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Diffraction of conduction electrons on deuterium film-covered metal surfaces
207
Surface Science 248 (1991) 207-214 North-Holland
Diffraction of conduction electrons on deuterium film-covered metal surfaces A.G. Kundzich, P.P. Lutsishin, O.A. Panchenko, S.V. Sologub and V.F. Shpagin Institute of Physics, Academy Received
of Sciences of the Ukrainian SSR, Prospekt Nauki, 46, 252650 Kiev-28,
26 June 1990; accepted
for publication
15 November
USSR
1990
A structural phase transition in a film of deuterium adsorbed on the W(110) face at low temperatures was studied within a temperature range from 1.8 to 10 K. Data on the phase transition, including its kinetics, were obtained by the method of surface scattering of conduction electrons, based on a static skin effect which arises in compensated metals in a strong magnetic field. In this case the conductivity of a plate is sensitive to the character of the surface scattering of electrons and consequently to the state of the adsorbed film. The paper discusses models of adsorbed films and possible mechanisms associated with the effect of adsorption on the surface scattering of electrons. The phase transition to an ordered structure is shown to occur in a submonolayer region of coverings, seemingly close to the molecular monolayer, and to be accompanied by formation of a commensurate (1 x 1) phase. The kinetics of growth of the new phase was studied and the activation energy which turned out to be __ of the adsorbed film ordering was determined, En, = 60 K.
1. Introduction An ideal metal surface scatters conduction electrons as an infinite two-dimensional diffraction grating, and therefore the electron reflection character depends on the surface state and can be specular if the boundary coincides with some basic crystallographic plane and is free from defects, including those in the form of adsorbed particles [1,2]. Adsorption generally increases the diffuse background in the surface scattering of electrons [3,4]. Formation of ordered submonolayer lattices of the adsorbate can as well change the character of the surface scattering of electrons [5]. Most experimental studies of hydrogen interaction with a metal surface, including that with the tungsten (110) face, have been conducted in the region of relatively high temperatures, where hydrogen (deuterium) adsorption is undoubtedly accompanied by the dissociation of molecules [6]; the situation can, however, change markedly at lower temperatures. As noted in ref. [7], stabilization of intermediate, “precursor”, states, which 0039-6028/91/$03.50
0 1991 - Elsevier
Science Publishers
are far from the thermodynamic equilibrium, is possible in this case, physically adsorbed hydrogen molecules, weakly bonded to the atomically smooth (110) face seeming to correspond to these states. According to ref. [7], molecular films remain stable over a broad temperature range, right up to T < 66 K. Since the phase diagram of the two-dimensional hydrogen-(110) tungsten system has been well studied and is known to consist primarily of two ordered phases, p(2 X 1) and (2 x 2) [8], the appearance of a different sequence of structures shown by the LEED method at low temperatures (T < 66 K) [9] as well indicates a freezing of the “precursor” states and formation of a molecular film. Due to this, molecular deuterium films are, for certainty, assumed to be the object of the present study. The electron scattering on the deuteriumcovered surface of single-crystal tungsten was used in the study as a tool for investigating the structural phase transition in a submonolayer adsorbate film at low temperatures. The selection of this adsorption system as the subject of investigation
B.V. (North-Holland)
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A. G. Kundzich et al. / Deuterium a&orbed on W(I 10)
was determined not only by a natural interest in the behavior of hydrogen and of its isotopes on the surface of a solid 161, but also by the fact that deuterium molecules adsorbed on the tungsten (110) face retain an appreciable mobility even at low temperatures, right down to liquid helium temperatures. The method relying on the surface scattering of electrons is nondestructive, and its application in this case was most well-grounded. Data on the character of the surface electron scattering in thin metallic films deposited under a high vacuum are most often obtained by studying their electrical conductivity [lO,ll]. We resorted to another approach, based on the static skin effect [12]. This galvanomagnetic phenomenon is observed in compensated metals at the following conditions: I> d, wCr z+ 1 (w, is the cyclotron frequency, r the momentum relaxation time, 6 the mean free path of electrons, and d the plate thickness). Meeting these conditions requires the cooling down the sample to liquid helium temperatures. The static skin effect under various conditions was experimentally studied in refs. [13,14]. When the above conditions are satisfied, then the electric current flowing through a plate sample concentrates in a narrow, on the order of the Larmor radius, layer near the surface, with the result that the conductivity of the plate becomes very sensitive to the character of the surface electron scattering and hence also to the surface state; therefore, adsorption can in this case change, sometimes by an order of magnitude, the magnetoresistance of the sample considerably. The study being reported was a continuation of earlier investigations [15,16]. Its objectives included studying the mechanisms and type of the phase transition, determining the critical concentration of particles, and examining the phase transition kinetics. The total experimental evidence yielded by the study leads to the conclusion that the phase transition in the deuterium film occurs in the region of concentrations close to a monolayer and is due to evolution of the (1 X 1) phase rather than to the (2 X 1) phase, as assumed earlier in refs. [15,16], which is an equilibrium phase and appears to have been formed under the electron beam action. An essential part of the study was the investiga-
tion into the magnetoresistance relaxation, caused by processes of the onset of a thermodyna~c equilibrium in films after reaching the critical concentration of particles. The investigations were conducted at various temperatures; their results were compared with the generalities of growth of the average size of a new phase domain with time, i(t), for two-dimensional systems [17-191.
