Isotope effects in the kinetics of simultaneous H and D thermal desorption from Pd

Article abstract of DOI:10.1016/j.jpcs.2007.08.005

The kinetics of simultaneous hydrogen and deuterium thermal desorption from PdH_xD_y has been investigated. A novel experimental approach for the study of the transition state (TS) characteristics of the surface recombination reaction is proposed based on the analysis of the H and D partitioning into H₂, HD and D₂ molecules. It has been found that the hydrogen molecular isotopes distribution is determined by the energy differences of the corresponding TS of the atom-atom recombination reactions. On the other hand, the mechanisms and activation energies of the desorption process have been obtained. At 420 K, the desorption reaction changes from a surface recombination limiting mechanism during desorption from β-PdH_xD_y to a reaction limited by the rate of β to α phase transformation during the two phase coexistence. Surface recombination reaction becomes again rate limiting above 480 K, due to a change in the catalytic properties of the Pd surface. TS energies obtained from the kinetic analysis of the thermal desorption spectra are in good accordance with those obtained from the analysis of the H₂, HD and D₂ distributions. Anomalous TS energies have been observed for the H-D recombination reaction, which may be related to the heteronuclear character of this molecule.

Full text of DOI:10.1016/j.jpcs.2007.08.005

ARTICLE IN PRESS
Journal of Physics and Chemistry of Solids 69 (2008) 116–127
www.elsevier.com/locate/jpcs
Isotope effects in the kinetics of simultaneous H and D
thermal desorption from Pd
Ã
F. Leardini , J.F. Ferna
´
ndez, J. Bodega, C. Sa
´
nchez
´ ´
Departamento de Fısica de Materiales, Universidad Autonoma de Madrid, 28049 Cantoblanco, Madrid, Spain
Received 16 May 2007; received in revised form 2 August 2007; accepted 10 August 2007
Abstract
The kinetics of simultaneous hydrogen and deuterium thermal desorption from PdHxDy has been investigated. A novel experimental
approach for the study of the transition state (TS) characteristics of the surface recombination reaction is proposed based on the analysis
of the H and D partitioning into H2, HD and D2 molecules. It has been found that the hydrogen molecular isotopes distribution is
determined by the energy differences of the corresponding TS of the atom–atom recombination reactions. On the other hand, the
mechanisms and activation energies of the desorption process have been obtained. At 420 K, the desorption reaction changes from a
surface recombination limiting mechanism during desorption from b-PdHxDy to a reaction limited by the rate of b to a phase
transformation during the two phase coexistence. Surface recombination reaction becomes again rate limiting above 480 K, due to a
change in the catalytic properties of the Pd surface. TS energies obtained from the kinetic analysis of the thermal desorption spectra are
in good accordance with those obtained from the analysis of the H2, HD and D2 distributions. Anomalous TS energies have been
observed for the H–D recombination reaction, which may be related to the heteronuclear character of this molecule.
r 2007 Elsevier Ltd. All rights reserved.
PACS: 68.43.Mn; 68.43.Vx; 82.20.Db; 82.20.Pm; 82.20.Tr; 82.65.+r; 82.80.Ms
Keywords: A. Metals; C. Differential scanning calorimetry; D. Electrochemical properties; D. Thermodynamic properties
1. Introduction
of surface reactions in MH [3,4]. In this context, the
microscopic description of the MH formation/decomposi-
tion processes is of fundamental importance.
Hydrogen is considered one of the main candidates to be
the energy carrier in the near future. This fact has
stimulated an important research activity on hydrogen
storage methods. Hydrogen storage in metal hydrides
(MH) appears to be a very suitable method [1]. One of the
main issues in this field concerns the kinetics of hydrogen
absorption/desorption. The formation/decomposition of a
MH involves both bulk (hydride to solid solution phase
transformations, diffusion of H atoms through the bulk
and from the bulk to the surface) and surface (dissociation
of H2 molecules/H–H recombination at the surface)
processes. In most cases, the H absorption/desorption
kinetics in/from a MH is limited by surface reaction steps
[2]. Accordingly, there is a growing interest on the catalysis
A suitable approach to investigate the kinetics of H
atoms in the course of chemical reactions is the analysis of
the H/D isotope effects. Owing to their relative mass
differences, the hydrogen isotopes have different zero-point
energies (ZPE) and local vibration modes within the wells
of the potential energy surface (PES). As a consequence of
these energy shifts, the reaction rates are usually higher for
the lighter isotope. This is denoted as the normal isotope
effect. However, there are some exceptions to this rule. A
typical case is the inverse isotope effect observed in the
H/D diffusion in Pd [5].
H/D isotope effects appear in very different conditions
and phenomena. The simplest reaction involving H and D
atoms is the isotope exchange reaction:
Ã
Corresponding author. Tel.: +34 914974777; fax: +34 914978579.
E-mail address: fabrice.leardini@uam.es (F. Leardini).
H2 þ D232HD:
(1)
0022-3697/$ - see front matter r 2007 Elsevier Ltd. All rights reserved.
doi:10.1016/j.jpcs.2007.08.005

ARTICLE IN PRESS
F. Leardini et al. / Journal of Physics and Chemistry of Solids 69 (2008) 116–127
117
Reaction (1) has been proved to be very useful to
investigate the kinetics and mechanisms of the interaction
of H2 with metal surfaces. This reaction has been
extensively investigated on mono- and polycrystalline
transition metal surfaces [6–14] as well as on transition
metal supported catalysts [15–18]. H/D kinetic isotope
effects in hydride forming metals have been also widely
investigated, mainly due to the potential applications of
MH for isotope separation processes. This kind of studies
is usually performed by heterophase hydrogen isotope
exchange (H2/MD and D2/MH) experiments [19,20].
In the present work, the kinetics of simultaneous
hydrogen and deuterium desorption from bulk PdHxDy
material is investigated by means of thermal desorption
spectroscopy (TDS). TDS was initially developed for the
study of the desorption kinetics of chemical species from
surfaces, but lately it has been proved to be also a valuable
technique to investigate the kinetics of MH decomposition
[21–23]. Two relevant facts support the election of Pd
hydride to perform this investigation. Firstly, the Pd/H2
system is the prototypic MH system. Historically, it was
the first MH that attracted research activities [24] and it has
been the most investigated MH since then. Secondly, Pd is
well known for its selectivity and activity in hydrogenation
reactions and it is one of the most used catalysts. Indeed,
Pd thin film overlayers are usually used to enhance the
kinetics of hydrogen uptake and release from MH [25,26].
Isotope effects in the kinetics of H(D) absorption/
desorption by/from a-Pd and a-Pd–Pt alloys have been
recently reported [27,28]. These studies show the existence
of an inverse isotope effect in the kinetics of a-Pd
decomposition. Nevertheless, to our knowledge, isotope
effects in the kinetics of PdHxDy decomposition (within the
hydride region) have not been investigated yet. Moreover,
there is only one previous TDS study on the simultaneous
H and D desorption from MH [29]. This investigation was
carried out in V and V-Ti intermetallic compounds,
although no quantitative analysis of the desorption kinetics
was reported in that paper.
dissolving metallic granulated lithium in a mixture of
H2O (18.6 MO cm) and D2O (499.6% isotopic purity,
0.08 MO cm) under Ar atmosphere. The H/D ratio in the
electrolyte was 0.2270.01. The electrolysis was performed
with a Princeton Mod.362 potentiostat in a three-electrode
open cell all constructed in Teflon. Pd foils were placed at
the bottom of the electrolytic cell with only one face in
contact with the electrolyte. Counter electrode was a Pt
grid located opposite to the cathode and the reference
electrode was a Pt wire placed near the cathode. Several
charge/discharge cycles were applied to the sample before
the experiments by accomplishing voltammograms be-
tween ꢀ0.2 and ꢀ3 V at a sweep rate of 0.02 V sꢀ1. Then,
Pd electrodes were charged at constant electrode potential,
EPd/Pt ¼ ꢀ3 V, until hydrogen–deuterium evolution was
observed. Finally, the electrolytic current was reversed by
applying an electrode potential equal to ꢀ0.2 V. The charge
through the electrodes during this oxidation stage was
below 1% of that passed during the cathodic polarization
of the electrodes. After the electrolytic H and D charging,
the foils were handled in air to perform the structural,
morphological and electrical characterization.
Structural characterization of the samples at RT has
been carried out by means of X-ray diffraction (XRD)
accomplished with the CuKa radiation in a y–2y Siemens
D-5000 powder diffractometer. Sample surface morphol-
ogy and composition have been studied with a Phillips
XL30 scanning electron microscope (SEM) equipped with
electron dispersive X-ray (EDAX) analysis.
Electrical resistivity measurements have been done by
Van der Pauw method [31] with a Keithley Mod. 2400
current source and a Keithley Mod.182 digital voltmeter.
Thermopower measurements have been performed as
described elsewhere [32].
A novel experimental approach for the study of the
transition state (TS) characteristics of the surface recombi-
nation reaction is proposed here based on the analysis of
the H and D distribution into H2, HD and D2 molecules.
This technique can give complementary information to
that obtained on TS from quantum-state resolved experi-
ments [30] and quantum-state integral measurements [14].
2. Experimental
Pd foils (Goodfellow, 99.95%) have been simultaneously
hydrogenated–deuterated by electrolysis in 0.1 M LiOH-
LiOD electrolyte at room temperature (RT). The original
thicknesses of the foils were 0.25 mm and the geometrical
area in contact with the electrolyte 0.57 cm2. The foils
were washed in an ultrasound bath with ethanol and
then with deionised water (18.6 MO cm) prior to the
electrolytic experiments. The electrolyte was prepared by
Fig. 1. Scheme of the experimental system used for TDS measurements:
(1) Ar bottle; (2) flow meter and controller; (3) differential scanning
calorimeter; (4) capillary tube; (5) rotary pump; (6) dosing valve; (7)
turbomolecular pump; (8) vacuum chamber; (9) Penning sensor; (10)
electronic setup; (11) PC acquisition data and controller system; (12) ion
source; (13) electrodes; (14) quadrupolar filter; (15) ion detector.

