Dynamical parameters of desorbing molecules

Surface Science Reports 5 (1985) 145-198 North-Holland, Amsterdam

DYNAMICAL

PARAMETERS

George COMSA

OF DESORBING

145

MOLECULES

and Rudolf DAVID

Institut fi~r Grenzfli~chenforschung und Vakuumphysik, Kernforschungsanlage d~lich, Postfach 1913, D - 5170 Ji~lich, Fed. Rep. of Germany Received 12 February 1985; manuscript received in final form 22 July 1985

The aim to uncover fundamental details of the desorption process as well as the needs of more applied research, like fusion, led recently to a growing interest in the study of the parameters of desorbing molecules. The main experimental methods and the most significant experimental results obtained so far are reviewed and discussed. The investigation of the parameters of desorbing molecules being one of the oldest fields of surface science, a number of pre- and misconceptions still hamper the mutual understanding and hereby impede progress. Accordingly, a relatively large space is dedicated to the historical development, to definitions, and even to semantics.

0 1 6 7 - 5 7 2 9 / 8 5 / $ 1 8 . 9 0 © E l s e v i e r S c i e n c e P u b l i s h e r s B.V. (North-Holland Physics Publishing Division)

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Contents 1. 2. 3. 4.

Introduction Some history Definitions, semantics Experimental 4.1. The supply of molecules to the surface 4.2. The measurement of the parameters of the desorbing flux 5. Results 5.1. Desorption flux versus desorption angles 5.2, Desorption flux versus velocity and desorption angles 5.3. Internal energy of desorbing molecules 6. Final discussion Acknowledgements References

147 148 154 165 165 168 176 177 182 190 192 196 196

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1. Introduction

Thermal desorption is one of the fundamental surface phenomena. In spite of being investigated both experimentally and theoretically for almost a century, the mechanism of desorption is still not understood in detail. However, the main phenomenological properties of desorption are well known. The most illustrative example is the Arrhenius behavior of the desorption rate, thermal desorption being a thermally activated process. The thermal programmed desorption procedure (TPD) proposed by Ehrlich [1] and by Redhead [2] is based on this behavior. The procedure allows one to obtain in an experimentally easy and apparently straightforward way the activation energy for desorption, a fundamental quantity, and even some more subtle information (see for a clear description of the procedure ref. [3]). Thermal programmed desorption has probably become the most widespread tool for the investigation of the interaction of adsorbates with surfaces. The desorption rate, the main parameter monitored in all these investigations, is meant to be the total desorption rate, i.e. the total flux of molecules desorbing in unit time from a unit area, irrespective of the magnitude and direction of the molecular velocity and internal energy. The integration over all directions, speeds and internal energies is performed automatically, even if often strongly biased, by the molecule detector (usually a mass spectrometer). As long as the general belief was that the distribution of the directions, of the speeds, and of the internal energies of desorbing molecules was governed by general laws (Knudsen, Maxwell, and Boltzmann, respectively), neither the fact that an integration was performed, nor that this integration was biased had to be blamed. Indeed, these laws being essentially independent of the specific properties of the particular adsorbate/substrate system, the integration would not lead to any loss of information; in addition, even a biased integration (e.g. preferential detection of low speed molecules) would not lead to errors in relative desorption rate determinations. Since it became obvious that there is no a priori reason for the parameters of the desorbing molecules (direction, speed, and internal energy) to be governed by general laws and especially that these laws do fail in describing the parameter distributions the situation should have changed radically. A large number of differential measurements of the desorption parameters, supplying new information on desorption in general and on the specific adsorbate/substrate system in particular had to be expected, as were, cautious inspections of the rate integration procedures. However, when an erroneous belief lasts for a long time, the new views spread slowly and misunderstanding remains behind. The aim of this paper is to help in accelerating the spreading and in reducing the confusion. We feel that the evolution of the knowledge of (and of the belief about) desorption parameters over more than one hundred years js instructive, and

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section 2, "History", is dedicated to it. Much of the confusion roots in improper definitions and even in semantics; we have tried to improve the situation by discussing various aspects in detail in section 3. The differential measurement of the desorbing flux involves specific problems which are treated in section 4 "Experimental". The present status of the experimental investigation of the dynamic parameters of desorbing molecules is reviewed (not exhaustively) in section 5, "Results". We have left out the whole field of "trapping-desorption" because it was excellently reviewed very recently by Barker and Auerbach [4]; this hopefully makes our paper clearer without loss of generality. Section 6, "Final discussion", outlines the importance of theoretical developments for the ability to extract and exploit the information contained in the differential measurements. Only a few examples of theoretical work are given, and no assessment of their value is given. The reader is referred to the quoted theoretical papers and the references therein.

2. Some history Even in the prehistory of surface science people asked questions about the angular and even velocity distribution of gas molecules scattered from a solid surface. As early as 1878, James Clerk Maxwell gave a pertinent answer [5]: " . . . of every unit area a portion f absorbs all the incident molecules, and afterwards allows them to evaporate with velocities corresponding to those in still gas at the temperature of the solid, while a portion 1 - f perfectly reflects all the molecules incident upon it". In the present terminology this would read: out of the incident molecules a fraction f (sticking probability) adsorbs, while a fraction 1 - f is specularly reflected; the adsorbed molecules eventually desorb, the distributions of their dynamical desorption parameters following the Knudsen (cosine), Maxwell, and Boltzmann laws. This latter statement concerning the desorbate parameters was not based on any thermodynamical or other theoretical argument, but only on an artificial model. Nevertheless, the statement was not challenged for many decades; it still represents one of the basic notions in the bulk of knowledge of the cultivated chemist or physicist, even of some experts in surface physics. The reasons are probably emotional rather than rational: the three distributions bear the names of the best known creators of the kinetic theory of gases; admolecules are in thermal equilibrium with the surface and the three distributions characterize a gas in thermal equilibrium (there is, however, no compelling link between the two facts). Even recently, people aware of the lack of physical basis for Maxwell's statement on desorption continue to name "equilibrium" and "non-equilibrium" desorption the desorption in which the distributions do or do not follow the three laws, respectively. Names can be chosen at will, but it would be appropriate to avoid a reinforcement of a deeply rooted misunderstanding.

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In 1915 Martin Knudsen criticized Maxwell's statements quoted above [6]. However, he did not mean the statement describing the behavior of desorbing molecules; on the contrary, based upon this statement and upon his own experimental results (various atom beams appeared to scatter following the cosine law) he concluded that f = 1 always. By 1929 at the latest the general validity of Knudsen's results and his conclusion was infirmed by Stern's diffraction experiments [7]. It was Clausing who, in 1930, clarified the fundamentals of the problem we are addressing here, namely the parameters of desorbing molecules [8]. Actually Clausing discussed only the angular distribution of the desorbing flux, but the generalization is trivial. First, following Gaede [9], he demonstrated that the second law of thermodynamics (and also the principle of detailed balance) demancls that at equilibrium the polar angle distribution of the molecules leaving the surface be cosine. Later on, the demonstration, but not the conclusion, was considered inconclusive [10]. Kuscer [11] and Wenaas [10] have used time reversal invariance and an assumption of a canonical distribution of states in the solid to show that the molecules leaving a surface at equilibrium are indeed characterized by the cosine distribution. There is, however, an additional, particularly relevant idea emerging from Clausing's paper [8]. The molecules leaving a surface at equilibrium consist of molecules having undergone in general various types of interaction with the surface: elastic scattering (specular reflection, diffraction in various channels), inelastic scattering (one or multiphonon annihilation or creation) or desorption (following adsorption). If more than one of these processes are effective, the distribution of the molecules leaving the surface, as a result of one of these processes, is in principle arbitrary even at equilibrium. The only constraint imposed by the presence of equilibrium is that the sum of all the distributions must be cosine. Thus, in particular, as long as desorption is not the only effective process, there is no a priori reason for the equilibrium angular distribution of desorbing molecules to be cosine. Under equilibrium conditions desorption is rigorously never the only effective process, because the sticking probability is never rigorously f = 1. Admittedly, Clausing's argument was less detailed but, nevertheless, the above conclusion was implicit. Desorption experiments performed since that time give evidence for the existence of both cosine and non-cosine distributions. They confirm Clausing's idea that the shape of the distribution is solely determined by the microscopic desorption mechanism and not by general thermodynamic constraints. There is, of course, a trivial constraint resulting simply from the definition of adsorption: the molecule has to be trapped long enough to "forget" its incident parameters. As a consequence, the shape of the distributions of desorbing molecules has to be related in some way (e.g. symmetrical) with respect to the only outstanding direction left over, i.e. the surface normal. In molecular beam scattering experiments the fraction of scattered mole-

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cules exhibiting a cosine distribution is currently assigned to desorbing molecules and used for the determination of sticking probabilities. This assignment has to be handled with caution. Indeed, the desorbing molecules might have a non-cosine distribution. Thus, a distribution symmetric with respect to the surface normal might be, in general, a better guess. On the other hand, scattering from adsorbates or other microscopic surface roughness and even inelastic scattering may contribute to a cosine or other normal symmetric distribution. The assignment of cosine distributions to desorbing molecules obviously originates in Maxwell's statement quoted above. As we have further shown, Knudsen used it to demonstrate that the sticking probability is always f = 1. In his book "Molecular Rays" [12], Fraser has again used this assignment to establish whether, in a given molecular beam experiment, molecules are adsorbed and then desorbed or only reflected. Fraser tried to classify the matter very (viz. too) sharply: he reserved the term "Cosine law" for the distribution of the molecules leaving the surface at equilibrium according to Gaede [9] and Clausing [8]; for the cosine distribution of desorbing molecules alone, which he believed to be cosine even after reading Clausing's paper and even under non-equilibrium conditions, he proposed the name Knudsen law. The cosine distribution of desorbing molecules received the status of a law. The confusion was perfect. The following evolution proved again that confusions, like makeshifts, can last a very long time [13]. To our present knowledge, it was not until 1963 that the possibility of deviations from the cosine distribution of desorbing molecules was considered. Hirth and Pound noted in their book on "Condensation and Evaporation" [14] that "when surface constraints introduce entropies of activation into the evaporation process.., deviations from the cosine law are possible". A few years later, 1968, Comsa [15] resumed Clausing's arguments and presented them in a more provocative way. He went beyond the statement presented above, that the angular distribution of desorbing molecules need not to be cosine even at equilibrium. AssumirLg that the detailed balance argument holds, even if restricted to the distribution of adsorbing and desorbing molecules [8] and using old "reflecting power" data for H e / L i F [16], he inferred that the angular distribution of desorbing He has to deviate from cosine, the distribution being peaked in the normal direction. The reasoning was straightforward, but of course oversimplified. The incident molecules were considered to be either specularly reflected or adsorbed; the "reflecting power" being dependent on the incident polar angle, the angular distribution of reflected molecules is non-cosine at equilibrium (less peaked in normal direction than cosine); in order to compensate for this (cosine distribution of molecules leaving the surface), the angular distribution of desorbing molecules has to be non-cosine also (more peaked in normal direction than cosine). Moreover, using an analogy with the total reflection of neutrons, Comsa proposed a tentative model to explain the shape of the inferred distributions: the existence of a

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potential energy barrier. Admittedly, these deductions were based on crude assumptions and data and thus the conclusions speculative [17]. But a large number of experiments performed since then shows that for many systems the distribution of desorbing molecules is non-cosine, namely strongly peaked in the normal direction. Even now the potential energy barrier is still the favored model among experimentalists to explain their data. Only 6 months after Comsa's paper the first experimental desorption data showing evidence for strong deviations from the cosine distribution were published by Van Willigen [18]. He reported that H 2 desorbed from Ni, Fe and Pd with an angular distribution of the type cos%q, with n having values up to 6. Van Willigen described the distributions fairly well by assuming the existence of the formerly proposed potential barrier [15] (activation energy for adsorptlon) and the restricted applicability of detailed balance (see above). The paper by Palmer et al. [17] afforded important experimental confirmations of the views reached so far. Three aspects are emphasized here: (1) The angular distribution of HD from N i ( l l l ) was found to be cos"# with 2.5 < n < 4.0 depending on the surface conditions. This result was obtained by supplying the hydrogen to the surface from the gas phase and not, as Van Willigen did, by bulk permeation. Thus deviations from cosine are present not only in the case of permeation supply. (2) The dependence of the sticking probability on the incident polar angle of a D 2 beam on the same surface was found to be described by c o s " - ~ . This was the first experimental indication for the restricted applicability of detailed balance (only to adsorption-desorption) even if the whole system is not in equilibrium. (3) The "reflecting power" was found, in a separate experiment, to vary as 1 - cos"-~O. A synthetic equilibrium construction (the summation of the desorbing intensities with the properly weighted reflected ones) led to the expected cosine distribution of the molecules leaving the surface at equilibrium. Palmer and O'Keefe [19] proved the fulfillment of the cosine distribution of leaving molecules also under true equilibrium conditions for He, H 2 and A r / L i F in a remarkably straightforward experiment. The cosirie distribution is followed, although both He and H z beams scattered from a LiF crystal surface give rise to a rich diffraction pattern. New, detailed results on angular distribution of hydrogen from Fe, Pt, Cu, Nb, etc. [20] and from Cu surfaces of various orientations [21,22] followed. Deviations from the cosine distributions were the rule, and the actual shape of the distribution did not seem to depend on the way hydrogen was supplied, by permeation [21] or from the gas phase [22]. In addition, the activation energy for dissociative adsorption of H 2 on Cu was measured directly by a molecular beam method [22]. All these data were carefully analyzed in a sound paper on detailed balance and quasi-equilibrium by Cardillo et al. [23]. The authors came to the conclusion that the equilibrium relationship between adsorption and desorption resulting from the application of detailed balance arguments can be used (with caution) even if the system is not in equilibrium, but behaves