2. Experimental The data on the surface electron scattering were obtained by a method based on the static skin effect. To meet the conditions for this effect, the sample was placed into a strong magnetic field and cooled with liquid helium. The magnetic field source was a superconducting system. A constant magnetic field (H = 30 kOe) was oriented in the plane of the plate sample and directed perpendicular to the measuring current in the plate. The experiments were conducted under ultrahigh vacuum, the background pressure in the vacuum device at room temperature being of - lo-” Torr. The device, made of glass, comprised a system for cooling the crystal and monitoring its temperature with respect to that of the helium bath, sorption pumps, and pressure transducers (fig. 1). The design provided for varying the sample temperature by controlling the current through it as well as for raising the temperature “flashwise” to T = 2500 K for cleaning its surface. Walls of the chamber accomodating the sample and the gate controlling the kinetic gas flow of deuterium to the plate surface were liquid helium-cooled as well; the helium bath temperature could be lowered to 1.7 K when required. The cooling of the walls excluded an uncontrolled overdeposition of deuterium and made it possible to stop its adsorption at the required moment as well as to study relaxation phenomena at a fixed particle concentration. Deuterium was fed through a tube extending from the helium cryostat to the outside, into the “warm” part of the glass vacuum device. The gas temperature was not monitored. In some cases, another vacuum device type was used, which made it possible to combine the LEED and static skin effect methods; in such cases the vacuum
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A.G. Kundzich et al. / Deuterium adwrbed on W(II0)
temperature T and effective deuterium pressure It is to be noted that Per, monitored only in the “warm” part of the device, determined the adsorption rate (or the time for AR(t) curves to reach saturation) and cannot be used in gas-kinetic calculations. The time in which the A R( t ) curve comes to saturation remains nevertheless a linear function of ( PC,)-1 over a broad pressure range. T and Per were experiment parameters, remaining unchanged in the course of deuterium adsorption. Lastly, it should be pointed out that the response AR(t) corresponded to adsorption on the front, i.e., the side of the plate facing towards the source. If the chamber walls were not cooled with liquid helium, the AR (1) signal shape could be distorted as a result of deuterium adsorption also on the back side. Fig. 2 shows AR/AR, versus t/r0 curves obtained within a temperature range from 1.8 to 10 K. (The procedure of changeover to relative coordinates AR/AR,, t/r0 was as follows: experimental data were presented in coordinates ln(1 P,,.
3
t Fig. 1. Schematic of experimental vacuum setup: 1: singlecrystal tungsten plate; 2: superconducting magnet; 3: cryostat; 4: external magnet-controlled gate; 5: external magnet; 6: sorption pump; 7: pressure transducer; 8: deuterium source.
device was arranged between electromagnet poles. This design was described in greater detail earlier
151.
Samples were prepared as follows. Plates sizing 3.0 X 10 X 0.5 mm3 were cut out of a tungsten single crystal. The face orientation accuracy was within * 20 angular minutes. The ratio of resistivities, characterizing the quality of the initial tungsten, was ~~~~~~~~~~= 7 X 104. The final thickness of the plates after grinding of the surface and its electrolytic polishing in a 3% NaOH solution amounted to - 0.1 mm. The samples were subjected to an ordinary procedure of high-temperature cleaning in an oxygen atmosphere. In measurements a signal proportional to the change in the magnetoresistance of the plate at adsorption or annealing of the film was recorded automatically. The H = constant condition was observed in all cases.
3. Results and discussion Some data on the critical concentration and character of the phase transition were derived simply from analyzing the shape of AR (t ) curves characterizing the plate magnetoresistance variations with the adsorption time at given sample
1.o
d 2
I
\_
0.5
a a
0L K
O0’ Fig. 2. Relative change of sample magnetoresistance as a function of dimensionless deuterium deposition time t/T, at various temperatures of the sample and pressure, Per = 1 x 10W4 Torr. AR/AR,=1 if t/To-co. Inset: fragments of similar dependences at T= 5.1 K and various P,,: (1) 8 X 10m6 Torr; (2) 1 x low4 Torr; and (3) 4x 10m4 Torr.
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A. G. Kundzich et’ al. / Deuterium adsorbed on W(Il0)
16
I
I
0
150
300
!
I
450
t(sec)
Fig. 3. Change of sample magnetoresistance as a function of oxygen and deuterium deposition time. Sample temperature: 4.2 K. Dashed lines show approximation of these data by the function F(t) (refer to text).
AR/AR,) =f(t) and then transformed to a linear dependence by selection of the parameter AR,. The slope of the straight line thus obtained is l/rO.) It is obvious that adsorption changes the sample magnetoresistance; however, the A R/AR, versus t/r0 curve has a complex bell-shaped form, which is also appreciably temperature-dependent: with increasing T the maximum of the curve shifts towards lower exposures; and, lastly, it has a shallow minimum in the long exposure region. Fig. 3 presents the AR/AR, versus t/r0 curve characterizing the magnetoresistance change as a function of oxygen adsorption time at T = 4.2 K for the same tungsten plate and, for comparison, also one of the curves for deuterium. It is essential to emphasize that the dependence for oxygen, in contrast to that for deuterium, is a smooth monotonic one and can be successfully approximated by a function of the form F(t) = 1 - e-‘/‘o. Proceeding now to the discussion of these results, we will make some general comments. In particular, it seems essential to analyze some models of surface structures from the standpoint of their influence on the scattering of conduction electrons.
