A Distinctive Feature of the Surface Structure of Quasicrystals: Intrinsic and Extrinsic Heterogeneity

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A Distinctive Feature of the Surface Structure ofQuasicrystals: Intrinsic and Extrinsic Heterogeneity

Patricia A. Thiel,* Barıs �nal, CynthiaJ. Jenks, Alan I. Goldman, PaulC. Canfield, Thomas A. Lograsso, JamesW. Evans, Marianne Quiquandon,Denis Gratias, Michel A. Van Hove

1326 – 1339

DOI: 10.1002/ijch.201100148

A Distinctive Feature of the Surface Structure ofQuasicrystals: Intrinsic and Extrinsic HeterogeneityPatricia A. Thiel ,*[a, b, d] Barıs �nal ,[a, d] Cynthia J. Jenks,[a] Alan I. Goldman,[a, c] Paul C. Canfield ,[a, c]

Thomas A. Lograsso,[a] James W. Evans ,[a, c, e] Marianne Quiquandon,[f] Denis Gratias,[f] and MichelA. Van Hove[g]

1. Introduction

The remarkable class of materials discovered by DannyShechtman — quasicrystals — has changed and chal-lenged our fundamental understanding of atomically-clean metal surfaces. Hence, it is appropriate to note thatShechtmanÏs 2011 Nobel Prize in Chemistry was preced-ed, just 4 years earlier, by the award of the same Prize toGerhard Ertl for elegant fundamental studies of surfacereactions on metals. Some of the developments that haveoccurred at the fertile intersection of these two fields —quasicrystals and surface science — are described in thisarticle. Understanding atomically-clean surfaces is espe-cially important, because it forms the basis for under-standing and predicting phenomena such as gas adsorp-tion, metal epitaxy, and friction.

In 1986, Per Bak[1] posed a famous question, “Whereare the atoms?”, thus highlighting a major challenge re-garding the bulk structure of quasicrystals. It has been noless of a challenge regarding the surface structure of qua-sicrystals. Understanding the interplay between bulkstructure and surface structure is the linchpin of thispaper (and by structure, we mean atomic identities aswell as atomic positions). We show that comparing thebulk structural information with surface data can explaina high degree of intrinsic heterogeneity at quasicrystalsurfaces, which is manifest in numerous types of experi-ments and which in turn can importantly affect otherproperties. We first examine the fivefold surface of icosa-hedral (i-) Al-Pd-Mn, then discuss the twofold surface ofdecagonal (d-) Al-Cu-Co. The two surfaces are similar in

that a variety of different types of terminations are possi-ble, based upon bulk structure models.

In the following section, we provide background on theexperimental determination of the structure of the five-

Abstract : This paper reviews a feature of atomically-cleanquasicrystal surfaces that distinguishes them from surfacesof crystalline materials. That feature is a high degree of het-erogeneity among different terraces, and among structurally-identical adsorption sites. The heterogeneity can be bothstructural and chemical in origin. A large variability is ex-pected even for a surface which is perfectly bulk-terminated,

and we call this intrinsic heterogeneity. Additional variabilitycan derive from the surface preparation process, which canyield metastable structures. We call this extrinsic heteroge-neity. Experimental evidence is given for both cases. Thisheterogeneity can be an important factor in understandingand predicting surface phenomena such as chemisorption.

Keywords: adsorption · quasicrystal · scanning probe microscopy · surface structure

[a] P. A. Thiel , B. �nal ,# C. J. Jenks, A. I. Goldman , P. C. Canfield ,T. A. Lograsso, J. W. EvansThe Ames LaboratoryIowa State University, Ames, IA 50011, USAphone:+1 515 294-8985e-mail: [email protected]

[b] P. A. ThielDepartment of ChemistryIowa State University, Ames, IA 50011, USA

[c] A. I. Goldman , P. C. Canfield , J. W. EvansDepartment of Physics and AstronomyIowa State University, Ames, IA 50011, USA

[d] P. A. Thiel , B. �nal #

Department of Materials Science and EngineeringIowa State University, Ames, IA 50011, USA

[e] J. W. EvansDepartment of MathematicsIowa State University, Ames, IA 50011, USA

[f ] M. Quiquandon, D. GratiasLEM CNRS-ONERA, 29 avenue de la Division Leclerc,F-92322 Cha tillon Cedex, France

[g] M. A. Van HoveDepartment of Physics and Materials Science,City University of Hong Kong, Hong Kong, China

[#] Present address: Department of Chemical Engineering,Massachusetts Institute of Technology, Cambridge MA 02139, USA

1326 Ó 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Isr. J. Chem. 2011, 51, 1326 – 1339

RReevviieeww P. A. Thiel et al.

