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Bulk Properties of Quasicrystals: Structural, Electronic, and Dynamical.

Title: "New building blocks in the 2/1 crystalline approximant of a Bergman-type icosahedral quasicrystal"

Authors: Q. Lin and J.D. Corbett

Contact:  J.D. Corbett             

Journal:  PNAS (2006) 103, 13589-13594.

Abstract:

The refined x-ray crystal structure of the phase Mg27Al10.7(2)Zn47.3(2) (Pa3) establishes it as the new 2/1 Bergman-type approximant of the icosahedral quasicrystal. The primitive cubic lattice consists of condensed triacontahedral and novel prolate rhombohedral (PR) clusters. Each triacontahedron encapsulates the traditional, multiply endohedral Bergman-type clusters, and each PR encapsulates an Al2 dimer. This phase exhibits the same long-range order as recently established for the Tsai-type Sc-Mg-Zn 2/1 approximant crystal, with substantial geometric and atomic distribution differences between the two only in the short range orders. This common feature suggests that Bergman- and Tsai-type quasicrystals may be more similar than earlier conceived. Factors germane to the formation of, and the differences between, Bergman- vs. Tsai-type 1/1 and 2/1 approximate structures are considered, including notably different distributions of the more electropositive elements.

Title: "Electronic tuning of Mg2Cu6Ga5. A route to crystalline approximant and quasicrystalline phases"

Authors: Q. Lin and J.D. Corbett

Contact:  J.D. Corbett             

Journal:  J. Am. Chem. Soc. (2005) 127, 12786-12787.

Abstract:

Studies of Mg2Cu6Ga5 reveal that this compound contains incomplete Bergman clusters in its structure and shows a pseudogap and empty bonding states just above the Fermi energy according to band calculations. Under a rigid band assumption, such a compound may be tuned to approximant and quasicrystal phases in which the required number of electrons are attained. Here, we replace part of Mg in the isotypic Mg2Cu6Ga5 with Sc, and both 1/1 approximant and icosahedral quasicrystal phases are obtained after some fine-tuning. This method closely correlates the pseudogap and bonding with Hume-Rothery concepts, thus giving useful directions for future quasicrystal searches, especially when approximants are not known.

Title: "Mg35Cu24Ga53: A three-dimensional cubic network composed of interconnected Cu6Ga6 icosahedra, Mg-centered Ga16 icosioctahedra, and a magnesium lattice"

Authors: Q. Lin and J.D. Corbett

Contact: J.D. Corbett

Journal: Inorg. Chem. (2005) 44, 512-518.

Abstract:
Single-crystal X-ray structural determinations for the Mg35.12(4)Cu24Ga53.58(6) and Mg35.6(4)Cu24Ga52.66(6) refined compositions (Fd3m, Z = 4) reveal empty (Cu,Ga)12 icosahedra and centered MgGa16 icosioctahedra that are interconnected at every vertex to a compact three-dimensional anion network. A small range of variable occupancy exists on one of three Ga and one of four Mg positions. The clusters are well-bonded and held in different sized cavities, in which they are also directly bonded to a Mg cation network. The two networks thus interpenetrate each other, and there are no spacers. The new phase is isostructural with K39In80, K17In41, and the electron-poorer Na35Cd24Ga56, all of which contain clathrate-II-type cation frameworks. Electron counting using the classic (MO-based) cluster assignments indicates that the refined structure is substantially ideal and closed-shell. The symmetry of the present structure does not suggest a ready conversion to an icosahedral quasicrystal or its approximants.

Title: "Solid and liquid thermal expansion and structural observations in the quasicrystalline Cd84Yb16 compound"

Authors: M.J. Kramer, T.A. Lograsso, and D.J. Sordelet

Contact: M.J. Kramer

Journal: Philos. Mag. Lett. (2005) 85, 151-162.

Abstract:
The structure of single-grain Cd84Yb16 samples aligned along the twofold and fivefold axes has been followed from 300 to 1050 K using high-energy synchrotron X-rays. The quasicrystal phase is stable up to its melting temperature of 914 K and has a large linear thermal expansion of 37.1 ppm K-1 over this temperature range. The samples melt congruently over a temperature range of less than 1 K. The liquid is 7% less dense than the solid and, upon cooling from the melt, the quasicrystal phase directly solidifies within a 1 K interval. The amount of undercooling achieved, about 5-25 K, was dependent on the cooling rate. The total scattering function of the liquid is consistent with a dilute liquid Cd structure. These results agree with suggestions that the structure of the liquid must undergo reordering in order to form the solid phases. However, there is no compelling evidence for icosahedral short-range order in the liquid prior to the formation of the quasicrystalline structure.

Title: "Micro-surface and bulk thermal behavior of a single-grain decagonal Al-Ni-Co quasicrystal"

Authors: J.A. Barrow, M.C. Lemieux, B.A. Cook, A.R. Ross, V.V. Tsukruk, P.C. Canfield, and D.J. Sordelet

Contact: D.J. Sordelet

Journal: J. Non-Cryst. Solids (2004) 334-335, 312-316.

Abstract:
Scanning thermal microscopy is used to examine the thermal behavior of specific surfaces of a ~0.8 cm3 single-grain Al74Ni10Co16 decagonal quasicrystal. The response of a micro-thermal probe in contact with aperiodic and periodic surfaces in air reveals the anisotropic heat flow of the decagonal structure. Heat dissipation with the probe on the aperiodic surface is higher than when the probe is on the periodic surface. While the SThM technique is generally considered to be constrained to the surface region below the nominally 2–5 μm probe tip radius, the heat flow data obtained are clearly comprised of contributions from both the lateral surface around the probe tip and a volume normal to the surface in contact. Heat flow in the decagonal Al74Ni10Co16 quasicrystal can be modeled by an elliptical distribution of thermal diffusion. Parameters for the model used in this study were obtained by making bulk thermal diffusivity measurements using the laser flash method on specimens along the 2- and 10-fold directions. The model was applied to a surface oriented 45° to the major axes and verified from bulk measurements obtained from a sample cut along this orientation.

Title: "Structural relationships between QC and meta-stable crystalline phases in melt spun Zr80Pt20 ribbons"

Authors: X.Y. Yang, M.J. Kramer, E.A. Rozhkova, and D.J. Sordelet

Contact: D.J. Sordelet

Journal: Mater. Res. Soc. Symp. Proc. (2004) 805, LL7.8.

Abstract:
Two competing meta-stable crystalline phases, a bcc hyperstoichiometric b-Zr(Pt) (Im3m) superstructure and a non-stoichiometric fcc e-Zr6Pt30 (Fd3m) phase, have been observed to coexist with a quasicrystalline (i) phase, respectively, in as-spun Zr80Pt20 ribbons with low oxygen content (184ppm mass O) and high oxygen content (4737 ppm mass O). Transmission electron microscopy (TEM) results show that the b-Zr(Pt) superstructure and i phase have a well defined orientational relationship, good crystallography match and nearly identical stoichiometry. Icosahedral two-fold axes coincide with <110>, <111>, <112> and <113> axes in b-Zr(Pt); {110}b-Zr planes register with icosahedral {211111} fivefold or {221001} twofold planes. The observed orientational relationship and the space group (Im3m) preclude b-Zr(Pt) as a cubic approximant to the i phase. Both b-Zr(Pt) and the i phase are distorted; b-Zr(Pt) maintains a basic b-Zr Bravais lattice with an aperiodic superlattice. Morphologies suggest that the i phase forms first, followed by an easy nucleation of the b-Zr(Pt) on the surfaces of the i phase. Also, a similar orientational relationship and lattice match between e-Zr6Pt30 and i phase has been revealed by TEM.

Title: "Growth and physical properties of the decagonal Al-Cu-Co quasicrystal grown from the ternary melt"

Authors: R.A. Ribeiro, S.L. Bud'ko, F.C. Laabs, M.J. Kramer, and P.C. Canfield

Contact: P.C. Canfield

Journal: Philos. Mag. (2004) 84, 1291-1302.

Abstract:
Large faceted single-grain quasicrystals of the approximate composition Al63.2Cu19.5Co17.3 and with a high degree of structural perfection are obtained through the slow cooling of a ternary melt with initial composition Al65Cu29Co6. X-ray diffraction patterns of crushed single-grain samples are exceptionally sharp, indicating a high degree of structural order, with no evidence of secondary phases. Transmission electron micrographs also reveal sharp diffraction patterns in the even-n layers but diffuse scattering in the odd-n layers. Temperature-dependent magnetization, electrical resistivity and specific heat are measured using bars cut perpendicular and parallel to the c axis and show diamagnetic behaviour: γ ≈ 0.5 mJ mol-1 K-2, ρc(2 K) ≈ 52 μΩ cm and ρq(2 K) ≈ 283 μΩ cm.

Title: "Local order in single grain Cd-Yb icosahedral phase"

Authors: Y.Q. Wu, M.J. Kramer, and T.A. Lograsso

Contact: M.J. Kramer

Journal: Mater. Res. Soc. Symp. Proc.(2004) 805, LL7.4.

