Desorption of hydrogen from tungsten (100)

327

Surface Science 136 (1984) 327-344 North-Holland, Amsterdam

DESORPTION OF HYDROGEN FROM TUNGSTEN (100) A. HORLACHER

SMITH, R.A. BARKER

Deparimeni of Chemistry and Department Rhode Island 02912, USA Received

* and P.J. ESTRUP

of Physics, Brown Uniuersrty, Prourdence,

24 June 1983

The desorption energy, Ed, and the preexponential factor, Y, for the desorption of hydrogen from W(100) have been determined as a function of coverage, B, from a series of isobars. The values of E, and Y depend strongly on coverage and weakly on temperature; they show a compensation effect, both quantities decreasing at about l/4 of the hydrogen saturation coverage: E,, drops from about 40 kcal per mole of H, to about 20 kcal per mole of H, and Y from lo3 to 10m5 s-’ cm2. These values differ from those extracted from earlier thermal desorption studies, but they are compatible with the measurements reported. Correlation of Ed(B) and v(6) with structural data for the H/W(lOO) surface shows that the higher Ed and Y values are associated with desorption from a reconstructed substrate. Effects of the reconstruction also appear in the coverage dependence of the partial molar entropy of the H/W surface layer, F,, which is zero or less at low coverages and rises to about 10 cal/K per mole of H at l/4 of saturation. Analysis of s,(e) indicates that the hydrogen-induced reconstruction reduces the entropy of the tungsten surface by lk per W atom.

1. Introduction The H/W(lOO) surface is a widely studied model system which has received special attention during the last few years after it was realized that the adsorption of hydrogen induces a reconstruction of the tungsten substrate [l-3]. This phenomenon has necessitated a reinterpretation [4-61 of the early LEED data [7] for the H/W(X)) surface. As will be discussed in this paper, it is necessary also to revise the existing models [8] of the hydrogen desorption kinetics on this surface. New results obtained from adsorption isobars [9] demonstrate that the desorption kinetics for H/W(lOO) is intimately connected to the changes in substrate structure. Previous measurements of the desorption kinetics have been made by thermal desorption (TD) (flash desorption) spectroscopy [lo-131, but the data have yet to be satisfactorily explained. Two desorption peaks, PI and &, are found at 450 and 550 K, respectively. The & peak appears only for initial * Present

address:

Xerox Palo Alto Research

Center,

Palo Alto, California,

0039-6028/84/$03.00 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

USA.

328

A. Horlacher Smrth et al. / Desorprron of hydrogen from W(lO0)

coverages greater than l/4 of saturation, whereas the & peak is found for all initial coverages. In the earlier analyses of these results [8,10,11,14] hydrogen desorption producing the /3, peak was described by first order kinetics with a constant and “typical” frequency factor of lOI s- ’ and the pz peak by second order kinetics and a constant frequency factor of lo-* s-r cm*. This gives a desorption energy of 26 kcal/mol for &-hydrogen and 32 kcal/mol for /3,-hydrogen. Explanations based on different binding sites producing the two peaks have been ruled out by electron energy loss spectroscopy (EELS) [15,16], which shows that hydrogen is bound atomically on W(100) at twofold sites at all values of the coverage, 0. The lattice gas model, which uses repulsive pair interactions between H adatoms on a uniform surface to account for the appearance of two desorption peaks, can only qualitatively explain the TD traces [14] and it does not agree with LEED results [17]. In the present work we have used adsorption isobars to determine the desorption energy, Ed( 19),and, independently, the preexponential term, F( 8), in the expression for the desorption rate from which the frequency factor, v, is derived. No assumptions about the value of v or the kinetic order of desorption were required to obtain Ed or F. The values are found to differ from those extracted from the TD measurements but are compatible with the experimental TD traces. By making the assumption that the adsorbed hydrogen is in equilibrium with its gaseous phase during an isobaric run the surface entropy and enthalpy are calculated from the isobars. Thermodynamic arguments lead to a better understanding of the relationship between the desorption rate and changes in substrate structure for this chemisorption system.

2. Experimental procedure The experimental methods used to study the surface structures of H/W(lOO) by means of low energy electron diffraction (LEED) have been described previously [6]. The isobars, in the form of temperature versus work function change, were obtained in the same ultrahigh vacuum system as the LEED data. The sample, a thin ribbon of W(lOO), could be cooled with liquid nitrogen or heated ohmically. A W-Re/S%W-Re26% thermocouple spot welded to the back of the sample allowed its temperature to be measured to within one degree. The work function change, A+, was measured continuously using a retarding potential method and a feedback circuit [18]. With the assumption that the work function for this adsorption system is only weakly dependent on temperature, T, a measurement of A+ amounts to a determination of the coverage, 8. At room temperature the sticking probability of hydrogen, a(e), has been measured by Madey [19] so that a plot of A+ versus exposure can be converted to a curve for A$ versus 8. The sticking probability has not been determined