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like it would be (quasi-equilibrium). They also emphasize the great simplification in treating chemical processes, which results when quasi-equilibrium conditions apply. The discussion has concentrated up to this point almost exclusively on the angular distribution. Conceptually, the argumentations concerning the velocity distribution and the angular distribution are identical [24]. So, too, are the conclusions, i.e. the molecules leaving a surface at thermal equilibrium have a Maxwell velocity distribution corresponding to the surface temperature; the desorbing molecules need neither to have a Maxwell distribution nor does their mean energy have to correspond to the surface temperature, and this not even at thermal equilibrium. The sticking probability depends always to some extent on the velocity of the incident molecules. F r o m detailed balance arguments we deduce that the velocity distribution of desorbing molecules deviates to the same extent (from the Maxwell distribution) that their mean energy will deviate, in general, from the mean energy of a gas at the surface temperature. The amount of the deviation depends, of course, on the specific properties of the system considered. Whether these deviations are detectable depends on the experimental sensitivity and resolution. The first evidence for such a deviation was presented by Dabiri et al. [25] who measured the velocity distribution of hydrogen desorbing in normal direction from a polycrystalline Ni surface: the distribution seemed to be Maxwellian but corresponding to a temperature 45% larger than the surface temperature, T~. Improvements in sensitivity led to further details of these deviations by measurement of mean energy and speed ratio (a measure for the velocity distribution width - see next section) versus desorbing angle [26,27]. The results obtained by Comsa et al. showed that the mean energy decreases strongly with increasing polar angle; if expressed in equivalent temperature, TE: from T E ~ Ts + 700 K at 0 = 0 ° (normal direction) to T E -- T~ at 0 = 70 ° for polycrystalline Ni [26] and even down to T E = T~ - 400 K for Ni(111) at 0 = 80 ° [27]. The shape of the velocity distribution appeared to be nonMaxwellian and to vary with ~: from about 0.75 of the width of a Maxwellian distribution with the same mean energy at ~ = 0 ° to about 1.2 times this width at 0 = 80 ° [27]. Both results emphasized the failure of the simple single energy barrier model [15,18] to describe the actual desorption behavior. For instance the model predicts a dramatic increase of T E with ~, in obvious contradiction with the data. Short-comings of the model already appeared when the angular distributions were analyzed in more detail, and Balooch et al. [22] prolmsed a barrier with a distribution of heights. As recognized earlier [23] the velocity distributions are more sensitive to the features of the model. Based upon velocity (mean energy) and angular distribution data and the idea of a distribution of heights, Comsa and David [28] proposed a crude model assuming that only two definite heights are present ( E a = 0 and > 0). They hoped that the model might describe average properties, as for instance mean

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energy versus angle. The model is mathematically very transparent and easy to handle, but physically hardly realistic. In spite of this, it described fairly well the data obtained so far. Surprisingly, the two-heights model was almost perfectly confirmed by new data obtained with an improved resolution [29]. The velocity distribution of hydrogen desorbing after having permeated through Pd clearly consists of two distinct distributions: one Maxwellian with the mean energy corresponding to the surface temperature and the other non-Maxwellian with a mean energy almost three times higher. This is exactly what a pure two-heights model formally predicts. It may seem paradoxical, but it was just this clear confirmation of the model prediction which pointed out the essential weakness of the model. Indeed, a real potential barrier cannot have only two barrier heights but must have a distribution of heights as assumed originally [22]; and such a real barrier can thus only lead to a superposition of continuously different velocity distributions and not to two distinct distributions as predicted by the rough two-height barrier approximation and as observed experimentally. This led Comsa et al. [29] to the assumption that the hydrogen atoms after permeating to the surface region may recombine and desorb by one of two mechanisms: either, first thermalize in the chemisorption well and then recombine and desorb (the classical permeation path proposed by Wagner [30]) or recombine and desorb without thermalization in the chemisorption well. Following one or the other path the hydrogen feels either the "outer" barrier (the activation energy for adsorption) which might be E a = 0 or an "inner" barrier (related to the activation energy for permeation) which is almost always E a > 0. The first path leads to the Maxwell distribution at surface temperature, the second to " h o t " molecules. Thus, there is not a single non-physical barrier with two heights but there are two barriers with different heights. This " t w o paths desorption after permeation" model describes a number of significant experimental data; it also leaves some questions open. This point has been presented here as an example to illustrate the new insights gained by the measurement of the dynamic parameters of desorbing molecules. The examples of deviations from the cosine and Maxwell distributions given so far were confined to molecules desorbing upon associative desorption. A new field of particular relevance was opened by Palmer and Smith [31] who reported on angular distributions of CO 2 desorbed upon the catalytic reaction between CO and O on a poly-Pt surface; the distributions could be fitted by c o s ~ with n up to 6. Becket et al. [32] reported that the mean energy of CO2 desorbing in normal direction, under similar conditions, corresponds to temperatures five times larger than the surface temperature. The characteristic behavior of desorbing CO 2 was felt to bear specific information on this important reaction. This triggered a number of rewarding investigations culminating in a recent paper by Segner et al. [33] in which remarkable details of the reaction dynamics could be uncovered.

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Finally, we come to the distribution of internal energies of desorbing molecules. The argumentation is, of course, again identical to the case of angular and velocity distributions and will not be repeated here. First evidence for deviations from the Boltzmann distribution corresponding to the surface temperature T~ appeared only much later, due primarily to experimental difficulties. By means of electron-beam-induced fluorescence, Thorman et al. [34] showed that the vibrational energy of N 2 desorbing from sulphur covered poly-Fe corresponds to a temperature T v up to nearly 2.5 times T~. A short time later Thorman and Bernasek [35] found that the rotational temperature T R of desorbing N 2 is only T R ~ 400 K independent of 1086 K < T~ < 1239 K. While the high vibrational temperature may be explained along similar lines as the high translational energy, the origin of the low and Ts independent rotational temperature seems to root in steric constraints during the N - N recombination on the Fe surface. This is another example for the kind of information supplied by measurements of desorption parameters. The measurement of the internal energy distribution of desorbing molecules seems to have appealed to more and more people in the last few years. For instance Mantell et al. [36] measured, by infrared emission spectroscopy, the internal energy of CO z desorbed upon the oxidation of CO on polycrystalline Pt at T~ = 775 K. The best fit of the emission spectrum was obtained for a minimum value of T v ---2000 K for the asymmetric stretch vibration of the CO 2 molecule. Methods of increasing sophistication were further developed in order to obtain detailed and conclusive information on the processes leading to the desorption of molecules. For instance, Cavanagh and King [37,38] have succeeded by means of laser-excited fluorescence to determine the internal state dependent flux and velocity distributions of N O desorbing from Ru(001); in other words they measure the mean translational energy of molecules which are in a known internal state. Such measurements give exciting insights into the details of the desorption process, including the channels through which the energy is partitioned between translational energy and the various internal energy states.

3. Definitions, semantics The preceding section has emphasized misunderstandings which for a long time have dominated and hampered the investigation of the parameters characterizing desorbing molecules. Hoping to prevent further confusion we will define and discuss some of the notions encountered in this field. This might seem unnecessary and the content trivial for insiders, however, some of the nuances might differ from established views (for a pertinent introduction, see ref. [39], oh. 2). The molecules impinging on or leaving a surface, in particular the desorbing

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molecules, represent a flux of particles. They are characterized by the flux density, i.e. by the number of particles impinging on, emitted from, or passing through a surface of unit area per unit time. According to this definition the flux is a property related to a surface area and a finite time interval. As seen in the preceding section, equilibrium and quasi-equilibrium play a central part in understanding the characteristic features of desorption. The properties of a gas at equilibrium are generally defined as the instantaneous properties of molecules in a given volume: e.g. velocity distribution, mean velocity and mean energy are all defined for molecules in a given volume; likewise homogeneity (the number density is the same in any partial volume) and isotropy (the velocities of the molecules in any partial volume are directed with equal probability in all directions). The corresponding quantitative expressions will be recalled below. At equilibrium there is no net flux; any flux is always fully compensated by an identical but opposite flux. Rigorously, at equilibrium no flux can be measured; we can only think of it, but this alone is useful. The expressions characterizing the properties of a flux of molecules in a gas at equilibrium (e.g. the flux of molecules impinging or being emitted from a surface) will be also redefined in this section. These expressions differ formally from the usual expressions characterizing a gas in equilibrium; this is because the "flux" expressions are related to a surface area and a time interval, while the usual expressions are related to the instantaneous picture of molecules in a volume. However, it is important to note that both sets of expressions characterize the same equilibrium state. Expressions like " . . . the stream properties are not the same as the properties of a gas in equilibrium" [39] might be confusing if they are not understood in the sense - probably meant by the authors - that the stream properties (e.g. the properties of the flux of molecules impinging on a surface during a time interval) of a gas in equilibrium are different from the volume properties (i.e. the instantaneous properties of the molecules in a volume) of the same gas in equilibrium. Let us first recall the usual expressions used to characterize a gas in equilibrium at a temperature T, neglecting the influence of external fields. The homogeneity is expressed by the fact that the number density n ( x , y, z) is independent of coordinates, n(x, y, z) = n, i.e., the number of molecules in any volume d x d y d z is n d x d y dz. (1) The velocities are characterized by a Maxwell distribution; the number of molecules per unit volume having velocities between vx, vx + dvx; Vy, oe + do e and vz, oz + d vz are at any time d3n = n ( ~ m

)3/2 e x p [ - m ( 2vx+ e + v ~ ) / 2 k a T ] d v x dve dv~,

(2)

where kB is the Boltzmann constant and m the mass of the molecules. The symmetry of eq. (2) with respect to v~, oy, vz emphasizes the isotropy of the

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velocity distribution. This recommends the use of polar coordinates and eq. (2) becomes d3n=n

<

exp

(

2-~BT)V

sin 0 d ~ d 0 d r ,

(2')

where the speed v is the modulus of the velocity, and 0 and q~ are the polar and azimuthal angle, respectively. Accordingly, the number of molecules in the unit volume with speeds between v and v + d v directed in any arbitrarily oriented unit solid angle is:

d3n sin 0 d~ dO `=

( m n\~/

t 3/2

( exp

my2 t 2 2-~BT) v

dr.

(3)

Or in a more familiar form, the number of molecules in the unit volume with speeds between v and v + dv is: dn=4~rn(~]m

13/2 exp(

2kBT mvz )v2dv.

(3')

The distribution (3') will be called in the following the "v 2'' T-Maxwell distribution. The distribution of the internal energies is not given explicitly here, because its shape is identical in both the usual and the "flux" formulations. It is a Boltzmann distribution corresponding to the temperature T and we will call it the T-Boltzmann distribution. Remember that the usual expressions above refer to the instantaneous distribution of molecules in a volume. In contrast the "flux" distributions below refer to molecules impinging on a surface during a time interval. The "flux" expressions are deduced straightforwardly from the usual expressions above. The equivalent of the homogeneity condition can be seen in the fact that the flux density, f , of molecules impinging on a surface does not depend on the location of the surface, i.e. the total number of molecules impinging on an area d A in the unit time interval is

f dA = ~(8kBT/~rm)l/Zn dA.

(4)

The number of molecules impinging per unit time on a unit area and having velocities characterized by v, v + dr; 8, O + dO and % ep + dep are obtained directly from eq. (2') by using the well known "slanted cylinder" construction (see e.g. ref. [39]). By choosing the polar coordinate axis normal to the surface the expression will be

d3f=d3nvcosO=n ~ ]

exp

2kBT ]

cos O sin 0 dq0 d 0 d r ,

(5)

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157

and normalized to unit solid angle: sin 8 d r p d S = n

~ }

2k~T

exp

The dependence on v in eq. (5) will be called in the following the "v 3'' T-Maxwell distribution, while the dependence on 8 is obviously the cosine distribution of the impinging molecules. Eqs. (4) and (5) characterize the gas in equilibrium as well as eqs. (1) and (2) (or (1) and (3)) do it. The two pairs of equations are different only because they refer to two different populations of the same gas in equilibrium: molecules impinging on a surface in a time interval and molecules momentarily present in a volume. As already mentioned, in a system in equilibrium, the molecules leaving a surface have an identical distribution with the molecules impinging on a surface [8,10,11]. Thus the molecules leaving a surface at equilibrium are also described by eqs. (4) and (5). If the sticking probability s = 1 the equations apply at equilibrium also for the desorbing molecules. (All impinging molecules adsorb, i.e. all leaving molecules are desorbing ones.) Rigorously s is never unity, but a function of v and 8. Thus the desorbing molecules need not follow eqs. (4) and (5). In many practical cases s might be very near unity in the whole significant range of v and 8 and then eqs. (4) and (5) must apply "within experimental error". Let us now analyze in more detail the v- and 8-dependence of the molecules leaving a surface at equilibrium, and start with the 8-dependence. The total flux leaving a surface area dA into a solid angle in the direction 8, ~p will be d2f V ( 8 , q0) d A = s i n S d ~ d 8

dA=

n (8kBT)I/2 ~ cosSdA.

