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The SF6 monolayer on graphite by X-ray diffraction
C. Marti, T. Ceva, B. Croset, C. de Beauvais, A. Thomy
To cite this version:
C. Marti, T. Ceva, B. Croset, C. de Beauvais, A. Thomy. The SF6 monolayer on graphite by X-ray diffraction. Journal de Physique, 1986, 47 (9), pp.1517-1522. �10.1051/jphys:019860047090151700�.
�jpa-00210349�
The SF6 monolayer on graphite by X-ray diffraction
C. Marti, T. Ceva, B. Croset, C. De Beauvais and A. Thomy (*)
Groupe de Physique des Solides de l’Ecole Normale Supérieure et de l’Université de Paris VII, Laboratoire associé au CNRS, Tour 23, 2, place Jussieu, 75251 Paris Cedex 05, France
* LARIGS, Laboratoire Maurice Letort, C.N.R.S., Laboratoire associé à l’Université de Nancy I,
B.P. 104, 54600 Villers-lès-Nancy, France
(Rep le 31 octobre 1985, révisé le 24 avril 1986, accepté le 14 mai 1986)
Résumé. 2014 La structure du film de SF6 adsorbé sur graphite a été étudiée entre 35 et 180 K par diffraction de rayons X. En dessous de 95 K environ, la monocouche complète est commensurable avec la surstructure (2 x 2)
de la face (001) du graphite; au dessus de 95 K, elle devient incommensurable, mais conserve sa structure hexago-
nale. Ces structures sont nettement différentes de la structure de tout plan du cristal 3D, ce qui explique le mouillage imparfait du graphite par SF6. Dans le domaine où la monocouche n’est pas complète, la condensation 2D mise
en évidence par les isothermes conduit à un solide incommensurable qui perd sa cohérence et de façon appréciable
seulement 20 K en dessous du point critique 2D (168 K).
Abstract 2014 The structure of the SF6 film adsorbed on graphite has been studied from 35 to 180 K by X-ray dif-
fraction. Below about 95 K the complete monolayer is commensurate with the (2 x 2) superstructure of the (001) graphite face; above 95 K, it becomes incommensurate, but keeps the hexagonal symmetry. These structures are
definitely different from the structure of any plane of the 3D-crystal and explain the incomplete wetting of graphite by SF6. In the submonolayer domain, the 2D-condensation shown by isotherms leads to an incommensurate solid which loses coherence, and noticeably only 20 K below the 2D-critical point (168 K).
Classification Physics Abstracts
68.55 - 68.60 - 78.70C
1. Introductioa
X-ray diffraction has been used only recently to study
the crystallographic structure of surfaces, either cover-
ed with adsorbed films or nacked : the structure of a
monolayer of krypton physisorbed on graphite was
studied with X-rays in 1978 [1]. This experiment (which could have been done much earlier), used very classical means like a 800 W X-ray generator and a
counter filled with xenon. The authors expected that X-rays would replace the more expensive neutrons
in most cases and allow numerous simple studies.
The trend afterwards was indeed toward sophis-
tication. A larger flux was sought from a 80 kW X-ray generator with rotating anode [2, 3] and then from
synchrotron radiation at Stanford [4-6] or Desy in Hamburg [7-9]. It allowed high resolution and fine studies of very interesting phase transitions. Even
the ability to study a monocrystal single surface was
demonstrated at Stanford with the help of grazing
incidence to suppress most of the bulk signal [10, 11].
The use of evanescent waves can also be related to this trend [12, 13]. But a lot of surface structures can
be resolved with the use of simple and cheap means.
An example was given with the coadsorption of xenon
and krypton on graphite, the phase diagram of which
was established at 45 K [14] with nearly the same equipment as in [1]. Another example is the case of
sulfur hexafluoride (SF6) physisorbed on graphite
which is presented hereafter.
SF6 is an attractive molecule for industrials, who
use the liquid dielectric to insulate transformators, etc.,
as well as for theoreticians who try to explain its phases from first principle [15, 16]. Indeed, the SF6/
graphite system was chosen for the two following
reasons : 1) its phase diagram has been determined
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:019860047090151700
1518
by volumetry [17], and 2) the adsorbate has a scat-
tering cross section for X-rays not too low whereas for the substrate this quantity is not too high.
