Temperature-dependent work function shifts of hydrogenated/deuteriated palladium: a new theoretical explanation

Surface Science 555 (2004) 43–50

www.elsevier.com/locate/susc

Temperature-dependent work function shifts ofhydrogenated/deuteriated palladium: a new

theoretical explanation

S. Halas a,*, T. Durakiewicz a,b, P. Mackiewicz a

a Mass Spectrometry Laboratory, Institute of Physics, Maria Curie–Sklodowska University, 20-031 Lublin, Polandb Los Alamos National Laboratory, Condensed Matter and Thermal Physics, MST-10 Group, Los Alamos, NM 87545, USA

Received 6 June 2003; accepted for publication 1 March 2004

Abstract

We explain the phenomena of work function (WF) variations of polycrystalline palladium film due to adsorption

and absorption of hydrogen. A small increase of the WF observed at temperatures above 120 K is an indication of a

spontaneous formation of H� ions at the surface, subsequently dissociating to electrons and neutral atoms which

completely desorb at temperatures above 400 K. A large lowering of the WF at low temperatures (about 2 eV at 78 K) is

associated with the formation of PdH. This process is treated quantitatively in the frame-work of the metallic plasma

model. The mechanism of the isotope effect on the lowering of the WF is explained by the vibrational frequency dif-

ference of H and D atoms confined in the palladium lattice.

� 2004 Elsevier B.V. All rights reserved.

Keywords: Chemisorption; Deuterium; Hydrogen atom; Isotopic exchange/traces; Palladium; Work function measurements

1. Introduction

Palladium atoms have 10 d electrons and no s

electron in the valence shell, unlike other transition

metals. This unique electronic structure of the Pd

results in very specific interactions between the Pd

and the H atoms in Pd–H systems. The most

striking experimental fact is that a thin Pd layer

readily and reversibly converts itself to PdHx invery low pressure of H2. Du�s et al. [1] have found

that x attains 0.84 when H2 pressure (in equilib-

* Corresponding author. Tel.: +48-815-376-275; fax: +48-

815-376-91.

E-mail address: [email protected] (S. Halas).

0039-6028/$ - see front matter � 2004 Elsevier B.V. All rights reserv

doi:10.1016/j.susc.2004.03.001

rium) is as low as 10�6 Torr. The process of pal-ladium hydride formation may be reversed by a

decrease of the gas pressure. Both the ambient

hydrogen pressure and temperature strongly affect

the electronic work function (WF) of the metallic

layer. For this reason Pd and perhaps other tran-

sition metals which reversibly absorb hydrogen,

may be useful in future devices where a continuous

adjustment of WF will be desirable.In a number of experiments performed by Du�s

and his coworkers [1–4] an increase of the WF by

ca. 0.3 eV was noticed in temperatures above 120

K compared to clean Pd-films. Below 87 K these

authors have observed a new interesting phenom-

enon, namely a gradual decrease of the WF with

an increase of the H/Pd ratio in bulk metal. The

ed.

mail to: [email protected]

44 S. Halas et al. / Surface Science 555 (2004) 43–50

most pronounced effect is reported at T ¼ 78 K in

the case of deuteriated Pd. For PdDx, where

x ¼ 0:7, the latter authors observed lowering of the

WF by 2.32 eV. Assuming that the experimental

WF for the pure Pd-film is 5.27 eV (see Section 4)

the deuteriated palladium may have a WF of lessthan 3.0 eV.

The primary motivation of this paper is to give

an explanation of the dual behavior of the Pd–H

system in a more simplistic way than it was pro-

posed by Grimley [5]. According to his model, the

increase in hydrogen adsorbate concentration

causes an increase in the magnitude of splitting

between induced localized states. There is a criticalconcentration above what the lower state merges

into the conduction band of the metal. Thereafter

the donation of electrons from hydrogen adatoms

into unoccupied states in the conduction band

occurs. This leads to formation of positively

charged hydrogen adspecies, resulting in a de-

crease of the WF.

In this paper we attempt to explain the behaviorof Pd–H and Pd–D systems by means of the con-

cept of the spontaneous plasma polarization near

metal surface and WF as the work against the

image force [6].

