Synchrotron X-ray diffraction applied to the study of physisorbed monolayers

Nuclear Instruments and Methods 208 (1983) 549-554 North-Holland Publishing Company

SYNCHROTRON MONOLAYERS

X-RAY DIFFRACTION

549

APPLIED TO THE STUDY OF PHYSISORBED

M. NIELSEN, J. BOHR, K. K J A E R a n d J. A L S - N I E L S E N Riso National Laboratory, Riso, DK-4000 Roskilde, Denmark J.P. M c T A G U E Brookhaven, National Laboratory, Upton L1, NYl1973, USA

The systems of physisorbed monolayers are primarily studied because of their approximate two dimensional character. By examples we shall show how synchrotron X-ray diffraction is applied to the study of crystalline order of rare gas atomic monolayer on graphite surfaces, and in particular how information may be obtained about fundamentals of two dimensional phase transitions.

1. Introduction We shall in this paper discuss how high intensity and high resolution X-ray diffraction can be used to study phase transitions in two dimensional (2-d) systems. The fundamental physics in studying these concerns the nature of the "topological excitations" (like dislocations or domain walls) which are predicted and may be observed to drive the continuous transitions like melting or the commensurate-incommensurate transition (see below) [1,2]. At the transition there is a divergence of the separation of such topological excitations and experimentally this may be observed as a narrowing of structure factors when approaching the transition temperature, Tc. Thus, two conditions for studying these phenomena are: (1) we must find a physical realization of a 2-d system which is sufficiently free of defects that these do not limit the divergence to be observed; and (2) our diffraction measurements must be done with sufficiently high m o m e n t u m resolution to observe the typical narrowing of the structure factor. We can combine the two conditions and then specify an effective experimental resolution as the size of the area over which we observe the intrinsic behaviour of the 2-d film. For an ideally ordered 2-d crystal structure this would be the area over which the Bragg scattering of the X-rays is coherent and an effective measure of it would be the width of the observed Bragg reflections. It is customary to give the effective resolution as a coherence length L. As this field of " 2 - d phase transitions" has developed in the latest years in general the theoretical predictions have been accompanied by specific proposals for studies of particular adsorbed monolayer films. However, the experimental hard facts have been that most experiments have been characterized by effective resolu0167-5087/83/0000-0000/$03.00 © 1983 North-Holland

tions of L = 1-200 ,~, which is often insufficient as we shall see. It was therefore a major breakthrough in this field when the first synchrotron X-ray diffraction measurement by Birgeneau et al. [3] showed that a coherence length of L - 2000 ,~ was obtainable. The measurements were done on a monolayer of Kr adsorbed on the graphite substrate U C A R - Z Y X . This substrate is still unique in giving adsorbed films of such quality, L - 2000 •~, and this includes all known solid surfaces. The spectrometers have been improved very much and high intensity measurements can now be performed with the instrumental resolution corresponding to L = 10000 A. In the following section first the experimental technique we use in Hamburg in the study of surface films will be discussed briefly (a more detailed description is given in the following paper [8]; then, experimental results demonstrating two kinds of 2-d phase transitions are shown, namely melting of a free floating solid and the transition from a commensurate solid structure (7~ × f 3 or 2 × 2) to an incommensurate structure by the mechanism of domain formation.

2. Technique The X-ray spectrometer (see fig. 1) is located at beam line D4 of the storage ring DORIS. The horizontal aperture here is 1 mrad but only a small fraction of this is used as no focussing elements have yet been installed. As monochromator are used two perfect G e ( l l l ) crystals. The second order reflection is thus forbidden and the third order reflection is eliminated by miss-setting one of the Ge crystals by about the Darwin-width of the (111) reflection. By this, most of the first order intensity is still transmitted but third Vll. SCATTERING~DIFFRACTION~RELATED TECHN.

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Fig. 1. Schematic top view of setup. Al: 4 × 6 mm 2 slit, A2:1 ×6 mm 2 slit; M I and M2: G e ( l l l ) monochromators; IC: ionization chamber monitor; C: cryostat, S: graphite sample cell; V: standard volume with pressure gauge: PSD: position sensitive detector. Vacuum beam-path with Be-windows between M~-M 2 and M 2-IC and C-PSD.