2. The substrate.
Papyex from Carbone-Lorraine was used It is a
graphite, exfoliated with the help of sulfuric acid and then compressed up to 1 g. cm- 3, about half of the natural graphite density. Its specific surface area is
lower than that of the uncompressed exfoliated graphite used in volumetric studies (40-80 M2. g- 1),
but is still about 20 m 2 . g - 1. Adsorption on Papyex
has been widely studied by neutron diffraction [ 18-23] ;
it was shown that half of its grains are preferentially
oriented : a rocking-curve of the 002 peak has a half-
width at middle-height of 190 [20]. X-ray diffraction
suggested that a coherence length of 350 A for adsorp-
tion domains could be the mean diameter of the
grains [1]; most of them would be 200 A thick (along
the c-axis).
The sample was constituted by 25 disks, 1 mm thick,
12 mm in diameter, weighting about 2.5 g on the whole.
Twelve disks were cut with a large electrical massicot to prepare a surface for the reflection of X-rays. This
method was found to be the best, nevertheless some
graphite planes are driven parallel to the sample
surface as shown by the intensity of the 002 peak given by misoriented grains : the ratio (after instrumental
corrections) of 002 peak to 100 peak is three times smaller for neutrons (which see the whole sample)
than for X-rays (which see a sheet 0.2 mm thick),
the scattering plane being parallel to the disks in both
cases.
The disks were backed at 1 400 OC at less than 10-4 torr and cooled under argon; they were put in
a copper sample-holder. The sample was then prevent- ed from any contact with air and if an accident hap- pened, outgassed immediately at more than 100°C and less than 10-4 torr. Vplumetry on exfoliated graphite showed that this procedure gives reproducible adsorption isotherms after a backing at only
800 °C [24].
The sample was used in a previous study [14, 25].
From the commensurate-incommensurate transition of krypton its surface area, supposed to be constant,
was given as 49.7 ± 0.5 m2.
3. The adsorbate.
o The temperatures of the 3D triple and critical
points of SF6 are :
. Above 94.3 K, SF6 crystallizes in the body-
centered cubic system [27] the parameter is a = 5.79 A
at 123 K [28] and 5.915 A at 193 K [29].
The linear thermal expansion coefficient would be 3 x 10-4 K-’, a high value for a normal solid
but to be compared with that of SeF6 which is 3.6 x
10- 4 K -1 in a similar temperature range [29]. This high value agrees with the cubic phase being a plastic.
The orientational disorder is shown by NMR [29],
Raman scattering [27], and has been studied by simu-
lation [ 15,16].
The molecule has S-F bounds of t = 1.57 A [27]
or 1.542 A [28], mostly parallel to the cubic cell edges.
Along these edges the distance between molecules is about two bound lengths and two ionic radii of F-
(r = 1.33 A). But the nearest neighbour distance is
a,13-12 = 5.014 A at 123 K and 5.12 A at 193 K;
it shows that the rotation of SF6 is not free around all directions but is allowed around the (111) axis, along
which the « thickness » of an oriented molecule is
2 - + r - 4.44 3= to 4.47 A. The densiest planes
are the 1110 } with a cross-section for a SF6 molecule
of a2/V2 = 24.74 A at 193 K or 23.7 A at 123 K.
A transition was found at 94.3 K [27] from the study
of vibrations around 600 cm -1. The kinetics of transformation is quite slow and the two phases seem
to coexist until the lowest temperature studied of 83 K.
This was also seen by NMR [29] between at least
63 K and 77 K, but it was noted that the ratio of two
lines depends on the way the sample is cooled; we
could understand these facts as indicating a first
order transition with strong hysteresis, but Salvi
et al. [40] found prompt reversibility at 94 K.