~

(5")

The cosine emission obvious in eqs. (5) is known in photon emission as Lambert's law and is often called diffuse emission. Unfortunately, diffuse emission is still often considered to correspond to an isotropic probability of emission of each molecule. This is obviously incorrect. Eqs. (5) require that the probability of emission of each molecule does not depend on azimuth, % but that it does depend on the polar angle, 8, like cos 8: maximum for normal and zero for grazing emission. This idea is also not new, but is repressed again and again. Clausing [8] expressed it in a few impressive sentences, which deserve to be quoted: " W e want to point out emphatically, that we are dealing here with an incomprehensible wonder machine which achieves the maintenance of the cosine law. One has especially to bear in mind that the emitted molecules following the cosine law, do not step out with the same probability for each direction, but with a very clearly specified preference direction". The cosine distribution is an elementary property of the molecule emission process (or

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detector

b

a-I COS "~' Fig. 1. (a) Poorly collimated detector. (b) Well collimated detector, a is the cross section of the solid angle seen from the detector at the sample surface distance.

even of the desorption process, if s = 1) at equilibrium and not the result of the geometrical factor cos ~ which may describe the dependence of the surface area seen by the detector. The geometrical factor, of course, plays a role in the polar angle dependence of the flux reaching the detector. We will illustrate this in the case of the cosine emission for two extreme situations: a poorly (fig. la) and a well collimated (fig. lb) detector. The detectors are mounted on a goniometer and thus can be moved always facing the surface on a sphere centered in the middle of the surface. We will assume that r << R where r is the radius of the emitting sample and R the distance to the detector; accordingly, the distance from any point of the surface to the detector can be taken equal to R. Or equivalently, the detector opening is seen from any point on the surface under the same solid angle dl2. The poorly collimated detector always "sees" the whole probe area A. Accordingly, in case of a cosine emission probability the flux detected varies like oor ~ Fpdiffuse

c o s O.

(6)

The dependence is cosine not because the apparent sample area seen by the detector (more precisely, the solid angle encompassed by the sample seen from the detector) varies like cos ~; but because the molecule emission probability varies like cos 0 (the detector sees always all adsorbed molecules). In case of an isotropic emission probability (e.g. B-rays emitted by a monolayer of a iso _ radioactive species) the detected flux would be constant: F~,r - constant. A well collimated detector "sees" only a limited area, a / c o s #, of the sample (a is the cross section of the view cone of the detector at the sample location, see fig. lb). This area obviously increases with ~ and thus compensates for the decrease in emission probability. Accordingly, as long as the

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159

Fig. 2. cosn# angular distributions normalized to the same total flux for n = 1, 5, and 12.

area seen by the detector does not surpass the probe edge and in case of a cosine emission probability the flux detected will be independent of ~: F~il~ru'e = constant.

(7)

(In optics one would say that the probe brightness is independent of angle Lambert's law.) In case of an isotropic emission probability the detected flux would be Fc~l~cc cos- lye, i.e. the brightness of the surface would increase with The detectors used to investigate the angular dependence of desorption are in general well collimated. Two obvious things have to be borne in mind: (a) the whole area "seen" by the detector has to be kept always inside the probe borders and (b) the angular distribution of the flux FcoH measured has to be multiplied by cos O in order to obtain the actual angular dependence of desorption (i.e, of the desorption probability of each molecule). Final remark: the distributions deviating from the cosine distribution found up to now are traditionally described by cos~0 with 0.6 < n < 12. A few examples of cos"t~ distributions normalized to the same total flux are plotted in polar coordinates in fig. 2. This description has absolutely no physical background. It originates in an arbitrary assumption used by Clausing [8] to demonstrate by intuitive examples that the molecules leaving a surface at equilibrium must have a cosine distribution.

G. Comsa, R. David / Dynamical parameters of desorbing molecules

160

0.5

1

1.5

2

2.5

I

I

I

I

I

0

g

0

Vfm~ I

~f Virtu s

"'flux"

L.

0

0

,

,

0.5

1

, , , ,

1.5

,

I

2

2.5

3

Fig. 3. "Volume" velocity distribution function ("/)2 T-Maxwell) and "flux" velocity distribution function (" v3" T-Maxwell) with characteristic velocities. ,,

Let us now compare the properties of the "v 2'' and "v 3'' T-Maxwell distributions, i.e. properties of the same gas in equilibrium: momentary population in a volume and population consisting of molecules impinging on (leaving from) a surface per unit time interval. First we compare the expressions of the three usual characteristic velocities: most probable, Vmp, mean, ~, and root mean square, vr,.,,s: "volume . . . . /)mp

flux" (on, from, through a surface) ,

f Urnp

(Sk.Tl'J2 ° = ~ 'rm J

(8) 1 8m - -

! .

The two distributions and the corresponding characteristic velocities are plotted in fig. 3. The characteristic "flux" velocities are larger than the " v o l u m e " ones. (The largest characteristic " v o l u m e " velocity Vrms is equal to the smallest characteristic "flux" velocity Vfp.) The larger velocities are obviously favored in the "flux" distribution; the origin can be seen for instance in the fact that the volume of the "slanted" cylinder is proportional to v. The relation between the " v o l u m e " and the "flux" mean kinetic energies of

6;. Comsa, R. David / Dynamical parameters of desorbing molecules

the

same gas

"volume .

161

in equilibrium is obviously similar: .

.

( E ) - t -7mVrm s2

.

flux" (on, from, through a surface)

=~kBT, (Ef)=½m

f 2 (Vrms) =2kaT.

(9)

The " v o l u m e " expression on the left is the familiar 3kBT value. The 2kBT value on the right should be likewise familiar for the population constituting the molecular flux at equilibrium. Accordingly, if the desorbing molecules obey the Maxwell law their mean energy will be 2kBT and not ~kaT, because the desorbing molecules represent a flux; they obey the "v 3" and not the "v 2" T-Maxwell law. The collimation shown schematically in fig. l b is used for the measurement of both the angular and velocity distribution of the desorbing flux. In fact, the collimation skims a molecular beam out of the total desorbing flux. The problems with the velocity distribution of desorbing molecules are thus similar to those encountered when handling molecular beams. The delicate aspects of these problems can be discussed more easily by directly treating the case of a molecular beam. The molecules leaving a surface at equilibrium (i.e. with a cosine and a "v 3" T-Maxwell distribution) can be simulated by the molecules leaving the area of the orifice of a Knudsen cell. Indeed, the Knudsen cell is by definition a volume in which the gas is in quasi-equilibrium; accordingly the gas molecules impinging on the volume enclosure and thus also oja the area of the orifice have a cosine and a "v 3" T-Maxwell distribution, and so they step through this area into the surrounding vacuum. (For the experimental conditions which have to be met by an ideal Knudsen cell see, e.g. ref. [27].) The molecular beam is obtained by collimation (see fig. 4), i.e. by placing at least one diaphragm in the path of the effusing molecules. The velocities of the molecules in the beam are almost parallel (i.e. the beam is "good") if the diameters of the orifice, d~,

.

• " •. . . ~ m '.' '.: ? : , b i - . • ' ~orifice ~ . . . "

".'

•

~

.

.

'

.

..'."

.

• "~'/'.J..--L,,~

dD dK

Knudsen cell

Fig. 4. Collimationof a molecularbeam out of the total flux effusingfrom a Knudsencell.

162

G. Comsa, R. David / Dynamical parameters of desorbing molecules

and of the diaphragm, d D, are much smaller than the distance, R, between orifice and diaphragm. We will now concentrate on the distribution of the modulus of these velocities, i.e. of the speeds. In spite of the well-defined conditions governing the production of Maxwell beams (the ideal Knudsen cell) the properties of these beams are described surprisingly confusing even in authoritative monographs and handbooks. For instance, in the classical "Molecular Beams" [40], Ramsey states that only expressions like eq. (5') - for O = 0 ° - but not expressions like eq. (3) are applicable to molecules "in the molecular beam". This statement is wrong. Indeed, in the stationary part of a molecular b e a m [41] originating in an ideal Knudsen cell, the beam molecules impinging on a surface are described by the "flux" eq. (5') and the molecules in a beam volume by the " v o l u m e " eqs. (3). It is obvious that if one equation correctly describes the "flux" population, the other will automatically describe the population in a volume. There are two reasons which may explain why such obvious errors are still present in the literature: one more emotional, the other physical. The emotional reason is related again to two great names, Stern and Einstein. In 1920, Stern [42] measured, in an ingenious experiment, the most probable velocity of Ag atoms impinging on a plate, i.e.

f _ ( 3 k B T / m ) 1/2.

Ump - -

Unfortunately, Stern made the mistake of using the " v o l u m e " expression Vmp = ( 2 k a T / m ) 1/2 when evaluating his data. Shortly later, Einstein [43] pointed out that the " v o l u m e " expression is not applicable to molecules exiting a Knudsen source orifice. Since that time " v o l u m e " expressions seem to be banished from the description of beams in spite of the fact that Einstein's point referred (correctly) only to molecules exiting a surface (see also ref. [44]). The physical aspect appears at first sight much more intricate. There is an apparent contradiction between the fact that a molecular beam consists of molecules exiting the orifice of a Knudsen cell (i.e. mean energy E f = 2 k B T ) and our statement that the distribution of the molecules in any partial volume of the stationary part of the b e a m is "v 2" T-Maxwellian (i.e. mean energy E = ~k~T). Let us first demonstrate that the statement is correct; we will consider for simplicity the beam portion which begins just in front of the orifice of the Knudsen cell. As shown above, the molecules which enter the b e a m (i.e. which exit the orifice) per unit time have a "v 3" T-Maxwell distribution ( 2 k a T - mean energy), the probability of the molecules in the Knudsen cell to exit the orifice being proportional to v. During the same unit time, the molecules of velocity v will distribute themselves homogeneously

G. Comsa, R. David / Dynamicalparameters of desorbing molecules

163

along the beam in a cylinder of height v, i.e. their concentration in a small b e a m volume in front of the orifice is reduced proportional to v - t . This obviously leads to a "v 2" T-Maxwell distribution (~kaT - mean energy) in the small volume. It can be shown [41] that the demonstration holds at any distance, d, measured from the orifice along the beam and for any molecular velocity v, if

d/v << t,

(10)

where t is the time elapsed from the moment the orifice was opened. By taking for v the smallest detectable moleculai" velocity (the number of slow molecules in a volume decreases with "v 2'') eq. (10) defines the length d of the stationary portion of the beam, t time units after the orifice was opened. In this portion the mean energy of the molecules in any beam volume, i.e. in the whole stationary part is 3k~T, just because (and not in spite of the fact that) the beam is fed with molecules of mean energy 2 kBT. The contradiction is only apparent because the beam, which has to be considered as a transitory phenomenon (orifice opened at t = 0), has besides a stationary part also a transitory one which extends from d as defined in eq. (10) to infinity. In this transitory part, with increasing distance x > d from the orifice, less and less molecules with low v will be found at a given time t. Accordingly, the mean energy of the molecules in a partial volume of the beam at a distance x from the orifice increases up to infinity when x goes to infinity (for details see ref. [41]). By averaging over the velocities of the molecules contained at a given time t in the whole beam volume (stationary and transitory) the result will be of course 2 kaT for any t, and thus there is no real contradiction. From the discussion above it is clear that eq. (3) no more holds for the molecules in a partial volume in the transitory region of the beam; but it is likewise clear that in the same region neither eq. (5') holds for the "flux" molecules. In the stationary region, however, both formulae do hold for the corresponding populations. The "molecular b e a m " discussion presented here m a y be considered to be of rather academic character (i.e. only important for understanding the basics of the phenomena, but less important in practice). The beams used nowadays in surface scattering experiments are almost exclusively nozzle beams [45] which have very non-Maxwellian velocity distributions (much narrower). However, even in this case, the correct use of "v 2 "- and "v 3 "-type distributions is necessary. The molecular beams are in general chopped, i.e. a short time (typically 1 0 - 2 - 1 0 -3 s) after opening the source orifice is closed again. Accordingly, a stationary region of the beam cannot build up; the chopped beam sections are transitory throughout and, even with Knudsen cell sources, neither eq. (3) nor (5') apply. The present paper is dedicated to the investigation of the parameters characterizing the flux of desorbing molecules, in particular of their deviation from the Knudsen, Maxwell, and Boltzmann laws.

164

G. Comsa, R. David / Dynamical parameters of desorbing molecules

The discussion is in this case of special practical importance because one has to know exactly what a distribution following these laws looks like. We approach the end of this section by mentioning a source of errors, which is related to the most widespread instrument used to detect the desorbing molecules: the electron impact ion source followed by ion detection with or without ion mass preselection. Let us take the simplest example, the measurement of the angular distribution of the desorbing flux by means of the well-collimated detector shown in fig. lb. The schematically drawn detector is in fact the ion source, the collimated desorbing molecules are passing through. The probability for a b e a m molecule to be ionized is proportional to the time spent in the source, i.e. inversely proportional to the molecule velocity v; the detector measures the molecular density in the beam volume and not the flux. The desorbing molecules being a flux, we have to transform the " v o l u m e " data into "flux" values. This implies the knowledge of the actual angular dependence of the velocity distribution - a less trivial problem. In case the transformation is not performed, errors as large as a factor of two in the angular distribution of the desorbing flux may be the consequence. If we want to avoid tedious velocity distribution measurements and still have the correct angular dependency of the desorption flux data, we may use "flux" detectors (see next section). Let us finally mention a source of confusion and even of errors, which originates from a non-rigorous notation. The mean energies (translational, internal) of the molecules are often expressed in kelvin. This is particularly useful for instance when energies of desorbing molecules are referred to, because deviations from the surface temperature become immediately obvious. Expressing energies in kelvin has a real physical significance only when the energy distribution is Maxwell or Boltzmann. Otherwise, i.e. in the presence of deviations from these laws, we have to bear in mind that the transformation of electron volts or kilocalories in kelvin is a simple convention; and, when dealing with conventions, one has to follow the rules in order to avoid errors. For the mean internal energies of the molecules (rotational and vibrational) the generally accepted transformations are (Erot)/k B = Trot and (Evibr)/kB ----- Tvib, respectively. In the case of the mean translational energy of the molecules in a flux the obvious transformation should be (Er)/2kB = Ttrans1, in view of the relation between "flux" energy and temperature in a volume at equilibrium (eq. (10)). Unfortunately, one still finds in the literature the expression E l k B = r t . . . . 1, probably a reminiscence of the transformation of the internal "Boltzm a n n " energies. This expression might be considered meaningful only in one particular case, when the velocity distribution is Maxwellian and E is taken to be 7lml)m p2 (see eq. (8)). One might say that vmp (the abscissa of the maximum) is an obvious feature of the velocity distribution of the molecules in the b e a m volume (i.e. measured with a mass spectrometer) and thus a value which is directly obtained in m a n y experiments. This is, however, not the case, because

G. Comsa, R. David / Dynamicalparameters of desorbing molecules

165

the experiments supply directly the time of flight (TOF) curve and not the velocity distribution. Last but not least E ~mUm p l 2 has no physical significance; it is not even the most probable energy of the molecules in the beam volume. =

4. Experimental Two types of experimental aspects have to be discussed in this section: the way of supplying atoms or molecules to the surface prior to desorption and experimental procedures to monitor the parameters of the desorbing flux.

