17).
Nucleation experiments are conducted by observing the condensation of evaporated gas from a heated source in a buffer argon (Ar) gas.
The Ar gas reduces the mean free path of the gas, thereby permitting a
reduction in the physical scale of the experimental system. In groundbased experiments subject to the Earth’s gravity, conditions for nucleation are not uniform because of the presence of thermal convection
generated by the heated source. In a microgravity environment of theorder of ~10−4 G, this thermal convection is fully suppressed, conferring
the following three advantages. First, the evaporated hot gas diffuses isotropically, and the temperature profile around the evaporation source
becomes concentric; consequently, nucleation occurs concentrically, as
confirmed by microgravity experiments conducted in an aircraft (fig. S3).
Second, the gases cool more slowly, and consequently, gaseous atoms
can collide with each other more frequently on a longer time scale of gas
cooling, providing a closer simulation of astronomical environments,
such as the ejecta of supernovae or outflows from asymptotic giant
branch stars. The nucleation process can be approximately describedin terms of the product of the time scale for the supersaturation increase(tsat) and the collision frequency of iron atoms (n); tsat n is about 103 to
104 for grain formation in supernovae and asymptotic giant branchstars (18, 19). A similar value of tsat n of ~104 can be achieved in microgravity experiments (see Materials and Methods), whereas tsat n is1

Institute of Low Temperature Science, Hokkaido University, Sapporo 060-0819, Japan.
Division of Theoretical Astronomy, National Astronomical Observatory of Japan, Osawa
2-21-1, Mitaka, Tokyo 181-8588, Japan. 3Institute of Space and Astronautical Science,
Japan Aerospace Exploration Agency, 3-1-1 Yoshinodai, Chuo-ku, Sagamihara, Kanagawa
252-5210, Japan. 4School of Physical Sciences, SOKENDAI (Graduate University for Advanced Studies), 3-1-1 Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210, Japan.
*Corresponding author. Email: ykimura@lowtem.hokudai.ac.jp

2

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The abundant forms in which the major elements in the universe exist have been determined from numerous
astronomical observations and meteoritic analyses. Iron (Fe) is an exception, in that only depletion of gaseous
Fe has been detected in the interstellar medium, suggesting that Fe is condensed into a solid, possibly the
astronomically invisible metal. To determine the primary form of Fe, we replicated the formation of Fe grainsin gaseous ejecta of evolved stars by means of microgravity experiments. We found that the sticking probability
for the formation of Fe grains is extremely small; only a few atoms will stick per hundred thousand collisions sothat homogeneous nucleation of metallic Fe grains is highly ineffective, even in the Fe-rich ejecta of type Ia
supernovae. This implies that most Fe is locked up as grains of Fe compounds or as impurities accreted onto
other grains in the interstellar medium.

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SCIENCE ADVANCES | RESEARCH ARTICLE

only about 102 in ground-based experiments (16, 17). Finally, the absence of thermal convection permits the reliable determination ofphysical quantities by comparison of the experimental results withvalues from the nucleation model. In ground-based experiments, thethermal convection supplies buffer gas continuously to the nucleationsites of grains, thereby complicating the interpretation of results.
Results of the microgravity experiment
In our microgravity experiments, the temperature and partial pressureof the Fe gas were determined simultaneously by observing shifts in theinterference fringes of two lasers emitting polarized green (532 nm) andred (635 nm) lights (Fig. 2, A to C, and fig. S4). When the Fe evaporation
source was electrically heated on a tungsten filament, the initial interference fringes in Fig. 2A were shifted because of a decrease in the refractive index of the warmed Ar buffer gas that filled the chamber at an
initial pressure of 4.0 × 104 Pa (for example, Fig. 2B). When the source
temperature was increased to 2226 ± 22 K, the interference fringes in theupper right corner of Fig. 2C disappeared. Nucleation of Fe grains canbe detected from this disappearance of interference fringes, which
results from scattering of the incident laser light by the newly formed
Fe grains. We define the position where this occurs as the nucleation
front (indicated by the dotted line in Fig. 2C), at which Fe grains nucleate and grow immediately. The derived temperature and partial pressure of Fe gas at the nucleation front were 907 ± 20 K and (2.23 ± 0.27) ×
103 Pa, respectively; the uncertainty in these values arose from inaccuracies in measurements of the shifts of the interference fringes (seeMaterials and Methods). The temperature and partial pressure of Fe justbefore the nucleation decreased smoothly from the evaporation source
to the nucleation front, whereas the number density of Fe was constant(Fig. 2D).
To examine the effects of Ar buffer gas, we performed an additional
experiment at a reduced Ar pressure of 2.0 × 104 Pa. The temperature
Kimura et al. Sci. Adv. 2017; 3 : e1601992