329

F P)

sf .25

1

,2

I

.4

EXPOSURE (I_) Fig. 1. Change in work function, A+, versus hydrogen exposure for W(IO0) at room temperature (solid curve) and 450 K (dashed curve). The latter curve levels off due to desorption.

directly at higher temperatures but the data shown in fig. 1 ]20] indicate that the same A#( B) curve can be used t~on~out the temperature range of interest here. As seen in fig. 1, hydrogen exposures at 300 and at 450 K produce nearly identical increases in Alp (until the trace at 450 K levels off due to desorption). This behavior is interpreted to mean that both A+ and u are approximately independent of temperature in this interval, otherwise any change in one due to increased temperature must cancel that of the other, which seems improbable. The conversion of A#J to 8 is particularly simple for H/W(lOO) because both a( 8) and A#(@) are nearly linear. All of the data are reported in terms of A+(B) rather than f? to avoid any problems arising from uncertainties in assigning absolute coverage values. Whenever calculations required absolute coverages the conversion from A# to 8 was made using a linear A~(~) that reaches 0.95 eV at saturation [7,11,19,21] at which point the coverage is taken to be two monolayers, equivalent to two H atoms for each surface W atom, i.e. 2 X 1015 adatoms/cm2 [4,7,19,22]. So a value of 0.24 eV for A+ is assigned to B = 0.5. King and Thomas [4] also determined A$ versus 8 and arrived at

330

A. Horlacher Smith et al. / Desorption of hydrogen from W(100)

slightly different results: at 8 = 0.5, A+ is 0.28 eV, and A+(B) rises more gradually at higher coverages to reach the same saturation value of 0.95 eV. The adsorption isobars [9] were obtained by heating the sample to temperatures above which no adsorption occurs and then allowing the sample to slowly cool while monitoring the increase in A$ as hydrogen adsorption proceeds. A set of four isobars is shown in the region marked “desorption” in fig. 2. The slow cooling rate establishes a steady state, i.e. the rate of adsorption, r,, equals the rate of desorption, r,, at any point (T, P, A+) on an isobar.

500

\

DESORPTION

T (K) 400

300

I

I

0

I

I

I

0.3

0.4

0.5

l9=+ A +hV) Fig. 2. Family of adsorption isobars, 1, 2, 3 and 4, and the phase diagram for H/W(lOO). The isobars, in the form of work function change, A+, versus temperature, correspond to pressures of 6 x 10e9 Torr, 2 x lo-* Torr, 6 x lo-* Torr and 2 x 10m7 Torr for isobars 1 to 4, respectively. The regions of the phase diagram are labeled according to observed LEED structures; the boundary between the I-(6x6) and 1D order region marks the coverage at which the split half-order beams of the former structure begin to streak.

A. Horlacher Smith et al. / Desorprion of hydrogen from W(lO0) 3.

331

Analysis of the isobars

3. I. Desorption energy and frequency factor Under the steady state condition described above, Ed and F can be calculated for any coverage. The Arrhenius form for the desorption rate and the usual expression for unactivated adsorption of a gas at pressure P give P0(277iUR~)-“~

=fFexp(-E,/RT),

(1)

where Ts is the temperature of the gas, M is the molar mass of the gas, and T is the surface temperature. The factor of l/2 is required since hydrogen adatoms desorb as molecules. The values of u, F, and Ed are, in general, dependent on coverage and temperature. From a pair of isobars, Ed and F/a can be determined at some coverage 8 from isosteric points (P,, TI) and ( P2, T2) (see fig. 2) if it is assumed that Ed and F/a are independent of temperature over the range TI to T2:

Eli(@)-

R ln(p,/P2) l/T,

-

l/T,

(2)

’ TAT,-T,)

g

= P,(Z~IWRT,)+~

(3)

The temperature difference between isosteric points on two neighboring isobars is = 15 K. To minimize any effects due to temperature, only values of Ed and F/a obtained from neighboring isobars were considered. Fig. 3 shows the results for E,,(t)) obtained from eq. (2) for the two middle isobars in fig. 2. The value of Ed(@) drops from 40 kcal per mol of H, for coverages below 0.5 monolayer to 20 kcal/mol above 0.6 monolayer. (These values are to be compared to those of the TD studies of 32 and 26 kcal/mol, respectively.) The large error bars reflect the sensitivity of eq.(2) to temperature; an error of one degree in T could change Ed by a few kcal/mol. The results of eq. (3) from the two middle isobars are also plotted in fig. 3 in the form of the frequency factor, v. It is obtained by assuming that F takes the form F(8)

= (nS8/2)ev,

(4)

where nS is the saturation coverage in adatoms per cm2 and (Y is the kinetic order for desorption; here (Y is taken to be two since the hydrogen adatoms desorb associatively. The value for the sticking probability at 300 K [19], a( 8) = OS(1 - e/2), was used to obtain v from F(O)/a(8). As seen, the frequency factor drops by about eight orders of magnitude from 2: lo3 s-i cm2 at low coverages to = 10V5 s-’ cm2 in the same coverage interval where Ed

A. Horlacher Smrth et al. / Desorptron of hydrogenfrom W(lO0)

332

45 0

IO5

lO

0 0

40

l

0 .