ARTICLE IN PRESS
F. Leardini et al. / Journal of Physics and Chemistry of Solids 69 (2008) 116–127
118
TDS has been performed in the experimental setup
1.5x104
1.0x104
5.0x103
depicted in Fig. 1. A differential scanning calorimeter
(Perkin-Elmer DSC4) is connected through a quartz
capillary tube and a dosing valve (Balzers UDV 040) to a
quadrupole mass spectrometer (QMS 200 Balzers) placed
inside a high vacuum chamber. A more detailed description
of the experimental system can be found in [23].
A constant Ar flow (57.6 sccm, 99.999% purity) passing
symmetrically through both heaters of the calorimeter was
used to carry the desorbed gases to the QMS. Thermal
desorption spectra have been obtained by heating the
samples between 298 and 623 K at a constant heating rate
equal to 0.333 K sꢀ1. Mass of the samples before and after
TDS experiments were measured with a balance Ohaus
Analytical Plus.
0.0
The current intensity and energy of the ionizing electrons
in the QMS were 2 mA and 100 eV, respectively. Detailed
calibrations of the gas analysis system have been performed
prior to TDS experiments [33]. At the experimental
conditions of the present TDS experiments, the i2, i3 and
i4 current peaks are essentially due to H+2 , HD+ and D2+
ions, respectively (the contribution of D+, H3+ and H2D+
ions to these current peaks were below 1%). In addition,
the influence of isotope exchange reactions among the
hydrogen ionic/molecular isotopes during the gas analysis
process has been found to be negligible. Therefore, the H2,
HD and D2 desorbed flows (fw) are related to the i2, i3 and
i4 peak currents, respectively, according to
1.0x104
5.0x103
0.0
30
40
50
60
70
80
90
im=qðwÞ ꢀ i0m=qðwÞ ¼ sm=qðwÞf w,
(2)
2θ (°)
where i0m=q represent the background signals from the
residual atmosphere present in the vacuum chamber and
Fig. 2. XRD patterns of Pd sample before (a) and after (b) electro-
chemical hydrogenation–deuteration. Diffraction peaks of a-Pd and b-Pd
hydride–deuteride are labelled with open circles and stars, respectively.
Diffracting planes corresponding to each XRD peak are indexed. Non-
labelled peaks correspond to diffraction produced by residual Cu Ka
radiation.
sm/q(w) is the detection sensitivity of the specie w.
The obtained detection sensitivities for H2, HD and D2
gases are equal to 1.62 ꢁ 10ꢀ4, 6.25 ꢁ 10ꢀ5 and 3.74 ꢁ
10ꢀ5 A molꢀ1 s, respectively, to within 73%. The observed
differences among the detection sensitivities of the hydro-
gen molecular isotopes come from the mass discrimination
effects in the gas collection, pumping and ion filtering
processes [33]. Experimental base lines have been recorded
before the TDS experiments to obtain the temperature
dependence of the i0m=q peak currents.
Table 1
Lattice parameters, resistivity and Seebeck coefficients of Pd and b-
PdHxDy at RT
Pd
b-PdHxDy
This work Literature
This work PdH0.6
PdD0.6
˚
a (A)
3.892(3)
9.9(1)
3.89019 [34] 4.022(3)
10.54 [37]
4.025[35] 4.025 [36]
17.9 [38] 20.0 [38]
5 [39]
r (mO cmꢀ1
)
18.5(2)
5.1(1)
3. Results
Sc (mV Kꢀ1
)
ꢀ11.0(1)
ꢀ11.5 [39]
3.1. Characterization of PdHxDy samples
Pd cathodes have been characterized by means of XRD,
electrical resistivity and thermopower measurements after
the electrolytic H/D charging in order to know the amount
of H and D atoms present in PdHxDy. Three Pd foils
charged with different H and D concentrations have been
investigated. The results derived from the kinetic analysis
of the TDS curves are reproducible to within 5%. Here,
only the results obtained from one of the samples will be
presented for the sake of clarity.
The XRD patterns of Pd before and after electrochemi-
cal hydrogenation are shown in Fig. 2(a) and (b),
respectively. These patterns can be indexed in the Fm3 m
crystallographic space group, characteristic of Pd and b-Pd
hydride–deuteride. Diffraction peaks of Pd and b-PdHxDy
have been labelled with open circles and stars, respectively.
Diffracting planes corresponding to each XRD peak have
been indexed. Non-labelled small peaks correspond to the
diffraction produced by non-filtered CuKb radiation.