Patricia A. Thiel is the John D. Corbett Professor of Chemistry, and of Materials Science and Engineering, at Iowa State University. She is also a FacultyScientist at the Department of Energy’s Ames Laboratory. She earned her B.A. at Macalester College and her Ph.D. at Caltech, and did postdoctoral re-search at the University of Munich with G. Ertl. Her interests are in surface properties and structures of intermetallics, and in thin film growth and re-laxation. She has received the Arthur W. Adamson Award from the American Chemical Society, and the David Adler Lectureship Prize from the Ameri-can Physical Society.Barıs �nal was born in Turkey. He received his B.S. and M.S. degrees in Chemical Engineering from Middle East Technical University (Ankara, Turkey)in 1999 and 2002, respectively. He completed his Ph.D. study in 2008 in Materials Science and Engineering at Iowa State University (USA) under thesupervision of Prof. Patricia A. Thiel, where he investigated quasicrystal surfaces using various surface-sensitive techniques including scanning tunnel-ing microscopy. He is currently working as a post-doctoral research associate at Massachusetts Institute of Technology (Cambridge, MA, USA). Hiscurrent research focus involves heterogeneous catalysis for energy conversions and development of microfluidic/microreactor platforms for measuringcatalyst performance in situ.Cynthia Jenks is the Assistant Director for Scientific Planning and the Division Director of Chemical and Biological Science at the Ames Laboratory.She received her B.S. in Chemical Engineering in 1986 from the University of California, Los Angeles. She received a M.S. degree in Chemical Engineer-ing in 1988 and a M.Phil and Ph.D. in Chemistry from Columbia University in 1991 and 1992, respectively. She did her postdoctoral work with PatriciaThiel at Iowa State University and the Ames Laboratory, and joined the scientific staff of the Ames Laboratory in 1995. Her research interests are in theareas of surface structure and reactivity, surface structure–property relationships, catalysis, and thin film growth.Alan I. Goldman is a Distinguished Professor in Liberal Arts and Sciences in the Physics and Astronomy Department at Iowa State University and aFaculty Scientist in the US Department of Energy’s Ames Laboratory. He received his Ph.D. in Physics from Stony Brook University and arrived at IowaState in 1988 after four years as a staff scientist in the neutron scattering group at Brookhaven National Laboratory. He is a Fellow of the AmericanPhysical Society (1999) and was the corecipient of three Outstanding Research Awards (two for work his work in Quasicrystalline Materials) from theUS Department of Energy. His current work focuses on X-ray and neutron scattering studies of structure, magnetism, and superconductivity in theiron pnictide superconductors.Paul Canfield is a Distinguished Professor of Physics at Iowa State University and a Senior Physicist at the US Department of Energy’s Ames Laborato-ry. He specializes in the design, discovery, growth, and characterization of novel materials, often in single crystal (or in this case, single grain) form.T. A. Lograsso currently serves as the Division Director for Materials Science and Engineering Programs at the Ames Laboratory. He received his Ph.D.in Metallurgical Engineering from Michigan Technological University (1986) in the area of solidification processing and phase transformations. In 1988he joined the Ames Laboratory, where he utilizes his solidification experience and background to synthesis and design novel materials in single crystalforms including intermetallic alloys, quasicrystals, and ferromagnetic shape memory, magnetocaloric, and magnetostrictive alloys. He has over 325publications and several patents.Jim Evans was born in Australia. He is currently a Professor of Physics & Astronomy and a Professor of Mathematics at Iowa State University, and alsoa Faculty Scientist in the Division of Chemical & Biological Sciences at the Ames Laboratory–USDOE. His research primarily involves non-equilibriumstatistical mechanics and multiscale modeling, especially the development of realistic atomistic-level models for surface phenomena. One focus areais the formation and stability of epitaxial metal nanostructures. Another is analysis of catalytic reaction processes both on metal surfaces and in meso-porous materials.Marianne Quiquandon obtained her Master’s degree in Materials Science in 1981 at the University Pierre et Marie Curie in Paris. She joined the CNRSin the Laboratory Centre d’Etude de Chimie M¦tallurgique (CECM/CNRS at Vitry near Paris) directed by Prof. M. Fayard. She obtained her Ph.D. in1988 on the dynamical theory of fast electrons in crystals and quasicrystals. She performed the first dynamical calculations of high-resolution imagessimulations and characterizations of defects in these materials, such as antiphase domains and dislocations. She specialized in quasicrystal structuredetermination studies using the high dimension space description, in close collaboration with D. Gratias and A. Katz, and extended the method to ap-proximants in identifying those structures in the (AlCuFe) ternary phase diagram. More recently, she proposed a unified 6D structural description forthe two prototypic F-icosahedral phases AlCuFe and AlPdMn.Denis Gratias obtained his Ing¦nieur degree from Ecole Nationale Sup¦rieure de Chimie de Paris in 1970. He joined the CNRS in the Laboratoire deM¦tallurgie Structurale directed by Prof. M. Fayard. He obtained his Doctorat d’Etat on interfaces in homogeneous crystals in 1978 and then joinedthe CECM-CNRS at Vitry near Paris. He then specialized in Group Action Theory with Prof. L. Michel at Institut des Hautes Etudes Scientifiques(IHES), and met Prof. J. W. Cahn in 1981 during his post-doctoral position with Prof. D. De Fontaine at the University of Berkeley, where he worked onStatistical Physics problems using the Cluster Variation Method. In 1984, Prof. Cahn invited him to the Institute of Theoretical Physics at the Universityof Santa-Barbara California to participate in a long-term seminar, which included a fascinating talk by Cahn on the first observations of quasicrystals byProf. D. Shechtman. This started a very long and intense collaboration on that subject.Born in Brussels, Michel A. Van Hove graduated from ETH-Zírich, did research at Philips in Holland, got a Ph.D. from University of Cambridge, andwas A postdoc at University of Wisconsin, Caltech, and University of Munich, before joining Lawrence Berkeley Laboratory in 1978 and, in 2005,moving to City University of Hong Kong to become Chair Professor of Physics and Head of its Department of Physics and Materials Science. Focusingin his research on theory and computation of low energy electron diffraction, photoelectron diffraction, holography, scanning tunneling microscopy,and total-energy calculations for structural determination of surfaces and nanostructures, he has earned an h-index of 64 and honors such as Fellow ofthe American Physical Society and the Ernst Mach Honorary Medal for Merit in the Physical Sciences.

Isr. J. Chem. 2011, 51, 1326 – 1339 Ó 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim www.ijc.wiley-vch.de 1327

A Distinctive Feature of the Surface Structure of Quasicrystals : Intrinsic and Extrinsic Heterogeneity

fold surface of i-Al-Pd-Mn, and Section 3 reviewscommon features of the bulk structure models that arerelevant to that surface. Section 4 examines evidence forboth intrinsic (bulk-structure-related) and extrinsic heter-ogeneities on this surface. Section 5 presents evidence forintrinsic and extrinsic heterogeneity on d-Al-Cu-Co, withparallels to i-Al-Pd-Mn.

2. Background: Experimental Determination ofthe Structure of the Fivefold Surface of i-Al-Pd-Mn

It is well-accepted that clean surfaces of crystalline metalsexhibit terrace-step morphologies. In 1994, Schaub et al.[2]

reported the first scanning tunneling microscope images

of an atomically-clean surface of an icosahedral quasicrys-tal, which also revealed a terrace-step morphology.Figure 1 is an image from our own laboratory, showingthe same type of quasicrystal surface: the fivefold surfaceof i-Al-Pd-Mn. Unlike a conventional crystalline material,these terraces are separated by steps of unequal heightswherein the heights are related by a non-integral constant(about 1.6). By contrast, steps of unequal height on acrystalline material are usually due to step bunching, andso their heights are related by an integer.

The relative step heights posed a puzzle. Why werethese particular values observed? The two most commonones in i-Al-Pd-Mn were (and are) 0.41 and 0.66 nm,which are denoted M (medium) and L (long), respective-ly. From the bulk models of icosahedral quasicrystals, itwas known that no two planes of atoms are identical, sowhy should particular step heights be favored at all?

