ARTICLE
Fast methane diffusion at the interface of two
clathrate structures
Umbertoluca Ranieri 1,2, Michael Marek Koza 2, Werner F. Kuhs 3, Stefan Klotz4, Andrzej Falenty 3,
Philippe Gillet1 & Livia E. Bove 1,4
Methane hydrates naturally form on Earth and in the interiors of some icy bodies of the
Universe, and are also expected to play a paramount role in future energy and environmental
technologies. Here we report experimental observation of an extremely fast methane
diffusion at the interface of the two most common clathrate hydrate structures, namely
clathrate structures I and II. Methane translational diffusion—measured by quasielastic
neutron scattering at 0.8 GPa—is faster than that expected in pure supercritical methane
at comparable pressure and temperature. This phenomenon could be an effect of strong
confinement or of methane aggregation in the form of micro-nanobubbles at the interface of
the two structures. Our results could have implications for understanding the replacement
kinetics during sI–sII conversion in gas exchange experiments and for establishing the
methane mobility in methane hydrates embedded in the cryosphere of large icy bodies in the
Universe.
DOI: 10.1038/s41467-017-01167-2 OPEN
1 EPSL, ICMP, École polytechnique fédérale de Lausanne (EPFL), Station 3, CH-1015 Lausanne, Switzerland. 2 Institut Laue-Langevin, 71 avenue des Martyrs,
CS 20156, 38042 Grenoble cedex 9, France. 3 GZG Abt. Kristallographie, Universität Göttingen, Goldschmidtstrasse 1, 37077 Göttingen, Germany. 4 Institut
de Minéralogie, de Physique des Matériaux et de Cosmochimie, Université Pierre et Marie Curie Paris 06, CNRS Unité Mixte de Recherche 7590, Sorbonne
Universités, F-75252 Paris, France. Correspondence and requests for materials should be addressed to U.R. (email: ranieriu@ill.fr)
or to L.E.B. (email: livia.bove@impmc.upmc.fr)
NATURE COMMUNICATIONS |8:  1076 |DOI: 10.1038/s41467-017-01167-2 |www.nature.com/naturecommunications 1
Gas clathrate hydrates are a general class of compoundscomposed of water (hosts) molecules and gas (guests)atoms or molecules1. Among them, clathrate hydrates
of methane are probably the most extensively studied. The
natural occurrence of methane hydrate-containing sediments
in permafrost areas and ocean shelves, the risk due to their
formation in oil and gas pipelines, as well as their potential
application as gas transportation media in soft conditions
(i.e., close to atmospheric pressure and room temperature)
explain the wide interest shown for these materials1, 2. Exchan-
ging the guests in natural gas hydrate deposits with CO2 has been
suggested as a two-in-one approach of energy recovery and
concomitant CO2 mitigation3. As they are believed to be the
dominant methane-bearing phase in the nebula from which the
outer planets and satellites are formed, the properties of methane
hydrates are also crucial to models of bodies in the outer solar
system4. From a physical−chemical point of view, methane
hydrates represent prototypical examples of hydrates of hydro-
phobic guests: the combination of low temperature, high pressure,
a weak gas–water interaction between the guest molecules and the
host lattice, and the relatively strong hydrogen bonds between
host molecules allow for the formation of open crystalline water
networks encaging CH4 molecules. The topology of the water
cages and the number of gas molecules trapped in these cages
critically depend on the specific thermodynamic conditions of
formation of the clathrate hydrate and on its formation
kinetics1, 5.