Model I. This model appears to correspond to films forming at oxygen adsorption on the tungsten surface cooled to low temperatures. Such layers can appear when several adsorption site types exist on the surface. At low adsorbate concentrations the filling of the most energetically favorable sites (which in the general case are bridge or threefold sites) is more probable. As the concentration increases, adsorption of particles into the “second” layer becomes possible, which is equivalent to adsorption into on-top sites; these sites may be considered as the “precursor” state. Existence of other adsorption site types is also possible. Thus, a statistical filling of several adsorption sites results in a film where the arrangement of particles does not correlate with the substrate symmetry. In the simplest case the existence of “active” and “passive” sites can be supposed. Such a hierarchy is physically obvious, e.g., with a polylayer adsorption, where the first layer exerts a higher influence than does the n th one. Since the probability of filling empty sites declines directly with the concentration of already occupied sites as S = C(l - f& ), C = constant, which is also applicable to “active” sites, then 6,, = 1 - e-f/70, where 0,, is the concentration of already filled “active” sites. Due to this, the data of fig. 3 for oxygen can be interpreted as follows: AR is a linear function of @_,. This formally resembles Langmuir’s kinetics, but 0,, can differ from the actual coverage. It is clear that a conventional monolayer with some concentration N,, corresponds to the asymptotic P(t) value, and therefore AR changes may be calibrated in 0,, units, while it is obvious that N,, does not coincide with the standard density of sites of the W(110) surface lattice. Model II. Adsorbed particles are in this case arranged in equivalent adsorption sites, not more than one particle corresponding to every unit cell of the surface lattice; this is an ordinary model of the lattice gas. Within the scope of the concept of the diffractional interaction of conduction electrons with a metal surface such a model presumes a nonmonotonic behavior of AR with increasing 8. In particular, at 0 G 8 G 0.5 an increase in the diffuse scattering of electrons, caused by the growth of the number of scattering centers on the crystal surface, should be expected. At 0.5 G 8 =G1,
211
A.G. Kundzich et al. / Deuierium a&orbed on W(I IO)
vacancies in the adsorbate lattice are filled and the (1 x 1) phase is formed. The higher the 6 value, the more perfect the (1 x 1) lattice, which has the symmetry of the substrate. It may be believed that in the range of 0.5 G 8 6 1 the AR value declines due to increasing specular reflection of electrons. By analogy with model I, AR - F(t) in the region of 0 < 19< 0.5 and AR - 1 - F(t) in the region of 0.5 < 0 < 1. Thus, the transition from a film with structure I to a film with structure II may be accompanied by a drmatic change in the surface electron scattering character, especially when the particle concentration is close to a monolayer. This fact has found a direct experimental substantiation. In particular, AR decrease to zero indeed corresponded to the growth of an ordered oxygen film at T = 700 K with formation at high 8 of the (1 x 1) phase which replicated the structure of the W(110) face [5]. Annealing a deuterium film, deposited up to saturation, at T > 100 K as well results in formation of an ordered (1 x 1) atomic phase and AR decrease to zero. A progressive deuterium evaporation from the sample surface as the temperature of heating is further increased leads to a new rise of the magnetoresistance AR; the corresponding curve is shown in fig. 4, where it is seen that the magnetoresistance once again acquires the initial value R after a full removal of deuterium from the surface. Formation of islands of an ordered phase may also be accompanied by an appreciable change in the surface scattering character. Even the simplest model of a commensurate film shows that rearrangement of particles with formation, e.g., of the (1 X 1) phase and empty surface areas can further reduce the surface scattering. In the general case, however, the growth of islands of an ordered phase with an arbitrary symmetry calls for a special analysis. Return now to the data of fig. 2. The family of A R/AR, versus t/r0 curves, presented here, is over a considerable length approximated by the function F(t). Our basis assumption is that deuterium molecules, adsorbing on a cold surface, form a film with structure I, which is indicated by the possibility of approximating experimental AR(t) curves
0
200
T(K)
100
600
Fig. 4. Progressive evaporation of deuterium. AR variation with temperature of heating. Measurement were made on other crystal.
with the function F(t). As can be ssen from fig. 2, the fit is the better, the lower the sample temperature. However, the departure of experimental curves from F(t), particularly marked in the high concentration region or at an elevated temperature, indicates the transition of the film to another state. If this film I-film II transition indeed occurs close to a monolayer, but so that 8 # 1, then the remaining vacant sites in the formed (1 X 1) phase can unite in the course of time to form voids-inclusions. Such a transition, at least at the stage of formation of a commensurate film, may be diffusionless (like the martensitic one) since, e.g., the passage of a particle from one adsorption site to another is energetically more favorable and requires no diffusion walks. Let us discuss some consequences of this model. Note, first, that the existence of a critical concentration 8,, is an important criterion of most phase transitions. Let us analyze from this standpoint the data presented in fig. 5. Every experimental point in this figure has its corresponding new film which was adsorbed at low temperatures on a surface cleaned of the preceding deposit and was then annealed. It is essential that the anneal-
212
A. G. Kundzich et al. / Deuterium &orbed
ing substantially reduced AR in a limited concentration region, while a further increase of the annealing temperature Tan does not change the indicated range of coverages. Since Tan -C 66 K, the system under study seemingly remains a molecular one. Fig. 6, presenting the same data, but in the magnetoresistance, AR, versus relative concentration, @_,, coordinates, shows the critical concentration region indeed to lie near the saturation coverage. We, of course, realize the conventionality of such estimates. Note also that the shape of AR(t) curves is governed not only by the rate of relaxation processes in the film, but also by the rate of inflow of new particles from the gaseous medium. From this standpoint it is interesting to examine the mechanism of formation of the AR(t) minimum, which is well marked for some curves measured in the region of high enough temperatures. An example of such a dependence is shown, in particular, in fig. 2. If the phase transition to a commensurate structure indeed proceeds close to a conventional monolayer and 6 + 1, then voids serving as the
0
LOO
200
600
t (set) Fig. 5. Change of sample magnetoresistance with deuterium deposition time. Solid curve: 4.2 K; points: results of film annealing to 20 K. Dashed curve was drawn “by eye”.
on W(1 IO)
tY
a
Fig. 6. Data of fig. 5, plotted in “magnetoresistance versus relative adsorbate concentration” coordinates, illustrating the closeness of 0,, to a monolayer.
drain for vacant points may develop within a (1 x 1) cluster. The first stage of the film I-film II transition proceeds in a diffusionless manner and rapidly, and appears to consist in freeing the “precursor” states, while the second stage, involving growth of the voids, proceeds slowly as being associated with diffusion walks of vacant sites within a cluster of the commensurate (1 X 1) phase. The evolution of the averag size of the islands (voids), i(t), is governed by the laws of growth of new phase domains and in the general case depends on the phase transition type, surface mobility, and other factors [17-191. Of course, separation of the commensurate film into a compact (1 x 1) phase and voids allows this process to be defined as a first-order phase transition. Since the increase of the average size of voids, or, more exactly, of their average area, due to the inflow of vacancies is not a linear function of time (for example, for a first-order phase transition, i(t) t’13) a moment will come when the balance is disturbed towards adsorption of particles from the kinetic gas flow. The drain of vacant sites (defects of a (1 X 1) cluster) corresponds to a AR decrease, while the
213
A.G. Kundzich et al. / Deuterium adsorbed on W(I IO)
adsorption of new particles within the limits of voids corresponds to a AR increase, and hence their balance yields the AR(t) minimum. Of course, the balance can be disturbed by changing the flow or the crystal temperature. As can be seen from the inset to fig. 2, increasing the flow as little as a few times indeed results in smoothing the A R( f ) curve. However, increasing the temperature allows a new equilibrium to be set, and hence every Per has its corresponding temperature range where conditions for the existence of the AR(t) minimum occur. The experimental setup made it possible to shut off the flow, then to increase the temperature and, after a delay needed for relaxation, to deposit a new amount of the substance. The deposition increased the ma~etoresistance, which indicates that empty portions indeed appear to emerge in the film, but their contribution to AR is small and their total area is not over a few percent of the total (1 X 1) cluster area and depends on the duration of the gas flow shutoff. The probability of filling of vacant points declines as S = ~(1 - 8), and hence macroscopic voids are predominantly filled at repeated depositions. Their filling closes the drain channels for the vacant points. It is
i
g -0.6
u
a
K 4.65K
4.6
-0.8
4.7 K 4.85K 5.0 K 5.3 K 1
Fig. 7. Samplemagnetoresistance relaxationat constant terium concentration and various temperatures.