4.1. The supply of molecules to the surface As already mentioned, it is impossible to investigate the desorbing molecules under true equilibrium conditions; in the presence of an equilibrium gas phase, there is no means whatsoever to distinguish between desorbing, reflected, diffracted or inelastically scattered molecules. The general aim is to make the molecules desorb from a quasi equilibrium adsorbate/surface situation in spite of the non-equilibrium necessary to detect and investigate the desorbing molecules. It is not straightforward to ascertain whether a given adsorbate/surface situation is a quasi equilibrium one or to quantify the departure from equilibrium and its consequences for the desorbing molecules. Additional experiments and assumptions are used, but the result is rarely trustworthy. In a number of cases, people have tried to demonstrate that the adsorbed molecules had "equilibrated" on the surface. This term allows a number of interpretations. For instance, the molecules are distributed on the various levels of the attractive potential as if the whole system were in equilibrium. This is, of course, rigorously not possible and we are back to the quasi equilibrium discussion. In other cases, a less stringent condition is imposed; equilibrated molecules have only to stay long enough on the surface, in order to "forget" their incident energy. This is often taken as the definition of adsorption, and then the condition is trivial: all adsorbed molecules are equilibrated. If, however, the definition of adsorption is less demanding, one comes to the embarassing situation that molecules desorbing under true equilibrium conditions might not have been previously equilibrated; the situation is embarassing because there is then no reason to seek an equilibration prior to desorption. If, on the contrary, the definition of adsorption is more demanding, we are in even more trouble, because we must accept that there are molecules which become "equilibrated" on the surface and then leave the surface through a non-desorption channel. There is also another way used by some people to state a posteriori whether the molecules were equilibrated on (or in equilibrium with) the surface. After having measured the angular, the velocity, a n d / o r the internal energy distri-

166

G. Comsa, R. David / Dynamical parameters of desorbing molecules

bution of desorbing molecules, they consider that the result of the measurement enables them to decide straightforwardly; if the desorbing molecules do not have a cosine, a T-Maxwell or a T-Boltzmann distribution it is concluded that the molecules were not equilibrated prior to desorption and vice versa. The conclusion is obviously unfounded because, as shown in the preceding section, even under true equilibrium conditions, the desorbing molecules need not follow any one of the above distributions. There is in fact no particular reason to seek a quasi equilibrium adsorbate/surface situation when investigating the dynamical parameters of desorption. This seemed important a number of years ago, in order to demonstrate experimentally that the desorbing molecules not only d'o not need to follow the three classical laws but actually do not follow them. This is, however, now clearly demonstrated for a number of different systems under more or less quasi equilibrium conditions. On the other hand, we are aware of the fact that we will never be able to make the demonstration in a direct experiment under rigorous equilibrium conditions; simply because we cannot distinguish the desorbing molecules under such conditions. What we feel now to be important is to define as exactly as possible the state of the adsorbed molecules prior to desorption. The measured distributions of the various parameters characterizing the desorbing molecules (which may or may not deviate from the classical laws) can then be used to uncover the detailed mechanism of the desorption from the respective adsorption state or even to define this state in a better way. Two different ways to supply the molecules to the surface are used in studies of desorption parameters, i.e. two ways to build up the adsorbate/surface situation prior to desorption: by permeation from the rear of the sample [18,20,21,25-29,34,35,46-50], and by adsorption from the gas phase [17,22,31-33,36-38]. The supply by permeation radically simplifies one of the experimental problems: provided the pumping speed in the sample chamber is large enough, the molecules leaving the front surface of the sample are exclusively desorbing molecules. In addition, the flux of desorbing molecules is continuous and, for a few systems, may reach substantial figures (e.g. for H z / P d - more than 1016 H 2 s -1 c m - 2 ) . This is the reason why this procedure originally used by Van Willigen [18] was applied in a large number of measurements. The supply by permeation is, however, limited to a relatively small number of systems: hydrogen/most metals, N J F e , O2/Ag. In addition, in most cases (except H z / P d , Nb, V), the temperature range is also rather narrow: low limit determined by a reasonable permeation flux, high limit by mechanical stability. A recent attempt to extend the temperature range by using thin films of low permeating material (e.g. Cu) on a mechanically stable, highly permeable substrate (e.g. Pd) was only partially successful due to metal-metal interdiffusion effects [50]. The sample mounting has, in the case of permeation supply, delicate technical aspects which are often underesti-

G, Comsa, R. Daoid / Dynamical parameters of desorbing molecules

2

5

3

167

6

9

1-/. 10

Fig, 5. Sample holder used in the case of permeation supply: (1) crystal sample, electron beam welded to (2) polycrystalline nickel setting and tube; (3) molybdenum shroud; (4) solder (gold); (5) molybdenum cage; (6) radiation shields; (7) tungsten filament; (8) nickel tube and flexible bellow for gas supply up to 1200 Torr; (9) tilt axis; (10) luminescence screen for ion focus control; (11) alignment spike for angular rotation around the polar angle axis (:t: 180 °) (from ref. [27]).

mated. The sample - in general a monocrystal - has to be welded tightly on a tube through which the permeation is substantially lower than through the sample. Besides usual cleaning procedures, the sample has to withstand rear pressures of the order of one bar and temperatures of about 1000 K without measurable geometrical changes, in particular without structural changes. A schematic of a sample holder together with the cross section.of the sample mounting design is presented in fig. 5 [27]. This mounting enabled the continuous use of one crystal for a couple of months before structural deterioration became apparent in LEED. When the adsorbates are supplied from the gas phase there are two ways to identify the desorbing molecules: (1) the desorbing molecules are a reaction product, which differs from any of the reaction participants, and (2) the molecules are adsorbed at low surface temperature, T~, the gas is pumped off and then the molecules are desorbed by temperature programmed desorption; the latter procedure has to be repeated until appropriate statistics are obtained. The requirements for sample mounting and processing do not differ from those common in other kind of desorption experiments. The reaction procedure can be performed continuously like the permeation one; the two procedures exhibit in addition more profound similarities. Indeed, the associative desorption of atoms having permeated through the bulk is obviously also a (recombination) reaction accompanied by desorption, In fact the same system was studied by both procedures: the angular distribution of the flux of H 2 desorbing from Cu upon permeation [21,49] and of HD desorbing upon isotopic exchange between H 2 and D 2 on a Cu surface [22]. The shape of the distributions obtained by means of the two procedures need not coincide. The distributions should in

168

G. Comsa, R. David / Dynamical parameters of desorbing molecules

fact depend upon the state of the hydrogen atoms prior to recombination; there is no a priori reason for this state to be the same whether the hydrogen atoms reach the surface region by permeation from the bulk or by dissociative adsorption from the gas phase. Interestingly enough, the distributions obtained in the experiments just quoted appear to coincide when the results, obtained with different methods in the same lab, are compared [21,22] and to be unlike when the permeation results obtained in different labs are considered [21,49]. This is probably a consequence of the strong dependence of the angular distribution of the flux on the actual geometrical and chemical state of the surface. The angular distributions of the desorbing flux of the system ( H 2 / N i ( l l l ) ) were studied also by both permeation [27] and temperature-programmed desorption [51] in different labs. The results are similar although they need not be, The choice of one of these procedures was initially dictated mostly by technical requirements: the possibility of obtaining reasonable statistics, while the surface is in a reproducible state. The problem is not trivial, if we compare it with a usual total desorption flux measurement. The measurement of the angular distribution is a double differential flux measurement, the measurement of the velocity distribution of the desorbing flux in a given solid angle is a triple differential measurement, etc.; the signal is correspondingly smaller. Fortunately, as the measurement procedures improve, the choice depends more and more on the nature of the information one is looking for.

4.2. The measurement of the parameters of the desorbing flux Let us start with the apparently simplest parameter, the angular dependency of the desorbing flux density f(O, q0). As schematically shown in fig. lb, besides the detector entrance opening at least one more aperture is needed for defining a beam of molecules desorbing in a certain solid angle. The molecules entering the detector desorb from a limited area of the sample: the sample area "seen" from the detector opening through the aperture. The area obviously increases with increasing polar angle ~. The flux intensity measured with the detector has to be corrected for this variation. In a first approximation the area increases as cos-xO. The actual dependency is somewhat different due to the finite dimensions of the sample and of the apertures [52]. As already mentioned the ionization of the molecules and the subsequent collection of the ions with (mass spectrometer) or without (ion gauge) mass selection is the most widespread procedure to measure the intensity of the desorbing flux. This is due to both simplicity and sensitivity. It was also shown in the preceding section that if the experimental arrangement is as shown in fig. lb, i.e. if the beam simply passes through the ionization region, the number of created ions will be proportional to the number density in the beam volume and not to the density of the flux. Only the latter actually characterizes the

G. Comsa, R. DavM / Dynamicalparameters of desorbing molecules

169

angle-resolved desorption flux. Two procedures were used up to now to measure directly the density of the flux. The starting point of both procedures is the fact just mentioned that the number of ions created in the ionizer is proportional to the number density of molecules. The idea is to construct a volume in which (or at least in a major part of which) the number density is proportional to the flux density of the beam entering the volume. The condition to be met is to randomize by wall collisions the strongly directional beam which enters the volume; the molecules which leave the volume have to originate from an almost isotropic distribution. In a stationary regime the number of molecules entering equals the number of those leaving the volume:

fA =Q, where f is the flux density of the beam molecules impinging on the area A of the volume orifice and Q the number of molecules leaving the volume per unit time. We assume for the moment that there are no molecule sources or sinks inside the volume and that the gas pressure in the volume is much larger than outside. As a consequence of the "isotropy" assumption the number of molecules leaving the volume is proportional to the number density n in the volume. Accordingly,

f= an/a.

(11)

Thus, if the ionizer is placed in the volume outside the " b e a m line" the number of ions created will be proportional to the flux density f. In the oldest of the two procedures the volume has only one orifice through which the beam molecules enter the volume and simultaneously the volume molecules leave it by effusion. Remembering eqs. (4) and (8), eq. (11) becomes:

f= ¼nS.

(11')

If the ionization and ion collection efficiency are known, eq. (11') gives the flux density in absolute numbers. By mounting instead of the simple orifice a long tube with the same cross section A, the sensitivity of the device can be substantially enhanced. Indeed, while the flow-in of a parallel beam is in principle not influenced by the presence of the tube, the low conductance of the long tube strongly decreases the flux of the molecules effusing from the volume. As a consequence, the stationary situation is reached only for much higher number densities in the volume at the same beam flux density. For instance, in the case of a very long tube (L/r >> 100) eq. (11') becomes

f= ~(r/L)nS.

(11")

Unfortunately, this - in principle - very efficient procedure is heavily handicapped by a practical problem: the ionizer and its surroundings are always potential sources of gas; the corresponding assumption made above does not

170

G. Comsa, R. Daoid / Dynamical parameters of desorbing molecules

10N PUMP 30 [/s

MAIN CHAMBER

1 W N IDOW~~]

COLLIMATOR

I I

Q3

SAMPLE

Q2 . . . . . . . . . al _:~ff~./-

IaETTERI

I

I ,I

ION GAUGE Fig. 6. "Randomizing volume" detector; the flux desorbing in a well defined solid angle (collimators a 1 and a 4) is randomized by wall collisions before entering the ion gauge or the pump (from ref. [56]).

hold. Indeed, the (in general hot) electron source, the various electrodes bombarded by electrons or ions continuously release a non-negligible gas quantity. The released gas is neither constant nor does it depend in a predictable manner on the gas density in the volume. This and the difficulty of outgassing the gauge properly through the low conductance orifice make the procedure largely unreliable. An attempt to circumvent this difficulty was tried by replacing the ionizing detector by a completely inert detector: a gas friction gauge [53,54]. The friction gauge, indeed, does not release any gas, but its sensitivity restrains the working range of the procedure to high beam intensities rarely encountered in desorption experiments. In the second procedure fi.rst described by Kobayashi et al. [55] and further developed by Cosser et al. [52] and Stein~ck et al. [56] the randomizing volume is continuously evacuated during the measurement through a second large port (fig. 6). In principle eq. (11) still holds, whereby (x stands for the pumping speed of the pump and n for the density increase - with respect to the base pressure - due to the instreaming beam flux fA. The conductance of the beam entrance orifice being orders of magnitude smaller than the conductance of the evacuating port, this increase is relatively small (e.g. backgroundto-signal ratio 30 to 1 [56]). This requires a very careful stabilization of the pumping speed and of the volume wall temperature. The relatively small

G. Comsa, R. David/Dynamicalparameters of desorbing molecules

171

_i chopper

channeltron

detector chamber

chopper chamber

sample chamber

Fig. 7. Schematic of a time-of-flight spectrometer for desorption analysis.