: 0

l

0 E \ 0

35

Y*

30

Oo

0

I 0

IO’ -f *

00

7

0

1

0 0

0

w”

10-l t

IO-'

ooooooooo

l

0

lo-s

l

25

0 0

l m ..

0.0..

?O

I

0.1

,\

I

0.2

0.3 A+

I

0.4

I

0.5

(eV1

Fig. 3. Plot of the desorption energy, Ed (filled circles), and the frequency versus A$ calculated from isobars 2 and 3 in fig. 2.

factor,

Y (open circles),

drops. The behavior of ~(0) closely follows that of Ed(@) thus exhibiting a compensation effect, as discussed in section 5. Ed(O) appears to be temperature dependent, particularly at low coverages where the value of Ed for a given coverage calculated from different isobar pairs decreases with increasing temperature. Thus, &( f3) from isobars 1 and 2 in fig. 2 is greater than the value obtained from isobars 3 and 4; this difference is about 15% of the value of Ed(O) over the temperature range covered in this study. The temperature dependence of ~(0) follows that of E,(e). Because of the limited temperature range of the isobars and the magnitude of the error bars a more detailed description of the effect is not possible. The expression for Ed(B) is similar to that for the isosteric heat of

333

A. Horlacher Smith et al. / Desorption of hydrogen from W(100)

desorption,

qsl = -R

q,, [23], for an adsorbate a In P i3(l/T)

(

in equilibrium

with its gaseous phase:

I

@’

The value of Ed determined from the isobars differs, in principle, from qs, since the temperature of the hydrogen gas does not equal that of the sample. However, this temperature difference should be an insignificant perturbation of equilibrium [24], so for H/W(lOO) we shall assume that Ed is equal to qsl. 3.2. Comparison

of EJ8)

and u(e) with the TD results

The values of Ed(e) and v(8) obtained from the isobars are quite different from those extracted from the TD measurements, referred to in section 1. But, as shown below, the values from the isobars successfully reproduce the experimental TD traces. Thermal desorption spectroscopy measures the rate of hydrogen desorption by monitoring the partial pressure of the desorbed gas as the surface temperature is raised. Since the pumping speeds of the vacuum systems used to do the TD measurements for H/W(lOO) were very fast the

IO3 IO’ _

0 E 40 \ 0 ”

‘d

IO-'

7,

io-’

“E 0

55 u.7 30 ‘.

400

600 T(K)

24 .I

.2

.3

e&l+

Fig. 4. (a) Simulated flash desorption trace (solid curve) for a hydrogen-saturated W(100) surface using the values of desorption energy, Ed, and frequency factor, Y, shown in (b). The dashed curve is an experimental trace for the same system [lo]. (b) Plot of Ed and P versus A+ obtained from the isobars in fig. 2. Those segments of the isobars closest to the T-0 trajectory of the experimental desorption trace were used to obtain Ed and Y.

334

A. Horlacher Smith et al. / Desorprron of hydrogen from W(IO0)

desorption rate is proportional to the hydrogen pressure [25], so that a TD trace approximates a plot of rd versus T. Fig. 4a shows a simulated thermal desorption trace, r, versus T, for a hydrogen-saturated surface, calculated by using the Ed(d) and v( 0) values given in fig. 4b; for comparison fig. 4a also shows an experimental trace for the same initial coverage [lo]. The positions of the two peaks agree well for both traces as does the ratio of the areas under the /3, peak to that of the & peak; it is 1.9 for the simulated trace and 2 for the experimental one. The values of E,(B) and v(0) in fig. 4b were obtained from segments of isobars closest to the T-8 trajectory of the experimental TD traces. Due to the observed temperature dependence of Ed and v fig,. 4b differs slightly from fig. 3. To produce the simulated trace a linear temperature ramp, T = TO+ bt, with b = 25 K/s, as in ref. [lo], and second order kinetics for all coverages were used. The expression for the desorption rate

rd=$=e2v(e)

exp

Ed(e) R(T, + bt)