The low-temperature phases (another transition at 50 ± 5 K towards a monoclinic structure has been
described) are far from being understood. Raynerd
et al. [39] were able to work on very small crystals
with electrons and obtain the following lattice unit :
a hexagonal cell with three molecules
this structure isomorphic to UCl6 is quite different
from that of UF6 or the low-temperature phases of MoF6 and WF6 (orthombic but with four molecules in the unit cell). It can be viewed as a modification of the cubic phase in which a third of the molecules are
rotated from their cubic (mean) orientation by 60°
around a ternary axis (plus some relaxation). It can
also be thought as deriving from a hexagonal close- packing of fluor atoms, but a dense (001) plane of
fluor is not a plane of SF6, two molecules staying
« above » such a plane and a third one « below » :
the densest planes are the I 10 > where SF6 has
a cross-section of acl,13 = 22.34 A2. The minimal distance between nearest-neighbour molecules is not known. Raynerg et al. use a very rough Lenard-Jones calculation and find 4.64 A ; a better simulated model
[16] shows that one third of the molecules rotates and the other two do not, it cannot endorse the rough ap-
proach, but the upper limit of the minimal distance is
c = 4.83 A.
The gas used came from the same bottle as in volumetric measurements [17], and was purified by
the same procedure, i.e. by pumping on the condensed
phase at 140 K inside the introduction system. The resulting purity was better than 99.9 %.
4. The submonolayer.
Adsorption isotherms (Fig. 1) clearly show a first
order transition from the lowest practicable tempe-
rature (125 K, where the equilibrium pressure is lower than 10- 3 torr) to a 2D critical point at 168 K.
An accident in the upper part of the isotherms at 135 and 140 K could suggest a 2D triple point near 130 K :
the three phases would have been a 2D gas, a 2D
liquid and a 2D solid The phase diagram would
have had an exceptional shape, with the 2D solid coexistence with the 2D liquid over a very small temperature range (from 130 to 145 K perhaps),
smaller than the coexistence temperature range of the 2D liquid and the 2D gas, and without any indication of being followed by a 2D line of second order transi- tion. We therefore intended firstly to pick up the dif- fraction pattern in the « vertical » part of the steps.
We introduced 12.8 x 1019 molecules of SF6 into
the adsorption cell. Compared with the volumetric measurements [17] this quantity corresponds to a
surface coverage of 0.63 (0 = 1 being the coverage
of point B1 at 125 K, cf. Fig. 1).
From about 1 to 2.5 A - 1 we observed a single peak (Fig. 2), e.g. at 1.46 A-1 for 75 K. The broad wing at large angles is characteristic of 2D structures. The
unicity of the peak is the signature of a hexagonal
2D-solid Furthermore, the continuous variation of its
position with temperature is indicative of an incom-
Fig. 1. - 2D phase diagram of the SF6-graphite couple as
considered in [17]. In thick lines : schematic adsorption isotherms; (1) 125 K, (2) 135 K, (3) 160 K, (4) 180 K.
Inside the dotted lines : 2D phase coexistence domains as
supposed in [17] (D gas-solid, O gas-liquid, @ liquid-
solid. 0 : fractional surface coverage ; 6 is taken equal to 1
at point M. It has been shown [38] that the region cor- responding to the monolayer completion is actually located
nearer to the saturating vapour pressure. C(3D) or Po axis :
3D condensation under saturating vapour pressure Po.
Fig. 2. - (10) diffraction profiles corresponding to the
coexistence domain (0 = 0.63) of the SF6 film adsorbed
on graphite at different temperatures.
x (diffusion vector) = B1t sin IX, À. = 1.5418 A, a : : Bragg angle. In the case of a 2D hexagonal structure : d 4 n
X /3-’
d being the distance between two nearest neighbour ad-
molecules. Curve at 135 K is experimental; others are eye-fitted
mensurate solid : from 75 to 135 K the peak shifts
from 1.46 A-1 to 1.38 A-1 without any other change.
The width of the peak does not vary significantly in
this temperature range; taking account of the reso-
lution and penetration of X-rays in graphite we find
a coherence length larger than 200 A (the largest Papyex patches are 350 A wide).
No remarkable change is observed around 130 K.
