Surface Science 178 (1986) 452-461

North-Holland, Amsterdam

EVIDENCE FOR MONO- AND DIATOMIC STEPS ON A CLEAVED Os(OOO1) SURFACE

H. SAALFELD, S. TOUGAARD *, K. BOLWIN and M. NEUMANN

Unrrersiliit Osnrrhriick, Fachbereich Physik, D-4500 Osnabriick. Fed. Rep. of Cermnn,v

Received 13 March 1986; accepted for publication 21 May 1986

The prominent role of defects on surfaces in catalysis is well known. A reliable tool to study

extended defects is provided by LEED. An analytical model for the low energy electron

diffraction at stepped surfaces of crystals with nonprimitive lattices (e.g.. hcp(0001) or diamond

(100)) is developed and compared to numerical calculations of statistically stepped surfaces.

Experimental data of a cleaved Os@OOl) surface then show the coexistence of mono- and diatomic

steps.

1. Introduction

Catalytic properties of surfaces are highly in~uenced by the existence of surface defects. One of the most powerful techniques for the investigation of extended surface defects is based on low energy electron diffraction. Thus during the past decade methods to extract information on surface step distributions through an analysis of LEED spot profiles (SPALEED) have

been developed [ 1 -lo]. Previous investigations have concentrated on surfaces where only one type

of steps occurs [l-lo]. In contrast, other surfaces as e.g. hcp(0001) and

diamond (100) have two types of steps (see fig. 1). In a recent work [ll] this problem was considered for the first time analytically.

In the present work analytical results for a surface with two types of steps are presented and compared both to numerical evaluations for surfaces with statistical step distributions and to experimental data for Os(OOO1). The conclusion is that a two-step model is essential for the description of extended defects for these systems.

* Alexander-von-Humboldt fellow, permanent address: Fysisk Institut, Odense Universitet, DK- 5230 Odense M. Denmark.

0039~6028/86/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

H. Saaljeid et al. / Mono- and diatomic steps on cleaved Os(OOO1) 453

2. Analytical model

The position of atoms on three neighboring terraces of an hcp(OOO1) surface are given by (see fig. 1)

g,=la+mb,

g,=g,+ua+(l-u)b+dIc/lcl,

g,=go+d,c/lcl~

(1)

Here, 1, m are integers; a, b, and c are the basis vectors of the hcp space lattice, and d,, d, are the two step heights. For the two possible types of steps on the hcp(OOO1) surface u = l/3 and u = 2/3, respectively.

The change in momentum for elastically backscattered electrons in the (h, k) direction is given by

Ak=ha*+kb*+Lc*, (2) where a*, b*, and c* are the hcp reciprocal lattice vectors. In eq. (2) h, k are integers, while L is determined by the elastic scattering condition. Then the energy of a normal incident electron elastically backscattered in the (h, k) direction is

Lc*+ (ha*+kb*)2 I ’

LP [eV A-‘].

steps I I I steps 1 1

hcp

Fig. 1. Schematic model of stepped fee (a) and hcp (b) surfaces. Steps are indicated by arrows. Note the existence of two different types of steps on the hcp(OOO1) surface.

454 H. Saalfeld Ed al. / Mono- and diatomc steps on cleaued Os(OOO1)

Assume we have a monotonic and regularly stepped surface. Then, for a given momentum transfer, the scattering amplitude is within the kinematic

approximation

s’= C exp[-i(n,a+ZOb+g,) Ak] + C exp[-i(n,a+1,6+g,) Ak] nolo rllll

+ c exp[-i(n,a+Z,b+g,) ilk].

n 212 (4)

Here n,, 1, run over all atoms on each of the three terraces. The unit (consisting of three terraces) which characterises a monotonic regufurb stepped surface must contain twice as many atoms on the intermediate layer compared to the two neighboring layers. From eq. (4) we then find the intensity Z of the

(h,k) beam

Za~+cos(g,~Ak)+~cos(g,~Ak)+cos((g,-g,).Ak). (5)

Intensity maxima correspond to in-phase scattering from neighboring terraces which in real space will produce a narrow spot. On the other hand intensity minima correspond to out-of-phase scattering in which case we have broad spots. Therefore, the energetic positions of half width extrema for a given

(h, k)-beam can easily be deduced from eqs. (2), (3) and (5) by analysing the behavior of ~Z/X.. Thus we find the characteristic values of Lc* for the half width minima

Lc* = 2rn/d, and Lc* = nn/d, (64

for the (OO)- and (lo)-beam respectively, where n is an integer. We get the same conditions for the (ll)-beam as for the (OO)-beam. For the half width maxima we find

~c*=${2n&[l-2v(h-k)]}. 1

The two possible values of u (l/3 and 2/3) give the same set of Lc* values in

eq. (6b). Eqs. (5) and (6) were derived under the assumption of a monotonic

regularly stepped surface (2di = d2). However, as shown in the next section, surfaces with a statistical step distribution produce half width extrema at the same energetic positions as eqs. (3) and (6).