2. Method

The idea of using the image potential as the

measure of WF is quite old, e.g. it may be found in

a paper by Langmuir [7]. The image force potential

of a conducting plane is usually expressed in terms

of the potential energy of an electron located at

distance x from the plane

uðxÞ ¼ e2

16pe0x; ð1Þ

Table 1

Electronic properties of Pd and PdH

Pd

Fermi energy (FE) (eV) 5.75

Number of free electrons per Pd atom (Z) 2

Wigner–Seitz radius (rs) 2.279 bohr

Lattice constant (a) 3.8824 �A

Work function (U) 5.27 eV

where e is elementary charge, e0 is the electric

constant. The above formula is used for explana-

tion of the Schottky effect, see e.g. [8], because the

barrier lowering occurs at relatively large distances

from a conducting plane. However the formula (1)cannot be used directly for WF calculation be-

cause uðxÞ tends to infinity, when x ! 0. On the

basis of the metallic plasma concept, we have

demonstrated previously that the expression for

the WF of a metals is [6]

U ¼ e2

16pe0d; ð2Þ

where d is the length of plasma polarization in the

direction perpendicular towards metal surface.

The magnitude of d depends on the free electrondensity (or Wigner–Seitz radius, rs) and the Fermi

energy, FE, and is in the order of 1 �A. The final

formula for WF of the transition metal is [6]

U½eV� ¼ 43:46

r3=2s FE1=2; ð3Þ

where rs and FE are expressed in bohr and eV,

respectively. The necessary data for Pd and PdH

exist in the literature and they are collected in

Table 1.

The evaluation of the rs value for a pure metal

may be made by the following formula [12]

rs ¼ 1:3882AZq

� �1=3

; ð4Þ

where A is atomic mass in grams, q is the bulk

density in g cm�3 and Z is the number of free

electrons per atom (which constitute the metallic

plasma). In the case of hydrogenated metal, the

lattice is somewhat expanded compared to pure

metal and each lattice cell occupied by hydrogen

PdH Remarks

7.05 Ref. [9]

1 See Section 4

Calculated by Eq. (4),

b � a b ¼ 1:035 after Ref. [10]

After Ref. [11]

S. Halas et al. / Surface Science 555 (2004) 43–50 45

atom may contain a lower number of free elec-

trons, than the Z for pure Pd, see Section 4.

Fig. 1. Schematic representation of the location of H� ion with

respect two neighbouring Pd atoms on the palladium (1 0 0)

surface, a is the lattice constant, d is the cut-off distance of the

free electron density distribution. Dashed area denotes the

space available for free electrons at 0 K.

3. Increase of WF at high T

At high temperatures, above 450 K, the equi-

librium state of a Pd–H2 system is shifted towards

the complete degassing of Pd from hydrogen,

hence no surface phenomena will influence the WF

of the hot Pd metal immersed in a low pressure H2

atmosphere. However at room temperature Du�set al. [1] noticed an increase of the WF by about0.2 eV compared to pure Pd-film at the equilib-

rium with H2 gas under pressures ranging from

10�6 to 10�2 Torr. A broad maximum of WF in-

crease was observed at temperature around 120 K.

The maximum increase of the WF was 0.40 eV at

that temperature, in which a nearly complete layer

of PdH (or PdD) was formed on the surface. Sim-

ilar magnitude of the WF increase was reported inthe single crystal experiments [13,14].

This phenomenon may be understood as a re-

sult of a spontaneous conversion of H atoms at the

surface into negative ions, H�. The presence of

negative ions gives rise to a lowering of the electric

potential of Pd surface. The potential lowering,

detected by the vibrating capacitor method, is

small because the thickness of the dipole layerformed by the negative charge of adsorbed H�

ions and positive image charge is relatively small.

A schematic representation of the location of H�

ion with respect to the neighbouring Pd atoms is

shown in Fig. 1. It is clear from this figure that in

the zero vibrating state the center of H� ion is

shifted by a small distance, d, away from the cut-

off distance, d, of electron density distribution.This ‘‘d’’ is the same as d in Eq. (2). Hence the

presence of H� ion on the surface will result in

local lowering of the surface potential, which is

equivalent to an increase of the WF. We may

estimate the average change in WF, DU, using the

model capacitor comprising two square plates of

surface area, S, being spaced by a distance, d, andcharged by elementary charge, e.