The most common structures formed by clathrate hydrates at
relatively moderate pressures are the clathrate structures I and II
(noted sI and sII). The unit cell of clathrate sI (space group
Pm‾3n) contains two small dodecahedral (512) water cages and six
bigger tetrakaidecahedral (51262) cages. The unit cell of sII (space
group Fd‾3m) contains 16 512 cages and eight large hexadecahe-
dral (51264) cages1 (Fig. 1). It is well accepted that methane
hydrates preferentially crystallise into sI1. However, cages char-
acteristic of sII have been transiently detected in the initial stages
of the formation of methane hydrates in both experiments6, 7 and
simulations8–12. This is not surprising since (i) the difference in
free energy between sI and sII is small13 and (ii) appearance of
metastable polymorphs or transient non-equilibrium states is
commonly observed during nucleation of hydrates5, 13–16. It is
noteworthy that sI and sII are topologically incompatible without
the intercalation of pentakaidecahedral (51263) cages;8 the inter-
play between kinetic factors and thermodynamic stability during
sI–sII cross-nucleation has been discussed in details17. In
methane hydrates at room temperature and pressures up to
0.6 GPa, sII has been reported to persistently coexist with sI18–20.
Therefore, the resulting coexistence of structures in high-pressure
samples can be seen as a frozen form on laboratory timescales of
the metastable sI–sII polymorphs usually encountered during
nucleation of methane hydrates.
Low-temperature translational and rotational excitations, as
well as cage-to-cage hopping of CH4 molecules trapped in
clathrate sI were previously investigated at ambient and
low pressures21–24. However, no information is available on
the extra-cage diffusivity of the guest molecules in methane
hydrates; this information could be highly relevant for the
modelling of the subcrustal layers of methane clathrates embed-
ded in the cryosphere of icy planets and large icy satellites25, 26.
Recently, a study based on molecular dynamics simulations
reported diffusion coefficient values in the nanosecond time scale
for methane diffusion at grain boundary-like structures of
defective clathrates27.
In this work, we probe the microscopic diffusion of methane in
a methane hydrate (CH4–D2O) sample exhibiting coexistence of
clathrate sI and sII by quasielastic neutron scattering (QENS)
measurements. Coexistence of structures is promoted by applying
high pressure. QENS is a well-suited technique to study dynamics
on the picosecond time and Å length scales28. Spectra of the
sI–sII clathrate show a clear quasielastic signal whose analysis
reveals a very fast extra-cage translational diffusion of methane
molecules on the picosecond time scale. For comparison, we also
measure methane hydrates in pure sI clathrate, in pure hexagonal
clathrate structure H (space group P6/mmm)26 and during
transformation from sI to structure H (noted sH); the spectra of
sI and sH do not exhibit any visible quasielastic signal, and the
spectra of sI–sH show a very weak signal, orders of magnitude
smaller than the signal from sI−sII.
Results
QENS experiments and elastic scattering. The experiments were
performed at the time-of-flight spectrometer IN6 at the Institut
Laue-Langevin in Grenoble (France) using a Paris-Edinburgh
sII
sI
20
sll peaks
sl peaks 11
0
20
0
21
0
21
1
22
0
31
0
22
2
32
0
32
1
sl–sll
sl
El
as
tic
 in
te
ns
ity
30
11
1
22
0
31
1
22
2
40
0
33
1
42
2
51
1
33
3
y
y
z
z
x
x
40 50 60
Scattering angle 2 (Degrees)
70 80 90 100 110
Fig. 1 Neutron diffraction patterns. Powder diffraction patterns of methane hydrate in pure sI clathrate at 0.4 GPa and 290 K and in the sI–sII clathrate at
0.8 GPa and 282 K. Breaks correspond to noisy detectors and to the strong Bragg peak of alumina from the anvils at 95°. The positions of the Bragg peaks
for sI (cell parameter 11.7 Å) and for sII (cell parameter 17.0 Å) are reported. On the right, we present views of the unit cells of sI and sII (512 cages in cyan,
51262 cages in purple, 51264 cages in blue)
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press and recently developed ceramics anvils29. The wavelength of
the incoming neutrons was 5.12 Å, resulting in an instrumental
resolution of 0.08 meV. This corresponds to an observation
time of ~8 ps. The sample exhibiting coexistence of clathrate sI
and sII was prepared according to the following procedure: we
compressed methane hydrate (originally in sI) to 0.8 GPa at
liquid nitrogen temperature and then warmed it up to 282 K. The
neutron powder diffraction pattern of the sample at 0.8 GPa and
282 K is presented in red in Fig. 1. It indicates that the sample
contained about half as much sII than sI, on the basis of peak
heights. The pattern was obtained directly on IN6 by comparing
the intensities of the elastic peaks, at each scattering angle,
with those measured on a vanadium standard which gives
isotropic elastic scattering. All the Bragg peaks of the sample
can be indexed within the space groups of sI and sII. Figure 1 also
depicts the diffraction pattern of pure sI clathrate. The diffraction
10
8
6
In
te
ns
ity
 (a
.u.