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Fig. 2. Photographs of interference images and the temperature and partialpressure during the experiment on Fe nucleation under microgravity. Colored
images of the interference fringes (see fig. S4 for monochromatic images) at representative times for the experiment with an initial pressure of Ar buffer gas of 4 × 104 Pa:(A) before heating of the evaporation source, (B) 0.4 s before the nucleation of Fe
grains, and (C) at the time of nucleation. Scale bar, 3 mm. In (C), the dotted line in
the upper right corner indicates the nucleation front of the Fe grains above which
the disappearance of interference fringes is due to scattering of light by abundantly
formed Fe grains. (D) Profiles of the temperature (squares), partial pressure (circles), andnumber density (triangles) of the Fe gas from the evaporation source to the nucleation
front in (B). The error for the x axis is within the symbols. The solid black and blue curves
are the temperature profile and the initial number density of Fe atoms, respectively,
used in the calculation. The temperature was expressed by Eq. 10 with a time t = x2 D−1,
where x is the distance from the evaporation source and D is the diffusion coefficientof Fe atoms. The labels are as follows: e, electrode; t, thermocouple; es, evaporation source.

and partial pressure of Fe at the nucleation front were 958 ± 37 K and(1.44 ± 0.29) × 103 Pa, respectively, with an elevated source temperatureof 2188 K.
Figure 3A shows the temperatures and partial pressures of Fe gas at
the nucleation front determined from the experiments. In the case of an
initial Ar gas pressure of 4.0 × 104 Pa, the nucleation temperature of Fe
grains (907 K) was significantly below the solid-vapor equilibrium temperature (2116 K) corresponding to the partial pressure of Fe [(2.23 ±0.27) × 103] at the nucleation front (Fig. 3B). Therefore, the degree ofsupercooling is as much as 1209 K. Because the equilibrium vapor pressure between gaseous and solid Fe at 907 K is 3.1 × 10−11 Pa, an extremely high supersaturation ratio of 7.2 × 1013 is realized at the nucleation
front. For the experiment at an initial Ar gas pressure of 2.0 × 104 Pa, theresulting supersaturation ratio was 2.4 × 1012 based on the equilibrium
vapor pressure between solid and vapor at the nucleation temperatureof 958 K.
Determination of the physical properties
By applying nucleation theory, we determined the sticking probability afor Fe grain formation to explain the nucleation temperature obtainedin the experiments. We used a semiphenomenological (SP) model, in
which the formation energy of a cluster in the classical nucleation theory(CNT) is corrected for the binding energy of dimers (see Materials
and Methods). In our calculations for grain formation, we defined
the nucleation temperature as the point at which half the initial gasphase Fe atoms have been consumed, because nucleation was detected
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Fig. 1. Schematic of the configuration and optical path of the doublewavelength Mach-Zehnder–type laser interferometer with a nucleation chamber.
The red and green lines show the optical paths of the red and green lasers, respectively.
The resulting images of interference fringes are recorded with a charge-coupled device
camera (cam). The evaporation source of Fe wire wrapped around a tungsten filament
0.3 mm in diameter and 68 mm in length is shown as the black solid line (es) in the
nucleation chamber (n). The other labels are as follows: b, beam splitter; c, collimator; d,dichroic mirror; e, electrode; g, gas line; l, lens; m, mirror; o, optical fiber; p, polarizer; s,
short-pass filter; t, thermocouple; v, vacuum gauge; gl, green laser; py, pyrometer; rl, redlaser; va, valve; vp, view port.