A slight widening could be guessed at 140 K and could
be confirmed with a better resolution and, mainly,
a longer counting time.
At 150 K the peak widens and its maximum dimi- nishes accordingly; the coherence length is about
110 A. At 160 K the peak is quite wide but the cohe-
rence length stays larger than 30 A, i.e. the order is still greater than in a true liquid.
We conclude that all the steps at nearly constant
pressure observed in adsorption isotherms are due to
a first order transition between a low-density phase
and a single high-density phase.
At low temperatures, the low-density phase is presumably a 2D gas without order and not seen by diffraction, whereas the high-density phase is a nearly perfect 2D crystal, i.e. with a coherence length equal
to the size of the substrate uniform domains.
1520
The 2D crystal looses continuously long-range
order as temperature is raised The loss of long-range
order has been well demonstrated for xenon [30] and.
argon [32] physisorbed on graphite. In those cases
however melting is not fully continuous : it is in fact
clearly first order in the case of xenon and « weakly »
first order [31] or second order with argon [32]. In
the case of SF6 we have no indication of a first transi- tion, transition between a solid and a liquid (the
accidents in the isotherms around 135 K concern
well-developed 2D-solids). This kind of behaviour is
expected for physisorption onto lamellar halides of
heavy metals, for which a single coexistence domain is seen in volumetric measurements [33, 34] ; the
ordered state was observed at low temperatures by
neutron diffraction for the Ar/NiC’2 and CH4/NiC’2 couples [35], but it was not demonstrated that it becomes disordered below the 2D critical point, as certainly must be the case.
A single domain was not observed on graphite until
now, to our knowledge, except for the physisorption
of cyclohexane [36]. In this case, the pseudo-solid, coexisting with a low-density phase, can be strongly compressed; the molecules lay certainly flat on the graphite at first and rises then perpendicularly to the
surface.
A second unexpected feature is the strong variation of thermal expansion. More than half of the dilatation between 75 and 140 K occurs over less than 20 degrees
around 120 K and 1.43 A -1; this sensitivity may be
related, not to the temperature range, but rather to the
density range of the accident in the isotherms (cf
domain 3, Fig 1) previously interpreted as a clue to
the existence of a 2D triple point, which in fact does
not exist as seen above.
5. The full monolayer.
In this case, we introduced 23.1 x 1019 molecules of
SF6, corresponding to 0 = 1.14. The spectra (Fig. 3)
exhibit a main peak (a peak) and a second one smaller (p peak) which increases with temperature mainly
above about 100 K. The P peak corresponds to SF6
3D crystallites formed on the surface at the neigh-
bourhood of defects. Such crystallites could effectively
be built due to the 0 value considered Moreover for
higher values of 0 (ex. : 0 = 4), at a given temperature, the J? peak becomes more important while the a peak
does not change. Consequently, when saturated, the monolayer has to be considered as a 2D solid with
hexagonal structure.
Between 35 and about 95 K, the position of the a peak
does not vary, corresponding to x = 1.475 A-’. This
position (which takes account of the shape of 2D peaks
in accordance with [20]) given its invariance with temperature, is an unequivocal signature of a commen-
surate 2D solid, the structure of which is the (2 x 2) superstructure of graphite basal planes (distance
between two nearest neighbour admolecules : 4.92 A).
Fig. 3. - (10) diffraction profiles corresponding to the full monolayer (0 = 1.14) of the SF6 film adsorbed on graphite
at different temperatures.
Above 95 K the full monolayer becomes incom- mensurate ; the peak moves to smaller angles (or x, cf. Fig. 3) without serious widening. If first order, the
transition between the commensurate and the incom- mensurate phases has a jump of the parameter smaller than 1 %.
We also note here that the dilatation coefficient varies strongly around 1.43 A -1, but at this coverage around 140 K (over less than 20 K).