The electrostatic energy of the capacitor is equal

to twice of the WF increase. It is because the ori-

ginal surface potential plane of pure metal divides

the space between capacitor plates into equal

parts. Hence, from the electrostatic formula we

have

2DU ¼ 1

2e

ee0S

d: ð5Þ

The surface area, S, related to a single adsorp-

tion site is equal to a2 for the Pd(1 0 0) plane, where

a is the Pd-lattice constant, see Table 1. For

practical calculation of DU the above formula may

be rewritten as follows

DU ¼ e2

4e0a2� d

¼ e2

8pe0a0

2pa0

a2� d

¼ 13:6 eV � 0:22 �A�1

� d; ð6Þ

where a0 is Bohr radius, while the d distance may

be calculated from the a and d values and theatomic radii of Pd and H� (R and r, respectively,see Fig. 1) as follows

d ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðRþ rÞ2 � a2=4

q� R� d: ð7Þ

From formula (7) one obtains d ¼ 0:115 �A,

employing a d value calculated from Eq. (2) for

pure Pd and the Pd and H� radii after CRC

Handbook [15]. Substituting the calculated d value

into (6), one obtains DU ¼ 0:34 eV, which is close

to the average WF increase detected by the

Fig. 2. A schematic plot of the potential energy versus distance

of H0 or H� nuclei from the first (1 0 0) plane of palladium

nuclei in the crystal lattice. W is the work of H� ion extraction

from the minimum vibration state to infinity, U is the work

function, EA is the electron affinity, DE is dissociation energy of

H� ion at the surface, Ed is the desorption energy of neutral

hydrogen atom, a is the lattice constant. Note that both the avalue and height of the potential barrier between the neigh-

bouring wells depend on the presence of H0 atom in the inner

(left) well.


vibrating capacitor method for nearly totally

covered Pd surfaces [1,13].

At certain temperature the thermal dissociation

of H� ion starts. The dissociation reaction

H� () H0 þ e;

may be considered as the first step of desorption of

H atoms from the surface. The dissociation energy

of H� ion in vacuum is EA¼ 0.75 eV (electronaffinity) [16]. In the case of H� ion at the Pd sur-

face the dissociation energy, DE, is significantly

lower than EA because the ion is confined in a

quantum well of limited size, see Fig. 2.

4. Decrease of WF at low T

At 78 K a strong lowering of WF has been re-

ported [1–4]. The lowering in the case of Pd satu-ration by deuterium and isotopically light

hydrogen is 2.30 and 1.59 eV, respectively [4]. We

can explain these effects by use the metallic plasma

model. For a lowering of the WF of PdHx at

sufficiently low temperatures one has to assume a

lowering of the density of free electrons, i.e. in-

crease of the rs parameter. The existence of nega-

tive hydrogen ions in the Pd lattice should be

excluded because their diameter of 3.08 �A exceeds

the available space in the interior of the lattice cell.

At low temperatures the H atoms are incorporated

into the lattice forming a weakly bounded H–Pd

systems.

We postulate a covalent character of the H–Pdbonding because it causes the localization of one

free electron in each occupied lattice cell. That

covalent bonding, however, by no means stops

the nearly free motion of the hydrogen atom

within the cell volume. This motion is much slower

than the motion of the Pd free electrons with the

kinetic energy of order of the Fermi energy.

The covalently bounded H atom can move fromone to another Pd atom with the kinetic energy

comparable to that of a hypothetic noninteracting

hydrogen atom confined in a small-size cell of the

Pd lattice. This motion produces a high pressure

within the cell and consequently causes an increase

of the lattice constant. The relative increase of the

lattice constant and rs parameter is the same.

Another reason for the increase of rs is a reductionof the number of free electrons per Pd atom, Z, dueto covalent bonding between hydrogen and palla-

dium atoms inside the lattice. This results in

ZPdH < ZPd, below we demonstrate that the best

choice for these Z values is as given in Table 1.

Let us calculate WF by means of formula (3)

taking into account the increase of rs and the shift

of Fermi energy. We will assume in calculation ofrs and FE of PdHx that these values are closely

approximated by the linear combination of the

end-member values

rsðPdHxÞ ¼ rsðPdÞ � ð1� xÞ þ rsðPdHxÞ � x; ð8Þ

and

FEðPdHxÞ ¼ FEPdð1� xÞ þ FEPdH � x; ð9Þwhere x denotes the molal fraction of hydrogen in

hydrogenated (deuteriated) palladium lattice. The

WF of PdHx may be expressed in the following

form

U ¼ UPd

1� xþ xZPd

ZPdH

� �13

b

" #32

1� xþ xFEPdH

FEPd

� �12

;

