Keywords:phase transition, Al-Ni-Co
Phase transitions between decagonal quasicrystals and periodic approximants are studied in the system Al-Co-Ni as a function of composition and thermal history by high resolution transmission electron microscopy and electron diffraction. There are two main types of transitions between quasicrystals and high-order approximants. On the one hand, there are transitions observed with continuously increasing linear phason strain and domain sizes exceeding the nanometer range. On the other hand, there are transitions via multiply twinned phason strained domains of a size in the nanometer range (NDS). In this case, the further transition to large periodic domains is not well studied yet. Furthermore, the prerequisites for the different kinds of transitions are still unclear.
To close this gap, we performed a series of annealing treatments in the system Al-Ni-Co. The results of this study indicate that large domains of periodic approximants resulting from a transition via NDS are much more perturbed than those resulting from a continuous transition. If the type of transition plays a decisive role for the real structure of approximants also in other cases, the manipulation of the type of transition might be of general interest with respect to the production of approximants for structure analysis.

20. Magnetism in Quasicrystals
Janez Dolinsek
Jozef Stefan Institute, Ljubljana, Slovenia

Keywords: Magnetism in quasicrystals, Kondo effect in quasicrystals

Magnetism in quasicrystals containing transition metals (AlPdMn, AlCuFe etc.) or rare earths (TbMgZn, TbMgCd, CdYb etc.) represents one of the open questions in the physics of quasicrystals. Some AlPdMn quasicrystals exhibit at low temperatures a spin glass phase that possesses all the features of canonical spin glasses- frustration due to RKKY oscillating interaction and randomness due to diluted quantity of moments that are placed randomly in the sample. In TbMgZn-type quasicrystals the moments are not diluted as all rare earth elements contain large magnetic moments. The moments are distributed on a lattice and are hence not placed randomly. Thermoremanent magnetization decay experiments show that these systems exhibit an unusual spin glass phase where the free energy is not organised ultrametricallyas characterized for the conanical spin glasses. TbMgZn-type quasicrystals resemble geometrically frustrated systems of magnetic momentsand are hence fundamentally different from canonical spin glasses where the moments are placed at random. Another unusual magnetic phenomenon was observed by NMR experiments on AlPdMn and AlCuFe quasicrystals. An anomalous narrowing of the NMR spectrum at low temperatures indicates vanishing of the local transferred hyperfine field of magnetic Mn and Fe moments in space which is consistent with Kondo like screening of moments by the conduction electrons. It appears that in magnetic quasicrystals there exist two opposite effects at low temperatures. The RKKY interaction combined with randomness tends to convert the spin system into a spin glass whereas the kondo-like screening of moments by the conduction electrons tries to drive the system towards a nonmagnetic state. The winner of these two competing effects determines the nature of the low temperature phase of magnetic quasicrystals.

21. Composition rules based on clusters for quasicrystals
Chuang Dong(a,b), Jianbing Qiang(a), Yingmin Wang(a), Xiaodong Wang(a),
Min Qi(a),Pat Thiel(b)
(a)State Key Lab for Materials Modification,
Department of Materials Engineering,
Dalian University of Technology,Dalinan 116024, China
(b)Ames Lab,Department of Chemistry,
Iowa State University,Ames,IA 500011, USA

Stable quasicrystals are multi-component alloy phases with narrow composition ranges. Although hundreds of stable quasicrystals have been found, little is known about their quantitative composition rules that can help design new materials. It has been proved experimentally that quasicrystals are both built up with basic clusters having icosahedral symmetries. The structure of the clusters can be obtained from known approximants. In this paper, we will attempt to combine cluster structures with phase diagram features such as the e/a-constant and e/a-variant lines, with the aim of figuring out composition rules for quasicrystal compositions in ternary alloy systems. Some simple rules can be pointed out and explained using the basic clusters, and they have been tested successfully in Zr-based and Al-based alloys.

22. Wetting on quasicrystals in ambient air
Jean-Marie Dubois
LSG2M-CIM (UMR 7584 CNRS-INPL-UHP),Ecole des Mines, Parc de Saurupt
F-54042, Nancy, France

Keywords:Wetting

Surface of quasicrystals of high lattice perfection is surprisingly large.Such behaviour cannot be understood on the basis of a comparison to other metallic systems and suggests that one should revisit the models commonly accepted for wetting on metals.
Rivier[1] has formulated a first theoretical approach of this result, taking explicitly into account the density of states at the outer most surface of the quasicrystal and the possible influence of the geometry of the water-quasicrystal interface. Yet, he ignored the presence of an oxide layer at the surface of any quasicrystal studied in ambient air. Such a layer is usually a few nanometers thick and therefore, according to standard models, the wetting behaviour should be that of the oxide layer and should not vary with the nature and precise composition of the quasicrystalline substrate underneath. This is precisely not what experimental data tell us.
In this paper, I will present a simplified model that considers the oxide layer as an inert spacer, simply responsible for a constant dispersive component of the adhesion energy. The variation of the dipolar component is assigned to the interaction between water dipoles and their images formed within the electron cloud of the quasicrystalline solid. Hence, it predicts a linear variation of the reversible adhesion energy with the square of the density of conduction states at the Fermi edge and with the inverse of the square of the oxide thickness. Experimental results are found in nice agreement with this model[2].
Beyond the specific case of quasicrystals and related Al-based alloys, I suggest that the image force component should also be taken into account, on top of the well-known Lishifts-van der Walls and Lewis-Bronstein contributions when dealing with wetting on oxidised metals or alloys. This conclusion has special relevance to many practical questions raised in cooking art, lubrication in mechanics or cutting/machining, textile industry, data storage, etc.
1. N. Rivier, J. Non Crys. Sol. 153-154 (1993) 458
2. Wetting on oxidised intermetallic surfaces, J.M. DUBOIS et al., Phys. Rev. Lett, submitted
List

34. UNIVERSAL MAGNETIC BEHAVIOUR OF ICOSAHEDRAL, F2 AND F2M Al-Pd-Mn QUASICRYSTALS
F. HIPPERT, M. AUDIER
LMGP/ENSPG, Domaine Universitaire, BP46, 38402 Saint Martin d'Heres Cedex, France
J.J. PREJEAN, A. SULPICE
CRTBT/CNRS, BP 166, 38042 Grenoble Cedex, France
V.SIMONET
Laboratoire Louis Neel/CNRS, BP 166, 38042 Grenoble Cedex, France
Y. CALVAYRAC
CECM/CNRS, 15 Rue G. Urbain, 94407 Vitry sur Seine, France

Keywords:quasicrystal, magnetism, Al-Pd-Mn , thermal treatment, Kondo effect
Magnetic properties of icosahedral, F2 and F2M Al-Pd-Mn single crystals were investigated in order to study parameters influencing the moment formation on Mn atoms. The temperature dependence of the magnetic susceptibility, measured on more than 20 samples, exhibits a universal behaviour whatever the structural state and the fraction of the Mn atoms which are magnetic (from 5 10-4 up to 2.5 10-2). This fraction depends on the sample composition. The effect is so strong that the magnetic properties reveal small concentration gradients existing along the growth direction of single grains obtained by Czochralski method. Thermal treatments also affect the magnetism : slowly cooled down samples are systematically less magnetic than rapidly cooled ones, whatever their composition and their structural state. The magnetism changes induced by thermal treatments are fully reversible. Moments suppressed by a slow cooling can be introduced again by a new annealing at high temperature followed by a rapid cooling.
Therefore, magnetism in Al-Pd-Mn quasicrystalline phases is an extremely sensitive probe of the atomic arrangement as the small fraction of the Mn atoms carrying a magnetic moment is strongly affected by very small differences of composition and thermal treatments. Let us note that the temperature dependence of the susceptibility is explained by a Kondo effect gradually affected by magnetic interactions as the concentration of magnetic Mn increases which is a usual behaviour in diluted magnetic alloys.

35. Ab initio Studies on Chemical Bonding in Cd- and Zn-based Quasicrystals
Y.Ishii and T.Fujiwara
Dept. of Physics, Chuo Univ., Kasuga, Tokyo 112-8551, Japan Dept. of Applied Physics, Univ. of Tokyo, Hongo, Tokyo 113-8654, Japan

Keywords:electronic structure, stability, Cd-Yb, Zn-Mg-Sc
Large clusters with successive atomic shells of icosahedral symmetry are believed to be basic structural units of the newly dicovered binary Cd-M (M=Yb and Ca) and ternary Zn-Mg-Sc quasicrystals. Recently ab initio studies on the electronic structures of cubic approximants Cd₆M have shown that the hybridization of low-lying unoccupied d states of Yb and Ca with a wide sp band is essential in stabilizing the Cd- and Zn-based compounds. This leads to questions how the icosahedral structure is preferred by such hybridization and if there is covalent natures in the electronic structures of quasicrystals without transition elements. In this paper, we shall investigate nature of chemical bonding in the Cd- and Zn-based compounds from ab initio calculations of electronic structures. We shall also discuss mechanism of stabilizing the cluster core with non-icosahedral symmetry, which is anticipated from structure of the cubic approximant Cd₆M.

36. Structure analysis of Zn-Mg-Ho(Y) icosahedral quasicrystals by modified Rietveld method using ellipsoid and sphere windows
Tsutomu Ishimasa (a), Kei Oyamada (a), Yasuomi Arichika (b), Eiji Nishibori (c), Masaki Takata (c), Makoto Sakata (c) and Kenichi Kato (d)
(a) Division of Applied Physics, Graduate School of Engineering, Hokkaido Univ., kita-ku, Sapporo 060-8628, Japan
(b) Division of Nuclear Engineering, Graduate School of Engineering, Nagoya Univ., Chikusa-ku, Nagoya 464-8603, Japan
(c) Division of Applied Physics, Graduate School of Engineering, Nagoya Univ., Chikusa-ku, Nagoya 464-8603, Japan
(d) Japan Synchrotron Radiation Research Institute (JASRI), 1-1-1 Kouto, Mikazuki-cho, Sayo-gun, Hyogo 679-5198, Japan

Keywords:Icosahedral phase, Structure analysis, Rietveld method, Zn-Mg-Ho, Zn-Mg-Y
Analysis in high dimensional space has become standard in the field of structural research of a quasicrystal. In such analysis, position and shape of each acceptance region are determined in a high-dimensional unit cell. However, we still do not have well-established method to reach the detailed shape of the window. In this situation, two diffraction methods, powder and single quasicrystal X-ray diffraction methods, may be complementary, because the powder method has several advantages: easiness of experimental technique and specimen preparation, and availability of instrument. Our purpose is to demonstrate potential and limitation of the powder diffraction method in the case of Zn-Mg-Ho and Zn-Mg-Y icosahedral quasicrystals.
Alloys used in this study are Zn₅₉Mg₃₁Ho₁₀ and Zn₅₉Mg₃₁Y₁₀, both of which consist of almost single phase of F-type icosahedral quasicrystal with 6-dimensional lattice parameter a6D=14.6925 A and 14.7223 A, respectively. Powder X-ray diffraction experiments were carried out at SPring-8 at the beam line 02B2 using wave length of 0.73486 A. The diffraction profiles were analyzed by modified Rietveld method, where spherical windows are assumed to be present at Node1, Node2, Bodycenter1, Bodycenter2 and ellipsoid-shaped one at Edgecenter according to the former work [1]. Simple but realistic structural models have been searched, which hold the perfect atomic ordering for the spherical windows and include mixing of Zn and Mg at Edgecenter. The analysis indicated that the quasicrystal structure of the two alloys can be understood by isomorphous substitution.
Two types of models have been obtained for the Zn-Mg-Ho (Y) quasicrystals, which are very similar to each other but have small difference. Both types showed nice agreement with experimental values of density and alloy composition, as well as rather nice fit in intensity distribution with Rwp factor of approximately 5%. Therefore, it was impossible to decide which model is correct in the limit of this study. The common feature of these two models can be summarized as follows; there is almost complete 3-dimensional Penrose tiling consisting of Zn at Node1 and Mg at Node2. Edge center positions of the Penrose tiles tend to be ocuupied by mixed atom of Zn_0.7Mg_0.3(or Zn_0.8Mg_0.2) belonging to Edgecenter. The prolate rhombohedron tends to have Bodycenter2 atom, namely Ho or Y, and Bodycenter1 atom on its long body diagonal. The major difference of the two models is the type of Bodycenter1 atom; in one model Bodycenter1 atom is Zn, but in the other model Mg.
[1] T. Ishimasa and T. Shimizu, Mater. Science Eng., 294-296, 232-236, (2000).

37. New group of stable icosahedral quasicrystals - structural properties and formation conditions
Tsutomu Ishimasa, Yasushi Kaneko
Division of Applied Physics, Graduate School of Engineering, Hokkaido University, kita-ku, Sapporo 060-8628, Japan

Keywords:Icosahedral phase, stable quasicrystal, atomic cluster
After the discovery of Cd-based icosahedral quasicrystals such as Cd-Ca, Cd-Yb [1] and Cd-Mg-R (R: Y and lanthanoid elements [2]), several new icosahedral quasicrystals have been discovered as equilibrium phases in Zn-Mg-Sc [3], Zn-Mg-Ti [4], and Cu-Ga-Mg-Sc [5] as well as some Ag-In based alloys [6]. The aim of our presentation is to demonstrate, in spite of the difference in the base metals, that they form one unique group which is different from the well-known Mackay- and Bergman-types. Common feature of this new group can be summarized as follows;
(1) All quasicrystals belong to P-type, except for Zn-Mg-Ti, and exhibit relatively high degree of structural perfection. Especially, the quality of Zn₈₀Mg₅Sc₁₅ and Cu₄₈Ga₃₄Mg₃Sc₁₅ quasicrystals is quite high.
(2) Majority of these quasicrystals form in the alloys based on sp-metals containing 8~15 at.% of transition metals having one or two d-electrons like Sc, Ti, Y, and the lanthanoid elements. Furthermore, these quasicrystals have almost the same value of electron concentration (e/a) ranging from 2.00 to 2.16. This fact suggests strong role of Hume-Rothery mechanism in stabilization of these quasicrystals.
(3)There exists a cubic 1/1 approximant at the alloy composition corresponding to each quasicrystal. Such approximants can be seen, for example, in Cd₆Yb, Cd₆Y, Zn₁₇Sc₃, and Cu_3.7Ga_2.3Sc. These approximants include unique local atomic configurations, or atomic clusters, exhibiting local icosahedral symmetry. These clusters consist of triple shells; the first shell with a shape of dodecahedron at the innermost, the second shell of an icosahedron, and the third shell of an icosidodecahedron according to the literatures.
[1] GUO, J. Q., ABE, E., and TSAI, A. P., 2000, Phys. Rev. B, 62, R14605
[2] GUO, J. Q., ABE, E., and TSAI, A. P., 2000, Jpn. J. Appl. Phys., 39, L770
[3] KANEKO, Y., ARICHIKA, Y., and ISHIMASA, T., 2001, Phil. Mag. Lett., 81, 777
[4] ISHIMASA, T., KANEKO, Y., and KANEKO, H., J. Alloys Compounds, in press.
[5] KANEKO, Y., MAEZAWA, R., KANEKO, H., ISHIMASA, T., submitted to Phil. Mag. Lett
[6] GUO, J. Q., ABE, E., and TSAI, A. P., J. Alloys Compounds, in press.

38. Magneto-resistance studies in Al₇₀Pd_20+xMn_10-x (x=0,1) icosahedral Quasi-crystal
Archna Jaiswal, R. Rawat, N. P. Lalla
Inter University Consortium for Department of Atomic Energy Facilities, University Campus, Khandwa road, Indore-452017,India

Keywords:Quasicrystal,weak-localization,interaction,Kondo- effect
Low-temperature four-probe d.c.-conductivity (-T) and magneto-resistance measurements up to field of 80 KOe has been carried out in the temperature range of ~ 1.38K to 300K for as prepared as well as annealed, icosahedral phases inAl₇₀Pd_20+xMn_10-x (x=0,1) .Samples were synthesized by induction melting under inert atmosphere. Structural and phase purity characterization was critically done using XRD, EDAX and back scattered SEM. In conductivity (-T) curve it was observed that as we go from higher temperature (300K) towards lower temperature, conductivity decreases, which can be explained by weak localization theory including dephasing dominated by e-e scattering. When the temperature is further lowered from about 122K, conductivity starts increasing, which can be attributed to the presence of spin-orbit scattering, causing anti-weak-localization. With further decrease in temperature the (-T) curve shows an inflexion followed by a sharp decrease in conductivity at ~ 9.31K, 7.838K and 3.602K for Al₇₀Pd₂₀Mn₁₀ (unannealed and annealed) and Al₇₀Pd₂₁Mn₉ samples respectively. The magneto-resistance, at temperatures ~ 20K, 6K and 3K is positive and follows B2 dependence, indicative of electron-electron interaction effect in the limit of low field and high temperature. These observations have been critically compared, examined and analyzed in the light of reported work by other groups. The sharp decrease in (-T) variation has been attributed as competition between spin-orbit scattering and suppressed Hartree term in electron-electron interaction. At ~ 1.4K the magneto-resistance shows a negative component which vanishes at ~ 50 KOe. The occurrence of negative magneto-resistance shows the presence of competing Kondo effect, which vanishes at around 3K for Al₇₀Pd₂₀Mn₁₀ phase. Various scattering parameters of weak-localization and interaction effects, active under the strong influence of spin-orbit scattering, have been refined through non-linear least square fitting of the data. It was also observed that the sample with lower Mn concentration Al₇₀Pd₂₁Mn₉ shows high magneto resistance. This feature also is a supporting evidence of the occurrence of interaction effect.

39. Influence of Alloying on the Formation of Zr-based Quasicrystals
R. Janlewing(a), D. Zander(a), L. Jastrow(a), L. Lyubenova(a), V. Khare(a,b), Uwe Köster(a)
(a) Dept. Chem. Eng., University of Dortmund, D-44221 Dortmund, Germany
(b)Centre d'Ingénierie des Matériaux, Ecole des Mines de Nancy, F-54042 Nancy, France

Keywords:Quasicrystal,alloying,icosahedral
Annealing of glassy Zr-Cu-Ni-Al precursor alloys leads in a narrow concentration range to the formation of icosahedral quasicrystals. The following arguments are very often considered to explain the formation of quasicrystals:
- Quasicrystals are assumed as Hume-Rothery phases stabilized at a particular electron-to-atom ratio e/a;
-the size relation of the atoms involved;
-the bond strength between the atoms;
-the quasicrystalline structure is assumed as a hybrid structure built from Al₂Cu- and MoSi₂-type structural units.
The aim of this paper is to investigate the influence of alloying on the quasicrystal formation by means of TEM and X-ray diffraction. For a detailed analysis nucleation rates were measured by means of crystallization statistics. Interfacial energies (between quasicrystals and amorphous matrix) as well as metastable melting temperatures for the quasicrystalline phase were derived by modeling the obtained nucleation rates in the framework of diffusion controlled classical nucleation theory.
Small additions of elements such as Si, Ta or Mo were found to change the phase selection during the early stages of crystallization significantly: Si additions lead to the formation of the tetragonal Zr₂Ni phase, Ta to the formation of the tetragonal Zr₂Cu phase and Mo to the formation of the fcc,so-called big-cube phase. Y, an element with a much larger diameter as Zr leads to very easy formation of quasicrystals even at lower temperatures. V, on the other hand, which is much smaller than Zr, behaves differently.
In order to understand the formation of the icosahedral structure also data on the influence of oxygen and hydrogen contamination as well as recent data on the exchange of Cu or Ni by noble metals such as Ag, Pd, Au and Pt will be discussed in detail. These results indicate that the quasicrystals are a hybrid of two structural elements, i.e. the tetragonal Zr₂Ni (Al₂Cu) and the tetragonal Zr₂Cu (MoSi₂) structure. Furthermore it is assumed that an icosahedral short-range order of the melt is stabilized by the addition of elements like Hf, probably Y or by contamination with very small amounts of oxygen, thus leading to a reduced interfacial energy between the quasicrystals and the amorphous matrix.

40. LINKING APERIODIC AND PERIODIC DIRECTIONS IN DECAGONAL QUASICRYSTALS
C. J. Jenks [1], J. Bjergaard[1], P. A. Thiel[1], P. Canfield[2], A. Cervellino[3], and W. Steurer[3]
[1] Department of Chemistry and Ames Laboratory, Iowa State University, Ames, IA 50011 USA
[2] Department of Physics and Astronomy, and Ames Laboratory, Ames, IA 50011 USA
[3] Laboratory of Crystallography, ETH-Zürich,CH-8006 Zürich Switzerland

Because of their aperiodic nature, lattice planes, in the traditional sense, do not exist for quasicrystals. For decagonal quasicrystals, it is proposed, however, that one can link the aperiodic and periodic directions using what are termed net planes (see W. Steurer and A. Cervellino, Acta Crystallogr. A, 2001, 57, 333-340.) These net planes are thought to play a critical role in the stability and growth of decagonal quasicrystals. To explore their potential role during growth and to shed light on their structural stability, we have studied single grain surfaces of decagonal Al-Ni-Co by low energy electron diffraction and scanning tunneling microscopy. Our results suggest that these planes do indeed exist. The nature of these net planes and our results will be discussed.

41. SURFACE STUDIES OF QUASICRYSTALLINE Al-Pd-Mn BY ANGLE-RESOLVED LOW ENERGY ION SCATTERING
C.J. Jenks[1], P.A. Thiel[1], A.R. Ross[2], T.A. Lograsso[2], J.A. Whaley[3], and R. Bastasz[3]
[1] Department of Chemistry and Ames Laboratory, Iowa State University, Ames, IA 50011 USA
[2] Department of Materials Science and Engineering and Ames Laboratory, Iowa State University, Ames, IA 50011 USA
[3] Sandia National Laboratories, Livermore, CA 94551 USA

Keywords:surface Al-Pd-Mn "low energy ion scattering"
We have used angle-resolved low-energy ion scattering to examine the clean surface structure and composition under ultra-high vacuum conditions of a single grain of icosahedral Al₇₁Pd₂₀Mn₉ oriented with a five-fold axis perpendicular to the surface. This technique is one of the few that is truly sensitive to the topmost layer of the surf. Our results are consistent with the surface maintaining five-fold symmetry after sputtering followed by annealing at 800 K. We find that the topmost surface layer is > 85 atomic % aluminum. A predominant neighbor atom distance of 7.6 ± 0.5 Å and a nearest neighbor distance of 3.0 ± 0.1 Å is calculated from our results. Our results are consistent with previous low energy electron diffraction intensity versus voltage (LEED-IV) calculations, recently published scanning tunneling microscopy results and a bulk model of Al-Pd-Mn quasicrystals.