Abstract:
Single grains of icosahedral Cd84Yb16 quasicrystalline phase were characterized using high resolution transmission electron microcopy (HRTEM) technique. Image reconstruction of the obtained multiple through-focal series for both the two and five-fold axes are consistent with the local cluster structure of concentric polyhedra consisting of Cd tetrahedron (1/3 occupied icosahedron), Cd dodecahedron, Yb icosahedron and a Cd icosidodecahedron. Edge-sharing of the clusters can result in complete tiling of the 2-D projections. Simple matching rules are being investigated to construct a 3-D model.

Title: "High-temperature thermal transport properties of a single-grain decagonal Al74Ni10Co16 quasicrystal"

Authors: J.A. Barrow, B.A. Cook, P.C. Canfield, and D.J. Sordelet

Contact: D.J. Sordelet

Journal: Phys. Rev. B (2003) 68, 104202/1-104202/4.

Abstract:
Thermal transport properties have been determined for a decagonal Al74Ni10Co16 quasicrystal in the temperature range 373–873 K. Differential scanning calorimetry and a laser flash method were employed in the determination of heat capacity and thermal diffusivity, respectively. Thermal conductivity was determined from the product of diffusivity, heat capacity, and density. A high degree of anisotropy was observed between the aperiodic and periodic axes. The anisotropic heat flow is described using the thermal ellipsoid model. The model was applied to a surface oriented 45° to the major axes and substantiated from bulk measurements obtained from a sample cut along this orientation. Within this temperature range, the thermal transport of this two-dimensional quasicrystal may be described in a manner similar to anisotropic metallic single crystals.

Title: "Investigation of i-AlCuFe quasicrystals and their ω and β approximants as thermoelectric materials"

Authors: P.N. Alboni, A.L. Pope, T.M. Tritt, A.R. Ross, C.J. Jenks, and D.J. Sordelet

Contact: C.J. Jenks

Journal: Mater. Res. Soc. Symp. Proc. (2002) 691, 233-237.

Abstract:

In the search for new thermoelectric materials, quasicrystals have been investigated due to their inherently low thermal cond. Crystalline phases called approximants which are closely related to the quasicrystals, however, have largely been ignored. These approximants have similar structure, yet the periodicity of a crystal. In this paper, we have investigated an icosahedral i-AlCuFe quasicrystalline phase as well as two of its corresponding approximant phases (ω and β). Electrical and thermal transport properties of these materials are presented. The viability of the i-AlCuFe quasicrystalline system and the ω and β approximant phases as thermoelectric materials is discussed.

Title: "The electrical conductivity of single-grain Al-Pd-Re quasicrystals"

Authors: I.R. Fisher, X.P. Xie, I. Tudosa, C.W. Gao, C. Song, P.C. Canfield, A. Kracher, K. Dennis, D. Abanoz, and M.J. Kramer

Contact: P.C. Canfield

Journal: Philos. Mag. B (2002) 82, 1089-1098.

Abstract:

Systematic electrical transport data are presented for single quasicrystals in the Al-Pd-Re family across the accessible width of formation. The temperature dependence of the electrical conductivity can be accounted for in terms of weak localization and electron-electron interactions for all compositions studied, in contrast with previous studies of cast and annealed polygrain material. These results indicate that the conductivity mechanism in the Al-Pd-Re system is not dramatically different from that of other quasicrystal families.

Title: "The local atomic structure of R-Mg-Zn (R=Y, Gd, Dy and Tb)"

Authors: M.J. Kramer, S.T. Hong, P.C. Canfield, I.R. Fisher, J.D. Corbett, Y. Zhu, and A.I. Goldman

Contact: M.J. Kramer

Journal: J. Alloys Compd. (2002) 342, 82-86.

Abstract:

The rare earth element in the R–Mg–Zn system provides a unique probe of the atomic structure of a face-centered icosahedral (fci) quasicrystal (qc). Unlike many of the other ternary and higher component qc systems, the compound around R8Mg42Zn50 allows for the substitution of one of its main components (R=Y, Er, Ho, Dy and Tb) without any appreciable change in its qc structure (space group or quasi-unit cell dimension). The large atomic number difference between Y and the heavy rare earth elements affords large differences in the scattering cross-sections for electrons, neutrons and X-rays. Using high quality flux grown single grains with resolution limited diffraction peaks, the local atomic structure was probed with a variety of complimentary techniques. The differences in the pair distribution function (PDF) due to loss of the anti-ferromagnetic ordering of the Tb between 4.2 and 30 K was used to probe the R site. High resolution TEM and single grain XRD have been used to determine the cluster structures. Results of this work suggest that there are local clusters in this fci compound consisting of five concentric polyhedra with 124 atoms: an icosahedron, dodecahedron, icosahedron, bucky-ball and a dodecahedron, similar to previous work. However, the HRTEM results indicate that the local structure consists only of these five shells which may edge share with the next cluster. Based on this atomic arrangement, the PDF results are consistent with R atoms partially occupying the vertices of the outer icosahedron and dodecahedron.

Title: "Absolute structure-factor measurements of an Al-Pd-Mn quasicrystal"

Authors: Y. Zhang, R. Colella, S. Kycia, and A.I. Goldman

Contact: A.I. Goldman

Journal: Acta Cryst. A (2002) 58, 385-390.

Abstract:

A number of X-ray reflections from an icosahedral quasicrystal Al-Pd-Mn have been measured with great accuracy on an absolute basis by making use of Bragg-case diffraction. Since the specimen had high crystal quality, the dynamical theory was used for analyzing the results and to extract structure factors from measured integrated intensities. Good agreement was found between theory and experiment for strong reflections. Anomalous transmission was found to be strong in the `good' regions of the quasicrystalline specimen and it was measured on an absolute basis, but the small residual strains present in the specimen prevented an accurate comparison between theory and experiment. A detailed discussion is presented on the parameters that mostly affect anomalous transmission in relationship to the adopted structural model.

Title: "Icosahedral quasicrystal Al71Pd21Mn08 and its ξ' approximant: Linear expansivity, specific heat, magnetic susceptibility,electrical resistivity, and elastic constants"

Authors: C.A. Swenson, I.R. Fisher, N.E. Anderson, Jr., P.C. Canfield, and A. Migliori

Contact: P.C. Canfield

Journal: Phys. Rev. B (2002) 65, 184206/1-184206/13.

Abstract:

Linear thermal expansivity (α, 1–300 K), heat capacity (Cp, 1–108 K), magnetic susceptibility (χ, 1–300 K), and electrical resistivity (ρ, 1–300 K) measurements are reported for a single-grain i-Al71Pd21Mn08 quasicrystal and its Al72Pd25Mn03 approximant, and 300 K elastic constants for the quasicrystal. The approximant α (αAp) and Cp (CpAp) data show “metallic” behavior, while the previously reported onset of a transition to a spin-glass state (Tf<1.8 K) dominates αQ and CpQ below 11 K. CpAp and CpQ superimpose above 16 K when plotted vs T/Θ0 using the experimental Θ0Ap=455(3) K and an adjusted Θ0ApQ=480(4) K. The 300 K elastic constants extrapolated to T=0 give Θ0Qel=505(1) K, suggesting that the normalization is valid only above 16 K. The lattice contribution to CpAp (and, indirectly, CpQ) shows strong (unique) deviations from Debye-like behavior (+3% at 0.84 K for the CpAp data fit). The various Grüneisen parameters (Γ) that are calculated from these data all are positive and normal in magnitude except for a large limiting approximant lattice value, Γ0Aplat=11.3, which may be related to the large dispersion effects in Cp. For the approximant, the combination of anisotropic and large resistivities, a small diamagnetic susceptibility, and a “large” linear (electronic) contribution to CpApAp=0.794 mJ/mol K2) suggests the existence of a pseudogap in the electronic density of states. The unusually large, highly volume dependent, dispersion at low temperatures for the quasicrystal and its approximant are not consistent with inelastic neutron scattering and other data, and raise questions about the role of phonons in quasicrystals. The present 300 K resistivities can be used with a published correlation to estimate γQ≈0.25 mJ/mol K2.

Title: "Transport properties of icosahedral quasicrystal Al72Pd19.5Mn8.5"

Authors: A. Bilusic, Z. Budrovic, A. Smontara, J. Dolinsek, P.C. Canfield, and I.R. Fisher

Contact: P.C. Canfield

Journal: J. Alloys Compd. (2002) 342, 413-415.

Abstract:

We present measurements of the thermoelectrical properties of polygrain icosahedral quasicrystal Al72Pd19.5Mn8.5 in the temperature range 10-300 K. Electrical resistivity has a relatively low room temperature value, ρR.T.=1.2 mΩ cm, by lowering the temperature it shows an increase with a maximum value at 120 K. Thermoelectric power is positive in the whole temperature ranges with a quite high room temperature value, SR.T.=70 μV/K. Thermal conductivity shows a maximum at 30 K, and a broad minimum around 125 K. The room temperature value is KR.T.=3.4 W/mK. The appearance of the maximum in thermal conductivity at 30 K comes mainly from structural scattering, while at temperatures above 120 K from the contribution of the localized phonon state.