Another aspect that was puzzling—indeed, controver-sial—was the observation of flat terraces. This is becauseclusters can always be identified in bulk quasicrystals. Inthe quasicrystal community, it had been postulated thatthe clusters accord a special stability to quasicrystals, andaffect bulk properties such as transport.[3] Others arguedthat clusters simply satisfy the need of the human mind tocategorize information. (This “cluster debate” remainsunsettled today. Arguments and evidence on both sides

have been summarized nicely by Steurer.[4]) In icosahe-dral quasicrystals, the clusters are rounded polyhedra con-taining a few tens of atoms, and any flat terrace necessari-

ly intersects some of them. One such cluster is illustratedin Figure 2. It was thus thought that the truncation ofclusters could destabilize the quasiperiodic arrangementat the surface. In fact, it was suggested that the flat terra-ces of Schaub et al. were not bulk-terminated quasicrys-talline surfaces, but rather crystalline surface phases, per-haps with large unit cells. (This provided a small echo ofthe original controversy attending ShechtmanÏs discovery,in which Pauling asserted that the new material wassimply a twinned, large-unit-cell crystal.[5,6])

Answers to some of these puzzles came from a structur-al study of this surface using low-energy electron diffrac-tion (LEED).[7,8] The structural determination was basedupon a full dynamical scattering analysis of intensity–volt-age (IV) curves. This type of analysis compares the IVcurves predicted for a certain surface structure with thosemeasured experimentally. The structure model is adjustediteratively until an optimal fit is obtained. Criteria existthat define a minimally-acceptable fit.[9] The surfacestructure is usually constructed from the bulk structure,as a starting point, and in this case a modification of abulk structure model for i-Al-Pd-Mn developed by Bou-dard et al. was used.[10] Hereafter, this model is called them-Boudard model. (The modification, indicated by theprefix m, served to correct unreasonably short bondlengths between some pairs of atoms in the originalmodel.[8]) However, a new method for calculating theideal IV curves had to be developed, since structural de-terminations up to then had always relied upon periodicboundary conditions, which were obviously not applicableto quasicrystals. The new method employed a kind ofaverage radial distribution function, derived from thebulk structural model, to describe the environment of

Figure 1. Semi-three-dimensional STM image of the fivefold sur-face of i-Al-Pd-Mn, 250 Õ 250 nm2. From ref. [29]. Copyright 2008 bythe American Physical Society.

Figure 2. The outer surface of a Mackay cluster, as defined in thetext. Black spheres are the vertices of one of the two outer poly-gons, and grey spheres are the vertices of the other polygon. Fromref. [54].

1328 www.ijc.wiley-vch.de Ó 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Isr. J. Chem. 2011, 51, 1326 – 1339


each scatterer.[7,8] (While this method was very successful,an even more powerful and simpler method has beendemonstrated recently by Pussi et al.,[11] in which an ap-proximant can be used to model the bulk structure of thequasicrystal.)

The results for the fivefold surface of i-Al-Pd-Mnshowed that the preferred terminations comprised afamily of self-similar groups, each consisting of two rela-tively-dense planes that are very closely spaced. The spac-ing between the planes at the surface is about 0.04 nm, acontraction of 20% from the bulk value of 0.05 nm. Thespacing of 0.04 nm is so small that the pair of planes is ap-propriately regarded (and will be denoted) as a single

layer with rumpling. A representation of the bulk struc-ture model, highlighting the dense rumpled layers, isshown in Figure 3. Actually, the existence of these self-similar dense layers, and the fact that they might play aspecial role in phenomena such as cleavage, had beennoted earlier by Boudard et al.[10] These LEED IV resultswere supported by results from a number of other tech-niques, including X-ray photoelectron diffraction(XPD)[12] and X-ray scattering.[13, 14]

The preference for these dense rumpled layers as sur-face terminations immediately explained the M and Lstep heights originally observed by Schaub et al. , sincethe step heights equaled the separations of layers in thestructural model. Those separations were related precise-ly by a factor known as the Golden Mean, an irrationalnumber with value 1.618. This is illustrated in Figure 4,which shows a different representation of the atomicplanes in a bulk structural model. Self-similar groups aremarked by brackets below the x-axis, the separations be-tween them being M (medium) or L (long).

The LEED IV results also allowed the conclusion thatatomic density was one of the factors governing surfaceterminations in quasicrystals, something that could beeasily understood from low-index surfaces of crystallineelemental metals, where “open” surfaces always havehigher surface energies than “closed” (i.e., denser) surfa-ces.[15] In turn, this suggested that, while clusters may still

be important in quasicrystals, the energetics favoring theformation of flat, dense surfaces outweighed any energet-ics favoring cluster preservation, at least for this surface.

The LEED IV results could not, however, exclude thepossibility that the surface was periodic rather than quasi-periodic. The LEED patterns themselves showed symme-tries and spot spacings consistent with bulk-termination,for the twofold and threefold as well as the fivefold surfa-ces.[16] Other techniques, as well, showed no evidence fordeviation from bulk termination.[17–19] However, becauseof the difficulty of distinguishing quasicrystals from high-order crystalline approximants, the issue was not settledconclusively until high-quality STM images of the finestructure on the terraces were obtained, and were suc-cessfully superimposed on a bulk tiling over a largearea.[20–22] Two key examples are shown in Figure 5.(While some conditions of surface preparation can pro-duce periodic overlayers, the parameters that produce pe-riodic vs. quasiperiodic surfaces are now fairly well-de-fined and well-understood.[19,21–26])

Next, consider the chemical compositions of the denseplanes. The LEED IV[7,8] and X-ray scattering data,[13,14]

plus low-energy ion scattering (LEIS) data,[8,27] all sug-gested that the top-most plane in the surface layer isnearly-pure Al, with no Pd. These experimental data,plus information from STM,[28] also showed that a smallamount of Mn (<10 at%) may be in the top plane to-gether with the Al. Details are reviewed elsewhere.[29,30]

Figure 3. Cross-sectional view of i-Al-Cu-Fe. The z-axis is perpen-dicular to the surface plane. Al atoms are large red circles. Cu andFe atoms are smaller, with Cu represented in blue and Fe atoms ingreen. The i-Al-Cu-Fe quasicrystal is essentially isostructural with i-Al-Pd-Mn. From ref. [83].

Figure 4. Schematic depiction of atomic planes in the m-Boudardmodel. The z-axis is the 5-fold axis. The height of each line is pro-portional to its planar atomic density. Within each vertical bar,black denotes Al, gray denotes Mn, and dots denote Pd. The heavyblock arrow on right shows the viewing direction as discussed inthe text. The view at bottom shows a group of planes with ex-panded z-axis, and gaps as discussed in the text. From ref. [29].Copyright 2008 by the American Physical Society.