6. Discussion
The lattice unit of the (2 x 2) super structure has an area of 20.96 A2, appreciably lower than the cross-
section of SF6 in the densiest planes ( I 10 > of the hexagonal low-temperature phase (22.34 A2) a figure
lower than the cross-section in the ( I 10 > planes of
the cubic phase at 95 K, i.e. 23.3 A2 (extrapolating linearly the lattice parameter to 5.74 A at 95 K). The
incommensurate cell has an area which grows up to 23.4 A, but meanwhile the cross-section in the perti-
nent cubic 3D-phase grows up to 24.4 A2 (at 180 K).
The density in the 2D phase is then always larger
than the density in the 3D-densiest planes by 5 to 10 %.
It should be noted that this higher 2D-density is not incompatible with the distance in the 3D phase : the
minimal intermolecular distance in the cubic phase
is at most 2 % larger than in the physisorbed state
(4.92 A below 95 K), which is larger than the minimal distance in the hexagonal phase (at most 4.83 A).
Indeed the arrangements are very different; in the 2D hexagonal solid a molecule has six neighbours at
4.92 A (in the commensurate phase); but a (110)
cubic plane is built with centered rectangles and
a molecule has four neighbours at 4.97 A (at 95 K)
and also four others at 5.74 A ; in a (110) plane of the hexagonal 3D-phase the local symmetry is also strongly distorded from the hexagonal one.
The non-wetting behaviour of SF6 is therefore not to be related to the differences of densities (not larger
than for argon which wets perfectly), but rather to the differences of symmetries and molecular arrangements between 2D and 3D-densiest planes.
Moreover the orientation of the admolecules rela-
tively to the (110) planes could hardly be chosen to
stick upon graphite. For CF4 adsorbed on graphite a (2 x 2) commensurate phase was also observed and it
was put forward that this molecule lays on graphite
upon a tripod of fluor atoms sitting in the middle of
carbon hexagons [20, 23]. This model also seems to be unavoidable for SF6 (Fig. 4). More precisely in
commensurate CF4, two neighbouring molecules
would line up four fluor atoms onto four carbon
hexagons; for this geometry of the fluor first plane on
Fig. 4. - Models for the commensurate (2 x 2) structure
of CF4 (a) after [20, 23] and SF6 (b) on graphite (0001).
graphite, the other fluor atoms of SF6 would have a
similar geometry, i.e. if the three fluor atoms lying
on graphite have enough room, so have the three other fluors of SF6. From the 3D crystallographic data a
minimal parameter for this geometry would be : 2.18 + (2 x 1.33) = 4.84 A and room seems to be
largely available. The contrary would be found with
CF4, for which the minimal distance between fluor atoms at 10 K in neighbouring molecules is 3.03 A [37],
and inside the same molecule is 2.16 A. Consequently
the minimal parameter would be for CF4 : 2.16 +
3.03 = 5.19 A. But the 3D data for CF4 have not been subjected to such refined treatment as for SF6, taking
into account the disorientation of the mecules. If we use ionic radii we would find a minimal parameter of 2.16 + (2 x 1.33) = 4.82 A. Indeed we think that
SF6 is somewhat larger than CF4 : the latter is com- mensurate at high temperatures and its incommen- surate phases are compressed; on the contrary, the former is commensurate at low temperatures and its incommensurate phase is delated
7. Conclusion
In the temperature range considered (35-180 K) the
2D phase diagram of SF6 on graphite seems to be relatively simple: we only found one phase coexistence domain instead of three as could be assumed from the isotherms. That is why the diagram initially pro-
posed [17] and represented in figure 1 is replaced by the diagram of figure 5. The dense phase which forms in the first order transition (AD) is an incommensurate solid of hexagonal structure. After the transition
(after D), this solid becomes more compact and
compresses while its hexagonal structure is preserved
up to the monolayer completion. The full monolayer
is incommensurate above 95 K, and becomes com- mensurate at lower temperatures.
Whatever the temperature, the structure of the
Fig. 5. - 2D phase diagram of SF6 on graphite couple
the most compatible with both X-rays and volumetric
measurements.
In thick lines : the same schematic adsorption isotherms
as in figure 1.
(1) : 2D gas-2D incommensurate solid coexistence domain.
The commensurate domain is outside the figure.