Title: "Electronic structure of quasicrystals deduced from auger and photoelectron spectroscopies"

Authors: V. Fournée, J.W. Anderegg, A.R. Ross, T.A. Lograsso, and P.A. Thiel

Contact: P.A. Thiel

Journal: J. Phys.: Condens. Matter (2002) 14(10), 2691-2703.

Abstract:

Specific features in the electronic structure of Al-transition metal quasicrystals are analyzed by a combination of Auger and x-ray photoelectron spectroscopies. We first demonstrate that different degrees of asymmetry in the transition metals' 2p core-level lineshape observed across different types of surface structure correspond to variations in the density of states at the Fermi level, DOS(EF). Using this effect, we explore the controversial issue of whether the quasicrystalline, decagonal AlNiCo system is electronically stabilized. We find strong evidence for the presence of a reduced DOS(EF) in this system, as expected for electronically stabilized compounds, and as observed in the quasicrystalline, icosahedral AlPdMn and AlCuFe alloys. Finally, qualitative information on the nature of the electronic states in quasiperiodic structures extracted from the core-valence-valence Auger lines are presented and discussed.

Title: "Analysis of gas phase clusters made from laser-vaporized icosahedral Al-Pd-Mn"

Authors: J.A. Barrow, E.F. Rexer, D.J. Sordelet, M.F. Besser, C.J. Jenks, S.J. Riley, and P.A. Thiel

Contact: P.A. Thiel

Journal: Mater. Res. Soc. Symp. Proc. (2001) 643, K5.4.1-K5.4.5

Abstract:

Laser vaporization of an icosahedral Al-Pd-Mn sample with detection by time-of-flight mass spectrometry is used to probe metal clusters made from the alloy. After sample vaporization, clusters form by gas aggregation and may contain several to hundreds of atoms. Multi-photon ionization/fragmentation of these clusters yields mass spectra showing many cluster sizes with enhanced intensity. Clusters are identified at masses near those of pseudo-Mackay and Bergman clusters; however, these clusters do not appear special relative to neighboring clusters. Results of this study and its relationship to the proposed cluster structures in quasicryst. materials are discussed.

Title: "Where are the atoms in quasicrystals? Experimental and theoretical studies of ternary and quaternary approximants"

Authors: G.J. Miller, C.-S. Lee, and W.-J. Tsai

Contact: G.J. Miller

Journal: Mater. Res. Soc. Symp. Proc. (2001) 643, K3.1.1-K3.1.11

Abstract:

Problems concerning complete structural characterization of quasicrystals involve locating the atomic positions as well as determing the distribution of elements at each site. Quasicrystalline approximants provide models for potential building units of quasicrystals, but a clear determination of the elemental decorations in such approximants remains incomplete. The experimental and theoretical studies of new quaternary Bergman phases in the Li-Mg-Zn-Al system and a new quasicrystalline approximant Li10Mg6Zn31Al3 (A16M34-type) are reported. A theoretical model using averaged Mulliken populations provides means to track the segregation of elements and vacancies at different sites as a function of valence electron concentration. As the Li content decreases, vacancies begin to occur at a specific site in the Bergman structure. The new approximant demonstrates how a truncated tetrahedra can play an important role in forming clusters with possible fivefold symmetry in quasicrystalline structures.

Title: "Li10Mg6Zn31Al3: A new intermetallic phase containing building blocks for decagonal quasicrystals "

Authors: C.-S. Lee and G.J. Miller

Contact: G.J. Miller

Journal: Angewandte Chemie International Edition (2001) 40(24), 4740-4742.

Abstract:

None

Title: "Structure and bonding around the zintl border"

Authors: G.J. Miller, C.-S. Lee, and W. Choe

Contact: G.J. Miller

Book: Inorganic Chemistry Highlights (2002), Ed. Meyer, G., Naumann, D. and L. Wesemann

Title: "Experimental and theoretical studies of elemental site preferences in quasicrystallline approximants (R-phases) within the Li-Mg-Zn-Al system "

Authors: C.-S. Lee and G.J. Miller

Contact: G.J. Miller

Journal: Inorg. Chem. (2001) 40, 338-345.

Abstract:

A series of ternary and quaternary R-phase compounds in the Li-Mg-Zn-Al system are synthesized from pure elements in sealed Ta tubes with starting compositions based on the suggestions from electronic structure calculations using relative Mulliken populations to quantify the site preferences for the various elements. Single-crystal structural analyses reveal new R-phase compounds with various Li/Mg and Zn/Al ratios. The space group of all compounds is Im3 (No. 204). Five quaternary phases [Li1.00(1)Mg0.63(2)Zn1.23(1)Al2.14(1) (1), a = 14.073(3) Å; Li1.00(1)Mg0.63(1)Zn1.42(1)Al1.96(1) (2), a = 14.088(3) Å; Li1.01(1)Mg0.62(1)Zn1.31(1)Al2.06(1) (3), a = 14.096(5) Å; Li1.03(1)Mg0.60(1)Zn1.78(3)Al1.59(3) (4), a = 13.993(5) Å; Li0.78(2)Mg0.85(2)Zn2.47(1)Al0.94(1) (5), a = 13.933(2) Å] and four ternary compounds [Li1.63Zn0.81(1)Al2.56(1) (6), a = 14.135(3) Å; Li1.63Zn1.42(1)Al1.95(1) (7), a = 13.966(5) Å; Li1.63Zn1.59(1)Al1.78(1) (8), a = 13.947(2) Å; and Li1.63Zn1.77(1)Al1.60(1) (9), a = 13.933(4) Å] are identified. The crystal structure exhibits an Al/Zn (M sites) network constructed from M12 icosahedra and M60 buckyball-type clusters. Li/Mg atoms (A sites) fill cavities within the Al/Zn network to give pentagonal dodecahedra (A20). The site-potential studies (relative Mulliken populations) indicate two groups of atomic sites (positively and negatively polarized), which are consistent with the single-crystal studies. Further differentiation of site potentials among the various electropositive sites leads to segregation of Li and Mg, which is also verified experimentally. The analysis of relative Mulliken populations in an intermetallic framework provides a useful method for elucidating elemental site preferences when diffraction techniques cannot unequivocally solve the site preference problem.

Title: "About the Al 3p density of states in Al-Cu-Fe compounds and its relation to the compound stability and apparent surface energy of quasicrystals"

Authors: E. Belin-Ferré, J.M. Dubois, V. Fournée, P. Brunet, D.J. Sordelet, and L.M. Zhang

Contact: D.J. Sordelet

Journal: Mater. Sci. Eng., A (2000) 294-296, 818-821.

Abstract:

We report the characteristic parameters of the Al 3p densities of states gained from a thorough study of many Al–Cu(–Fe) intermetallics including quasicrystalline and approximant phases using X-ray emission spectroscopy. These parameters are the density of states at the Fermi energy EF, the average binding energy due to Al 3p states and the second moment of their distribution. Hence, we demonstrate that the contribution to the compound stability arising from localization of Al 3p states via the Hume-Rothery mechanism is maximum for the icosahedral state. We also show that Al-transition metal sp-d hybridization is enhanced in the presence of icosahedral order. Finally, we confirm the already pointed out relationship between depth of the pseudo-gap at EF and apparent surface energy of the samples.

Title: "Heat capacities of icosahedral and hexagonal phases of Zn-Mg-Y systems"

Authors: A. Inaba, H. Takakura, A.-P. Tsai, I.R. Fisher, and P.C. Canfield

Contact: P.C. Canfield

Journal: Mater. Sci. Eng., A (2000) 294-296, 723-728.

Abstract:

Heat capacity measurements have been performed in the temperature range 4–300 K for an icosahedral phase of Zn–Mg–Y alloy (Zn55Mg35Y10) and the related crystalline phases, a hexagonal phase (Zn65.2Mg27.9Y6.9) and the Laves phase of MgZn2, to study the feature of lattice vibrations in quasicrystals. A single quasicrystal of Zn56.8Mg34.6Y8.7 was also investigated for comparison. The vibrational density of states is delineated in terms of the temperature dependence of the apparent Debye temperature (ΘD) on a reduced basis using the limiting value at high temperature (Θ). A deeper minimum (ΘD~0.82) is observed at substantially lower temperatures (T/Θ∞~0.055) in the quasicrystals than in the crystals, which suggests significant enhancement of the density of states at the corresponding energies. The fact is compatible to that obtained previously for Al–Cu–Ru, Al–Pd–Re and Al–Pd–Mn systems. The presence of some defects or inhomogeneity in quasicrystals might be responsible for the anharmonic lattice vibrations.