Surface termination by the Al-rich planes can be ra-tionalized on the basis that Al has a lower surface energythan transition metals (TMs). For example, the surfaceenergy of Al is 1.2–1.3 J m¢2, whereas that of Pd is 1.9–2.1 J m¢2.[15] Thus, if atomic densities are equal, one wouldnaturally expect the Al-richest planes to be preferred ter-minations.

The widths of the gaps that separate a plane from itsneighbors, in a bulk structure model, is also informative.�nal et al.[29] noted that in the model of Figure 4, mostAl-rich planes in the dense layers are separated fromtheir neighboring plane by a gap of 0.156 nm. In Figure 4,these are gaps to the right of the dense layers. This valueis the widest possible spacing between two adjacent denseplanes in the m-Boudard and similar models. (This valueof 0.156 nm is not the step height, since step height wouldbe the spacing between adjacent 0.156 nm gaps.) Most Pd-containing planes in the dense layers are separated fromtheir nearest neighbors by a gap of only 0.078 nm. InFigure 4, these arre the gaps to the left of the denselayers. These gaps are illustrated in the bottom ofFigure 4, which is expanded along the z-axis to show onelocal set of planes more clearly.

In quasicrystals, it has been proposed that the spacingbetween adjacent planes influences the selection of termi-nations.[10,31] This reflects the fact that a larger interplanargap implies weaker bonding between planes. This correla-tion between interplanar spacing and bonding supportsthe hypothesis that the Al-rich planes are the preferredtype of termination.

3. Bulk Structure Models for i-Al-Pd-Mn:Common Features Relevant to Fivefold Surfaces

The foregoing discussion skirted the fact that there areseveral bulk structural models for i-Al-Pd-Mn. The sim-plest ones are those in which each atomic position is fully

occupied by a specific element (so-called deterministicmodels),[10,32–35] while the non-deterministic models[36,37]

are more complex. The m-Boudard model is a determinis-tic model. The deterministic models can be thought of asapproximations to the others, and are appealing becausethey are much more tractable.

It has been said that about 85 % of the atomic sites arecommon to all of the deterministic models.[38] In order tounderstand why, it is useful to discuss some of their struc-tural features in terms of six-dimensional (6D) space. The6D space is conventionally divided into two three-dimen-sional (3D) subsets, called physical or parallel space, andinverse or perpendicular space.[39,40] In perpendicularspace, the deterministic models for i-Al-Pd-Mn have threeatomic surfaces (ASs) — also called acceptance domains,or occupation domains — that contain information aboutthe positions of the atoms and their chemical identities.The different models are all similar in having most of theatoms confined in two large ASs, with a small fraction ofatoms in a third AS. Furthermore, the two main ASs arealways located at the same two nodes in the 6D lattice,called n0 = (0,0,0,0,0,0) and n1 = (1,0,0,0,0,0). The locationof the third AS is model-dependent but its contribution ismuch smaller than the others. In all the deterministicmodels, the AS at n0 is primarily Al, while the AS at n1

contains a larger fraction of TM atoms.[30]

By projecting the ASs from 6D space to 2D space fol-lowing known procedures, the planes perpendicular toany direction can be generated.[41] An important point isthat each fivefold plane is generated by only one AS.[42; 43]

Dense planes are generated from the central part of theASs at the nodes, and less dense planes are generatedfrom the periphery of the ASs. The similarities in themajor ASs lead to strong similarities in the dense planesamong different models, at least in terms of atomic posi-tions. This means that the terminating surface layers arealso very similar in the different models, at least with re-spect to atomic positions.[29]

Recently, there has been speculation that the chemicaldecorations of the two major ASs in the deterministicmodels are incorrect, and perhaps should be reversed.The detailed arguments are beyond the scope of thisreview. If true, this mistake in chemical decoration wouldhave strong implications for the surface structure.[44]

Therefore, the sensitivity of the bulk models to chemicalvariations of the two main ASs was tested.[30] This wasdone using a model of i-Al-Pd-Mn, illustrated in Figure 6,which captured all of the standard 6D features commonto the deterministic models. The chemical decoration ofthe ASs was varied using two independent parameters 0� x � 1 and 0 � y � 1 representing the occupation fac-tors of the atomic species Pd and Mn on the AS centeredat n0. The parameters (x, y) could be varied in a way thatkept constant both the overall composition, and also theshape and volume of the relevant ASs in perpendicularspace. The approach is illustrated in Figure 6. At (0,0),

Figure 5. STM images showing local motifs, with patterns superim-posed to show the arrangements of motifs found in bulk structuremodels. (A) Fivefold surface of i-Al-Cu-Fe, from ref. [20]. Copyright2002 by the American Physical Society. (B) Fivefold surface of i-Al-Pd-Mn, from ref. [21]. Copyright 2002 by the American Physical So-ciety.



the AS at n0 is pure Al, thus generating a structure wherethe corresponding dense fivefold planes are occupied bypure Al. At the opposite extreme, (1,1) corresponds to amodel where the AS at n0 has a maximum number of TMatoms.

The relevant experimental data were the X-ray diffrac-tion data originally collected by Boudard et al.[10] The var-

iation of R-factor (the quality of fit to the data) was thenmapped as a function of (x, y). The function R(x,y) isshown in Figure 7. The R-factor varies from 6.5 % at (0,0) to 16.6% at (1, 1). The absolute difference, 10%, israther small given that the difference between the two ex-tremes is a large change in the chemical decoration, thatis, complete exchange in the locations of Mn and Pd. Thisrelatively weak influence of the chemistry on the overalldiffraction data could be the origin of the multiplicity of

atomic models of i-Al-Pd-Mn concerning the chemicalorder. The second point is that the surface R(x, y) showssmaller change with respect to y than with respect to x.This corresponds to low sensitivity to changes of the posi-tion of Mn, but higher sensitivity to changes in the posi-tion of Pd. The R-factor variation of Figure 7 is clearly infavor of locating all Pd atoms on n1. These results arenicely consistent with the surface analysis data that showalmost pure Al, no Pd, and little or no Mn on the termi-nating planes.

In making comparisons between surface science dataand bulk structural models, it has been common to com-pare the data with only a single bulk model. In general,good agreement has been obtained.[45–47] However, thisapproach leaves open the question of whether differentmodels might yield different degrees of agreement withexperimental surface data. A recent analysis by �nalet al.[29] addressed the ways that surface terminations indifferent bulk models might have different characteristics,such as atomic density and chemical composition. In lightof the above discussion of the similarities between denseplanes in different models, it is perhaps not surprisingthat there was little difference between large-scale aver-age values of atomic density and chemical composition,within the family of preferred terminations shown inFigure 4.