( a n d higher) harmonics are almost eliminated because their Darwin widths are smaller. In most of the measurements the radiation scattered from the sample is measured with a position sensitive detector (PSD). This is a proportional gas-flow counter and with this it is impossible to pulse height discriminate against higher order c o n t a m i n a t i o n ; therefore the double m o n o c h r o m a t o r was used. With this setup the instrumental resolution is p r e d o m i n a n t l y determined by the width of the sample seen from the PSD. We used a 1 m m slit m o u n t e d close to the sample. By changing the slit width or the length of the detector arm we can adjust the resolution to m a t c h the p h e n o m e n a u n d e r study. In most cases we used the 1 m m slit and a 600 m m detector arm, giving a resolution of L = 1200 ,~. As a graphite substrate we have exclusively used U C A R - Z Y X which is degassed at 800°C a n d then contained in an all metal sealed cell with Be windows. The cell is connected via a capillary to a s t a n d a r d filling volume and a pressure gauge outside the Displex cryostat holding the sample cell. The substrate is a powder of graphite grains with large (002) surfaces having the h o n e y c o m b structure. The mosaic spread of the grains leads to the following: if we adsorb atomic monolayers on the substrate and these crystallize in perfect 2-d crystals, then the ideal diffraction result would not be &functions but sawtooth shaped intensity curves. As a function of the m o m e n t u m transfer Q the scattering intensity has sharp steps at the values defining the length of the reciprocal lattice vectors and then a sloping decrease of intensity on the high Q side the shape of which is determined by the orientational distribution of the graphite grains. All analyses of diffraction results have to account for this sawtooth curve by p r o p e r unfolding but the shape of the

curve is given by the substrate and does not depend on the adsorbate. Also, the measured Bragg curves are a powder averages where all orientations of the azimuthal angle a r o u n d the (002) direction of the graphite grains have the same weight. Thus only longitudinal fluctuations in the 2-d films contribute to the b r o a d e n i n g of the Bragg curves.

3. Melting of free floating solids In fig. 2 the h o n e y c o m b structure of graphite surfaces is shown schematically. The monolayer films of rare gases in some cases (Kr and He) form the comm e n s u r a t e v ~ × !/3, 30 ° structure a n d in other cases (Ar, Xe) form i n c o m m e n s u r a t e structures with no registry between the periodicity of the film and that of the

Fig. 2. The hexagons illustrate the surface structure of the graphite substrates. The circles show adsorbed atoms and in the upper structure they are located above every third hexagon center and form a ~3 x ~ commensurate phase. The lower structure illustrates an incommensurate "free floating" phase.

M. Nielsen et aL / Study of physisorbed monolayers graphite surface• Both situations are shown in the figure. The commensurate solid is translationally locked to the surface whereas the incommensurate solid can be translated freely and is characterized as free floating. Such solids are predicted to have the following ideal behaviour [l]: At low temperatures they crystallize in "quasi long range ordered" structures which at the first Bragg point have structure factors of the form