)
In
te
ns
ity
 (a
.u.
)
In
te
ns
ity
 (a
.u.
)
4
2
0
10
8
6
4
–1
0
2
4
6
8
0 1
2
0
10
8
6
4
2
0
10
282 K
0.6 Å–1 0.6 Å–1
1.0 Å–1 1.0 Å–1
1.4 Å–1 1.4 Å–1
212 K
8
6
4
2
0
10
8
6
4
2
0
10
8
6
4
2
0
–3 –2 –1 0
–h (meV)
1 2 –3 –2 –1 0
–h (meV)
1 2
Fig. 2 Examples of measured QENS spectra. QENS spectra of methane hydrate in the sI–sII clathrate at 0.8 GPa and selected temperature T and
momentum transfer Q values. Experimental data (empty circles) are compared to their best fits (black lines). Error bars were calculated by the square root
of absolute neutron count combined with the law of propagation of errors. Quasielastic Lorentzian (solid green lines) and elastic (dashed green lines)
components are also shown (upshifted by the value of the flat background for clarity). In the inset, a Lorentzian fit is compared to the 2D diffusion fit
(blue line) of the same spectrum
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patterns of pure sH clathrate and of the sample transforming
from sI to sH are presented in Supplementary Fig. 1. We recorded
QENS spectra of the sI–sII clathrate at the constant temperature
T of 282 K and pressure of 0.8 GPa during 6 h. The amount of sII
was constant during this time. Then we continuously decreased
the temperature to 200 K over 15 h to characterize the T depen-
dence of the probed diffusion at 0.8 GPa. Spectra measured
between 282 and 200 K were merged into three groups of 5 h of
acquisition time each, corresponding to the following average
temperature values: 267, 238 and 212 K. Upon cooling down, the
relative amount of sI and sII remained approximately constant.
The diffraction patterns recorded at 267, 238 and 212 K are
reported in Supplementary Fig. 2. More details about the
experiments are given in the Methods section.
Fitting of the QENS spectra. Figure 2 depicts typical QENS
spectra of the methane hydrate sample exhibiting coexistence of
clathrate sI and sII at 0.8 GPa. Examples of spectra of methane
hydrate in pure sI clathrate, in pure sH clathrate and in the sI–sH
clathrate are shown in Supplementary Fig. 3. Spectra in Fig. 2
show a clear quasielastic signal, i.e., a broadening of the elastic
line produced by interactions of the neutrons with diffusing
atoms of the sample. Since the incoherent cross-section of
hydrogen is almost two orders of magnitude larger than that of
other atoms, the measured signal is essentially due to the
dynamics of protons in the guest molecules30, 31. We first applied
the most common model used to fit quasielastic data, i.e., a
Lorentzian function (whose half-width-half-maximum is noted
Γ). A delta function was used to fit the elastic line of the
spectra, which is due to the contribution of the water network and
of the slowly-diffusing or non-diffusing methane molecules
trapped in the clathrate structures. Total best fits to the experi-
mental data are presented in Fig. 2 and can be seen to accurately
describe the spectra. Based on the integrated areas of the qua-
sielastic and elastic lines (after subtraction of the empty cell
measurement), we roughly estimate that about one third of the
methane molecules in the sample contribute to the fitted qua-
sielastic signal, at each investigated T. More details on this esti-
mation are given in Supplementary Note 1. Since cage
occupancies in the newly formed sII clathrate might be lower
compared to the starting sI clathrate hydrate, part of the methane
molecules in the starting sI clathrate could indeed have been
released from the starting sI hydrate into the grain boundary
network during transformation from sI to sII and would be
available to perform extra-cage translational diffusion. However,
a minimum level of occupancies is required to ensure stability of
sII and one can estimate that no more than 10% of the methane
in the sample could have been released without destabilization of
the water matrix. The existence of a fraction of fast diffusing
methane molecules as high as one third strongly suggests that an
appreciable fraction of water molecules in the sample are in a
disordered state. Such disordered regions would form at the front
line of the transformation between clathrate sI and sII, and their
sizes are most likely far below the typical size of the crystallites
(that is a few micrometres32). This point is further discussed in
Supplementary Note 2. Moreover, the absence of a prominent
quasielastic signal in the spectra of the sI–sH methane clathrate
hydrate highlights the very particular nature of the interfaces
between coexisting sI and sII, compared to the temperature-
induced or pressure-induced structural transition taking place at
high driving forces between two stable forms of methane hydrates
such as sI and sH. The micro-structural properties of sI and sII
coexisting assemblies certainly deserve to be further investigated.