However, the chemical composition varied significantlyamong models, particularly when each termination wasindexed with the height of the downward-going step (i.e. ,the distance to the nearest termination, going deeper intothe bulk, such as right-to-left in Figure 4). This leads tothe possibility that in the future, a surface science experi-ment could be designed to measure compositions of indi-vidual terraces. If this were possible, one could determinethe correlation between the composition of individual ter-races and the adjoining step heights. This would be arather sensitive way to discriminate among different exist-ing bulk models. However, such an experiment wouldhave to provide a good statistical average over many ter-races. Sampling just a few terraces would not be reliablesince, as shown elsewhere,[29] the ranges of terrace compo-sitions and structures overlap among different step types.

4. Structural and Chemical Heterogeneities onthe Fivefold Surface of i-Al-Pd-Mn

It has been reported that different terraces can behavequite differently as templates for nucleation and growthof metal films.[48,49] For instance, Figure 8 shows a fivefoldsurface of i- Al-Pd-Mn upon which a small amount (0.13monolayers) of Ag has been deposited at room tempera-ture.[48] The Ag islands appear as small spikes. One is en-circled and labeled in Figure 8 A. It is clear that some ter-races are nearly free of Ag islands, while others havemany. Although the sampling statistics are small, it seems

Figure 6. Schematic illustration of the approach used to test R(x,y)as discussed in the text, where R is the R-factor, and (x,y) are chem-ical occupancy parameters. The parameters x and y vary between0 and 1. Each of the two ASs (one at n0 and one at n1) consists ofconcentric shells, represented by the three objects labeled p (orp’), b, and a. For x = 0, y = 0, the AS at n0 is pure Al, thus generat-ing a structure where the corresponding dense fivefold planes areoccupied by pure Al. At the opposite extreme, values of x = 1 andy = 1 correspond to a model where the AS at n0 is maximallycharged in Pd and Mn atoms and n1 is pure Al. Surfaces studiesfavor the case (x = y = 0). From ref. [30].

Figure 7. Values R(x, y) of the R-factor that results from fitting tothe X-ray diffraction data of Boudard et al.[10] Values of R at thefour extreme points (x, y) are: (0,0) 6.51, (0,1) 8.89, (1,0) 15.87, and(1,1) 16.56. From ref. [30].



that terraces above ML bunched steps have a much lowerdensity of Ag islands than terraces above L or LMbunched steps. Extensive modeling of the nucleation andgrowth of Ag islands on this surface revealed that themost likely explanation was that the diffusion coefficientof Ag atoms differed from one type of terrace to another,due to a heterogeneity in adsorption sites.[48,50] This differ-ence in diffusion coefficient led to island nucleation onsome terraces (where the diffusion coefficient was small-er), and attachment to step edges on other terraces(where the diffusion coefficient was larger).

It has also been reported that terrace widths are small-er for terraces bounded by an M-type step than an L-typestep.[51] Furthermore, step bunching on these 5-fold surfa-ces has been attributed to differences between differentterminations.[31] Because of such observations, there hasbeen speculation that step heights on quasicrystals, suchas L and M, may correspond to distinctive densities, com-positions, or other features on the adjoining terraces.[51]

An analysis of the favored terminations in the bulk struc-tural models, described below, shows that such correla-tions indeed exist. From this point forward the discussionis restricted to the m-Boudard bulk model, although anal-ogous conclusions result using other models.[29]

Consider first a structural characteristic, the density ofthe top plane in the terminating layer. Table 1 shows that

the density of the topmost plane, for terraces bordered byL-steps, is about 80% lower than for the other type ofterrace, those bordered by M-steps. Consider next a com-positional characteristic, the average Al, Pd, and Mn con-centrations in the terminating layer. Table 1 shows thatterraces bordered by L-steps should contain significantlymore TM, and less Al, than terraces bordered by M-steps.Thus, there is both a structural and chemical correlationbetween step height and the characteristics of the associ-ated terraces. Bulk models other than the m-Boudardmodel provide the same correlation in atomic density, butdifferent correlations in atomic compositions.[29]

Not only the average composition and structure of aterrace is important, but also the local structure, becausethis defines the adsorption sites for deposited adatoms,and also controls growth kinetics of solid films and nano-structures. Quasicrystals naturally present multiple typesof adsorption sites, where a site is defined as a local mini-mum in the potential energy surface that describes the in-teraction between an adsorbed atom and the surface. Agood illustration of the variety expected for a quasicrystalis shown in Figure 9, which is a potential energy surfacecalculated for an Al adatom on 5-fold i-Al-Cu-Fe.[52,53] Avariety of adsorption sites exists as a consequence of thediverse range of local atomic configurations that can beidentified.

Inspection of STM images reveals two visually domi-nant motifs of sites on the fivefold surfaces of icosahe-dral, Al-based quasicrystals. Because of their appearancein STM images, these sites are known as dark stars andwhite flowers. Three dark stars and one white flower areencircled in Figure 10. As an illustration of the impor-tance of these types of sites, the dark stars — or at leastsome of them[54] — constitute trap sites for diffusing Aland Ag adatoms. Both STM data[55] and atomistic model-ing[52,53] indicate that aggregating adatoms initially formstarfish-shaped nanoclusters at the dark star sites, whichsubsequently grow into larger clusters. Similarly, thewhite flowers constitute trap sites for diffusing Pb ada-toms.[56] The remainder of this discussion focuses on thedark stars, but analogous arguments apply to the whiteflowers, and presumably to other sites as well.

Figure 8. STM images of Ag islands on terraces, following deposi-tion at 365 K. Steps are labeled with their height, where L =0.66 nm and M = 0.41 nm. (a) 326 Õ 326 nm2, 0.13 ML. (b) 500 Õ500 nm2, 0.10 ML. From ref. [48].

Table 1. Correlations between densities and compositions of terminations, and step heights, in the dense fivefold layers of i-Al-Pd-Mn, ac-cording to the m-Boudard model. Heights of L- and M-type steps are 0.660 nm and 0.408 nm, respectively. A layer is a pair of planes.

Type of step borderingtermination in down-going direction

Average atomic densityin top plane of termina-tion, nm¢2

Average atomic densityin top plane, L : M ratio

Average concentration of elements in terminating layer, at %(Range of values for individual terminating layers is given in pa-rentheses.)