and Ed(e) and v(e) from fig. 4b were used to calculate rd versus T [26]. As mentioned in section 1, the earlier analyses of TD traces used kinetic orders of one and two for the /3, and p2 peaks rather than second order throughout. The orders were assigned based on the dependence of the position of the peak temperature on the initial coverage 0,; the peak temperature should shift with 0, for second order kinetics but not for first order [8,25,26]. For the experimental traces the fi2 peak temperature shift with 0, is more pronounced than that for the & peak, but the latter also shifts with a,. In ref. [lo] the & peak temperature is 450 K at 0, = 2 and about 465 K for the trace with the smallest initial coverage that gives a & peak. The simulated traces for several initial coverages show the same variation in the peak temperature: 0, = 2 gives 450 K and 8, = 0.8 gives 465 K. So second order kinetics for all coverages, together with the appropriate coverage dependence of Ed and v, appears to be consistent with all the available data. 3.3. Isosteric heat and desorption entropy As stated in section 3.1 it is assumed that the steady state established in the isobaric measurements is near equilibrium so that thermodynamic quantities can be calculated from the isobars. Thus, the isosteric heat of adsorption, qst, is equated with Ed. The isosteric heat of adsorption is the difference between the molar enthalpy of the gas, h g,_and the partial molar enthalpy of the surface (adsorbate + metal substrate), h, [23]: q,,=hhg-2K

5,

h, = @h,.m)

T.PI

(7)

A. Horlacher Smith et al. / Desorption of hydrogen from

W(100)

335

where h, is the molar enthalpy of the surface. The factor of 2 is required since hydrogen adsorbs dissociatively. For an adsorbate in equilibrium with its gaseous phase at a standard pressure P” the partial molar entropy of desorption, ASS, is [23]

where S: is the molar entropy of the gas to be adsorbed at PO. From tabulated values of si [27] and experimental values of qst (Ed) the partial molar entropy

IO

5

_ I

0

I0

;

0 0

Iv?

I

-5

0

o”o

-10

-

0

0 00 0

1

0

0.1

0.2

0.3

0.4

0.5

A # (eV) Fig. 5. Plot of the partial molar entropy of the surface, S,, versus A+ calculated from isobars 1 and 2 (open diamonds) and isobars 2 and 3 (filled squares) using eq. (8) and tabulated values of si [27]. The expected partial molar configurational entropy, S, , for an immobile adsorbate (eq. (ll)), and partial molar (2D) translational entropy of a fully mobile adsorbate (eq. (10)) versus A+ are included for comparison.

336

A. Horlacher Smrth et al. / Desorptron of hydrogen from W(lG0)

of the surface S, = (as,/M),, can be obtained. The results are shown in fig. 5 which includes values for S, found from the two middle isobars and from the two lowest isobars in fig. 2. S, rises at about 0 = 0.5 from zero or less to about 10 cal K-’ per mole of H adatoms.

4. Structure

of the H/W(lOO)

surface

Structural data for H/W(lOO) in the T-8 region of the adsorption isobars indicate that there is a strong correlation between changes in the parameters describing the desorption rate, E,, and Y, and the hydrogen induced reconstruction of the W(100) surface. This conclusion is based on results of measurements using probes of local structure, high energy ion scattering (HEIS) and electron energy loss spectroscopy (EELS), together with new LEED studies of the H/W(lOO) phase diagram. High energy ion scattering studies [22] of H/W(lOO) at 300 K show that at all coverages below 8 = 0.5 the tungsten surface atoms are displaced from their lattice positions by = 0.2 A and that at higher coverages the tungsten surface gradually returns to the undistorted structure. EELS spectra [15,16] at 300 K agree with these results. Three H-W vibrational modes, which depend on coverage, are observed on the H/W(lOO) surface. The vibrational energies [16] at low coverage, 155, 55 and 120 meV, gradually shift with increasing cover-

Fig. 6. Model of the H/W(lOO) surface in the hydrogen induced (& x 6/z>phase near 8 = l/3 [4,6]. The hatched circles represent the top layer of W atoms and the smaller filled circles designate adsorbed hydrogen atoms.