ARTICLE IN PRESS
F. Leardini et al. / Journal of Physics and Chemistry of Solids 69 (2008) 116–127
119
The lattice parameters of Pd and b-PdHxDy obtained
from the analysis of the XRD patterns are summarized in
Table 1, together with the results reported by other
authors. A good agreement is observed between the present
experimental values and those obtained in previous works.
This coincidence and the practical absence of diffraction
peaks corresponding to a-Pd in the XRD pattern of
PdHxDy (only a weak diffraction peak from the (2 0 0)
plane of a-Pd is observed) reflect that the sample
value comes from the 16% of error in the mass loss
measurement and the 6% of error in the x/y ratio.
The morphology and composition of the Pd foils have
been investigated by SEM–EDAX analysis. No remarkable
differences have been observed in the cathode surface
before and after electrolytic hydrogenation–deuteration.
3.2. Thermal desorption spectra of PdH0.35D0.26
composition is close to the limit of the a-b transition, bmin
.
TDS of the PdH0.35D0.26 foil is shown in Fig. 3a. This
spectra consists of a single desorption peak for each one of
the hydrogen molecular isotopes. The H2, HD and D2
flows have been normalized to their maximum values in
order to clarify the comparison among them. Absolute
values of H2, HD and D2 flows at the maxima of TDS
At RT this limit corresponds to a content of 0.61 H+D
atoms per Pd atom [35]. This value, together with the x/y
ratio determined by integration of the QMS signals
during TDS (see Section 3.2) gives x ¼ 0.3570.01 and
y ¼ 0.2670.01.
peaks are 6.72 ꢁ 10ꢀ8, 9.61 ꢁ 10ꢀ8 and 3.09 ꢁ 10ꢀ8 mol sꢀ1
,
The measured resistivities of the Pd and PdHxDy
samples are shown in Table 1, together with the values
reported for Pd [37], PdH0.6 [38] and PdD0.6 [38] materials.
It can be seen that there is a relatively large isotope effect
that affects the resistivities of Pd hydride and deuteride. By
considering that the electrical resisitivity of b-Pd(H-D)0.6
depends linearly on the relative H and D content, the
respectively.
H2
1.0
0.8
0.6
0.4
0.2
0
HD
D2
electrical resistivity of PdH0.35D0.26 would be 18.7 mO cmꢀ1
This value agrees with the present experimental result and
confirms the calculation of the H and D concentration in
the Pd matrix.
The measured Seebeck coefficients of Pd and PdHxDy
(Table 1) are close to the values reported for Pd and PdH0.6
[39]. As far as we know, no data on the Seebeck coefficient
of Pd deuteride have been previously reported. The present
result on the Seebeck coefficient of PdH0.35D0.26 implies
that there are not large differences between the Seebeck
coefficients of Pd hydride and deuteride.
.
The obtained x and y ratios are also consistent with the
electrolytic separation factor (S) between the atoms
contained in the hydride and in the electrolyte. For hydride
forming electrodes, S is defined as
0.6
0.5
0.4
0.3
0.2
0.1
0
β
ðH=DÞliq
ðH=DÞM
S ¼
,
(3)
where (H/D)M and (H/D)liq refer to the fractions of H and
D in the metal hydride and in the electrolyte, respectively.
S is determined by the difference in the absorption rates of
H and D atoms by Pd during the electrolysis [33]. From the
measurements of the H and D fractions in the PdHxDy
sample and in the electrolyte, a S value equal to 6.270.6 is
obtained, which is quite close to those reported by Farkas
[40] (S ¼ 6.6) and Dandapani and Fleischmann [41]
(Sꢂ7.2).
α+β
α
325
350
375
400
425
T (K)
450
475
500
525
Lattice parameter, resistivity and Seebeck coefficient
measurements indicate a total (H+D) content close to bmin
(0.61), what is in good agreement with the value obtained
from the integration of the TDS peaks and from the mass
loss measurements of the sample before and after TDS.
The mass of the PdHxDy sample was 13.3470.01 mg and
the mass loss after the desorption 0.1270.02 mg. These
data give x+y ¼ 0.6770.15. The large error in the x+y
Fig. 3. (a) Normalized H2, HD and D2 flows desorbed from PdHxDy as a
function of temperature during a linear temperature ramp (0.333 K sꢀ1);
(b) H plus D fraction remaining in the sample as a function of
temperature. This fraction has been obtained by integration of TDS
curves. Dashed lines show the temperature dependence of the two phase
coexistence limits [31]. Vertical dotted lines show the temperatures at
which the H+D concentration crosses the limits of the b-PdHxDy and a-
Pd phases.

ARTICLE IN PRESS
F. Leardini et al. / Journal of Physics and Chemistry of Solids 69 (2008) 116–127
120
An inverse isotope effect is observed. The desorption
been assumed to be determined by the equilibrium constant
of reaction (1):
peak is shifted to higher temperatures for H2 than for D2,
being the HD peak between the H2 and D2 ones. The
temperatures at which the maxima of the peaks occur are
448.5, 458.3 and 461.9 K for D2, HD and H2, respectively.
It should be noted that these temperature shifts are not due
to the time required for the transport of the desorbed
molecules from the sample surface to the gas analysis
system. In fact, the observed shifts are opposite to what
would be observed if they were caused by the transport of
gases because the diffusion of the heavier molecule towards
the QMS is slower. Besides, the experimental system has
been constructed to reduce the transport time as much as
possible and it has been estimated to be o10 s [23].
2
½HDꢃ
Keq
¼
.
(4)
½H2ꢃ½D2ꢃ
The statistical value of Keq for equally probable
combination of H and D atoms is 4. However, a lower
value is found in practice due to the fact that a pair of H2
and D2 molecules is energetically more favourable than two
of HD. Exact calculations of Keq were made by Urey and
Rittenberg [46] based on the partition functions of the
molecules. In the temperature range of the present TDS
experiments their results can be approximated by
ꢀ6:75 ꢁ 10ꢀ3
kT
The TDS peaks for the three hydrogen molecular
isotopes are asymmetric, with a sharper fall of the desorbed
flows at temperatures higher than that corresponding to
their maxima. A detailed examination reveals that this fall
is sharper for HD than for H2 and D2. Similar H2
desorption peaks have been reported from TDS of b-PdHx
powder [42] and b-PdHx foils [43] formed by solid–gas
reactions and from thermogravimetric analysis of electro-
chemically loaded PdHx foils [44].
An x/y ratio equal to 1.3770.08 in PdHxDy has been
obtained after integration of the H2, HD and D2
desorption peaks. Error comes mainly from the uncertainty
in the determination of the detection sensitivities sm/q(w).
Besides, the integration of the TDS curves allows the
obtaining of the temperature variation of the H plus D
fraction in Pd, as shown in Fig. 3b. The two phase
coexistence limits [35] are also plotted in Fig. 3b (dashed
lines), in order to emphasize the temperatures at which the
total H plus D concentration crosses the limits of the
b-PdHxDy and a-Pd phases, namely 420 and 475 K,
respectively. The small H/D isotope effects in the limits
of the b-PdHxDy and a-Pd phases [45] have been neglected.
ln Keq
¼
þ 1:4471,
(5)
.
where k is the Boltzmann constant expressed in eV Kꢀ1
The integration of the H2, HD and D2 flows desorbed
from PdH0.35D0.26 yields a ratio among the three molecular
isotopes of ꢂ2:3:1. Those ratios disagree with the expected
ones either from statistical or equilibrium partitioning of H
and D atoms into H2, HD and D2 molecules. A detailed
examination of the relative amounts of H2, HD and D2
desorbed molecules reported in previous experimental
works also reveals deviations from statistical or equili-
brium partitioning among the molecules [11,19,47,48]. In
particular, experimental results on hydrogen-deuterium
exchange on Pd [19] showed departures from the equili-
brium value predicted by Eq. (5), although equilibrium was
later assumed to simplify the theoretical analysis. It is
worth to note, however, that experimental values of the
relative amounts of H2, HD and D2 molecules are not given
in most of the previous works [6–10,12–18].
It will be shown here that the assumptions of equilibrium
or statistical partitioning of H and D atoms into the three
molecular isotopes are only valid under certain circum-
stances. We will deal with the general case in which H2, HD
and D2 molecules are formed by surface recombination of
H and D atoms. Two limiting cases must be distinguished:
4. Discussion
4.1. Partitioning of H and D atoms into H2, HD and D2
molecules
(i) Surface recombination reaction is at equilibrium (i.e.,
takes place in the forward and backward directions).
(ii) Surface recombination is out of equilibrium (i.e., takes
place in the forward direction only).
The desorbed H2, HD and D2 molecules are formed at
the sample surface by recombination of H and D atoms.
Therefore, the way in which H and D surface atoms are
partitioned into the three molecular isotopes must depend
on the characteristics of these reactions. Owing to ZPE
differences, significant isotope effects are expected among
the kinetics of the H–H, H–D and D–D recombination
reactions. However, earlier kinetic studies on the isotope
exchange reaction (1) on metal surfaces have usually
assumed no isotope effects in the rates of H and D
recombination reactions [9–13], in order to simplify the
theoretical analysis. This assumption implies a statistical
partitioning of H and D atoms into H2, HD and D2
molecules. In other works [19], the relative concentrations
of the hydrogen molecular isotopes in the gas phase have
In the first case, the molecules are continuously
dissociated and formed at the surface and, therefore,
equilibrium partitioning of H and D atoms into hydrogen
molecules is expected. However, in the majority of the
experiments involving H and D atoms to form H2, HD and
D2 molecules by surface recombination (such as TDS), the
molecules are rapidly removed from sample surface by
means of a pumping system or a carrier gas flow. Under
these circumstances it is reasonable to assume that surface
recombination reaction occurs in the forward direction
only (i.e., case (ii) holds), whichever be the rate-determin-
ing step of the whole reaction. Accordingly, the H2, HD