AlPdMn

L 6.8

0.78

65.1(57.6–72.3)

24.3(23.2–25.3)

10.6(3.0–17.0)

M 8.8 76.9(72.7–83.3)

17.5(8.1–24.1)

5.6(2.5–8.6)



These sites are related to the cluster shown in Figure 2.This is a Mackay cluster, which has 3 shells and 50 atomson average, including a central atom. In this cluster, theinner polyhedron is an incomplete dodecahedron, some-times termed a disordered dodecahedron because thenumber and positions of atoms vary from cluster to clus-ter. This incomplete dodecahedron is enclosed by 2 inter-penetrating, equal-diameter polyhedra containing (ideal-ly) 42 atoms. (Note that here the term “Mackay cluster”is used in a way that is consistent with current discussionsof quasicrystals. In the original definition given byMackay,[57] the cluster included more, larger shells.)

The dark stars can be identified as Mackay clustersthat are cut at the two levels shown by the arrows inFigure 2.[54] In bulk models of i-Al-Pd-Mn, there are var-iations in chemical and structural order of the Mackayclusters. For example, an extensive analysis of Mackayclusters in the Boudard model has shown that at least

22% of the Mackay clusters lack one or more atoms inthe outer two shells.[58] For the purposes of surface sci-ence, it is most appropriate to use only atomic positionsin the top two planes (shown on the right of Figure 2) toidentify the surface dark star sites within the frameworkof the bulk models, regardless of the Mackay clusterÏsdegree of perfection deeper in the bulk.

The ideal dark star is a pentagonal hollow surroundedby 5 pentagons of atoms in the top plane, as shown in Fig-ure 11A. Even considering only the top two surfaceplanes, different degrees of perfection are possible: somedark stars are incomplete, as shown in Figure 11B and C.In experiments as well, dark stars with different configu-rations can be identified. Based upon their likely corre-spondence with the 3 configurations in Figure 11 A–C,they are labelled as A, B, and C in Figure 10.

Structural heterogeneity also arises from the atomic po-sitions of atoms in the second plane, which can containatoms from the disordered dodecahedron. (If atoms fromthis shell contribute to the topmost plane, then the site isprobably not a dark star at all.[54]) Thus, within the con-text of any single structural model, the dark star sites arepredicted to be structurally heterogeneous.

For the m-Boudard model, large-scale average densitiesof different types of dark stars are given in Table 2. Thenumber density of dark stars in individual terraces (notshown) correlates with the step height of M or L, becausethe number density of dark stars is related to the atomicdensity of the terminating planes.

Considerable chemical heterogeneity is also predictedfrom the bulk structure models. Table 3 shows that theatomic identities in the second-plane are quite variablefor the m-Boudard model. The chemical variation in com-plete white flowers is also given.

Figure 9. Potential energy surface calculated for an Al adatom onfivefold i-Al-Cu-Fe, 7.5 Õ 7.5 nm. Darkest blue indicates strongestbonding between the Al adatom and the surface. Starfish-shapedregions of strong bonding are the dark star sites. See refs. [52, 53]for details.

Figure 10. STM image (unfiltered) of a clean fivefold surface of i-Al-Pd-Mn quasicrystal, 25.1 Õ 12.1 nm2. Letters A, B, and C denotethree types of dark stars. A complete white flower (WF) is alsomarked. From ref. [54].

Figure 11. Schematic depiction of the atoms in the top planearound a complete dark star (A), two incomplete dark stars (B, C),and a complete white flower (D), based on bulk structural models.From ref. [54].



Experimental evidence of heterogeneity is given by theline profile indicated by the dashed arrow in Figure 12 Aand shown fully in Figure 12 B. The profile crosses darkstars with two different depths. The data available are in-sufficient to distinguish among the different possiblecauses listed above.

It is likely that chemisorption is influenced by thechemical nature of the atoms in the top two planes.Hence, some sites should be more inert than others.Chemical variability should be taken into account whenpredicting adsorption properties of quasicrystals basedupon theoretical calculations. This chemical variabilitycould also be turned to advantage. In principle, studies ofchemisorption could be used to test the validity of bulkstructural models through the local chemical decorationsof adsorption sites.

Until now, we have discussed the intrinsic heterogenei-ty, the variation which is expected in surfaces based on

the bulk structure. Importantly, however, experimentshows that differences between terraces can also arisefrom preparation conditions — an extrinsic effect. Thisprobably occurs because surfaces evolve and go throughmetastable configurations in the course of surface prepa-ration. To understand this, it is worth illustrating the evo-lution of surface morphology associated with typical ionbombardment and annealing. The transition is illustratedschematically in Figure 13. The surface begins in a veryrough state after sputtering at room temperature. As thesample is annealed, it smoothens and eventually achievesthe terrace-step structure shown in Figure 1. The exten-sive mass transport that leads to quasicrystalline surfacesin i-Al-Pd-Mn takes place between about 700 and 900 K.

One study showed that if the quasicrystalline surfacephase was annealed at relatively low temperature, it in-cluded metastable terminations.[59, 60] The fine structure onthese metastable terminations indicated a quasicrystallinesurface structure.[59] The signature of these transitory ter-minations was a dense network of voids, through whichthe more stable termination at the bottom of the voidsbecame progressively exposed with increasing annealing

Table 2. Average and range of densities of cut Mackay pentagonal hollow sites in surface terminations. These features are equated with thedark star sites observed in STM. The configurations A, B, C are illustrated in Figure 11.

Densities of A-type dark stars(cut Mackays),nm¢2

Densities of B-type dark stars(cut Mackays), nm¢2

Densities of C-type dark stars(cut Mackays), nm¢2

All types of cM pentagonal hollowscombined (A+B+C), nm¢2

Range Average Range Average Range Average Range Average0–0.170 0.038 0–0.150 0.022 0–0.840 0.190 0–0.840 0.250

Table 3. Chemical decorations of dark star and white flower sites in the m-Boudard model.

Atomic group in the dark starsite

Composition in different con-figurations A, B, or C as de-fined in Figure 11

Atom or atomic group in thewhite flower site

Composition in a complete configurationas illustrated in ref. [54]

Pentagon in top plane Al (A, B, C) Center atom Al MnPentagon in second plane Pd (A),

Mn (A, B, C),Pd+Mn (A, B, C),Al+Pd+Mn (C)

Ten-atom ring in first plane Al Al

Pentagon in second plane Pd,Al+Pd,Al+Pd+Mn

Al,Al+Pd

Figure 12. (A) STM image of the clean fivefold surface of i-Al-Pd-Mn quasicrystal. The image size is 8.6 Õ 4.5 nm2. The dashed arrowsindicate the cut of the line profiles shown in (B). From ref. [54].