Momentum transfer Q dependence of the QENS signal. Figure 3
depicts the parameter Γ as a function of Q2. The Q dependence of
Γ provides information about the characteristic time and nature of
the probed motion. The monotonic increase of Γ rules out that the
measured quasielastic signal is due to a localised (rotational)
dynamics of methane, which would be indicated by a Q-inde-
pendent Γ. Instead, it clearly highlights that a translational
diffusion process is at the origin of the signal28. It must be also
noted that the rotational quasielastic contribution of methane
molecules trapped in clathrate sI is very large (half width above
5 meV) at 150 K22 and thus only contributes to the background of
the spectra here. Similar rotational behaviour can be reasonably
expected for CH4 molecules in a clathrate sII, as no indication of
inequivalent environments for the guest molecule emerged from
the low-temperature rotational spectra of sI methane clathrate23
(although methane occupies the two types of cages of sI). As can
be seen in Fig. 3, Γ extrapolates to 0 for Q→ 0. Hence, the
measured quasielastic signal is not associated with an intra-cage
diffusive motion of CH4 molecules, since for a particle restricted to
move in a confined geometry Γ shows30, 31 a plateau at small Q.
For example, for a particle moving within a sphere of radius R, Γ
shows33 a plateau for Q< π/R. The Q dependence of Γ is best
approximated within the random jump diffusion model of Singwi
and Sjolander by:
Γ Qð Þ ¼ 
hDQ
2
1þ DQ2τ ; ð1Þ
with D representing the isotropic translational diffusion
coefficient and τ the mean residence time between jumps28. The
corresponding formula for a continuous free translational
diffusion process would be Γ(Q)= ħDQ2. Fits of Γ(Q2) according
to Eq. (1) are presented in Fig. 3; the values obtained for D and
τ are reported in green in Fig. 4. The translational diffusion
coefficient turns out to be of the order of 10−4 cm2 s−1 and its
temperature dependence is rather weak (25% over the investigated
T range). An Arrhenius fit of D provides an activation energy of
0.48± 0.11 kcal mol−1. This value is small compared to the acti-
vation energies reported in literature for the cage-to-cage hopping
of CH4 in sI clathrates (for example, 12.4 kcal mol−1 in ref. 21) and
points at van der Waals interactions as main rate-limiting inter-
actions for the observed methane diffusion. The parameter τ is a
fraction of picosecond and does not show any temperature
dependence within the error bars over the investigated T range.
2D diffusion model. The choice of a Lorentzian fit function for
the quasielastic signal implicitly assumes that the probed motion
is three-dimensional (3D)28. An other possibility is that the
0.0
0.0
0.2
0.4
0.6
0.8
1.0
0.4 0.8 1.2
Q2 (Å–2)
Γ 
(m
eV
)
1.6 2.0
212 K
238 K
267 K
282 K
Fig. 3 Momentum transfer Q dependence of the QENS signal. Half-width-
half-maximum Γ of the Lorentzian quasielastic component of the fits
(Fig. 2) as a function of Q2 at 0.8 GPa and the investigated temperatures.