ARTICLE IN PRESS
F. Leardini et al. / Journal of Physics and Chemistry of Solids 69 (2008) 116–127
121
T (K)
and D2 desorbed flows (fHH, fHD and fDD, respectively) can
be written as
500
475
450
425
400
375
2.0
1.6
1.2
0.8
0.4
ꢀ
ꢁ
EꢄHH ꢀ 2EpH
kT
f HH ¼ nHH exp ꢀ
y2H,
(6a)
(6b)
(6c)
A
ꢀ
ꢁ
EꢄHD ꢀ EpH ꢀ EpD
kT
f HD ¼ nHD exp ꢀ
yHyD,
ꢀ
ꢁ
EꢄDD ꢀ 2EpD
kT
f DD ¼ nDD exp ꢀ
y2D,
B
where nHH, nHD and nDD are the prexponential factors of
the H–H, H–D and D–D recombination processes; EHꢄ H
,
EꢄHD and EꢄDD are the corresponding energy levels of the
transition states; EHp and EpD are the energy levels of H and
D atoms at the precursor (surface) states of molecular
formation and yH and yD are their respective concentra-
tions.
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
In order to quantify the relationship among the H2, HD
and D2 desorbed flows let us to define, in analogy with
Eq. (4):
103/ T (K-1)
Fig. 4. Arrhenius plot of the relative H2, HD and D2 flows desorbed from
PdHxDy (black points). Two regions appear with different activation
energies denoted as A and B in the figure. The vertical dotted line shows
the temperature at which the change from region A to B occurs (ꢂ480 K).
Solid lines represent the linear fit to the data in both regions. The line
predicted by the equilibrium exchange reaction between H2 and D2,
Eq. (5), has been also plotted (dashed line) for comparison purposes.
f 2HD
K ¼
.
(7)
f HHf DD
Introducing Eqs. (6a)–(6c) into (7) and taking loga-
rithms, it is obtained:
ꢂ
ꢃ
n2HD
nHHnDD
2EꢄHD ꢀ EꢄHH ꢀ EꢄDD
kT
ln K ¼ ln
ꢀ
.
(8)
by (7) is uniquely determined by the atom–atom recombi-
nation reaction, according to Eq. (8). Therefore, the
logarithmic plot in Fig. 4 can be taken as a direct insight
into the TS of the surface recombination reaction.
In the absence of isotope effects in the atom–ꢄatom
recombination reaction, nHD ¼ 2nHH ¼ 2nDD and EHH
¼
EꢄHD ¼ EꢄDD, what implies a statistical partitioning of
atoms into the molecular isotopes (i.e., K ¼ 4). However,
we believe that this assumption is unrealistic because large
ZPE differences among H–H, H–D and D–D pairs at the
TS are expected.
4.2. Kinetic analysis of the thermal desorption spectra
In order to analyze the kinetics of the thermal desorption
process, one should consider the desorption mechanism
which can be summarized in up to six sequential steps:
Experimental TDS data of PdH0.35D0.26 have been
analyzed according to Eq. (8) and the results are shown
in Fig. 4. The line predicted by the equilibrium exchange
reaction (5) is also plotted (dashed line) for comparison
purposes. Experimental points in Fig. 4 show two regions
(A and B) that can be fitted by Eq. (8). According to the
present model, this behaviour denotes a change in the
energy levels of the TS of the atom–atom recombination.
This change occurs at ꢂ480 K and it is quite abrupt. The
temperature range where the transition takes place is of
about 10 K. The least square fits of experimental points in
Fig. 4 (solid lines) give energies of ꢀ0.05170.001 and
ꢀ0.9670.07 eV in regions A and B, respectively. The
appearance of negative energies simply reflects that the TS
energy of the H–D recombination is below the mean value
between H–H and D–D ones. This finding contrasts with
the predictions of simple quantum considerations, as it will
be shown in Section 4.3.
a) Diffusion of H and D atoms through b-PdHxDy.
b) Transformation of b-PdHxDy into a-Pd.
c) Diffusion of H and D atoms through a-Pd.
d) Transition of H and D atoms from bulk to surface
states.
e) Surface recombination of H and D atoms to form H2,
HD and D2 physisorbed molecules.
f) Desorption of physisorbed molecules into the gas phase.
It should be noted that these steps are not simulta-
neously present during the complete desorption reaction.
According to Fig. 3b, the total H and D concentration
crosses the limits of the b-PdHxDy and a-Pd phases.
During desorption from b-PdHxDy steps (b) and (c) are
absent, whereas the same occurs with steps (a) and (b)
during desorption from a-Pd. Therefore, one should
analyze separately the desorption kinetics depending on
the steps involved in each region.
It is worth to emphasize that although the rates of H2,
HD and D2 desorption may depend on other steps of the
whole process, the relationship among these flows defined

ARTICLE IN PRESS
F. Leardini et al. / Journal of Physics and Chemistry of Solids 69 (2008) 116–127
122
It must be pointed out here that only the values of the
and D atoms given by lattice gas theory [22], it is obtained:
!
activation energies of the desorption process will be
obtained from such analysis. The frequency factors
appearing in the kinetic equations cannot be obtained
from the present experimental data because there are some
unknown variables in these equations, such as the
geometrical factors ‘M’.
ꢄ
EAHH ꢀ 2Eb
kT
x
ꢄ
ꢅ
2
f HH ¼ MAs nAHH exp ꢀ
,
(11a)
H
1 ꢀ x
!
ꢀ
ꢁ
(11b)
ꢄ
EAHD ꢀ EbH ꢀ EbD
kT
x
y
ꢄ
ꢅ
f HD ¼ MAs nAHD exp ꢀ
,
1 ꢀ x 1 ꢀ y
4.2.1. Desorption from b-PdHxDy
Below 420 K, the PdHxDy sample is in the b-phase (see
Fig. 3b). The H and D concentration gradients within the
sample in this temperature region are small and, therefore,
diffusion does not control the desorption process. These
gradients can be evaluated from the ratios Dx/x and Dy/y,
where Dx and Dy are the variations of the H and D
concentrations inside the sample during a typical diffusion
time t [42]:
!
ꢀ
ꢁ
ꢄ
2
EADD ꢀ 2Eb
kT
y
f DD ¼ MAs nADD exp ꢀ
,
(11c)
D
1 ꢀ y
where EbH and EbD are the energies of H and D atoms,
respectively, in bulk b-PdHxDy sites. The superscript A in
the TS energies of the atom–atom recombination reaction
denotes that this is the TS corresponding to region A in
Fig. 4.
Dx ¼ f HtH,
Dy ¼ f DtD,
(9a)
The H2, HD and D2 flows desorbed from b-PdHxDy
have been fitted by Eqs. (11a)–(11c) and the results are
shown in Fig. 5. Activation energies equal to 0.87870.004,
0.82270.004 and 0.81870.003 eV mole cꢀ1 for H2, HD
and D2, respectively, have been obtained from the least
square fit of experimental points in this figure. The
activation energies decrease in the order H24HD4D2,
as expected from the temperature shift of H2, HD and D2
desorption peaks (Fig. 3a). This result is somewhat similar
to that found by Jin et al. [27,28], who reported an inverse
isotope effect in the kinetics of H(D) desorption from a-Pd.
On the other hand, these activation energies imply the
existence of an activation barrier for the surface recombi-
nation reaction, because they are higher than the formation
(9b)
where fH and fD are the H and D desorption rates. On the
other hand, t can be estimated according to t ¼ L2/p2Dc,
where L is the diffusion length and Dc is the diffusion
coefficient of H or D (Dc ¼ D0 exp(ꢀEd/kT)). We have
used a diffusion length of one-half of the Pd foil thickness.
Therefore, Dx and Dy should be considered as an
estimation of the H and D concentration gradients between
the centre and the surfaces of the Pd foil.
The diffusion coefficient of H in b-Pd hydride is given by
D0 ¼ 0.9 ꢁ 10ꢀ3 cm2 sꢀ1 and Ed ¼ 0.228 eV [49]. Deuterium
diffusion coefficients have been calculated from reported
data [50] of the ratio between H and D diffusion
coefficients in Pd as a function of temperature. The
obtained Dx/x and Dy/y values at 400 K are equal to
0.013 and 0.014, respectively. From those results it is clear
that the desorption process cannot be fitted by a diffusion
limited mechanism.
T (K)
420
410
400
390
380
370
H2
The analysis of the thermal desorption curves of bulk
MH in the case of a process limited by surface recombina-
tion was done by Stern et al. [21,22] and was successfully
applied to Pd hydride powder [42]. They considered two
limiting cases, depending on the relative position of the H
energy levels in the bulk and at the precursor (surface)
states of the recombination reaction. According to their
results, for a H/Pd ratio in the sample below 0.7, the H
bonding energy in the bulk is higher than at the precursor
states. Under these circumstances the H concentration
at the precursor states is low and the H2 flow can be
written as
HD
D2
-26
-28
-30
!
ꢄ
EAHH ꢀ 2mH
kT
f HH ¼ MAs nAHH exp ꢀ
,
(10)
2.4
2.5
2.6
2.7
1000/T (K-1)
where MAs is a constant, nHAH is the frequency factor of
H–H recombination and mH is the chemical potential of H
atoms in the hydride. By writing analogue expressions for
HD and D2 flows and taking the chemical potential of H
Fig. 5. Arrhenius plot of the H2, HD and D2 desorption by considering a
surface recombination mechanism (To420 K). Solid lines in this figure are
the linear fits of experimental data.