A. Horlacher Smith et al. / Desorption of hydrogen from W(Io0)

337

ages above 0.5 monolayer to 130, 80 and 160 meV, respectively. The model shown in fig. 6 [4-61 is consistent with these results; at T 2: 300 K and at low coverage the H atoms are bonded at twofold bridge sites on tungsten “dimers” produced by a pair of W atoms moving together. At higher coverage the reconstruction disappears as the surface W atoms return to their normal positions. LEED data for H/W(lOO) have been obtained for large regions of the T-8 plane. The sequence of LEED patterns produced by hydrogen adsorption is due to scattering from the tungsten surface and not from hydrogen adatoms [28]. The phase diagram for this system at submonolayer coverages is shown in fig. 2; it is a revision of one previously reported [5,6] with major changes made in the boundary between the incommensurate and disordered regions. As hydrogen adsorbs at about room temperature an ordered (fi x a) phase is formed with the proposed structure shown in fig. 6. At 6 = 0.3 the half-order beams of the (fi X fi) pattern split, with the formation of the incommensurate I-(a x a) phase. With further adsorption to about 0.5 monolayer, the split beams begin to streak in the direction perpendicular to the splitting. The structures of the incommensurate phases have not been definitively established [4,6]; however, since HEIS and EELS cannot distinguish between the (\/2: x 0) and I-(a x 6) phases, the structure of the surface on a local scale must be similar. The onset of streaking coincides with diminishing surface atom displacements, i.e. the I-(a x a) pattern is from a reconstructed surface whereas the streaked pattern arises from a surface partially relaxed to the normal lattice. Previously, no direct data were available for the surface structure in the T-8 region covered by the isobars. Results obtained in the present study show that surface distortions persist up to the desorption temperature. The following LEED patterns can be observed by moving down isobar 2 in fig. 2: above = 480 K a pattern with faint half-order beams, reminiscent of that from the room-temperature low coverage (1 X 1) phase, is present; it is followed directly by an I-(\/z X fi) structure. The splitting of the half-order beams continues until T = 440 K when these beams begin to streak. This progression is seen for all of the isobars, but with different landmark temperatures. In all cases the coverage at which the split beams begin to streak is = 0.5 monolayer (A+ = 0.24 eV). This corresponds to the coverage at which E,(d) and v(8), in fig. 3, begin to drop. Evidently, the larger values of Ed and Y occur for a reconstructed surface. It is interesting that Ed and Y fall at the coverages where the two local probes, HEIS and EELS, first show a decrease in the W atom displacements. Thus, the most important factor in determining the kinetics of desorption appears to be the magnitude of the substrate distortions.

338

A. Horlacher Smith et al. / Desorpiion of hydrogen from W(100)

5. Discussion 5.1. Surface entropy and enthalpy Discussions of thermodynamic changes upon adsorption usually emphasize changes in the state of the adsorbate and assume that the substrate is unaffected. Such an approach is inappropriate for H/W(lOO), as shown by investigations of the phase diagram [5,6,29,30]. The same conclusion is reached by study of the partial molar entropy of the surface. The possible contributions to Ss from the hydrogen adatoms are vibrational, S,, translational, s,,, and configurational (for an immobile adsorbate), SC [23]. The molar vibrational entropy for i harmonic modes of frequency o, is ln( l-e-X~/T where x, = hw,/k. The H-W modes detected by EELS at low coverage would give s, = 1.4 Cal/K. mol, a value which decreases to = 1 Cal/K. mol over a few tenths of a monolayer near 8 = 0.5. Therefore, the vibrational component of ss is small. For a perfect two-dimensional gas S,, takes the form

itr=

[63.8 + R

h(e)]

The configurational SC= -Rln

cal/K-mol.

entropy is a temperture-independent

(10) quantity given by

(11)

In fig. 5, Str and ZCare plotted against coverage (A+) for comparison with the experimental results for S,. At high coverage there is reasonable agreement between Ss and gtr, i.e. the entropy of a completely mobile adsorbate. At low coverage, on the other hand, S, is well below both of the calculated curves. The rise in Zs at 8 = 0.5 resembles the behavior seen for hydrogen adsorbed on Pd(100) [31] where it was explained by a transition from an immobile layer, at low coverage, to a mobile layer at higher coverage. However, this type of “melting” cannot explain the data in fig. 5; it is improbable that the H atoms on W(lOO), at any coverage, are immobile at a temperature of 400-500 K, and even if they were, a further reduction of the entropy would be needed to get agreement with the experimental data at low 8. Since there are no other degrees of freedom of the adsorbate to freeze out, it must be concluded that the observed S, reflects changes in the thermodynamic properties of the substrate. According to one model [6,32] of H/W(lOO) the adatoms are uniformly distributed over the surface and a full monolayer of substrate atoms participate in the reconstruction. The entropy change per W atom required to explain the results is therefore considerably smaller than the apparent entropy change per

A. Horlacher Smith et al. / Desorpiion of hydrogen from W(lO0)

339

H atom. Integration of S,(e) gives an initial drop in S, of O-6 Cal/K (depending on the temperature) per mole of H, followed by a rise of 4-7 Cal/K . mol. The corresponding entropy changes of the tungsten layer are no larger than = 2 Cal/K. mol or = lk per W atom, where k is Boltzmann’s constant. Fig. 7 shows a plot of the required -entropy change of the tungsten surface per W atom, Asw, versus hydrogen coverage (in the form of Acp) when it is assumed that the hydrogen adatoms possess the full 2D translational entropy Z,,. The values of As, were obtained from the equation