Error bars correspond to one standard deviation. The best fits to the data
according to Eq. (1) are shown as dashed lines
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methane diffuses essentially bi-dimensionally on the length scale
probed by the instrument, if the grain boundary network or the
intercalated disordered regions between crystals of sI and sII
are sufficiently thin. In such a case the fit function for the
quasielastic signal is no longer Lorentzian and has a logarithmic
singularity at ω= 034 (see Supplementary Note 3 for its expres-
sion). Nevertheless, the singularity is suppressed by the
convolution with the instrumental resolution and the convoluted
fit function differs from the convoluted Lorentzian only near
ω= 0 where it is more peaked35. The inset of Fig. 2 depicts an
example of fit using this 2D diffusion fit function and compares it
to the Lorentzian fit of the same QENS spectrum. The two fits are
actually indistinguishable outside the instrumental resolution-
dominated region close to ω= 0 and this is true for all other
measured spectra. Therefore it is not possible to unequivocally
establish if bulk or planar diffusion is taking place. The values for
the translational diffusion coefficient and the mean residence time
obtained in the 2D diffusion model are reported in blue in Fig. 4.
The activation energy (0.57± 0.12 kcal mol−1) is comparable to
that obtained in the 3D diffusion model. More details about the
data analysis are given in the Methods section.
Discussion
The methane diffusion probed in the present study is much faster
than that reported in the literature for the cage-to-cage hopping of
CH4 molecules through clathrate sI. Cage-to-cage hopping is a rare
event that requires distortion of the host network36 and the asso-
ciated diffusion coefficient is of the order of 10−11 to 10−12 cm2 s−1
at 250 K, as revealed by experimental21 and computational24 stu-
dies. Similar conclusions have been reported for the cage-to-cage
hopping of other guest molecules37, 38, including molecules
forming clathrate sII37. It is also interesting to compare the present
results to the translational diffusion coefficients of CH4 in bulk
water–methane mixtures and bulk pure methane. At 0.02 GPa and
273K, the diffusion coefficient of methane in water was found to be
0.16 × 10−4 cm2 s−1, i.e., an order of magnitude smaller than
those measured here39. This value was obtained for the
moderate methane-saturated concentration that is possible at low
pressures39. In pure methane the experimental diffusion coefficient
is 2.08 × 10−4 cm2 s−1 at 0.164 GPa and 298K40. Its temperature
dependence is rather strong, with an activation energy of ~1.0 kcal
mol−1 between 223 and 323K at 0.15GPa. The diffusion coefficient
at 0.8 GPa can be estimated based on the assumption that its
product with the shear viscosity is constant along isotherms
(Stokes–Einstein relation). The pressure dependence of the
viscosity in methane at 298 K is known41 and one gets a value of
0.5 × 10−4 cm2 s−1 at 0.8 GPa and 298 K. This value is reported in
Fig. 4 and is a factor of 2–3 smaller than our results extrapolated at
the same T. Based on the same assumption, it is possible to estimate
that pure methane at about 0.2–0.3 GPa should show a diffusion
coefficient comparable to that measured here.
To summarise, we observed a remarkably fast mobility
of methane molecules at the interface of two clathrate structures
(I and II) and measured the associated translational diffusion
coefficient D at 0.8 GPa and temperatures between 212 and 282 K.
The obtained coefficients are 7–8 orders of magnitude higher than
those reported in literature for cage-to-cage hopping of methane
through clathrate sI at low pressure, one order of magnitude
higher than that of methane dissolved in water at low pressure
and a factor of 2–3 higher than that expected for pure bulk
supercritical methane at comparable pressure and temperature.
The activation energy (of about 0.5 kcal mol−1) is a factor of two
smaller than that of pure methane at 0.15 GPa and more than one
order of magnitude smaller than that of the hydrogen bond in the
water network and of the cage-to-cage hopping process as
reported in literature21. This fast mobility involves a sizable
fraction of the methane in the sample (approximately one third, as
rough estimation), does not induce destabilization of the clathrate
structures and is probably observable for times much longer than
the duration of our experiment (~21 h).
