Phononic crystals are to sound what photonic crystals are to light and crystals are to electrons. If the wavelength is of the same order of magnitude as the typical distances between the objects in their ordered arrangement, then the interaction is dominated by diffraction besides refraction. Depending on the spectral properties of the material, band gaps appear for certain frequencies. In special cases, these gaps are omni-directional. A huge amount of application-driven research has been performed on photonic crystals, much less on phononic crystals, and almost nothing on phononic quasicrystals. We present here the first experimental studies on two-dimensional, quasiperiodic, phononic crystals. Our experiments have been performed with ultrasound on phononic crystals and quasicrystals consisting of steel cylinders in water. The pros and cons of phononic quasicrystals are discussed.

Several existing models of icosahedral quasicrystals (QCs) are improved upon and studied by ab initio electronic structure methods. The following approach is used to optimize the models: 1) interchange of atoms in the existing (skeletal) models based on available knowledge of the local atomic environments, and 2) subsequent relaxation of the atomic positions using forces determined via first principles density functional methods. After minimizing the total energy, we investigate the ground state, and compare calculated results with available photo-emission spectroscopy (PES) and Mössbauer spectroscopy data. Significant improvement with respect to the starting (skeletal) model is achieved in several cases. We also examine the validity of the concept of negative valences of the transition metal atoms in QCs as advanced by Friedel.

Two competing meta-stable crystalline phases, a bcc hyperstoichiometric β-Zr(Pt) (Im3m) superstructure and a non-stoichiometric fcc ε-Zr6Pt3O (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 β-Zr(Pt) superstructure and i phase have a well defined orientational relationship, good crystallographic match and nearly identical stoichiometry. Icosahedral two-fold axes coincide with <110>, <111>, <112> and <113> axes in β-Zr(Pt); {110}β-Zr planes register with icosahedral {211111} fivefold or {221001} twofold planes. The observed orientational relationship and the space group (Im3m) preclude β-Zr(Pt) as a cubic approximant to the i phase. Both β-Zr(Pt) and the i phase are distorted; β-Zr(Pt) maintains a basic β-Zr Bravais lattice with an aperiodic superlattice. Morphologies suggest that the i phase forms first, followed by an easy nucleation of the β-Zr(Pt) on the surfaces of the i phase. Also, a similar orientational relationship and lattice match between ε-Zr6Pt3O and i phase has been revealed by TEM.

Zr65Ni10Cu7.5Al7.5Ag10 bulk metallic glass with a diameter of 2 mm and a length of 50 mm was prepared by copper-mould casting. The metallic glass obtained follows two-step crystallization reactions with the initial formation of metastable quasicrystals from amorphous phase, followed by the formation of a stable intermetallic Zr2Cu from the post-formed quasicrystals. In this paper, the microprocess of the amorphous-to-quasicrystalline transformation of Zr65Ni10Cu7.5Al7.5Ag10 bulk metallic glass was studied in detail by TEM and high resolution TEM coupled with nanobeam EDX. It was found that the amorphous-to-quasicrystalline transformation in the present system does not follow the traditional nucleation/growth mechanism. Instead, it undergoes a series of inter-processes and follows the sequence of phase transformation of amorphous → FCC Zr2Ni → Tetragonal Zr2Ni → Quasicrystals. Nanobeam EDX revealed that atomic diffusion was involved in all inter-processes of the phase transformations, suggesting that the amorphous-to-quasicrystalline transformation in the present bulk metallic glass is a non-polymorphous reaction.

High energy synchrotron x-rays (124.63 keV) are used to investigate the initial stages of the devitrification for the Zr70Pd20Cu10 metallic glass prepared by melt-spinning (MS). Due to the excellent signal:noise, we are able to determine the initial nucleating phase by analyzing the differences in the total scattering function S(Q) as a function of time at a temperature ∼ 50 K below the crystallization temperature. The alloy undergoes a structural relaxation prior to nucleation and growth. Devitrification proceeds from nucleation of the icosahedral phase. The differential pair distribution function (dPDF) indicates that the as-quenched alloy may have icosahedral-like order which undergoes local rearrangement to true icosahedral order at an annealing temperature 50 K below the crystallization temperature. More importantly, time-resolved high-energy synchrotron is shown to have excellent sensitivity to the initial atomic rearrangements preceding nucleation in metallic glasses.

The development of quasicrystalline (qc) order from different initial states (amorphous, nano- or poly-qc) was studied in rapidly quenched Ti-Zr-Ni(-Ag), Ti-Zr-Fe, and Zr-Cu-Ni-Al alloys by means of mechanical spectroscopy (vibrating-reed technique), including both the irreversible changes of Young's modulus and the Snoek-type relaxation peak of absorbed hydrogen as a probe, which are obviously sensitive to quite different types of ordering processes. The strongest annealing effects on Young's modulus were found for extreme nano-qc material at the amorphous limit, whereas order-induced narrowing of the hydrogen peak occurs only at comparatively larger grain sizes. More important differences in the properties of the hydrogen peak are found between quasicrystals of different compositions. The results are briefly discussed with respect to their implications for the amorphous-to-quasicrystalline transition and for the experimental distinction between different types of icosahedral quasicrystalline order.