42. Space of Fibonacci chains as an extended space of leaves on the torus and its implication to the space of Penrose tiling
Hyeong-Chai Jeong
Department of Physics, Sejong University, Kwangjin-ku, Seoul 143-747, Korea

Keywords:Penrose tiling, Fibonacci chain, Noncommutative geometry
The space of Fibonacci chains (F-chains) are studied from the perspective of noncommutative geometry. Using the torus representation and the cut-procedure, we establish the relationship between the space of F-chains and the space of leaves on Kronecker foliation. We embed the C^*-algebra of noncommutative torus into an approximately finite-dimensional algebra on the space of F-chain explicitly and show that the singular leaf corresponds to two different classes of F-chains. The relationship between the space of Penrose tiling and the space of the two-dimensional (2D) leaves in the 5D torus is also studied. The K-theory on the noncommutative algebra of the 2D wrapping planes on the 5D torus is considered. We further discuss possible investigation of the topological character for the decapod defects in quasicrystals in terms of noncommutative geometry.

43. Thermal properties of a 1D interface with a quasiperiodic potential
H.T.Jeong(a), H.-C.Jeong(b), and D.H.Kim(a)
(a) Center for Non-crystalline Materials, Yonsei University, Seoul, Korea
(b) Department of Physics, Sejong University, Seoul, Korea

The thermal equilibrium properties of a one-dimensional(1D) interface in a 2D square lattice with a quasiperiodic potential are studied. The interface configurations are restricted to the subset of restricted solid-on-solid configurations with the average slope equals to the best approximant to the golden mean for the given system size. The quasiperiodic potential is chosen such that the flat interface has the minimum energy. We study the equilibrium properties of the interface by using Monte Carlo simulation and show that the roughening transition occurs at finite temperature. This result may imply that the steps on decagonal quasicrystal surfaces can remain as flat at finite temperature.

44. Formation condition of stable Cu-Ga-Mg-Sc icosahedral quasicrystal
Yasushi Kaneko, Ryo Maezawa and Tsutomu Ishimasa
Division of Applied Physics, Graduate School of Engineering, Hokkaido University, Kita-ku, Sapporo, 060-8628, Japan

Keywords : Cu-Ga-Mg-Sc, icosahedral phase, stable quasicrystal
Recently, the Ag-In-Ca and Ag-In-Yb icosahedral quasicrystals have been discovered by Guo et al. These quasicrystals are formed by replacement of Cd in Cd84Ca16 and Cd84Yb16 icosahedral quasicrystals with Ag and In in a ratio of one to one in order to keep the value of average number of electrons per atom at e/a = 2.00. In the periodic table, the elements of Ag and In are located at both sides of Cd. This replacement method has a possibility to be applied to other alloy systems. The Zn80Mg5Sc15 icosahedral quasicrystal is a good candidate for this application because the local atomic structure of Zn80Mg5Sc15 is similar to those of Cd-based quasicrystals. Furthermore Zn and Cd belong to the same IIB group in the periodic table. The purpose of this work is to investigate whether an icosahedral quasicrystal is formed by replacement of Zn in the Zn80Mg5Sc15 quasicrystal by Cu and Ga, and whether the ratio of Cu and Ga is one to one. Samples were synthesized by induction melting under an argon atmosphere, and then annealed. When the Zn in Zn80Mg5Sc15 was replaced by Cu and Ga in a ratio of one to one, namely at a (Cu0.50Ga0.50)80Mg5Sc15 alloy, powder X-ray diffraction experiment indicated that the icosahedral quasicrystal was not formed in the alloy annealed at 973 K as well as as-cast alloy. The 1/1 cubic approximant crystal was formed as a major phase in these alloys. On the other hand, in the (Cu0.59Ga0.41)82Mg3Sc15 alloy annealed at 1043 K, the icosahedral quasicrystal was formed as an almost single phase. The value of e/a of this quasicrystal was calculated to be 2.01 in stead of 2.15 in the Zn-Mg-Sc quasicrystal. Here the valence number of Cu was assumed to be unity. Powder X-ray diffraction and electron diffraction experiments indicated the high degree of the structural perfection of the Cu-Ga-Mg-Sc quasicrystal. Furthermore, the local atomic configuration of the icosahedral quasicrystal is deduced to be similar to that of the Zn-Mg-Sc quasicrystal from the similarity of intensity distribution in the powder X-ray diffraction patterns. The icosahedral quasicrystal was also formed in an as-cast alloy with the same composition as a major phase. The quasicrystal is expected to be a stable phase by comparing the annealed and as-cast alloys.

45.HRTEM observations of thermally-induced tile rearrangements in Al-Cu-Co(-Si)decagonal quasicrystals
Edagawa Keiichi(a),P. Mandal(b), K. Suzuki(a), T. Hashimoto(a), K. Hosono(a)(c), R. Tamura(c) and S. Takeuchi(c)
(a)Institute of Industrial Science, Univ. of Tokyo,Komaba, Meguro-ku, Tokyo 153-8505,Japan
(b)Ames Laboratory,Iowa State University, Ames, IA 50011,USA
(c)Dept of Mater. Sci. & Tech., Tokyo University of Science, Japan

Keywords:Al-Cu-Co, Al-Cu-Co-Si, phason, phase transition
In-situ high-temperature HRTEM observations have been made for Al-Cu-Co and Al-Cu-Co-Si decagonal quasicrystals, to investigate structural changes mediated by phason motions. Tiling patterns with the edge length of 2nm were constructed by connecting white spots in the HRTEM images. Local tile-rearrangements, which can be interpreted as phason flips have been observed for both Al-Cu-Co and Al-Cu-Co-Si systems. For the Al-Cu-Co system, frequent phason flips could be observed only at high temperatures above 1143K. Here, transitions between two local tile configurations or those among several configurations have mostly been observed. A perp-space analysis showed that they correspond neither to phase transition to other phase nor to relaxation of phason strain. In contrast, for the Al-Cu-Co-Si system, the phason flips have been observed very frequently already at 1073K. In addition, the phason flips in the Al-Cu-Co-Si system are correlated with each other and appear to induce entire structural change. To elucidate the relation between the structural change observed here and the phase transition from a decagonal quasicrystal to a crystal approximant, which has previously been reported for this system, the perp-space analysis is underway.

46. Crystallization of Liquids and Glasses to Quasicrystals
K.F.Kelton
Department of Physics
Washington University
St.Louis, MO 63130, USA

Keywords:Crystallization,icosahedral phase, undercooled liquids,metallic glasses, nucleation

The local structures of metallic glasses and undercooled liquid metal alloys are presumed to contain a high degree of icosahedral short-range order.Recent specific heat and x-ray diffraction results obtained on levitated TiZrNi liquids are presented and shown to strongly support this of the amorphous structure.
The icosahedral quasicrystal (i-phase) is the primary crystallizing phase in many Al-transition metal alloys. We have recently shown the primary crystallization of a metastable, high temperature i-phase in a TiZrNi liquid; the i-phase is stable only at much lower temperatures, making it a candidate for a ground-state quasicrystal. Further, for a growing number of alloys that can be prepared as glasses, the quasicrystal is the primary crystallizing phase. This is particularly true for the Zr-based alloys that form bulk metallic glasses. Here, nucleation studies in these liquids and glasses will be reviewed. All data indicate significant icosahedral order in these amorphous systems.
The Zr-based glasses frequently crystallize to a nanoscale microstructure, possibly reflecting the ease of nucleation of the i-phase and the difficulty in its growth. However, since other devitrified glasses that do not form quasicrystals, frequently form a similar nanostructure, other crystallization mechanisms such as nanoscale liquid-liquid phase separation prior to crystallization, may be in competition. Further, in many cases, the ordered phase has a different chemical concentration from the glass, making long range diffusion important. A new model for homogeneous nucleation, coupling the interfacial and the long-range diffusion fluxes, is advanced to explore this.

47. Precipitates in a Mg-Zn-Y alloy reinforced by an icosahedral quasicrystalline phase
I. J. Kim, D. H. Bae and D. H. Kim
Center for Non-crystalline Materials, Department of Metallurgical Engineering, Yonsei University, 134 Shinchondong Seodaemungu, Seoul, 120-749, Korea

Keywords:Mg-Zn-Y, icosahedral, icosahedral precipitate, Aging hardening
Mg-rich Mg-Zn-Y alloys, reinforced by icosahedral quasicrystalline particles, have been developed by thermomechanical processes. The cast Mg-Zn-Y alloys consist of a thermally stable icosahedral quasicrystalline phase (I-phase) in-situ formed as a second phase of the eutectic in the primary a-Mg matrix. The locally located I-phase can be granulated and distributed in the a-Mg matrix by hot-extrusion and/or hot-rolling, providing the particle-reinforced metal matrix composite [1]. The alloys exhibit high strength with good ductility at room temperature, and also show excellent formability at elevated temperatures due to the fine grain structure of the alloys developed via dynamic crystallization that mostly occurs near the I-phase particles. In such alloy system, the alloys are also strengthened by some precipitates observed in the as-rolled samples. However, the precipitate hardening behavior is not clear in such a ternary alloy system.
In this study, we investigate the formation of precipitates under two different aging conditions for the as-cast and as-hot rolled Mg96Zn3.4Y0.6 samples. First, at the aging temperature of 190oC, the hardness value increases continuously up to the aging time of 24hr, and then slightly decreases to 240hr. TEM observation reveals that mostly fine disc shape MgZn2 precipitates are distributed in the a-Mg matrix. The coherent interphase boundary of the small precipitates (diameter: 100nm, height: 10nm) is found to lose its coherency as the precipitates grow during aging. Second, at the aging temperature of 350oC, a bit above the Mg-Zn binary eutectic temperature, the hardness value slightly increases up to the aging time of 10hr, and only nano-scale I-phase precipitates are formed in the a-Mg matrix. However, the size of the I-phase precipitates does not vary during aging possibly due to limited diffusivity of Yttrium. Although the strengthening effect of I-phase precipitates is not significant, their formation in the matrix is interesting. Details of the formation of I-phase precipitates and their strengthening behavior in such an alloy will be presented.
[1] Deformation behavior of Mg-Zn-Y alloys reinforced by icosahedral quasicrystalline particles, D.H. Bae, S.H. Kim, D.H. Kim and W.T. Kim, Acta Materialia, vol.50 (9) (2002) 2343-2356

48. Phason-elastic energy in a model quasicrystal
Ulrich Koschella, Franz Gähler, Johannes Roth and Hans-Rainer Trebin
Institut für Theoretische und Angewandte Physik Universität Stuttgart Pfaffenwaldring 57/VI 70550 Stuttgart,Germany

Keywords:elasticity; phason; ground state
For the standard two-dimensional decagonal binary tiling quasicrystal with Lennard-Jones potentials we have measured the five generalized phason-phonon elastic constants at temperature zero by molecular dynamics relaxation simulations. One of the phason elastic constants turned out to be negative, rendering the system metastable.
Therefore, in a next step we analyzed the phason elastic constants in dependence of the two-body interaction potentials by counting the frequencies of atomic neighborhoods as a function of phason strain. This calculations guided us to a modification of the potentials which stabilizes the binary tiling quasicrystal.
For these new potentials the elastic constants were determined with the same simulation method as above. The elastic constant for stoichiometry preserving phason strains becomes positive, and the system is stable.
For the determination of the ground state we made Monte-Carlo cooling simulations. With the unmodified Lennard-Jones potentials the tenfold clusters typical for the binary tiling structure do not show up. Rather, a phase separation into various crystalline states without five- or tenfold motifs is observed [Lee et al., Phys. Rev. B 64, 224201]. The modified potentials, on the other hand, strongly prefer tenfold clusters. The cooling simulations yield a ground state which is a super-tile random tiling structure with mainly doubly inflated thick Penrose rhombs. To correct the stoichiometry, several other types of super-tiles occur in between these rhombs.

49. Electrical resistivity measurement of the Al₆₅Rh₂₇Si₈ cubic approximant
Naokiyo Koshikawa, Shinichi Yoda(a), K. Keiichi Edagawa(b), Ryuji Tamura and Shin Takeuchi(c)
(a) National Space Development Agency of Japan, Tsukuba 305-8505, Japan
(b) Institute of Industrial Science, University of Tokyo, Tokyo, 153-8904, Japan
(c) Department of Material Science, Science University of Tokyo, Noda, 278-8510,Japan

Keywords: electron Transport properties
To understand the electron transport properties of quasicrystal(QC), measurement of the approximant phase is important. Recently, as for the approximant phase of Mackay icosahedron type (MI-type) QC, electrical resistivity measurements has been performed together with the Rietvelt analysis and calculation of electron density of state for the approximant crystals, and the results contribute to the understanding of electron transport properties of QC and its approximants.
As for the electrical resistivity measurement of 2/1 cubic crystal approximant, some experiments have been performed by using the ribbon samples made with spinning single-roll method, but no results has been reported on bulk sample. Bulk sample is needed to evaluate the absolute value of resistivity. Recently, we obtained the bulk single-phase 2/1 cubic approximant in Al-Rh-Si system, and we decided to measure the electrical resistivity of it. Our previous result shows that the related 1/0 cubic approximant phase in Al₇₃Rh₂₇ shows the metallic temperature dependence of resistivity in lower temperature range(4K-300K) and has value 350 mW/cm in room temperature. From now we will investigate the 2/1 cubic approximant in Al-Rh-Si system at the composition of Al(63-66)-Rh(27-28)-Si(7-9) at 4K-300K and will discuss the compositional dependence.

50. Electronic Structure and Conductivity Scaling of Quasiperiodic Approximants of Decagonal Aluminium
M. Krajci (a,b) and J. Hafner (a)
(a)Institut fur Materialphysik and Centre for Computational Materials
Science, Universitat Wien,Sensegasse 8/12, A-1090, Wien, Austria
(b)Institute of Physics, Slovak Academy of Sciences, 84228 Bratislava,
Slovak Republic

We present ab-initio calculations of electronic structure and transport properties of a monoatomic quasiperiodic system, decagonal aluminium (d-Al). We study the influence of quasiperiodicity on the transport properties at the example of a system which is sufficiently realistic to represent real Al-based quasicrystals, but does not involve the additional complexity of a strong s,p-d hybridization which determines the properties of many crystalline and quasicrystalline Al-transition metal alloys. The structure of d-Al is based on the densest known quasicrystalline sphere packing, the local atomic arrangement is closely related to crystalline FCC Al. The electronic density of states of d-Al is found to be very close to the free electron limit. If the Brillouin zone integration is taken to convergence, we find that electronic spectrum is smoothened with an increasing order of the approximant. The analysis of the participation ratio demonstrates a small deviation of the eigenstates from extended behaviour with scaling exponent of g=0.94. This would suggest a deviation from purely ballistic transport properties. The examination of the level spacing distribution demonstrates a small but distinct deviation from the statistics of the Gaussian orthogonal ensemble, suggesting a deviation from the purely diffusive regime as well. This investigation of the transport properties of a series of six periodic approximants with increasing linear dimensions is based on a self consistent calculation of the electronic eigenstates and the Kubo-Greenwood formula. A detailed scaling analysis demonstrates small deviation of the eigenstates from extended behaviour and shows that transport properties belong to the subballistic regime. with a scaling exponent of diffusivity b=0.6 that is somewhat larger than the quantum diffusion limit b=0.5, but distinctly smaller than the ballistic transport. In this sub ballistic or over diffusive regime the conductivity diverges in the thermodynamic limit, leading to metallic behaviour. The effect of quasiperiodicity is strong enough to induce substantial deviations from ballistic transport but strong enough to reach the quantum diffusion regime.

51. Covalent bonding and band-gap formation in Al--transition-metal quasicrystalline approximants
M. Krajci (a,b) and J. Hafner (a)
(a)Institut fur Materialphysik and Centre for Computational Materials
Science, Universitat Wien,Sensegasse 8/12, A-1090, Wien, Austria
(b)Institute of Physics, Slovak Academy of Sciences, 84228 Bratislava,
Slovak Republic

Keywords:Electronic structure, transport properties, icosahedral approximants,AlPdRe, covalent bonding, semiconducting gap

We demonstrate that in some quasiperiodic transition-metal aluminides a special bonding between the Al(s,p) and transition-metal (TM) d-orbitals is responsible for formation of a semiconducting gap in the electronic spectrum. We analyzed the electronic charge distribution and have found an enhanced charge density along the Al-TM bonds that is characteristic for covalent bonding. The character of the hybrid-orbitals forming the covalent bonds has been further investigated using the crystal-orbital overlap population analysis. We show that the narrow gap at the Fermi level arises from the bonding -antibonding splitting of the hybrid-orbitals. The semiconducting gap is observed in three lowest approximants to the icosahedral quasicrystals of the fci AlPdTM class. This suggests a possible explanation of anomalously high resistivity of the aluminum based icosahedral AlPdMn and AlPdRe quasicrystals. We also show that replacement of a 3d by a 5d transition metal enhances the bonding-effect, leading thus to an increased resistivity of i-AlPdRe in comparison with i-AlPdMn. However, the observed covalent bonding and band gap formation is not specific to quasicrystals and has been observed also in crystalline Al-TM compounds. We conclude that it is not the quasicrystallinity but the unusual Al-TM bonding that is responsible for a substantial part of anomalies observed in the transport properties of Al-TM quasicrystals.

52. Icosahedral Short Range Order in Zr-based Metallic Glasses
M. J. Kramer, M. F. Besser, N. Yang, E. Rozhkova and D. J. Sordelet
Metal and Ceramic Sciences Program, Ames Laboratory(USDOE), Department of Materials Science and Engineering, Iowa State University Iowa State University Ames, Iowa 50011-3020,USA
Y. Zhang and P.L. Lee
Advance Photon Source (APS), Argonne National Laboratory, Argonne, Il 60439,USA

Keywords:high-temperature X-ray diffraction, icosahedral order, metallic glass,devitrification
The unique quasiperiodic structure of quasicrystals may arise from isosahedral order in the super-cooled liquid prior to solidification. Bulk-metallic glasses provide a window into investigating the relationship between structural order in liquid state and that of the solidified compound since the time scales for atomic motion in the quenched liquid are very slow compared to that of the liquid; therefore the structure of the glass can be more readily studied. In addition, the short-range order in a given metallic glass is highly dependent upon both thermal history and composition. Changes in the local order alter the energy landscape and, in turn, can profoundly influence the phase selection process during devitrification. Using high-energy, high-temperature X-ray diffraction (HTXRD), we are investigating the short-range order in Zr-Pd(Cu) based metallic glasses and comparing the atomic pair distributions in the as-quenched alloys to that observed in the liquid and to the metastable quasicrystalline and crystalline phases. The HTXRD data for the Zr70Pd30 alloy shows coexistence of the quasicrystalline Zr2Pd (I4/mmm) crystalline phases over a range of 25 K. Conversely, the Zr70Pd20Cu10 alloy shows an abrupt transformation of the quasicrystalline phase to the Zr2(PdCu) intermetallic (Zr2Si type structure, I4/mcm) that polymorphically transforms to the Zr2Ni type structure (I4/mmm) over a very narrow temperature range. Changes in the short-range order from glass formation through devitrification will be discussed. The similarities in short-range order of the structure of the liquid to the amorphous state will also be addressed.
The work at Ames Laboratory was supported by the U.S. Dept. of Energy through Iowa State University under contract No. W-7405-ENG-82. The Midwest Universities Collaborative Access Team (MUCAT) sector at the APS is supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, through the Ames Laboratory under Contract No. W-7405-Eng-82. Use of the Advanced Photon Source, SRI-CAT and MUCAT, was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, under Contract No. W-31-109-Eng-38.

53. Hume-Rothery controlled formation of structurally complex alloy phases in the ternary Ga-Mg-Pd system
Guido Kreiner (a), Yuri Moguilnikov (a), Ulrich Burkhardt (a) and Melanie Schäpers (b) (a) Max-Planck-Institut für Chemische Physik fester Stoffe, Nöthnitzer-Str. 40, 01187 Dresden, Germany
(b) Fachbereich Chemie der Universität Dortmund, 44221 Dortmund, Germany

Keywords:Approximant, Intermetallics, Phase diagram, Ga-Mg-Pd
A tiling approach to the structure of icosahedral quasicrystals of the Bergman cluster type taking decoration rules from higher approximants up to 3/2-2/1-2/1 into account was discussed in [1]. The experimental findings support the conclusion that quasicrystals and large approximants related to the AlMgZn class represent packings of Pauling triacontahedra (PT) occupying nodes and a special site in the interior of the D cells of Henley's canonical cell tilings [2]. Mihalcovic et. al. [3,4] have proposed theoretically a canonical cell tiling structure for icosahedral quasicrystals of the Mackay icosahedron type using a molecular dynamical approach. However, little is known on the long range order from experiments for Mackay icosahedra with 55 atoms per cluster (MI-55). Such Mackay icosahedra are characteristic for ternary alloy phases with one transition and two main group metals as components and a free electron per atom ratio of 1.7.
An overview is given on the synthesis and x-ray single crystal structure analysis of several complex intermetallic phases including MI-55 and PT type approximants. Phase analysis was done using powder diffraction, chemical analysis, thermal analysis and metallography. The following points are addressed: (a) Hume-Rothery and size factor rule versus cluster type and chemical disorder; b) the role of the magnesium concentration versus cluster arrangement; (c) decoration rules and canonical cell tiling structure for MI-55 approximants; (d) approximants as structurally complex alloy phases (SCAPs) of Frank-Kasper and I3-cluster type.
[1] G. Kreiner, J. Alloys and Comp. 338, 261 (2002)
[2] C.L. Henley, Phys. Rev. B 43(1), 993 (1991)
[3] M. Mihalkovic, W.-J. Zhu, C.L. Henley and M. Oxborrow, Phys. Rev. B 53(14), 9002 (1996)
[4] M. Mihalkovic, W.-J. Zhu, C.L. Henley and R. Phillips, Phys. Rev. B 53(14), 9021 (1996)

54. Estimation of Gibbs Free Energy difference in Bulk Glass Forming (BMG) Alloys
Kirit N. Lad(1), K. G. Raval(2), and Arun Pratap(1)
(1)Condensed Matter Physic Laboratory, Applied Physics Department, Faculty of Technology and Engineering, M. S. University of Baroda, Vadodara-390 001,India
(2)Electronics Department, Narmada College of Science and Commerce, Bharuch - 392 011,India

Keywords:Bulk Metallic Glasses, Glass Forming Ability
Gibbs free energy change for crystallization of an undercooled liquid, f´G, is an important parameter in the nucleation theory. Its study is important for the amorphous phase formation in metallic alloys. It is well-known that the exact temperature dependence of f´G can be calculated if the heat capacities of the liquid and crystal are known as a function of temperature. However, the heat capacity data of undercooled liquid is not available easily due to its metastable nature. Therefore, in case of non-availability of the specific heat data in the undercooled region, the functional dependence of f´G on undercooling must be estimated theoretically. Various expressions for f´G are available in the literature. These expressions depend on some kind of assumption for the temperature dependence of the heat capacity. Thompson and Spaepen (TS) have shown that some knowledge of the crystal and liquid heat capacities of a material is necessary for choosing an appropriate approximation for f´G. Assuming that no specific heat data is available, one has to look for an approximation for f´G with minimum number of known experimental parameters. Further, since the nucleation frequency has exponential dependence on f´G, the accuracy of an estimate of f´G is often critically important when used in the analysis of nucleation phenomena. For the metallic glass-forming alloys, the evaluation of the Gibbs free energy difference is important for predicting the glass-forming ability. It is believed that small Gibbs free energy difference is associated with the high glass-forming ability of bulk metallic glass formers.
A new expression is obtained for the Gibbs free energy difference (f´G) between the crystalline and undercooled liquid phases of metallic glass forming alloys. The new expression is a result of modification of the Thompson and Spaepen (TS) derivation for f´G. Gibbs free energy has been calculated for three metallic glass forming alloys namely, Al30La50Ni20, Ni40Pd40P20 and Pd40Cu30Ni10P20. All these multicomponent systems possess excellent glass-forming ability. The incorporation of Cu in ternary system namely, Ni40Pd40P20 converts it into quaternary alloy Pd40Cu30Ni10P20 decreasing f´G in the entire temperature range. This makes the bulk glass formation possible in Pd40Cu30Ni10P20. This also shows that metallic alloys with more than three elements exhibits high glass-forming ability which is in agreement with one of the empirical rules that requires multicomponent alloy system consisting of more than three elements, for achieving high glass-forming ability in metallic glasses. This further supports the ¡¥confusion principle¡¦ put forward by Greer.