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where G O is a reciprocal lattice vector. S ( Q ) diverges at Q = G O but wings extend out in the Brillouin zone. Introducing the finite size and finite instrumental resolution gives then an intensity curve around the Bragg point with a Gaussian central peak, the width of which is given by L, and with broad wings extending out into the zone. The intensity of the wings, controlled by the temperature dependent 7, increases from zero at T = 0 to about 1 / 3 of the central peak intensity near the melting point. N o w for the melting transition, a specific mechanism, " t h e unbinding of dislocation pairs" has been described and detailed structure factor functions predicted. The melted phase, called hexatic, is characterized by quasi long range ordered angular correlations (which we cannot observe with our diffraction technique) and the structure factor becomes a Lorentzian function with a particular T dependence of the correlation length, ~ [1]. Two of the experimentally studied systems may have this behaviour, namely, low density Ar monolayers [4] and high density Xe monolayers [5]. In fig. 3 the phase diagrams of At, Kr and Xe films on graphite are shown. The temperatures are normalized with the corresponding triple point temperatures of the bulk substances and the significant differences between the diagrams indicate that there is no valid law of corresponding states. The Kr monolayers are stabilized by the substrate potential in the commensurate 7'3 structure and " m e l t " at a higher reduced temperature than Xe and Ar. Both of the latter films are supposed to be free floating, Ar with a layer density higher, Xe with a lower density than the commensurate Kr layers. At low layer densities (p), Xe films have a 3-d like first order melting transition with a triple point line. However at high p values, as indicated by the dotted line in the figure, the melting transition becomes continuous and in this region Heiney et al. [5] have measured very accurate structure factor functions using the crystal spectrometer in Stanford with wigglers and a focussing mirror. Their results are in agreement with the theoretical predictions [1]. We have in D E S Y concentrated our measurements on the Ar monolayers and we conclude that for this system the melting transition is continuous at all densities; the lower panel of fig. 3 shows the phase diagram. Because Ar is a weak X-ray scatterer we could not

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obtain diffraction groups accurate enough for detailed line shape analysis. The melting transition is seen as an onset of broadening of the diffraction group and within 1-2 K above this temperature the groups get so broad that we cannot observe them anymore. In order to conclude whether the dislocation unbinding is the responsible mechanism for the melting transition, a new series of measurements has been done in collaboration with D. Moncton at the crystal spectrometer in Stanford; fig. 4 shows examples of observed groups. The analysis of these is not yet completed. The continuous nature of the melting is documented and the line shapes will give information about the paramenters ~ and ~ to be compared with predictions and the corresponding values for high density Xe layers.

4. T h e c o m m e n s u r a t e - i n c o m m e n s u r a t e

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atoms or molecules are adsorbed above specific positions of the h o n e y c o m b graphite lattice. The phase transitions from such structures to i n c o m m e n s u r a t e free floating structures or to isotropic fluids have been studied intensively. Especially for the first kind of transitions synchrotron X-ray diffraction has c o n t r i b u t e d significantly a n d we shall discuss examples of that. The m e c h a n i s m responsible for the transition can be given a simple geometrical interpretation which is illustrated in fig. 5. We assume that the c o m m e n s u r a t e structure (C) is that of ( 3 x ( 3 (see fig. 2) in which a particle is located above the center of every third hexagon center. Thus there are three equivalent structures only distinguished by a translation of the entire film by the vector from one center to a neighbouring center a n d we may label the three structures A, B and C. W h e n more particles are adsorbed than can be accomodated in the pure C phase then a c o m m e n s u r a t e - i n c o m mensurate ( C - I ) transition takes place by the formation of domains such that inside each d o m a i n we have a

c o m m e n s u r a t e A, B or C structure and all the extra particles are located in the d o m a i n walls (see fig. 5). It is the wall formation which drives the phase transition a n d it is the wall geometry which determines the nature of the transition, and fortunately this behaviour may be followed in a diffraction experiment. Both the d o m a i n configurations shown in figs. 5b a n d 5c have been observed experimentally. Fig. 6 shows diffraction groups observed near the (10) reflection of the weakly i n c o m m e n s u r a t e Kr monolayers on graphite [6]. The lower left panel shows a double group from which the d o m a i n pattern is identified to be that of fig. 5b. The high Q c o m p o n e n t is, relative to the position of the single peak of a pure c o m m e n s u r a t e x/3 × f 3 structure at Q = 1.703 A - ~ shifted twice as much as the smaller peak (the satellite) is shifted towards the low Q side. F r o m these shifts we can find the size of the hexagonal domains a n d from the intensity of the two peaks we can calculate the width of the d o m a i n walls. In the particular m e a s u r e m e n t of fig. 6 the C - I transition was induced by a special technique in which a 2-d spreading pressure was applied with the help of a coadsorbed film of D 2. In the upper left panels the D 2 spreading pressure is decreased a n d the observed diffraction patterns show that coexistence takes place between a phase having the lowest panel diffraction pattern and the pure C phase with a single peak at Q = 1.703 ,~ 1. This means that this phase transition is of first order. Theoretically all C - I transitions in which the hexagonal d o m a i n structure (fig. 5b) is formed are predicted to be of first order, at low temperatures. Additional features are observed at higher temperatures where fluctuations in the d o m a i n p a t t e r n s are important. The alternative d o m a i n p a t t e r n of fig. 5c, called the stripe structure, has been found to describe the C - I transition of N 2 and C F 4 monolayers. The C F 4 films have the 2 × 2 c o m m e n s u r a t e structure and the adsorption sites are above vertex points of the graphite surface. W i t h o u t discussion of any of the implications of this, the gross