pressure variations during measurements allow, however, reliable detector performance. In addition, due to the large pumping speed, the gauge can be outgassed properly. The angle resolved velocity distribution of desorbing flux density, f(t~, q~, v) has been measured almost exclusively by time-of-flight (TOF) techniques (see, e.g. fig. 7). By means of appropriate apertures the molecule desorbing in a small solid angle centered around #, ~ are skimmed out. The resulting molecular beam is cut in short packets by means of a mechanical chopper. At the end of a flight path of L = 10-100 cm the arrival time t (t = 0 is the starting time of each packet at the chopper) of individual molecules is measured and their velocity deduced, v = L/t. The detection of the molecules (arrival time determination) is performed by electron impact ionization, subsequent individual ion collection and pulse versus t counting. It is obviously necessary that the molecules fly directly through the ionizer and that they do not return after wall collisions. The v-1 dependency of the ionization probability causes in this case no complications because the velocity of each molecule is known and can be corrected automatically. The flight time between ionization and detection must be taken into account but this is merely a constant offset for all ions regardless of the velocity of their parent atoms. The time resolution (and thus the velocity resolution) is determined by the chopper gate time and by the ratio l/L between effective ionizer length and flight path length. When conventional choppers are used, neither the gate nor the ratio can be reduced without a corresponding reduction of the signal effectively

172

G. Comsa, R. David / Dynamical parameters of desorbing molecules

measured. The result is as usual a compromise. The difficulty of the problem is illustrated by a numerical example: in a "good" angle resolved experiment (1 ° in polar angle), fig. 7, less than one ion is counted out of 1012 molecules desorbed from the sample area "seen" by the ionizer ( - 1 mm 2) [27]. The very low ionization probability ( - 1 0 - 6 for a path length of a few millimeters in the ionizer) is the main reducing factor. A substantial enhancement of the ionization probability would involve the presence of a space charge within the ionizer; the residence time of the ions in the ionizer would become non-negligible and out of control. The numerical example just given was obtained with a conventional chopper. In this type of chopper, the chopper gate is opened only after the "slowest" molecules of the preceding packet have reached the ionizer. This is in fact particularly unfavorable in the case of broad velocity distributions like those which may be expected in desorption experiments. For instance, in the experiment shown in fig. 7 the interval between two chopper gate openings had to be Tmin= 2770/~s in order to allow more than 99.994% of the D 2 molecules with a 1000 K Maxwellian distribution ( t m p - 220 /~s) to reach the ionizer before the next opening. The chopper gate was kept open 100 /~s. The compromise between chopper resolution (only about ½/mp) and transmission (less than 4%) was indeed rather poor. The measured TOF distribution is obviously severly affected by the convolution with the 100/~s gate function. In principle the distribution can be deconvoluted. This involves, however, derivation operations which are reliable only in the case of a very good statistics. In view of the discussion above, this requires unrealistic measuring times. A limited solution of the problem was proposed by Moran [57] and described in detail by Kenney et al. [58]: the moments of the distribution are derived by a deconvolution procedure involving only integration operations. The first three moments of the velocity distribution (flux, ~f, and V~m~)can be obtained with a reasonable accuracy even from rather noisy TOF distributions. This procedure was used successfully in a number of cases, leading to a substantial extension of our knowledge on desorption (see e.g. refs. [25-27]). However, detailed features of the TOF distribution itself which might have been smoothed out by the 100/~s gate convolution could not be uncovered in this way. The investigation of such detailed features became possible by the use of pseudorandom choppers. The chopper blade bears, instead of one slot in the conventional case, 2 t-1 slots with l integer. The equal width slots are separated by 2 t - l - 1 bars of same width and are distributed in a pseudorandom sequence. In fig. 8 a chopper blade with a double sequence of 255 elements each, i.e. l = 8, is shown. The arrival times at the ionizer are registered in a multichannel analyzer running synchroneously with the chopper blade. The TOF distribution is obtained by cross-correlation deconvolution, which involves only multiplication operations (see for details ref. [59]). The resolution corresponds to the width of one slot. Accordingly, for the same resolution the

G. Comsa, R. David / Dynamicalparameters of desorbing molecules

173

Fig. 8. Copper-beryllium pseudorandom chopper blade with two identical sequences, each consisting of 255 elements. The disc is mounted to one end of a ferromagnetic stainless steel shaft for magnetic suspension and drive (from ref. [59]).

transmission is 2 l-1 times larger than in the case of a conventional chopper, whereas the non-modulated background remains in principle unchanged. The essential feature of the pseudorandom procedure is that transmission and resolution are uncoupled. The effective transmission is always 25% while the resolution can be increased by increasing l; there are only mechanical and electronical limitations. These can be always pushed further and further. In special cases other T O F procedures can be used. For instance, He adsorbed on a thin nickel-chrome heater film was flash desorbed by a very short heat pulse ( - 100 ns); after a flight path of 1.1 mm, the arrival time on the surface of a bolometer was monitored as a function of polar angle [60]. Let us now outline finally a few procedures for the measurement of the internal energy distribution of desorbing molecules. This field has expanded remarkably in the last few years. The first procedure applied was the electronbeam-induced fluorescence; the vibrational [34] and then both the vibrational, Tv, and the rotational, TR, temperature [35] of N 2 associatively desorbing from poly-Fe surfaces were measured. The schematic diagram of the experimental system is shown in fig. 9. The I'42 molecules desorbing from the Fe membrane interact with a 2100 eV electron beam. Nitrogen molecules in the

174

G. Comsa, R. David / Dynamical parameters of desorbing molecules

I

N2 BEAM

TO PUMPS ~ FLUORESCENCE ELECTRON BEAM tN"~ 7o~ [~,1"-"-

t/4 METER MONOCHROMATOR

D

_

I ~,, IB--I-~, ME~ANE C ~ I ~

PHOTON COUNTER

I RECORDER

HERMeCOOPLE

Fig. 9. Electron-beam-induced fluorescence apparatus used for the study of vibrational and rotational temperatures of N 2 desorbing associatively from Fe (from ref. [34]).

electronic ground state, N 2 X 12 g+, are ionized by electron impact to the N f B 2"~u+ state. This state fluoresces to the N f X 2,~g+ state. The fluorescence emission is collected, focussed, than dispersed by a monochromator and counted as individual photon events with a photomultiplier. The excitation and emission process being well understood, the N~ fluorescence spectrum can be used to assign a vibrational temperature to the nitrogen molecules prior to electron excitation. Similarly, rotational temperatures can be calculated from the rotational spectrum. This technique has been used previously as an internal state diagnostic for rarefied gas flow (see ref. [35] for details of its application to desorbing molecules at low pressures). More straightforward, because the excitation process can easily be made highly selective, is the laser excited fluorescence (LEF). A tunable laser beam is used to probe the density of the desorbing molecules in various rotational levels (J") of the electronic ground state. For instance, in the case of N O / R u ( 0 0 1 ) (see for details ref. [61]) a laser beam tunable about the origin of the _ A ~ + ~ X 2 / ' / 1 / 2 , 3/2 transition at 44140.78 cm -1 was used. The N O molecules are desorbed from the Ru(001) surface by TPD. During one T P D run the laser is tuned to excite a specific J ' ~ J " transition. Because only one rotational level is probed at a time, it is sufficient to simply count the photons of the fluorescence emission by means of a photomultiplier. Fluctuations of the laser power, frequency, and bandwidth are accounted for by monitoring simultaneously the LEF signal from a reference cell containing N O at known concentration and temperature. The procedure is repeated for each J " level in random sequence, until reasonable statistics for each level are obtained. As a result the rotational population distribution is obtained. It gives the straightforward answer whether the distribution is Boltzmann or not; in the affirma-

G. Comsa, R. David /Dynamicalparameters of desorbing molecules

175

tive Trot is obtained, if not at least a mean internal energy and thus an effective temperature Trelf is calculated. Note that this distribution corresponds to the desorbed NO molecules present in a volume in front of the surface. The distribution over the rotational levels of the desorbing flux is in principle different, unless the velocity distribution is not correlated with the internal state of the molecules. There is obviously no reason for the last assumption to be true. The use of LEF for determining J " populations of H 2 is technically more difficult. The lowest lying electronic states of H2 being in deep vacuum ultraviolet their selective excitation requires very short wavelength radiation and is rather inefficient. This, combined with the inefficient detection of the pumped molecules by emission fluorescence is a challenge for practicable measurements of coUisionally unrelaxed internal state distributions. In spite of these difficulties, Zacharias and David have recently shown for H 2 desorbing from Pd that such measurements are feasible with reasonable statistics [62]. They used single photon excitation (h = 106 nm obtained by frequency tripling) in the B 1~ + (v' = 3) ~ X 12;g (v" = 0) Lyman band around ?~= 106 nm. Zare and coworkers focussed their attention on the improvement of the detection of selectively excited molecules. They succeeded in making the detection efficiency nearly unity [63]; accordingly the overall sensitivity of the procedure is drastically increased. The rovibrational state distributions are determined via a so called 2 + 1 resonance-enhanced multiphoton ionization [64]. The procedure is as follows (see for details refs. [63,64]): the desorbing H 2 (or D2) molecules are selectively excited E, F 1z~g+ ~ X 1~ g+, by two-photon excitation; the excited molecules are then ionized by an efficient ( - u n i t y ) one-photon ionization H~- X 2Zg÷ + ~ H 2 X 1Z g+, and finally the ions are collected with an efficiency approaching unity. Like in the LEF procedure, the detection of the pumped molecules (here one photon ionization followed by ion collection) has not to be state selective because the resonant (here two-photon) excitation is already state selective being tuned on an individual (v", J " ) level in the ground state. Unlike the L E F procedure, this one allows an almost ideal detection of the pumped molecules. These very recent developments led to the first measurement of the rotational and vibrational distribution of desorbing H 2 and D 2 [62,64]. This is particularly exciting, because just for these molecules the largest amount of TOF data was collected so far and thus an almost complete set of desorption parameters for a few systems will be available soon. In principle the most straightforward way to study the internal distribution of desorbing molecules is to monitor directly the radiation emitted by these molecules after desorption. Unfortunately, this emission is in most cases too weak for a reasonable detection. There is only a couple of systems for which such measurements are published: CO2 desorbing from a Pt surface as the product of the CO oxidation [36,65,66] and CO desorbing upon C oxidation

176

G. Comsa, R. David / Dynamical parameters of desorbing molecules'

[67]. The first measurements were performed and published almost simultaneously by Bernasek and Leone [65] and by Mantell et al. [36]; the method is called infrared chemiluminescence [65]. In one case the emission was detected by radiometry with filters; the desorption took place in the presence of about 1 mbar of Ar, i.e. the desorbing CO 2 collided with Ar atoms [65]. In the other case the emission was analyzed by Fourier transform infrared spectrometry under essentially collision-free conditions [36]. A decisive step towards the final goal of fully resolving the dynamical parameters of the desorbing molecules was achieved a couple of years ago by King and Cavanagh [37,68]. They reported the measurement of the rotational state selected velocity distribution of NO molecules desorbing from Ru(001). They used the LEF procedure as described above and analyzed the Doppler profile of the excitation curve. From the width of the Doppler profile they deduced the tangential translational mean energy of the desorbing molecules which were excited by the laser beam, i.e. which were all in a given rotational state. Such measurements are of particular importance for the understanding of the energetics of the desorption mechanism; they show whether there is an "individual" correlation between translational and internal energy in the desorbing flux, i.e. whether desorbing molecules with excess (or deficit) translational energy have an excess or deficit of internal energy. The dynamical parameters of the desorbing flux will be considered as fully resolved if the velocity distribution of the flux of molecules desorbing in a small solid angle (~, ~p) with a well defined internal energy (v", J") is measured or, of course, alternatively the internal energy distribution of the flux desorbing in a small solid angle with a given velocity between v and v + d v, or the further permutations. This represents a quadruple differential measurement, and accordingly the signal-to-noise problems are severe. However, the recent progress shows that the goal will be reached before long.

5. Results

A selection of the experimental results obtained so far will be presented here. The selection criterion will be primarily: the ability to illustrate basic trends in the behavior of the desorption parameters. Of course, the most general trend emerging from the experiments is the deviation of the flux distribution versus angle, velocity, and internal energy from the Knudsen, T~-Maxwell and Ts-Boltzmann laws, respectively.

5.1. Desorption flux versus desorption angles Let us start with the historical result of Van Willigen [18] who first showed experimentally that the desorption flux of associatively desorbing H 2 versus

G. Comsa, R. David / Dynamicalparameters of desorbing molecules

\

(

177

I

Fig. 10. Angular distribution of H z desorbed from Pd, Fe and Ni at 900 K. A and B are theoretical curves corresponding to the Van Willigen model (from ref. {181). polar angle # strongly deviates from the cos v%Knudsen law (fig. 10). Hydrogen atoms were supplied by permeation from the rear of the probes. Desorption patterns from poly-Pd, poly-Fe and poly-Ni are shown. No details on surface preparation and cleanliness were reported. As mentioned in section 3, the polar angle dependencies of the desorbing flux measured so far are described well by cos~O. This is surprising because the expression cosnt~ lacks any physical background. There are, however, two very careful measurements which are not fitted by a simple cos%~ function. They are shown in figs. 11 and 12. In fig. 11 the data of Cosser et al. [52] obtained for N 2 desorbing from a specially prepared W(310) surface are plotted; upon N 2 adsorption on the clean surface, the surface was exposed to - 7 × 10 -5 m b a r s 02 at 300 K. It is believed that before desorption nitrogen diffuses through the oxide film. The polar plot suggests that the distribution "is composed of two components, a cosine law component (solid line) and a component (strongly) peaked around the surface normal" [52]. The other example is taken from a recent paper by Segner et al. [33]. It represents the angular distribution of CO 2 desorbing as the product of the oxidation of CO incident on a P t ( l l l ) surface precovered with oxygen (fig. 12). The cosS0 dependency fits the data only up to 0 = 30 °, however, an expression of the type lco2(Va) = a cos O + (1 - a ) cosVv~,

(12)

fits the data in the whole range by taking a = 0.57 and a = 0.29 for oxygen precoverage 0o = 0.05 and 0o = 0.25, respectively. Both results are reminiscent

178

G. Comsa, R. Dauid / Dynamical parameters of desorbing molecules

0°

7"5' /°, / ' I "d ' ,

15° ~ 22.50 ,, ,

\

,,,

-7,5° \

~

\'t

- 1 50

/ _22.50

, /',j /

Ic°I I

05

.