55. Bulk Termination of the Icosahedral Al₇₀Pd₂₁Mn₉ Surface
J. Ledieu (a), E.J. Cox (a), Z. Papadopolos (b), G. Kasner (b), Q. Chen (c), N.V. Richardson (c), R.D. Diehl (d), T.A. Lograsso (e), A.R. Ross (e), and R. McGrath (a)
(a) Surface Science Research Centre, The University of Liverpool, Liverpool L69 3BX, UK
(b) Institut für Theoretische Physik, Universität Magdeburg, PSF 4120, D-39016 Magdeburg, Germany
(c) School of Chemistry, The University of St Andrews, KY 169ST, UK
(d) Department of Physics, Pennsylvania State University, University Park, PA 16802, USA
(e) Ames Laboratory, Iowa State University, Ames, IA 50011, USA

Keywords: STM, AlPdMn, Surface, Bulk Model

In early work, we have shown using threshold analysis of STM images that the flat surface of Al₇₀Pd₂₁Mn₉ could be partly tiled with pentagons [1]. However large protrusions on the flat surfaces were found to break the tiling and comparison with models was not possible. In the work presented here we carry this tiling approach to fruition, using a combination of experimental and theoretical methods.
The preparation of the quasicrystalline Al₇₀Pd₂₁Mn₉ surface has been optimised.Terraces up to 1/2 micron wide with a corrugation (Zrms) of 0.27 Å have been observed. We present very high quality atomic resolution STM images recorded on consecutive terraces. Pentagons of edge length 7.8 +/- 0.2 Å are recognised within the planes. Using autocorrelation and tiling techniques, the surface is shown to be consistent with a bulk termination of the model of Boudard et al.[2]. The experimentally derived tiling matches that expected from the model based on the F-phase three-dimensional tiling T*((P1)r)[3]. The variation of the density of the five-fold depressions has been observed in accordance with previous works [4]. Finally the first in situ evidence of the reality of five-fold depressions is presented here. [1] J. Ledieu, A.W. Munz, T.M. Parker, R. McGrath, R.D. Diehl, D.W. Delaney and T.A. Lograsso, Surf. Sci. 433-435 (1999) 666.
[2] M. Boudard, M. de Boissieu, C. Janot, G. Heger, C. Beeli, H.-U. Nissen, H. Vincent, R. Ibberson, M. Audier, and J.M. Dubois, J. Phys.: Cond. Matter 4, 10149 (1992).
[3] J.ledieu, R. McGrath, R.D. Diehl, T.A. Lograsso, D.W. Delaney, Z. Papadopolos and G. Kasner, Surf. Sci. Lett. 492 (2001) L729.
[4] G. Kasner, Z. Papadopolos, P. Kramer and D. Bürgler, Phys. Rev. B 60, 3899 (1999).

56. Composite coating of Al-Cu-Fe-X (X=Si, B) quasicrystalline and WC-Co mixed powders
S.M.Lee[1], B.M.Moon[1], E.Fleury[2], D.H.Kim[2] and W.T.Kim[3]
[1]Korea Institute of Industrial Technology
[2]Yonsei University, Center for Non-crystalline Solids
[3]Chongju University, Department of Physics

Keywords: composite coating, Al-Cu-Fe-X (X=Si, B), WC-Co powders, high velocity oxygen fuel spraying, tribology, wear property, friction coefficient, surface energy
We present an experimental study on the effect of the quasicrystalline phase on the surface and tribological properties of WC-Co coatings. Composite coatings were fabricated by deposition of Al-Cu-Fe-X (X=Si, B) and WC-Co powders onto mild steel substrates using thermal spraying technique in air. Prior to the composite coating manufacturing, various preliminary properties of both pure quasicrystalline coating and WC-Co coating layers were examined. Effects of alloying elements, such as Si and B on the tribological properties of the quasicrystalline coating layers were systematically investigated. Based on the preliminary data of the pure coating layers, Al-Cu-Fe-X quasicrystalline powders and WC-Co powders were mixed as a starting material for the spraying process with the aim of improving the frictional and surface properties of the WC-Co ceramic coating layers. In the composite coating, quasicrystalline components were expected to possess better friction property and low surface energy, enabling to achieve non-sticking behavior of the coating layer together with enhanced working performance of the coating, while WC-Co components were expected to show higher hardness and wear resistance. Combined analyses of OM, SEM-EDX, TEM, DTA were employed for the microstructural characterization of the coating layers. Tribological properties including friction and wear were systematically investigated as a function of the volume fraction of the quasicrystalline phase in the mixed coating layer. Pin-on-disc and reciprocating wear devices were utilized for the measurement of the tribology property. Surface energy of the composite coating layer was also measured in order to evaluate the non-sticking behavior.

57. Thermoelectric properties of quasicrystals: a phenomenological approach
Enrique Macia

Keywords:Seebeck coefficient, thermoelectrics
We present a theoretical study on the thermal and electrical conductivities of quasicrystals (QCs) as well as on their possible use as thermoelectric materials. We consider a realistic model for the spectral conductivity, deriving closed analytical expressions for the transport coefficients satisfactorily describing their temperature dependence over a wide temperature range. In this way, we shall introduce a phenomenological model describing the thermoelectric power of icosahedral QCs. By comparing our analytical results with available experimental data we relate the purported sensitivity of the thermopower curve to minor variations in the chemical composition with the main features of the electronic structure of the considered samples. Finally, we show that QCs closely follow Wiedemann-Franz's law over a wide temperature range, hence supporting the common procedure of substracting to the experimental thermal conductivity data the electronic contribution as prescribed by this law.

58. Evidence for a marginally conducting state in AlFeCu and AlPdMn quasicystals
D.Mayou
LEPES-CNRS, 25 Avenue des Maryrs BP166
38042 Genoble, France

Icosahedral phases such as AlCuFe and AlPdMn , have exotic electronic transport properties. In particular, at zero or low frequency, the conductivity of these QCs increases with disorder and with frequency [1-2]. Moreover recent studies [3-4] of AlPdMn have shown that the conductivity increases nearly linearly with the concentration of defects. This behavior is exactly at the opposite of that of standard metals, and has received at present no detailed explanation.
On the theoretical side it is found that the so-called critical states [5] , which are specific to quasiperiodic systems, have peculiar diffusion properties. In the absence of defects, an electron propagates on a distance L(t) which follows a power-law of time L(t) = A tB where the exponent B depends on the energy and on the hamiltonian. It has been shown recently that this leads to peculiar transport properties that are in qualitative agreement with the experimental behavior [6] in the case B<1/2.
A more detailed analysis [7] shows that the experimental results for conduction of AlCuFe and AlPdMn are consistent with the limit B=0. This is remarkable since, as far as we know, the diffusion exponent is never found so close to B=0 in the quasiperiodic models studied so far. This indicates a state which is marginally conducting and close to a localized state. This marginally metallic state could be related to the fact that the Fermi energy is close to marginal critical states similar to those proposed recently by Fujita and Niizeki [ 8].
The Drude formula for the conductivity of metals can be generalized (by taking properly into account the limit B=0) and then provides a very good quantitative fit to experimental results for the variation of the conductivity with frequency and disorder [7]. In particular we obtain a very good fit of the optical conductivity of AlCuFe and AlPdMn and explain the mysterious linear variation of conductivity with frequency below 8000 cm-1 [2]. In this model we explain naturally the nearly linear increase of conductivity with disorder [3] and the so-called inverse Mathiessen rule [1]. We find that for typical conductivities 200--500 (Ohm cm)-1 the scattering time Ts due to disorder is rather large Ts = 4--2 10-14 s . This is in agreement with the high structural quality of these alloys. This is also comparable to the scattering time estimated for AlCuCo alloys [6]. Other phenomenon such as quantum interferences effects and electron-electron interaction effects, which are observed experimentally, give only corrections to the present scheme in the case of AlCuFe and AlPdMn.
[1] C. Berger in Lectures on Quasicrystals, Edited by F. Hippert and D. Gratias (LesEditions de Physique, Les Ulis 1994).
[2] C.C. Homes et al. Phys.Rev. Lett. 67, 2694 (1991). Basov, D.N. et al. in Proceedings of the Fifth International Conference on Quasicrystals. Edited by C. Janot and R. Mosseri (World Scientific 1995)
[3] J.J. Préjean, C. Berger, A. Sulpice and Y. Calvayrac Phys. Rev. B 65 140203(R) (2002)
[4] G. Trambly de Laissardière and D. Mayou Phys. Rev. Lett. 85, 1964 (2000)
[5] T. Fujiwara, T. Mitsui and S. Yamamoto , Phys.Rev.B 53, R2910 (1996)
and M. Krajci, J. Hafner and M. Mihalkovic Phys. Rev. B 65 024205 (2002)
[6] D. Mayou, Phys.Rev.Lett. 85, 1290-1293 (2000)
[7] D. Mayou Submitted to Phys. Rev. Lett.
[8] N. Fujita and K. Niizeki Phys.Rev.Lett. 85, 4924-4927 (2000) List

73. Synthesis and Characterization of Al- Al₆₅Cu₂₀Fe₁₅ quasicrystalline particulate composites
N.K.Mukhopadhyay, S.K.Sahu, J.P.Pathak and R.K.Mondal
Centre for Advanced Study
Department of Metallugical Engineering
Institute of Technology
Banaras Hindu University,Varanasi-221005,India

Aluminum matrix composites represent a family of materials whose stiffness, strength, thermal and electrical properties can be tailored by selecting the matrix alloy, their type and size as well as the amount of reinforcements. The aim of the present work is to explore the possibilities of using Al₆₅Cu₂₀Fe₁₅ quasicrystalline (QC) particles as reinforced phase in aluminum matrix through liquid metallurgy route. The amount of the above dispersoid QC materials has been varied from 2-10wt% in commercial aluminum matrix.
Using impeller mixing and bottom discharge chill-casting technique, it is observed that it is possible to disperse uniformly and discontinuously QC materials in the matrix to a limited amount. Beyond that, the agglomeration of QC particles has been observed, specifically in 10wt% composite. On increasing the amount of QC particles, the grain size of the matrix was found to decrease from 100-150mm to 50-60mm, suggesting that QC particles can act as a grain refiner in commercial alloy. From microstructural studies we find a reaction zone around the QC particles, which varies between 0.2 -0.5mm. This reaction zone arising from the diffusion bonding where the concentration of transition metal is high compared to that in matrix is expected to give rise to a strong interface. Mechanical properties are found to be better in 8wt% composite material. For a given load and constant sliding speed, there is an indication of overall improvement in regards to wear properties. The implication of the present investigation will be discussed.

74. Glass forming ability and crystallization behavior in Ti-Zr-Cu-Ni-Be alloys
J. M. Park, Y. C. Kim, J. H. Jun, D. H. Bae, W. T. Kim and D. H. Kim
Center for Noncrystalline Materials, Dept. of Metallurgical Eng., Yonsei University,134 Shinchon-dong, Seodaemun-ku, Seoul 120-749 Korea

Keywords:Ti-Zr-Cu-Ni-Be alloy, glass forming ability, crystallization, icosahedral
Ti-rich amorphous alloys are of scientific and commercial interest due to high specific strength. The glass forming ability and crystallization behaior in Ti-rich Ti-Zr-Cu-Ni-Be alloys with the composition range of Ti40-50Zr15-35Cu4-10Ni2-10Be8-22 have been investigated in the present study. With increasing Ti content glass transition behavior becomes less clear, and glass transition temperature decreases. However, the melting temperature of the alloy decreases significantly, for example, the liquidus temperature of 700oC is obtained in Ti39Zr33Cu7Ni6Be15 alloy. Some of the alloys investigated show good glass forming ability. Amorphous rods of Ti-Zr-Cu-Ni-Be alloys with a diameter of 3 mm are successfully fabricated by injection casting. Thermal analysis shows that the amorphous phase crystallizes via two exothermic reactions followed by an endothermic reaction. Microstructural analysis shows that the first exothermic reaction corresponds to precipitation of icosahedral phase. The crystallization sequence of amorphous Ti40Zr28Cu9Ni7Be16 alloy is: amorphous phase - icosahedral + amorphous phases - icosahedral + Laves phases - Laves phase. The formation of the icosahedral phase is discussed based on the results of thermal and microstructural analysis.

75. Initial Oxidation of Quasicrystals - an Investigation by High-Resolution
D. Plachke, A. Khellaf, and H.D. Carstanjen
Max-Planck-Institut für Metallforschung, Stuttgart, Germany

Keywords:oxidation, surfaces, AlPdMn, AlNiCo, depth profiles, RBS, ERD
The present contribution is dealing with the initial oxidation of surfaces of i-AlPdMn and d-AlNiCo single quasicrystals. Clean surfaces exhibiting LEED patterns of 5-fold and 10-fold symmetry, respectively, were prepared by subsequent sputter and anneal cycles under UHV conditions. During this treatment concentration depth profiles of the near surface region were taken by use of high-resolution Rutherford backscattering spectroscopy (RBS). In particular after sputtering an enrichment of the heaviest species, e.g. of Pd in case of AlPdMn, was observed at the surface. For the RBS measurements an electrostatic analyzer for MeV particles was used which has been set up at the MPI in Stuttgart and which allows depth profiling with monolayer depth resolution.
The prepared surfaces were than oxidized at various temperatures and oxygen depth profiles taken in dependence of oxygen exposure. For this purpose high resolution elastic recoil detection (ERD) was used (depth resolution in the monolayer range), again using the electrostatic analyzer. These investigations were accompanied by measurements of the near-surface stoichiometry by RBS during oxidation.
The present contribution describes in its first part the high resolution RBS and ERD techniques used in this study. In the second part RBS data taken during sample preparation are presented. This is followed by results on the oxidation experiments. Partially the data considerably deviate from data obtained by AES measurements due to the limited depth information obtainable by AES.

76. Quantitative correlation between the electrical conductivity and the concentration of magnetically probed defects in AlPdMn single grain quasicrystals
J.J. Préjean (1) , C. Berger (2) * , A. Sulpice (1) , Y. Calvayrac (3)
(1) Centre de Recheches sur les Très Basses Températures, CNRS, BP 166, F-38042 Grenoble Cedex 9, France
(2) Laboratoire d'Etudes des Propriétés Electroniques des Solides, CNRS, BP 166, F-38042 Grenoble Cedex 9, France
(3) Centre d'Etude de Chimie Métallurgique, CNRS, 15 rue G. Urbain, F-94407 Vitry-sur-Seine, Cedex France
* On sabbatical at GATECH school of Physics, Atlanta, GA, US

Keywords:Quasicrystal, electrical conductivity, magnetism, Kondo effect, AlPdMn
We have found a remarkable quantative relation between the conductivity s(T) and the concentration of magnetic Mn atoms in Al-Pd-Mn quasicrystals. We have studied weakly magnetic single grains where the fraction of Mn atoms which are magnetic can be as low as 5 10^-4. We show that we can finely tuned this fraction with the sample composition and heat treatments. We have performed magnetization and conductivity measurements in the 2K-300 K range on the very same samples in the same annealed state. We show that, at any constant temperature, s(T) increases linearly with the concentration x of magnetic moment in the sample : s(T)= xa(T) + ds(T). Above 100 K, the increasing rate of s with the magnetic Mn concentration a(T) is almost temperature independent, while a ln(T) type additional contribution is observed in a(T) below 100 K reflecting the s(T) upturn. From this work, we conclude (1) that the fundamental state of Mn atoms in AlPdMn quasicrystals is a zero electronic spin state; (2) that local defects (vacancies, substitutional disorder) depend drastically on the chemical composition and on the annealing processes (we argue that moments appear on Mn atoms in a defective local environment [1,2]); (3) that the dependence of s on the magnetic concentration in the whole temperature range is in fact related to the presence of local defects ( magnetically probed in the present case); (4) that the ln(T) type contribution observed for s(T) is due to a Kondo-like effect. We also conclude that QC-specific transport properties can be clearly observed only for x < 5 10-4, i.e. for defects about 30Å apart from one another.
[1] J.J. Préjean, C. Berger, A. Sulpice and Y. Calvayrac, Phys. Rev. B 65
[2] F. Hippert, M. Audier, J.J. Préjean, A. Sulpice, V. Simonet and Y. Calvayrac, this conference

77. STRUCTURE DEFECTS OF ICOSAHEDRAL QUASICRYSTALS AS ELECTRICALLY ACTIVE CENTRES
A.F. Prekul, N. Yu. Kuz'min, N. I. Shchegolikhina
Institute of Metal Physics, Ural Division, Russian Academy of Sciences 620219 Ekaterinburg, Russia

Keywords:Electron structure, defects
New results of dilatometric experiments on rapidly quenched quasicrystalline alloys Al-Cu-Fe in the course of their annealing are reported. It is established that icosahedral (I-) phases with conductive carriers of different signs (either electrons or holes) have different senses of the volume changes upon ordering. The effect discovered serves as a direct experimental support for the assumption [1] that the structure defects in icosahedral quasicrystals are electrically active centres. The correspondence of sign of free carriers to sign of the volume changes indicates that the emergence of defects is accompanied by the electron transference from the defect to conduction band or from valence band to the defect. In the first case, the defect is charged positively and, owing to the enhancement of the direct Coulomb repulsion of atoms, gives rise to local expansion of the lattice. In the second case, the defect is charged negatively and weakening of the direct Coulomb repulsion results in local contraction of the lattice. Upon annealing, when the number of defects decreases, the sample volume either decreases or increases to an equilibrium value, respectively. In both cases, the number of free carriers and the residual conductivity of the sample decrease.
Thus, the structure defects turn out to play role either donors or acceptors. This circumstance allows identification of extrinsic properties of I-phases and opens up a series of novel opportunities of understanding physical properties of real quasicrystals. First of all, it concerns the nature of residual conductivity that is direct related to the very presence of the structure defects and is controlled by their number. According to [2], an ideal icosahedral lattice is featured by the states of free (non-ionized) atoms of components. Consequently, the appearance of free carriers is related to the changes in the electronic configuration of some of these atoms. Second, it concerns the Curie-like constituent of magnetic susceptibility at low temperatures.The tendencies of magnetism in I-phases are such that atoms of components of defectless Al-Cu-Fe I-phases have no localized magnetic moments [3]. Hence, free carriers and the Curie-like component of magnetic susceptibility are the counterparts of one and the same phenomenon. Then, in case all defects are alike and the defect configuration of an atom has nonzero spin, there arises, on the one hand, the possibility of analyzing the defect concentration using magneto-chemical techniques and, on the other hand, a linear dependence of the free carrier concentration and the residual conductivity on the Curie constant. At last, the evident fact should be taken into account that if at the Fermi level of real I-phases there are both electrons and holes, then owing to the effect of compensation, the volume change averaged over the sample will not be observed. Hence, upon considering I-phases in the framework of traditional band conceptions, the semiconductor version of the ground state of quasicrystals becomes more preferable than the semimetal version. In this case, the Fermi level of real I-phases is always situated either near the bottom of nearly empty conduction band or close to the top of almost full valence band, and the real I-phases, different in number of defects and the residual conductivity value, form a homological series of states at the metal-insulator transition on filling the band.
All these novelties are discussed basing on the available experimental data on the conductivity, magnetic susceptibility, heat capacity and Hall effect.
[1] A.F.Prekul, N.Yu.Kuzmin, N.I.Shchegolikhina Proc. Int.Conf. on Quasicrystals, Sendai, Japan, 2001. J.of Alloys and Compounds 1(2002) 000-000
[2] A.F.Prekul, N.Yu.Kuzmin, N.I.Shchegolikhina, Proc. Int.Conf. «Aperiodic Structures 2001», Krakow, 2001, p.138-141
[3] S.Matsuo, H.Nakano, T.Ishimasa, Y.Fukano, J.Phys.: Condens. Matter 1(1989) 6893

78. Quasicrystals in Ti-Zr-Ni Alloy System
J.B.Qiang, Y.M.Wang, D.H.Wang, C.H.Liu and C.Dong
State Key Lab for Materials Modification,
Dalina University of Technology, Dalian 116024, China

Our previous investigation revealed that both e/a-constant and e/a-variant lines are common phenomena in Al-based ternary quasicrystalline systems. The ideal compositions of ternary quasicrystals lie at the crossing points of the e/a-constant and e/a-variant lines, which can be viewed as empirical criteria to the search for quasicrystals. In the present work, we try to apply these empirical criteria to locate the composition of the quasicrystal in the Ti-Zr-Nisystem.
We prepared a series of Ti-Zr-Ni alloys along two e/a-constant lines (e/a=1.20/1.25) by suction casting and proved that the icosahedral phase exists in the compositional range of Zr_50~15Ti_30~65Ni₂₀(all in at.%) and Zr_53~13Ti_30~70Ni₁₇. Among them, Ti₄₀Zr₄₀Ni₂₀ is the best one at which almost single quasicrystalline bulk alloy was formed. Deviating from this ideal composition, a Ti/Zr solution is found in the as-cast alloys to coexist with the icosahedral phase, forming a eutectic-like structure. According to DSC results, the Ti₄₀Zr₄₀Ni₂₀ quasicrystal has the highest thermal stability up to 660°C, and above 660°C it transforms to C14-type Laves phase plus b-Ti/Zr solid solution. In the Ti-Zr-Ni phase diagram, a linear composition zone of the quasicrystal extends along the e/a-constant lines (e/a=1.20-1.25). The well-defined approximantssuch as the C14 and 1/1-W phases are also located near this zone, showing typical e/a-constant phase phenomenon. The e/a-variant lines defined by linking Ti₂Nito Zr and Zr₂Ni to Ti, exactly cross the composition of Ti₄₀Zr₄₀Ni₂₀, which is in good agreement with reported composition of Ti_41.5Zr_41.5Ni₁₇.