In t 0
4
2
6
8
0
-1 ~
I
-2 CX p-3 ‘E II -L-
.
-5-
l
-6-
T
+
+ 0 0 + B 0 0
=- 5.3 K x- 5.0 K A - 4.65 K l -L.7 K +-4.65 K e -1.6 K
Fig. 8. Data of fig. 7, plotted in double logarithmic scale.
probably for this reason that films deposited up to saturation remain stable with time. Let us, omitting the initial stage of transition to film II, turn to the analysis of the further evolution of the system. At this stage the adsorbed film appears to represent a continuous cluster of the p(1 x 1) phase with both voids and single vacancies existing within it. “Second-layer”, or “precursor-state”, particules exist probably as well. A further evolution of the system consists in migration of individual vacancies and their connection to vacancy clusters as well as in passage of “second-layer” particles into the first layer. Such a process can result in reducing the surface electron scattering, and therefore the sample magnetoresistance can change as follows: AR(t) = [t(t)]*, where L is the average island size. On the other hand, the growth of submonolayer film islands with time is known to obey the law i(t) = tX [17-191. Fig. 7 shows the data characterizing the magnetoresistance relaxation rate at various temperatures (at a constant adsorbate concentration on the surface). Fig. 8 presents the same data in a double logarithmic scale; for convenience of plotting, the AR sign in this figure is reversed. It is obvious that magnetoresistance relaxation depen-
214
A.G. Kundzich et al. / Deuterium
In t
0
2
L
6
0
0
-0.2
Ill A.F. Andreev, Usp. Fiz. Nauk 105 (1971) 113. PI R.F. Green, in: Solid State Surface Science, Vol. 1 (Dek-
i d-0.6 lx 4 q
X-
- 5.3 K
.
5.0 K
d - 4.85 K -1 .a
adsorbed film and of their effect on the scattering of carriers on the surface.
References
ID IO-O.4
-0.8
a&orbed on W(I IO)
*-&.I
K
+ - L.&K ' - L.6 K
-1.2 Fig. 9. Data of fig. 7, plotted in semilogarithmic scale.
dences can indeed be approximated by a power function AR(t) - kt2x, where k = F(T). An estimate of the exponent yields x - 0.48. Assuming the temperature dependence of k to follow the Arrhenius law, the activation energy of ordering of adsorbed deuterium molecules can be estimated: ED, = 60 K. At late stages of the process, however, a transfer to a logarithmic law of the growth, AR = c In t, takes place. The logarithmic growth region is reached faster as the temperature is increased, which is evidenced by the data of fig. 9. The obtained results show a good agreement with predictions of the theory of kinetics of phase transitions on the surface of a solid, which is still another corroboration of the validity of the suggested interpretation of processes occurring in an
ker, New York, 1969). 131 A.A. Kharlamov, O.A. Panchenko and I.N. Jakovkin, Zh. Eksp. Teor. Fiz. 71 (1976) 760. 141 A.A. Mitrjaev, O.A. Panchenko, 1.1. Razgonov and V.S. Tsoi, Surf. Sci. 75 (1978) 376. [51 P.P. Lutsishin, T.N. Nakhodkin, O.A. Panchenko and Ju.G. Ptushinskij, Zh. Eksp. Teor. Fiz. 82 (1982) 1306. [61 K. Christmann, Surf. Sci. Rep. 9 (1988) 1. [71 R.F. Polizzatti and G. Ehrlich, J. Chem. Phys. 71 (1979) 259. VI M. Altman, J.W. Chung, P.J. Estrup, J.M. Kosterlitz, J. Prybyla, D. Sahu and S.C. Ying, J. Vat. Sci. Technol. A 5 (1987) 1045. [91 V.V. Gonchar, Ju.M. Kagan, O.V. Kanash, A.G. Naumovets and A.G. Fedorus, Zh. Eksp. Teor. Fiz. 84 (1983) 249. 1101 D. Dayal and P. Wissmann, Vakuum Technik 38 (1989) 121. [ill D. Dayal, H. Finsel and P. Wissmann, in: Thin Metal Films and Gas Chemisorption (Elsevier, Amsterdam, 1987) p. 53. WI M.Ja. Azbel, Zh. Eksp. Teor. Fiz. 44 (1963) 986. w31 A.A. Mitrjaev, O.A. Panchenko and G.M. Pugach, Zh. Eksp. Teor. Fiz. 75 (1978) 1356. 1141 O.A. Panchenko, A.A. Kharlamov and Ju.G. Ptushinskij, Zh. Eksp. Teor. Fiz. 64 (1974) 780. v51 P.P. Lutsishin, O.A. Panchenko and S.V. Sologub, Pis’ma Zh. Eksp. Teor. Fiz. 41 (1985) 31. WI P.P. Lutsishin, O.A. Panchenko and S.V. Sologub, Izv. Acad. Nauk SSSR 52 (1986) 1466. v71 I.M. Livshits and V.V. Slezov, Zh. Eksp. Teor. Fiz. 35 (1958) 479. [18] J.D. Gunton, in: Springer Series Surface Sciences, Vol. 8 (Springer, Berlin, 1987) p. 238. [19] K. Heinz, in: Springer Series in Surface Sciences, Vol. 8 (Springer, Berlin, 1987) p.202.