ð10Þ

Table 2

WF as a function of molal H/Pd ratio, the difference between

columns demonstrates the influence of the increase of the lattice

constant due to hydrogen absorption

x WF [eV]

b ¼ 1:035 b ¼ 1

0 5.27 5.27

0.1 4.98 5.02

0.2 4.72 4.78

0.3 4.48 4.56

0.4 4.25 4.35

0.5 4.04 4.16

0.6 3.85 3.98

0.7 3.67 3.81

0.8 3.50 3.66

0.9 3.34 3.51

1.0 3.20 3.37

Fig. 3. Lowering of WF of Pd exposed to hydrogen gas in low

temperatures calculated according to formula (10) and experi-

mental data from Du�s and Nowicka [4], where their ratio of the

‘‘positive hydrogen’’ to palladium at surface is converted to our

x ¼ H=Pd in bulk metal by a scaling factor of 3.0.


where b denotes the relative increase of the lattice

constant of PdH with respect to Pd and

UPd ¼43:46

½rsðPdÞ�32FE

12

Pd

; ð11Þ

is the calculated value of the WF of pure poly-

crystalline palladium.

In the first step of the calculation we will con-sider UPd as a function of ZPd and FEPd. The for-

mula (11) should yield a value close to that

determined experimentally. However, the experi-

mental values for polycrystalline Pd range from

4.8 to 5.15 eV [17,18], while new determination for

(1 1 1) surface yield 5.60 and 5.55 eV [19]. The

reason for such a large spread of the experimental

values is a strong interaction of Pd with traces ofhydrogen, oxygen and water [10,20]. Instead we

choose the value 5.27 eV obtained for iridium by

the thermionic emission method [21]. This value

should be a better choice because in recent exper-

iments with Pd deposited on Ir layers, and vice

versa, no difference in the measured WFs was de-

tected within the experimental error of 0.05 eV for

these two metals [11].Employing FEPd ¼ 5.75 eV and ZPd ¼ 2 (Table

1) we calculate UPd ¼ 5:27 eV using Eq. (11).

Excellent agreement with the experimental WF

value suggests that ZPd ¼ 2 is acceptable, and this

value is therefore our choice for the pure Pd lattice.

Consequently for the PdH lattice we have to assume

ZPdH ¼ 1, because one free electron per Pd atom is

covalently bounded with hydrogen. Using theb ¼ 1:035 and FE ¼ 7:05 eV for PdH crystal (Table

1), we calculated the WF for the PdHx system as a

function of x. The results of this calculation are

shown in Table 2 and they are plotted in Fig. 3.

As it is seen from Fig. 3, our results are in

excellent agreement with the experimental values

reported by Du�s and Nowicka [4] when we employ

a scaling factor of 3.0 to their ratio of the ‘‘positivehydrogen’’ to palladium in order to convert that

ratio to the H/Pd ratio in bulk PdHx. It would be

ideal if the rise of H/Pd ratio would be directly

proportional to the surfacial concentration of the

‘‘positive hydrogen’’. However, according to Fig. 5

in Ref. [4], the relationship between bulk and

surfacial ‘‘positive hydrogen’’ concentration is

somewhat nonlinear.

5. Isotope effect

According to Urey [22] the isotope effect results

primary from the difference of the zero-energy

levels of the isotope species. In the quantum wells


shown in Fig. 2 the zero-energy levels of D0 and

D� are located below respective levels of H0 and

H�, while the profiles of the quantum wells are

identical because no differences in the size and

electronic structure of the isotopic species are

encountered. Hence the heavy isotope species D0

and D� are released at higher temperatures than

H0 and H� species. Reversely, when temperature is

lowered then PdDx will be formed earlier than

PdHx. This implies a stronger WF lowering in

isothermic experiments with deuterium than with

light hydrogen.

The quantum well in which the particles H0 and

D0 are confined is relatively wide. Taking intoaccount that the radius of H0 (or D0) atom inside

the lattice cell is 2/3 bohr, we estimated the size of

the quantum well as 1.94 �A and the shift of the

zero-energies of the isotopic species as 0.027 eV.

This value was estimated from the quantum-

mechanical formula for the energy levels of a

square well. If we express this zero-energy shift in

Kelvins, then we have DT ¼ 32 K. It means thatthe same lowering of the WF due to Pd hydroge-

nation by H requires a temperature of 32 K lower

than in the case of D.