79. FORMATION AND STABILITY OF NANOQUASICRYSTALLINE PHASE IN Al-Cu-Fe AND Al-Cu-Co SYSTEMS BY HIGH-ENERGY BALL MILLING
R. V. Koteswara Rao, N.K. Mukhopadhyay* and B.S. Murty
Department of Metallurgical and Materials Engineering,
Indian Institute of Technology, Kharagpur-721 302, India,
*Department of Metallurgical Engineering, Institute of Technology,
Banaras Hindu University, Varanasi-221 005, India

Quasicrystalline (QC) phases are known to be quite stable up to melting point in a number of systems such as Al-Cu-Fe, Al-Cu-Co. However recent studies on these, so called stable QC phases have shown that they transform to crystalline phases on irradiation. Recent studies by the present investigators have shown that these QC phases are not quite stable on high energy ball milling. The present paper reports a detailed study of mechanical alloying (MA) and mechanical milling (MM) of two well known stable compositions of quasicrystalline phase, namely, Al₆₅Cu₂₀Fe₁₅ and Al₆₅Cu₂₀Co₁₅. In addition MA of Al₇₀Cu₂₀Fe₁₀ composition has also been carried out to understand the formation and stability of QC phase.
Elemental powder blends of Al₆₅Cu₂₀Fe₁₅ and Al₆₅Cu₂₀Co₁₅ compositions have been mechanically alloyed and alloy ingots of the above compositions have been mechanically milled to study the possible formation and stability of nanoquasicrystalline phase. In addition, Al₇₀Cu₂₀Fe₁₀ has also been mechanically alloyed. In case of MA and MM, the milling has been carried up to 80h and 40h, respectively. MA/MM has been carried out in a planetary ball mill (Fritsch Puverisette P-5). All the mechanically alloyed as well as mechanically milled samples have been subjected to heat treatment at 773K, 873K, 973K, 1073K for different timings up to a maximum of 24h to study the stability of the phase formed after final hours of milling. The milled as well as heat treated samples were characterized by XRD and TEM.
In case of MA, formation of quasicrystalline phase has been observed in Al-Cu-Fe system in both the compositions investigated, but not in case of Al-Cu-Co system. The quasicrystalline phase formed during MA was found to be unstable on extended milling hours and transformed to an ordered cubic crystalline phase (B2 Phase). The quasicrystalline phase synthesized by casting route in Al₆₅Cu₂₀Fe₁₅ and Al₆₅Cu₂₀Co₁₅ has also transformed to B2 phase during milling. The B2 phase formed on MA/MM has been found to be stable on further heat treatments with the temperature and time window studied.

80. Studies of Icosahedral AlPdRe Quasicrystals Across the Metal-Insulator Transition
O. Rapp(a), V. Srinivas(a,b), P. Nordblad(c), and J. Poon(d)
(a)SSD, IMIT, KTH-Electrum 229, 164 40 Stockholm-Kista, Sweden
(b) Dept. of Physics and Meteorology, Indian Institute of Technology, Kharagpur, 721 302 India
(c)Dept. Material Science, Uppsala University, Box 534, SE 751 21 Uppsala, Sweden
(d)Physics Dept. University of Virginia,Charlottesville, Virginia 22901, USA

Keywords:Icosahedral AlPdRe, Metal-insulator tansition, electronic transport,magnetic susceptibility

In high resistivity icosahedral AlPdRe, phase pure quasicrystals can be formed within a wide range of low temperature resistivities r(4.2 K) and resistance ratios R [=r(4.2 K)/r(295 K)]. For increasing r(4.2 K) and R, a metal insulator transition, MIT occurs, as can be inferred from the magnetoresistance, MR. At small R, the MR is well described by weak localization and enhanced electron-electron interaction effects, which are characteristic for metals with weak electronic disorder. For large R-values the MR instead follows Efros-Shklovski variable range hopping theory, describing electronic transport in the insulating state. Evidence will be discussed that the MIT can be controlled by the parameter R. In contrast, an MIT cannot be straight forwardly identified from the low temperature conductivity, s, as a function of R or T. At low T, s(R) is found to decrease smoothly with R, without any particular feature characterizing the crossing of an MIT. s(T) saturates at very low temperatures at a constant value which decreases with increasing R and remains finite up to the largest values of R investigated. Nor is there any distinctive feature in the diamagnetic susceptibility c across the MIT. Enhanced paramagnetic interactions are usually observed in electronically disordered systems in the proximity of an MIT, as is also theoretically expected due to poor screening. In contrast, c(T, R) of i-AlPdRe depends weakly on temperature and R, and remains within c = - (5±1) x10^-7 cm³/g for all samples and temperatures studied. This is a further anomalous property of quasicrystals. The problem to reconcile the observation of an MIT in the magnetoresistance with a finite zero temperature conductivity will also be adressed.

81. Synthesis and Characterization of Single Grain Cd-Yb Icosahedral Phase
A. R. Ross, M. J. Kramer and T. A. Lograsso
Metals and Ceramics Sciences, Ames Laboratory, Ames, Iowa 50011

Keywords:Cd-Yb, single crystal, transmission electron microscopy
We report, for the first time, the synthesis of a bulk single grain of icosahedral Cd84Yb16 quasicrystalline phase. Synthesis was accomplished using both tantulum and alumina crucibles, by controlled solidification in a Bridgman configuration. Single grains on the order of 0.75 cm3 have been characterized using scanning electron microscopy, powder X-ray diffraction and transmission electron microscopy. The as-grown samples are single phase with little compositional differences present along their length. Furthermore, no evidence of the formation of porosity, common to almost all ternary quasicrystalline phases, was found in the as-grown or annealed Cd-Yb. Initial structural characterization by X-ray diffraction and TEM of powdered single grains from both crucibles have verified the primitive icosahedral structure of the as-solidified alloy. Further work is ongoing to characterize the degree of quasiperiodic perfection of these quasicrystals.

82. Crack Propagation of Quasicrystals and Random Tilings
Christoph Rudhart (a), Hans-Rainer Trebin (a) and Peter Gumbsch (b)
(a)Institut fuer Theoretische und Angewandte Physik Universitaet Stuttgart,Pfaffenwaldring 57/VI,70550 Stuttgart,Germany
(b)Institut für Zuverlaessigkeit von Bauteilen und Systemen Universitaet Karlsruhe,Kaiserstr. 12,76131 Karlsruhe,Germany

Keywords:Crack propagation, mode-I cracks, two-dimensional decagonal model,quasicrystals, random tilings, molecular dynamics
Numerical experiments have been performed on the propagation of mode-I cracks in two-dimensional decagonal model quasicrystals, both ordered and randomized ones. In particular, the dependence on temperature, applied load and underlying structure has been investigated. The samples are endowed with an atomically sharp crack and subsequently loaded by linear scaling of the displacement field. The response of the system is followed by molecular dynamics simulations. For temperatures below 30% of the melting temperature T_m the crack velocity grows monotonically with the applied load and the model quasicrystal shows brittle fracture. For large overloads the crack becomes unstable and branches. In this low temperature regime we observe crack tip velocities in a range of 20%-50% of the shear wave velocity v_s. For temperatures above 30% of T_m the crack does not remain atomically sharp but is blunting spontaneously and it is not possible to obtain a stable initial condition. To circumvent this problem we establish a linear temperature gradient along a strip. From the low temperature regime, where a sharp tip can be stabilized, the crack is driven into a region of elevated temperature.
In the range of 70%-80% T_m the quasicrystal fails by a void formation process. Thus at low temperatures the crack propagates along planes as in periodic crystals, whereas at high temperatures a glass like behaviour is dominant.

83. EXAFS study of hydrogenation in Ti-Zr-Ni and Ti-Hf-Ni quasicrystals and approximants
A.Sadoc(a,b),E.H.Majzoub(c), V.T.Heutt(d) and K.F.Kelton(d)
(a)LPMS,Universite de Cergy-Pontoise, Neuville sur Oise, 95031
Cergy-Pontoise Cedex,France
(b)LURE, Centre Universitaire Paris-Sud, BP 34,91898,Orsay Cedex,France
(c)Sandia National Laboratories, 7011 East Avenue,Livermore,CA 95441,USA
(d)Department of Physics, Washington University,St.Louis, MO 63130,USA

Keywords :Local Structure, hydrogenation, quasicrystals, approximant

An understanding of the mechanism of hydrogen absorption in metals and intermetallics is of considerable importance for both technological and scientific reasons. Metal-hydrogen systems are used in a variety of technological applications, including hydrogen storage materials and metal-hydride batteries.
Since the discovery of quasicrystals (QC's), a large body of theoretical and experimental work has been devoted to the study of these materials. Among their physical properties, it has been found that some titanium/zirconium-based QCs have a larger capacity for hydrogen storage than competing crystalline materials [1]. In most transition metal alloys,hydrogen atoms prefer to sit in tetrahedrally coordinated sites. Icosahedral QC's are also likely dominated by tetrahedral order and thus provide a variety of sites for interstitial hydrogen.
The effect of hydrogenation on the local structure of Ti-Zr-Ni alloys, quasicrystals and bcc crystalline approximants, has been studied by means of extended X-ray absorption fine structure (EXAFS) experiments, performed above the Ti, Zr and Ni K absorption edges, using the synchrotron radiation. The alloys were loaded to different hydrogen to metal ratios (0, 0.84, 1.2, 1.4, 1.56 and 1.7) in order to follow the evolution of the local structure with hydrogenation. Drastic changes are observed in the hydrogenated alloys with modifications of distances and increase of disorder [2]. Very recent results on Ti-Hf-Ni alloys will also be presented.

84. FORMATION OF QUASICRYSTALLINE RELATED INTERMETALLIC COMPOUNDS IN CONVENTIONALLY CAST Al-Fe-V-Si ALLOY
K.L. Sahoo, S. Das, and B.S. Murty*
National Metallurgical Laboratory, Jamshedpur 831007, India
*Indian Institute of Technology, Kharagpur 721 302, India

Keywords:Al-Fe-V-Si alloy, quasicrystalline like phases
Al-Fe-V-Si alloys are recently emerging as potential light weight materials for high temperature applications. Allied Signal Inc., USA, has commercialised some alloys in Al-Fe-V-Si system, namely, FVS 0611, FVS0812, FVS1212 through rapid solidification processing (RSP). Various phases such as Al6Fe, Al7Fe2, Al13Fe4, Al19Fe6, Al3Fe with different crystal structures form in Al-Fe systems depending upon the composition and solidification parameters. The star shaped clusters and ten armed decagonal quasicrystals were reported earlier in Al-Fe alloys by rapid solidification processing (RSP). The present paper reports the evolution of ten armed rod shaped Al-Fe-V-Si alloys are recently emerging as potential light weight materials for high temperature applications. Allied Signal Inc., USA, has commercialised some alloys in Al-Fe-V-Si system, namely, FVS 0611, FVS0812, FVS1212 through rapid solidification processing (RSP). Various phases such as Al6Fe, Al7Fe2, Al13Fe4, Al19Fe6, Al3Fe with different crystal structures form in Al-Fe systems depending upon the composition and solidification parameters. The star shaped clusters and ten armed decagonal quasicrystals were reported earlier in Al-Fe alloys by rapid solidification processing (RSP). The present paper reports the evolution of ten armed rod shaped quasicrystalline related phase in conventionally cast Al-Fe-V-Si alloy. The uniqueness of this report lies in the fact that the cooling rate adapted is much lower (» 10K/s) when compared to RSP (106K/s).
The alloy of nominal composition Al-8.3Fe-0.8V-0.9Si (wt.%) has been prepared from high purity (99.9%) Al, Al-Fe, Al-Fe-V, Al-Si master alloys. Melting was carried out in electric resistance furnace in clay bonded graphite crucible coated with alumina. Melt was cast in different moulds in order to vary the cooling rate in the range of 1 to 20K/s. The microstructure of the castings was examined by optical microscopy, SEM and TEM. TEM samples were prepared by jet polishing technique using 20% HNO3 in methanol at 243K.
The microstructural analysis has shown the formation of rod type phase in Al matrix at cooling rate » 1K/s. At higher cooling rates (10-20K/s), the morphology of the second phase has changed to ten-armed star shaped with angle between any two adjacent arms being close to 36o. Such unique microstructure resembles the decagonal quasicrystals. The EDX analysis has confirmed the composition of ten-armed phase close to Al13Fe4. The TEM studies have indicated that the novel morphology could be a result of irrational twinning during its growth.

85. Structural changes of Ni-rich Al-Co-Ni decagonal quasicrystals
K. Saito¹(a), T. Ohsuna(b), W. Sun(b) and K. Hiraga(b)
(a)Department of Materials Engineering, Akita University, Akita 010-8502, Japan
(b)Institute of Materials Research, Tohoku University, Sendai 980-8577, Japan

It is well known that there are some highly-ordered decagonal quasicrystals showing different diffraction patterns in the Ni-rich side of an Al-Co-Ni decagonal phase. The purpose of the present work is to study stable regions of those quasicrystals and their structural changes by heat-treatment.
The so-called Ni-rich basic decagonal quasicrystal in an Al₇₂Ni₂₀Co₈ alloy is stable at 900^oC and undergoes a structural change to a different quasicrystal with superlattice reflections by annealing at 650^oC for 64 hrs. On the other hand, the so-called S1-type decagonal quasicrystal with superlattice reflections in an Al₇₁Ni₁₉Co₁₀ alloy annealed at 900^oC for 48 hrs changes to a basic quasicrystal without any superlattice reflections at 1150^oC, and to the type-I quasicrystal with different-typed superlattice reflections by annealing at 650^oC for 64 hrs.
In this paper, quasiperiodic arrangements of atom clusters in the above structural changes will be discussed by high-resolution transmission electron microscopy (HRTEM) and high-angle annular detector dark-field transmission electron microscopy (HAADF-STEM) observations of Al-Co-Ni alloys annealed at various temperatures.
¹Corresponding author:ksaito@ipc.akita-u.ac.jp

86. ALCHEMI studies on Al-Ni-Co decagonal quasicrystals
Koh Saitoh(a), Michiyoshi Tanaka(a) and An Pang Tsai(b)
(a) Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai 980-8577, Japan
(b) National Institute for Materials Science, 1-2-1, Sengen, Tsukuba 305-0047, Japan

Al-Ni-Co alloy forms decagonal quasicrystals with various superlattice orders as the composition and temperature are changed. The superlattice ordered phases always have a very weak order of a 0.8nm periodicity along the decagonal axis, whereas decagonal Al72Ni20Co8, which shows only fundamental reflections, has a 0.4nm periodicity. It had been considered that the 0.8nm periodicity is attributed to a chemical order between Ni and Co, though no experimental confirmation had been made. We first applied ALCHEMI (atom location by channelling enhanced microanalysis) technique on Al72Ni20Co8 and revealed that Ni and Co occupy at a common site in disorder.
In the present study, we have applied the ALCHEMI technique for decagonal Al70Ni18Co12 with a superlattice order to reveal the chemical order of the constituent elements. Channelling patterns, which measure characteristic X-ray emissions as a function of the incident direction of the electron beam, were taken at incidences perpendicular and parallel to the decagonal zone axis. The ratio patterns between the constituent elements clearly show that Al occupies at a definite site different from the transition metals and that the transition metals occupy at common site in disorder. Therefore, it has been found that the superlattice order is not attributed with a chemical order but with a topological order. Furthermore, the chemical order in a decagonal quasicrystal of Al70Ni15Fe15, which exhibits weak spots instead of the diffuse streaks, has also been investigated by ALCHEMI.

87. Microstructural Studies on Zr_69.5Cu₁₂Ni₁₁Al_7.5
R. T. Savalia, G. K. Dey, P. Mukhopadhyay and S. Banerjee
Materials Science Division, Bhabha Atomic Research Centre, Trombay Mumbai 400 085, India

Keywords:High resolution electron microscopy, Glass formation
A large number of alloy systems have now been identified where the quasicrystalline phase can be obtained by crystallization of an amorphous phase. In this study microstructural examination of one such alloy has been carried out. This alloy is well known for its quasicrystal formation tendency after rapid solidification and crystallization and has also received considerable attention by way of studies pertaining to hydrogen storage.
In this study the microstructure of this alloy has been examined after different solidification and heat treatment conditions. The as solidified microstructure has been examined in the arc melted button as well as in the melt spun ribbon. The arc-melted button showed a very fine dendritic microstructure. In addition to the dendrites it has also been possible to see the presence of an amorphous phase in the arc melted buttons, an observation which suggests that glass formation does not require very high cooling rates in this alloy. Electron diffraction has indicated that the crystalline phases having the dentritic morphology were isostrucural with Zr₂Ni and Zr₂Cu. The nature of the interfaces between the crystalline phases and the crystalline and the amorphous region has been examined in detail using high resolution electron microscopy (HREM). Though electron diffraction indicated that the melt spun structure was fully amorphous HREM has indicated the presence of a few quenched in nuclei in the amorphous matrix.
The microstructure developed after crystallization of the arc-melted ingot as well as of the melt spun ribbons has been examined. Crystallization has been carried out at 633 K and 673 K. The nature of the phases forming after crystallization of the amorphous phase has been compared with those forming form the liquid during solidification. The interfaces present in the crystallized microstructure have also been examined and compared with those forming during solidification. Particular emphasis has been given to the study of the interface between the quasicrystalline and the crystalline phases.

88. A Comparative Study of the Atomic Dynamics of Decagonal and Icosahedral AlPdMn
M. Scheffer and J.-B. Suck
Technical University Chemnitz, Institute of Physics, Materials Research and Liquids, D-09107 Chemnitz, Germany

Keywords:neutron scattering, dynamic properties, decagonal and icosahedral AlPdMn
The generalized vibrational density of states (GVDOS) of decagonal Al69.8Pd12.1Mn18.1 has been investigated by inelastic neutron scattering at the ILL in Grenoble. The data are compared to the GVDOS of the icosahedral phase Al71Pd19Mn10 and to the crystalline phase Al74Pd22Mn4 ($\xi$'). Whereas the contents of Al of these phases are nearly the same, the dynamic properties show remarkable differences. The two characteristic maxima in the GVDOS, which can be found for the icosahedral and for the structurally related crystalline phase $\xi$', were not observed in the data of the decagonal phase. This indicates a significant difference in the local atomic structure of the decagonal and the icosahedral phase.

89. Inelastic Neutron Scattering Study of the Dynamics of Al₉Co₂
M. Scheffer and J.-B. Suck
Technical University Chemnitz, Institute of Physics, Materials Research and Liquids, D-09107 Chemnitz, Germany

Keywords:neutron scattering, dynamic properties, Al--Co--Ni
The generalized vibrational density of states (GVDOS) of polycrystalline Al9Co has been investigated by inelastic neutron scattering at 300 K at the ILL in Grenoble. The data are compared to the GVDOS of the decagonal phase Al71.5Co15.5Ni13 [1] and the crystalline phase Al13Co4.In contrast to the decagonal phase, the GVDOS of Al9Co2 shows a pronounced band structure. This band structure shows the same characteristics as the GVDOS of the phase Al13Co4. At higher energies, the GVDOS of Al9Co2 exceeds the densities of the decagonal and the Al13Co4 phase.
[1] F. Dugain, M. Mihalkovic, J.-B. Suck, Mater. Sci. Eng. A 226/228 (1997) 967

90. Tribological behavior of plasma sprayed Al-Cu-Fe + Sn QC composite coatings
Tianmin SHAO, Xiankun Cao
State Key Lab. of Tribology, Tsinghua University Beijing P.R.China
Eric Fleury
Center for Non Crystalline Materials, Yonsei University, Seoul, Korea

Key words:quasicrystal, plasma sprayed composite coating, tribological behavior.
Quasicrystalline (QC) materials have a combination of many excellent properties, however, their industrial applications are limited due to the low fracture toughness in the range of temperature up to 0.7Tm. The lack of toughness is considered as one of the primary factor for the poor wear properties of QC coatings at ambient temperature. To overcome the brittleness of quasicrystals, production of QC-based composite coatings with the incorporation of high toughness materials was first considered by Sordelet et al. [Mat. Sci. Eng., A255 (1998) 54]. These authors showed that the addition of 1 vol.% of FeAl enabled a significant improvement of the wear properties of Al-Cu-Fe plasma sprayed coatings. This result was somewhat surprising since the properties of brittle materials, such as glasses and ceramics, are usually improved with the addition of volume fraction of ductile phase varying between 10 to 30 vol.%. The improvement of the wear properties with the addition of only 1 vol.% of ductile phase was explained by the large area covered by the FeAl splats within the plane of the coating. However, since the FeAl phase exhibited a better wear resistance than QC phase, the improvement of the wear properties did not result directly from the improvement of the fracture toughness of the coatings. In this paper, we intend to present results on the effect of a ductile phase on the tribological properties of Al-Cu-Fe-based composite coatings. Sn was chosen as the soft phase since it is not miscible with Al, and composite powders with different volume fraction of Sn from 0 to 30% have firstly been prepared by gas atomization. The powder size of -200+400 mesh was selected for the deposition of the quasicrystalline-based composite powders onto medium carbon steel substrates by air plasma spray. The friction and wear behavior were performed with a ball on disk tester under reciprocating motion. Different test conditions were investigated in the aim of studying the load bearing capacities of the coatings and the dependence of the friction and wear with the sliding velocity. The microstructures of the QC composite powders and of the coatings before and after wear test were studied by means of X-ray diffraction analysis and scanning electron microscope. The effect of the Sn addition on the tribological performances of the coatings is discussed in term of microhardness, fracture toughness and phase distribution.

