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Quasicrystals are crystalline alloys that are highly ordered but with no structural period. Some of the potential applications of quasicrystals are explored in this paper:

R. McGrath, U. Grimm and R.D. Diehl, "The Forbidden Beauty of Quasicrystals," Physics World 17, 23-27 (2004)

Basic Quasicrystal Information

There are many excellent websites that provide descriptions of quasicrystal structures and how they are related to Fibonacci numbers and to tilings. Here are a few of them:

Diffraction from Quasicrystals

Diffraction studies of quasicrystals present a challenge because of their a periodicity. Diffraction techniques were developed for periodic structures, and the analysis of diffraction from quasicrystals has required some new ways of thinking and some new methods of analysis.

In order to build some intuition about diffraction from quasicrystals, we studied the laser diffraction for periodic and aperiodic gratings. In the American Journal of Physics we present methods for using laser diffractions as an aid in the interpretation of diffraction data. Some of the resources we created in this study can be found here: Diffraction from 1D and 2D Quasicrystalline Gratings. More resources for laser diffraction can be found at:

We reviewed some of the intricacies of interpreting LEED patterns from quasicrystals in this paper: R. D. Diehl, J. Ledieu, N Ferralis, A. W. Szmodis and R. Mc Grath, "Low-Energy Electron Diffraction Studies (LEED) from Quasicrystals Surfaces" J. Phys. Condens. Mat. 15, R63-R81 (2003)

We have used low-energy electron diffraction to determine the surface geometry of the decagonal Al-Ni-Co quasicrystal.

Our first attempts used a structure model based on a bulk structure obtained from x-ray diffraction. Here are two references:

W. Steurer, T. Haibach, B. Zhang, S. Kek, and R. Lu. Acta Crystalogr., Sect. B: Struct. Sci. 49, 661

A. Cervellino, T. Haibach, and W. Steurer. Acta Crystalogr., Sect B: Struct. Sci. 58, 8

This method involves the use of a large slab for the structure model. Approximations wre made to average over atomic positions and composition. This is because there are far too many parameters to vary in the analysis if we were to allow all of the atoms to relax.

The drawback to this method is that we are not able to check all possible configurations of atoms, due to the averaging employed. In order to overcome this drawback, we developed a new method that uses periodic structures for the structure models. The structure models are known as "periodic approximants" because they are periodic, but their local structures approximate the structures found in the quasicrystals. Using such models it is possible to carry out fully atomistic analyses and gain insight into the local ordering in the quasicrystal. The approximants used in these studies were selected from the alloy database ( and are shown below. Although the structure found was very close to that using the quasicrystal model described previously, the insight grained allowed an improvement of that analysis too.

Initially, we used periodic aproximant structures that have 25-50 atoms per unit cell. Although we obtained very good agreement with these models, they are too small to fully represent the types of local order that are present in the quasicrystal

More recently, we have been able to extend this analysis to a very large periodic unit cell, the so-called W-approximant, which has 534 atoms per unit cell. By applying symmetry, it was possible to reduce the number of adjustable parameters in the analysis to produce a tractable calculation. The final result of this analysis was satisfactory, but our opinion is that we can learn more about these structures using the smaller approximant unit cells, because as the cell size increases, the interpretation of the structures becomes more difficult.

The results of all of these dynamical LEED analyses are summarized in this Table:


Film Growth on Quasicrystals

All known quasicrystals are alloys, i.e. they are made from more than one element. Interestingly, the physical properties of quasicrystals are very different from periodic materials having similar compositions. To study the effects of the structure in these materials is complicated by their composition; Therefore, it would be useful to be able to create single-element quasicrystals to simplify their study.

One approach to this is to use an alloy quasicrystal as a substrate and to grow some other material on this surface, where quasicrystal acts as a template to produce quasicrystalline ordering in a film made of a single element. This idea is explored in this paper: R. McGrath, J. Ledieu, E. J. Cox, N Ferralis, and R. D. Diehl, "Quasicrystal Surfaces as Templates for Artificial Aperiodic Systems: from Nanoclusters to Epilayers" J. Non-Cryst. Solids 334-5, 500-504 (2004)

More recent reviews of film growth on quasicrystalline surfaces have been written.

Fournée V and Thiel P A 2005. J Phys. D: Appl. Phys. 38 R83.Opens New Window

Sharma H R, Shimoda M, and Tsai A P 2007 Adv. Phys. 56 403.Opens New Window

We have studied the growth of Cu films on the iconahedral Al-Pd-Mn quasicrystal using serveral experimental techniques.

From the STM and LEED pattern measurements, we have determined that the Cu film consists of aperiodically-spaced rows of periodically spaced Cu atoms. An STM image of the CU film is shown here. A really interesting aspect of this film is that the aperiodicity clearly comes from the substrate, and surprisingly this aperiodic structure, which is not at all natural for copper, is maintained to at least 25 layers!