SCIENCE ADVANCES | RESEARCH ARTICLE

experimentally from the scattering of laser light. Consequently, a significant fraction of the Fe gas had to be locked up in Fe grains. Figure 4A
shows the result of a simulation with a = 1.8 × 10−5 and the surface tension (s) of bulk Fe (2.48 N m−1) (20). As the gas cools, the nucleation
rate increases markedly because of the increase in the supersaturation
ratio. Consequently, the number density of the remaining Fe gas decreases,
and the nucleation rate decreases rapidly. The nucleation rate reaches amaximum at 1012 K, and the nucleation temperature is calculated to be
907 K. Therefore, this model with a = 1.8 × 10−5 reproduces the experimental results closely. By taking into account inaccuracies in temperature, the sticking probability of Fe at ~900 K is found to be 1.4 × 10−5 to
2.0 × 10−5. The resulting sticking probability depends on the definitionof the nucleation temperature; for example, a = 1.2 × 10−5 when the
nucleation temperature is defined as the point at which 10% of the initial
gas atoms are consumed, or a = 1.2 × 10−4 at 90% consumption. Notethat the grain formation model with a = 1 predicts a nucleation temperature of about 1750 K (Fig. 4A) and therefore cannot explain theexperimental results.
We also examined the dependence of the results on the surface tension. Because the surface tension s of nanometer-scale Fe particles is likely to differ several tens of percent from that of bulk Fe (2.48 N m−1), we
considered a wider range of values s = 1.0 to 3.3 N m−1. As shown in Fig.
4B, the variability of the sticking probability is small in the plausible rangeof surface tensions of Fe. As mentioned above, the supersaturation ratio isremarkably high for nucleation of Fe grains in our experiments. As a result, the size of critical nuclei, which is the minimum number of atoms
present in a small cluster that can grow continuously and with thermodynamic stability, should be small and is actually the dimer, as can beevaluated by means of Eq. 14. The formation of dimers from isolated
atoms is the largest barrier to grain formation, because the forming dimer
dissociates into the gas phase using the excess energy from the bonding.
Therefore, the formation energy of a cluster is mainly determined by thebinding energy of the dimer rather than by the surface tension, leading us
to conclude that the binding energy of the dimer, as well as the sticking
probability, is crucial for homogeneous nucleation.
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Fig. 4. Estimation of the sticking probability by simulations to explain the
results of the experiments. (A) Result of calculations for the formation of Fe
grains for a sticking probability of a = 1.8 × 10−5 and a surface tension of s =2.48 N m−1, which was obtained by applying the SP nucleation model. The
dashed and solid curves show the time variation in the nucleation rate J andthe number density of gas-phase Fe atoms n1(t), respectively. The vertical dottedline shows the nucleation temperature derived from microgravity experiments.
The thin gray curve shows the number density of Fe atoms for a = 1 and s =2.48 N m−1, for which nucleation occurs at a much higher temperature (1700 K)
than the experimental result. (B) Plot of the sticking probability a against the surface tension s estimated from a comparison of the results of experiments and thesimulations. The blue and orange points plot results for experiments in Ar gas at
2.0 × 104 Pa and 4.0 × 104 Pa, respectively. The vertical dot-dashed green line
shows the bulk surface tension of molten Fe (20).

DISCUSSION

The extremely low sticking probability of Fe suggests that homogeneous
nucleation of metallic Fe grains is highly inefficient. A similarly small
sticking probability (a = ~10−5) has been reported for the formationof metallic zinc grains in a microgravity nucleation experiment (21).
We have also measured a small sticking probability (a = 3.4 × 10−5 ±1.2 × 10−4) for metallic nickel grains in a microgravity experiment performed in an aircraft. In contrast, the sticking probability for the formation of grains including Fe in ground-based laboratory experiments is
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Fig. 3. Temperatures and partial pressures of Fe gas at the nucleation front, obtained from the microgravity experiments. (A) The blue and orange points witherror bars indicate the temperatures and partial pressures of Fe gas just before the nucleation for the experiments at initial Ar gas pressures of 2.0 × 104 Pa and 4.0 × 104 Pa,
respectively. The green and red lines show the relationship between the temperature and the partial pressure of Fe gas to explain the shifts in the interference fringes for thegreen and red laser beams; the solid and dashed lines are the results for Ar gas at 2.0 × 104 Pa and 4.0 × 104 Pa, respectively. (B) The equilibrium vapor pressure of Fe between
the vapor and solid is shown by the solid curve. The two square symbols are the same as the points in (A). The temperatures measured at the evaporation source are shown by
the blue and orange vertical lines for experiments in Ar gas at 2.0 × 104 Pa and 4.0 × 104 Pa, respectively. The large gap between the two square symbols and the solid curveshows the presence of a very large supersaturation at nucleation.