Reduced wetting and friction are two essential surface properties that to a large extent currently embody the technological potential of quasicrystalline coatings. By quasicrystalline compounds, one considers here the whole family of complex Al-(Cu or Pd)-(Fe, Cr or Mn) intermetallics, which comprises true quasicrystals, their approximants and some crystalline materials of related composition.

Although covered by a layer of native Al2O3 oxide, wetting by water on these materials exhibits a clear correlation between the reversible adhesion energy of water and the bulk density of states at the Fermi energy. Similarly, in high vacuum, the friction coefficient measured in contact against a hard-steel rider is characteristically smaller than the one measured against conventional metallic alloys (including steel). Observing that wear is nearly non existent under such friction conditions, experiment allows us for the first time to derive a fair estimate of the true surface energy of quasicrystals and related complex metallic alloys. Similarly to wetting, the electronic density of states seems to determine the friction characteristics of these compounds.

We present experimental results on the structure of Ag thin films grown on high-symmetry surfaces of both quasicrystals and approximants. For coverages above ten monolayers, Ag form fcc nanocrystals with (111) plane parallel to the surface plane. Depending on the substrate surface symmetry, the Ag nanocrystals exist in one, two or five different orientations, rotated by a multiple of 2π/30. The orientation relationship between crystalline films and substrates appears to be determined by the following principles: high atomic density rows of the adsorbate are aligned along high atomic density rows of the substrate.

The propagation of mode-I cracks in a two-dimensional decagonal model quasicrystal is studied by molecular dynamics simulations. The samples are endowed with an atomically sharp seed crack and a temperature gradient. Subsequently the crack is loaded by linear scaling of the displacement field. The response of the crack running into regions of increasing temperature is monitored.

For low temperatures below 30% of the melting temperature Tm the model-quasicrystal fails by brittle fracture. We observe that the crack follows the path of dislocations nucleated at its tip. The crack propagates along well defined planes and circumvents tightly bound clusters. In the medium temperature regime from 30% to 70% Tm the crack is blunting spontaneously by dislocation emission. In the range of 70%-80% Tm the quasicrystal fails by nucleation, growth and coalescence of micro-voids. This gradual, dislocation-free crack extension is caused by plastic deformation which is mediated by localized rearrangements comparable to so-called shear transformation zones in amorphous solids.

The evolution of the short-range order in a Ti-Hf-Ni 3/2 approximant phase, has been studied as a function of hydrogenation by means of extended X-ray absorption fine structure (EXAFS). The local structure of the non-hydrogenated alloy has been derived from that of 1/1 Ti-Zr-Ni. After hydrogenation, drastic changes are observed in the local structure of Ti-Hf-Ni. Preliminary results of the EXAFS analysis are also presented for an amorphous Ti-Hf-Ni alloy.

The electrical resistivity, thermoelectric power, and thermal conductivity were investigated for the Al71.6-xMn 17.4Six and Al71.6-xRe 17.4Six (7 ≤ x ≤ 12) 1/1-cubic approximants. A large thermoelectric power ranging from -40 to 90 μV/K and a low thermal conductivity less than 3 W/K·cm were observed at room temperatures. The electrical resistivity at room temperature for these approximants was kept below 4,000 μΩcm, that is much smaller than that in the corresponding quasicrystals. As a result of the large thermoelectric power, the low thermal conductivity, and the low electrical resistivity, large dimensionless figure of merit ZT = 0.10 (n-type) and 0.07 (p-type) were achieved for the Al71.6Re17.4Si11 and Al71.6Mn17.4Si11 at room temperature, respectively.

The propagation of mode I cracks in a three-dimensional icosahedral model quasicrystal has been studied by molecular dynamics techniques. In particular, the dependence on the plane structure and the influence of clusters have been investigated. Crack propagation was simulated in planes perpendicular to five-, two- and pseudo-twofold axes of the binary icosahedral model.

Brittle fracture without any crack tip plasticity is observed. The fracture surfaces turn out to be rough on the scale of the clusters. These are not strictly circumvented, but to some extent cut by the dynamic crack. However, compared to the flat seed cracks the clusters are intersected less frequently. Thus the roughness of the crack surfaces can be attributed to the clusters, whereas the constant average heights of the fracture surfaces reflect the plane structure of the quasicrystal. Furthermore a distinct anisotropy with respect to the in-plane propagation direction is found.