Surface Science 248 (1991) 207-214 North-Holland
Diffraction of conduction electrons on deuterium film-covered metal surfaces A.G. Kundzich, P.P. Lutsishin, O.A. Panchenko, S.V. Sologub and V.F. Shpagin Institute of Physics, Academy Received
of Sciences of the Ukrainian SSR, Prospekt Nauki, 46, 252650 Kiev-28,
26 June 1990; accepted
for publication
15 November
USSR
1990
A structural phase transition in a film of deuterium adsorbed on the W(110) face at low temperatures was studied within a temperature range from 1.8 to 10 K. Data on the phase transition, including its kinetics, were obtained by the method of surface scattering of conduction electrons, based on a static skin effect which arises in compensated metals in a strong magnetic field. In this case the conductivity of a plate is sensitive to the character of the surface scattering of electrons and consequently to the state of the adsorbed film. The paper discusses models of adsorbed films and possible mechanisms associated with the effect of adsorption on the surface scattering of electrons. The phase transition to an ordered structure is shown to occur in a submonolayer region of coverings, seemingly close to the molecular monolayer, and to be accompanied by formation of a commensurate (1 x 1) phase. The kinetics of growth of the new phase was studied and the activation energy which turned out to be __ of the adsorbed film ordering was determined, En, = 60 K.
1. Introduction An ideal metal surface scatters conduction electrons as an infinite two-dimensional diffraction grating, and therefore the electron reflection character depends on the surface state and can be specular if the boundary coincides with some basic crystallographic plane and is free from defects, including those in the form of adsorbed particles [1,2]. Adsorption generally increases the diffuse background in the surface scattering of electrons [3,4]. Formation of ordered submonolayer lattices of the adsorbate can as well change the character of the surface scattering of electrons [5]. Most experimental studies of hydrogen interaction with a metal surface, including that with the tungsten (110) face, have been conducted in the region of relatively high temperatures, where hydrogen (deuterium) adsorption is undoubtedly accompanied by the dissociation of molecules [6]; the situation can, however, change markedly at lower temperatures. As noted in ref. [7], stabilization of intermediate, “precursor”, states, which 0039-6028/91/$03.50
0 1991 - Elsevier
Science Publishers
are far from the thermodynamic equilibrium, is possible in this case, physically adsorbed hydrogen molecules, weakly bonded to the atomically smooth (110) face seeming to correspond to these states. According to ref. [7], molecular films remain stable over a broad temperature range, right up to T < 66 K. Since the phase diagram of the two-dimensional hydrogen-(110) tungsten system has been well studied and is known to consist primarily of two ordered phases, p(2 X 1) and (2 x 2) [8], the appearance of a different sequence of structures shown by the LEED method at low temperatures (T < 66 K) [9] as well indicates a freezing of the “precursor” states and formation of a molecular film. Due to this, molecular deuterium films are, for certainty, assumed to be the object of the present study. The electron scattering on the deuteriumcovered surface of single-crystal tungsten was used in the study as a tool for investigating the structural phase transition in a submonolayer adsorbate film at low temperatures. The selection of this adsorption system as the subject of investigation
B.V. (North-Holland)
208
A. G. Kundzich et al. / Deuterium a&orbed on W(I 10)
was determined not only by a natural interest in the behavior of hydrogen and of its isotopes on the surface of a solid 161, but also by the fact that deuterium molecules adsorbed on the tungsten (110) face retain an appreciable mobility even at low temperatures, right down to liquid helium temperatures. The method relying on the surface scattering of electrons is nondestructive, and its application in this case was most well-grounded. Data on the character of the surface electron scattering in thin metallic films deposited under a high vacuum are most often obtained by studying their electrical conductivity [lO,ll]. We resorted to another approach, based on the static skin effect [12]. This galvanomagnetic phenomenon is observed in compensated metals at the following conditions: I> d, wCr z+ 1 (w, is the cyclotron frequency, r the momentum relaxation time, 6 the mean free path of electrons, and d the plate thickness). Meeting these conditions requires the cooling down the sample to liquid helium temperatures. The static skin effect under various conditions was experimentally studied in refs. [13,14]. When the above conditions are satisfied, then the electric current flowing through a plate sample concentrates in a narrow, on the order of the Larmor radius, layer near the surface, with the result that the conductivity of the plate becomes very sensitive to the character of the surface electron scattering and hence also to the surface state; therefore, adsorption can in this case change, sometimes by an order of magnitude, the magnetoresistance of the sample considerably. The study being reported was a continuation of earlier investigations [15,16]. Its objectives included studying the mechanisms and type of the phase transition, determining the critical concentration of particles, and examining the phase transition kinetics. The total experimental evidence yielded by the study leads to the conclusion that the phase transition in the deuterium film occurs in the region of concentrations close to a monolayer and is due to evolution of the (1 X 1) phase rather than to the (2 X 1) phase, as assumed earlier in refs. [15,16], which is an equilibrium phase and appears to have been formed under the electron beam action. An essential part of the study was the investiga-
tion into the magnetoresistance relaxation, caused by processes of the onset of a thermodyna~c equilibrium in films after reaching the critical concentration of particles. The investigations were conducted at various temperatures; their results were compared with the generalities of growth of the average size of a new phase domain with time, i(t), for two-dimensional systems [17-191.