Title: "Electrical resistivity, thermopower, and thermal conductivity of single-grained (Y, Tb, Ho, Er)-Mg-Zn icosahedral quasicrystals"

Authors: K. Gianno, A.V. Sologubenko, M.A. Chernikov, H.R. Ott, I.R. Fisher, and P.C. Canfield

Contact: P.C. Canfield

Journal: Mater. Sci. Eng., A (2000) 294-296, 715-718.

Abstract:

We report on measurements of the temperature dependence of the electrical resistivity ρ, the thermopower S, and the thermal conductivity λ of single grained RE-Mg-Zn (RE=Y, Tb, Ho, Er) icosahedral quasicrystals between 5 and 300 K. The resistivity of all four samples is very weakly temperature dependent with a negative slope dρ/dT. The S/T versus temperature curves exhibit a maximum at temperatures between 12 and 15 K. This feature is observed for all here investigated quasicrystalline materials. The appearance of a maximum in the thermal conductivity of (Y, Ho, Er)-Mg-Zn, and a plateau in that of Tb-Mg-Zn is ascribed to a power-law temperature dependence of the mean free path of delocalized quasilattice excitations at intermediate temperatures. A progressive suppression of the maximum in the thermal conductivity data as the de Gennes factor increases indicates for a coupling of the spin system to the lattice.

Title: "Diffusion of 57Co in decagonal Al-Ni-Co quasicrystals"

Authors: C. Khoukaz, R. Galler, H. Mehrer, P.C. Canfield, I.R. Fisher, and M. Feuerbacher

Contact: P.C. Canfield

Journal: Mater. Sci. Eng., A (2000) 294-296, 697-701.

Abstract:

Self-diffusion of 57Co in decagonal Al–Ni–Co single quasicrystals was studied for both principal directions as a function of the temperature by means of the radiotracer method. In combination with serial sectioning, diffusivities were measured over a large temperature range from 732 to 1273 K. Below about 1120 K diffusion is described by an Arrhenius behaviour along both the periodic and the quasiperiodic directions. The magnitude of the activation enthalpies and pre-exponential factors support a vacancy-type diffusion mechanism. A small anisotropy of diffusion which is temperature-dependent but never exceeds 30% was detected. Above 1120 K, a kink in the Arrhenius curve is observed. We attribute this behaviour to a phase transition from the decagonal basic Co-rich phase to an ordered modification.

Title: "Phason strain and structural perfection in the R-Mg-Zn icosahedral phases"

Authors: A. Letoublon, I.R. Fisher, T.J. Sato, M. De Boissieu, M. Boudard, S. Agliozzo, L. Mancini, J. Gastaldi, and P.C. Canfield

Contact: P.C. Canfield

Journal: Mater. Sci. Eng., A (2000) 294-296, 127-130.

Abstract:

The structural perfection of eight samples of icosahedral Zn–Mg–R (R=Y, Ho and Tb) single grains has been studied by high resolution X-ray diffraction. Four samples present a systematic peak shift proportional to Qper characteristic of a linear phason strain. Two other samples present a peak splitting proportional to Qper . Only two samples had their Bragg peak position corresponding to the ideal one, with a width increasing linearly with Qper . The perfection of one of these last two samples was investigated by synchrotron monochromatic X-ray topography. It was found to be a microstructure similar to the one exhibited by conventional crystals grown by the same technique (flux-growth).

Title: "Magnetic properties of icosahedral R-Mg-Zn quasicrystals (R=Y, Tb, Dy, Ho and Er)"

Authors: I.R. Fisher, Z. Islam, J. Zarestky, C. Stassis, M.J. Kramer, A.I. Goldman, and P.C. Canfield

Contact: P.C. Canfield

Journal: J. Alloys Compd. (2000) 303-304, 223-227.

Abstract:

Large (up to 0.5 cm3) single grains of icosahedral R-Mg-Zn quasicrystals (R = Y, Tb, Dy, Ho and Er) have been grown via a self-flux technique. The samples have a composition of approximately R9Mg34Zn57, and are extremely well-ordered, with little or no evidence of phason strain. These samples have allowed a detailed study of the magnetic behavior of local 4f moments in a quasiperiodic environment. Neutron scattering experiments using powdered single-grains show no evidence for long range magnetic order in the R-Mg-Zn quasicrystals. However, magnetization and magnetic susceptibility measurements indicate a spin-glass state, with freezing temperatures Tf= 5.8, 3.6, 2.0 and 1.3 K for R = Tb, Dy, Ho and Er respectively. Deviations from a Curie-Weiss temperature dependence of the susceptibility are small, and only occur for temperatures up to 5 K above Tf, indicating the absence of any significant cluster glass behavior. The rare earth dilution series (Y1-xGdx)-Mg-Zn have lower freezing temps. than (Y1-xTbx)-Mg-Zn, despite the larger de Gennes factor of Gd3+ over Tb3+, indicating that crystal electric fields play a significant role in the freezing phenomenon. This difference between Heisenberg and non-Heisenberg moments is further explored via several (Gd1-xRx)-Mg-Zn pseudo-ternary quasicrystal series.

Title: "Where are the elements in complex aluminides? An experimental and theoretical investigation of the quasicrystalline approximants, Mg2-y(ZnxxAl1-x)3+y"

Authors: C.-S. Lee and G.J. Miller

Contact: G.J. Miller

Journal: J. Am. Chem. Soc. (2000) 122(20), 4937-4947.

Abstract:

The first detailed investigation of the crystalline R-phases in the Mg-Zn-Al ternary system is reported and will assist with the interpretation and understanding of similar quasicrystalline phases in this phase diagram. Although Mg32(Zn,Al)49 was originally reported by Bergman and Pauling (1956), some details regarding its structure and atomic arrangement remain to be solved. Single-phase product can be obtained from reaction compositions Mg1.63(ZnxAl1-x)3.37 with 0.35 ≤ x ≤ 0.65. A combination of single-crystal X-ray diffraction, powder neutron diffraction, energy dispersive spectroscopy, densities, and theoretical modeling is needed to elucidate a complete structural model for these phases. Single-crystal X-ray diffraction gave an R-phase structure (space group Im3, Z = 32) for specimens of Mg1.76(1)Zn1.46(6)Al1.65(3) (a = 14.364(3) ), Mg1.75(1)Zn1.80(2)Al1.31(1) (a = 14.212(1) ), and Mg1.73(1)Zn2.46(6)Al0.69(3) (a = 14.131(1) ). Neutron powder diffraction on three similar bulk specimens gave Mg1.76(1)Zn1.34(5)Al1.76(5) (a = 14.2697(1) ), Mg1.75(1)Zn1.76(5)Al1.34(6) (a = 14.1804(1) ), and Mg1.73(1)Zn2.06(3)Al1.09(3) (a = 14.11247(6) ). For all phases in the Mg-Zn-Al system, one crystallographic site (M4) has ca. 33% vacancies and shows a mixture of Mg and Zn atoms. Mg atoms occur next to vacancies on these sites. Theoretical calculations are used to explain the observed phase width involving Zn and Al, the trend in observed site occupancies, and occurrence of vacancies in this structure. A range of nonbonding states near the Fermi level accounts for the phase width and allows a range in valence electron concentration between 2.07 and 2.48 for the existence of this structure. Valence electron concentrations in Mg-Zn-Al, however, necessitate the occupation of some metal-metal antibonding orbitals, which creates a driving force for vacancies. Since Mg can replace atoms in the (Zn,Al) framework, the R-phases are true intermediates between Zintl phases on one hand and Hume-Rothery intermetallic phases on the other.

Title: "Low-temperature transport, thermal, and optical properties of single-grain quasicrystals of icosahedral phases in the Y-Mg-Zn and Tb-Mg-Zn alloy systems"

Authors: M.A. Chernikov, S. Paschen, E. Felder, P. Vorburger, B. Ruzicka, L. Degiorgi, H.R. Ott, I.R. Fisher, and P.C. Canfield

Contact: P.C. Canfield

Journal: Phys. Rev. B (2000) 62, 262-272.

Abstract:

We present a comprehensive series of results of electrical transport (electrical conductivity, magnetoconductivity, Hall effect), thermal (specific heat), and optical (reflectivity) measurements in varying temperatures ranges between 1.5 and 300 K on high-quality single-grain quasicrystals of icosahedral Y-Mg-Zn. This data set is augmented by the specific-heat and optical-reflectivity data obtained from a single-grain quasicrystal of icosahedral Tb-Mg-Zn. For Y-Mg-Zn, both the electrical conductivity σ(T) and magnetoconductivity δσ(H) may be described by calculations considering quantum interference effects. A detailed comparison of the weak-localization contributions to σ(T) and δσ(H) with our experimental data provides estimates of the inelastic and spin-orbit relaxation rates. The inelastic relaxation rate is found to be proportional to T3. The dominant contributions to the optical conductivity σ1(ω) spectrum, obtained from the reflectivity R(ω) data in the frequency range between 16 and 9.7 x 104 cm-1, are a strong Drude feature at low frequencies and a prominent absorption signal centered at approximately 6 x 103 cm-1. A comparison of the spectral weight of the Drude contribution to σ1(ω) with the magnitude of the linear-in-T term γT of the low-temperature specific heat Cp(T) yields the itinerant charge-carrier density ni=7.62 x 1021 cm-3 or 0.13 charge carriers per atom. The low ni value is corroborated by the results of the Hall effect measurements. For Tb-Mg-Zn, the optical conductivity σ1(ω) spectrum reveals features similar to those of Y-Mg-Zn. The low-temperature specific heat Cp(T) of Tb-Mg-Zn is strongly influenced by a spin-glass-type freezing of Tb moments and by crystal-electric-field effects.