The values for iS(8) in fig 5 corresponding to the lowest isobar pair (which shows the largest change in & at 8 = 0.5) were used together with s,,(e) given by eq. (10). As seen, As, decreases with increasing hydrogen coverage to - 1.5k per W atom at B = 0.7 and then begins to increase. It must be noted, however, that the experimental measurements were not done at constant temperature. Correction for the temperature changes were made by assuming that the heat capacity of the W(100) surface is 3Nk, i.e. the limiting (classical) value. A temperature drop from 520 to 390 K while A+ increases from zero to 0.33 eV corresponds to the T-8 path midway between isobars 1 and 2. The dashed curve in fig. 7 shows As, at = 500 K after the entropy drop due to the cooling of the crystal is subtracted: sw drops by 0.8k and has a minimum at

0

a- 1 \

.

\ 0

-0.5

/

’

\

/ \

ns,

l

k

/

/

\_/

,’

’

-1.0

0

a

- 1.5 I

I

0.1

0.2

I

0.3

0 I

0.4

I

0.5

A# (eV) Fig. 7. Entropy change, As, (in units of Boltzmann’s constant k, per tungsten atom) of the tungsten (100) surface versus work function change, A+. The dots show As,, calculated from data in fig. 5. The dashed curve is the estimated isothermal entropy change (at = 500 K).

340

A. Horlacher Smith et al. / Desorptron of hydrogen from W(100)

19= 0.55. This decrease is entropy can be explained by a modification of the phonon spectrum expected to accompany the reconstruction [34]. For example, a decrease of 0.8k per W atom can be accounted for by an increase in the Debye temperature 0, from 200 to 300 K. The drop in sw indicates that hydrogen adsorption initially produces a more rigid lattice and subsequently, as W atom displacements diminish at higher coverages, the lattice becomes softer again. It is interesting that an increase in Debye temperature from 200 to 400 K was observed for the temperature-induced reconstruction of the clean tungsten (100) surface [33]. Similar LEED studies of the Debye temperature of H/W(lOO) would be useful in verifying the contribution of the tungsten surface to Ss. As mentioned in section 3.1, Ed tends to decrease with increasing temperature. Since S,(e) is determined primarily by the term E,(B)/T this trend will be reflected also in sw, i.e. the drop in sw will be smaller at higher temperatures. The entropy decrease associated with the reconstruction must be accompanied by a decrease in the surface enthalpy, h,. Since the enthalpy of the gas phase is approximately constant during the experiments, this enthalpy change, according to eq. (7), will appear in the isosteric heat. The measured drop in qst (cf. fig. 3) is in the range 20-30 kcal per mole H,, depending on the temperature. The corresponding change per surface W atom is 2: 0.1 eV, a value which in this interpretation is a measure of the enthalpy of the hydrogen-induced reconstruction. It has been suggested by King and Thomas (KT) [4] that the changes in entropy and enthalpy of reconstruction can also be obtained from the temperature dependence of I,,,, the half-order beam intensity in the (a x fi) LEED pattern. KT assume that the (fi X fi) phase co-exists with an unreconstructed to the fraction, [, of the surface (1 x 1) phase and that Z, 2 is proportional covered by the (\/z x \$2 ) phase, Ah, and As for the (a x \/2) + (1 X 1) transformation are then obtained by assuming that (1 - 5) = edgIRT where Ag is the change in Gibbs free energy. The results are Ah = 2.2 kcal/mol and As = 4.4 Cal/K . mol. Jaeger and Menzel [35] have interpreted the temperature dependence of the electron-stimulated desorption (ESD) cross-section in the same way and get values that are 50% higher. However, it seems difficult to justify the assumed relationship between Z,,z and Ag, and there are other reasons why these results cannot be directly compared with those obtained from the isobar data. The latter refer to a roughly horizontal path in the phase diagram whereas KT’s LEED measurements are for a vertical path (at 0 = 0.2). Furthermore, the present LEED data show that at this coverage surface distortions are prominent at the desorption temperature whereas KT would predict them to be small. The initial effect of a temperature increase at this coverage is probably a loss of long-range order [29,36] and not a disappearance of the W atom displacements.