6. Discussion

In this section we discuss the advantages andthe shortcomings of the metallic plasma approach

applied to the Pd–H system. Originally this

method was applied by Halas and Durakiewicz [6]

to the WF calculation of polycrystalline metals,

soon after the WF of lanthanides and actinides

have been calculated [23]. Later on the ionization

potentials of small metallic clusters [24] and face-

dependent WF have been calculated by thismethod [25]. In paper [26] Halas and Durakiewicz

have presented the quantitative description of the

WF changes of polycrystalline tungsten the surface

of which is covered by Cs atoms. The initial slopedUdH, where H is the coverage, and the minimum Uvalue were found to be in excellent agreement with

the classical experiments made by Taylor and

Langmuir [27].In this paper we describe the cause of the large

variations of the WF of thin palladium film

deposited on a glass surface in UHV and subjected

to various doses of hydrogen gases (H2 or D2) in

the frame-work of the metallic plasma model. Such

experiments were performed by Du�s et al. [1–4] fortemperatures varying from room temperature

down to 78 K (liquid nitrogen cooling). Otherstudies on Pd–H system were performed recently

for several planes of the single crystal [13,28], but

only for the high temperatures, where the WF of

the covered surface was higher than that of pure

surface.

The calculations performed in Section 3 refer to

the Pd(1 0 0) surface with the single layer of H�

ions. Such a layer may be formed at the beginningof H2 dosing to the evacuated system. It is formed

due to dissociative adsorption of hydrogen and its

spontaneous conversion to H� at room tempera-

ture (or at lower temperatures). This process may

be described in terms of charge transfer. The cal-

culated WF increase due to the formation of a H�

layer is in a good agreement with the experiments

[1–4,13,28] and with the ab initio theoretical cal-culations [29,30]. The simple model presented in

Section 3 has a drawback: the ionic radius (of H�

in this case) is not defined as strictly as the lattice

constant or the atomic radii. It should be also

noted that the d value may be modified due to

absorption of H atoms. We do realize that com-

plex phenomena of hydrogen adsorption on Pd

surface cannot be quantitatively described bysimple electrostatics and geometrical consider-

ations.

In Section 4 we have extended the metallic

plasma model to the Pd metal which has confined

hydrogen atoms in the lattice cells. The absorbed

hydrogen may influence on the WF of the PdHx

because the Fermi energy of PdH is higher than

that of the Pd metal and because of the hydrogenbonding with the neighbouring Pd atoms, thereby

one of the two free electrons (assessed for pure Pd

lattice) becomes localized as the remaining eight

electrons in the valence shell. Hence the Wigner–

Seitz radius, rs, is shifted to high values. Another

reason of the increase of the rs value is well-known

lattice increment of hydrogenated Pd in compari-

son to the pure metal. The calculated results for arealistic b ¼ 1:035 and for b ¼ 1 indicate that the

effect of the lattice increment is relatively small


(Table 2). It seems therefore that the metallic

plasma model for the WF calculation in Section 4

is fully justified. Note, however, that the plasma

model requires the knowledge of Fermi energy

what may be found from the density of the elec-

tronic states of a system. The distribution of theelectronic states may be successfully calculated by

the ab initio methods [29,30] or it may be deter-

mined experimentally by the scanning tunneling

microscopy employing the differential voltage

contrast method [31].

The theoretical explanation presented in Sec-

tion 4 does not require adsorption of a ‘‘positive

hydrogen’’ which was assessed by Du�s and Now-icka [4]. However, recently such an adsorption site

on the Pd(2 1 0) surface for molecular H2 was

discovered by Schmidt et al. [32], were the H2

molecule gets to be highly polarized, thereby a WF

decrease of 0.35 eV was observed at temperatures

below 50 K. This effect disappeared at tempera-

tures above 100 K. Therefore in a very specific

conditions a layer of ‘‘positive hydrogen’’ maybe formed, which further may lower the WF

slightly.

In Section 5 we explain the D/H isotope effect of

different absorption rate with temperature on the

basis of well-known theory of isotope effects [22],

which bases solely on statistical mechanics.

7. Conclusions

In the palladium–hydrogen system two effects

may shift WF simultaneously:

(1) A small WF increase is due to adsorption of H

atoms, the fraction of which is converted to the

negative ions at temperatures below 400 Kaccording to statistical mechanics.

(2) A large WF lowering at temperatures below

120 K are due to PdHx formation by a weak

covalent bonding.

Both effects may be simply explained in the

frame-work of the metallic plasma model. The

large isotope effect of D substitution may be ex-plained by zero-energy difference in the quantum

well in which H or D atoms are confined.