SCIENCE ADVANCES | RESEARCH ARTICLE
where a is the coefficient of volume expansion (0.003663 K−1 for Ar
and 0.003661 K−1 for Fe in this experiment), DT = T – 273.15 K, and pressure P0 = 101,325 Pa. The values of NAr – 1 are (2.813 ± 0.017) × 10−5 and(2.790 ± 0.017) × 10−5 at 532 and 632.8 nm, respectively, at 1.0 × 104 Pa
and 293.15 K (31). The values of NFe – 1 are 3.837 × 10−4 and 1.163 × 10−4
at 532 and 633 nm, respectively, at 2.0 × 104 Pa and 293 K (32).
The product of the shift in the fringes, Dd, and the wavelengthof the laser, l, are proportional to the change in the optical path
length L, defined as L = Nl, where l is the physical length (taken
to be the length of the tungsten filament, which was 68 mm, in thisexperiment). The shifts in the positions of the interference fringes
for the green (DdG) and red lasers (DdR) after heating are given by
the following equations l
DdG ¼ NG;ArðTi ;Pi Þ  NG;ArðT;PPFe Þ  NG;FeðT;PFe Þ þ 1
lG

ð2Þ

and

 l
DdR ¼ NR;ArðTi ;Pi Þ  NR;ArðT;PPFe Þ  NR;FeðT;PFe Þ þ 1lR

ð3Þ

where Ti and Pi are the initial temperature and pressure, respectively, of Ar before the source temperature was elevated, and thesubscripts G and R indicate quantities for the green and red lasers,
respectively. Because the total pressure in the chamber P wasmonitored by using a pressure gauge, and DdG and DdR can beobserved in the images, it was possible to determine the gas temperature (T) and the partial pressure of Fe (PFe) simultaneously byusing Eqs. 1 to 3. The amounts of fringe shift at the nucleation
front just before the nucleation were DdG = 6.5 and DdR = 6.4
for the experiment at an initial Ar gas pressure of 4 × 104 Pa.
Model and numerical simulation
To interpret the results of our experiments, we performed numericalsimulations of the nonequilibrium condensation of Fe on the basis of
nucleation theory (18, 33), by applying an SP nucleation model, which isone of the most successful and useful models (34, 35). The SP model
modifies the CNT by adding extra terms for the formation energy ofa cluster, obtained by using the second virial coefficient of the vapor.
This model succeeded in achieving agreement with the nucleation rates
derived from experimental data or from MD simulations for various
materials (34–37). In homogeneous nucleation theory, the nucleation
rate J (that is, the rate at which the stable nuclei are formed per volume)is expressed as follows(∞

MATERIALS AND METHODS

J¼

)−1
1
þ
i¼1 R ðiÞne ðiÞ∑

ð4Þ

Determination of the temperature and partial pressure of Fe
In order to determine the partial pressure of evaporated Fe gas, wemeasured small changes in the refractive index by individually observing
shifts in the interference fringes at two wavelengths. The refractive indicesof Ar, NAr(T,P), and Fe, NFe(T,P), can be expressed as a function of thetemperature T (K) and pressure Pgas (Pa), as follows

where R+(i) is the accretion rate from an i-mer (a cluster containing i
atoms) to an (i + 1)-mer. The equilibrium number density of i-mers ne(i)is given by½Ngasð273:15;P0 Þ  1 PgasNgasðT;PÞ  1 ¼
1 þ aDT
P0



