Influence of the concentration of H₂–D₂ mixtures on their triple-point dewetting behavior
Triple-point dewetting of pure gases like hydrogen and deuterium on solid substrates is a well-known phenomenon. This property persists even for the mixed system of H₂ and D₂. There exists an effective triple-point temperature T₃⁽mix⁾ , between the T₃ of pure H₂ and the one of pure D₂, which depends...
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irk-123456789-1289092018-01-15T03:04:10Z Influence of the concentration of H₂–D₂ mixtures on their triple-point dewetting behavior Tibus, Stefan Sohaili, Masoud Klier, Jürgen Leiderer, Paul Physics in Quantum Crystals Triple-point dewetting of pure gases like hydrogen and deuterium on solid substrates is a well-known phenomenon. This property persists even for the mixed system of H₂ and D₂. There exists an effective triple-point temperature T₃⁽mix⁾ , between the T₃ of pure H₂ and the one of pure D₂, which depends on the species concentrations. We present new investigations for a wide range of H₂–D₂ concentrations measured under different thermodynamic conditions. This allows us to map out T₃⁽mix⁾ as function of concentration, which can be different in the melting or solidifying direction. Furthermore, it turns out that the time the system needs to reach an equilibrium state can be very long and depends on concentration. This is not observed for the pure H₂ and D₂ system. Sometimes the relaxation times are so extremely long that significant hysteresis occurs during ramping the temperature, even if this is done very slowly on a scale of hours. This behavior can be understood on the basis of mixing and demixing processes. Possible differences in the species concentrations in the gas, liquid, and especially solid phase of the system are discussed. A preliminary phase diagram of the H₂–D₂ system is established. 2003 Article Influence of the concentration of H₂–D₂ mixtures on their triple-point dewetting behavior / Stefan Tibus, Masoud Sohaili, Jürgen Klier, Paul Leiderer // Физика низких температур. — 2003. — Т. 29, № 9-10. — С. 970-974. — Бібліогр.: 12 назв. — англ. 0132-6414 PACS: 67.70.+n, 67.70.-s, 64.70.Dv, 64.75.+g http://dspace.nbuv.gov.ua/handle/123456789/128909 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Physics in Quantum Crystals Physics in Quantum Crystals |
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Physics in Quantum Crystals Physics in Quantum Crystals Tibus, Stefan Sohaili, Masoud Klier, Jürgen Leiderer, Paul Influence of the concentration of H₂–D₂ mixtures on their triple-point dewetting behavior Физика низких температур |
| description |
Triple-point dewetting of pure gases like hydrogen and deuterium on solid substrates is a well-known phenomenon. This property persists even for the mixed system of H₂ and D₂. There exists an effective triple-point temperature T₃⁽mix⁾ , between the T₃ of pure H₂ and the one of pure D₂, which depends on the species concentrations. We present new investigations for a wide range of H₂–D₂ concentrations measured under different thermodynamic conditions. This allows us to map out T₃⁽mix⁾ as function of concentration, which can be different in the melting or solidifying direction. Furthermore, it turns out that the time the system needs to reach an equilibrium state can be very long and depends on concentration. This is not observed for the pure H₂ and D₂ system. Sometimes the relaxation times are so extremely long that significant hysteresis occurs during ramping the temperature, even if this is done very slowly on a scale of hours. This behavior can be understood on the basis of mixing and demixing processes. Possible differences in the species concentrations in the gas, liquid, and especially solid phase of the system are discussed. A preliminary phase diagram of the H₂–D₂ system is established. |
| format |
Article |
| author |
Tibus, Stefan Sohaili, Masoud Klier, Jürgen Leiderer, Paul |
| author_facet |
Tibus, Stefan Sohaili, Masoud Klier, Jürgen Leiderer, Paul |
| author_sort |
Tibus, Stefan |
| title |
Influence of the concentration of H₂–D₂ mixtures on their triple-point dewetting behavior |
| title_short |
Influence of the concentration of H₂–D₂ mixtures on their triple-point dewetting behavior |
| title_full |
Influence of the concentration of H₂–D₂ mixtures on their triple-point dewetting behavior |
| title_fullStr |
Influence of the concentration of H₂–D₂ mixtures on their triple-point dewetting behavior |
| title_full_unstemmed |
Influence of the concentration of H₂–D₂ mixtures on their triple-point dewetting behavior |
| title_sort |
influence of the concentration of h₂–d₂ mixtures on their triple-point dewetting behavior |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2003 |
| topic_facet |
Physics in Quantum Crystals |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/128909 |
| citation_txt |
Influence of the concentration of H₂–D₂ mixtures on their triple-point dewetting behavior / Stefan Tibus, Masoud Sohaili, Jürgen Klier, Paul Leiderer // Физика низких температур. — 2003. — Т. 29, № 9-10. — С. 970-974. — Бібліогр.: 12 назв. — англ. |