0.05

"i",,~.~,'~0,=025 -20

0

20 &O 60 80 o Yr

Fig. 11. Angle resolved desorption intensities of Ne/W(310 ) after exposing the N z saturated crystal to - 7 x 10-5 mbar s oxygen at 300 K (from ref. [52]). Fig. 12. Angular distribution of the CO2 desorbing flux as the product of the oxidation of CO incident on a Pt(lll) surface precovered with oxygen: (e) 0o = 0.05; (x) 0o = 0.25. Solid lines correspond to eq. (12) with a = 0.57 and 0.29 for 0o = 0.05 and 0.25, respectively, cosS~ is plotted as dashed line for comparison (from ref. [33]).

of earlier evidence from T O F data showing that the desorbing process takes place through two parallel channels [29]: one "classical" (obeying K n u d s e n and Maxwell laws) and one characterized by substantial deviations from the classical laws (see below this and next section). Segner et al. succeeded in fitting all their C O 2 desorption data taken under very different surface conditions simply by using eq. (12) with only one free parameter, a. T h e y f o u n d characteristic dependencies of the best fit a-values on O and C O precoverage, surface defects, surface temperature, and "subsurface oxide". F r o m the analysis of these findings Segner et al. obtained interesting information on C O oxidation and on the energy transfer between the CO 2 reaction p r o d u c t and the surface. These results are a striking illustration for the a m o u n t of information contained even in the angular distribution of the desorbing flux, the "simplest" of all desorption parameters. Interestingly enough, they confirm further, that the flux c o m p o n e n t deviating f r o m cos 0 is well described by cos"~. The influence of surface coverage (in particular of " n a t u r a l " impurities like C and S) on the desorption of hydrogen from various surfaces has been

G. Comsa, R. David / Dynamicalparameters of desorbing molecules

179

[E 5

~

f

cr

~4-z

/~

m

if_

{,U,

x

iIJ

0 0.2 0.4 0.6 0.8 1.0 8s,FRACTIONAL COVERAGE OF S ON Ni

Fig. 13. Representativen (cos"0 fit) versus sulphurcoverageplot for H 2 desorptionfrom Ni(ll0), Ni(lll) and poly-Ni(from ref. [46]).

investigated since the earliest studies of the angular distribution of the flux. The results are by far less detailed than the recent ones on CO 2 desorption by Segner et al. [33] and in part apparently contradictory. The first systematic study of n (simple cos"~ plots of desorption flux) versus sulphur coverage on various Ni surfaces (Ni(110), Ni(111) and poly-Ni) was performed by Bradley et al. [46] (fig. 13). The plot shows that for clean and for fully sulphur covered surfaces the distribution follows the Knudsen law, i.e. n = 1 while at half coverage (0 s -- 0.5 is the natural limit for sulphur segregating from Ni bulk) it attains the maximum deviation from the Knudsen law with n ~ 4. This kind of behavior is certainly not general and even in cases when it applies some aspects have to be clarified. Unfortunately, being the only plot of this type yet published it is considered to be widely applicable; this is why we have to discuss it here in some detail. Bradley et al. [46] have plotted the results for Ni(110) (see fig. 13) and they state clearly that "Essentially identical results were obtained with Ni(111) and poly-Ni membranes". Experiments performed since that time demonstrate that at least for Ni(111) the behavior suggested in fig. 13 is certainly incorrect. Comsa et al. [27] have shown that for clean Ni(111) (8 s < 0.02) the desorption flux versus polar angle plot lies between cos3v~ and cosS~ (somewhat nearer to cos3v~) and thus deviates from the Knudsen law beyond any margin of error. For the "sulphur covered" N i ( l l l ) surface (8 s < 0.3) the distribution was located between the same two curves, this time somewhat nearer to cosSv~. Even this very slight broadening of the plot when going from the "sulphur covered" to the clean N i ( l l l ) surface had a trivial geometrical origin: detailed phase contrast and interference images of the surfaces have shown that on the clean surface, due to the extended cleaning procedures, domains inclined up to 10°-15 ° are present. Two investigations performed with different techniques in different laboratories have confirmed

180

G. Comsa, R. David / Dynamical parameters of desorbing molecules

recently that H 2 desorbing from clean Ni(111) surfaces are far from being Knudsen-like; Steinr~ck et al. [69] could describe their data using a unique cosn0 fit with n = 4.5-4.7, while Robota et al. [70] found that their data lie between cos40 and cos6~. The conclusion for a clean Ni(111) surface is that n is certainly not 1 as claimed in fig. 13 and that no significant increase with increasing Os could be observed in carefully done experiments. The situation is, however, different for Ni(ll0); in this case the behavior shown in fig. 13 up to 0s = 0.5 is confirmed by recent experiments; for a clean Ni(110) surface Steinr~ck et al. [69] found 1.15 < n < 1.25 and Robota et al. [70] n -- 1, while for a sulphur covered (0.2 < 0s < 0.45) N i ( l l 0 ) surface Schumacher [71] obtained much sharper distributions ranging between cos2Sv~ and cos6~q. The desorption behavior of two low index faces of the same crystal being so different demonstrates clearly that the dependency of n o n 0impurity shown in fig. 13 is certainly not general, and we have to expect, of course, different behavior for different substrates. This was actually found: the desorption from Pd(100) behaves, from this point of view, as in the Ni(110) case [29], at least up to 0 s ~ 0.5, i.e. n increases from n = 1 with increasing 0s; while the desorption from Cu(100) and C u ( l l l ) behaves similarly to the desorption from Ni(111) [49], i.e. n -- 8 already for the clean surface and does not depend substantially on sulphur coverage. Let us infer cautiously some tendencies from the data discussed so far. The polar angle distribution of the flux may be characterized by a cosn~ dependency or more precisely by a linear combination of two distributions with n = 1 and n > 1, respectively. Even different clean facets of the same crystal may behave differently. The presence of impurities (S, C) lead to a substantial increase in n, if n = 1 f o r 0impurity = 0; otherwise the impurities seem to play a minor role. We may even go somewhat further if we consider in some detail the difference in desorption behavior between Ni(110) and Ni(111). The "classical" nearly cos v~ behavior of clean Ni(11.0) had to be expected. Indeed, the incident angle integrated sticking probability of H 2 o n clean Ni(110) is s o = 0.96 [72]. Accordingly, the sticking probability versus incident angles s0(0i) should be almost constant. F r o m detailed balance arguments it is obvious that at equilibrium the desorbing flux should be almost coslv~ (i.e. n = 1). When the N i ( l l 0 ) surface is covered with sulphur, s o becomes << 1 and thus may depend on Oi, and thus n may also deviate from unity. On the other hand, the angle-integrated sticking probability of H 2 o n clean N i ( l l l ) was found to be only s o --0.05 [72]; thus the sticking probability might be incident angle dependent even for a clean surface. This was found, indeed, by Steinrgck et al. [51] to be s 0 ( 0 i ) = cos350i . They found also that the angular distribution of the desorbing H 2 flux from the same surface is cos4"Sv~ [51,69]. This is an impressive confirmation of the applicability of detailed balance arguments under quasi equilibrium conditions. It shows also that in this case the angular

G. Comsa, R. David / Dynamical parameters of desorbing molecules

181

distribution of the flux is not particularly sensitive to some of the parameters characterizing the equilibrium situation: when measuring So.(Oi) the surface temperature was Ts = 190 K and the incident beam was T = 300 K Maxwellian, while when measuring the desorption flux the surface temperature was substantially higher ( Ts = 395 K at the location of the fl2-peak); the velocity distribution in the desorbing flux corresponded probably to an even much higher temperature (see below). This lack of sensitivity of the angular distribution of the flux cannot be generalized for other parameters; we have just seen that the angular distribution of the flux from N i ( l l l ) seems to be in a first approximation insensitive even with respect to the presence of impurities, while the behavior of the N i ( l l 0 ) appears to be just opposite. We return for a moment to fig. 13. We have discussed so far the left side of the curve (8 s < 0.5) and found confirmation for this behavior in the case of N i ( l l 0 ) and Pd(100), but infirmation in the case of N i ( l l l ) , Cu(100) and C u ( l ] l ) . For the right side of the curve (8 s > 0.5) there are almost no data to make a meaningful comparison. In order to avoid confusion, it is necessary to mention here the peculiar definition of 8s in the range > 0.5 used by Bradley et al. [46], 8s = 1 - (7.15 lS/1Ni) -1, where I s and INi are the Auger peak intensities at 150 and 62 eV, respectively. This means that 0s = 1 does not correspond to one monolayer of sulphur, but to a significantly thicker sulphur layer corresponding to I S / I N i --~ o0. After seeing that the angular distribution of the desorbing flux may depend strongly on the surface orientation ( N i ( l l l ) versus Ni(ll0)), we have to ask whether there is also an azimuthal dependence, i.e. whether the shape of the polar angle distribution varies with the azimuth q~. Unfortunately, only few reliable data on cp-dependency are available so far. They show that the dependency, if at all present, is weak, mostly within the limit of the experimental accuracy. For instance, Steinrtick et al. [69] fitted the polar angle dependency of the H 2 flux desorbing from the fl2-state of clean N i ( l l l ) in the [211] (and [21i]) azimuth with cos4'7v~ and in the [0ill (and [011]) azimuth with cos4Sv~. Even in the case of the asymmetric (clean) N i ( l l 0 ) surface, the difference found is very small, cos1'15~ and cos1'25~, for the [110] and [001] azimuths, respectively [69]. The authors conclude that within the margin of error, the crystal symmetry does not show up. Schumacher [71] reached a similar conclusion, from measurements on sulphur covered Ni(ll0). Even the polar angular dependency of the D 2 flux desorbing from the stepped N i [ 9 ( l l l ) × (111)] surface does not show particularly exciting features when compared with the desorption from a N i ( l l ] ) surface. Indeed, Schumacher [71] measured the polar angle dependency of the desorbing D 2 flux in the range - 80 ° < ~ < + 80 ° of the azimuthal direction normal to the step rows. The dependency could be brought in coincidence with the dependency from the N i ( l l l ) surface provided the origin t~ -- 0 ° on the stepped surface was taken midway between the perpendicular directions to the (111) terraces and to the macroscopic plane of the stepped surface.

182

G. Comsa, R. David / Dynamical parameters of desorbing molecules

Let us finish the survey on the angular distribution of the desorbing flux, with an example demonstrating the influence of the reaction preceding desorption. Matsushima [73,74] examined the polar angle distribution of CO 2 desorbing from P t ( l l l ) . The experiments were performed by angle resolved thermal programmed desorption. Matsushima found three different distributions, which he described, as usual, by cosn0: for the desorption of physisorbed CO 2, n = 1; in the other two cases CO 2, desorbed by the recombination of preadsorbed CO and oxygen, exhibited a much more peaked distribution. CO 2 desorbing around 160 K was associated with the interaction between adsorbed O22- and CO; the corresponding angular distribution was n = 16 + 3. While CO 2 desorbing around 260 K, and associated with the recombination of adsorbed O and CO, had a broader, but still strongly peaked, angular distribution: n = 9 _+ 1. The remarkable shape differences between the angular distributions of CO 2 desorbing from the same surface suggest again [33] that the recombination product CO 2 possesses excess energy compared to physisorbed CO2 and that this energy is only partially transfered to the surface prior to desorption. Such data may contribute substantially to the understanding of both mechanisms, reaction and desorption.

5.2. Desorption flux versus velocity and desorption angles Let us start here again with a historical experiment; the first evidence for the existence of deviations from the Ts-Maxwellian distribution of the desorbing flux. The T O F data for D 2 desorbing in the normal direction from the poly-Ni surface (~ = 0 °) at T~ = 1073 K presented by Stickney's group [25,58] are shown in fig. 14. For comparison a T~ = 1073 Maxwellian distribution folded with the chopper gate function ("open" time: r = 114 #s) is also shown. It is obvious that the desorbing molecules are substantially hotter than expected for a Ts-Maxwellian distribution. The evidence that also the velocity distribution of desorbing molecules deviates from a "classical" law (T~-Maxwell) was probably even more shocking than deviations from the cosine law. Indeed, the latter might be ascribed to some simple geometrical constraints (see e.g. ref. [75]); deviations from the Ts-Maxwell distribution, however, certainly root deeper in the microscopic mechanism of the desorption process. The TOF spectrum in fig. 14 is heavily folded by the relative long "open" time of the chopper: • = 114 ~s compared with the most probable flight time of the D 2 molecules trap = 170 /~s. AS a consequence, any detailed feature which might be present in the distribution would have been smeared out. As already mentioned in section 4.1 a direct deconvolution of the T O F distribution is not possible unless data with a very good statistics are gathered; this, however, requires unreasonable measuring times. Following a procedure proposed by Moran [57] and described in detail by Kenney et al. [58], Dabiri et al. [25] have partially solved the problem; they deconvoluted the first three

G. Comsa,R. Dauid / Dynamicalparameters of desorbingmolecules

Z-.-- . : - L -~ -] - ~ 2 ~ -~-i4 : t . : l ~ ~

....L ~ £ ,

I

;

! [:4.

::f::i, :: '

,

.

' . i , ,'-r-q " 1 - : - ~

',

r

- :u

. I

P t-

183

7-r ..... _

_ . ..!_=_.Z...... E. L_Z I ]

'

iy~:

:-I ~I ~

;

....

:

-~Tq

-I

:

~rotot~tj

!

.

.1~

. . . . . ~

"-4~

.........

t TOF

"

_._i-. ....

