5582
J . Phys. Chem. 1989, 93, 5582-5584
Effect of Adsorbate-Induced Surface Reconstruction on the Apparent Arrhenlus Parameters for Desorption V. P. Zhdanov Institute of Catalysis. Novosibirsk 630090, USSR (Received: January 4, 1989)
The effect of adsorbate-induced surface reconstruction on the apparent Arrhenius parameters for desorption is analyzed in the framework of the model that predicts a first-order phase transition at temperatures below the critical one, T < T,. The desorption is assumed to occur at T > T,. The reconstruction is shown to result in the compensationeffect (the synchronous variation of the preexponential factor and the activation energy with increasing coverage).
1. Introduction To describe desorption at finite coverages, the lattice-gas models are customarily used.' In the framework of these models, the surface lattice is usually assumed to possess well-defined twodimensional periodicity closely resembling the atomic ordering in the bulk. This assumption is correct for many systems. In some instances, however, the surface lattice reconstructs into a phase with new symmetry.2 This can occur spontaneously with temperature or can be induced by adsorbed particles. The purpose of the present paper is to consider the effect of the adsorbateinduced reconstruction on the apparent Arrhenius parameters of the desorption rate constant. The detailed description of desorption depends on whether the phase transition is continuous or first order. We have earlier discussed the effect of the continuous phase transition on desorption3 and surface d i f f ~ s i o n . The ~ adsorbate-induced reconstruction was shown to result in a strong (on the order of lo5) coverage dependence of the preexponential factor for desorption. The direction of the variation is in accordance with the compensation effect (the preexponential factor and the activation energy decrease with increasing coverage). Besides, the coverage dependence of the sticking coefficient can be weak. In this paper, we consider the opposite model of reconstruction. In particular, the presented model predicts a first-order phase transition at low temperatures. 2. Model of Reconstruction A real surface reconstruction induced by adsorption is a very complex phenomenon. To simplify the consideration, we use the following assumption^:^ Any surface atom is located in positions 1 or 2. For a clean surface, position 1 is stable and position 2 is metastable (Figure 1). Adsorbed particles are described in the framework of the lattice-gas model. The metastable phase is assumed to be stabilized by the interaction between surface atoms and adsorbed particles. In the mean-field approximation, the total free energy of the system (per one site) is represented as5
Fad = -E,B
+ zte2/2 + T[e In e + (1 - e) In (1- e)]
F, = AEx
+ T [ xIn x + (1 -
X)
In (1-
where Fadand F, are the free energies of adsorbed particles and surface atoms, Fintis the interaction energy (this energy stabilizes the metastable phase), 0 is the adsorbate coverage, E, is the adsorption energy, e is the energy of the lateral interaction of adsorbed particles (positive for repulsion), z is the number of the nearest-neighbor sites, AE is the energy difference between positions 2 and 1, x is the coverage of surface atoms located in position 2, (Y is the interaction energy parameter; the Boltzmann constant is set to unity. Strictly speaking, the number z changes during reconstruction. For simplicity, this effect is neglected in our model. In the case of thermodynamic equilibrium, we have aF/ax = 0, or A E + TIn[x/(l-x)]-zat9=0
(1)
The chemical potential of adsorbed particles is defined as I.L
= a F / a e = -E,
+ zee + T In [e/(i
- e)] - Z(Y% (2) (3)
(4) Equation 3 defines a phase diagram of the system. At temperatures below the critical one, f C T,, the right-hand part of this equation is a nonmonotonous function of coverage. Thus, the phase separation (the first-order phase transition) occurs at T C T,. The real value of the chemical potential in the two-phase region is defined by the Maxwell rule (for more details see ref 5).
The model presented yields a qualitative description of adsorbate-induced reconstruction that occurs when a clean Ir( 100) This or Pt( 100) surface is exposed to hydrogen, CO, or model has been used to calculate a phase diagram of the adsorbed overlayer and adsorption isotherms5 and to interpret thermal desorption spectra in the H/Pt( 100) system.' A similar model has been used to simulate kinetic oscillations in CO oxidation on Pt(100).8
x)]
Fin,= -zaex (1) Zhdanov, V. P.; Zamaraev, K. I. Vsp. Fir. Nauk 1986, 149,635; Sou. Phys.-Vsp. (Engl. Transl.) 1986, 29, 755. (2) Estrup, P. J. In Chemistry and Physics of Solld Surfaces; Vanselow, R., Howe, R., Eds.; Springer: Berlin, 1984; Vol. V, p. 205. Willis, R. In Dynamical Phenomena at Sutfaces, Interfaces and Superlattices; Nizzoli, F., Rieder, K.-H., Willis, K. F., Eds.; Springer: Berlin, 1985; p 126. Ying, S . C. Ibid., p 148. (3) Zhdanov, V. P. Surf. Sri. 1989. 209, 523. (4) Zhdanov, V. P. Langmuir, in press. (5) Zhdanov, V. P. Surf.Sci. 1985, 164, L807.