Fig. 2 shows the intensity versus Lc * for the (OO)- and (lo)-beams, respectively (solid curves). Also shown are the same curves evaluated for a one step model (dashed curves). The one step model [l] is obtained by removing the intermediate layer (u = 0) in eqs. (1). For the (OO)- and (ll)-beams the number of extrema is twice as large in the one step model compared to the two step model. For the (lo)-beam the number of extrema is the same in both models, but note that the positions of intensity minima are different.

H. Suarfeld et al. / Mona- and diatomic steps on cleaved Os(OOO1) 455

a

12n-I)$ f2n+l) z

Fig. 2. Intensity as a function of Lc * for (a) the (OO)- and (b) (lo)-beams, respectively. Solid curves: two step model. Dashed curves: one step model. The (ll)- and (OO)-beams behave

identical.

The above evaluation is valid for the hcp(0001) surface. For the diamond (100) surface the result of a similar analysis was recently published [ll].

3. Numerical evaluation

To test the range of applicability of eq. (6), which is evaluated for a monotonic regularly stepped surface, we study in this section the result of statistical step distributions. The surfaces considered are composed of parallel stepped atomic rows (see fig. 1). The steps are generated with the geometric

456 H. Saalfeld et al. / Mono- and diatomic steps on cleaoed Os(OOO1)

I

(2n-113 2nz

iC*

Fig. 3. Intensity as a function of Lc* for the (~)-beg under variation of the probability P2 for a

step to be diatomic. Note that intensity increases at former intensity minima as Pz is increased.

For P2 = 0 and P2 + 1.0 the I( Lx’) curves are similar to the corresponding analytical curves in

fig. 2a.

dist~bution, under variation of the average terrace width (W) and the prob- ability for a step to go down ( Pd). For fixed parameter values, 2000 different surfaces were averaged. The transfer width was 150 atoms.

As an example figs. 3 and 4 (solid curves) show the resulting I( .Lc*) curves

(2n-11%

Fig. 4. Intensity as a function of Lc * for the (lo)-beam under variation of Pz. Note that the positions of intensity minima move gradually from the asymmetric l/3 positions to the symmetric l/2 positions as Pz is increased. For Pz = 0 and P2 41.0 the I( kc*) curves are similar to the

corresponding analytical curves in fig. 2b.

H. Saalfeld et al. / Mono- and diatomic steps on cleaved Os(OOO1) 457

for IV= 30 atoms and Pd = 0.5, corresponding to a macroscopically flat

surface. A comparison to fig. 2 shows that the positions of extrema are nearly identical to the analytical values. Similar results were obtained for other values of W and Pd. This demonstrates that although eqs. (5) and (6) were derived

for a monotonic regularly stepped surface it can be applied also to surfaces with a statistical step distribution.

While the positions of half width extrema are nearly constant under variation of W, the half width value varies strongly with W. This effect has been studied extensively in the past and based on this, methods to extract detailed information on terrace width distributions have been developed [3-lo]. Therefore this effect will not be considered further here.

As noted above the one step and the two step models yield quite different results for the position of half width extrema. To study this effect further, we

performed numerical calculations on surfaces with the coexistence of mono- and diatomic steps. The latter were introduced through a parameter P2 which is the probability for a given step to be diatomic.

Figs. 3 and 4 show I(Lc*) curves under variation of P2. For increasing values of P2 the intensity increases in the (OO)-beam at former intensity minima positions. For both beams the position of intensity minima moves gradually as P2 is varied. In the limiting cases P2 = 0 and P2 + 1 the observed 1( L.c*) curves are, as expected, nearly identical to those resulting from the analytical model (see fig. 2).

In order to quantify this effect we rewrite (6b) in the form

Lc* = RX/d,, (6~)

which defines X, and introduce a quantity R,, which describes the asymmet-

ric behaviour

R = x”-- - XmilQ” max

mm*.*, - Xmi”*” .

Here X,,,, denotes the half width maximum between the half width minima Xminzn,XtinZn+,. Note that R,, = l/3 for Pz = 0 and R,, = l/2 for P2 = 1. Fig. 5 shows for the (lo)-beam R,, as a function of P2. In these calculations the parameters W and Pd were also varied. The dependence of W and Pd

however, is seen to be small. The observed scattering is then mainly due to numerical noise.