We infer that the rapidity of the methane diffusion probed
here could be an effect of confinement in the extensive grain
boundary network32 or intercalated disordered regions between
crystals of clathrate sI and sII. Similar behaviour was already
reported in literature. For example, the diffusivity of CH4 is only
4 × 10−11 cm2 s−1 in zeolite 4A42, ~10−4 cm2 s−1 in silicalite43 and
is predicted to be of the same order of magnitude as that of the
gas phase (10−1 cm2 s−1) in infinitely long single-walled carbon
nanotubes44. Alternatively, the observed fast diffusion could also
well be explained by the spontaneous formation of micro-scale to
nano-scale gas bubbles from a supersaturated water–methane
mixture. Micro-nanobubbles formation was suggested to occur
after decomposition of hydrates in different works45–47. The
diffusion properties of methane inside these bubbles can be
considerably different from the bulk fluid and a first study of
CH4-mobility in nanobubbles suggested indeed an enhanced
diffusion48. Further investigation including large-scale molecular
dynamics simulations of the guest diffusivity at the structures
interface are needed to shed light on these points.
In the context of energy recovery from natural gas hydrate
deposits with CO2 injections, gas replacement rates are key
parameters to assess its technological viability. Earlier experi-
mental evidences underlined greatly enhanced replacement rates
during sI–sII conversion49, 50 in comparison to the case of iso-
structural sI–sI replacement51. If extended to moderate pressures,
our results might provide an explanation for that. Likewise, our
results should be taken into account in the modelling of methane
clathrates layers existing at depth in the interiors of large icy
bodies in both solar and extra-solar systems25, 26, for which the
steady-states depend on the diffusion timescales as compared to
the formation and dissociation rates. As an example, the observed
fast mobility of methane could be relevant to understand the
phenomenon of methane release into the atmosphere of Titan,
which is likely to originate from methane clathrates embedded in
its crust and mantle25, 26.
Methods
Sample production. The procedure followed to prepare the CH4–D2O methane
hydrate sample was described in refs. 21, 52. It basically consists in keeping D2O ice
under an atmosphere of 6 MPa of CH4 gas at a temperature close to the melting
during 4 weeks. The starting deuterated ice was a powder of ice Ih of spherical
shape (typical diameter of several tens of micrometres21) previously produced by a
shock-freezing method through spraying liquid D2O (99.9% deuterated) into liquid
nitrogen. The spraying was done in a glove box under dry nitrogen atmosphere to
2.0
1.5
1.0
0.5
0.0
300280260240220200
a b
2 D
3 D
Pure CH4
D
 
(10
–
4 c
m
2  
s–
1 )
T (K) T (K)
0.6
0.4
τ 
(ps
)
0.2
0.0
300280260240220200
Fig. 4 Translational diffusion coefficient D and mean residence time τ.
Temperature dependencies of D (a) and τ (b) for methane hydrate in the
sI–sII clathrate at 0.8 GPa, as obtained in the 3D and 2D diffusion models
employed in this work. Error bars correspond to one standard deviation.
Arrhenius fits of D are shown as dashed lines. Estimated value for D in
pure methane from literature40, 41 is also reported. Legend of a also
applies to b
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avoid contamination with atmospheric water. The quality of the prepared methane
hydrate sample was checked by X-ray diffraction. We found that the sample was in
clathrate sI with a negligible amount of water ice impurity (below 2%). The size of
the crystallites is typically a few micrometres32. Typical methane occupation is 86%
for the small cages and 99% for the large cages52.
Experimental details. The QENS experiments were carried out using the VX5
Paris-Edinburgh press. The procedure of loading the methane hydrate sample in
the clamp module53 of the press was done under liquid nitrogen. The sample was
first compacted to a spherical pellet (of ~40 mm3) using a dedicated press operating
under liquid nitrogen. The pellet was subsequently loaded into a precooled type-25
copper-beryllium encapsulating gasket and the sample-gasket assembly was placed
in an aluminium ring between precooled ceramics anvils. We used recently
developed zirconia-toughened alumina ceramics anvils which are highly trans-
parent to neutrons. Their performances are described in ref. 29.