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Физика низких температур |
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2025-07-09T10:12:50Z |
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| fulltext |
Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10, p. 970–974
Influence of the concentration of H2–D2 mixtures on their
triple-point dewetting behavior
Stefan Tibus, Masoud Sohaili, Jürgen Klier, and Paul Leiderer
Department of Physics, University of Konstanz, Konstanz D-78457, Germany
E-mail: Stefan.Tibus@uni-konstaz.de
Triple-point dewetting of pure gases like hydrogen and deuterium on solid substrates is a
well-known phenomenon. This property persists even for the mixed system of H2 and D2. There
exists an effective triple-point temperature T3
( )mix , between the T3 of pure H2 and the one of pure
D2, which depends on the species concentrations. We present new investigations for a wide range
of H2–D2 concentrations measured under different thermodynamic conditions. This allows us to
map out T3
mix( ) as function of concentration, which can be different in the melting or solidifying
direction. Furthermore, it turns out that the time the system needs to reach an equilibrium state
can be very long and depends on concentration. This is not observed for the pure H2 and D2 sys-
tem. Sometimes the relaxation times are so extremely long that significant hysteresis occurs during
ramping the temperature, even if this is done very slowly on a scale of hours. This behavior can be
understood on the basis of mixing and demixing processes. Possible differences in the species con-
centrations in the gas, liquid, and especially solid phase of the system are discussed. A preliminary
phase diagram of the H2–D2 system is established.
PACS: 67.70.+n, 67.70.–s, 64.70.Dv, 64.75.+g
1. Introduction
Wetting of solid substrates, exposed to a gas in ther-
modynamic equilibrium, is an ubiquitous phenomenon
with both fundamental aspects [1,2] and important ap-
plications [3–5]. Microscopically the wetting of a sub-
strate by a liquid film is caused by a strong sub-
strate-particle attraction mediated by van der Waals
forces. At present an almost complete microscopic un-
derstanding of wetting on a well-defined solid sub-
strate is available [1,2,6]. The main prediction of all
these studies, for given thermodynamic parameters
such as temperature and pressure, is that the thickness
of the liquid film is a function of the substrate-particle
and interparticle interactions. In other words, if the
van der Waals force between substrate-adsorbate be-
comes stronger than the interparticle interaction then
complete wetting of the substrate, i.e., diverging of the
thickness of the liquid layer at the coexistence line is
expected. Dewetting will occur if the attraction is
weak. In the latter case the growing of the liquid film
will become energetically unfavorable and dewetting
will take place by forming droplets on a very thin (a
few atomic layers) liquid film on the substrate. In the
solid phase, however, even in the case of strong sub-
strate-adsorbate interaction dewetting occurs due to the
lateral stress induced by substrate roughness [7,8]. This
leads to the T3 dewetting as observed in our systems.
In this work, we have investigated the wet-
ting-dewetting of both pure and binary system of H2
and D2 on a gold substrate. Applying D2 as impurity
component in the H2–D2 dilute mixture was moti-
vated by both its similar structure to H2 and its differ-
ent physical properties from H2. Moreover, D2 is a
slightly weaker wetting agent in the solid phase than
H2 [9] and has a relatively small zero-point motion (in
comparison with H2 negligible [10]). Therefore the in-
teraction between molecules and substrate atoms is to
be different for H2 and D2. Regarding substrate
roughness our experiments are in a range where the
difference between the two isotopes (in their pure
form) is negligible. We discuss how the concentration
of D2 modifies the effective triple-point of the
two-component system.
2. Experimental procedure
All the experiments presented here were performed
by utilizing the surface plasmon spectroscopy, which
allows to determine the layer thickness of an adsorbed
© Stefan Tibus, Masoud Sohaili, Jürgen Klier, and Paul Leiderer, 2003
medium with high resolution (up to a few tenths of a
monolayer). The substrate in our measurements was a
gold film (45 nm thick) evaporated onto the base of a
glass prism. The experimental setup is shown in
Fig. 1, more details can be found in Ref. 11. However,
the signal processing in comparison to the previous ex-
periments has improved, therefore it resulted in more
precise measurements giving results with improved ac-
curacy. The system was fully computer controlled, so,
e.g., parameters like temperature could be swept up
and down in time very slowly in small steps. This was
done several times to check for reproducibility of the
measured data. The height and width of the ramping
steps, as will be discussed in the results, were chosen,
firstly, according to the normal relaxation of the sys-
tem under investigation and, secondly, to fulfill the
equilibrium thermodynamic conditions during the
experiment.