ARTICLE IN PRESS
F. Leardini et al. / Journal of Physics and Chemistry of Solids 69 (2008) 116–127
123
enthalpies of b-Pd hydride and deuteride [45]. These
barriers are higher than those obtained by Stern et al.
[42]. Such differences should be attributed to the different
surface conditions of the Pd samples. In fact, the height
of the activation barrier for recombinative desorption is
extremely sensitive to the presence of oxides [51,52] and
other surface impurities [28,29,53].
where c is a constant. The factors x/(x+y) and y/(x+y)
account for the probability of a H or D atom be located at
the b/a interface, respectively.
In this model, the desorbing sample must be regarded as
a shrinking core of b-PdHxDy enveloped by a growing
layer of a-Pd [54]. Due to the fact that the hydrogen and
deuterium partial pressures in the volume near the sample
are much lower than the equilibrium pressures of the b/a
transformation, the H and D concentration in a-Pd can be
safely assumed to be negligible. This implies that all the
remaining H and D atoms are in the b-PdHxDy inner core.
Accordingly, the volume of this core should be propor-
tional to the total number of atoms in the sample (x+y),
while the area of the b/a interface should be proportional
to (x+y)2/3. Taking into account those considerations, Eqs.
(12a) and (12b) take the form:
4.2.2. Desorption during coexistence of the a and b phases
According to the model described in the previous
section, if surface recombination is still rate limiting during
the coexistence of b-PdHxDy and a-Pd, the molecular
desorbed flows should be described by zero-order processes
[42]. This is because the constancy of the H and D chemical
potentials during the two-phase coexistence. However, the
experimental H2, HD and D2 desorbed flows do not fit to a
zero-order process.
!
EbH=a ꢀ EbH
kT
f H ¼ M0bnH exp ꢀ
b
minxðx þ yÞꢀ1=3
,
.
(14a)
(14b)
The role of bulk diffusion has been analyzed as described
above. In this case, diffusion coefficients in both b-PdHxDy
and a-Pd phases have been used. Diffusion coefficients are
!
x
y
EbD=a ꢀ EbD
kT
faster in a-Pd than in b-PdH D . According to Volk and
¨
f D ¼ M0bnD exp ꢀ
b
minyðx þ yÞꢀ1=3
Alefeld [50] the best fit to diffusion coefficient data of
H in a-Pd is given by D0 ¼ 2.9 ꢁ 10ꢀ3 cm2 sꢀ1 and
Ed ¼ 0.230 eV. Again, D diffusion coeficients in a-Pd have
been calculated from the reported ratio between H and D
diffusion coefficients [50]. By using a and b diffusion
coefficients, the lower and higher limits, respectively, for
Dx/x and Dy/y can be estimated. The obtained values at
455 K are 0.02oDx/x, Dy/yo0.07. These concentration
gradients imply that the kinetics of H and D desorption in
this region is not controlled by diffusion.
Accordingly, there is only one possible mechanism to
explain the desorption kinetics during the two-phase
coexistence region, i.e., the transition of H and D atoms
from the b-PdHxDy to the a-Pd phase. In this case, the
rates of H and D desorption can be written as
The experimental H and D desorbed flows have been
fitted by Eqs. (14a) and (14b), respectively, and the results
are shown in Fig. 6. According to the present model, H and
D atoms desorb from the b-PdHxDy inner core and,
therefore, the b to a phase transformation should control
the process until the end of the desorption process.
However, it can be seen from Fig. 6 that the model only
fit the experimental data up to ꢂ480 K. This is the
temperature at which the change from region A to region
T (K)
525
500
475
450
425
!
EbH=a ꢀ EbH
kT
f H ¼ MbnH exp ꢀ
xb=a
,
(12a)
(12b)
-3.5
-4.0
-4.5
-5.0
-5.5
H
D
!
EbD=a ꢀ EbD
kT
f D ¼ MbnD exp ꢀ
yb=a
,
where Mb is a constant, nH and nD are the frequency factors
of the b to a transformation, EbH/a and EDb/a are the
corresponding TS energies for H and D atoms and xb/a and
yb/a are the numbers of H and D atoms at the bXa
interface. These numbers will depend on the b-phase
concentration (bmin, which depends on temperature ac-
cording to the dashed line shown in Fig. 3b) and on the
area of the bXa interface (Ab/a):
2.0
2.1
2.2
1000/T (K-1)
2.3
2.4
x
xb=a ¼ c
yb=a ¼ c
bminAb=a
,
(13a)
x þ y
Fig. 6. Arrhenius plot of the H and D flows by considering a b to a
transformation mechanism (420oTo480 K). Solid lines in this figure are
the linear fits of experimental data.
y
bminAb=a
,
(13b)
x þ y