To prepare the sample exhibiting coexistence of clathrate sI and sII, the gasket
was sealed by applying a load of 100 kN on the anvils under liquid nitrogen. This
corresponds to a pressure of about (0.8± 0.1) GPa in the sample, on the basis of
our calibration of the used anvils. The assembled clamp was then warmed up from
liquid nitrogen temperature to room temperature out of the beam before insertion
(~12 h later) in the Paris-Edinburgh press. During the experiment, temperature
was decreased by cooling down the whole Paris-Edinburgh press in a liquid
nitrogen cryostat. It is known that the cooling of samples in such a pressure cell is
approximately isochoric and this leads to a small pressure drop (typically below 5%
for a change in temperature between 282 and 200 K). The measured Bragg peaks
did not shift with temperature within the angular resolution of the instrument.
During a different sample loading, the gasket was sealed by applying a smaller
load (50 kN), corresponding to a sample pressure of 0.4 GPa. After being warmed
up to 290 K, this sample was still in pure structure I (see Fig. 1 for the diffraction
pattern). We compressed this sample isothermally at 290 K and observed
transformation to clathrate sH, in agreement with previous studies20, 26.
During another sample loading, the gasket was sealed by applying a higher load
(120 kN), corresponding to a sample pressure of 1.0 GPa. After being warmed up to
295 K, this sample was found to contain a mixture of structure I and structure H.
The relative amount of structure H was found to slowly increase over time and the
transformation was completed within ~12 h.
The instrumental energy resolution was estimated by measuring a sphere of
vanadium of the same size as the sample, which was loaded into the gasket and the
Paris-Edinburgh press in the same set-up as the sample at ambient pressure and
ambient temperature.
Data analysis details. The scattering angles 2θ covered by the detectors of IN6
are in the range 10°−115°. Spectra measured by several detectors were grouped
together into constant-Q spectra with 0.2 Å−1 steps, from 0.4 to 1.8 Å−1. For the
data analysis, we did not consider the two highest Q values (1.6 and 1.8 Å−1) for
which competition of the quasielastic signal with the flat background gives rise to
large uncertainties for the free-fitting parameters. Six free-fitting parameters were
used in the data fitting with the 3D diffusion model: intensities and half-width-
half-maximum of the Lorentzian and delta functions, flat background and zero-
shift of the energy-transfer axis. Six free-fitting parameters were used as well in the
data fitting with the 2D diffusion model, D2D(Q) substituting the half-width-half-
maximum of the Lorentzian. Stokes/anti-Stokes detailed balance and convolution
with the instrumental energy resolution function were taken into account. Multiple
scattering contribution to the spectra was neglected as the estimated sample
transmission is about 89% of the incident beam.
Data availability. Raw data were generated at the Institut Laue-Langevin large-
scale facility. Derived data supporting the findings of this study are available from
the corresponding authors upon request.
Received: 10 May 2017 Accepted: 23 August 2017
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Acknowledgements
This work was supported by the Swiss National Science Foundation through FNS Grant
200021–149847, and by the French state funds managed by ANR within the Blanc
International programme PACS (reference ANR-13-IS04-0006-01) and the Investisse-
ments d’Avenir programme (reference ANR-11-IDEX-0004-02) and more specifically
within the framework of the Cluster of Excellence MATériaux Interfaces Surfaces
Environnement (MATISSE) led by Sorbonne Universités. We acknowledge the Institut
Laue-Langevin for provision of beam time through LTP 6-6, and Claude Payre and James
Maurice for technical assistance during the experiments. We thank José Teixeira (LLB)
and Robert Pick (IMPMC) for a critical reading of the manuscript.
Author contributions
U.R., W.F.K. and A.F. prepared the sample. U.R., M.M.K., W.F.K., S.K. and L.E.B.
performed the experiments. U.R., M.M.K. and L.E.B. analysed the data. All authors
discussed the results and contributed to writing the manuscript.
Additional information
Supplementary Information accompanies this paper at 10.1038/s41467-017-01167-2.
Competing interests: The authors declare no competing financial interests.
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