91. A LOCAL APPROACH OF MAGNETISM IN ICOSAHEDRAL Al-Pd-Mn PHASES THROUGH NUCLEAR MAGNETIC RESONANCE STUDIES
V. SIMONET
Laboratoire Louis Neel/CNRS, BP 166, 38042 Grenoble Cedex, France
F. HIPPERT
LMGP/ENSPG, Domaine Universitaire, BP46, 38402 Saint Martin d'Heres Cedex, France
C. BERGER
LEPES/CNRS, BP 166, 38042 Grenoble Cedex, France
Y. CALVAYRAC
CECM/CNRS, 15 Rue G. Urbain, 94407 Vitry sur Seine, France

Keywords:Structurally complex alloy phases, intermetallics quasicrystal approximant

Binary, ternary and higher metallic alloys can form crystal structures based on giant unit cells containing hundreds, up to more than a thousand atoms. Giant-unit cell intermetallics were studied quite early, Pauling's first work dates from the twenties of the last century. Nevertheless to date only very little is known on their physical properties. The electronic and steric reasons which force an atomic system into such structures are essentially unknown, and the mechanisms and kinetics of the diffusion processes governing atomic ordering and crystal growth are not understood.
The giant unit cells have a complex substructure based on polyhedral atom arrangements or clusters which, partially overlapping or linked by bridging elements, are making up the cells. Such clusters are, e.g., the 13 atom icosahedron, the 17 atom Friauf polyhedron, the 54 atom Mackay-type and the 105 atom Bergman cluster. In the beta-AlMg phase (Samson, 1965) the 23 crystallographically different atoms produce 41 different polyhedra. Particularly frequent are coordination icosahedra. In b-AlMg there are 672 icosahedra in the unit cell which in total contains 1168 atoms. Additional complexity is introduced by partial site occupation and chemical disorder. It is suggested to call these materials "structurally complex alloy phases (SCAP)". Many of the high-order quasicrystal approximants belong to this group of materials. However, the approximants do only represent a small subgroup.
It is particularly interesting that the cluster substructure defines a physical length scale which is substantially smaller than the unit cell dimension. This gives rise, in the electronic density of states, to a pseudo-gap and to novel deformation mechanisms based on a new kind of defect, metadislocations.
In the past studies on structurally complex alloy phases were hampered by the lack of suitable large-grain or single crystalline materials. Due to recent progress in crystal growth of ternary alloys the situation is about to change. This progress is largely due to the particular efforts dedicated to the growth of quasicrystals. Actually many of the tools developed for quasicrystal research and much of what has been learned in 20 years on these materials can help to understand the structurally complex alloy phases. This opens up new possibilities for research on this largely unknown class of materials.

115. THE STRUCTURE OF QUASICRYSTALLINE Al-Cu-Fe COATINGS, PRODUCED BY EBPVD
A. I. Ustinov(1,2) , B. A. Movchan(1), and S. S. Polischuk(2)
(1) International Center of Electron Beam Technologies of E. O. Paton Electric Welding Institute, Kyiv 03150, Ukraine
(2) G.V. Kurdumov Institute for Metal Physics, Kyiv 03142, Ukraine

Keywords:Al-Cu-Fe; Quasicrystal; EBPVD; Texture
The practical applicability of quasicrystalline coatings underlies the interest to studying their structure and properties. Plasma spraying has become widely accepted now to produce coatings with a quasicrystalline structure. However, several studies report a low quality of the coatings produced by this process, because of high porosity and the presence of oxides. In order to form thick quasicrystalline coatings with a perfect microstructure, we developed a one-stage technology, based on high-rate electron beam evaporation of an ingot of the specified composition. It was established, that at substrate temperature above a certain critical temperature the EBPVD method can produce thick (up to 100 mm) Al-Cu-Fe coatings with a quasicrystalline structure, formed directly by vapour condensation on the substrate.
X-ray diffraction analysis of the coatings formed at vapour condensation on stainless steel substrates at the temperature of 400-800 C, showed that their phase composition changes essentially, when the substrate temperature rises above 520 C. The coating structure is crystalline below the above-mentioned temperature, and quasicrystalline above it. Coating microhardness remained constant across the thickness and was 8.5 to 9.5 GPa.
Analysis of the studied coating microstructure by SEM indicates that the all coatings are characterized by the presence predominantly of two phase, namely quasicrystalline and cubic. X-ray analysis of the structure of coatings, produced under various conditions, demonstrated, that a ratio between the peak intensity of quasicrystalline phase can be different. The study of the texture of both icosahedral and cubic phases by a texture diffractometer indicate that the distribution of pole density is non-uniform for the all condensates. Axial textures of both icosahedral and B2-cubic phase were observed. By the nature of their distribution, the studied specimens can be divided into three groups: (1) the direction of axial texture coincides with a 2-fold axis of the icosahedral structure , while crystalline phase (B2) have <111> axial texture; (2) two-component axial texture of I-phase + and <111> or <113> texture of B2 phase; (3) weak texture of both icosahedral and cubic phases.
Our results and their analysis suggest that the axial texture of the quasicrystalline phase is the consequence of nucleating of grains of the icosahedral phase on the crystalline grains, being oriented in keeping with the known orientation relations between these phases. The differences between the obtained orientations can be associated with the presence of additional crystalline phases (for instance, monoclinic) in some cases, as well as with the kinetic factors during deposition.

116. Electronic conductivity of quasicrystals at low temperatures in the framework of fractional Fermi surface model
Yu.Kh.Vekilov and E.I.Isaev
Theoretical Physics Department
Moscow State Institute of Steel and Alloys
4,Leninskii prospect,Moskow 119991,Russia

Experiments show that at low temperatures the perfect quasicrystal (i- Al-Pd-Re) exists at the ``critical'' state of the metal-insulator transition [1,2]. The power law temperature dependence (sigma= T<sup>{2alpha/3}</sup>) is obtained on ``critical'' wave functions (Psi= r^{-alpha}) for variable range hopping conductivity using the fractional Fermi surface model [3,4].The Mott law (sigma =sigma₀ exp{[-(T₀/T)^{1/4}]} is found considering the electron localization in the momentum space. Then the ``resonances'' (and resonances of resonences) are appeared under condition |U_{g-g'}| > |E_g - E_{g'}|, where U_{g-g'} is the Fourier transform of lattice potential, and g, g' are reciprocal vectors, and the electronic states are delocalized in the momentum space. As a consequence, the exponentially decaying states appear which give the Mott law in the insulating state.
1. J.Delahaye, and C.Berger, Phys.Rev. B64, 094203 (2001)
2. V.Srinivas, and M.Rodmar, R.Konig, S.J.Poon, O.Rapp, Phys Rev.,B65, 094206 (2002).
3. S.E.Burkov, A.A.Varlamov, D.V.Livanov, Phys.Rev., B53, 11504 (1996)
4. Yu.Kh.Vekilov, E.I.Isaev, D.V.Livanov, JETP, 94, 172 (2002).

117.Interacting fermions in one-dimensional quasiperiodic systems
J. Vidal(a), D. Mouhanna(b) and T. Giamarchi(c)
(a)Groupe de Physique des Solides, CNRS UMR 7588, Universitat, Paris 6 et 7,2, place Jussieu, 75251 Paris Cedex 05 France
(b)Laboratoire de Physique Thorique et Hautes Energies, CNRS UMR 7589, Universitat Paris 6 et 7, 4, place Jussieu, 75252 Paris Cedex 05 France
(c)Laboratoire de Physique des Solides, CNRS UMR 8502, Universitat, Paris-Sud,Batiment 510, 91405 Orsay, France

In this lecture, we discuss the competition between a quasiperiodic potential and the interactions in one-dimensional system. This field has been recently investigated by different methods (bosonization, exact diagonalizations, density matrix renormalization group) and has revealed very interesting features among which an unusual type of metal-insulator transition. The position of the Fermi level in the spectrum completely determines the value of the critical interaction. Using a perturbative approach based on the renormalization group, we show that for particular filling factor, the smallest attractive interaction between particles can even turn the system into a metallic phase whereas it is always insulating in the noninteracting case.

118. PATH RENORMALIZATION OF 1--D APERIODIC CHAINS
Dieter Walther
Institute of Condensed Matter (TKM), University Karlsruhe, D-76128 Karlsruhe,Germany

Keywords:Real-space renormalization, 1-D D0L words, electronic properties
Our concept of Path Renormalization introduced in [1], based upon a real-space rescaling/renormalization procedure (via Feshbach--Operator) for the one particle Green's function of tight-binding like models, is extended to general 1--D D0L words on finite alphabets. Roughly speaking D0L words are words upon an alphabet generated by substitutions. We present the general approach which yields an algorithm determining the correlation between the matrix elements of the one-particle Green's function G{\mu \nu} and a possible successions of given elementary rescaling/ renormalization transformations (RTs) to calculate Green's function. Along the way one recovers nice connections between symbolic dynamics, real space renormalization and crossed produkts of the corresponding C*-algebras [3]. Applications may be found on charakterizing the dynamical/ electonic spectrum (in the spirit of [3,4]) and the calculations of the multifractal alpha)-spectrum in the spirit of [5] now for all D0L words. Nummerical calculations of the (local) densities of states (LDOS/DOS) will be presented.
[1] D. Walther & R v. Baltz, PRB 55, 8852 (1997)
[2] J. Bellissard et. al., in "Directions in Mathematical Quasicrystals", M. B. Baake & R. V. Moody eds. AMS (2000)
[3] J A G Roberts, Physica A228, 295 (1996)
[4] D. Damanik, J. Math. Anal. Appl. 249, 393 (2000)
[5] M. Holzer, PRB 38, 5756 (1988)

119. AC CONDUCTANCE FOR FIBONACCI CHAINS
DIETER WALTHER and RALPH V. BALTZ

Keywords:AC conductance, Fibonacci Chain
We present a real-space renormalization procedure for calculating the AC conductance (Kubo's formula) of periodic approximants of Fibonacci chains [1]. The method is based on the calculation of the 2 times 2 transfer matrix and a new 5 times 5 matrix, both reflecting the underlying selfsimilar structure of the Fibonacci chain. This property allows for application of a renormalization approach, in the spirit of e.g. [2] and many others, done for the 2 times 2 transfer matrix.
[1] D. Walther & R v. Baltz, J. Low Temp. Phys. 126, 1211 (2002)
[2] M. Kohmoto, PRB 34, 5043 (1986)

120. Tile Hamiltonians for Decagonal Quasicrystals
M. Widom, I. Al-Lehyani, C.L. Henley, M. Mihalkovic and S. Naidu
Carnegie Mellon University, Department of Physics, Pittsburgh PA 15213 USA

A tile Hamiltonian (TH) replaces the actual atomic interactions in a quasicrystal with effective interactions between and within tiles. We studied AlNiCo and AlCoCu decagonal quasicrystals described as ideally-decorated Hexagon-Boat-Star (HBS) tiles using ab-initio methods. The dominant term in the TH counts the number of H, B and S tiles. Phason flips that replace an HS pair with a BB pair lower the energy. This is the main rule governing AlNiCo configurations. The edge orientation in AlCoCu is due to Co/Cu chemical ordering. Tile edges meet in vertices with 72 or 144 degree angles. We find strong interactions between edge orientations at 72 degree vertices that force a type of matching rule. Simulations using these tile hamiltonians will be discussed.

121. Two-dimensional quasicrystals and their unit cells
Janusz Wolny and Bart³omiej Kozakowski
Faculty of Physics and Nuclear Techniques, University of Mining and Metallurgy,al. Mickiewicza 30, 30-059 Kraków, Poland

Keywords:structure of quasicrystals; Penrose tiling; Average unit cell.
In this paper average unit cell for a quasicrystal is constructed by statistical approach. For the Penrose tiling it was already shown that such a unit cell is fully equivalent to oblique projection of the atomic surface onto physical space. The obtained statistical distributions can be easily extended to imperfect structures by using Gaussian approximation. This leads to simple analytical expressions for diffraction intensities, which can be very useful in the structure refinement.
Diffraction analysis of Penrose tiling (and also other quasicrystals) can be successfully performed in physical space using the statistical approach. Fourier transform of the probability densities of the average unit cell leads to the envelope functions, which fully describe the diffraction intensities of the main reflections and their satellites. For ideal Penrose tiling this approach is equivalent to the higher-dimensional analysis. The probability distribution in the average unit cell coincides with the pentagons obtained during the oblique projection of the atomic surface into physical space. In this sense the atomic surface in perp-space is just the average unit cell risen up to higher-dimension. However, all the calculations can be done in physical space only and any modifications towards other structures, including defected structures, are straightforward and can be easily accomplished. To reduce the number of parameters describing the probability distributions, for example the simple Gaussian distributions can be used. As it is shown, this approximation quite well describes the diffraction pattern of Penrose tiling also. Gaussian approximation is very useful for defected or random tilings, however, for perfect Penrose tiling much better results can be obtained for flat distributions of elliptical shape. The greatest advantage of the presented approximation is the analytical formula written in physical space and describing in a very simple way the envelope function (i.e. the line which can be fitted directly to the experimental diffraction pattern) with only few parameters, namely the widths of the gaussian distributions. By fitting these widths of the statistical distributions one obtains the average unit cell directly from the diffraction pattern.

122. Synthesis of nano-quasicrystalline Al₇₀Ni₁₅Co₁₅ decagonal phase through high energy ball milling
T.P.Yadav(a), N.K.Mukhopadhyay(b), O.N.Srivastava(a)
(a)Department of Physics,Banaras Hindu University,Varanasi-221005
(b)Department of Metallurgical Engineering, Institute of Technology, Banaras Hindu University, Varanasi-221005, India

Al-Ni-Co system exhibits the existence of a stable decagonal(D) phase with various degree of order in periodic and quasiperiodic planes. Now it is a routine technique to grow micron to cm size rods of the decagonal phase slow cooling technique. There are attempts to develop nano-scale microstructure by various non-equilibrium processing techniques. The aim of the present investigation is to employ mechanical milling (MM) technique for the synthesis of the nano-D phase. The alloy ingot was prepared by melting the constituent pure metals in the induction furnace, and then crushed to around 200 mesh size, as a starting material in the attritor. The milling was performed at 400rpm for 5h, 10h, 20h and 40h under hexane medium with ball: charge ratio as 20:1.
The alloy ingot was found to consist of predominantly the mm-size D-phase along with a minor phase, Al₃Ni.During the course of milling, the disordering was noticed from the broadening of the peaks and lowering of the peak-height in the x-ray diffraction patterns. However, no new phase was found to appear unlike the case of Al-Cu-Co and Al-Fe-Cu system where transformation to B2 phase was observed.Milled powder after 10h showed the diffraction peaks confirming the evolution of nano-D phase. Using the Scherrer's formula, the particle size was estimated to be around 10-15nm.The size aspects and the phase constituents were further confirmed by the transmission electron microscopic investigation.The stability of the nano-D phase in the milled powder was investigated under various annealing treatments.The composition of the as-cast ingot and the milled powder was analyzed by EDX.The micro-mechanisms of evolution and stability of nano-D phase under mechanical milling and subsequent annealing will be discussed.

123. Effect of Cu Substitution in AlCoNi Decagonal System
T.P.Yadav, R.S.Tiwari, O.N.Srivastava
Department of Physics,Banaras Hindu University,Varanasi-221005
Institute of Technology,Banaras Hindu University, Varanasi-221005, India

Keywords:Decagonal,quasicrystal

A stable decagonal phase has been observed in both the as-cast and rapid solidified AlCoNi and AlCoCu alloys which have been found to form in each composition range of 15 to 20 at% Co and 10 to 15 at% Ni or 15 to 20 at%Cu. In the present investigation copper has been substituted in the place of Co and Ni in Al₇₀Co₁₅Ni₁₅. Thus phase corresponding to Al₇₀Co_15-xCu_xNi₁₅ and Al₇₀Co₁₅Ni_15-xCu_x have been investigated. It is found that when copper concentration reaches to a value of 5 atomic percent leading to the phase corresponding to Al₇₀Co₁₀Cu₅Ni₁₅ and Al₇₀Co₁₅Ni₁₀Cu₅ the disorder marker i.e. the streaking of î î î î î 3 rows becomes predominant. In the case of Al₇₀Co_15-xCu_xNi₁₅ when the whole of Co is replaced by Cu resulting in the phase Al₇₀Cu₁₅Ni₁₅, the decagonal phase disappears and the only phase observed is the vacancy ordered phase. On other hand in Al₇₀Co₁₅Ni_15-xCu_x, when Cu concentration reaches to a value of 10 atomic percent and the corresponding composition becomes Al₇₀Co₁₅Cu₁₀Ni₅, the decagonal and crystalline phases are founded to be present.The details of the mechanism of this substitution and relevant aspect will be described and presented.

124. Magnetic and electrical properties of Cu-Ga-Mg-Sc icosahedral quasicrystals
Hidetoshi Yamada(a), Senni Motomura(a), Ryo Maezawa(b), Hiroshi Nakano(c), Tsutomu Ishimasa(b) and Susumu Matsuo(d)
(a)Graduate School of Human Informatics, Nagoya University Furo-cho, Chikusa-ku, Nagoya, 464-8601, Japan
(b)Graduate School of Engineering, Hokkaido University Kita 13, Nishi 8, Kita-ku, Sapporo, 060-8628, Japan
(c)Center for Multimedia and Information Technologies, Kumamoto University, Kumamoto 860-8555, Japan
(d)School of Infomatics and Science, Nagoya University Furo-cho, Chikusa-ku, Nagoya, 464-8601, Japan

Keywords:magnetic susceptibility, conductivity, psuedogap in DOS, Pauli paramagnetism
We measured temperature dependence of the magnetic susceptibility of the new Cu-Ga-Mg-Sc icosahedral quasicrystals and Cu-Ga-Sc cubic approximant phase in the range of temperature T(2K-300K). In the range of 2K-150K, the susceptibility decreased with the increase in temperature. In the range of 150K-300K, it increased with the rise in temperature. In the range of 50K-300K, for the case of Cu-Ga-Mg-Sc the data could be fitted to the Curie-Weiss law with the additional term proportional to the second power of temperature. On the other hand for the case of Cu-Ga-Sc the data could be fitted to the Curie-Weiss law with the additional terms proportional to the second and fourth power of temperature. Increase tendency of the susceptibility with the rise in temperature was accounted for in terms of the temperature dependence of Pauli paramagnetism, which indicated a psuedogap in the electronic density of states (DOS) near Fermi energy. Below 50K a discrepancy was found between the data and the fitted curve. We measured also temperature dependence of electrical resistivity and magnetoresistance.

125. Structure refinement of i-Al-Pd-Re quasicrystals by synchrotron radiation data.
A. Yamamoto(a), H. Takakura(a), T. Ozeki(b), A. P. Tsai(a) and Y. Ohashi(b)
(a)National Institute for Materials Science
(a)Tokyo Institute of Technology

This paper reports a detailed quasicrystal structure analyzed by an imaging plate Weissenberg camera and synchrotron radiation for the first time. The structure of icosahedral Al-Pd-Re quasicrystals (i-Al-Pd-Re) is determined by using the low-density elimination method (LDEM) and synchrotron radiation data (SPring-8 BL04B2). The electron density in 6-dimensional space given by LDEM showed that it is iso-structural to i-Al-Pd-Mn and its Re sites correspond to Mn sites in the latter. The structure refinement with the same occupation domains as in our i-Al-Pd-Mn analysis[1] gave an R-factor of 0.055 for 560 independent reflections. Some atoms largely shift from their ideal positions. We confirmed that the introduction of atom shifts is essentially important for getting detailed structures or small R-factors. The detailed atom positions are slightly different from those of i-Al-Pd-Mn.
[1] A. Yamamoto, H. Takakura and A. P. Tsai, J. Alloys and Comp. in press.

126. Hydrogen Induced Transformations in Zr-Cu-Ni-Al Quasicrystals
Daniela Zander(a), Varsha Khare(a,b), Uwe Köster(a)
(a)Dept. Chem. Eng., University of Dortmund, D-44221 Dortmund, Germany
(b)Centre d'Ingénierie des Matériaux, Ecole des Mines de Nancy, F-54042 Nancy, France

Keywords:Zr-Cu-Ni-Al quasicrystal, hydrogenation, amorphization
Zr-based quasicrystals can store hydrogen up to a content close to the highest value known for crystalline materials. The high number of potential interstitial sites for hydrogen and the favorable hydrogen-metal chemistry make quasicrystalline alloys candidates for hydrogen storage applications. The objective of this paper is to present our recent results on the effect of hydrogen on the stability of Zr_69.5Cu₁₂Ni₁₁Al_7.5 quasicrystals.
Quasicrystals are formed during thermal annealing of melt-spun glassy precursor Zr-Cu-Ni-Al ribbons. Hydrogenation was performed electrochemically in a 2:1 glycerin-phosphoric acid electrolyte. The microstructure of Zr-Cu-Ni-Al quasicrystals was investigated by X-ray diffraction and TEM. The icosahedral phase in Zr_69.5Cu₁₂Ni₁₁A l_7.5 was shown to absorb hydrogen up to H/M = 2.0. Hydrogenation leads to an increase of the (quasi-)lattice constant up to about 8% and microstructural changes as indicated by the weakening of the contrast of the quasicrystals in TEM as well as a disappearance of the weak diffraction spots in the corresponding diffraction pattern. A more detailed investigation reveals the formation of approximants at hydrogen contents above H/M = 0.4 and the variation in the order of approximants from lower to higher order with increasing amount of hydrogen. In addition, amorphization was observed starting with nucleation and growth of amorphous hydrides at the interface between quasicrystals and amorphous matrix. The reason for the amorphisation reaction might be the change in the ratio e/a and/or the increase of the quasilattice parameter, similar to the amorphisation in Zr₃Al due to a lattice expansion above a critical value.
Desorption at lower temperatures is hindered by the formation of thin ZrO₂ layers. Pd coating can be one way to hinder the formation of such oxide layers which changes not only the hydrogen absorption, but also the hydrogen desorption in quasicrystalline Zr_69.5Cu₁₂Ni₁₁A l_7.5 considerably. Only partial desorption of hydrogen was observed to occur prior to the decomposition of the quasicrystalline phase. Hydrogenation up to about H/M =0.4, probably below the content necessary for the formation of approximants,seems to be fully reversible.

127. Stability and phase boundaries of icosahedral phase and f-Al₁₀Cu₁₀Fe₁ phase in the Al-Cu-Fe system
Liming Zhang,Reinhard Lueck
Max-Planck-Institut fuer Metallforschung,
Heisenbergstr. 3, D-70569, Stuttgart, Germany

Keywords:Stability, quasicrystal,f-Al₁₀Cu₁₀Fe₁ , Al-Cu-Fe

Phase equilibria of the ternary Al-Cu-Fe system were investigated in the region of the icosahedral quasicrystal phase. Differential thermal analysis, magnetothermal analysis, light microscopy and scanning electron microscopy with energy dispersive spectroscopy were applied. The liquidus projection surface is constructed; phase equilibria are described precisely as isopleths and isothermal sections. The thermal stabilities of icosahedral and f-Al₁₀Cu₁₀Fe₁ phases are determined from heating experiments. Phase boundaries of both icosahedral and f phases are especially considered. The Scheil reaction scheme including icosahedral and f phases is reported. A shrinkage of the phase field with decreasing temperature gives indication of the compositional influence on the stability of icosahedral phase. It is re-confirmed that the f-Al₁₀Cu₁₀Fe₁ phase exists in Al-Cu-Fe system; it forms from b-Al(Cu,Fe) phase through a solid-state polymorphous reaction at 650 °C, and it is stable below the formation temperature. On the other hand, an ordered b phase with B2 structure is found for the same composition in as-cast and moderately cooled alloys, this metastability is characterized by a suppressed formation of the f-phase during cooling.