A. Horlacher Smlrh et al. / Desorptron of hydrogen from W(100)

341

5.2. Frequency factor and compensation effect The frequency factor u in the expression for the desorption discussed in terms of transition state theory [37] which predicts v = (n’-*)(kT/h)

rate is often

exp(As$/R),

(13)

where h is Planck’s constant and As* is the entropy of activation. If As* = 0 then for first order kinetics (i.e. cy= 1) v = 1013 s-t and for second order kinetics Y = 10e2 cm2 s-‘. The se are the typical values, referred to in section 1, which have been used in analysis of the TD results. The present results (fig. 3) show large deviations from the typical values which, in the framework of transition state theory, would imply large changes in As’. The data in fig. 3 also show that the drop in ~(0) closely follows that in Ed(e). This compensation effect, or coupling of Ed and Y, would be explained in transition state theory by a concommitant change in the enthalpy and entropy of activation so as to maintain the value of the free energy of activation [38]. In the case of hydrogen desorption from W(100) it appears to be unnecessary to introduce assumptions about the transition state. Both the anomalous values of Y and the compensation effect can be understood by considering only the changes in the substrate surface. Combination of eqs. (l), (4) and (8) gives

Values of Y for different

coverages

(at constant

temperature)

are related

by

The last result follows because the factor in front of the exponential is of the order of unity and because changes in si are insignificant under the experimental conditions. Eq. (15) shows that a coverage-dependent change in the surface entropy directly affects the value of v. Clearly, in cases where such changes occur, due to reconstruction or other causes, the common assumption of a constant frequency factor for desorption is invalid. Thermodynamic considerations also suggest an explanation of the compensation effect [39]. At equilibrium the chemical potential of the adsorbate equals that of the gas, i.e. CL,=~~-T~~=RTI~(P/PO).

06)

This equation implies a simple connection between Ed (or qst) and Y. The latter is directly related to $s (cf. eq. (14)) and, since qst is the difference between h, and h,, and h, does not change under the experimental conditions, a decrease in qsl can be equated with an increase in h,. Such a change is seen in fig. 3

342

A. Horlacher Smrth et al. / De-sorption of hydrogen from W(100)

where Ed drops by 20 kcal/mol over a narrow coverage and temperature range (A8 = 0.2 and AT- 35 K). According to eq. (16) this decrease is possible only if it is compensated by an increase in FS and hence by a decrease in v. The assumptions made lead to the explicit relationship v a exp( E,/RT).

(17)

According to the arguments presented here a compensation effect in the desorption rate is to be expected for any surface undergoing a phase transition [39,40]. If the phase transition involves reconstruction, as for H/W(lOO), the effect is likely to be especially noticeable since unusually large changes in the surface entropy and enthalpy may then occur. If no reconstruction is involved, the changes may be too small (Q 10%) to be detected by the method used here. This may explain why the (1 x 1) + I-(a X fi) transition observed by LEED at high T and low 8 has no observable effect on the isobars, as seen in fig. 2. The absence of any significant change in the W atom displacements during this transition is consistent with the structural model discussed in section 4.

6. Summary and conclusions The rate parameters Ed(B) and v(0) for desorption of hydrogen from W(100) have been determined from adsorption isobars and are found to be quite different from those reported in flash desorption studies. Nonetheless, the values derived from the isobars successfully predict the experimental thermal desorption results. The important differences from the TD studies are a frequency factor that varies with coverage, showing a compensation effect with Ed rather than the constant values assumed in the TD analysis, a larger difference between the high and low coverage values of Ed, and second order desorption kinetics at all coverages rather than second order and first order for 8 below and above 0.5, respectively. Information from LEED and from probes of local surface structure shows that at low coverages, when Ed and v are high, hydrogen desorbs from a reconstructed tungsten substrate and at higher coverages from a surface where displacements of tungsten surface atoms have decreased. This differs both from the lattice gas model where hydrogen desorbs from a static substrate and where the drop in Ed(O) is due to adatom-adatom repulsions, and from models that assume the presence of more than one binding state. By assuming equilibrium between the adsorbed and gaseous hydrogen the partial molar entropy of the surface, S,(e), can be determined. The value of &(e) rises at about 0 = 0.5 while Ed(O) and v(S) fall. The low coverage values of f, and the magnitude of the rise in S,(e) shows that a loss in entropy of = 1K per surface W atom is associated with the substrate reconstruction. The corresponding enthalpy decrease is = 0.1 eV per W atom. The value of v can

A. Horlacher Smith et al. / Desorption of hydrogen from W(iO0)

343

be directly related to S, through the rate equations for adsorption and desorption and the expression for A&. The observed compensation effect can then be explained by the relation between Ed and S, which holds when the adsorbate and gas phase are in equilibrium.

Acknowledgments

We wish to thank M.W. Cole, E.F. Greene, L.D. Roelofs and S.C. Ying for helpful discussions. We acknowledge support by the National Science Foundation through grant DMR 79-24396 (for A.H.S. and P.J.E.) and through the Brown University Materials Research Laboratory (for R.A.B.).