Title: "Low-temperature thermal conductivity of a single-grain Y-Mg-Zn icosahedral quasicrystal"

Authors: K. Gianno, A.V. Sologubenko, M.A. Chernikov, H.R. Ott, I.R. Fisher, and P.C. Canfield

Contact: P.C. Canfield

Journal: Phys. Rev. B (2000) 62, 292-300.

Abstract:

The authors report measurements of the thermal conductivity κ(T) of a single-grain icosahedral Y8.6Mg34.6Zn56.8 in the temperature range between 0.1 and 300 K. The quasilattice thermal conductivity κph increases monotonically with T by three orders of magnitude between 0.1 and 23 K. Above 23 K, κph(T) decreases substantially with increasing temperature, typical for high-quality single grain quasicrystals. The decrease ends in a minimum at approximately 140 K. The interpretation of our data is based on a Debye-type relaxation time approximation. At very low temperatures, the corresponding fit reveals that the phonon mean free path is of the order of the smallest sample dimension, while at high temperatures, a power-law decrease of the phonon scattering time with increasing temperature is evident from the effect of structural scattering on the mean free path of itinerant quasilattice excitations. The behavior of κph(T) at intermediate temperatures may best be fit by assuming the existence of stacking-fault-like phonon scatterers. No clear evidence for a scattering of phonons by tunneling states has been observed. If compared to previously reported measurements of the thermal conductivity of quasicrystals, these data indicate the very high structural perfection of this quasiperiodic material.

Title: "Plastic deformation of icosahedral Zn-Mg-Dy single quasicrystals"

Authors: M. Heggen, M. Feuerbaher, P. Schall, H. Klein, I.R. Fisher, P.C. Canfield, and K. Urban

Contact: P.C. Canfield

Journal: Philos. Mag. Lett. (2000) 80, 129-136.

Abstract:

Plastic deformation experiments were performed on Zn-Mg-Dy icosahedral single quasicrystals at temperatures between 490 and 530° C and at strain rates of 10-5- and 10-6 s-1. The stress-strain curves show strong yielding followed by a steady-state regime with a const. flow stress level up to strains of about 8%. Thermodynamic activation parameters of the deformation process were determined and are discussed in comparison with those found for icosahedral Al-Pd-Mn. Microstructural investigations by TEM on deformed samples were performed and indicate a deformation mechanism mediated by dislocations.

Title: "Solute diffusion of Ni in icosahedral Al-Pd-Mn quasicrystals"

Authors: T. Zumkley, H. Nakajima, and T.A. Lograsso

Contact: T.A. Lograsso

Journal: Philos. Mag. A (2000) 80(5), 1065-1074.

Abstract:

This paper presents the results of an experimental study of Ni solute diffusion in the single-grain icosahedral quasicrystalline compound Al70Pd21Mn9. Ni solute diffusion coefficients were measured over a temperature range from 699 to 1074 K. The radiotracer technique in combination with serial sectioning of the diffusion specimens was used to determine concentration depth profiles. No deviation from Arrhenius behavior was detected in the temperature range covered by the present experiments. The results are compared with the available diffusion data on quasicrystals and on diffusion in Al and various diffusion mechanisms proposed for quasicrystals are discussed. The most striking fact is that the diffusion of Ni and the diffusion of other transition-metal elements are found to be much slower than diffusion of non-transition-metal elements such as Ge and Zn in i-(Al-Pd-Mn) quasicrystalline alloys. Moreover, the activation enthalpies of diffusion of the transition-metal elements turned out to be considerably higher than those measured for the non-transition-metal elements. The present study shows that the diffusion of Ni atoms is likely to proceed by a vacancy mechanism via Al and Pd sites.

Title: "Dynamical diffraction and x-ray standing waves from atomic planes normal to a twofold symmetry axis of the quasicrystal AlPdMn"

Authors: T. Jach, Y. Zhang, R. Colella, M. de Boissieu, M. Boudard, A.I. Goldman, T.A. Lograsso, D.W. Delaney, and S. Kycia

Contact: A.I. Goldman

Journal: Phys Rev. Lett. (1999) 82(14), 2904-2907.

Abstract:

We have observed dynamical diffraction in the [[(024024) and [[(046046) reflections of the icosahedral quasicrystal AlPdMn in the back-reflection geometry (qB = 90°). The x-ray fluroescence from the Al and Pd atoms exhibits strong standing wave behavior, similar to that observed in crystalline meterials. The data indicate a long-range order of each species of atoms, with the coherent positions attributable to distributions of the Al and Pd, which we compare to a centrosymmetric model. We observe deviations from the model which imply small departures from inversion symmetry along the twofold symmetry axis and from the expected coherent fractions for Al.

Title: "Magnetic and transport properties of single-grain R-Mg-Zn icosahedral quasicrystals (R = Y, (Y1-xGdx), (Y1-xTbx), Tb, Dy, Ho and Er)"

Authors: I.R. Fisher, K.O. Cheon, A.F. Panchula, P.C. Canfield, M. Chernikov, H.R. Ott, and K. Dennis

Contact: A.I. Goldman

Journal: Phys. Rev. B (1999) 59, 308-321.

Abstract:

We report measurements of the dc magnetisation, the low-field ac magnetic susceptibility and the electrical resistivity of large (up to 0.5 cm3) single-grain samples of icosahedral R-Mg-Zn (R = Y, Tb, Dy, Ho and Er). The dc magnetisation and ac magnetic susceptibility data both indicate that icosahedral Tb-Mg-Zn and Dy-Mg-Zn undergo a transition to a spin-glass state at Tf = 5.8 and 3.6 K respectively, while low-temperature ac susceptibility measurements show that Tf = 1.95 and 1.3 K for Ho-Mg-Zn and Er-Mg-Zn respectively. For the series of solid solutions Y1-xTbx)-Mg-Zn, the freezing temperature Tf varies approximately as x2/3. The (Y1-xGdx)-Mg-Zn solid solutions have lower Tf values than (Y1-xTbx)-Mg-Zn for the same magnetic rare earth concentraions (x), indicating that local moment, anisotropy caused by crystalline electric field effects plays a significant role in increasing Tf. On the other hand, angular dependent studies show that the dc mangetisation for T > Tf is isotropic within the experimental uncertainty. The electrical resistivity ρ(T) of the single-grain samples is only weakly temperature dependent, with a small, negative dρ/dT. Absolute values of the resistivity fall in the range between 150 and 200 μΩ cm, which is distinctly lower than the values previously reported for other thermodynamically stable icosahedral quasicrystals.

Title: "A reinvestigation of long-range magnetic ordering in icosahedral Tb-Mg-Zn"

Authors: Z. Islam, I.R. Fisher, J. Zarestky, P.C. Canfield, C. Stassis, and A.I. Goldman

Contact: A.I. Goldman

Journal: Phys. Rev. B (1998) 57(18), R11047-R11050.

Abstract:

The authors present results of a study of possible magnetic ordering in the icosahedral phase of Tb-Mg-Zn probed by bulk magnetization measurements and neutron diffraction. Measurements on both crushed single grains and cast polycryst. samples of Tb-Mg-Zn were performed. Magnetization measurements on both samples reveal only a spin-glass-like transition at approximately 5.8 K while neutron diffraction from the crushed single grains reveals only short-range magnetic ordering at low temperatures, with no evidence of the long-range magnetic ordering reported by Charrier et al. (1997). Likewise, the cast polycrystalline samples exhibit primarily diffuse magnetic scattering at low temperature, but at least one relatively sharp diffraction peak was observed. The authors' results indicate that for single grain samples there is no long-range magnetic ordering and that, at best, the magnetic ordering in these quasicrystalline alloys is not very robust.

Title: "Diffusion of 54Mn and 68Ge in single grain icosahedral Al70Pd21.5Mn8.5 quasicrystals"

Authors: W. Sprengel, T.A. Lograsso, and H. Nakajima

Contact: T.A. Lograsso

Journal: Diffus. Defect Data, Pt. A (1997) 143-147, 849-854.