PFe
DGi
exp 
ne ðiÞ ¼
kT
kT

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significantly larger (a = ~10−2 to 1) (16, 22). How then does gravity
affect the sticking probability? One possibility is localized enhancement of gas density as a result of thermal convection; a higher density
leads to a higher collision frequency of atoms, which might cause
overestimation of the sticking probability. Another possibility is a heterogeneous effect; for example, small amounts of residual oxygen andwater gas might be continuously supplied to the nucleation region by
thermal convection. If seed nuclei of Fe oxides form rather than metallic
Fe, atomic Fe might be able to stick to Fe oxides more efficiently than tometallic Fe.
The primary sources of cosmic Fe are considered to be type Ia supernovae, which are driven by thermonuclear fusion of white dwarfs (23).
Iron atoms produced around the centers of type Ia supernovae are
injected into the interstellar medium as cooling Fe-rich ejecta, in which
Fe gas is believed to condense as pure Fe grains (24). However, despite
the production of large quantities of Fe atoms, the formation of Fe
grains has not yet been observed in type Ia supernovae (25). A theoretical model of grain formation shows that small amounts of Fe grains
with a radius of 10 nm could form in type Ia supernovae if the sticking
probability is assumed to be 1 (26). However, our results show that the
sticking probability for the formation of Fe grains is extremely low, suggesting that homogeneous nucleation of Fe grains is much more difficult thanpreviously expected. This explains why no metallic Fe grains have been observed in type Ia supernovae. In addition, the ejecta of type Ia supernovae
are subjected to strong radiation fields for up to several hundred days after
the explosion; the energetic photons and electrons could destroy small
clusters, causing additional suppression of grain condensation.
If this is so, where in the universe is the Fe? Core-collapse supernovae arising from massive stars also produce Fe atoms and disperse theminto the interstellar medium (27). It has been argued that an abundantmass of metallic Fe grains formed in the ejecta of supernova 1987A is
required to explain the far-infrared flux observed by the Herschel Space
Observatory (28). However, even if core-collapse supernovae synthesize
Fe grains with high efficiency, we cannot conclude that cosmic Fe exists
predominantly in the form of pure Fe grains because core-collapse
supernovae are not the dominant source of Fe in the present universe(27). In addition, given the very low sticking probability determinedfrom our experiments, Fe may not condense as the pure metal, but instead, it may condense onto other species of grains through heterogeneous nucleation. Many studies suggest that grains can grow throughaccretion of gas-phase atoms in interstellar environments, such as dense
molecular clouds. In this case, it would be unnatural for Fe gas to accrete
predominantly onto Fe grains rather than onto existing silicate or carbonaceous grains (29, 30). Therefore, most of the Fe might be captured
as impurities and/or components of other grains through physical andchemical processes in the interstellar medium.

SCIENCE ADVANCES | RESEARCH ARTICLE
where PFe is the partial pressure of Fe gas, k is the Boltzmann constant, and DGi is the free energy associated with the formation of acluster of size i from the gas phase. The accretion rate R+(i) is given by

In the calculations, we consider a gaseous system containing Fe gasthat cools with a characteristic time tT. In this case, the temperature T of
the gas as a function of time t is given by2Rþ ðiÞ ¼ an1 vth 4pr12 i3TðtÞ ¼ T0 expðt=tT Þð6Þ

where n1 is the number
density of Fe atoms, vth is the thermal velocpﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
ity of gas given by kT=ð2pmÞ, and a is the sticking probability. The
radius of an atom r1 is defined as (3m/4prm)1/3, where m is the massof an atom and rm is the bulk density.
Because of the exponential dependence of the free energy on J, evaluation of the free energy DGi is important. Here, we used values of DGi
given by an SP model. In the SP model, DGi is expressed asð7Þ

where S (= PFe/PFe,e) is the supersaturation ratio, s is the surface tension,
A1 is the surface area of a monomer, and A2 is a correction term
determined from the second virial coefficient. PFe,e is the equilibrium
vapor pressure of bulk Fe materials at a given temperature (Fig. 3B).
Although we have no experimental data on the second virial coefficient of refractory metals such as Fe, we can evaluate A2 by using
a relationship between the second virial coefficient and the chemical
potential of a dimer. According to Tanaka et al. (33), A2 is expressed as
A2 ¼ ½ð2