3. General Equations for Desorption The detailed description of desorption depends on whether the desorption temperature is below or above T,. In the first case, desorption from a two-phase adsorbed overlayer can proceed via several channels, namely, out of the dilute phase and out of the (6) Kiippers, J., Michel, H. Appl. Sur$ Sci. 1979, 3, 179. Norton, P. R.; Davies, J. A.; Creber, D. K.; Sitter, C. W.; Jackman, T. E. SurJ Sci. 1981, 108, 205. Behm, R. J.; Thiel, P. A.; Norton, P. R.; Ertl, G. J . Chem. Phys. 1983, 78, 7437. (7) Sobyanin, V. A,, Zhdanov, V. P. Surf. Sci. 1987, 181, L163. (8) Imbihl, R.; Cox, M. P.; Ertl, G.J . Chem. Phys. 1985, 83, 1578.
0022-3654/89/2093-5582$01.50/0 0 1989 American Chemical Society
The Journal of Physical Chemistry, Vol. 93, No. 14, 1989 5583
Adsorbate-Induced Surface Reconstruction
B
0
9
Figure 1. Hypothetical potential energy for displacement of a surface atom. The solid line is the potential curve for a clean surface, the dashed line for an adsorbatehcoveredsurface; q is a coordinate displacement.
0.6
0.4
0.2
I T
-
=
550
b
x
-0.2
0.2
where kdo = vo exp(-Eo/T) is the desorption rate constant for the unreconstructed surface at 8 0, vo and Eoare the corresponding Arrhenius parameters, PA,iis the probability that an adsorbed particle has the environment marked by index i, t i is the lateral interaction of the adsorbed particle and its environment (including the interaction with the displaced lattice atoms), and ti* is the lateral interaction of the activated complex with the same environment. Using eq 5 , we neglect the precursor states. Moreover, the partition function of the activated complex is assumed to be independent of the number of the nearest-neighbor adsorbed particles. The interaction ti* is usually believed to be weak in comparison with other interactions. Neglecting this interaction, we can rewrite eq 5 as (see arguments in ref 11)
e
Figure 2. Phase diagram of the adsorbed overlayer. A is a one-phase region; B is a two-phase region. 0
condensed phase, and the description of desorption depends on whether evaporation from the dense phase into the dilute phase is so fast that during the desorption process a quasi-equilibrium is maintained between the adsorbed phases or evaporation is the slowest process and, thus, rate-determir~ing.~In the second case (at T > Tc),the description of desorption is simpler because the desorption occurs from a one-phase adsorbed overlayer. For simplicity, we consider desorption at T > T,. In the framework of the lattice-gas model, the rate constant of monomolecular desorption is described by lo
0.8
0.6
0.4
0.8
1.6
e
1.7
looo/~
1.0
Figure 3. The desorption rate as a function of coverage (a) and temperature (b).
Substitution of eq 3 into eq 6 yields kd = kdo@
(7) Thus, the function a, determined by eq 4, describes the effect of adsorbate-induced reconstruction on desorption. Using eq 6 and 7 and expression 4, we suppose that reconstruction is fast in comparison with desorption and thus thermodynamic equilibrium is maintained in the adsorbed overlayer. Assuming that the desorption rate constant can be expressed in the phenomenological form we can calculate the apparent Arrhenius parameters for desorption by
(9) Kreuzer, H.J.; Payne, S.H. Surf. Sci. 1988, 200, L433. (10) Zhdanov, V. P. Surf.Sci. 1981, Z Z Z, 63.
560
5 80
6 20
600
T, K
Figure 4. Thermal desorption spectra for initial coverages 0.25,0.5,0.75,
and 1.0. It is also of interest that in the framework of the considered model the coverage dependence of the sticking coefficient is bel - 8, because we have assumed that lieved to be weak, 4 8 ) ti* = 0 and that the partition function of the activated complex is independent of the environment.
-
4. Results of Calculations and Conclusions To calculate the phase diagram of the overlayer (Figure 2), the coverage and temperature dependence of the desorption rate constant (Figure 3), and thermal desorption spectra (Figure 4), we have used the following reasonable set of parameters: za = 7 kcal/mol, zt = 5 kcal/mol, A,!? = 3 kcal/mol, Eo= 35 kcal/mol, vo/@ = loi2 K-' (j3 is the heating rate). At low (0 < 0.2) and high (8 > 0.8) coverages, the desorption rate is seen (Figure 3) to increase with increasing coverage. This
5584
J. Phys. Chem. 1989, 93, 5584-5587 4
3
0.5
,-.