The X values corresponding to experimentally observed energies for half

width extrema are by eqs. (6~) and (3)

X = 2d, (E/150.4)“’ + { E/150.4 - [(ha* + kb*)/2a] ‘}‘/‘). (

A comparison of experimentally observed positions of half width maxima to the curve in fig. 5 should give the possibility of estimating P2 for a given

458 H. Sualfeld et crl. / Mono- and dratomic steps on cleaued Os(OOO1)

0 w=50atoms,Pd=05

0 ~30 atoms,Pd=07! a w=30atoms,P,=OE:

I

0 0.5

pz

1

Fig. 5. Position of half width maxima R max (i.e. intensity minima) for the (lo)-beam. The position

is given relative to the distance between two half width minima (i.e. intensity maxima). (Compare

with figs. 3 and 4.)

surface. Note that knowledge of the layer spacing is not needed since R,, is independent of d,.

4. Experimental details

An osmium single crystal, produced by the crystal growth group of the University of Osnabrtick, was cleaved to get a randomly stepped Os(OOO1) surface. This sample was mounted in a standard UHV chamber with a base pressure below 5 x lop l1 Torr and prepared in a few cleaning cycles. In each , cycle the crystal was annealed at 800°C in an oxygen atmosphere of about lo-’ Torr to reduce the carbon contamination on the surface. To remove the remaining oxygen and sulphur the sample was annealed by electron bombard- ment with up to 1 kV electrons and currents of loo-150 mA. Temperatures up to 2OOO”C, measured with a W-Re thermocouple, were reached. The purity was checked with AES using a CMA system. After several cleaning cycles, the surface contamination was less than 0.5%. The LEED measurements were done with a fast computer-controled video-LEED-system, using a standard 4 grid LEED optics.

H. Saatferd et al. / Mono- and dicrtomic steps on cleaued Os(ooor) 459

5. Experimental results and discussion

The profiles of the LEED-spots were near Gaussian, therefore the half widths are determined by the ratio of the peak area to the peak height. Fig. 6

5 2 1 L i L

I 1 I I , I 300 LOO 500 600 700

ELECTRON ENERGY (eV)

Fig. 6. Half width as a function of electron energy of (a) the (OO)-, (b) (lo)- and (c) (ll)-beams from a cleaved and annealed Os(OOO1) surface. The angle to the surface normal of the incident

electron beam was 6 = 5” for the @@-beam and 19 = O” for the (IO)- and (Il)-beams. The arrows

indicate the positions of’cakulated half width maxima ( t) and minima (1) according to eqs. (6b) and (6a) respectively using Pz = 0 and d, = 2.16 A.

460 H. Snalfeld et ~1. / Mono- and drutomic steps on cleuved Os(OOO1)

shows the half width versus electron energy of the (OO)-, the (lo)- and the (ll)-beam, respectively. Structure due to in-phase and out-of-phase scattering is clearly seen. Notice the asymmetry of the half width maxima positions

especially in the (lo)-beam data. From eqs. (7) and (8) and the data for the (lo)-beam in fig. 5 we find the mean value R,, = 0.4 & 0.04. This is between the limits of the analytical models for monoatomic steps only (R,, = l/3)

and diatomic steps only ( R,, = l/2). By comparison with the numerical

calculations (fig. 5) we deduce from R,, a remarkable amount of diatomic

steps of lo-50%. Additionally we know, that these diatomic steps produce twice as many half width extrema in the (OO)- and (ll)-beams as expected for

monoatomic steps only. In fact, the data of the (OO)- and (ll)-beams show a structure equivalent to the existence of diatomic steps. Thus, applying the one step model [l] a step height d = 4.4 -t 0.1 A is found, which is approximately

the bulk value c = 4.32 A. Recently Moritz et al. [12] pointed out, that dynamic effects on a Si(100)

surface yield also twice as many half width extrema for the (OO)-beam as expected for monoatomic steps only. The dynamic effects can be described by different scattering factors Fl and F, for the two different terraces of nonprimitive stepped surfaces. For certain symmetry planes Fl is equal to F,.

This is the case for the (ll)-beam. Therefore the additional half width extrema

in the (ll)-beam cannot be explained by dynamic effects. Summarized, the experimental data compared with the numerical calcula-

tions and the analytical model shows the coexistence of mono- and diatomic steps on a cleaved Os(OOO1) surface.

6. Conclusion

An analytical model is developed for monoatomic regularly stepped surfaces on materials with nonprimitive lattices. Numerical calculations show the

applicability of this model to randomly stepped surfaces. Experimental data of a cleaved Os(OOO1) surface, compared with the

numerical calculations show the coexistence of mono- and diatomic steps with a remarkable amount of diatomic steps.

Acknowledgements

Financial support by the Deutsche Forschungsgemeinschaft is acknowl- edged. One of us (ST) is grateful for support by the Alexander-von-Humboldt Stiftung.

H. Saarferd et al. / Mono- and diatomic steps on cleaved Os(OOOI)

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