2=3

 1ÞsA1  E þ mV þ mR þ mT ð2

1=3

1

 1Þ





ħω
ħω
mRe 2 kT
; μR ¼ −kT ln
μV ¼ kT ln 1− exp −
;
þ
kT
2
2ħ2

ð9Þ

where w is the vibrational frequency of a dimer and Re is the equilibrium distance between nuclei. Consequently, we can evaluate A2 as afunction of T for given s, E, w, and Re. In our calculation, we adopted thevalues E/k = 8600 K, w = 8.9 × 1012 s−1, and Re = 2.4 × 10−10 m (38). In
the SP model, the formation energy of a cluster is determined by thebinding energy and chemical potentials arising from vibrational, rotational, and translational motions of dimers and the bulk surface tension.
The formation energy for small clusters is primarily determined by thebinding energy of the dimer rather than by the bulk surface tension,
because the value of E is markedly dependent on the material. Note that
the SP model gives the exact values of the free energy of monomer anddimer (DG1 and DG2), because DG1 = 0 is satisfied and DG2 corresponds
to the chemical potential of the dimer. There are large deviations fromthe values evaluated by CNT for clusters of fewer than about 10 atoms.
Consequently, the correction term in DGi is crucial for small clusters.
Kimura et al. Sci. Adv. 2017; 3 : e1601992

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n1 ðt Þ ¼ n1 ð0Þ  ∫0 J ðt′Þtrðt; t′Þ 3
dt′
r1

ð11Þ

where J(t′) is the nucleation rate at time t′ and r(t,t′) is the radius ofgrains nucleated at t′ and measured at t. The growth equation of a grainradius r(t,t′) is expressed in the form
∂rðt; t′Þ
4p
¼ a r13 n1 ðt Þvth
∂t
3

ð12Þ

The radius of the critical nuclei r(t,t′) isrðt; t′Þ ¼ i1=3
∗ r1

ð8Þ

where E is the binding energy of a dimer and ℏ is Planck’s constant(32). In Eq. 8, mV, mR, and mT are the chemical potentials arising fromvibrational, rotational, and translational motions of the dimers, as
given by( )PFe;e mkT −3=2
μT ¼ kT ln
kT 4pħ2

where T0 is the initial temperature, which corresponded to the temperature of the heated source in our calculations (see below). As the gas
temperature decreases, nucleation and grain growth proceed, consuming gas-phase Fe atoms. The number density of Fe gas n1(t) is given by

ð13Þ

where i∗ is the number of atoms in the critical cluster, which is thesmallest thermodynamically stable cluster and determined by dne(i)/di = 0; that is0i∗ ¼ @

σA1 þ

qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ13
ðσA1 Þ2 þ 3A2 kT ln S
A
3kT ln S

ð14Þ

By using Eqs. 4 to 14, which describe the nucleation rate and thenonequilibrium condensation, we simulated the condensation processof Fe by treating the sticking probability a and the surface tension s as
parameters.
In the calculations, we adopted initial partial pressures of Fe of PFe (t = 0)[= n1(0)kT] = 1440 and 2230 Pa and initial temperatures of T0 = 2188 and2226 K for the experiments in Ar gas at initial pressures of 2.0 × 104 Pa and4.0 × 104 Pa, respectively. The time scale for cooling tT was taken as thetime required for the Fe gas to arrive at the nucleation site by diffusion fromthe evaporation source: tT ≈ X2D−1, where X is the distance from the evaporation source to the nucleation site (X = 1.29 × 10−2 m and 1.14 × 10−2 m)
and D = vmeanl/3 is the diffusion coefficient (D = 3.07 × 10−3 m2 s−1 and
1/2
1.56 × 10−3 m2 s−1). Here, vmean = (8kT/pm)
pﬃﬃﬃ −1is the mean velocity of the−1gas (vmean = 783 or 771 m s ), and l = ( 2nsÞ is the mean free path of agas molecule (l = 1.18 × 10−5 m or 6.06 × 10−6 m). The mean cross sectionof an Fe atom s is 4.988 × 10−20 m2, and the number density of Ar gas n is
1.20 × 1024 m−3 (2.34 × 1024 m−3) for the experiments in Ar gas at an initialpressure of 2.0 × 104 Pa (4.0 × 104 Pa), where we used the total gas pressuresof 26,550 Pa (50,683 Pa), as measured in the experiments. The obtained
time scale for cooling is tT = 5.42 × 10−2 s and 8.33 × 10−2 s for the experiments in Ar gas at initial pressures of 2.0 × 104 Pa and 4.0 × 104 Pa,
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2