-
w
1
o
0
\
>c v
I
2
xo
2
-0.5
0
3u
-1
0
0.2
0.4
0.6
0.8
e
Figure 5. Apparent Arrhenius parameters for desorption as functions of coverages calculated at 550 K < T C 650 K.
is explained by repulsive lateral interactions between adsorbed particles. At intermediate coverages, 0.2 < 0 < 0.8, the desorption rate decreases with increasing coverage. The latter is explained by surface reconstruction (preferential occupation of metastable positions by surface atoms with an increase in adsorbate coverage). The adsorbate-induced changes in the surface are seen (Figure 4) to result in thermal desorption spectra that are characterized
by a shift of the peak maximum to higher temperatures with increasing initial coverage and by narrow peak widths. The order of desorption is about zero. Using the Arrhenius plots (see, e.g., Figure 3b), we have calculated the apparent Arrhenius parameters for desorption (Figure 5 ) . At intermediate coverages, reconstruction is seen to lead to an increase in desorption activation energy with increasing coverage. The coverage dependence of the preexponential factor for desorption is not strong (on the order of 10) and is in accordance with the compensation effect (the synchronous variation of the preexponential factor and the activation energy). In summary, we have analyzed the effect of adsorbate-induced surface reconstruction on the apparent Arrhenius parameters for desorption. The model presented here predicts first-order phase transition at low temperatures, T < T,. The desorption has been assumed to occur at T > T,. The reconstruction is shown to result in the compensation effect. The latter conclusion seems to be rather general because the opposite model of reconstruction3 also leads to the compensation effect. Of course, the compensation effect may be either weak (Figure 5 ) or strong (ref 3). Besides, the coverage dependence of the sticking coefficient can be weak. All these effects are frequently observed in real systems.12 Thus, the adsorbate-induced changes in the surface seem to play an important role in the kinetics of the surface rate processes. ( 1 1) Zhdanov, V. P. Surf. Sci. 1983, 133,469. (12) Seebauer, E. G.; Kong, A. C. F.; Schmidt, L. D. Surf. Sci. 1988,193, 417. Smith, A. H.; Barker, R. A,; Estrup, P. J. Surf. Sci. 1984, 136, 327. Estrup, P.J.; Greene, E. F.; Cardillo, M. J.; Tully, J. C. J . Phys. Chem. 1986, 90,4099.
Variable-Temperature Magic-Angte-Spinning Technique for Studies of Mobile Species in Solid-State NMR Tadashi Tokuhiro, Francis Bitter National Magnet Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts 021 39
Mark Mattingly, Bruker Instruments, Incorporated, Manning Park, Billerica, Massachusetts 01821
Lennox E. Iton, Materials Science Division, Argonne National Laboratory, 9700 S . Cass Avenue, Argonne, Illinois 60439
and Myong K. Ahn*st Department of Chemistry, Indiana State University, Terre Haute, Indiana 47809 (Received: January 20, 1989)
The utility of variablstemperature (VT) magic-angle-spinning (MAS) Fourier transform nuclear magnetic resonance (FT-NMR) spectroscopy is demonstrated for the study of mobile species in solids, especially when quadrupolar nuclei are being observed. A new VT-MAS probe is described for use in the temperature range 150-400 K, using spectrometers with high-field superconducting magnets. It has bzen utilized in studies of the bonding and dynamics of alkali-metal cations in hydrated zeolites at an applied field of 7.05 T. Results are presented for the cases of Cs/Na-A and Cs/Li-A zeolites, in which the Cs' ions exchange rapidly, at 293 K, between six-ring and eight-ring sites in the large cage, so that on the time scale of the NMR measurements the ions are indistinguishableand a single '33Csresonance is observed. Below 250 K, two well-resolved signals are observed in the Cs/Na-A zeolite, 107 ppm apart. These are easily assigned to the Cs' ions in the two sites, the large difference in chemical shifts being attributed to the stronger bonding of Cs' ions at the six-ring sites. Three sites are distinguished in the Cs/Li-A zeolite, the third site being assigned to a position near a four-ring in the large cage.
Introduction The magic.angle-spinning (MAS) techniquei in solid-state nuclear magnetic resonance (NMR) has been an extremely potent *Towhom correspondence should be addressed. Argonne National Laboratory Faculty Research Leave Appointee.
tool in the elucidation of silicon/aluminum distributions in the frameworks of aluminosilicate zeolites.* The %i NMR chemical (1) Schaefer, J.; Stejskal, E. 0. in Topics in Carbon-13N M R Spectroscopy; Levly, G . C., Ed.; Wiley-Interscience: New York, 1979; Vol. 3, p 283. (2) Klinowski, J. Prog. NMR Spectrosc. 1984, 16,237, and references therein.
0022-3654/89/2093-5584$01.50/00 1989 American Chemical Society