ARTICLE IN PRESS
F. Leardini et al. / Journal of Physics and Chemistry of Solids 69 (2008) 116–127
124
T (K)
B is observed in the plot of the relative desorbed flows
(Fig. 4), which was ascribed to a change in the kinetics of
the surface recombination reaction.
510
500
490
480
Activation energies equal to 0.56970.003 and
0.53570.003 eV atomꢀ1 for H and D, respectively, have
been obtained from the slopes of the least square fits of the
experimental points in Fig. 6. These values imply the
existence of an inverse isotope effect in the b to a transition.
As far as we know, no previous results on this isotope
effect have been reported. In addition, there is only one
previous estimation of the activation energy of the b to a
transition in the Pd–D system [55]. It was obtained from
the analysis of the effective diffusion coefficient of D in
single crystal Pd within the two-phase coexistence region.
-14
-16
-18
-20
-22
H2
HD
D2
The reported activation energy value was 0.45 eV atomꢀ1
which is in reasonable agreement with the present result.
,
4.2.3. Final stage of desorption
1.96
1.98
2.00
2.02
1000/T (K-1)
2.04
2.06
2.08
As it has been stated in the previous section, above 480 K
the desorption kinetics is not controlled by the b to a phase
transition. This has been ascribed to the change in the
kinetics of the surface recombination reaction, which
becomes again rate limiting above this temperature. This
implies that the rate of the b to a phase transition is now
faster than the whole desorption rate. Given that the mean
H plus D concentration in the sample in this temperature
range is below the a-Pd phase limit (see Fig. 3b), it is
expected that the inner b-nucleus will disappear and the
sample will be completely transformed into a-Pd.
Again, the role of bulk diffusion on the desorption
process has been estimated. Diffusion coefficients in a-Pd
have been used. At 495 K, the obtained Dx/x and Dy/y
ratios are equal to 0.07 and 0.06, respectively.
Following the analysis done in Section 4.2.1 for a surface
recombination limiting mechanism, the H2, HD and D2
flows will be described by the following equations:
Fig. 7. Arrhenius plot of the H2, HD and D2 desorption by considering a
surface recombination mechanism (T4480 K). Solid lines in this figure are
the linear fits of experimental data.
recombination in b-PdHxDy (Section 4.2.1). Similar incre-
ments in the activation energies of the atom–atom
recombination have been observed in TDS experiments
of TaDx foils [56]. In these experiments, the surface
composition was in situ monitored by means of Auger
spectroscopy. The change of the activation energy occurred
at the same temperature where a decrease in the oxygen
surface concentration was observed. The authors argued
that the increment in the activation energy of the H–H
recombination reaction was due to the energy involved in
the process of diffusion of oxygen atoms from the surface
layer to the bulk.
Later experiments [57] performed in ultrahigh vacuum
conditions with TaHx and ZrHx foils with different degrees
of oxidation confirmed the observation of a rise in the
activation energy of the H–H surface recombination. In
this case, however, the effect was ascribed to the energy
involved in the O desorption in the form of H2O molecules.
The H2O/HDO/D2O desorption rates could not be
monitored in our TDS experiments, due to a secondary
effect that masked these signals. This effect consists on the
hydrogen-induced water formation in the gas analysis
chamber. Indeed, the H2O/H2 ratio in the present TDS
experiments was similar to that observed during calibration
experiments with H2–Ar mixtures (typically in the range of
10ꢀ3–10ꢀ2). This ratio is in agreement with the previous
investigations on the H2-induced H2O production [58,59].
Accordingly, the H2O/HDO/D2O signals coming from the
H2/HD/D2-induced reactions within the QMS were much
higher than those expected from the H2O/HDO/D2O
desorption from the sample. This last quantity is several
orders of magnitude lower than the H2/HD/D2 desorbed
!
ꢄ
ꢄ
ꢅ
EBHH ꢀ 2EaH
kT
x
2
f HH ¼ MBs nBHH exp ꢀ
,
(15a)
1 ꢀ x
!
ꢀ
ꢁ
(15b)
ꢄ
ꢄ
ꢅ
EBHD ꢀ EaH ꢀ EaD
kT
x
y
f HD ¼ MBs nBHD exp ꢀ
,
1 ꢀ x 1 ꢀ y
!
ꢀ
ꢁ
ꢄ
2
EBDD ꢀ 2EaD
kT
y
f DD ¼ MBs nBDD exp ꢀ
,
(15c)
1 ꢀ y
where MBs is a constant, nBHH, nBHD and nDB D are the
frequency factors of the H–H, H–D and D–D recombina-
tion in region B (see Fig. 4) and EaH and EDa are the energies
of H and D atoms, respectively, in a-Pd sites.
The fits of the experimental data by Eqs. (15a)–(15c) are
shown in Fig. 7. The obtained activation energies are equal
to 4.2070.06, 3.6570.02 and 4.0870.05 eV mole cꢀ1 for
H2, HD and D2, respectively. Those values are about five
times greater than these found for the atom-atom

ARTICLE IN PRESS
F. Leardini et al. / Journal of Physics and Chemistry of Solids 69 (2008) 116–127
125
flows. Even if one assumes that all the oxygen atoms
HH
HD
DD
region B
0
0
present as impurities in the carrier Ar flow, whose
concentration is o1 ppm, react with the desorbing H and
D atoms at the Pd surface to form water molecules, the
estimated H2O/H2 ratio would be about one order of
magnitude lower than the measured one.
-50
-1
-3.5
2H or 2D in
-350
-400
-450
-500
atom-atom
TS
β/α TS
In any case, neither O diffusion into the bulk nor H2O/
HDO/D2O desorption can account for the present results.
Within these models, the change of the activation energy of
the desorption process is due to the extra energy needed
either to diffuse O atoms into the bulk or to desorb them as
H2O/HDO/D2O molecules. Both processes would lead to a
similar increment in the activation energies of H2, HD and
D2 molecules. By contrast, it is observed that the activation
energy increments are different for the three hydrogen
molecular isotopes. We hypothesize that the increment of
the activation energies of the H–H, H–D and D–D
recombination reactions should be attributed to a change
of the surface catalytic properties due a modification of the
surface composition. This modification would shift the
energy levels of the TS’s of the surface recombination
reaction, which are different for each one of the molecular
isotopes. This interpretation is further supported by the
fact that the change in the activation energies occurs in the
same temperature range than the change in the TS energies
deduced from the analysis of the relative H2, HD and D2
distributions (Fig. 4). This point will be considered in more
detail in the next section. On the other hand, the
modification of the surface composition should be ascribed
to the diffusion of bulk impurities to the surface or to the
growing of the surface oxide layer. Oxygen transitions from
surface to subsurface or bulk sites have been reported in Pd
[60] at temperatures between ꢂ350 and 500 K. This would
imply that the oxide layer present at the sample surface
could growth, assisted by the oxygen diffusion into the
bulk, due to the impurity levels of oxygen in the carrier Ar
gas (ꢂ1 ppm). Further experiments must be accomplished
to test the proposed model.
-4.0
-4.5
-5.0
region A
Heat of
solution
Heat of
formation
2H or 2D in
α-Pd
2H or 2D in
β- PdHxDy
Gas Surface
α-Pd
β-PdHxDy
Fig. 8. Schematic diagram for the energy levels of H and D atoms in their
desorption from PdHxDy.
energies in bulk b-PdHxDy sites (EbH and EDb ) can be
obtained from the enthalpies of the b to a transition of Pd
hydride and deuteride [45], respectively. The energies of H
and D atoms at the TS’s of the b to a phase transformation
and of the atom-atom surface recombination have been
calculated from EHa , EDa , EHb , EbD and the activation energies
obtained in the analysis of the TDS curves (Section 4.2).
The observed isotope effect in the TS energies (Fig. 8)
can be understood in the following terms. The TS is usually
represented as a saddle point at the PES, with a maximum
along the reaction coordinate and a minimum in at least
one of the normal coordinates. The dynamics of atoms or
molecules along these normal coordinates generates
quantized energy levels at the TS, which will depend on
the mass of the atoms/molecules. The existence of such
quantized states in the TS of chemical reactions is
supported by some experimental evidences and it has been
the subject of recent reviews [62,63]. TS energies of the b to
a transition shown in Fig. 8 are more positive for H than
for D atoms, as expected from the ZPE differences.
Moreover, these differences are higher at the TS of the b
to a transition than in bulk b-PdHxDy sites. This is the
cause of the inverse isotope effect in the activation energies
of the b to a phase transformation. A similar situation is
observed for the TS of H and D diffusion in a-Pd.
Differences between ZPE of H and D atoms are higher at
the TS of the diffusion process that in a-Pd octahedral
sites, which is the reason to observe a higher diffusion
coefficient for D than for H [5,64].
4.3. Transition state energies
The schematic diagram appearing in Fig. 8 shapes the
energy levels of H and D atoms during the desorption
reaction. The zero-energy level has been taken as the
energy of a pair of free H atoms. The energy levels of H2,
HD and D2 molecules in the gas phase (E0HH, EH0 D and
E0DD) have been calculated from the reported dissociation
energies of the three molecular isotopes [61]. It must be
noted that dissociation energies refer to H2, HD and D2
dissociation into atoms in their fundamental states. There-
fore, the energy difference between free H and D atoms
(3.6 ꢁ 10ꢀ3 eV) must be taken into account in the calcula-
tion of H2, HD and D2 energies. The energy of H atoms in
bulk a-Pd sites (EHa ) has been obtained from EH0 H and the
enthalpy of solution of H2 in a-Pd. [35]. From EaH and the
reported ZPE difference between H and D atoms in a-Pd
[45], EaD can be calculated. On the other hand, H and D
Concerning the TS of the H–H, H–D and D–D surface
recombination reactions, it is worth to note that when TS
energies in Fig. 8 are introduced into Eq. (8), the values