3. Results
Presented here are the results of wetting-dewetting
measurements of both pure H2 and D2 as well as mix-
tures of both isotopes. As typical examples for the
mixed systems we discuss 10 and 50 % D2 samples.
The numbers are molar-percentages of D2 in the mix-
ture of H2 and D2, and the samples were prepared as
follows: after taking an adsorption isotherm of H2 at
16 K and then raising the temperature to 19 K
followed an adsorption isotherm of D2 in order to
reach a certain concentration ratio. Afterwards,
ramping the temperature in the range of 10 to 20 K
was done. In Fig. 2 the T3 dewetting of pure H2 and
D2 and the effective triple-point wetting-dewetting of
the mixture of them are plotted. It is observed that for
each mixed system the cooling and warming curves re-
veal a large hysteresis, which is not found for the pure
H2 and D2 temperature runs. The hysteresis reveals to
be solid and stable.
The triple-point temperatures for pure H2 and D2
are 13.85 and 18.55 K, respectively. These tempera-
tures, which indicate the onset of dewetting, show
within an accuracy of 50 mK no significant hysteresis.
For the 10 %-doped system, the dewetting (cooling)
and wetting (warming) temperatures are 14.30 and
14.65 K, respectively. For the 50 %-doped system the
dewetting and wetting temperatures are 16.75 and
17.30 K, respectively. In order to examine the genuine-
ness of the hysteresis, another 50 % mixture of H2–D2
was prepared, but this time at room temperature.
Thereafter the adsorption isotherm of the mixture was
taken at 20 K. Furthermore three complete cycles, i.e.,
cooling from 20 K down to 10 K and return with steps
of 25 mK/min and a resolved time of 2 min between
two successive steps, were done. Figure 3 summarizes
the results. A hysteresis of essentially the same width
exists even when doing the measurements at lower
Influence of the concentration of H2–D2 mixtures on their triple-point dewetting behavior
Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10 971
10 12 14 16 18 20
50
100
150 pure H 2
mix.1, cooling
mix.1, warming
mix. 2,cooling
mix. 2,warming
pure D2
13
.8
5
K
14
.3
0
K
14
.6
5
K
16
.7
5
K
17
.3
0
K
18
.5
5
K
T, K
d
,
Å
0
Fig. 2. The dewetting curves (film thickness d against
temperature) of pure H2 (�), pure D2 (�), cooling (�)
and warming (�) of 10 %-doped mixture (mix. 1), and
cooling (�) and warming (�) of 50 %-doped mixture
(mix. 2). For pure systems the cooling and warming
curves trace the same path. Arrows show the positions to-
gether with the values of the wetting transition, i.e., the
effective T3.
Cryostate
Gold
surface
stepping
motor
to minimum
of resonance
S
M
C
U
� �2
Lock-in
amplifier
DetectorResonance
angle
Resonance
width
SMP
Bimorph+
Fig. 1. Experimental setup: Surface plasmon resonance is
enhanced at the interface of a gold substrate and an ad-
sorbed medium. The angle of the incident light is modu-
lated by means of a bimorph. Via a lock-in amplifier the
intensity signal is coupled back to a stepping motor con-
trol unit (SMCU) so that the angle of minimum intensity
(i.e. resonance) is kept. From the shift in angle relative to
the bare gold surface the thickness of an adsorbed film can
be determined.
ramping speeds, e.g., 10 mK/min. We should mention
that during the first scan the hysteresis appeared in a
more pronounced way as shown in Fig. 3.
In the inset of Fig. 3 the associated vapour pressure
curves are plotted. It shows that the slope of each
curve levels off somewhere in the middle of the curve
and rises again. The effective triple-points of wetting
and dewetting occur exactly at the point of the lower
kink for both cooling and warming curves. In order to
understand this behavior, in Fig. 4 we have redrawn
the supplementary vapour pressure curves of Fig. 2.