128. Limited conductivity in an octagonal quasicrystal
Eeuwe Sieds Zijlstra
Max-Planck-Institut fuer Festkoerperforschung,Heisenbergstrasse 1, 70569,Germany

Keywords:limited conductivity, octagonal tiling
Conductivity of an s-band model on the octagonal tiling is studied. Using perturbation theory it is shown that there is only one channel available for electronic transport, when the kinetic term in the Hamiltonian is small. This feature is independent of the size of the approximant and reveals a microscopic mechanism that is capable of severely limiting conduction processes in a quasicrystal. Numerical evidence indicates that the same result is valid even in case of realistic kinetic energies at some values of the Fermi energy.

129. Role of planar defects and their energies in periodic to quasiperiodic trans formations - A Monte Carlo Simulation
U.D.Kulkarni
Materials Science Division, Bhabha Atom ic Research Centre,Trombay, Mumbai 400 085,India

The method of projection from higher dimensional lattices is a convenient means to establish the lattice correspondence between various quasiperiodic structures, on the one hand, and some simple wellknown periodic structures known as their rational approximants, on the other. A quasiperiodic structure and its approximants are all made up of identical constituent tiles and differ only in the nature of the arrangements of the tiles present within them. In quite a few systens, the transformation from a simple periodic structure to its quasiperiodic counterpart has been to be continuous in nature and has been found to be mediated by long period modulated structures, which comprise regions of the simple periodic structure separated by periodically arranged faults. Occurrence of faults would thus appear to be the initial stage of a continuous periodic to quasiperiodic (P to QP) traqnsformation. Energy of such faults is therefore expected to play an important role in bringing about a P to QP transition. The method of projection has been found to be remarkably successful in both explaining the diffraction effects associated with a P to QP transition and in predicting the atomic structure of the faults encountered in these transitions. A special example of quasiperiodicity is a quasiperiodic superlattice (QPSL) structure, which has an underlying periodic lattice and shows a quasiperiodic chemical order in the disorered underlying lattice. A QPSL structure, consisting of tiles of three different types, can be thought of as an intermediate state of the Al5Ti3 to Al11Ti7 superlattice transition observed in Al-rich TiAl intermetallics. Either of these periodic superstructures of fcc can transform continuously into the QPSL by suitable changes in alloy chemistry. The early stages of such transformations are marked by the occurrence of antiphase boundaries (APBs, also known as order faults) in these periodic structures. In the present work, involving Monte Carlo simulation of ordering, it has been shown that the entire transformation, with all its intermediate states can be brought about by changing the energy of such APBs in a continuous manner. The results of the simulation throw light on the atomic structures of the imperfectly ordered intermediate states of the P to QP transition, which show various patterns of diffuse intensity in the selected area electron diffraction patterns.

130.Epitaxy on quasicrystalline surfaces
Masahiko Shimoda

Keywords: surface,epitaxy,X-ray photoelectron spectroscopy, rheed
It is well known that quasicrystals exhibit several unusual properties such as low electric/heat conductivity, large hardness and negative temperature coefficient of the electric resistivity. If quasicrystalline phase formed in various materials such as pure metals, oxides and semiconductors, several novel phenomena or properties would be expected. Until now, however, the quasicrystalline phase is obtained only in limited combinations of metal elements under restricted conditions.
We propose that epitaxy on quasicrystalline surfaces is an alternative way to produce quasicrystalline structure. So far, we have found that Au depositions onto a quasiperiodic surface could form an epitaxial layer of Au-Al alloy. We have also found that In surfactant promotes the formation of the Au-Al alloy film, suggesting that the surface energy is one of the important factors for the epitaxial film growth on the quasicrystalline surface.
On the basis of these findings, we are performing systematic studies on depositions of various metal elements. In this report, we will present the results on the elements such as Sn, In, Pb and Bi, which has smaller surface energy than Au.

131. Vacancy Ordered Phases in Al-Cu-Ni as Average Lattices
Anandh Subramaniam(a) and S. Ranganathan(b)
(a)Regional Research Laboratory, Bhopal-462026, India
(b)Department of Metallurgy, Indian Institute of Science, Bangalore-560012, India

Keywords:Vacancy Ordered Phases, Quasiperiodicity, Average Lattices, Projection
Vacancy ordered phases (VOP) in the Al-Cu-Ni system have an arrangement of vacant and filled sites in the truncated Fibonacci sequence, along the [111] direction. In the absence of a geometrically enforced irrational lengthscale the limiting sequence is not a quasicrystal. The implication of having commensurate lengthscales and quasiperiodicity (QP) in conjunction is studied using the concept of average lattices. Further, these structures are analysed using projection formalism with approximations in both parallel and perpendicular spaces.
(a)Presenting Author:anandh333@rediffmail.com

132. Strctural stability of Al-Co-Cu-Ni decagonal phase
A.K.Pramanick,R. K. Mandal and G. V. S. Sastry
Center of Advanced Study, Department of Metallurgical Engineering. Institute of Technology,Banaras Hindu University, Varanasi-221005, India

Keywords:Decagonal Quasicrystals, Digonal quasicrystals, lowering of symmerty
Structural stability of Al-Co-Cu-Ni decagonal phase has been explored with respect to heat treatment in this study. Decagonal phases are found to from, in alloys of Al-Co-Cu-Ni quaternary system with Al65Co15Cu20 and Al70Co15Ni15 as ternary end members. Characteristic features of aforesaid alloy series are reported earlier [1,2,3]. Both in as-cast and rapidly solidified condition they form decagonal phases. From the knowledge of DTA plots of the alloys and on the basis of literature, two compositions Al68.85Co15Cu6.15Ni10 and Al67Co15Cu8Ni10 were selected for this study. Heat treatment was carried out at 900ºC for 435 hours for as-cast Al68.85Co15Cu6.15Ni10 alloy and at 450ºC for 65 hours for Al67Co15Cu8Ni10 in rapidly solidified condition. Only for the later composition, ion milling was done before their detailed TEM investigations. In the both cases, we observed lowering of symmetry in the 10-f diffraction patterns. Former shows the symmetry of (2/m 2/m 2/m) and later shows symmetry of a digonal (222) quasicrystal. These results will be compared with our observation of digonal quasicrystal in rapidly solidified condition of Al70Co15Cu5Ni10.
1. Pramanick, A. K., Mandal, R.K., and Sastry, G. V. S., Jl. of Material Science and Engineering A, 304-306 (2001) 818-821
2. Pramanick, A. K., Mandal, R.K., and Sastry, G. V. S., Jl. of Materials Science and Engineering A, 294-296 (2000) 173-176
3. Pramanick, A. K., Mandal, R.K., and Sastry, G. V. S., Jl. of Ferroelectrics, 250 (2001) 273-279

133. Structure analysis of i-CdYb quasicrystals
H. Takakura(1), M. de Boissieu(2), A. Yamamoto(1) and A. P. Tsai(3)
(1)Advanced Materials Laboratory, NIMS, 1-1 Namiki, Tsukuba 305-0044 Japan
(2)LTPCM, UMR CNRS 5614, ENSEEG, BP 75 38402 St Martin d'Heres Cedex France
(3)Materials Engineering Laboratory, NIMS, 1-2-1, Sengen, Tsukuba 305-0047,Japan

Keywords:structure analysis, synchrotron radiation, i-Cd-Yb
Structure of i-Cd-Yb quasicrystals has been analyzed by using single crystal synchrotron radiation data. About 5500 independent reflections were observed at ESRF-D2AM beam-line with incident energy 20.6keV (0.60187¢ò). For searching a starting model for the structure analysis, the low-density elimination method (LDEM) was applied to limited 1000 independent reflections. A plausible six-dimensional electron density of i-Cd-Yb showed that there are three independent large occupation domains (ODs) in a six-dimensional primitive unit cell and they are located on vertex, body-center and edge-center positions. It was suggested that the largest OD located on the body-center position contains majority of Yb. According to these results, a structure model of i-Cd-Yb that consists of three largeindependent ODs has been constructed. The ODs are made of small polyhedra (rhombic triacontahedra etc.) having edge length of a/tau^3 as in our structure analysis of i-Al-Pd-Mn quasicrystals. Here, the a is the icosahedral lattice parameter of i-Cd-Yb and the tau is the golden mean. Preliminary refinement for the structure model gave an R-factor of 0.121 for 500 independent reflections with 56 parameters. A successive shell structure of atoms and their chemical ordering in the refined i-Cd-Yb structure is consistent with that seen in Cd6Yb cubic crystal.

134.Z-contrast observation of icosahedral quasicrystals and approximant
Eiji Abe(a,b) S. J. Pennycook(a) and A. P. Tsai(b)
(a) Oak Ridge National Laboratory, Solid State Division, P.O. Box 2008, Oak Ridge, TN37831-6031 USA
(b) National Institute for Materials Science, 1-2-1, Sengen, Tsukuba 305-0047, Japan

Keywords:icosahedral quasicrystal, Z-contrast, atomic cluster, local symmetry
In atomic-resolution transmission electron microscopy of icosahedral quasicrystals, the image contrast reflects the projected 3-dimensional quasiperiodic structure, so that we cannot derive the atomic model directly from the projected images. However, a direct structural observation is still essential even for the icosahedral quasicrystals to converge to a convincing atomic structure. Here we demonstrate that, for the icosahedral Zn6Mg3Ho compound, the observed Z-contrast images are fairly well explained by the Ho atomic arrangement proposed by x-ray diffraction analysis; Ho occupies an even-body-center site of the 3-dimensional Penrose lattice [Takakura et al, Phys. Rev. Lett., 86 (2000) 236]. Consequently, the present direct structural observation strongly supports the validity of the proposed Ho site.
Recently, novel quasicrystalline compounds have been discovered in binary Cd-Yb and Cd-Ca systems. A cubic crystal composed of the icosahedral atomic cluster exists at a very similar composition. Interestingly, the atoms in the 1st shell of the cluster are located at cubic sites, breaking the icosahedral symmetry. These cubic sites are shown to be half-occupied by x-ray diffraction analysis, and hence the stable local configuration of 4 atoms would be not cubic but tetrahedral or some other arrangement. Here we directly observe the icosahedral cluster to see where and how atoms are arranged at the center of the cluster. Preliminary Z-contrast observation of the Cd-Ca cubic crystal suggests that Cd atoms seem not to be at the cubic sites. We will discuss the possible atomic configurations around the center of the cluster.
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135.Synthesis of (Al65Cu20Fe15) 100-xSix Quasicrystals by Mechanical Alloying
B. S. Murty(a), P. Barua(b) and V. Srinivas(b), F. Schurack(c) and J. Eckert(c)
(a)Department of Metallurgical and Materials Engineering,Indian Institute of Technology, Kharagpur-721 302,India
(b)Department ofPhysics and Meteorology, Indian Institute of Technology, Kharagpur-721 302,India
Institut fur Festkorper- und Werkstofforschung Dresden, Institut fur Metallische Werkstoffe, Postfach 27 00 16, D-01171 Dresden, Germany

The alloys in the quasicrystalline (QC) state have attracted considerable interest due to their peculiar properties, which may be related to their unique atomic structure. Although perfect quasicrystals (QCs) present attractive choice in wide area of applications, relatively few investigations have been aimed at identifying the practical methods that can become suitable for the manufacture of commercially viable products. Besides this, other problems such as (i) formation of QC phase in the extremely narrow composition range, (ii) sensitivity of the properties to the compositional changes and (iii) structural disorder and presence of impurity phases, further complicate the processing of the QC materials. Therefore, there is an urgent need to extend the QC formation composition zone with higher stability and negligible impurity phase. Among various QC alloys, Al-Cu-Fe system is of special interest as it can be prepared with a remarkable structural perfection and therefore allows one not only to understand microstructure but also the inherent properties of i-phase. Recently it has been demonstrated through a series of experiments that by mechanical alloying (MA) it is possible to extend the i-phase formation range. It is well known that another parameter, which plays an important role in extending the phase formation range or for amorphous phase formation, is substitutional elements. Substituting the semi-metal elements such as Si, B, and the i-phase formation domain can further be extended.
We have investigated the effect of Si on Al-Cu-Fe quasicrystalline fine powders prepared by MA technique. Icosahedral quasicrystalline phase has been synthesized by MA of (Al65Cu20Fe15)100-xSix (x=0-15) compositions. As prepared and heat treated samples have been characterized by detailed X-ray diffraction and electron microscopic investigation. Present study indicates that MA improves the quasicrystalline phase forming ability (QFA). This range can be further enhanced by addition of Si along with stability of quasicrystalline phase. The quasicrystals observed in the present study are in nanophase. It is quite evident from the present study that one can extend the i-phase formation range to a large extent by following MA route in the (Al-Cu-Fe)-Si system if the e/a ratio is maintained in the range of 1.70-2.32, which is quite large compared to the range obtained through MA and rapid solidification processing routes in Al-Cu-Fe system.

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136.Arctic octahedron in three-dimensional rhombus tilings and related integer solid partitions
Nicolas Destainville,Mike Widom, Remy Mosseri, Francis Bailly
Laboratoire de Physique Quantique (IRSAMC), Universite Paul Sabatier, 118 route de Narbonne,France

Keywords:Random tilings; Integer partitions;Configurational entropy; Boundary effects; Transition matrix Monte Carlo algorithms
Three-dimensional integer partitions provide a convenient representation of codimension-one three-dimensional random rhombus tilings. Calculating the entropy for such a model is a notoriously difficult problem. We apply transition matrix Monte Carlo simulations to evaluate their entropy with high precision. We consider both free- and fixed-boundary tilings. The latter fill a rhombic dodecahedron. Our results suggest that the ratio of free- and fixed-boundary entropies is sigma_{free}/\sigma_{fixed}=3/2, and can be interpreted as the ratio of the volumes of two simple, nested, polyhedra. This finding supports a conjecture by Linde, Moore and Nordahl concerning the ``arctic octahedron phenomenon'' in three-dimensional random tilings : at the large-size limit, the tilings are strain-free and homogeneous inside a regular octahedron embeded in the rhombic dodecahedron whereas they are frozen outside this octahedron. This phenomenon is reminiscent of the ``arctic circle phenomenon'' in 2 dimensions and is due to the macroscopic effect of boundaries on tilings.

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137.Crystal Structure of a 2/1 Cubic Approximant in the Al-Rh-Si system
K.Sugiyama(a), W.Sun(b) and K.Hiraga(b)
(a)Department of Earth and Planetary Science, The University of Tokyo, Hongo 7-3-1, 113-0033, Japan
(b)Institute for Materials Research, Tohoku University, Katahira 2-1-1, 980-8577, Japan

Keywaords: icosahedral phase, approximant, structure, single crystal X-ray diffraction
The structural information on approximant phases have been frequently used for providing structural models of quasicrystals. The most typical example is the relation between the cubic a-AlMnSi and icosahedral Al-Mn-Si, where a-AlMnSi is considered as a 1/1-approximant produced by a rational cut of a periodic six-dimensional space. A number of structural studies with respect to cubic approximants suggests that 1/1-AlPdMnSi(Pm3, a=1.23nm) and 2/1-AlPdMnSi(Pm3, a=2.02nm) approximants for icosahedral Al-Pd-Mn present an unique atomic cluster with local icosahedral symmetry. Recent discovery for a 2/1 approximant phase(Pm3 a=1.99nm) in the Al-Rh-Si system prompted us to study another example for the icosahedral atomic cluster. The structure of a cubic 2/1-AlRhSi approximant was determined by means of single crystal X-ray diffraction. A structural model with R(F) less than 0.10 clearly revealed an icosahedral atom cluster of about 2nm in diameter. The structural features for the atom cluster in the 2/1-AlRhSi are quite similar to those of the 2/1-AlPdMnSi. The 2/1-AlRhSi approximant can be referred as a second example with the icosahedral atom cluster different from those of Mackay and Bergman.

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138.Quasicrystal Strengthened Magnesium Alloys by Extrusion
Alok Singh, A.P. Tsai and M. Nakamura
National Institute for Materials Science
1-2-1 Sengen, Tsukuba 305-0047, Japan

Keywords:applications, magnesium alloys, mechanical behaviour, nanoparticle, orientation relationship
Icosahedral quasicrystal can exist in equilibrium with magnesium in very dilute magnesium alloys [1]. Recently, this has been used to produce high strength magnesium alloys. A fine microstructure of Mg and icosahedral phase in Mg-Zn-Y alloys obtained by hot rolling showed improved mechanical behaviour over the commercial magnesium alloys [2]. We have produced magnesium Mg-Zn-Y alloys and extruded at 400^oC to achieve a fine microstructure. The microstructure and the mechanical behaviour of these alloys were studied and compared to an AZ6 alloy.
Alloys Mg96.5Zn3Y0.5, Mg95Zn4.2Y0.8, Mg92.5Zn6.4Y1.06, Mg95Zn4.24Y0.76 and AZ6 were prepared by induction melting and extruded at 400^oC with a reduction ratio of 10:1. Observation by optical microscope showed that the microstructure of the extruded alloys was much finer than the as cast alloys. Tensile tests were performed at room temperature, 100^oC, 200^oC and 300^oC. Sections from these specimens were mechanically thinned ion-milled for observation in the transmission electron microscope.
Facetted icosahedral quasicrystalline particles of size of the order of 0.2 Ã occurred in the interdendritic regions while nanometer size (20-50 nm) particles occurred in the grains. They showed a definite orientation relationship with the matrix, with an icosahedral twofold axes parallel to the hexagonal axis, and another twofold axes along the [100]. These particles were facetted on twofold planes which were along the basal plane and {100} planes of the magnesium matrix.
After the extrusion the yield stress (YS) of the alloys increased five times, to about 250 MPa at room temperature (ultimate tensile strength (UTS) about 340 MPa and elongation about 15%). In extruded condition the AZ6 alloy showed a comparable strength. It is also comparable to the strength (YS 220 MPa, UTS 370 MPa) of an alloy of similar composition hot rolling 400^oC , reported by Bae et al. [2]. At higher temperatures, however, the strength fell more rapidly than the AZ alloy. While at 200^oC the YS of Alloy-2 was determined to be about 110 MPa, that of the AZ alloy was about 130 MPa (respective elongations 19% and 28%). Further work is in progress for obtaining higher strengths.
[1] A.P. Tsai, Y. Murakami and A. Niikura, Phil. Mag. A 80 (2000) 1043
[2] D.H. Bae, S.H. Kim, D.H. Kim and W.T. Kim, Acta Mater. 50 (2002) 2343

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139.Thermoelectric Properties of Al-based Icosahedral Quasicrystals and Approximants
Tomohiro Nagata*(a), Kazuhiro Kirihara(b), Atsushi Yamaguchi(a), Kaoru Kimura(c,a)
(a) Department of Materals Science, University of Tokyo, Tokyo 113-8656, Japan
(b) National Institute of Advanced Industrial Science and Technology, Tsukuba 305-8656, Japan
(c) Deparatment of Advanced Materials Science, University of Tokyo, Tokyo 113-0033, Japan

Keywords: AlPdRe, AlPdReRu, Electrical Conductivity, Seebeck Coefficient,Thermal Conductivity
Icosahedral AlPdRe quasicrystals show semiconductorlike electronic properties and low themal conductivity. These non-metallic properties are caused by formation of pseudogap and effect of electron localization, which have a potential of thermoelectric materials. The thermoelectric performance is estimated by the figure of merit, Z=(S^2B)!&&R/B&J where S is Seebeck coefficient, B&R electrical conductivity and B&J thermal conductivity. We present the composition dependence of S and B&R of icosahedral AlPdRe and AlPdReRu quasicrystals. As the concentration of transition metal (either Pd or Re) increases, S rapidly increases. The strong composition dependence is related to the pseudogap structure in the electron density of states at the Fermi energy, and to the variation in bonding nature between Al and transition metal. Glass-like transport behavior in thermal conduction is also observed. The dimensionless thermoelectric figure of merit, ZT, has a maximum value of approximately 0.1 in the temperature range from 600 to 700 K and reveals strong composition dependence. By Ru addition to the AlPdRe quasicrystal, ZT value reaches maximum value at higher temperature.

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140. Atomic and Electronic Structure of ksi'-Al-Pd-Mn Approximant and i-Al-Pd-Mn Quasicrystal Surfaces
D. Naumovic(1), P. Aebi(1), M. Bovet(1), F. Clerc(1), C. Koitzsch(1), L. Schlapbach(1),C. Beeli(2), K. Kunze(3), T. A. Lograsso(4), D. W. Delaney(4), A. R. Ross(4)
(1) Département de Physique, Université de Fribourg, Pérolles, CH-1700 Fribourg, Switzerland
(2)Laboratory of Solid State Physics, ETHZ, Hönggerberg, CH-8093 Zürich, Switzerland
(3)Institute of Geology, ETHZ, Sonneggstrasse 5, CH-8092 Zürich, Switzerland
(4) Ames Laboratory, Iowa State University, Ames, Iowa 50011, USA

Keywords:Photoemission, electronic structure, structure, surface, Al-Pd-Mn,quasicrystal, approximant
An electronic structure study of ksi'-Al-Pd-Mn approximant and icosahedral (i) Al-Pd-Mn quasicrystal [1] surfaces using ultraviolet photoemission spectroscopy (UPS) was performed in combination with an atomic structure survey of the surfaces using X-ray photoelectron diffraction (XPD), low-energy electron diffraction (LEED) and electron backscattering diffraction (EBSD).
In previous structural surface studies [2,3] it has been noticed that different surface terminations are possible depending on the quasicrystal sample preparation: sputtering, heat treatment,... . A combined geometrical and electronic structure study was performed on differently prepared i-Al-Pd-Mn monograin surfaces. Surfaces with drastically different electronic properties, ranging from crystalline to quasicrystalline behaviour, and atomic surface arrangments -disordered or ordered with crystalline or quasicrystalline structures- have been prepared using Ar+ sputtering and subsequent annealing of different faces (cut perpedicularly to 2-,3- and 5-fold symmetric axes) of i-Al-Pd-Mn. For instance, a stable decagonal phase surface was produced on a 5f i-Al-Pd-Mn substrate [3].
Recently pseudo-10f and 2f ksi'-Al-Pd-Mn approximant surfaces have been studied using similar preparation procedures. The XPD pattern of the pseudo-10f surface annealed at 500°C resembles the one obtained from the decagonal quasicrystalline phase. However the XPS composition is different, as well as the shape of density of states close to the Fermi edge. A decrease of the density of states was observed on both approximant surfaces similar as for a quasicrystal, but the Fermi cut-off is clearly sharp. Such surfaces are somehow less metallic than the ones obtained by sputtering either a quasicrystal or an approximant surface. By sputtering approximant surfaces we obtain ordered crystalline surfaces with bcc domains and different orientations, similarly to what was observed on quasicrystals.
[1] Monograin samples have been provided by Ames Laboratory (see coauthors), Y. Calvayrac (CECM-CNRS, Vitry-sur-Seine, France), and Ph. Ebert (Forschungszentrum Juelich, Germany).
[2] D. Naumovic et al., Phys. Rev. B60 (1999) R16330; D. Naumovic et al., Mat. Sci. and Eng.: A 294-296 (2000) 882; and references therein.
[3] D. Naumovic et al., Phys. Rev. Lett. 87 (2001) 195506.