ARTICLE IN PRESS
F. Leardini et al. / Journal of Physics and Chemistry of Solids 69 (2008) 116–127
126
obtained from the linear fit of the experimental points in
Fig. 4 are reproduced within the experimental error. This
accordance confirms the goodness of the calculation of the
TS energies and, therefore, corroborates the kinetic
analysis of the TDS curves.
dissociation threshold of the molecule [67]. The fact that
the anomalies observed in the TS energies are more
pronounced in region B, for which the TS energy is closer
to the free atoms state, could be related to the former view.
The present results motivate further experiments in order
to clarify the origin of these anomalies, such as quantum-
state integral measurements (i.e., the analysis of the
angular and velocity distributions) and quantum state
resolved experiments (i.e., the analysis of the rotational and
vibrational distributions) of the desorbed molecular
isotopes.
On the other hand, the energy spacing among the H–H,
H–D and D–D TS shows an anomalous behaviour.
Considering the simplest case of a two-dimensional PES
in which the potential along the normal coordinate is
harmonic, the relative ZPE differences at the TS of H–H,
H–D and D–D recombination can be calculated. Applying
the rule for calculating isotopic energy levels [65], the
difference between ZPE of H–H and H–D TS should be
ꢂ0.45 times the difference between H–H and D–D. This
implies that ZPE of H–D TS should lie slightly above the
mean value between H–H and D–D ones. This picture
describes well the differences between ZPE of H2, HD and
D2 molecules in the gas phase. However, as it can be seen in
Fig. 8, H–D TS energies lay below the mean values of H–H
and D–D TS energies. The effect is more pronounced in
region B, in which TS energy of H–D is even lower than the
corresponding value for D–D.
Anomalous behaviours among H2, HD and D2 mole-
cules desorbed from Pd have been also observed by
Schroter et al. [66]. They found that the energy spacing
¨
between the two first vibrational levels in the TS of the
atom-atom recombination does not scale with the isotopic
mass ratio of the molecules. Assuming that the energy
difference between vibrational states is proportional to
ZPE, as in the case of a harmonic potential, the ratio
between the ZPE differences for the three molecular
isotopes can be obtained from the experimental results of
5. Conclusions
The kinetics of simultaneous hydrogen and deuterium
desorption from PdHxDy has been investigated by means
of TDS.
On the one hand, the H and D partitioning into the H2,
HD and D2 desorbed molecules has been analyzed. It has
been found that this partitioning is determined by the
differences among the TS energies of the H–H, H–D and
D–D recombination reactions. This finding contrasts with
previous investigations that assumed either equilibrium or
statistical partitioning of H2, HD and D2 molecules. The
analysis of the relative concentration of the hydrogen
molecular isotopes allows to follow the position of the
H–D TS energy with respect to the mean value between the
H–H and D–D ones during the course of the desorption
reaction. As a consequence, the influence of the surface
properties on the atom-atom recombination reaction can
be easily monitored from the analysis of the H2, HD and
D2 distributions.
The kinetics and mechanisms of the PdHxDy desorption
have been derived from the analysis of the TDS curves.
During desorption from the b-PdHxDy phase (To420 K),
a surface recombination mechanism (with activation
energies equal to 0.87870.004, 0.82270.004 and 0.8187
0.003 eV mole cꢀ1 for H2, HD and D2, respectively) has
been observed. The desorption reaction has been found
to be rate limited by the rate of the b to a phase
transformation during the two-phase coexistence region,
with activation energies equal to 0.56970.003 and 0.5357
0.003 eV atomꢀ1 for H and D, respectively. Finally, surface
recombination becomes again rate limiting above ꢂ480 K
due to a change in the surface activation barrier of the
atom-atom recombination. This produces an increase
of a factor ꢂ5 in the activation energies of the atom-
atom recombination (4.2070.06, 3.6570.02 and 4.087
0.05 eV mole cꢀ1 for H2, HD and D2, respectively).
TS energies of the b to a phase transformation and of the
atom–atom recombination reaction have been calculated.
TS energies for the H–D surface recombination have been
found to be below the arithmetical mean value between the
H–H and D–D TS energies. This fact contrasts with the
predictions of simple quantum considerations. Tentative
explanations related to the heteronuclear character of the
Schroter et al. [66]. It is found that ZPE of H–D
¨
recombination lies also below the mean value between
H–H and D–D ones.
Tentative explanations of the above mentioned anoma-
lies can be given on the basis of the heteronuclear character
of the HD molecule. This gives rise to the breakdown of the
inversion symmetry and to the appearance of several
properties qualitatively different from those of the homo-
nuclear species. A review of the phenomena associated to
the inversion symmetry breakdown in HD has been
recently done by de Lange et al. [67]. One of such
phenomena is the existence of a permanent dipolar
moment in the ground state of the HD molecule. This
implies that TS energy of HD could be lowered by the
presence of a surface electric field. However, by considering
a typical electric field of 107 V mꢀ1, the dipolar moment of
the HD molecule in the TS should be 6–7 orders of
magnitude greater than the corresponding value in the
fundamental state in the gas phase (ꢂ10ꢀ3 D [68]) if the
observed energy shifts are to be explained. Such a value
seems to be unreasonable. On the other hand, the breaking
of the inversion symmetry also produces the electronic
coupling between states of g and u symmetry and this can
lead to the appearance of new states not observed in the
homonuclear species. This effect is stronger near the