The solid curves, placed between the vapour pressure
curves of pure H2 and D2, are calculated pressure
curves of the binary systems of H2–D2 with different
concentrations of D2 derived from the partial pressure
law
P T C P T C P Ttotal D D D H( ) ( ) ( ) ( )� � �
2 2 2 2
1 , (1)
where CD2
is the D2 concentration in the mixture and
P TD2
( ) and P TH2
( ) are the pressure of H2 and D2 at
given temperature T, respectively. Having obtained
these values, one can calculate the total pressure of
the mixture under the assumption that the concentra-
tion of the species remains constant in the solid, li-
quid and gas phase. It is known, that even for an
ideal binary mixture this condition does not hold, and
the data plotted in Fig. 4 illustrate this deviation.
The data demonstrate that the concentration of D2 in
the liquid phase increases as the temperature raises
and vice versa. Furthermore, the size of the hysteresis
and the deviations from the predicted standard curves
depend on the concentration of the D2 phase in the
mixture. The size of the hysteresis is largest for con-
centrations around 50 % and diminishes with increas-
ing fraction of either species.
Using Eq. (1), one can extract the D2 concentra-
tion in the liquid phase from the measured vapour
pressure curves of the pure H2, D2, and the mixture of
them. So we have
C
P T P T
P T P TD
mix H
D H
2
2
2 2
�
�
�
( ) ( )
( ) ( )
, (2)
where P Tmix( ) is the vapour pressure of the mixture
at a given temperature. Figure 5 displays the evolving
of the D2 concentration in the liquid phase of the two
previously introduced sets of mixtures (see Figs. 2
and 4). The solid line, which is extended between the
T3’s of the pure H2 and D2, is a fit to the transition
line obtained from Fig. 6. The small dips in the
curves, near 13.85 K, occur precisely at the position
of the T3 of pure H2. The concentration of D2 in the
liquid phase increases gradually as the temperature
rises and vice versa. The noticeable effect is the steep
increase (decrease) of D2 concentration along the
transition line during warming (cooling) of the sys-
tem. In summary, in Fig. 6 the effective triple-points
of all the investigations are plotted against the D2
concentration in the liquid phase. The curve fitted to
the data shows that the behavior of the wet-
ting-dewetting temperature against the liquid concen-
tration of D2 is not linear. (It should be pointed out
that the effective T3 values of both heating and cool-
ing, T3
( )up and T3
( )down , lie on this curve.)
The observed behavior can be interpreted by taking
into account the temperature dependent differences in
concentration in the gaseous, liquid and solid phases
inside the sample cell. Let us consider, e.g., a mixture
with a nominal D2 concentration of 50 %: i) When we
972 Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10
Stefan Tibus, Masoud Sohaili, Jürgen Klier, and Paul Leiderer
d
,
Å
100
50
0
10 12 14 16 18 20
T, K
T, K
16 17 18 19
100
200
300
P
, m
b
a
r
Wetting transition
Hysteresis
diminishes
after 1 st
cooling but
does not
vanish
warming
cooling
1st cooling
1st warming
warming2nd
cooling2nd
3rd
3rd
Fig. 3. The dynamics of an equimolar mixture of H2–D2
is shown by monitoring the film thickness d over tempera-
ture. The temperature scans are done three times. The big
hysteresis during the first cooling and warming is attri-
buted to incomplete mixing. The inset shows the associ-
ated vapour pressure curves.
pure H2
2pure D
14 16 18
T, K
100
200
P
,
m
b
a
r
sa
t
mix.1,warming
mix.2,warming
isoconcentrations
mix. 1, cooling
mix. 2, cooling
Fig. 4. The corresponding vapour pressure curves of
Fig. 2. The solid lines are calculated vapour pressure
curves (Eq. (1)) for different concentrations of D2. Pure
H2 and D2 pressure curves are also plotted.
start at high temperature at gas-liquid coexistence, a
thick liquid wetting film will be present on the sub-
strate, as it is observed in our measurement. As the
temperature is lowered and the liquidus curve of the
mixture is reached (at � 17 K in this case [12]), solid
will start to form at the bottom of the sample cell,
with a concentration distinctly higher than 50 %
(given by the solidus curve at that temperature).