In order to determine the structure of this aperiod Cu film, we are carrying out a dynamical LEED analysis. LEED patterns fro mteh Cu film are shown here. The best structure model we have obtained is for a body-centered tetragonal structure, but we feel that the agreement is not yet at a good enough level, and these studies aer still in progess.

References for this work:

J. Ledieu, J. Hoeft, D. E. Reid, J. Smerdon, R. D. Diehl, T. A. Lograsso, A. R. Ross, and R. McGrath, "Pseudomorphic growth of a single element quasiperiodic ultrathin film on a quasicrystal substrate," Phys. Rev. Lett. 92, 135507 (2004)Opens New Window

J. Ledieu, J. Hoeft, D. E. Reid, J. Smerdon, R. D. Diehl, T. A. Lograsso, A. R. Ross, and R. McGrath, "Copper adsorption on the fivefold Al70Pd21Mn9 quasicrystal surface," Phys. Rev. B 72, 035420 (2005)Opens New Window

K. Pussi, D. E. Reid, N. Ferralis, R. McGrath, T. A. Lograsso, A. R. Ross, and R. D. Diehl, "Low-Energy Electron Diffraction (LEED) Study of an Aperiodic Thin Film of Cu on fivefold AlPdMn," Phil. Mag. (2008)Opens New Window

Gases Absorbed on Quasicrystals

Quasicrystalline surfaces are candidates for superlubricity, a phenomenon that can occur where there is no commensurability between two contact surfaces. This potential for little or no friction, along with their high hardness and oxidation resistance, makes them attractive for the use as coating on machine parts, for instance in automotive engines. In any real application, it is probable that a lubricant would be used, which might affect the superlubricity.

We have studied the evolution of the ordering of Xe on the Al-Ni-Co surface using LEED.

The main findings were:

  1. Xe adsorbs layer-by-layer.
  2. Xe has a quasicrystalline stucture at low coverage.
  3. There is a transition to a periodic hexagonal structure as the 2nd layer adsorbs, and subsequent adsorption is consistent with fcc(111) Xe.
  4. The isosteric heat of adsorption for the first layer is 250 meV/atom.

Our experimental studies were extended with the help of our theoretical collaborators, who created models for the gas-surface potentials and performed grand canonical Monte Carlo simulations for Xe, Kr, Ar, Ne, and other gases. These studies showed:

  1. The phase transition from quasicrystalline to hexagonal is a first-order transition.
  2. The existence of this phase transition depends on the size of the adatom relative to the substrate length and scale, and for rare gases only occurs for Xe.
  3. The five rotational domains occur as a natural consequence of entropic dislocations in the overlayer, and not from substrate defects.

This work is very important for providing insight into the periodic ordering of films in quasicrystalline surfaces. Although quasicrystals are aperiodic, their structures have certain periodic elements. These periodic elements are in fact those that give rise to the diffraction peaks, i.e. if you think of diffraction as a Fourier transform (which it is, essentially), then each peak in the tourier transform corresponds to a particular periodicity in the structure. What we have found for rare gas adsorption is that Xe happens to have a size very close to a natural period in the surface of AlNiCo, therefore it can easily form a periodic structureon the quasicrystal surface. It turns out that this is true for metak films too.


R. A. Trasca, N. Ferralis, R.D. Diehl, and M.W. Cole, "The adsorption of Xe and Ar on quasicrystalline AlNiCo," J. Phys. Condens. Mat. 16, S2911-S2921 (2004)Opens New Window

S. Curtarolo, W. Setyawan, N. Ferralis, R.D. Diehl, and M.W. Cole, "Evolution of Topological Order in Xe Films on a Quasicrystal Surface," Phys. Rev. Lett. 95, 136104 (2005)Opens New Window

R.D. Diehl, N. Ferralis, K. Pussi, M.W. Cole, W. Setyawan, and S. Curtarolo, "The Ordering of a Xe Monolayer on quasicrystalline AlNiCo," Philos. Mag. 86, 863-868 (2006)Opens New Window

W. Setyawan, N. Ferralis, R.D. Diehl, M.W. Cole, and S. Curtarolo, "Xe Films on a decagonal AlNiCo quasicrystalline surface," Phys. Rev. B 74, 125425 (2006)Opens New Window

W. Setyawan, R.D. Diehl, N. Ferralis, M.W. Cole, and S. Curtarolo, "Noble Gas Films on a decagonal AlNiCo quasicrystal," J. Phys. Condens. Mat. 19, 016007 (2007)Opens New Window

R.D. Diehl, W. Setyawan, N. Ferralis, R.A. Trasca, M.W. Cole, and S. Curtarolo, "Ordering of Rare Gases Films on a decagonal AlNiCo quasicrystal," Philos. Mag. 87, 2973-2980 (2007)Opens New Window

R.D. Diehl, W. Setyawan, and S. Curtarolo, "Gas Adsorption on quasicrystalline surfaces," J. Phys. Condens. Mat. (2008)Opens New Window


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