2. Experimental The data on the surface electron scattering were obtained by a method based on the static skin effect. To meet the conditions for this effect, the sample was placed into a strong magnetic field and cooled with liquid helium. The magnetic field source was a superconducting system. A constant magnetic field (H = 30 kOe) was oriented in the plane of the plate sample and directed perpendicular to the measuring current in the plate. The experiments were conducted under ultrahigh vacuum, the background pressure in the vacuum device at room temperature being of - lo-” Torr. The device, made of glass, comprised a system for cooling the crystal and monitoring its temperature with respect to that of the helium bath, sorption pumps, and pressure transducers (fig. 1). The design provided for varying the sample temperature by controlling the current through it as well as for raising the temperature “flashwise” to T = 2500 K for cleaning its surface. Walls of the chamber accomodating the sample and the gate controlling the kinetic gas flow of deuterium to the plate surface were liquid helium-cooled as well; the helium bath temperature could be lowered to 1.7 K when required. The cooling of the walls excluded an uncontrolled overdeposition of deuterium and made it possible to stop its adsorption at the required moment as well as to study relaxation phenomena at a fixed particle concentration. Deuterium was fed through a tube extending from the helium cryostat to the outside, into the “warm” part of the glass vacuum device. The gas temperature was not monitored. In some cases, another vacuum device type was used, which made it possible to combine the LEED and static skin effect methods; in such cases the vacuum
209
A.G. Kundzich et al. / Deuterium adwrbed on W(II0)
temperature T and effective deuterium pressure It is to be noted that Per, monitored only in the “warm” part of the device, determined the adsorption rate (or the time for AR(t) curves to reach saturation) and cannot be used in gas-kinetic calculations. The time in which the A R( t ) curve comes to saturation remains nevertheless a linear function of ( PC,)-1 over a broad pressure range. T and Per were experiment parameters, remaining unchanged in the course of deuterium adsorption. Lastly, it should be pointed out that the response AR(t) corresponded to adsorption on the front, i.e., the side of the plate facing towards the source. If the chamber walls were not cooled with liquid helium, the AR (1) signal shape could be distorted as a result of deuterium adsorption also on the back side. Fig. 2 shows AR/AR, versus t/r0 curves obtained within a temperature range from 1.8 to 10 K. (The procedure of changeover to relative coordinates AR/AR,, t/r0 was as follows: experimental data were presented in coordinates ln(1 P,,.
3
t Fig. 1. Schematic of experimental vacuum setup: 1: singlecrystal tungsten plate; 2: superconducting magnet; 3: cryostat; 4: external magnet-controlled gate; 5: external magnet; 6: sorption pump; 7: pressure transducer; 8: deuterium source.
device was arranged between electromagnet poles. This design was described in greater detail earlier
151.
Samples were prepared as follows. Plates sizing 3.0 X 10 X 0.5 mm3 were cut out of a tungsten single crystal. The face orientation accuracy was within * 20 angular minutes. The ratio of resistivities, characterizing the quality of the initial tungsten, was ~~~~~~~~~~= 7 X 104. The final thickness of the plates after grinding of the surface and its electrolytic polishing in a 3% NaOH solution amounted to - 0.1 mm. The samples were subjected to an ordinary procedure of high-temperature cleaning in an oxygen atmosphere. In measurements a signal proportional to the change in the magnetoresistance of the plate at adsorption or annealing of the film was recorded automatically. The H = constant condition was observed in all cases.
3. Results and discussion Some data on the critical concentration and character of the phase transition were derived simply from analyzing the shape of AR (t ) curves characterizing the plate magnetoresistance variations with the adsorption time at given sample
1.o
d 2
I
\_
0.5
a a
0L K
O0’ Fig. 2. Relative change of sample magnetoresistance as a function of dimensionless deuterium deposition time t/T, at various temperatures of the sample and pressure, Per = 1 x 10W4 Torr. AR/AR,=1 if t/To-co. Inset: fragments of similar dependences at T= 5.1 K and various P,,: (1) 8 X 10m6 Torr; (2) 1 x low4 Torr; and (3) 4x 10m4 Torr.
210
A. G. Kundzich et’ al. / Deuterium adsorbed on W(Il0)
16
I
I
0
150
300
!
I
450
t(sec)
Fig. 3. Change of sample magnetoresistance as a function of oxygen and deuterium deposition time. Sample temperature: 4.2 K. Dashed lines show approximation of these data by the function F(t) (refer to text).
AR/AR,) =f(t) and then transformed to a linear dependence by selection of the parameter AR,. The slope of the straight line thus obtained is l/rO.) It is obvious that adsorption changes the sample magnetoresistance; however, the A R/AR, versus t/r0 curve has a complex bell-shaped form, which is also appreciably temperature-dependent: with increasing T the maximum of the curve shifts towards lower exposures; and, lastly, it has a shallow minimum in the long exposure region. Fig. 3 presents the AR/AR, versus t/r0 curve characterizing the magnetoresistance change as a function of oxygen adsorption time at T = 4.2 K for the same tungsten plate and, for comparison, also one of the curves for deuterium. It is essential to emphasize that the dependence for oxygen, in contrast to that for deuterium, is a smooth monotonic one and can be successfully approximated by a function of the form F(t) = 1 - e-‘/‘o. Proceeding now to the discussion of these results, we will make some general comments. In particular, it seems essential to analyze some models of surface structures from the standpoint of their influence on the scattering of conduction electrons.