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141. Synthesis and characterization of textured quasicrystalline films in Ti-Zr-Ni system
V. Brien(1), A. Dauscher(2), S. Weber(2), P. Weisbecker(1), F. Machizaud(1)
(1)Laboratoire de Science et Génie des Matériaux et de Métallurgie, UMR 7584, CNRS-INPL-UHP, Parc de Saurupt, ENSMN, 54042 NANCY Cedex, FRANCE
(2)Laboratoire de Physique des Matériaux, UMR 7556, CNRS-INPL-UHP, Parc de Saurupt, ENSMN, 54042 NANCY Cedex, France

Two deposition techniques (thermal evaporation and laser ablation) have been tried and compared in order to find out a technique to prepare Ti41.5Zr41.5Ni17 quasicrystalline films. Indeed, this phase presents faculties of hydrogen storage and requires a film shape to optimize future possible batteries.Thermal deposition conditions'influence has been studied within the 293-593K range for the thermal evaporation technique and within the 293-623 K range for laser ablation. The paper presents the chemical compositions profiles obtained by Secondary Neutral Mass Spectometry and of the thicknesses obtained by profilometry on SNMS craters. It also presents the films structures studied by grazing X-rays diffraction and Transmission Electron Microscopy (imaging and diffraction). Comparison of all these are done. The work allows the identification of a process and of experimental deposition conditions for the synthesis of a thicker film composed of the known icosahedral phase of the Ti-Zr-Ni system. Such a film has been synthetized and 4 circles X-ray diffractometry was used to characterize its structure. The paper also shows the grown film is strongly textured. The grains adopt such a texture that the 5 fold axis of the icosahedral phase is mostly oriented 6° away from the normal of the film.

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142.ENERGY vs ENTROPY STABILISATION OF QUASICRYSTALS
M.Vijayalakshmi
IGCAR, KALPAKKAM-603 102, INDIA

Keywords:stability, entropy, energy
The mechanism of stability of thermodynamically stable quasicrystals continues to remain a debate in the literature of quasicrystals. The ground state structure at T-` 0, and the consequent implication in the arrangement of tilings are related issues which would be resolved when the main question of stabilisation criterion of quasicrystals is unambiguously identified. The energy stabilisation mechanism implied Penrose tiling arrangement of atoms, while the concept of entropic stabilisation of quasicrystals strongly suggested the random tiling arrangement. The newly emerging unifying approach is the 'cluster model', which can explain the existence of energetically stable Penrose tiles and the entropy stabilised random tiles, in a single framework of the model.
The paper discusses the present scenario of the mechanism of stabilisation of quasicrystals in the light of experiments to study the low temperature instability of quasicrystal phase, which is generally one of the key evidences in favour of entropy stabilisation mechanism.

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143. Cluster Disordered Glue Model and the Role of Glue Atoms in Stabilizing the Quasicrystalline Structure
R. Chidambaram, P. Modak, R. S. Rao, and B. K. Godwal
High Pressure Physics Division, Bhabha Atomic Research Centre, Mumbai-400 085, India

Keywords:quasicrystal model, cluster-disorder-glue , quasicrystal-stability
The discovery of quasicrystals led to the observations and interpretations of many of their physical properties, often in the intermediate region between metallic and insulator regimes, sometimes with the introduction of new concepts [1-3]. However, there is still no consensus on the underlying mechanism for the formation of the quasicrystalline state itself, though many models have been introduced. These models range from energetically stable and unique (Penrose tilings)/degenerate (weak matching tilings) to entropically stable (random tilings) hypothesis. With the large amount of data available now, the low energy clusters and entropy emerge as the two dominant factors contributing to the stability of quasicrystalline state. Based on these, we hypothesize a Cluster Disordered Glue Model, according to which the clusters take up near perfect icosahedral symmetry, with their centers nearly in the positions corresponding to the related crystalline phase while maintaining the quasicrystalline rotational symmetry. The glue atoms occupy the space between second nearest neighbour clusters and would become disordered (without moving too far from the positions corresponding to the related crystalline phase), thus increasing the entropic contribution to free energy and also leading to small random displacements of the clusters. The so-called phason disorder, which in reality, is only widening of diffraction peaks can be interpreted in terms of substitutional disorder; there is some evidence that quasicrystals with less substitutional disorder have also lower .phason disorder.. We have carried out first principles electronic structure internal energy calculations in the Al-Mn crystalline systems related to Al-Mn-Si quasicrystal, to show the role of glue atoms in the formation of the pseudogap for stability [4]. The disorder in the glue atom distribution is studied by assuming different co-ordinate positions of the glue atoms while the icosahedral cage has been kept frozen in the cluster calculations by density based ab initio molecular dynamics (MD) simulations. Further MD simulations are being carried out to verify in detail our hypothesis.
References:
1. R. Chidambaram et al., Phys. Rev. B48, 3030 (1993).
2. S. J. Poon, Adv. Phys. 41, 303 (1992).
3. R. S. Rao, B. K. Godwal, S. K. Sikka and R. Chidambaram, Phys. Rev. B50, 15632 (1994).
4. P. Modak, R. S. Rao, B. K. Godwal and R. Chidambaram, Phil. Mag. B80, 1681 (2000).

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144. A Comparative Study of the Atomic Dynamics of Icosahedral and Decagonal ZnMgY
J.- B. Suck*, M. Scheffer*, R.Sterzel**
* Materials Research and Liquids, Institute of Physics, TU-Chemnitz, D-09107 Chemnitz, Germany
** Institute of Physics, J. W. Goethe University, D-60054 Frankfurt/Main, Germany

Keywords:Atomic Dynamics, icosahedral and decagonal ZnMgY, short range order
From the thermodynamically stable quasicrystals there are up to now only two alloy systems, in which icosahedral and decagonal quasicrystals have been found, AlPdMn and ZnMgY/RE. The icosahedral quasicrystals of these two alloy systems belong to two different structural classes, of which the latter belong to the Frank-Kasper type of quasicrystals. We have determined the Generalised Vibrational Density of States (GVDOS) and the total dynamic structure factor of icosahedral and decagonal ZnMgY by thermal neutron inelastic scattering at the spallation neutron source ISIS (UK) in a wide range of energy- and momentum transfers. We find considerable differences in their atomic dynamics outside the changes of the partial weighting factors due to the differences in composition: the GVDOS and dynamic structure factor of the decagonal phase is characterised by a more pronounced structure and partly by shifts of energy bands. These results we relate more to differences in the short-range order of these two different quasiperiodic structures than to their different long-range order.

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145. Quasicrystalline and Crystalline Phases in an Al - Pd - Mn - Fe Alloy
R Divakar, E Mohandas and V S Raghunathan
Materials Characterisation Group, Indira Gandhi Centre for Atomic Research, Kalpakkam 603102, India

Keywords:Al-Pd-Mn-Fe, hrtem, interfaces
The Al - Pd - Mn - Fe quaternary system has been studied as an extension of the well-known ternary Al-Pd-Mn quasicrystalline alloys. Quasicrystalline phases have not been reported in this system in literature nor are any predicted based on the criteria such as the e/a ratio for this system. The present paper reports the details of the effect of small Fe additions to the ternary Al - Pd - Mn quasicrystalline alloy. An icosahedral quasicrystalline phase coexisting with crystalline phases has been obtained through heat treatment of an arc-melted Al70Pd20Mn5Fe5 alloy. The icosahedral phase shows the solubility of Fe in the quasilattice to be very small. More than one crystalline phase is seen to coexist with the quasicrystalline phase in the quaternary system. This is in comparison to the ternary Al70Pd20Mn10 where the orthorhombic R phase has been seen to be the primary crystalline phase coexisting with the quasicrystalline phase. Characterisation of the various phases found using analytical TEM techniques is reported. A HRTEM study of the crystalline - quasicrystalline interfaces will also be presented.

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146.Limit periodic tilings and lattice substitution systems
Dirk Frettlöh
FB Mathematik, Univ. Dortmund, 44227 Dortmund,Germany

Keywords:lattice substitution systems ; nonperiodic tilings ; model sets
A lattice substitution system (F,V) is a partition V=(V_1, ... V_n) of a d-dimensional lattice, together with a substitution F, such that F(V)=V. Some well-known nonperiodic substitution tilings, like the chair- or the sphinx-tilings, give rise to lattice substitution systems. In [1] a mitperiodic tilings and lattice substitution systemscondition on (F,V) is given, which is equivalent to every V_i being a model set, hence pure point diffractive. If the V_i are no model sets, the computation of this condition will not terminate. We will give two sufficient conditions for V not consisting of model sets, which are computable in finite time; together with an example, which - until now - is not covered by any of the three conditions mentioned.
Furthermore, we discuss the relations between d-dimensional tilings and lattice substitution systems, i.e. we give necessary conditions on a tiling to give rise to a lattice substitution system and describe the relations between them in terms of mutual local derivability.
[1] Lee, Moody: Lattice Substitution Systems in Model Sets, Disc.Comp.Geom. 25 (2001) 173-201

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147. Al-Cu-Fe Quasicrystalline Coating on Al and Cu Substrates by Laser Cladding
Krishanu Biswas, G. Phanikumar, R.Galun*, B.L.Mordike* and K.Chattopadhyay
Department of Metallurgy,Indian Institute of Science,Bangalore 560 012, India
*Techinical University of Clausthal Claushthal Zellefeld,Germany

Keywords:AlCuFe, quasicrystalline coating, laser cladding
A comparative study of the effect of substrate on the nature of the quasicrystalline clad composites of Al-Cu-Fe alloys obtained by laser cladding process has been studied. Elemental powder mixture of composition of Al65Cu23Fe12 is used to prepare composite quasicrystalline coating on both aluminum and copper substrates using laser power of 6-8 kW. The clads on aluminum substrates are also remelted to alter the growth conditions of different phases.
In case of the clads on aluminum substrates, x-ray diffraction analysis reveals the presence of icosahedral phase in addition to monoclinic Al13Fe4 phase. The as clad microstructures contain rod like Al13Fe4 dendrites with icosahedral phase and CuAl2 in the interdendritic spaces. The remelted tracks show ten-point star shaped Al13Fe-4 dendritic morphology. The hardness measurements indicate very high hardness (HV0.025 >700) in case of as clad samples. In case of remelted tracks, clad layers show very high hardness but the hardness drops to lower value in the remelted layer (HV0.025 >300).
In case of clads on copper substrates, the x-ray diffraction analysis shows the presence of icosahedral phase along with Al13Fe4 and copper alumindes. The Al13Fe4 dendrites are present both in the form of unbranched, blocky blades and long rod-like dendrites. The hardness measurements indicate the very high value in all samples ((HV0.025 >1200).The detailed microstructural analysis along with solidification pathways in both cases will be presented in the presentation.

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148. Growth of Quasicrystals in Space:Possible Fallouts and the Indian Experiment
S.C. Sharma, K.Suseelan Nair, M.C.Mittal, P. Ramachandra Rao ** and K. Chattopadhyay*
Materials & Metallurgy Group, Vikram Sarabhai Space Centre, Trivandrum - 695 022, India
* Materials Research Centre, Indian Institute of Science, Bangalore-560 012, India
** Banaras Hindu University, Varanasi - 221 005, India

An experiment on the growth of quasicrystals under microgravity conditions has been planned using a recoverable space capsule to be launched by Indian Space Research Organization. The experiment consists of growing a Ga-Mg-Zn quasicrystal in an isothermal furnace and comparing the growth behaviour of space processed quasicrystal with those grown under terrestrial conditions. The primary aim of the experiment is to establish the effect of convection and more importantly the sedimentation on the growth of the stable quasicrystals. Due to large density difference, the composition of the melt ahead of the growing quasicrystals is expected to change under terrestrial condition inhibiting the growth of large quasicrystals. The growth process in that case can switch to yield one of the approximant phases neighbouring the quasicrystalline phase field. We expect that under microgravity condition this can be avoided leading to a more perfect quasicrystalline growth. The influence of the local change in chemistry due to sedimentation can also affect the phason concentration in the quasicrystal. These aspects of growth have not been well studied in the literature and experiments under microgravity condition can throw significant light on this issue. In the presentation we shall present an analysis of the issues involved and the methodology planned to be used for the space experiment.

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149. Novel phason-type anti-phase boundary in Al-Pd-Mn icosahedral single quasicrystal
Jianbo Wang(a), Renhui Wang(a), and J. Gastaldi(b)
(a)Department of Physics, Wuhan University, Wuhan 430072,, PR China
(b)CRMC2-CNRS, Campus de Luminy, case 913, 13288 Marseille Cedex 09, France

Loop-shaped contrasts (LSCs) were observed in as-grown Al70.3Pd20.6Mn9.1 icosahedral single quasicrystal (IQC) by means of traditional x-ray topography (XRT) (Lang's technique). Various diffraction vectors were excited to record XRT images, containing isolated LSCs. The contrast of a LSC vanished when some diffraction vectors were excited. Detailed analysis reveals that the extinction is due to G^par.R^par = 0, rather than G.R = 0, with R being a lattice vector R=[1-1 0-1 01] in the six dimensional space. This fact is further confirmed by synchrotron radiation experiments and indicates that the displacement vector inducing such type of LSCs should be phason-type component R^par. Analytical expressions were derived as a first order approximation, in which the coupling between phonon type and phason type displacements was neglected, for the elastic displacement fields, including both phonon- and phason-type components, induced by spherical inclusions in IQCs. The phonon-type component obtained is the same as that for a spherical inclusion in conventional elastically isotropic crystals, while the expression for the phason-type displacement, which decreases with increasing the distance r to the sphere center as r-1, is derived for the first time. Computer simulation of the XRT images by substituting this expression to the software approved the conclusion that this type of LSCs should correspond to a novel, peculiar class of anti-phase domain boundary, of which the interior is a local isomorphism with a non-zero phason-type displacement R^ relative to the IQC matrix. The concept of the local isomorphism was suggested at the early stage of the quasicrystal study [1,2], but we provide its direct experimental observation here for the first time. Detailed discussion of the formation of this novel class of defects and its implication to the nucleation and growth of IQC phase will be presented in another paper [3].
This project was supported by the National Natural Science Foundation of China.
[1] D. Levine, P.J. Steinhardt, Phys. Rev. B 34 (1986) 596
[2] J.E.S. Socolar, P.J. Steinhardt, Phys. Rev. B 34 (1986) 617
[3] R. H. Wang, J. B. Wang, J. N. Gui and J. Gastaldi, in this volume

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150. Local isomorphism and its implication to the growth of quasicrystals
Renhui Wang(a), Jianbo Wang(a), Jianian Gui(a), and J. Gastaldi(b)
(a)Department of Physics, Wuhan University, Wuhan 430072, PR China
(b)CRMC2-CNRS, Campus de Luminy, case 913, 13288 Marseille Cedex 09, France

Atomic structures of, defects in, and crystalline approximants of any quasicrystal can be very well described as a three-dimensional cut of a crystal in a N-dimensional (ND) hyperspace, under various conditions. By such a cut-and-projection description of quasicrystals almost all the experimental results carried out on quasicrystals can be interpreted except a question: How can the atoms follow so strict rules imposed by a cut of a crystal in the ND space during the growth which may be very rapid? This question was answered partly by introducing a covering description [1] of the atomic structure of quasicrystals.
Recently, we [2] identified a type of loop-shaped contrasts, in an as-grown Al70.3Pd20.6Mn9.1 icosahedral single quasicrystal, to be a novel, peculiar class of anti-phase domain boundary, of which the interior is a local isomorphism with a phason-type displacement R^ relative to the quasicrystal matrix. Local isomorphisms may nucleate (1) at the beginning of the nucleation of a quasicrystal grain; or (2) during the growth process when there are some accidents, which prevent the growth of a perfect grain. For example, when the growth rate is much quicker than the atom diffusion, or when some inclusions or voids are formed. Therefore, a quasicrystal grain may multiply nucleate from a same seed and grow up after a same manner as in the case of crystals.
This project was supported by the National Natural Science Foundation of China.
[1]P. Gummelt,in: Proc. of 5th Intern. Conf. on Quasicrystals, (1995), p.84
[2]J. B. Wang, R. H. Wang and J. Gastaldi, in this volume

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151. Preparation of novel Raney copper catalysts from Al-Cu-Fe-(Zn, Ce) quasicrystals
An Pang Tsai(1) and Michiaki Yamasaki(2)
(1)National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, 305-0047, Japan
(2)Graduate School of Science and Technology, Kumamoto University, 2-39-1 Kurokami, Kumamoto, 860-8555, Japan

Keywords:Quasicrystals, Steam reforming of methanol, Raney Cu catalyst, Leaching
The catalytic activity for methanol steam reforming on the AlCuFeZn and AlCuFeRE (RE = Y, La, Ce, Pr, Nd) quasicrystal catalysts has been investigated. The novel Raney Cu catalysts prepared from AlCuFeZn quasicrystal alloy and quasicrystal-containing AlCuFeRE alloys by leaching treatment have higher catalytic activity than the catalyst prepared from ternary AlCuFe quasicrystal. The hydrogen production rates on the AlCuFeZn and AlCuFeCe catalysts reach 262 l/kgomin and 214 l/kgomin at 573 K, respectively. Improvement of catalytic activity by addition of Zn and RE is due to increase of specific surface area of the catalyst after leaching treatment. The results will be presented in detail.

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152. Quasi-Periodic Crystals - the Role of Transmission Electron Microscopy
Dan Shechtman
Technion, Haifa,Israel

The discovery of the Icosahedral Phase in 1982 was one of the striking victories of transmission electron microscopy. Indeed, the first observations of dislocations and early stages of precipitation processes in the first days of electron microscopy were extremely important, and contributed a great deal to modern materials science, but the role of TEM has been mainly supportive, rather than ground breaking. Most of the crystalline defects, so elegantly studied by TEM, thanks to our understanding of contrast phenomena, were known before. The support of TEM, which produced dramatic images and diffraction patterns provided in most cases a final proof or rejection of existing theories and speculations. For the crystallographers' community, X-ray diffraction was the undisputed king, the reliable research tool in town.
Enters the Icosahedral Phase, the first observed Quasi-Periodic crystal. Unexpected, not predicted, and flatly rejected by the paradigm: "A crystal is ordered and periodic". TEM was the only tool by which the I phase could have been discovered. The techniques needed for structural analysis of the I phase: contrast analysis, composition analysis and high-resolution images are all standard in modern transmission electron microscopy. X-ray diffraction could not provide any of the these, since the first produced I phase crystals were only a few microns in size, and the specimens contained several phases in addition to the I phase. The results provided in the first article on the I phase in 1984 were very convincing to the TEM community, but very controversial in the community of crystallographers. It was not until 1987 that large enough crystals were grown to enable single crystal x-ray diffraction, and the community of crystallographers was slowly convinced.
Electron diffraction in the transmission electron microscope became a major tool for the discovery of new crystal structures. Most, if not all of the new quasi-periodic structures that were found since 1984 were discovered by electron diffraction in the TEM.

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153. The role of the phi-phase in the solidification process of Al-Cu-Fe icosahedral quasicrystal
Dongshan Zhao(b), Renhui Wang(a), Jianian Gui(a), Ningfu Shen(b), Wenbang Qu(a),Zhijun Zhang(c)
(a)Department of Physics, Wuhan University, Wuhan 430072, China
(b)Materials Engineering College, Zhengzhou University, Zhengzhou 450002, China
(c)Key Lab. of Lubrication and Functional Material, Henan University, Kaifeng 475001, China

A series of Al-Cu-Fe alloys with compositions of Al48~60Cu33~50Fe0~10 was prepared and the phase constituents of these alloys quenched from various temperatures were identified by using XRD, SEM, EDXS and EBSD attached to SEM, and TEM (including HRTEM). The present investigation prefers the polythermal projection and reaction scheme as shown in Fig.1. Compared with the suggestion proposed by Gayle et al. [1], Faudot [2], and Zhang & Lueck [3], the main amendment is to divide the previous b-region into beta+phi two regions.

Polythermal projection around the region where IQC is the primarily solidified phase
(1) eutectic (before U8): L=beta+phi
(2) quasiperitectic at U8: L+beta=phi+IQC
(3) quasiperitectic at U5: L+IQC=phi+omega
(4) eutectic (before U6): L=phi+epsilon
(5) quasiperitectic at U6: L+epsilon=phi+eta
(6) eutectic (between U5 and U7): L=phi+omega
(7) quasiperitectic at U7: L+phi=eta+omega
This project was supported by the National Natural Science Foundation of China
[1] F. W. Gayle, A. J. Shapiro, F. S. Biancaniello, and W. J. Boettinger, Metall. Trans.A 23A, 2409(1992)
[2] F. Faudot, Ann. Chim. Fr. 18, 445(1993)
[3] L.M. Zhang and R. Lueck, J. Alloys Comp. , in the press
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154. Observation of pseudo-gap and Kondo behaviour in Al₇₀Pd_30-xMn_x quasicrystals

Gayathri N. Banerjee^#, S. Banerjee^# and R. Goswami^$
#Saha Institute of Nuclear Physics, 1/AF, Bidhannagar, Kolkata-700064
^$Materials Science and Engineering Department, Rensselaer Polytechnic Institute, 110 Eighth Street, Troy, NY 12180

The Al70Pd30-xMnx quasicrystals show very interesting magnetic properties as a function of x. We have studied the critical composition (x=7,9 and 11) of the quasicrystal structure using the technique of point contact spectroscopy at 4.2K. The study of the evolution of the point contact spectra from the point contact regime to the tunneling regime gives an interesting aspect to the understanding of the different contributions to the magnetism as well as the electronic properties of these quasicrystals. In the point contact regime (usually observed at low contact resistances), the presence of a zero bias anomaly in the conductance and its voltage dependence can give us information regarding the magnetic nature of the sample. In the tunneling regime (observed at high contact resistance), the conductance is directly related to the electronic density of states of the sample and hence any features in the DOS will be reflected in the tunneling conductance spectra. Our samples show a clear zero bias anomaly in the point contact conductance as a function of the bias voltage which becomes more pronounced as the Mn concentration (x) increases indicating that magnetism of the samples increases as x increases, x=9 being the critical composition. The zero bias feature in the point contact spectroscopy shows clear signature of Kondo-like behaviour. In the tunneling regime, there is clear evidence of the pseudo gap near the zero bias. Using the technique of point contact spectroscopy, we have been able to see the Kondo behaviour as well as the pseudo gap in these quasicrystals.