Abstract:

The diffusivity of 54Mn and 68Ge in single grain icosahedral Al70Pd21.5Mn8.5 quasicrystals was determined by a precision grinding technique. At 870-1100 K the temperature dependence of the Mn and Ge diffusivity can be described by Arrhenius equations with an activation energy Q = (181 +/- 0. 5) kJ/mol and a pre-exponential factor D0 = 3.4 times. 10-4 m2/s for Mn, and Q = (148 +/- 0. 7) kJ/mol and D0 = 1.4 .perp. 10-4 m2/s for Ge, respectively. The experimental results are discussed together with diffusion mechanisms proposed for quasicrystals from theorertical considerations.

Title: "Mn self-diffusion in single grain icosahedral Al70Pd21.5Mn8.5 quasiccrystals"

Authors: W. Sprengel, T.A. Lograsso, and H. Nakajima

Contact: T.A. Lograsso

Journal: Phys Rev. Lett. (1996) 77(26), 5233-5236.

Abstract:

The self diffusivity of 54Mn in single grain icosahedral Al70Pd21.5Mn8.5 >quasicrystals has been determined by a precision grinding technique. In the range from 870 to 1093K the temperature dependence of the Mn self-diffusivity D follows the Arrhenius equation with an activation energy of Q = (180.8+/-4.6) kJ mol-1 and a pre-exponential factor of D0 = 3.4x10-4 m2 s-1. The experimental results are discussed together with diffusion mechanisms proposed for quasicrystals from theoretical considerations.

Title: "Photoelectron spectra of an AlPdMn quasicrystal and a related crystalline alloy"

Authors: C.J. Jenks, S.-L. Chang, J.W. Anderegg, P.A. Thiel, and D.W. Lynch

Contact: C.J. Jenks

Journal: Phys. Rev. B (1996) 54, 6301-6306.

Abstract:

Photoelectron spectra of a five-fold quasicrystalline alloy, Al70Pd21Mn9, and a related cubic alloy, Al60Pd25Mn15, reveal two noteworthy features. The first is that the Pd 3d lines fall at binding energies which are 2.2 eV higher than in pure Pd. A similar shift is observed for Pd in other alloys. The second noteworthy feature is that the Mn 2p3/2 line is very sharp in the quasicrystal. Fitting the experimental peaks with a Doniach-Sunjic lineshape suggests that the position and density of Mn states near EF is very sensitive to the structural and/or chemical environment of Mn in the alloys, and that this accounts for the shape of the 2p3/2 Mn line. The sharpness of the Mn line may be a fingerprint of the quasicrystalline phase within the AlPdMn family.

Title: "Electronic band dispersion and pseudogap in quasicrystals: Angular-resolved photoemission studies on icosahedral Al70Pd21.5Mn8.5"

Authors: X. Wu, S.W. Kycia, C.G. Olson, P.J. Benning, A.I. Goldman, and D.W. Lynch

Contact: D.W. Lynch

Journal: Phys. Rev. Lett. (1995) 75(4), 4540-4543.

Abstract:

Angular-resolved photoelectron spectra from the fivefold surface of ingle-grain icosahedral Al70Pd21.5Mn8.5 exhibit a quasiperiodic dispersion of 300 meV at 2.3 eV binding energy. Low energy electron diffraction studies confirm quasicrystalline order at the surface. A distinct pseudogap feature is observed with a density of states near the Fermi level decreasing as a square-root power law.

Title: "Optic modes in the AlPdMn icosahedral phase"

Authors: M. Boudard, M. de Boissieu, S. Kycia, A.I. Goldman, B. Hennion, R. Bellissent, M. Quilichini, R. Currat, and C. Janot

Contact: A.I. Goldman

Journal: J. Phys.: Condens. Matter (1995) 7, 7299-7308.

Abstract:

The dynamics of the icosahedral phase AlPdMn have been reinvestigated on a centimetre-size single grain using inelastic neutron scattering measurements. As previously found, well defined acoustic modes are observed close to strong Bragg reflections. Transverse acoustic phonons remain resolution limited for wavevectors smaller than 0.35 Å-1 and a broadening occurs for larger wavevectors. Beside acoustic modes, the scattering function S(Q, ω) shows an extremely rich structure. A series of broad (1 THz) dispersionless excitations appears with energies close to 1.8, 3, 4 and 5.5 THz. These excitations were found at different points in reciprocal space and present intensity variation. Some of these 'optic' bands might be associated with crossings at quasi-Brillouin zone boundaries. The system has also been investigated at high temperatures up to 800 °C. Beyond a 10% reduction of the sound velocity, results are identical to those obtained at room temperature. In particular the transverse acoustic modes remain resolution limited for wavevectors smaller than 0.35 Å-1.

Title: "A new cluster concept and its application to quasi-crystals of the i-AlMnSi family and closely related crystalline structures"

Authors: G. Kreiner and H.F. Franzen

Contact: H.F. Franzen

Journal: J. Alloys Compd. (1995) 221, 15-36.

Abstract:

A number of complex metal alloys, including the structure types of λ-Al4Mn, Al10Mn3, Al5Co2, BHf9Mo4, C7Co6W20, Zr6Ni6TiSiOx, Al23V4, μ-Al4.12Mn, Al13Cr4Si4, NiTi2, CFe3W3, Al10V, Al18Cr2Mg3, Al45V7, Al31Mn6Ni2, Al11Mn3Zn2, Al9Mn2Si, Hf54Os17, Rh13Sc57, Ag17Mg54, GaMnSc9, Mg44Rh7, Na6Tl, Mg6Pd and Fe11Zn39, representing several hundred different intermetallic structures, are discussed by means of a new cluster concept. The basic building block of the cluster concept consists of 36 atoms in three vertex-connected icosahedra with bi-capped pentagonal coordination polyhedra for the link atoms. Togehter with a small set of connection types, the structures mentioned above can then be described as being composed of only one building block. This approach enables a good visualization of the structures, points out the similarities of the structural principles between different structures, and is helpful in the structure solution of complex metal alloys. Quasi-crystals for the icosahedral i-AlMnSi and i-TiTM (TM, transition metal) classes are closely related to phases of the above family by similarities in the diffraction pattern and by phase formation. Therefore, we suggest that the structure of the quasi-crystals of both classes have similar underlying structural principles, so contain the basic building block mentioned above. A model for the structure of the quasi-crystals, based on a zonohedral tiling of the Penrose local isomorphism class with four different unit cells, is discussed. The application of the rules of the cluster concept yields atomic decoration of the unit cells with reasonable chemistry in terms of local coordination polyhedra and their three-dimensional arrangement.

Title: "Crystal structure of λ-MnAl4"

Authors: H.F. Franzen and G. Kreiner

Contact: H.F. Franzen

Journal: J. Alloys Compd. (1995) 202, L21-L23.

Abstract:

In this letter we report the preparation of large single crystals, the structure solution, and the crystal structure of λ-MnAl4.

Title: "NMR and NQR study of the electronic and structural properties of Al-Cu-Fe and Al-Cu-Ru quasicrystals"

Authors: A. Shastri, F. Borsa, D.R. Torgeson, J.E. Shield, and A.I. Goldman

Contact: A.I. Goldman

Journal: Phys. Rev. B (1994) 50, 15651-15667

Abstract:

27Al and 63,65Cu NMR measurements are reported for powder samples of stable Al-Cu-Fe and Al-Cu-Ru icosahedral quasicrystals and their crystalline approximants, and for an Al-Pd-Mn single-grain quasicrystal. Furthermore, 27Al NQR spectra at 4.2 K have been observed in the Al-Cu-Fe and Al-Cu-Ru samples. From the quadrupole-perturbed NMR spectra at different magnetic fields, and from the zero-field NQR spectra, a wide distribution of local electric-field gradient (EFG) tensor components and principal-axis-system orientations was found at the Al site. A model EFG calculation based on a 1/1 Al-Cu-Fe approximant was successful in explaining the observed NQR spectra. The average local gradient is largely determined by the p-electron wave function at the Al site, while the width of the distribution is due to the lattice contribution to the EFG. Comparison of 63Cu NMR with 27Al NMR shows the EFG distribution at the two sites is similar, but the electronic contribution to the EFG is considerably smaller at the Cu site, in agreement with a more s-type wave function of the conduction electrons. The overall spread of EFG values is well reproduced by the calculation based on the approximant. However, the experimental spectra indicate a much larger number of nonequivalent sites when compared with the simulated NQR spectra based on the 1/1 approximant. The short-range, local chemical order is well represented by the approximant, but differences in coordination must be included at intermediate range in the quasicrystal. Measurements of 27Al Knight shift, magnetic susceptibility, and nuclear spin-lattice relaxation time as a function of temperature yield results which indicate a reduction of the density of states at the Fermi level by a factor of 7 or 8 from the value in Al metal, consistent with the notion of a pseudogap for these quasicrystals. No differences in the measured parameters were detected as a function of composition of the quasicrystalline alloys, arguing against a fine structure in the density of states at the Fermi level.

Title: "Distribution of nonequivalent aluminum sites revealed in Al-Cu-Ru and Al-CU-Fe by 27Al NQR"

Authors: A. Shastri, F. Borsa, D.R. Torgeson, and A.I. Goldman

Contact: A.I. Goldman

Journal: Phys. Rev. B (1994) 50, 4224-4227.