Model I. This model appears to correspond to films forming at oxygen adsorption on the tungsten surface cooled to low temperatures. Such layers can appear when several adsorption site types exist on the surface. At low adsorbate concentrations the filling of the most energetically favorable sites (which in the general case are bridge or threefold sites) is more probable. As the concentration increases, adsorption of particles into the “second” layer becomes possible, which is equivalent to adsorption into on-top sites; these sites may be considered as the “precursor” state. Existence of other adsorption site types is also possible. Thus, a statistical filling of several adsorption sites results in a film where the arrangement of particles does not correlate with the substrate symmetry. In the simplest case the existence of “active” and “passive” sites can be supposed. Such a hierarchy is physically obvious, e.g., with a polylayer adsorption, where the first layer exerts a higher influence than does the n th one. Since the probability of filling empty sites declines directly with the concentration of already occupied sites as S = C(l - f& ), C = constant, which is also applicable to “active” sites, then 6,, = 1 - e-f/70, where 0,, is the concentration of already filled “active” sites. Due to this, the data of fig. 3 for oxygen can be interpreted as follows: AR is a linear function of @_,. This formally resembles Langmuir’s kinetics, but 0,, can differ from the actual coverage. It is clear that a conventional monolayer with some concentration N,, corresponds to the asymptotic P(t) value, and therefore AR changes may be calibrated in 0,, units, while it is obvious that N,, does not coincide with the standard density of sites of the W(110) surface lattice. Model II. Adsorbed particles are in this case arranged in equivalent adsorption sites, not more than one particle corresponding to every unit cell of the surface lattice; this is an ordinary model of the lattice gas. Within the scope of the concept of the diffractional interaction of conduction electrons with a metal surface such a model presumes a nonmonotonic behavior of AR with increasing 8. In particular, at 0 G 8 G 0.5 an increase in the diffuse scattering of electrons, caused by the growth of the number of scattering centers on the crystal surface, should be expected. At 0.5 G 8 =G1,
211
A.G. Kundzich et al. / Deuierium a&orbed on W(I IO)
vacancies in the adsorbate lattice are filled and the (1 x 1) phase is formed. The higher the 6 value, the more perfect the (1 x 1) lattice, which has the symmetry of the substrate. It may be believed that in the range of 0.5 G 8 6 1 the AR value declines due to increasing specular reflection of electrons. By analogy with model I, AR - F(t) in the region of 0 < 19< 0.5 and AR - 1 - F(t) in the region of 0.5 < 0 < 1. Thus, the transition from a film with structure I to a film with structure II may be accompanied by a drmatic change in the surface electron scattering character, especially when the particle concentration is close to a monolayer. This fact has found a direct experimental substantiation. In particular, AR decrease to zero indeed corresponded to the growth of an ordered oxygen film at T = 700 K with formation at high 8 of the (1 x 1) phase which replicated the structure of the W(110) face [5]. Annealing a deuterium film, deposited up to saturation, at T > 100 K as well results in formation of an ordered (1 x 1) atomic phase and AR decrease to zero. A progressive deuterium evaporation from the sample surface as the temperature of heating is further increased leads to a new rise of the magnetoresistance AR; the corresponding curve is shown in fig. 4, where it is seen that the magnetoresistance once again acquires the initial value R after a full removal of deuterium from the surface. Formation of islands of an ordered phase may also be accompanied by an appreciable change in the surface scattering character. Even the simplest model of a commensurate film shows that rearrangement of particles with formation, e.g., of the (1 X 1) phase and empty surface areas can further reduce the surface scattering. In the general case, however, the growth of islands of an ordered phase with an arbitrary symmetry calls for a special analysis. Return now to the data of fig. 2. The family of A R/AR, versus t/r0 curves, presented here, is over a considerable length approximated by the function F(t). Our basis assumption is that deuterium molecules, adsorbing on a cold surface, form a film with structure I, which is indicated by the possibility of approximating experimental AR(t) curves
0
200
T(K)
100
600
Fig. 4. Progressive evaporation of deuterium. AR variation with temperature of heating. Measurement were made on other crystal.
with the function F(t). As can be ssen from fig. 2, the fit is the better, the lower the sample temperature. However, the departure of experimental curves from F(t), particularly marked in the high concentration region or at an elevated temperature, indicates the transition of the film to another state. If this film I-film II transition indeed occurs close to a monolayer, but so that 8 # 1, then the remaining vacant sites in the formed (1 X 1) phase can unite in the course of time to form voids-inclusions. Such a transition, at least at the stage of formation of a commensurate film, may be diffusionless (like the martensitic one) since, e.g., the passage of a particle from one adsorption site to another is energetically more favorable and requires no diffusion walks. Let us discuss some consequences of this model. Note, first, that the existence of a critical concentration 8,, is an important criterion of most phase transitions. Let us analyze from this standpoint the data presented in fig. 5. Every experimental point in this figure has its corresponding new film which was adsorbed at low temperatures on a surface cleaned of the preceding deposit and was then annealed. It is essential that the anneal-
212
A. G. Kundzich et al. / Deuterium &orbed
ing substantially reduced AR in a limited concentration region, while a further increase of the annealing temperature Tan does not change the indicated range of coverages. Since Tan -C 66 K, the system under study seemingly remains a molecular one. Fig. 6, presenting the same data, but in the magnetoresistance, AR, versus relative concentration, @_,, coordinates, shows the critical concentration region indeed to lie near the saturation coverage. We, of course, realize the conventionality of such estimates. Note also that the shape of AR(t) curves is governed not only by the rate of relaxation processes in the film, but also by the rate of inflow of new particles from the gaseous medium. From this standpoint it is interesting to examine the mechanism of formation of the AR(t) minimum, which is well marked for some curves measured in the region of high enough temperatures. An example of such a dependence is shown, in particular, in fig. 2. If the phase transition to a commensurate structure indeed proceeds close to a conventional monolayer and 6 + 1, then voids serving as the
0
LOO
200
600
t (set) Fig. 5. Change of sample magnetoresistance with deuterium deposition time. Solid curve: 4.2 K; points: results of film annealing to 20 K. Dashed curve was drawn “by eye”.
on W(1 IO)
tY
a
Fig. 6. Data of fig. 5, plotted in “magnetoresistance versus relative adsorbate concentration” coordinates, illustrating the closeness of 0,, to a monolayer.
drain for vacant points may develop within a (1 x 1) cluster. The first stage of the film I-film II transition proceeds in a diffusionless manner and rapidly, and appears to consist in freeing the “precursor” states, while the second stage, involving growth of the voids, proceeds slowly as being associated with diffusion walks of vacant sites within a cluster of the commensurate (1 X 1) phase. The evolution of the averag size of the islands (voids), i(t), is governed by the laws of growth of new phase domains and in the general case depends on the phase transition type, surface mobility, and other factors [17-191. Of course, separation of the commensurate film into a compact (1 x 1) phase and voids allows this process to be defined as a first-order phase transition. Since the increase of the average size of voids, or, more exactly, of their average area, due to the inflow of vacancies is not a linear function of time (for example, for a first-order phase transition, i(t) t’13) a moment will come when the balance is disturbed towards adsorption of particles from the kinetic gas flow. The drain of vacant sites (defects of a (1 X 1) cluster) corresponds to a AR decrease, while the
213
A.G. Kundzich et al. / Deuterium adsorbed on W(I IO)
adsorption of new particles within the limits of voids corresponds to a AR increase, and hence their balance yields the AR(t) minimum. Of course, the balance can be disturbed by changing the flow or the crystal temperature. As can be seen from the inset to fig. 2, increasing the flow as little as a few times indeed results in smoothing the A R( f ) curve. However, increasing the temperature allows a new equilibrium to be set, and hence every Per has its corresponding temperature range where conditions for the existence of the AR(t) minimum occur. The experimental setup made it possible to shut off the flow, then to increase the temperature and, after a delay needed for relaxation, to deposit a new amount of the substance. The deposition increased the ma~etoresistance, which indicates that empty portions indeed appear to emerge in the film, but their contribution to AR is small and their total area is not over a few percent of the total (1 X 1) cluster area and depends on the duration of the gas flow shutoff. The probability of filling of vacant points declines as S = ~(1 - 8), and hence macroscopic voids are predominantly filled at repeated depositions. Their filling closes the drain channels for the vacant points. It is
i
g -0.6
u
a
K 4.65K
4.6
-0.8
4.7 K 4.85K 5.0 K 5.3 K 1
Fig. 7. Samplemagnetoresistance relaxationat constant terium concentration and various temperatures.