Fig. 14. Time-of-flight plot of D 2 desorbing in normal direction from poly-Ni at T~= 1073 K. Dashed line: TOF plot of a 1073 K Maxwellian distribution folded with the actual gate function (114 ~s). The solid line is drawn to guide the eye (from ref. [25]). m o m e n t s of the d i s t r i b u t i o n . F r o m these m o m e n t s , they o b t a i n e d the flux, the m e a n energy ( E ) a n d the speed ratio S of the d i s t r i b u t i o n . In spite of b e i n g o n l y a v e r a g e d properties, i.e. i g n o r i n g the details of the d i s t r i b u t i o n , these p r o p e r t i e s were very useful in the investigations which followed. T h e m e a n energy a n d the speed r a t i o d a t a are given here in units which m a k e d e v i a t i o n s f r o m the T c M a x w e l l d i s t r i b u t i o n easily recognizable. T h e m e a n energy is expressed in 2 k B units, i.e. b y a " t e m p e r a t u r e " T = ~ E ) / 2 k B ; the n o r m a l i z e d speed ratio, a m e a s u r e of the d i s t r i b u t i o n width, is d e f i n e d as S = (32/9~r - 1) -1/'2 [(V[ms)2/(~f)

2 - 1] 1/2.

A T~-Maxwell d i s t r i b u t i o n is c h a r a c t e r i z e d b y T(E > = T~ a n d S = 1, A c c o r d i n g to these definitions the T O F s p e c t r u m in fig. 14 o b t a i n e d at T~ = 1073 K is c h a r a c t e r i z e d b y T = 1560 _+ 120 K a n d S = 0.95 + 0.07. Thus, the s h a p e of the d i s t r i b u t i o n is M a x w e l l i a n b u t c o r r e s p o n d i n g to a t e m p e r a t u r e 45% larger t h a n the t e m p e r a t u r e of the p o l y - N i surface. These values are s o m e w h a t in d i s a g r e e m e n t with the p r e d i c t i o n s o f the o n e - d i m e n sional b a r r i e r m o d e l of V a n Willigen [18]. I n d e e d , using a n g u l a r d i s t r i b u t i o n flux d a t a o b t a i n e d b y the same a u t h o r s for the same system, the p r e d i c t i o n was: T = 1860 K a n d S = 0.475 for ~ = 0 °. The d i s a g r e e m e n t is p a r t i c u l a r l y e v i d e n t for the speed r a t i o (i.e. for the w i d t h of the distribution). E x p e r i m e n t a l

G. Comsa, R. David / Dynamicalparameters of desorbing molecules

184 2000-

"~\ " 0

o

o o

8

o

•

0

\0

0

\\ \I

", • \ \ \ o \ \

1500

',5 \

(%1

\

W v IL

TS=II43K

\

o \

x o

1000

700

i'o 2'o 3'o 4'o s'o

7'o 8'o g'o

desorption angle .~ [degree]

Fig. 15. Angular dependencies of the mean energy of the D 2 desorbing flux are shown for the sulphur covered (O) and sulphur free (O) Ni(lll) surface. For comparison the dependence for a polycrystalline surface (dashed) and for a T~-Maxwelliandistribution (dash-dotted) (from refs. [26,27]).

distribution widths are often broader than theoretical predictions so that further experiments seemed to be necessary to decide the issue. The Van Willigen model predicts a strong increase of T with polar angle (T should become infinite for 0 ~ 90 °) while S should decrease to zero for ~ 90 °. This was a good test, but the difficulty in gathering decent statistics for the T O F data strongly increases with the polar desorption angle (cos45~ dependence for Ni(111)). Only by substantial improvement of the measuring procedure, could Comsa et al. obtain Dz-TOF spectra versus 0 for poly-Ni [26] and for Ni(111) [27]. The corresponding T values for all three cases decrease strongly with ~ increasing above 50 °, while S increases from values around 0.8 at ~ = 0 ° to 1.2 at 0 = 80 °. This is exactly opposite to the model predictions. In order to get a better feeling for the shape of the T O F spectra from which the "deconvoluted" T and S values in figs. 15 and 16

G. Comsa, R. David / Dynamical parameters of desorbing molecules

185

O0 o

.o 1.25

i

~ 1.1~ 1.(?-

.

I

"~ a) 0.9- o. . . . . . . . . . N E

i

0.8-

~ 0.7 c

.

.

.

.

f

"i~ |o

;

' 30 ' 2o 50. . 60 . . 70 80 9'0 20 desorption angle ~ [degree]

Fig. 16. Angular dependencies of the speed ratio of the desorbing D 2 flux are shown for the sulphur covered (e) and sulphur free (O) Ni(111) surfaces. For comparison the dependence for a polycrystalline surface (dashed) and for a T~-Maxwellian distribution (dash-dotted) (from refs. [26,27]).

are extracted, three of them are shown in fig. 17. The spectra are obtained from " s u l p h u r covered" Ni(111) at ~ = 0 °, 60 ° and 80 °. These spectra illustrate the three categories of distributions observed: " h o t t e r " than the surface and narrow, -T~-Maxwellian, and finally "colder" than the surface and broad. Also plotted are the T~-Maxwellian (dashed) and the T(E)-Maxwellian (solid) curves convoluted with the ~-= 100 #s gate function. Further measurements, performed with the same device and data handling procedure, have shown that within the margin of error neither T{E ) nor S show any isotopic effect for H 2, H D and D 2 [26]. The measurements show in addition that while T;e ) is proportional to the surface temperature in the range 950 < T~ < 1150 K, S is constant in the same range. It was not until p s e u d o r a n d o m chopping was used, that the direct analysis of T O F distribution curves became possible. The T O F spectra emerging after a cross correlation treatment of the raw data, were affected with a gate function convolution of only 10/~s, i.e. negligibly convoluted with respect to the natural widths of the main structures present in the spectra [59]. The first system measured was D z desorbing from Pd(100) [29]. T O F - D 2 spectra from sulphur covered Pd(100), 0 s - 0 . 5 and T~ = 360 K measured at five polar angles are shown in fig. 18. It is obvious that the desorbing D 2 flux consists of two distinct groups of molecules: one with an almost T~-Maxwellian distribution and the other m a d e up of m u c h faster molecules. Because of the negligible convolution, the two groups could be evaluated separately. The first group nearly follows the classical laws with T~E> ~ T~, S = 1 and cos 8. The second group was strongly "non-classical": T(E } -- 1030 K (i.e. T(E ~ ~ 3 ~ ) , S = 0.53 and the angular distribution of the flux was cos1°#. Because the flux distribution of this second group is so strongly peaked a r o u n d 0 = 0 °, the distributions for # = 60 ° and 80 ° in fig. 18 are purely T~-Maxwellian. The set of T O F curves in fig. 19 measured at 0 = 0 ° and T ~ = 5 0 0 K

186

G. Comsa, R. David / Dynamical parameters of desorbing molecules

8000'

Ni(111)-D 2 8 =0°

6000 _

~experiment

F--

~ k):1871K 5=0.719

~000

2001

~

-Moxwellian Ts =11/,3K I

_~X

Moxwellian T,,E~187tK

60009=60 °

~,~=1367K S=1.019

4000

Ts=l143K 2000

T~1367K

o 5oo0 0 =80 °

r, \ \ " -~

I

xperitmmt ~=771K

~.=

S=1.222

.5

Moxwel[ian TS=11&3K \ \ "JMaxweHion T<.~=771K

u

\

o

,,,e

2;o' ~;o' ~ o '

8;o',;oo

time of flight [psecl Fig. 17. Time-of-flight spectra measured ( × ) for D 2 molecules desorbing from sulphur covered Ni(111) at 0 = 0 °, 60 °, 80 °. The curves represent Maxwellian spectra corresponding to TS= 1143 K (dashed) and to T(e) = ( E ) / 2 k B (solid) convoluted with the gate function "r = 100/~s (from ref.

[271).

illustrates the influence of sulphur coverage [29]. It appears that while from clean Pd(100) the distribution is purely T~-Maxwellian, the distribution at the highest sulphur coverage, 0s = 0.65, is almost entirely "non-classical". The

G. Comsa, R. Daoid / Dynamical parameters of desorbing molecules

5

lI

187

Pd(IOO)-D2 Ts=360K es-~0.5

4 %

/

oo

"~ 3

200

///

~ 2

z.o°

~ *~,

80 o

qo I0~.__.~

r

i

~ J

i

i

~.e._

~

i

~

i

i

0

-~'~',!

i

i

i~I

10 20 time of flight[xlO-4sec]

Fig. 18. Sequence of D 2 time-of-flight curves with desorption angle # as parameter. Upstream pressure P , = 400 Torr; measuring time for one spectrum: 120 rain (from ref. [29]).

inspection of the curves in figs. 18 and 19 strongly suggests that there are two distinct channels for desorption: on the clean surface only the classical channel is open, while the adsorbed sulphur atoms gradually block this channel and open the "non-classical" one. Further experiments have shown that the blocki n g / o p e n i n g effect does not depend on the nature of the adsorbate but only on its presence. Indeed, the presence of adsorbed CO, H [48] or even of adsorbed Cu [50] on the Pd(100) surface has the same effect as the presence of sulphur; even the value of T for the "non-classical" group is the same. This shows that the blocking/opening is more like a mechanical than a chemical effect. Using the same apparatus and procedure Comsa and David were able to obtain, in addition, T O F spectra for D 2 desorbing from Cu(100) and C u ( l l l ) [49]. The identical spectra obtained from clean (0 s < 0.03) and sulphur covered (0 s = 0.3) Cu(100) at 1000 K are plotted for O --- 0 ° in fig. 20. A T~ = 1000 K Maxwell spectrum is also plotted (dashed). It is immediately obvious that the desorbing D 2 flux consists almost exclusively of very fast molecules, the T~-Maxwellian component being absent. F r o m the plot in fig. 20 one obtains:

G. Comsa, R. David / Dynamical parameters of desorbing molecules

188

Pd (100) - D2 T~= 500 K 2o Q x

15

eC

e~

'~

5

0 u

0

5 time of flight[xl0"4sec]

10 20

Fig. 19. Sequence of D 2 time-of-flight curves with sulphur coverage 0s as parameter. P~ = 400 Torr; measuring time per spectrum between 10 and 60 rain (all normalized to 60 rain) (from ref. [291).

T
G. Comsa, R. David / Dynamical parameters of desorbing molecules t

/~k

/

/ /

¢-

l

189

Cu(lOO)-D2

rs=lOOOK

"\

~\

0=00

~\ x\ \\

II

\

. Os=0.3 * Os
,., (T=I~OK) \\%\

Q.

/

x

x

x

x

x

~

1 2 3 /, "time of flight[x10-4s]

Fig. 20. Time-of-flightspectra of D 2 molecules desorbed from a clean (©) and from a S-covered (×) Cu(100) surface (measuring time for one run 3.5 h). The dashed curve represents a T~= 1000 K Maxwell spectrum.

not possible. However, the T O F spectra measured at T~ = 360 and 400 K and = 0 ° with thick Cu layers ( - 50 A) are still exciting. The peak characteristic for the Cu surface is extremely narrow ( F W H M only slightly larger than the 10 #s channel width) and its mean energy corresponds to T = 7T,. The T O F measurements presented so far were all obtained for hydrogen molecules leaving the surface by associative desorption of the atoms; the hydrogen atoms were supplied to the surface by permeation from the rear face of the crystal. The main features of the desorption distributions which do not follow the T,-Maxwellian distribution m a y be summarized as follows: the flux distributions are all strongly peaked in the normal direction (n >> 1); T is much larger than Ts for 0 = 0°; with increasing 0, T is constant or decreases, and even values substantially lower than T~ are observed at 0 = 80°; the widths of the T O F distributions are narrow for 0 = 0 ° (S < 1); with increasing 0 they become larger surpassing even the Maxwellian width (S > 1). These features are confined neither to the hydrogen associative desorption nor to the supply by permeation. Indeed, Becker et al. [32] (see also ref. [4]) found very similar results for CO 2 desorbing from poly-Pt. CO 2 was produced by CO oxidation, with both CO and 02 being supplied from the gas phase. The measured parameters of the CO 2 desorbing flux were: T = 3560 and 2140 K at T , - 880 K for v~ = 0 ° and 45 °, respectively; the distribution width was narrow at 0 = 0 ° and reached almost Maxwellian width only at 0 = 45 °. Some differences with respect to the trends observed so far were emphasized by Somorjai's group [76,77] using also pseudorandom chopping. In one paper [76] they studied the desorption of D 2 0 produced by the oxidation of deuterium on P t ( l l l ) . The striking feature of the T O F spectra of D 2 0 obtained in

190

G. Comsa, R. David / Dynamical parameters of desorbing molecules

the range 664 < T~ < 913 K "is that they lack the high energy tail" of the T~-Maxwell distribution. Accordingly, T~E) --0.5T~ and S < 1 for 0 - - 7 ° is obtained systematically. The authors infer from their flux measurements a cos ~ distribution; due to the large error bars, the data are as well compatible for instance with cos°70. In the more recent paper [77], the desorption of H D from Pt(557) was investigated. H D was the product of the H 2 - D 2 exchange r e a c t i o n , H 2 and D2 being supplied from the gas phase. The angular distribution is cos2~, similar to preceding results. However, the H D molecules desorbing normal to the surface are "colder" than the surface: T(E ) ~ 500 K at T~ = 690 K. The result is very interesting, but has to be considered with some caution due to the very short flight path (14.4 cm) and the relatlvely large channel width (13 /~s). For instance, a shift of only one channel (this can hardly be excluded when figs. 3 and 5 in ref. [77] are compared) could lead to T(E ~ -- 800 K, i.e. > Ts.