ARTICLE IN PRESS
F. Leardini et al. / Journal of Physics and Chemistry of Solids 69 (2008) 116–127
127
HD molecule have been proposed to explain the observed
anomalies.
[33] F. Leardini, J. Bodega, J.F. Ferna
´
ndez, I.J. Ferrer, C. Sa
´
nchez,
Recent Res. Devel. Electrochem. 8 (2005) 257 (Kerala: Transworld
Research Network).
[34] A. Kern, W. Eysel, Mineralogisch-Petrograph, Inst., Univ. Heidel-
berg, Germany, ICDD Grant-in-Aid, 1993.
¨
[35] E. Wicke, H. Brodowski, in: G. Alefeld, J. Volk (Eds.), ‘Hydrogen in
Acknowledgements
Metals II’ Topics in Applied Physics, vol. 29, Springer, Berlin, 1978,
pp. 73–155.
This work has been supported by Spanish MEC under
contracts MAT2004-01903 and MAT2005-06738-C02-01.
One of us (FL) also thanks to the Spanish MEC for
a Ph.D. fellowship under the FPU program. Technical
assistance from Mr. F Moreno is gratefully acknowledged.
Finally, we want to thank one of the reviewers for several
useful suggestions, mainly for his/her contribution to Fig. 8.
[36] R. Felici, L. Bertalot, A. DeNinno, A. LaBarbera, V. Violante, Rev.
Sci. Instrum. 66 (1995) 3344.
[37] CRC Handbook of Chemistry and Physics, 82nd ed., ed Lide DR,
CRC Press, Boca Raton, 2001–2002
[38] M.C.H. McKubre, S. Crouch-Baker, M. Riley, R.C. Rocha-Filho,
M. Schreiber, S.I. Smedley, F.L. Tanzella, Aspects of the electro-
chemical loading of hydrogen and its isotopes into palladium, in:
Presented at ECS Meeting, Phoenix, Arizona, 1991
[39] C.L. Foiles, Solid State Commun. 33 (1980) 125.
[40] A. Farkas, Trans. Farad. Soc. 33 (1937) 552.
[41] B. Dandapani, M. Fleischmann, J. Electroanal. Chem. 39 (1972) 323.
[42] A. Stern, A. Resnik, D. Shaltiel, J. Phys. F.: Met. Phys. 14 (1984)
1625.
References
[1] L. Schlapbach, A. Zuttel, Nature 414 (2001) 353.
¨
[2] L. Schalpbach, in: L. Schalpbach (Ed.), Hydrogen in Intermetallic
Compounds, vol. II, Springer, Berlin, 1992 Ch.2.
[3] A. Borgschulte, R.J. Westerwaal, J.H. Rector, H. Schreuders,
B. Dam, R. Griessen, J. Catal. 239 (2006) 263.
[43] A.L. Cabrera, E. Morales, J.N. Amor, J. Mater. Res. 10 (1995) 779.
[44] L.E.A. Berlouis, P.J. Hall, A.J. MacKinnon, A.W. Wark,
D. Manuelli, V. Gervais, J.E. Robertson, J. Alloys Compds. 253/
254 (1997) 207.
[4] K.S. Jung, D.H. Kim, E.Y. Lee, K.S. Lee, Catal. Today 120 (2007) 270.
[5] G. Sicking, J. Less Common Met. 101 (1984) 169.
[6] K.E. Lu, R.R. Rye, Surf. Sci. 45 (1974) 677.
[45] R. Laser, K.H. Klatt, Phys. Rev. B 28 (1983) 748.
¨
[7] S.L. Bernasek, G.A. Somorjai, J. Chem. Phys. 62 (1975) 3149.
[8] I.E. Wachs, R.J. Madix, Surf. Sci. 58 (1976) 590.
´
[9] M. Salmeron, R.J. Gale, G.A. Somorjai, J. Chem. Phys. 70 (1979)
[46] H.C. Urey, D. Rittenberg, J. Chem. Phys. 1 (1933) 137.
[47] Z. Liu, L.C. Feldmann, L.H. Tolk, Z. Zhang, P.I. Cohen, Science 312
(2006) 1024.
2807.
[48] P. Franzen, R. Behrisch, C. Garcıa-Rosales, D. Schleussner,
´
D. Rosler, J. Becker, W. Knapp, C. Edelmann, Nucl. Fusion 37
¨
[10] T. Engel, H. Kuipers, Surf. Sci. 90 (1979) 162.
[11] StJ. Dixon-Warren, A.T. Pasteur, D.A. King, J. Chem. Phys. 103
(1995) 2261.
(1997) 1375.
[49] E.F.W. Seymour, R.M. Cotts, W.D. Williams, Phys. Rev. Lett. 35
(1975) 165.
[50] J. Volk, G. Alefeld, in: G. Alefeld, J. Volk (Eds.), ‘Hydrogen in
[12] M.F. Bertino, J.P. Toennies, J. Chem. Phys. 110 (1999) 9186.
[13] P. Hahn, M.F. Bertino, J.P. Toennies, M. Ritter, W. Weiss, Surf. Sci.
412/413 (1998) 82.
¨
¨
Metals I’ Topics in Applied Physics, vol. 28, Springer, Berlin, 1978,
pp. 321–348.
[14] T.H. Lin, G.A. Somorjai, J. Chem. Phys. 81 (1984) 704.
[15] J. Magnusson, Ind. Eng. Chem. Res. 26 (1987) 877.
[51] G. Krenn, C. Eibl, W. Mauritsch, E.L.D. Hebenstreit, P. Varga,
A. Winkler, Surf. Sci. 445 (2000) 343.
[52] L.-G. Petersson, H. Dannetum, J. Fogelberg, I. Lundstrom, Appl.
¨
[16] H. Backman, J. Jensen, F. Klingstedt, J. Warna, T. Salmi,
´
¨
D.Y. Murzin, Appl. Catal. A 273 (2004) 303.
[17] M.G. Basallote, S. Bernal, J.M. Gatica, M. Pozo, Appl. Catal. A 232
(2002) 39.
Surf. Sci. 27 (1986) 275.
[53] F.J. Castro, G. Meyer, G. Zampieri, J. Alloys compds. 330–332
(2002) 612.
¨
[18] H. Backman, K. Rahkamaa-Tolonen, J. Warna, T. Salmi,
D.Y. Murzin, Chem. Eng. J. 107 (2005) 89.
[19] G.W. Foltz, C.F. Melius, J. Catal. 108 (1987) 409.
[20] D.A. Outka, G.W. Foltz, J. Catal. 130 (1991) 268.
[54] F.J. Castro, G. Meyer, J. Alloys Compds. 330–332 (2002) 59.
[55] W.C. Chen, B.J. Heuser, J. Alloys Compds. 312 (2000) 59.
[56] E. Porschke, D. Shaltiel, K.H. Klatt, H. Wenzl, J. Phys. Chem. Solids
¨
[21] A. Stern, S.R. Kreitzman, A. Resnik, D. Shaltiel, V. Zevin, Solid
State Commun. 40 (1981) 837.
[22] A. Stern, A. Resnik, D. Shaltiel, J. Less Comm. Met. 88 (1982) 431.
47 (1986) 1003.
[57] D.E. Shleifman, D. Shaltiel, I.T. Steinberger, J. Alloys Compds. 223
(1995) 81.
[23] J.F. Ferna
´
244.
ndez, F. Cuevas, C. Sa
´
nchez, J. Alloys Compds. 298 (2000)
[58] H.F. Dylla, W.R. Blanchard, J. Vac. Sci. Technol. A 1 (1983) 1297.
[59] J.R.J. Bennett, R.J. Elsey, Vacuum 44 (1993) 647.
[60] J.-W. He, U. Memmert, P.R. Norton, J. Chem. Phys. 90 (1989) 5088.
[61] G. Herzberg, Phys. Rev. Lett. 23 (1969) 1081.
[62] K. Liu, Annu. Rev. Phys. Chem. 52 (2001) 139.
[63] R.T. Skodje, X. Yang, Int. Rev. Phys. Chem. 23 (2004) 253.
[64] X. Ke, G.J. Kramer, Phys. Rev. B 66 (2002) 184304.
[65] G. Herzberg, Molecular Spectra and Molecular Structure I. Spectra
of Diatomic Molecules, Nostrand Reinhold, New York, 1950.
[24] T. Graham, Phil. Trans. Roy. Soc. (London) 156 (1866) 415.
[25] M.A. Pick, J.W. Davenport, M. Strongin, G.J. Dienes, Phys. Rev.
Lett. 43 (1979) 286.
[26] F. Cuevas, M. Hirscher, J. Alloys Compds. 313 (2000) 269.
[27] Y. Jin, M. Hara, J.L. Wan, M. Matsuyama, K. Watanabe, J. Alloys
Compds. 340 (2002) 207.
[28] Y. Jin, L. Wang, M. Hara, K. Watanabe, Mater. Trans. 48 (2007) 560.
[29] S. Hayashi, J. Alloys Compds. 359 (2003) 281.
[30] L. Schoter, H. Zacharias, R. David, Phys. Rev. Lett. 62 (1989) 571.
¨
[66] L. Schroter, S. Kuchenhoff, R. David, W. Brening, H. Zacharias,
¨
Surf. Sci. 261 (1992) 243.
¨
[31] L.J. Van der Pauw, Phil. Res. Rep. 13 (1958) 1.
´
[32] J.R. Ares, M. Leon, N.M. Arozamena, J. Sanchez-Paramo, P. Celis,
I.J. Ferrer, C. Sanchez, J. Phys.: Condens. Matter 10 (1998) 4281.
´
[67] A. De Lange, E. Reinhold, W. Ubachs, Int. Rev. Phys. Chem. 21
(2002) 257.
[68] J.B. Nelson, G.C. Tabisz, Phys. Rev. Lett. 48 (1983) 1393.