In t 0
4
2
6
8
0
-1 ~
I
-2 CX p-3 ‘E II -L-
.
-5-
l
-6-
T
+
+ 0 0 + B 0 0
=- 5.3 K x- 5.0 K A - 4.65 K l -L.7 K +-4.65 K e -1.6 K
Fig. 8. Data of fig. 7, plotted in double logarithmic scale.
probably for this reason that films deposited up to saturation remain stable with time. Let us, omitting the initial stage of transition to film II, turn to the analysis of the further evolution of the system. At this stage the adsorbed film appears to represent a continuous cluster of the p(1 x 1) phase with both voids and single vacancies existing within it. “Second-layer”, or “precursor-state”, particules exist probably as well. A further evolution of the system consists in migration of individual vacancies and their connection to vacancy clusters as well as in passage of “second-layer” particles into the first layer. Such a process can result in reducing the surface electron scattering, and therefore the sample magnetoresistance can change as follows: AR(t) = [t(t)]*, where L is the average island size. On the other hand, the growth of submonolayer film islands with time is known to obey the law i(t) = tX [17-191. Fig. 7 shows the data characterizing the magnetoresistance relaxation rate at various temperatures (at a constant adsorbate concentration on the surface). Fig. 8 presents the same data in a double logarithmic scale; for convenience of plotting, the AR sign in this figure is reversed. It is obvious that magnetoresistance relaxation depen-
214
A.G. Kundzich et al. / Deuterium
In t
0
2
L
6
0
0
-0.2
Ill A.F. Andreev, Usp. Fiz. Nauk 105 (1971) 113. PI R.F. Green, in: Solid State Surface Science, Vol. 1 (Dek-
i d-0.6 lx 4 q
X-
- 5.3 K
.
5.0 K
d - 4.85 K -1 .a
adsorbed film and of their effect on the scattering of carriers on the surface.
References
ID IO-O.4
-0.8
a&orbed on W(I IO)
*-&.I
K
+ - L.&K ' - L.6 K
-1.2 Fig. 9. Data of fig. 7, plotted in semilogarithmic scale.
dences can indeed be approximated by a power function AR(t) - kt2x, where k = F(T). An estimate of the exponent yields x - 0.48. Assuming the temperature dependence of k to follow the Arrhenius law, the activation energy of ordering of adsorbed deuterium molecules can be estimated: ED, = 60 K. At late stages of the process, however, a transfer to a logarithmic law of the growth, AR = c In t, takes place. The logarithmic growth region is reached faster as the temperature is increased, which is evidenced by the data of fig. 9. The obtained results show a good agreement with predictions of the theory of kinetics of phase transitions on the surface of a solid, which is still another corroboration of the validity of the suggested interpretation of processes occurring in an
ker, New York, 1969). 131 A.A. Kharlamov, O.A. Panchenko and I.N. Jakovkin, Zh. Eksp. Teor. Fiz. 71 (1976) 760. 141 A.A. Mitrjaev, O.A. Panchenko, 1.1. Razgonov and V.S. Tsoi, Surf. Sci. 75 (1978) 376. [51 P.P. Lutsishin, T.N. Nakhodkin, O.A. Panchenko and Ju.G. Ptushinskij, Zh. Eksp. Teor. Fiz. 82 (1982) 1306. [61 K. Christmann, Surf. Sci. Rep. 9 (1988) 1. [71 R.F. Polizzatti and G. Ehrlich, J. Chem. Phys. 71 (1979) 259. VI M. Altman, J.W. Chung, P.J. Estrup, J.M. Kosterlitz, J. Prybyla, D. Sahu and S.C. Ying, J. Vat. Sci. Technol. A 5 (1987) 1045. [91 V.V. Gonchar, Ju.M. Kagan, O.V. Kanash, A.G. Naumovets and A.G. Fedorus, Zh. Eksp. Teor. Fiz. 84 (1983) 249. 1101 D. Dayal and P. Wissmann, Vakuum Technik 38 (1989) 121. [ill D. Dayal, H. Finsel and P. Wissmann, in: Thin Metal Films and Gas Chemisorption (Elsevier, Amsterdam, 1987) p. 53. WI M.Ja. Azbel, Zh. Eksp. Teor. Fiz. 44 (1963) 986. w31 A.A. Mitrjaev, O.A. Panchenko and G.M. Pugach, Zh. Eksp. Teor. Fiz. 75 (1978) 1356. 1141 O.A. Panchenko, A.A. Kharlamov and Ju.G. Ptushinskij, Zh. Eksp. Teor. Fiz. 64 (1974) 780. v51 P.P. Lutsishin, O.A. Panchenko and S.V. Sologub, Pis’ma Zh. Eksp. Teor. Fiz. 41 (1985) 31. WI P.P. Lutsishin, O.A. Panchenko and S.V. Sologub, Izv. Acad. Nauk SSSR 52 (1986) 1466. v71 I.M. Livshits and V.V. Slezov, Zh. Eksp. Teor. Fiz. 35 (1958) 479. [18] J.D. Gunton, in: Springer Series Surface Sciences, Vol. 8 (Springer, Berlin, 1987) p. 238. [19] K. Heinz, in: Springer Series in Surface Sciences, Vol. 8 (Springer, Berlin, 1987) p.202.