Abstract:

The distribution of nonequivalent aluminum sites was studied in Al-Cu-Fe nd Al-Cu-Ru stable icosahedral quasicrystalline phases using 27Al NQR spectra taken at 4.2 K. The observed spectra-which give directly the distribution of nonequivalent aluminum sites-were broad, asymmetric, and structureless. A simple electric-field-gradient model calculation accounted for the spectral width in terms of a wide distribution of local atomic environments, and an estimate for the lower limit on the number of nonequivalent aluminum sites was found.

Title: "Structural determination of the 1/1 rational approximant to the icosahedral phase in Ti-Cr-Si alloys"

Authors: J.L. Libbert, K.F. Kelton, A.I. Goldman, and W.B. Yelon

Contact: A.I. Goldman

Journal: Phys. Rev. B (1994) 49, 11675-11681.

Abstract:

We report the discovery and structural refinement of a large unit cell bcc crystalline phase in a Ti-Cr-Si alloy that is a 1/1 rational approximant to the icosahedral phase in that system. The crystal structure was determined from a Rietveld analysis of x-ray and neutron powder diffraction data. Our results demonstrate that this phase is closely related to the α(Al-Mn-Si) phase, which in turn, is closely related to the structure of the icosahedral phase in the Al-transition-metal alloys. The neutron data indicate that the structure contains a significant amount of oxygen located in the Mackay clusters. Partial ordering of this oxygen may provide an explanation for the localized diffuse scattering often observed in the i phase and related crystalline phases in Ti-transitional-metal alloys.

Title: "Dynamical X-ray Diffraction From an Icosahedral Quasicrystal"

Authors: S.W. Kycia, A.I. Goldman, T.A. Lograsso, D.W. Delaney, D. Black, M. Sutton, E.Dufresne, R. Bruning, and B. Rodricks

Contact: A. I. Goldman

Journal: Phys. Rev. B (1993) 48, 3544-3547.

Abstract:

We present direct evidence of dynamical diffraction of x-rays from a quasicrystal. High-resolution x-ray diffraction measurements of the Al-Pd-Mn face-centered icosahedral quasicrystal were performed, revealing a mosaic full width at half maximum of less tha 0.001 degrees. In a second experiment, the anomalous transmission of x-rays (the Borrmann effect was observed). These measurements show that nearly perfect quasicrystals may be grown to centimeter-size dimensions allowing x-ray techniques based upon dynamical diffraction to be brought to bear on the analysis of icosahedral structures.

Title: "Dynamics of the AlMnPd icosahedral phase"

Authors: M. deBoissieu, M. Boudard, R. Bellissent, M. Quilichini, B. Hennion, R. Currat, A.I. Goldman, and C. Janot

Contact: A.I. Goldman

Journal: J. Phys.: Condens. Matter (1993) 5, 4945-4966.

Abstract:

A centimetre-sized single grain of the perfect AlPdMn icosahedral phase was grown by slow cooling from the melt. It has been fully characterized to be of perfect icosahedral symmetry, i.e. without any frozen-in phason strain. The dynamical properties of this icosahedral phase have been studied by means of inelastic neutron scattering measurements on a triple-axis spectrometer. The response function S(Q, ω) was measured around several Bragg reflections and along the high-symmetry twofold, threefold and fivefold axes of the icosahedron. In the long-wavelength limit there are well defined phonons whose width is limited by the instrumental resolution. The isotropy of acoustic modes is verified and the corresponding sound velocities are in good agreement with ultrasonic measurements made on the same sample. At shorter wavelengths, gaps are expected. By analogy with 1D models and electron density of states calculations, the positions in reciprocal space where the strongest gaps are expected may be estimated. This defines a set of three main pseudo-Brillouin zones which are quasiperiodically stacked around each strong Bragg reflection chosen as the zone centre. In the limit of the instrumental resolution no gap could be detected, even when two branches crossed.

Title: "Large unit cell crystalline approximant in Ti-Cr-Si alloys"

Authors: J.L. Libbert, K.F. Kelton, P.C. Gibbons, and A.I. Goldman

Contact: A.I. Goldman

Journal: J. Non-Cryst. Solids (1993) 153-154, 53-57.

Abstract:

We report the discovery of a new, apparently stable, large unit cell bcc structure in slowly cooled Ti---Cr---Si alloys. This bcc phase, which is also found in Ti---Mn---Si and Ti---V---Si alloys, is likely the crystal approximant related to i-phase formation in the Ti-3d transition metal alloys. Single phase samples of this material were obtained by prolonged annealing at 1200°C. We report the results of a Rietveld structural analysis performed on X-ray powder data obtained from these single phase samples which indicate that this phase is closely related to the α(Al---Mn---Si) phase, a crystal approximant related to the icosahedral phase in Al---Mn---Si systems.

Title: "NMR study of the electronic properties of Al-Cu-Fe and Al-Cu-Ru quasicrystals"

Authors: A. Shastri, F. Borsa, A.I. Goldman, J. Shield, and D.R. Torgeson

Contact: A.I. Goldman

Journal: J. Non-Cryst. Solids (1993) 153-154, 347-352.

Abstract:

27Al and 63Cu Knight shift (K) and relaxation rates (T1−1) are compared for the quasicrystalline (QC) phase and the crystalline (C) phase of Al65Cu23Fe12, and for quasicrystals of Al85−xCuxRu15 with x = 17, 20. The 27Al K is small (K = 0.013 ± 0.003%) and temperature independent. Within error, no differences were found between QC- and C-phases of AlCuFe, nor between AlCuRu samples with x = 17, 20. 27Al and 63Cu T1−1 vs T in AlCuRu displays Korringa-like behavior in the range 5 < T < 50 K with T1T independent of composition. The NMR results are compared with specific heat data which change as a function of concentration x, suggesting large changes of density of states (DOS) at the Fermi level. The two sets of measurements could be reconciled by separating the s-band and d-band effects but the possibility that some of the observed effects are due to disorder modes cannot be ruled out.

Title: "Phase stabilities in the Al-Cu-Ru system"

Authors: J.E. Shield, R.W. McCallum, A.I. Goldman, P.C. Gibbons, and K.F. Kelton

Contact: A.I. Goldman

Journal: J. Non-Cryst. Solids (1993) 153-154, 504-507.

Abstract:

Isothermal sections of the Al---Cu---Ru phase diagram at 500 and 800°C have been determined for Al concentrations greater than 60 at.%. At 500°C, the icosahedral phase is not thermodynamically stable, whereas at 800°C it is stable over a fairly broad compositional region. The formation of the fci phase from the low temperature tetragonal phase is by a nucleation and growth process. The first-order transformation to the fci phase is endothermic, indicating that the fci phase is at a higher energy than the tetragonal phase.

Title: "Dynamical properties of the AlPdMn icosahedral phase"

Authors: M. DeBoissieu, M. Boudard, H. Moudden, M. Quilichini, R. Bellissent, B. Hennion, R. Currat, A.I. Goldman, and C. Janot

Contact: A.I. Goldman

Journal: J. Non-Cryst. Solids (1993) 153-154, 552-556.

Abstract:

A centimetre-sized single grain of the perfect AlPdMn icosahedral phase can be grown by slow cooling from the liquid. This phase has been shown to have perfect icosahedral symmetry, i.e. without any frozen phason strain. The dynamical properties of this icosahedral phase have been studied by mean of inelastic measurements on triple axis spectrometers. The dispersion relations around several Bragg reflections were measured. Pseudo-zone boundaries can be defined, similarly to those previously obtained in the AlLiCu phase. A dispersionless optic mode was identified around 4 THz.

Title: "An approximant to the Al-Cu-Ru icosahedral phase"

Authors: J.E. Shield, L.S. Chumbley, R.W. McCallum, and A.I. Goldman

Contact: A.I. Goldman

Journal: J. Mater. Res. (1993) 8, 44-48.

Abstract:

The crystal structure and space group of an approximant phase to the face-centered icosahedral (FCI) phase in the Al-Cu-Ru system is reported. The crystal structure is simple cubic, with a = 12.38 Å. The space group has been determined to be Pm3, which is the same space group as α-AlMnSi, an approximant to the simple-icosahedral (SI) phase. With isostructural phases, the SI and FCI alloys in Al-transition metal alloys also are structurally similar. We also report the crystal structure and space group of a tetragonal phse which is apparently not an approximant phase.

Title: "Twinned one-dimensional quasicrystals in Bridgman grown Al(Si)-Cu-Co alloys"

Authors: L.X. He, T. Lograsso, and A.I. Goldman

Contact: A.I. Goldman

Journal: Phys. Rev. B (1992) 46, 115-119.

Abstract:

Single grains of Al60Si2Cu18Co20 with a decaprismatic morphology were grown by the Bridgman method and studied by transmission electron microscopy and x-ray diffraction. Although the diffraction patterns of these grains superficially resemble that of a decagonal quasicrystal, a closer inspection reveals that they are composed of tenfold twins of a one-dimensional quasicrystal along with small domains of three crystalline approximant phases.