1

DGi ¼ ði  1ÞkT ln S þ sA1 i3  1 þ A2 i3  1

ð10Þ

SCIENCE ADVANCES | RESEARCH ARTICLE

SUPPLEMENTARY MATERIALSSupplementary material for this article is available at http://advances.sciencemag.org/cgi/
content/full/3/1/e1601992/DC1
Supplementary Text
fig. S1. Time evolution of the acceleration gravity in the sounding rocket during the
microgravity experiment.
fig. S2. Photographs of the experimental systems.
fig. S3. Examples of nucleated particles in a microgravity environment.
fig. S4. Images of interference fringes during the Fe nucleation experiment under microgravity.

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Acknowledgments: We thank N. Ishii and all project members of the sounding rocket S-520-28
experiment of the Japan Aerospace Exploration Agency (JAXA). Funding: This work was supported by
a Grant-in-Aid for Scientific Research (S) from KAKENHI (15H05731), by a Grant-in-Aid for Young
Scientists (A) from KAKENHI (24684033) of the Japan Society for the Promotion of Science, by aGrant-in-Aid for Scientific Research (C) from KAKENHI (2640023 and 15K05015), by a Grant-in-Aid for
Scientific Research on Innovative Areas (16H00927), and by the Steering Committee for Space
Biology and Microgravity Science of Institute of Space and Astronautical Science, JAXA. Author
contributions: Y.K. designed the project, performed the experiments, and analyzed the data.
K.K.T. performed the calculations. Y.K., K.K.T., and T.N. interpreted the data and cowrote themanuscript. Y.K., S.T., and Y.I. prepared the experimental system. S.T. and Y.I. prepared the interface
between the experimental system and the sounding rocket. Competing interests: The authors
declare that they have no competing interests. Data and materials availability: All data needed toevaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials.
Additional data related to this paper may be requested from the authors.
Submitted 23 August 2016
Accepted 30 November 2016
Published 18 January 201710.1126/sciadv.1601992
Citation: Y. Kimura, K. K. Tanaka, T. Nozawa, S. Takeuchi, Y. Inatomi, Pure iron grains are rare in
the universe. Sci. Adv. 3, e1601992 (2017).

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respectively. In these estimations, we adopted the mean temperatures (1614or 1567 K) between the evaporation source and the nucleation site. There isan uncertainty in the value of tT within a factor of 2 because tT is proportional to T–3/2, leading to small deviations from the evaluated value of a toexplain the experiments (within a factor of 2).
It is known that the nucleation process can be approximately described in terms of the product of the time scale for the supersaturation
increase tsat and the collision frequency of iron atoms n (18). The collision frequency of iron atoms n was 2.52 × 106 s−1 or 3.96 × 106 s−1 forexperiments in Ar gas at initial pressures of 2.0 × 104 Pa and 4.0 × 104
Pa, respectively. Because tsat was evaluated from tT kT/H with the latent
heat (H/k = 4.5 × 104 K), the corresponding values of tsat n were
calculated to be 4.9 × 103 and 1.1 × 104, which are similar to those in
the grain formation environments of supernovae and asymptotic giant
branch stars (19), whereas tsat n was determined to be ~102 in groundbased experiments because of the smaller value of tT (~10−4 s) (16, 17).

Pure iron grains are rare in the universe
Yuki Kimura, Kyoko K. Tanaka, Takaya Nozawa, Shinsuke
Takeuchi and Yuko Inatomi (January 18, 2017)
Sci Adv 2017, 3:.
doi: 10.1126/sciadv.1601992

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