Upon decreasing T further, the D2 concentration in
the remaining liquid — both at the bottom of the cell,
and on the surface where we measure the film thick-
ness — drops, until eventually all bulk liquid has
crystallized. At that point (T3
( )down ) the drop in film
thickness, characteristic of T3 dewetting, starts to
take place. ii) For a run starting at low temperature,
on the other hand, the bulk solid has — due to
homogenization at T > 12 K [12] — a homogeneous
concentration of about 50 % throughout the whole
sample. Upon increasing T the first bulk liquid will ap-
pear in the cell when the solidus curve is met (�15.5 K
in this case). However, only at higher temperature the
thickness of our film, when in coexistence with bulk
liquid of the right concentration, will have reached its
«complete wetting value» of about 100 Å, identifying
T3
( )up . Since T3
( )down and T3
( )up do not coincide, due to
the paths in the phase diagram as described, a hyster-
esis results, as it is in fact observed.
4. Conclusions
In summary we have shown that mixtures of the
simple van der Waals adsorbates of hydrogen isotopes
are well-suited for investigations of the wetting be-
havior of binary systems. In pure H2 and D2 the ad-
sorbed films display the phenomenon of triple-point
wetting (i.e., dewetting sets in rapidly as the tempera-
ture is decreased below T3), and we have studied how
this behavior is affected, when instead of a one-com-
ponent system a mixture of H2 and D2 is used (where
strictly speaking a triple-point does not exist). It is
found that the feature typical for triple-point wetting
— the rapid drop in film thickness below T3 — per-
sists, but the characteristic onset temperature is differ-
ent for cooling and for heating, in contrast to pure sys-
tems. We attribute this hysteretic behavior to the
different concentrations of the hydrogen isotopes in
the solid, liquid and gas phases, respectively. Our re-
sults suggest that the method applied here does not
only yield insight into the wetting behavior of mixed
systems, but a further analysis of the data should also
provide detailed information on the phase diagram of
H2–D2 mixtures.
Acknowledgments
This work is supported by the Deutsche
Forschungsgemeinschaft under grant Le 315/20
within the Priority Program «Wetting and Structure
Formation at Interfaces».
1. S. Dietrich, in: Phase Transitions and Critical
Phenomena, C. Domb and J. Lebowitz (eds.),
Academic Press, London (1988), Vol. 12.
2. R. Evan, in: Liquids at Interfaces, Proceeding of the
Les Houches Summer School, Session XLVII, J. Char-
volin, J. F. Joanny, and J. Zinn-Justin (eds.),
Elsevier, Amsterdam (1990).
3. H. Gau et al., Science 283, 46 (1999).
4. K. Kargupta and A. Sharma, Phys. Rev. Lett. 86,
4536 (2001).
Influence of the concentration of H2–D2 mixtures on their triple-point dewetting behavior
Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10 973
12 14 16 18
0
20
40
60
80
T, K
C
D
2
T of H23
mix.1, cooling
mix.1, warming
mix. 2, cooling
mix. 2, warming
transition line
Fig. 5. The rising (falling) of the D2 concentration in the
liquid phase (Eq. (2)) during warming (cooling) for the
two mixtures, as presented in Fig. 2. Along the transition
line the rising is rather steep, which in turn is the sign of
wetting (dewetting) when warming (cooling).
0 20 40 60 80 100
cD2, liquid
T3, H2
T3, D2
14
16 16
18 18
T
,
K
T c3( )
transition line
14
T = A + Bc + Cc3 D2 D2
2
T
,
K
Fig. 6. The experimental data of the effective triple-points
of all the investigated mixtures as well as the ones for pure
H2 and D2. The solid curve is a fit to the data, with A =
= 13.83 (which is the T3 of H2), B = 6.366 �10–2, and C =
= –1.646 �10–4.
5. J. Bico, C. Marzolin, D. Quéré, et al., Europhys.
Lett. 47, 220 (1999).
6. S. Dietrich and M. Schick, Phys. Rev. B33, 4952
(1986).
7. F.T. Gittes and M. Schick, Phys. Rev. B30, 209
(1984).
8. A. Esztermann, M. Heni, and H. Löwen, Phys. Rev.
Lett. 88, 055702 (2002).
9. G. Mistura, H.C. Lee, and M.H.W. Chan, J. Low
Temp. Phys. 96, 221 (1994).
10. D.L. Demin, N.N. Grafov, V.G. Grebinnik, V.I.
Pryanichnikov, A.I. Rudenko, S.A. Yukhimchuk, and
V.G. Zinov, J. Low Temp. Phys. 120, 45 (2000).
11. M. Sohaili, J. Klier, and P. Leiderer, J. Low Temp.
Phys. 122, 249 (2001).
12. M.A. Strzhemechny, A.I. Prokhvatilov, G.N.
Shcherbakov, and N.N. Galtsov, J. Low Temp. Phys.
115, 109 (1999).
974 Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10
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