5.3. lnternal energy of desorbing molecules The first internal energy data exhibiting deviations from T~-Boltzmann behavior appeared much later, but were by no means less exciting. They are due to Bernasek's group [34,35]. Both T,~b and Trot of N 2 molecules associatively desorbing after permeation through a poly-Fe membrane were estimated by using electron-beam-induced fluorescence. The basic trends which also seem to be confirmed on other systems are the following: (1) the vibrational temperature of N z desorbing from sulphur contaminated Fe is substantially larger than the surface temperature, reaching values up to Tvib ~ 2.5T~; with decreasing contamination Tvib decreases down to values still slightly larger than T~; (2) the rotational temperature is very low, Trot -- 400 + 30 K, and constant irrespective of T~ and contamination. The measurements were performed in the range 1086 < T~ < 1390 K. The data correspond to the properties of N 2 desorbing in a relatively broad desorption angle centered around the surface normal. Further results concerning the internal energy of molecules desorbing associatively after atom permeation supply were obtained very recently. Zare's group [64] has investigated, by resonance-enhanced multiphoton ionization, H 2 and D 2 desorbing from Cu(110) and Cu(111); Zacharias and David [62] used laser-induced fluorescence to study H 2 desorbing from poly-Pd. The rotational distributions showed in both cases a similar trend: they are mildly non-Boltzmann and their mean energy corresponds to Trot < Ts. Kubiak et al. [64] measured in addition the (v" = 1 ) / ( v " = 0) vibrational population ratio for H 2 desorbing from Cu(110) and C u ( l l l ) and found it to be - 5 0 and - 1 0 0 times, respectively, greater than the value expected for an equilibrium ensemble at T~. (The same figures were obtained for D2. ) Very interesting vibrational distribution data of the desorbing products

G. Comsa, R. David / Dynamicalparameters of desorbing molecules

191

resulting from the surface reaction between gasphase supplied C, O and CO were obtained by the Yale Molecular Beam group applying Fourier transform IR techniques [36,66,67]. Simultaneously with Bernasek and Leone [65], Mantell et al. [36] were the first to use the IR emission of desorbing molecules in order to obtain information on the internal energy distribution. Both groups looked at CO 2 resulting from the CO oxidation on a clean poly-Pt surface at T~ = 700-800 K. The conclusion was that the nascent CO2 molecules were vibrationally highly excited, most of the excess energy corresponding to Tvib --- 2000 K being in the asymmetric stretch. Further investigations of this reaction by Brown and Bernasek [78] have shown that the amount of excess energy is reduced when O atoms are adsorbed in excess; the CO coverage, however, has no significant influence. While in none of the experiments mentioned so far, vibrational levels beyond the second level have been probed, Kori and Halpern [67] found CO molecules excited up to p = 7, resulting from the oxidation of C on poly-Pt at T~ = 1000-1400 K by O and 02 (at this surface temperature even r = 3 would have been insignificantly populated). The population still followed a statistical distribution. By changing the experimental conditions for the CO oxidation (CO adsorbed on a preoxidized poly-Pt surface at room temperature and O atoms supplied directly from the gas phase) Kori and Halpern [66] succeeded in producing even higher excited CO2 molecules exhibiting a clearly inverted distribution (Vm~ ~ 16, Vaverage = 9). These results demonstrate again the sensitivity of the internal energy distribution of the desorbing molecules with respect to the details of the surface reaction. Kori and Halpern were able to deduce from their data very interesting information on the reaction-desorption process. They proposed in addition a CO2 chemical laser based upon the population inversion observed in the surface catalyzed reaction of O atoms with CO on Pt oxide. Particular attention to the rotational energy of desorbing molecules was paid by Cavanagh and King [61,38]. They investigated by laser-excited fluorescence the rotational energy of NO during thermal programmed desorption (TPD) from clean and oxygen precovered Ru(001). In this way, they were able to associate the observed rotational temperature with the molecules contained in the given desorption peak, i.e. with molecules originating from a given adsorption state. Under the conditions of their experiment, with oxygen precoverage, two desorption peaks (at 280 and 475 K) were present in the T P D spectrum. The rotational temperatures observed were T~ot = 255 + 25 K and 375 _+ 35 K, respectively. In the case of the oxygen free surface only one peak, at 455 K was present, and the corresponding Trot = 235 + 35 K. In all cases the distribution was Boltzmann, Thus, while the molecules desorbing at low temperature have a classical Ts-Boltzmann distribution, the others have 0.8Ts and 0.5Ts Boltzmann distributions depending whether they originate from an oxygen precovered surface or not. The same authors have opened a new and so

192

G. Comsa, R. David / Dynarnical parameters of desorbing molecules

far last chapter in characterizing the parameters of desorbing molecules [37,68]: they measured the state selected translational temperature of NO desorbing from Ru(001) by Doppler spectroscopy of the laser-excited fluorescence lines. In spite of the results being yet contradictory, this really opens the way to understanding, in great detail, the dynamics of desorption.

6. Final discussion

As stated in the introduction, one of the aims of this paper is to review the status of the experimental investigation of the dynamic parameters Of desorbing molecules. The ultimate reason for performing such experiments was the conviction that these parameters do not necessarily follow general laws and thus that the results may contain valuable information on the processes leading to desorption. (For a remark on the cognitive value of the failure of general laws see ref. [79], pp. 120, 121). The data obtained so far confirm the expectations at least in part, the parameters of desorbing molecules indeed show a multifaceted rich behavior in contrast to the monotony of a "general law" behavior. Concrete information on details of the desorption process may be obtained from experimental data ensuing from specific systems only on the basis of pertinent theories and models. More and more remarkable theoretical papers focussing on the behavior of the parameters of desorbing particles are appearing (see e.g. refs. [80-86] and references therein). Most of the theoretical approaches investigate the desorption as a phonon-induced process. This is normal because the interaction with phonons leads ultimately to the desorption of an adsorbed particle. Calculation difficulties with multiphonon processes led eventually to the one-phonon approximation. Accordingly, most of the results are directly applicable only to weakly bound adsorbates, especially to noble gases (this statement holds also for some "non-phonon" approaches). Unfortunately, the experimental data are limited so far, with a few exceptions, to the desorption of chemisorbed particles involving in most cases recombination and reaction processes. The lack of overlap between theory and experiment hampers for the moment the gain of detailed information. The situation seems, however, to be improving rapidly. The development of small, rapid heaters and bolometers at Caltech and their remarkable application to adsorption-desorption studies of He ([87] and references therein) are an important step in improving the overlap. The first experimental evidence for the non-applicability of detailed balance when the quasi equilibrium conditions are not properly fulfilled [87] are the first promising results. The overlap between experiment and theory will certainly improve also by further theoretical developments including desorption of strongly bound particles involving energetic recombination and reaction processes. Such work has already been done sporadically. For instance, Tully [88] has examined in a

G. Comsa, R. David /Dynamicalparameters of desorbing molecules

193

stochastic classical trajectory study the R_ideal-type reaction of gas-phase oxygen atoms with carbon adsorbed on Pt(111). This paper triggered the very interesting experiments by Kori and Halpern [67] presented in the preceding section. In spite of the reduced overlap a number of theoretical statements are very valuable for experimentalists. Here are two examples: It was again Tully [81] who made an important observation concerning the very delicate definition of the adsorption (equilibration) of a particle (see e.g. section 4.1 above). He noted that, at least for realistic Ar and Xe on Pt(111) potentials, it is sufficient that the energy of the particles becomes at some time less than - 3kTs; changing this value to - 4kT~, - 5kT~, etc. had no significant effect on the resulting angular and velocity distribution of the desorbing particles. This is probably not a very general definition but is instead a very useful definition of adsorption (equilibration), with respect to the behavior of the desorbing particles. Another interesting result is the correlation found by Doyen [84] between the mean energy of the particles desorbing normal to the surface and the shape of the angular distribution of the flux (cos%~); in the notations of the present paper, the relation which seems to be verified in many cases [70] is

r(~>lo=0=

3+n

4 T~.

The experimental confirmation of this theoretical relation will certainly lead to further theoretical developments allowing the extraction of detailed information from the experimental data. It is worthwhile to remark finally that in spite of the fact that the one-phonon theories are actually not applicable, for instance, to the associative desorption of hydrogen, some of the theoretically predicted tendencies (e.g. flux distribution peaked in the normal direction, decrease of T(E> with increasing t~) are supported by the hydrogen desorption data. It is difficult to say whether this is a simple coincidence or the result of a deeper lying relationship. In the absence of a directly applicable theory, the experimentalists - in particular those investigating the associatively desorbing hydrogen molecules have used, over the years, an activation barrier model. This model speculatively proposed by Comsa [15] was used for the first time to describe the angular distribution of the desorbing flux measured by Van Willigen [18]. As outlined in section 2 the subsequent application to new data, in particular to velocity distribution data [22-29], led to substantial transformations of the model, which still retained its main attractive features. The potential energy diagram implied by Van Willigen's one-dimensional activation barrier model is presented in fig. 21. The assumption is that, after recombination, the hydrogen molecule at a reaction parameter distance corresponding to the maximum of the activation barrier, E a, is equilibrated with the surface; when desorbing the molecule gains momentum perpendicular to the surface. This accounts for the peaked angular flux distributions observed by Van Willigen and for the high

G. Comsa, R. David / Dynamical parameters of desorbing molecules

194 .............

"....... ~,>'---][ .....

OH

,"

>

"

/

M+H

<[ .>

/ /

O1

~H2

--.53~

r

""-O1 _

M+~H 2

~H2

Fig. 21. Energy diagram for the hydrogen-metal surface (M) with a one-dimensional activation barrier E a for adsorption; all energies per atom; D½H2 dissociation energy; Q½ H2 hydrogen molecule heat of adsorption; QH hydrogen atom binding energy.

translational energies measured later on. The actual angular distribution (and the velocity distribution) of the desorbing molecules is calculated by assuming the restricted applicability of detailed balance: the distribution of equilibrium gas molecules incident from the right side in fig. 21, which are able to overcome the barrier (Ea is an activation barrier for adsorption!), is calculated and then taken to be equal to the distribution of the desorbing molecules. The existence of an activation barrier, i.e. of a region of high potential energy is very appealing; it is a straightforward way to understand how desorbing molecules can have mean energies up to T -- 7T~ [50]. Fig. 21 also gives very clear evidence that the still widespread opinion that the excess energy of the desorbing molecules originates in the recombination energy D½H2 is incorrect. During recombination, the energy D{ H2 (per H atom) is indeed liberated but as obvious from fig. 21 the binding energy of an H atom (Q~ = Q{ H2 + D½ H~) is larger than the binding energy of a H 2 molecule (per H atom, with exactly this quantity (see also ref. [79]). Thus, the existence of a potential barrier (region of high potential energy) seems to be necessary to explain the very high translational and internal energies observed so far. However, this barrier is not necessarily the usual activation barrier for adsorption, i.e. it does not need to lie outside the chemisorption well. For instance, in order to explain the two distinct distributions of D: desorbing from Pd(100) (figs. 18 and 19) a model involving the potential diagram in fig. 22 was proposed [29]. The model is particularly well suited to illustrate the desorption of hydrogen which was supplied to the surface by bulk permeation; it shows a two channel behavior.

G. Comsa, R. David / Dynamical parameters of desorbing molecules

................... ~/';'~-l----

QH=63~

!

Qp=24

/

/

/

! !

/

! /

/

/

/

195

Pd+H

/

D1 =53~ 2H2

Qlu_=lO-"j ~,/.1--Had 2n2 ~ -Fig. 22. Energy diagram for the system h y d r o g e n / P d . All energies in kcal per mol and per atom. E b last bulk barrier; Qp permeation energy; Qs solution energy.

For clean Pd(100), the H atoms coming from the left equilibrate in the chemisorption well, recombine and desorb with a Knudsen and Maxwell distribution. In the presence of impurities (S, CO, Cu) this channel is more and more clogged and the hydrogen has to follow the other channel: The H atoms recombine without equilibrating in the well retaining the potential energy of the last bulk barrier (Eb). The barrier model with all its variants explains many of the desorption features, but not all of them. The model is for instance not able to explain the existence of very low mean energies observed at large t~ values (T(e) < T~ [27]). The potential barrier model is used currently to explain also the desorption features of other systems (see e.g. refs. [33,78]). The theoreticians were generally not particularly keen in further development of this very rough model. That this may be rewarding is obvious from Schaich's paper [89]; by combining an activation barrier with frictional forces, he was able to explain qualitatively the features of desorption distributions. Summarizing we can say the following: General thermodynamic considerations have shown that, even at equilibrium, the parameters of desorbing molecules are not required to follow the Knudsen, Maxwell, and Boltzmann laws. Assuming detailed balance restricted to adsorption-desorption, and because the sticking probability must depend to some extent on ~, v and c i (internal energy) - this being a "common sense" argument - one has been led

196

G. Comsa, R. David / Dynamical parameters of desorbing molecules

to the conclusion that the three laws above m u s t fail in describing the desorption parameters even at equilibrium. Experiments have confirmed these predictions under more or less precisely defined "quasi-equilibrium" conditions. Microscopic theories and models are continuously improving the description of the actual behavior of the desorption parameters; more detailed information on the processes leading to desorption will be extracted before long. This development went from general to particular. Thermodynamics asks in addition that, at equilibrium, the parameters of the ensemble of molecules leaving the surface (by desorption, diffraction, inelastic scattering .... ) must follow the three general laws. It would be a challenging goal for theorists to go the reversed path: to demonstrate on the basis of microscopic theories, developed for each of the scattering processes, that their equilibrium synthesis has the right behavior. We cannot forsee whether this will bring new, detailed information; it will certainly give a good feeling and will include the answer to Goodstein's recent [87] request for an explanation concerning the adsorption-desorption detailed balance.

Acknowledgements Thinking over the various aspects of this review was stimulated by the atmosphere of our institute, by fruitful discussions with m a n y of its members and by efficient technical help. We would like to acknowledge nominally those who in our institute have directly contributed to the investigation of the desorption parameters during the past decade: Klaus Rendulic, Olaf Schneider and Bernd-Josef Schumacher. The skillful technical help of Karl Veltmann and the careful typing and retyping of the manuscript by Maria Kober are likewise gratefully acknowledged.

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G. Comsa, R. David / Dynamicalparameters of desorbing molecules

197

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198

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