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155. Electronic Properties of Quasicrystals : Why is Less More?

T. V. Ramakrishnan
Department of Physics, Indian Institute of Science, Bangalore-560012, India

For about a decade now, it has been known that stable metallic quasicrystals have very high electrical resistivities, often well exceeding the Mott maximum resistivity limit. It is also observed that less is more in these systems, namely the less structurally disordered the quasicrystal is, the higher its resistivity; this has been demonstrated for example by deliberately damaging the quasicrystal, and is implied by the increase in resistivity on reducing temperature (thermal disorder). The Hall effect also shows strange anomalies; eg. it is large and changes sign with temperature in some systems. The ac conductivity is distinctly non Drude like.
We propose here ideas with which one can make sense of these facts. Experimentally, the most intense diffraction spots imply (say in Al Cu Fe) a Brillouin-Jones zone with 42 faces. Because of (phason) Debye Waller factor effects, hierarchically close spots are very weak. Modelling the system as one with Fermi surface close to the Brillouin zone (Hume Rothery- Jones alloy) we realize that the system is a semi metal, with very small Fermi velocities or current matrix elements. The small conductivity is due not to large disorder, but to the fact electrons near the Fermi surface are in almost stationary states carrying very little current. The mixing due to disorder increases the current matrix elements, so that the conductivity increases. We show that other observed properties can be explained starting with these ideas.

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156. SEM and AFM Studies of 5-fold Surface of AlPdMn Quasicrystal Subjected to UHV Treatment

Yu Fuxiao¹,Maarten Bischoff¹, Amy R. Ross², Thomas A. Lograsso², Yvonne Calvayrac³, Herman van Kempen¹ and Ted Janssen^1
1Research Institute for Materials, University of Nijmegen, Toernooiveld 1, 6525 ED, Nijmegen, The Netherlands
²Department of Materials Science and Engineering, Iowa State University, Ames, USA
³Centre d'etudes de Chimie Metallurgiques, CNRS, Vitry, France

The understanding of the 5-fold surface structure of the AlPdMn quasicrystal benefited largely from studies with techniques such as low energy electron diffraction (LEED), photoemission spectroscopy and scanning tunneling microscopy (STM). These techniques probe different interactions and consequently, the size of the probed area from which the structural information is collected varies. These investigations have in common that they are always performed on surfaces that are prepared in ultrahigh vacuum (UHV) either by ion sputtering and annealing cycles or by cleavage of the bulk sample. In view of the aperiodic nature of the surface structure and the fact that the quasicrystalline phase is extremely sensitive to the chemical composition, it is of importance to ask whether the surface structure, which is obtained from different experiments, represents the global structure. In other words, we need to know whether the surface is uniform from atomic to macroscopic scales. To answer this question, we have studied two 5-fold surfaces (with and without gold capping layers) of the AlPdMn quasicrystal by means of scanning electron microscopy (SEM) and atomic force microscopy (AFM) in ambient conditions. These surfaces were prepared in UHV by ion sputtering and annealing cycles for STM studies. We show that very complicated inhomogeneous microstructures can be developed on the 5-fold surfaces. The surfaces are characterized by the nano-sized clusters even in areas where STM shows structures with 5-fold symmetry on the terraces. Therefore, care has to be taken when interpreting the experimental results obtained on the surfaces of quasicrystals. The formation of the complex surface microstructure is explained in terms of sublimation and sputtering during the sample preparation.

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157. Magnetic Properties of Al_70-xPd₁₅Mn₁₅M_x(M=B,Si,Ge; 0<x<8)

D. Bahadur¹ and R. A. Dunlap^2
1Department of Metallurgical Engineering and Materials Science, Indian Institute of Technology, Bombay, India
²Department of Physics, Dalhousie University, Halifax, NS, B3H 3J5, Canada.

The icosahedral alloys of the composition, Al_70-xPd₁₅Mn₁₅M_x(M=B,Si,Ge; 0<x<8) have been synthesized by melt spinning. X-ray diffraction results show that all the samples could be indexed to single phase icosahedral systems. Magnetic properties have been characterized by magnetization studies and ferromagnetic resonance. There is a clear evidence of two distinct Mn sites in all samples except when Ge content is 8%. One of the sites is magnetic , while the other is non magnetic. Different metalloid atoms influence the magnetic properties differently. While the composition with Boron indicates that Mn sites are coupled through B atoms, when neighbouring icosahedra are in specific edge sharing configuration. Si containing Al-Mn-Pd alloys do not show any evidence of ferromagnetism and it appears that there is only a small percentage of magnetic atoms and they do not couple ferromagnetically. The composition with Ge, however, produces 100% paramagnetic atoms. The difference in magnetic behavior of these compositions have been explained on the basis of elctronic configuration, atomic size and possible hybridization of the transition metals with these metalloid atoms. Anderson's theory of moment formation and indirect coupling of 3d moments through the induced polarization of the intervening p shells have been invoked to explain the ferromagnetic behavior.
References
1. D.Bahadur, C.M.Srivastava, M.Foldeaki, A. Giguere and R.A.Dunlap, Materials science and Engg. A304, 830, 2001.
2. D.Bahadur, C.M.Srivastava, M.H. Yewondwossen and R.A.Dunlap, J.Phys. cond. Matter. 7, 9883, 1995.

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158. From approximants to quasicrystals - are there any fundamental differences

Xiaodong Zou and Sven Hovmöller
Structural Chemistry, Stockholm University, SE-106 91 Stockholm, Sweden

One approach of solving quasicrystal structures is from their approximants. In many cases, a series of approximants is related to a quasicrystal. The unit cell dimensions of different approximants within the same series increase by the golden number t, t2, t3… At the end of such a series, when the unit cell dimensions become infinite, a quasicrystal is formed. Based on this, a few structure models have been proposed for different quasicrystals. However, there is no general procedure for solving quasicrystal structures from their approximants.
Recently we have derived a new general approach for solving quasicrystal structures from their approximants. By analysing the structure factor phases and amplitudes of the approximants within a series, we found the common features among those approximants. Those common features should also exist in the corresponding quasicrystal. In this way, we can generate the perfect structures of quasicrystals. For example, the approximants starting with Al13Fe4 (C2/m, a = 15.489, b = 8.083, c = 12.476 Å and b = 107.71°) approach the decagonal quasicrystal in the Al-Fe system. This method can be applied to any quasicrystal.

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159. Plastic Deformation of Binary Icosahedral Quasicrystal of Cd-Yb

Y. Imai, T. Shibuya, R. Tamura and S. Takeuchi
Department of Materials Science and Technology, Tokyo University of Science, Noda, Chiba 278-8510, Japan

Polycrystalline icosahedral quasicrystals of Cd84.6Yb15.4, produced by melting and annealing in a sealed alumina crucible, have been compressed in vacuum at high temperatures. As-grown specimens could be plastically deformed only above 700K with the yield strength rapidly decreasing with increasing temperature. The true stress vs true strain relation showed that the flow stress decreases continuously to a large true strain of unity; the decrease of the flow stress is almost 90% of the yield stress at 700K and it is about half at 773K. Thus, the temperature dependence of the flow stress at a large strain is rather weak. As a result, once a specimen was initially deformed to a large strain at 773K, the specimen could be plastically deformed even below 600K without fracture. The temperature change tests for the same specimen showed that the flow stress at the same temperature at the same strain is sensitive to the deformation history. These results indicate that the deformation-induced phason-defects, the distribution of which is temperature dependent, drastically reduces the lattice resistance for the dislocation glide. The activation volumes of plastic deformation, obtained from the stress relaxation tests, are small, of the order of 0.1nm3 at high stress level, suggesting that the elementary process of the dislocation glide is the Peierls-mechanism like process.

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160. Electronic Transport of the Icosahedral Zn-Mg-Sc Quasicrystal and Its Cubic Approximant Zn17Sc3

J. Hasegawa, R. Tamura and S. Takeuchi
Department of Materials Science and Technology, Tokyo University of Science, Noda, Chiba 278-8510, Japan

The electrical resistivity and specific heat measurements have been performed for the recently discovered P-type icosahedral Zn-Mg-Sc[1] of high structural perfection and its crystalline approximant Zn17Sc3. The resistivity of the i-phase shows a negative temperature coefficient with rho_300K = 330 mu-Omega-cm, while it possesses a positive temperature coefficient with rho_300K = 250 mu-Omega-cm for the approximant. The transport of the approximant is found to be fairly well described by the Bloch-Gruneisen theory, showing that the transport of the 1/1-approximant is essentially the same as normal metals despite its high residual resistivity. The electronic specific heat coefficient is found to be small and almost the same for both alloys; 0.55 and 0.65 mJ/(mole K^2) for the quasicrystal and the approximant, respectively. Hence the marked difference in the resistivity behavior between them is mainly attributed to the difference in the electronic diffusivity, which probably arises from their different long-range orders. Furthemore, the small specific heat coefficients are found to be in agreement with the result of the electronic structure calculation[2], indicating the presence of a dip in the density of states at the Fermi level for the P-type $i$-phase as well as its crystalline approximant.
[1] Y. Kaneko, Y. Arichika, and T. Ishimasa, Phil. Mag. Lett. 81, 777 (2001).
[2] Y. Ishii, private communication.

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161. Fullerenes as fractal quasicrystals?

A. I. Lazarev
G.A.Razuvaev-Institute of Organometallic Chemistry of RAS, Tropinin Str. 49, Nizhny Novgorod, GSP-445, 603950, Russia.

Recently interest to carbon nanotubes formed from the cycles with 6-fold symmetry has considerably increased. Earlier we offered models of the quasicrystalline structures containing the closed stable fractal shapes with a rotation symmetry of 6-th, 3-rd, 2-nd and 1-st orders [ICQ'6]. In particular, the concept of quasicrystalline carbon was proposed [IWFAC'99]. The fragments of the closed stable fractal shapes on quasicrystalline structures of carbon were used as initial structures for the formation of fulleren-like structures and nanotubes in the presence of atoms of metals. One of factors formula A= (m2 + mn + n2) was used by us earlier for representation of prime numbers - twins [Aprd'97]. It was shown by us, that the numbers or their combinations (m, n) can be expressed in a cartesian plane as aperiodic structures and fractal images [ICQ'7]. The prime numbers - twins in such representation are very diverse (incommensurable numbers form figures similar to Lissajous figures). The consideration of incommensurable numbers (m, n) and relevant by them to aperiodic structures and fractal shapes on hexagonal lattices can appear to be useful for model operation of the precursors of fulleren-like structures.

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162. A basis for the classification of quasicrystals
H. S. Jeevan and S. Ranganathan
Department of Metallurgy, Indian Institute of Science, Bangalore-560012, India

In a seminal paper entitled . A basis for the synthesis of quasicrystals. Ramachandra Rao and Sastry (1985) indicated that the occurrence of icosahedral coordination in a crystalline compound provided favourable conditions and synthesised quasicrystals in Mg-Zn-Al system. This left open the question about the factors promotimg the occurrence of icosahedral coordination. Following this Mg-Zn-RE quasicrystals were discovered by Luo and coworkers(1993) and Tsai and coworkers (1994)and were regarded as analogous to Mg-Zn-Al with the trivalent Al replaced by rare earths. Later it was realized that they were based on Zn as a main alloying element and led to the discovery of Cd based quasicrystals by Guo & Tsai (2000). Later investigations by Ishimasa and Kaneko (2002) and Tsai (2002)showed Cu-Ga-Mg-Sc and Ag-In .RE formed quasicrystls and were regarded as systems based on copper, silver etc. In a significant paper Tamura (1994) showed that the important element in the icosahedral cluster is the largest size atom. Following this, we propose a classifiction of quasicrystals as centerd on Li, Mg, Al, Ga , Rare Earths and Ti, Zr, Hf . The term centered is to indicate the importance of this element, even though composition wise it may no be the majority constituent. The usefulness of Pettifor maps in this context will be illustrated. It will also b advocated that for bulk metallic glasses a similar classifiction centered on the largest size atom rather than the major element in composition may offer a better classification.

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163. Experimental Overview of Complex Intermetallic Structures

M. Laridjani¹, P. Donnadieu² and F. Dénoyer^1
1Laboratoire de Physique des Solides, UMR 8502, Bâtiment 510, Université Paris-Sud, 91405 Orsay Cedex, France.
²Laboratoire de Thermodynamique et Physico-Chimie Métallurgiques, ENSEEG, INPG, UMR 5614, Domaine Universitaire, BP 75, 38402 Saint-Martin d'Héres Cedex, France.

A complete investigation of the Fourier space of complex intermetallic Mg39Al61 is reported. X-ray patterns reveal the reciprocal space of the whole system consisting in selective reflections and coherent diffuse scattering. Their temperature dependence are studied. Selective reflections are interpreted as incommensurately modulated states and a structural analysis of the coherent diffuse scattering is presented. The same type of coherent diffuse scattering curve was also observed in several quasicrystalline alloys. In all the studied cases, the disorder is interpreted by the presence of icosahedral arrangements that are reminiscent of Frank units in supercooled alloys.

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164. Icosahedral structures and helices in gamma-brass structure

Eric Lord and S. Ranganathan
Department of Metallurgy, Indian Institute of Science, Bangalore-560012, India

As pointed out by Boerdijk, the packing of spheres centred at the vertices of the Boerdijk-Coxeter helix can be extended by adding more spheres over the mid points of edges of the helices. Specifically, an extra vertex is placed over the mid-point of each edge of the type {1} helix, forming an equilateral triangle with the two vertices of that edge. This determines additional, only slightly irregular, tetrahedra, so that every edge of the type {1} helix is shared by five tetrahedra. Further extensions of this helical sphere packing are possible. The next stage of adding spheres gives a rod-like structure in which every sphere of the original helix is surrounded by twelve others, configured as a somewhat distorted icosahedron. Thus each tetrahedron of the initial B-C structure is then shared by four icosahedra. This 26-sphere cluster is a slightly distorted form of the 26-atom gamma-brass cluster. The gamma-brass structural unit was for a long time regarded as a modified B2 structure; it is more accurately described as a tetrahedral cluster of four interpenetrating icosahedra. These clusters bond to each other to form chains along the [111] axes.

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165. Sliding on a quasiperiodic substrate

T. Janssen
Institute for Theoretical Physics, University of Nijmegen, The Netherlands.

For a crystal moving over a periodic substrate (another crystal) the coupling of the centre of mass energy to the internal phonons depends strongly on whether the two periodicities are commensurate or incommensurate. In the latter case a sliding mode may exist with very low frequency. For the motion of a crystal on a quasiperiodic substrate (crystal on a quasicrystal) the coupling scheme is very different. It depends on the rank of the Fourier module spanned by the Fourier modules of crystal and substrate.
The transfer of centre of mass motion to phonons in the crystal will be discussed and illustrated with examples from numerical calculations in simple models.

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166. On the formation and morphology of quasicrystalline T₂ phase in artificially aged Al-Li-Cu-Mg-Zr alloy

K. Satya Prasad, A. A. Gokhale and D. Banerjee
Defence Metallurgical Research Laboratory, Kanchanbagh P.O., Hyderabad-500058, India

The equilibrium phases T2 (Al6CuLi3), . (AlLi) and C [Al6(Cu,Mg)] are known to form in commercial Al-Li alloys (such as 8090) on artificial ageing, in addition to the metastable, strengthening phases like .. (Al3Li), S (Al2CuMg) and T1 (Al2CuLi). The morphology, distribution and crystallography of these phases in 8090 alloy have not been studied in any great detail in the past. The T2 phase is known to have a quasicrystalline structure with m 5 symmetry. In the present work, we have examined the formation of T2 phase in greater detail over a wide range of ageing conditions. The sequence of precipitation and specific site location of the T2 phase in the 8090 alloy has been established. Its crystallography and morphology have been determined, and the specific role of heterogeneous nucleating sites examined. It was found that the faceted precipitates of .. (Al3Zr) act as catalysts in nucleating the T2 phase particularly in the under-aged condition. Independent nucleation of T2 is also observed in over-aged condition. Since the faceted morphology of .. occurs only under certain combinations of composition and processing, it implies that the same conditions indirectly influence the formation of T2.
A total of four different orientation relationships (OR) between T2 and matrix were identified. However, no unique OR existed between .. and T2. The OR between T2 and matrix seemed to influence morphology of T2, with majority of the OR.s favouring a rod morphology.

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167. Nucleation and stability of crystalline intermetallic compounds in commercial Al-Li-Cu-Mg and Al-Cu-Mg alloys

A. K. Mukhopadhyay and K. S. Prasad
Defence Metallurgical Research Laboratory, Kanchanbagh, Hyderabad-500058, India

A majority of the work on quasaicrystals is related to aluminium alloys. In mid 1980's, these studies received a major boost when icosahedral T2 - Al6CuLi3 phase was found to form as a major grain boundary precipitate during artificial aging of a commercial Al-Cu-Li alloy. Structural studies using intermetallic compounds based on Al-Cu-Li-Mg thereafter revealed that T2 phase dissolves some amounts of Mg, whilst, increasing Mg content has the effect of replacing T2 phase by quaternary phases such as tetragonal C (a = 1.4 nm and c = 5.41 nm) and hexagonal Z (a = 1.4 nm and c= 2.8 nm). It was reported that there are orientation relationships between the icosahedral T2 and the bcc compound R-Al5CuLi3 (a = 1.39 nm) in the Mg free Al-Cu-Li system. The cubic Al2LiMg compound (a = 2.0 nm) in the Cu free Al-Li-Mg alloy was also found to bear similarities to the description of C phase structure as a modulated fcc structure with a = 2.0 nm. Furthermore, the cubic R-Al5CuLi3 phase (a = 1.39 nm) is isomorphous with the cubic T-(AlZn)49Mg32 (a = 1.4 nm) in the Al-Zn-Mg system, the cubic Al3Li2Zn (a = 1.39 nm) in the Al-Li-Zn system and the cubic Al6CuMg4 (a = 1.42 nm) in the Al-Cu-Mg system. The above findings point out that an approach route toward better understanding of the structure of quasaicrystals and / or to search for quasaicrystals in alloy systems based on Al-Cu-Mg, Al-Zn-Mg etc would be to examine first the nucleation and stability of the said crystalline intermetallic compounds in the respective alloy systems, and then modify the compositions of such alloys in favour of the formation of the quasaicrystalline phases.
As an example for the said approach route, in this paper using commercial Al-Li-Cu-Mg alloys, we report on the stability of the crystalline C phase in that increasing Cu:Mg ratio destabilizes the C phase in favour of the quasaicrystalline T2 phase. Using an Al-Cu-Mg alloy [having composition lying in the a (Al) + q (Al2Cu) + S (Al2CuMg) phase field in the ternary Al-Cu-Mg phase diagram], it is further shown that trace addition of Ag has the effect of stablizing the cubic T - Al6CuMg4 phase. Also, Si addition to a commercial Al-Cu-Mg-Mn alloy has the effect of increasing the nucleation frequency of the orthorhombic Al20Cu2Mn3 phase, and inducing the formation of a cubic phase, s-Al5Cu6Mg2, that is otherwise not in equilibrium with Al. The implication is that selection of alloy composition and alloying additions is the key toward the study of quasaicrystals or related crystalline intermetallic compounds / approximant structures in commercial Al alloys.

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168. Nanocrystallisation and Nanoquasicrystallisation in (Ti/Hf)-Zr-Ni Ternary alloys

Joysurya Basu, D. V. Louzguine*, A. Inoue* and S. Ranganathan
Department of Metallurgy, Indian Institute of Science, Bangalore-560012, India
*Institute for Materials Research, Tohoku University, Katahira 2-1-1, Aoba-Ku, Sendai, Japan

Hume-Rothery rules depict the basic conditions for the formation of solid solutions. In recent years it has been observed that the violation of these rules gives rise to amorphous phases in many metallic systems. Ti, Zr and Hf containing alloys throws a few challenging questions as far their glass forming ability is concerned, keeping in view their size consideration and confusion principle. These amorphous alloys upon heat treatment gives rise to nanocrystalline and nanoquasicrystalline materials and composites.
Two alloys of nominal composition, Ti41.5Zr41.5Ni17 and Zr41.5Hf41.5Ni17, have been rapidly solidified in order to obtain the amorphous phase. Ti-Zr-Ni amorphous alloy is stable upto 4250C and it crystallises in three steps. This alloy at the onset of crystallisation gives rise to nano-icosahedral quasicrystalline phase which is stable up to 4h of annealing at 4500C. At the later stages this quasicrystalline phase transforms into cF96 Zr2Ni phase. In Zr-Hf-Ni alloy complete amorphous phase could not be obtained after melt spinning at 40 ms-1 wheel speed. In the amorphous matrix localised precipitation of cF96 Hf2Ni phase can be seen and this alloy upon crystallisation gives rise to the same phase.
Ti, Zr and Hf are isoelectronic as they belong to the same group of the periodic table. In this present study complete replacement of Ti by Hf leads to poorer glass forming ability and the crystallisation behaviour changes completely. A closer examination of the ternary phase diagram indicates that the amorphous alloys during crystallisation does not follow the equilibrium path. The onset of crystallisation can be attributed to the compositional fluctuation in the amorphous matrix.

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169. Metastable Phase Transformation of Early Transition Metals Induced by Mechanical Milling

I. Manna¹, P. P. Chattopadhyay² and H. -J. Fecht^3
1Metallurgical and Materials Engineering Department, I.I.T., Kharagpur-721302, India
²Metallurgy Department, B. E. College (D.U.), Howrah-711103, West Bengal, India
³Materials Divison, Albert Einstein Allee 47, University of Ulm, D-89081 Ulm, Germany

Mechanical milling of elemental powder leads to significant grain refinement through a process of welding, fragmentation and dynamic recrystallization. The milling products are often metastable or non-equilibrium products like glass/amorphous, quasicrystals, etc. We have earlier reported that elemental niobium undergoes a metastable bcc . fcc polymorphic transition in planetary ball milling. Recently, we have detected a similar polymorphic change in elemental titanium and zirconium (hcp to fcc) induced by high-energy mechanical milling. The transformation remains incomplete unless the total strain and strain rate are adequate. In this paper, we will present the experimental evidence of this change monitored by x-ray diffraction and high-resolution transmission electron microscopy. In addition, we will provide chemical analysis data to assess the role of impurity in such transformation. Electrical resistivity measurements have established that the milling products are metallic and not intermetallic or ceramic. It is believed that nanocrystallization is a prerequisite for structural instability that propels this change in crystal structure. The transformation seems irreversible in nature. Comparison with the data on similar phase transitions reported in the literature shows that strain alone cannot account for this polymorphism. We will present a detailed analysis on the genesis and stability of this hitherto unknown polymorphic change in early transition metals under severe plastic strain. Finally, a thermodynamic analysis will be presented to explain the scope of evolution of metastable phases like polymorphs and quasicrystals by mechanical milling.

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