Figure 13. Schematic depiction of the proposed model for evolu-tion of long-range surface morphology at 700–950 K. Fromref. [59]. Copyright 2005 by the American Physical Society.



temperature. An example is shown in Figure 14. Similarresults have been reported for the fivefold surface of anisostructural quasicrystal, i-Al-Cu-Ru.[61] The voids pro-vide evidence that terminations from different familiescoexist, at least under some circumstances. The void-richterraces appear at a stage which is intermediate between

the rough, sputter-annealed surface, and the smooth,step-terrace morphology illustrated in Figure 10. Appa-rently, there are kinetic limitations associated with masstransport that lead to different types of terraces with dif-ferent stabilities, as the quasicrystalline surface re-grows.Perhaps there are “mistakes” in the stacking sequences,or the surface exposes dense planes that fall outside ofthe layers enclosed by brackets in Figure 4. At slightlyhigher temperatures, a new process begins which facilitateremoval of the least-stable terminations. This process maybe selective evaporation of metal.[59] Mn begins to evapo-rate preferentially at about the temperature where thevoids disappear.[25]

Low-energy electron microscopy (LEEM) is a tech-nique that should be able to distinguish differences instructure among quasicrystal terraces. In fact, this tech-nique has been used to study the fivefold surface of i-Al-Pd-Mn.[62] LEEM has an advantage over STM in its readycapability for surface imaging at elevated temperatures.The LEEM results did show some heterogeneity amongterraces at room temperature, but a surprising result ap-peared at high temperatures. Although the LEED patternremained fivefold, the surface exhibited two types ofsteps arranged in a way that required periodic layer stack-ing. This suggests that the individual layers retain 2D qua-sicrystallinity, but errors can be introduced in the third di-mension, perpendicular to the surface. This is surprisinglysimilar to the results which will be presented in the fol-lowing section, for a different type of quasicrystal.

In summary, the fivefold surfaces of icosahedral qua-sicrsystals have two sources of heterogeneity. The first

can be called intrinsic. It is the inherent heterogeneityamong different terraces (terminations), even if the terra-ces correspond only to the ideal terminations in a bulkmodel. This heterogeneity is both chemical and structural.Heterogeneity follows systematic trends if one indexesthe average features of terraces to the corresponding stepheights (separations between ideal terminations). In fact,the trend in chemical heterogeneity could be implement-ed to distinguish among different bulk structural models.Local heterogeneity in adsorption sites is also very signifi-cant, both in the bulk structural models and in the experi-mental data. The second source of heterogeneity is extrin-sic. This is related to the conditions of sample prepara-tion, which may produce metastable quasicrystalline ter-minations or quasicrystalline terminations that arestacked in the “wrong” sequence. The following sectionpresents a startling example of this in a different quasi-crystalline system.

5. Structural and Chemical Heterogeneities onthe Twofold Surface of a Decagonal Quasicrystal

The twofold surfaces of decagonal quasicrystals have gar-nered special attention because they simultaneously in-corporate periodic and quasiperiodic axes, thus allowingin situ comparisons of the effect of periodic and quasi-periodic order on surface properties. (This approach hasbeen used to compare the effects of periodicity and quasi-periodicity on properties of bulk decagonal quasicrystalsfor some time.[63–67]) A comparison of friction forces on atwofold decagonal surface was an interesting example, be-cause it showed that friction is lower by a factor of 8along the quasiperiodic direction, for the atomically-cleansurface.[68,69] Under more realistic sliding conditions, thefriction anisotropy persisted although at a reducedlevel.[70, 71] Understanding the exact role of quasiperiodicli-ty in friction remains a challenge for the field of surfacescience.[40,72]

The twofold surfaces of the Al-rich decagonal phasesbear interesting similarities to the fivefold surfaces of theicosahedral phases. Experimentally, they can be preparedso that they exhibit a terrace-step morphology. In thebulk structure, no two (infinite) atomic planes are identi-cal. The atomic planes in the bulk contain variableamounts of Al and TMs. Experimental evidence suggeststhat the surface structure is usually bulk-terminated, andterraces containing relatively high amounts of Al are fa-vored. There are two main step heights, most commonlydenoted S and L on these surfaces, but other values arealso observed. All step heights are related (to within ex-perimental error) by the Golden Mean. For instance,STM showed that the twofold d-Al-Ni-Co surface couldbe prepared as terraces, separated by steps of heights0.19, 0.47, 0.78, and 1.26 nm.[73,74] Terraces were preferen-tially Al-terminated and their structure was in general

Figure 14. STM images of fivefold i-Al-Pd-Mn, illustrating the exis-tence of void-rich and nearly-void-free terraces. (A) 5000 Õ 5000 æ,after annealing at 900 K. (B) 5000 Õ 5000 æ, after annealing at915 K. From ref. [59]. Copyright 2005 by the American Physical So-ciety.



agreement with bulk models.[73] The terraces includedboth periodic and aperiodic axes. Mader et al. have re-ported results for the same surface that are similar in theaspects described above, although details differ.[75,76]

Recently, a twofold surface of a different decagonalphase, d-Al-Co-Cu, was examined using STM andLEED.[77–79] Again, most of the surface features could beinterpreted using a bulk structure model. For this system,the model developed by Deloudi and Steurer was used.[80]

Step heights and steps sequences matched with the thick-ness and the stacking sequence of blocks of planes, sepa-rated by gaps in the model. The surface terminationswere dense (~10 at. nm¢2) and were of three types. Thefirst two types were pure or almost pure Al, while thethird contained 30–40 at.% TM. Experimentally, the Al-rich terraces could be distinguished from the TM-rich ter-races because they exhibited a stronger bias dependencein STM. This interpretation was supported by experimen-tal and theoretical information about the partial densityof states, showing that at the Fermi surface Al sp-statesdo not contribute strongly, but rather TM d-states domi-nate.[81,82]

Studies of Ag deposition on this surface provided anexample of how different terraces can react differentlywith deposited adatoms.[78] Specifically, growth of Ag wassmoother on the TM-rich terraces and rougher on the Al-rich ones. The first Ag atomic layer was even pseudomor-phic on the TM-rich terraces. The variation of roughnesswith temperature showed that this is an equilibriumeffect. Density functional theory supported the differentgrowth modes in terms of differences in the adhesionenergy of a Ag slab with Ag, Al, Cu, and Co slabs.[78]

Interestingly, the TM-rich terraces often included nano-domains of the Al-rich structure, whereas the Al-rich ter-races almost never exhibited these kinds of defects.[77–79]

Figure 15A, B shows such an area at different biases, atrelatively low magnification. The TM-rich matrix isshown in white in the schematic of Figure 15C. Thismatrix responds most strongly to the change in bias, ascan be seen by comparing Figure 15A, B.