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features of the phase transition m a y be u n d e r s t o o d on the basis of fig. 7 showing the observed diffraction groups near the (10) Bragg reflection of the (2 × 2) structure. T h e reciprocal space of this is the regular triangular lattice. As the stripe phase is formed, this implies an uniaxial compression of the structure in real space and a corresponding expansion of the reciprocal space. As a result, the powder diffraction p a t t e r n becomes a doublet with the intensity ratio 4 : 2 of the two c o m p o n e n t s , a n d the smallest c o m p o n e n t with the multiplicity of 2, stays at the c o m m e n s u r a t e position. The figure shows how this particular p a t t e r n evolves in a continuous way when the temperature is decreased t h r o u g h the transition at T = 75 K. F r o m such m e a s u r e m e n t s we can, at least in principle, give a detailed description of these phase transitions. In practice the most intense s y n c h r o t r o n X-ray b e a m s are needed if critical exponents shall be determined.

6. C o n c l u s i o n

The s y n c h r o t r o n X-ray diffraction technique has p r o v e n to be very powerful in the study of phase transitions of physisorbed monolayers on graphite. It is c o m p l e m e n t a r y to the L E E D technique because of a 10 times better m o m e n t u m resolution a n d because it may b e applied at all vapor pressures. L E E D can however detect angular epithaxy because it uses a single-crystalline surface, a n d often due to the strong scattering intensity it can detect more reflections than with X-rays a n d give i n f o r m a t i o n about, e.g., molecular orientations (N2, 02). The d e v e l o p m e n t of more intense X-ray beams from synchrotrons is going to be i m p o r t a n t for the kind of research described here. T h a t will allow us to measure the Bragg profiles at higher indices where the line shapes are different from that at Go; this is i m p o r t a n t for interpreting the properties of the free floating solids. Similarly for C - I transitions the splitting of the Bragg profiles at the higher indices reflections will give a m u c h more accurate interpretation of the d o m a i n wall mechanism.

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[1] Y. lmry and L. Gunthen, Phys. Rev. B3 (1971) 3939; Y. Imry, Crit. Rev. Sol. Star. Mat. Sci. 8 (1979) 157; B.I. Halperin and D.R. Nelson, Phys. Rev. 41 (1978) 121. [2] P. Bak, Rep. Progress Phys. (June, 1982). [3] R.J. Birgeneau, E.M. Hammond, P. Heiney and P.W. Stephens, in Ordering in two dimensions, ed., S.K. Sinha (Elsevier-North-Holland, Amsterdam, 1980) p. 29. [4] J.P. McTague, J. Als-Nielsen, J. Bohr and M. Nielsen, Phys. Rev. B25 (1982) 7765. VII. SCATTERING/DIFFRACTION/RELATED TECHNIQUES

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M. Nielsen et al. / Study of physisorbed monolayers

[5] P.A. Heiney, R.J. Birgeneau, G.S. Brown, P.M. Horn, D.E. Moncton and P.W. Stephens, Phys. Rev. Lett. 48 (1982) 104. [6] M. Nielsen, J. Als-Nielsen, J. Bohr and J.P. McTague, Phys. Rev. Lett. 47 (1981) 582.

[7] K. Kj~r, M. Nielsen, J. Bohr, H.J. Lauter and J.P. McTague, Phys. Rev. B26 (1982) 5168. [8] J. Bohr~ K. Kj~r, M. Nielsen and J. Als-Nielsen, these Proceedings, p. 555.