Acknowledgements

Thanks are due to Professor R. Du�s, Institute

of Physical Chemistry of the Polish Academy of

Sciences, for his cordial encouragement, stimulat-ing discussion with the representative of Mass

Spectrometry Laboratory (S. Halas) and help in

collecting of the literature. We appreciate con-

structive criticism of two unknown reviewers of

the manuscript.

References

[1] R. Du�s, E. Nowicka, Z. Wolfram, Surf. Sci. 216 (1989) 1.

[2] E. Nowicka, Z. Wolfram, R. Du�s, Surf. Sci. 247 (1991) 248.

[3] E. Nowicka, R. Du�s, Prog. Surf. Sci. 48 (1995) 3.

[4] R. Du�s, E. Nowicka, Langmuir 16 (2000) 584.

[5] T.B. Grimley, in: W.E. Garner (Ed.), Chemisorption,

Butterworths, London, 1957.

[6] S. Halas, T. Durakiewicz, J. Phys.: Condens. Matter 10

(1998) 10815.

[7] I. Langmuir, Phys. Rev. 43 (1933) 224.

[8] H. Ibach, H. L€uth, An Introduction to Principles of

Materials Science, Springer-Verlag, Berlin, Heidelberg,

1995, Polish edition PWN Warszawa 1996.

[9] Landold-B€ornstein, in: J.L. Olsen, K.-H. Hellwege (Eds.),

Electron States and Fermi Surfaces of Alloys, vol. 13a,

Springer-Verlag, Berlin, 1981.

[10] R. Nowakowski, P. Grzeszczak, R. Du�s, Surf. Sci. 507–510

(2002) 813.

[11] U. Harms, R.B. Schwarz, Phys. Rev. B 65 (2002) 085409-1.

[12] A. Kiejna, K.F. Wojciechowski, Metal Surface Electron

Physics, Elsevier Science, Oxford, 1996.

[13] H. Conrad, G. Ertl, E.E. Latta, Surf. Sci. 41 (1974) 435.

[14] R.J. Behm, K. Christmann, G. Ertl, Surf. Sci. 99 (1980)

320.

[15] CRC Handbook of Chemistry and Physics, 61th, CRC

PRESS Inc., Boca Raton, FL, 1981.

[16] H.E. Gove, Nukleonika 25 (1980) 31.

[17] V.S. Fomenko, Handbook of Thermionic Properties,

Plenum Press Data Division, New York, 1966.

[18] H.B. Michaelson, J. Appl. Phys. 48 (1977) 4729.

[19] Landold-B€ornstein, New Series III/24b, Springer, Berlin,

1994.

[20] J.M. Heras, G. Esti�u, L. Viscido, Appl. Surf. Sci. 108

(1997) 455.

[21] R.G. Wilson, J. Appl. Phys. 37 (1966) 3170.

[22] H.C. Urey, J. Chem. Soc. (1947) 562.

[23] T. Durakiewicz, S. Halas, A1. Arko, J.J. Joyce, D.P.

Moore, Phys. Rev. B 64 (2001) 045101-1.

[24] T. Durakiewicz, S. Halas, Chem. Phys. Lett. 34 (2001) 195.

[25] K.F. Wojciechowski, A. Kiejna, H. Bogdan�ow, Mod.

Phys. Lett. 13 (1999) 1081.

[26] S. Halas, T. Durakiewicz, Annales Universitatis Mariae

Curie-Sklodowska Sectio AAA 54 (1999) 63.


[27] J.B. Taylor, I. Langmuir, Phys. Rev. 44 (1933) 423.

[28] M.G. Cattania, V. Penka, R.J. Behm, K. Christmann, G.

Ertl, Surf. Sci. 126 (1983) 382.

[29] W. Dong, V. Ledentu, Ph. Sautet, A. Eichler, J. Hafner,

Surf. Sci. 411 (1998) 123.

[30] S.Wilke, D. Hennig, R. L€ober, Phys. Rev. B 50 (1994) 2548.

[31] S. Milshtein, E. Thurkins, N. Merritt, K. Novaris, J.

Therrrien, Scanning 23 (2001) 232.

[32] P.K. Schmidt, K. Christmann, G. Kresse, J. Hafner,

M. Lischka, A. Groß, Phys. Rev. Lett. 87 (2001) 096103-1.

Temperature-dependent work function shifts of hydrogenated/deuteriated palladium: a new theoretical explanation

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