References [l] [2] [3] [4] [5] (61 [7] (81 [9] [lo] [ll] [12] [13] [14] [15] [16] (171 [18] [19] [20] [21] [22] [23] [24] [25]

T.E. Felter, R.A. Barker and P.J. Estrup, Phys. Rev. Letters 38 (1977) 1138. M.K. Debe and D.A. King, J. Phys. Cl0 (1977) 1303. R.A. Barker and P.J. E&up. Phys. Rev. Letters 41 (1978) 1307. D.A. King and G. Thomas, Surface Sci. 92 (1980) 201. P.J. Estrup and R.A. Barker, in: Ordering in Two-Dimensions, Ed. S. Sinha (North-Holland, Amsterdam, 1980) p. 39. R.A. Barker and P.J. Estrup, J. Chem. Phys. 74 (1981) 1442. P.J. Estrup and J. Anderson, J. Chem. Phys. 45 (1966) 2254. L.D. Schmidt, in: Interactions on Metal Surfaces, Ed. R. Gomer (Springer, New York, 1975) p. 62. R.A. Barker, A.M. Horlacher and P.J. Estrup, J. Vacuum Sci. Technol. 20 (1982) 536. P.W. Tamm and L.D. Schmidt, J. Chem. Phys. 51 (1969) 5352. T.E. Madey and J.R. Yates, in: Structure et Proprittts des Surfaces des Sohdes (CNRS, Paris, 1970) No. 187, p. 155. D.L. Adams and L.H. Germer, Surface Sci. 23 (1970) 419. R. Jaeger and D. Menzel, Surface Sci. 63 (1977) 232. D.L. Adams, Surface Sci. 42 (1974) 12. A. Adnot and J.D. Carette, Phys. Rev. Letters 39 (1977) 209; W. Ho, R.F. Willis and E.W. Plummer, Phys. Rev. Letters 42 (1978) 12. M.R. Barnes and R.F. Willis, Phys. Rev. Letters 41 (1978) 1727; R.F. Willis, Surface Sci. 89 (1979) 457. P.J. Estrup, J. Vacuum Sci. Technol. 16 (1979) 635. R.A. Barker, T.E. Felter, S. Semancik and P.J. Estrup, J. Vacuum Sci. Technol. 17 (1980) 755. T.E. Madey, Surface Sci. 36 (1973) 281. R.A. Barker, PhD Thesis, Brown University (1979). B.D. Barford and R.R. Rye, J. Chem. Phys. 60 (1974) 1046. I. Stensgaard, L.C. Feldman and P. Silverman, Phys. Rev. Letters 42 (1979) 247; L.C. Feldman, P. Silverman and I. Stensgaard, Surface Sci. 87 (1979) 410. D.O. Hayward and B.M.W. Trapnell, Chemisorption (Butterworths, London, 1969); A. Clark, The Theory of Adsorption and Catalysis (Academic Press, New York, 1980). C. Jedrzejek, O.L.J. Gijzeman and K.F. Freed, Surface Sci. 107 (1981) 43. P.A. Redhead, Vacuum 12 (1962) 203.

344 [26] 1271 [28] 1291 [30] [31] [32] [33] 1341

[35] [36] [37] 1381 (391 (401

A. Horlacher Smith et al. / Desorption of hydrogen from W(lO0) G. Ehrlich, Advan. Catalysis 14 (1963) 271. JANAF Thermochemical Tables, 2nd ed., Natl. Bur. Std. Ref. Data Ser., NBS No. 37 (1971). R.A. Barker, P.J. F&up, F. Jona and P.M. Marcus, Solid State Commun. 25 (1978) 375. S.C. Ying and L.D. Roelofs, Surface Sci. 125 (1983) 218. L.D. Roelofs and P.J. Estrup. Surface Sci. 125 (1983) 51. R.J. Behm, K. Christmann and G. Ertl, Surface Sci. 99 (1980) 320. R.A. Barker and P.J. Estrup. J. Vacuum Sci. Technol. 18 (1981) 546. P. Heilman, K. Heinz and K. Miiller, Surface Sci. 89 (1979) 84. A. Fasolino, G. Santoro and E. Tosatti. Phys. Rev. Letters 44 (1980) 1684; A. Fasolino, G. Santoro and E. Tosatti. in: Proc. Conf. on Phonon Physics, Bloomington. IN, 1981, to be published; A. Fasolino, G. Santoro and E. Tosatti, Surface Sci. 125 (1983) 317. R. Jaeger and D. Menzel, Surface Sci. 100 (1980) 561. P.J. Estrup, L.D. RoeJofs and S.C. Ying, Surface Sci. 123 (1982) L703. S. Glasstone, K.J. Laidler and H. Eyring, The Theory of.Rate Processes (McGraw-Hill. New York, 1941). K.J. Laidler, Trans. Faraday Sot. 55 (1959) 1725. P.J. Estrup, E.F. Greene, A.M. Horlacher and M. Pickering, Bull. Am. Phys. Sot. 28, No. 336 (1983). P.J. Estrup, E.F. Greene, M. Cardillo and J. Tullis. to be published.