Title: "Phonons in icosahedral and cubic Al-Li-Cu"

Authors: A.I. Goldman, C. Stassis, M. De Boissieu, R. Currat, C. Janot, R. Bellissent, H. Moudden and F.W. Gayle

Contact: A.I. Goldman

Journal: Phys. Rev. B (1992) 45, 10280-10291.

Abstract:

We describe the results of inelastic-neutron-scattering measurements on single grains of icosahedral Al-Li-Cu and the related cubic R phase. Measurements along the high-symmetry twofold, threefold, and fivefold axes of the icosahedral phase clearly show the existence of well-defined propagating modes, with isotropic dispersion, near strong Bragg peaks. The spectral weight of the acoustic phonons scale linearly with the integrated intensity of the associated zone centers. In several cases we are able to identify ‘‘quasi’’-Brillouin-zones, with stationary points at the ‘‘special’’ high-symmetry points of a simple icosahedral lattice. While the phonon dispersion for transverse and longitudinal acoustic modes along the twofold axis of the cubic R phase is quite similar to that found for the icosahedral phase, differences are found in the higher-energy modes; the behavior of the higher-energy modes of the icosahedral phase is consistent with an enhanced degree of spatial localization for these excitations.

Title: "Icosahedral phase stabilities in Al-Cu-Ru alloys"

Authors: J.E. Shield, C. Hoppe, A.I. Goldman, R.W. McCallum, K.F. Kelton, and P.C. Gibbons

Contact: A.I. Goldman

Journal: Phys. Rev. B (1992) 45, 2063-2072.

Abstract:

By examining a wide region of the Al-Cu-Ru phase diagram, a thorough analysis of the compositional and thermal stability of the icosahedral phase has been completed. The primary solidification product of rapid solidification was a topologically and chemically disordered icosahedral phase with an extensive compositional region. Crystallization through exothermic events of the as-solidified materials produced crystalline phases, without the formation of the face-centered-icosahedral (FCI) phase. However, the FCI phase doe form at higher temperatures through an endothermic reaction, indicating that it is a stable phase of the system, but only at elevated temperatures. Of the alloys studied, the FCI phase field was found to encompass Al65Cu23Ru12, Al65Cu20Ru15, Al70Cu15Ru15. The transformation to the FCI phase involves an intermediate approximnt phase that is very similar to the FCI structure. Also, a cubic approximant containing atomic arrangements with local icosahedral symmetry similar to α-Al Mn Si was determined to exist near the FCI phase field.

Title: "Inelastic neutron scattering measurements of phonons in icoshedral Al-Li-Cu"

Authors: A.I. Goldman, C. Stassis, R. Bellissent, H. Moudden, N. Pylca, and F.W. Gayle

Contact: A.I. Goldman

Journal: Phys. Rev. B (1991) 43, 8763-8766.

Abstract:

Inelastic-neutron-scattering measurements on a single grain of icosahedral Al-Li-Cu are presented. Within experimental error the acoustic-phonon dispersion at small, but finite, q is independent of direction, confirming the isotropic elasticity expected for icosahedral crystals. By following the longitudinal-phonon dispersion curve along a fivefold axis we can identify the location of ‘‘quasi-Brillouin-zone boundary.’’ The measurements also suggest the presence of an optical or localized mode along the twofold axis at approximately 10–11 meV. We compare these results to theoretical calculations for one- and two-dimensional quasiperiodic systems.

Title: "Al-Cu-Ru: An icosahedral alloy without phason disorder"

Authors: C.A. Guryan, A.I. Goldman, P.W. Stephens, K. Hiraga, A.P. Tsai, A. Inoue, and T. Masumoto

Contact: A.I. Goldman

Journal: Phys. Rev. Lett. (1989) 62, 2409-2412.

Abstract:

We present high-resolution x-ray diffraction measurements of the recently discovered face-centered icosahedral phase of Al65Cu20Ru15. Analysis of the diffraction-peak profiles shows that this alloy is better ordered than the simple-icosahedral alloys previously studied. In particular, the peak broadening is well accounted for by simple lattice strain, with no measurable dependence of the peak widths on phason momentum. This implies a significantly diminished role for phason disorder in this system relative to the simple-icosahedral alloys.

Title: "Diffuse scattering from the icosahedral phase alloys"

Authors: A.I. Goldman, C.A. Guryan, P.W. Stephens, J.M. Parsey Jr., G. Aeppli, H.S. Chen, and F.W. Gayle

Contact: A.I. Goldman

Journal: Phys. Rev. Lett. (1988) 61, 1962-1965.

Abstract:

We present neutron and x-ray measurements of the diffuse scattering from single-grain smples of the icosahedral phase of Al-Li-Cu. The x-ray measurements were analyzed to determine the integrated intensity of the diffuse scattering relative to the sharp diffraction peaks, as well as the length scale of the correlqations which produce the diffuse scattering. The neutron data show that these correlations are static rather than dynamic in nature. In addition, we present simple model based on the disordered packing of icosahedral clusters of atoms, which reproduces the unusual ringlike nature of this scattering. Quantitatively, this model overestimates the degree of disorder present in these alloys.

Title: "Structure of icosahedral clusters in cubic Al5.6Li2.9Cu "

Authors: C.A. Guryan, P.W. Stephens, A.I. Goldman, and F.W. Gayle

Contact: A.I. Goldman

Journal: Phys. Rev. B (1988) 37, 8495-8498.

Abstract:

We present a structure refinement of crystalline Al5.6Li2.9Cu based on x-ray and neutron-diffraction data. We find that clusters of atoms form nearly ideal icosahedra in a bcc lattice, with different positions and occupancies than those proposed in previous work. Since neutrons and x rays have very different scattering amplitudes for Al, Li, and Cu, and since their respective diffraction profiles therefore consist of different peak intensities, the close agreement of the structural parameters from the two fits is a strong argument for the correctness of our results. These should be useful in packing-model descriptions of the related icosahedral phase.

Title: "Anisotropic packing and diffraction peak shifts in icosahedral glasses"

Authors: A.I. Goldman and P.W. Stephens

Contact: A.I. Goldman

Journal: Phys. Rev. B (1988) 37, 2826-2828.

Abstract:

We show that the anisotropic random packing of units with icosahedral symmetry produces diffraction patterns with distortions similar to recent electron and x-ray diffraction measurements. Using the Hendricks-Teller formalism discussed in an earlier paper, we show that the peak shifts predicted by the introduction of phason strain in an ideal quasilattice may also be described by this anisotropic, random-packing, icosahedral glass model.

Title: "EXAFS study of Al-Mn-Ru-Si icosahedral alloys"

Authors: P.A. Heiney, P.A. Bancel, A.I. Goldman, and P.W. Stephens

Contact: A.I. Goldman

Journal: Phys. Rev. B (1986) 34, 6746-6751.

Abstract:

We report extended x-ray-absorption fine-structure measurements on the Mn and Ru K absorption edges in rapidly quenched icosahedral alloys of Al86Mn14, Al75.5Mn17.5Ru4Si3, and Al75.5Mn15.5Ru6Si3, as well as the crystalline forms of Al6Mn and Al6Ru. In the icosahedral phase, we find an asymmetric distribution of Al atoms around Mn sites, containing at least two Al-Mn distances. The asymmetry becomes more pronounced with increasing Ru content. The Ru atomic environment appears to include an additional very short Ru—Al or Ru—Si bond.

Title: "Sharp diffraction maxima from an icosahedral glass"

Authors: P.W. Stephens and A.I. Goldman

Contact: A.I. Goldman

Journal: Phys. Rev. Lett. (1986) 56, 1168-1171; 57, 2770.

Abstract:

We consider densely packed assemblies of icosahedra, such that icosahedral bond-orientational order is enforced throughout the sample. The peaks in the calculated diffraction patterns may be put in a one-to-one correspondence with the electron and x-ray diffraction patterns from icosahedral Al-Mn alloys, allowing the determination of the packing-unit size. We show that these maxima are not Bragg diffraction peaks, but have an intrinsic width, and may be understood as resulting from the interference between two or more characteristic lengths, as originally discussed by Hendricks and Teller.

Title: "Structure of rapidly quenched Al-Mn"

Authors: P.A. Bancel, P.A. Heiney, P.W. Stephens, A.I. Goldman, and P.M. Horn

Contact: A.I. Goldman

Journal: Phys. Rev. Lett. (1985) 54, 2422-2425.

Abstract:

We report electron-microscopy and high-resolution x-ray-scattering measurements of rapidly quenched Al6Mn. The electron-diffraction pattern shows icosahedral symmetry. Peaks in the x-ray-diffraction pattern can be indexed to a mixture of fcc Al and a phase whose reciprocal lattice is described by a sum of icosahedral vectors. The half-width of the sharpest x-ray peak is 0.01 Å-1. A comparison is made with current theories of quasicrystalline order.


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