On an atomic scale, the different responses of TM andAl atoms allowed individual rows of atoms to be identi-fied.[79] This was important, because it revealed a kind ofin-plane coherence between the structure of the TMmatrix and the Al nanodomains. For instance, in Fig-ure 15D,E the nanodomains share some rows of atomswith the TM-rich matrix. This is observed best at positivebias (Figure 15E), where some lines extend straight fromthe TM-rich matrix into the nanodomain. One such lineis marked by the arrow in the lower right of Figure 15E.Using both the bias dependence and the bulk structuremodel, the straight lines in the TM-rich regions wereidentified as rows containing only TM atoms. Within theAl-rich nanodomains, the lines are mixtures of Al andTM atoms. Structurally, such a row is contiguous acrossthe nanodomain boundary, but chemically, it has a sharptransition. This, and other features of the STM images, al-lowed the Al-rich terminations to be identified as one ofthe two specific types, that is, the one containing about85 at.% Al.

Insight into the origin of the nanodomains was provid-ed by observation of a TM terrace bounded by a bunchedstep.[79] The TM terrace happened to include a nanodo-main along the step edge. The STM data revealed thatthe sequence of the steps in the bunch where it boundedthe TM matrix was L-(LSL)-S-L-LS, which is a portion ofa Fibonacci sequence, as expected for a quasicrystallinematerial. The step sequence at the location of the nano-domain was l-(S-S-t¢1S-L)-S-L-LS, which corresponds toa faulted portion of a Fibonacci sequence. This provedthat the nanodomain was associated with a stacking errorin the bulk direction, while the TM-rich terrace encom-passing the nanodomain was not.

Additional observations provided insight into thereason why nanodomains form.[79] First, one might conjec-ture that the presence of nanodomains at surfaces was in-dependent of the surface itself, that is, that nanodomainswith stacking errors existed in the bulk, and the surfacejust happened to intersect and expose them. However,nanodomains were almost always restricted to the TM-rich terraces. Only a few exceptions were observed, andin those cases, TM-rich nanodomains existed on 85 %-Alterraces. If the defective regions formed in the bulk, thennanodomains should be present on all types of termina-tions in equal densities.

The preference for nanodomains to appear on TM-richterraces suggested that the driving force for nanodomainformation lies in the chemical composition of the termi-

Figure 15. (A, B): STM images, 100 Õ 100 nm2, of a clean TM-richterrace with nanodomains, at inverted bias voltages. The arrowshows an atomic row that extends from the TM-rich matrixthrough the nanodomain. (D, E): Higher-magnification view of theparts of A and B indicated by the black boxes. Image size is 33 Õ33 nm2. (C, F): Maps of the corresponding STM images, showingthe TM-rich areas in white and Al-rich areas in black. From ref. [79].Copyright 2011 by the American Physical Society.



nation.[79] Based on chemical content alone, TM-rich ter-races are expected to have higher surface energies, andhence be less stable, than Al-rich ones. The developmentof Al-rich nanodomains is, in effect, a mechanism bywhich a TM-rich terrace can be replaced by an Al-richtermination. If the energetic cost of the stacking error isless than the cost of maintaining the TM-rich terrace, rel-ative to an Al-rich termination, then the nanodomainswill form as observed. It was therefore postulated thatthe formation of nanodomains involves more than justthe surface layer, but is driven by surface energetics. Theenergetic cost of creating the stacking error consistsmainly of creating the interface between the nanodomainand the TM matrix. However, that cost is clearly mitigat-ed by the coherence of the atomic-scale features thatbridge the nanodomain and the matrix (Figure 15 D,E).

If this picture is correct, then the TM-rich terracesmust be a kind of intermediate feature formed duringsample preparation. They develop during the process de-picted in Figure 13, but then (with increasing time and/ortemperature) convert into Al-rich regions. In fact, it islikely that the few terraces that were observed, consistingof 85 at% Al matrix with a few TM-rich nanodomains,had actually started out as TM-rich terraces and evolvedtoward Al-rich terraces. This picture is very similar tothat evoked by the voids on Al-Pd-Mn (Figure 14). Per-haps metastable features are common on quasicrystal sur-faces, contributing to what is termed, in this article, ex-trinsic heterogeneity—structural and chemical differencesbetween terraces that depend on conditions of samplepreparation, due to transitory existence of metastablequasicrystalline terminations.

6. Conclusions

In this article, we have argued that quasicrystalline surfa-ces exhibit a distinctive degree of heterogeneity. This het-erogeneity exists whether one is comparing average prop-erties (such as composition or planar atomic density)among different terraces, or even chemical compositionsof structurally-equivalent local adsorption sites on asingle terrace. Intrinsic heterogeneity can be related tobulk structural models, and extrinsic heterogeneity is re-lated to conditions of sample preparation. Experimentalevidence exists for both types of heterogeneity. Thedegree of heterogeneity appears to be quite distinctive,relative to common crystalline alloys and intermetallics,and even relative to the approximants whose surfaceshave been studied to date. This heterogeneity is an impor-tant factor in understanding and predicting phenomenasuch as chemisorption.

Acknowledgements

We are grateful to the many scientists who contributed tostudies of the atomic and chemical structure of clean qua-sicrystal surfaces. The list of those who worked on thesetopics at Ames Laboratory and Iowa State University asstudents and postdocs includes Tanhong Cai, ThomasDuguet, Ian Fisher, Vincent Fourn¦e, Chandana Ghosh,Martin Gierer, Yong Han, Mark Heinzig, Patrick Pinhero,Wolfgang Raberg, Kyle Schnitzenbaumer, Zhouxin Shen,and Chen-Ming Zhang. Other important contributors andcollaborators include Sheng-Liang Chang, Drew Delaney,Da-Jiang Liu, Frank Ogletree, Jeong Park, Miquel Sal-meron, and Amy Ross. The writing of this article was sup-ported by the Office of Science, Basic Energy Sciences,Materials Sciences and Engineering Division of the USDepartment of Energy (USDOE) under Contract No.DE-AC02–07CH11358 with the US Department ofEnergy. JWE was supported for modeling of film growthby NSF Grant CHE-1111500.

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Received: October 26, 2011Accepted: October 31, 2011



A Distinctive Feature of the Surface Structure of Quasicrystals: Intrinsic and Extrinsic Heterogeneity

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