The stability of single-crystalline icosahedral Cd-Yb was investigated using X-ray diffraction methods in the temperature range 20 K ≤ T ≤ 900 K at ambient pressure and from ambient temperature to 873 K at about 9 GPa. Single-crystals remain stable at low temperatures and in the investigated HP-HT-regime. At high temperatures and ambient pressure, the quasicrystal decomposes. The application of mechanical stress at low temperatures yields to the same decomposition, the formation of Cd. A reaction of icosahedral Cd-Yb with traces of oxygen or water causing the decomposition seems reasonable, but a low-temperature instability of this binary quasi-crystal cannot be ruled out totally.

Electronic transport measurements have been made on bulk icosahedral Al70Pd22.5Re7.5 quasicrystal (QC's) samples, having increasingly larger resistance temperature ratios, rT = R(4.2 K)/R(292 K). Data were taken between 0.023 K to 292 K and in magnetic fields up to 17.9 T. Both the zero field resistivity and the magnetoresistance (MR) changed from metallic behavior to weakly insulating behavior to highly insulating behavior, as the resistance temperature ratios rT's of the samples were made larger. For the insulating samples, the resistivities ρ's followed simple inverse temperature power laws above 50 K going as ρ(T) = a0/Tz, where z = 1 ± 0.1.The insulating QC samples exhibited saturation behaviors of their resistivities below 2 K. Below 0.3 K, the strongly insulating QC's displayed activated variable-range hopping (VRH) laws in their conductivity; the hopping exponents y's in the VRH laws varied between 0.19 ≤ y ≤ 0.43. A simple model including conductivity contributions both from the primary insulating QC phase and from a secondary metallic phase yielded good fits to the resistivity and MR data.

We have investigated the surface properties of quasicrystalline and approximant phases in the Al-(Cu)-Cr-Fe system upon aging in ambient conditions. We found that some of these properties (like the electrochemical behavior, wetting or friction) slowly evolves with the length of exposure to normal atmospheric conditions, reaching a stable state only after several days. This report essentially focuses on one of these alloys, an Al65Cr27Fe8 approximant phase with g-brass structure. In a first part, we describe the effect of aging on the electrochemical behavior of this alloy and we propose an interpretation based on a simple electrical model of the oxidized surface. In a second part, we present a model describing the surface as a stacking of several layers (oxides, oxy-hydroxides, contamination) whose thickness evolves with time. The model is supported by X-ray reflectivity, angle-resolved photoemission spectroscopy and secondary neutral mass spectroscopy measurements.

The present level of understanding of the effects of irradiation of quasicrystalline targets with swift heavy ions has been reviewed here. The results of systematic deposition of large amount of energy densities (12 keV/nm < (dE/dx)e < 40 keV/nm) in Al-Cu-Fe based system are discussed in terms of resistivity measurements (in-situ measurements of resistivity changes with increasing flux (ions/cm2) and ex-situ resistivity vs temperature measurements before and after irradiation) & standard and high-resolution X-ray diffraction measurements made before and after irradiation. The studies are aimed at understanding the changes that may occur in these alloys as a result of the relaxation of such highly excited states of matter. Also, we attempt to learn whether such changes are typical to the long-range quasicrystallinity of the system or not.

In order to obtain reliable experimental information on the long-range order, the role of the valence electron concentration and the type of disorder for Mackay icosahedron type quasicrystals we have studied binary and ternary Mg based approximant phases. An overview is presented on the crystal structures, homogeneity ranges, physical properties, and electronic structures of the following intermetallic phases: Mg6Pd, Mg57Pd13, Mg56.4Pd13.5, Mg306Pd77, Mg3Pd, Mg5Pd2, Mg2Pd, Ga30-xMg32+xPd21-y, Ga15-x-yMg38+yPd13+x, GaMg3Pd2, Ag17Mg54, Ag7Mg26, and AgMg4.

Mandal and Lele (1989) have proposed a six dimensional model for the structural description of the decagonal phases. The integral linear combination of six basis vectors for indicating a physical vector in their model, however, leaves the problem of redundancy in indexing. While revisiting their model, we have noted that the condition of a null vector in physical space permits the formulation of unique indexing scheme both in physical reciprocal and direct spaces, we will demonstrate that our scheme, unlike all previously discussed ones, relies only on the information contained in the model. It will also be shown that diffracted spot having equivalent indices possesses identical intensity. This aspect, though equally important, has been totally ignored in the past. We shall substantiate our claim by taking examples from the known decagonal phases. We shall also present parity condition on indices that will be helpful in discussing subtle features of diffraction patterns. The notion of weak and strong diffracting conditions is explained based on the zone rule in physical space in terms of Cartesian components of direct and reciprocal vectors.

We report here the results obtained for the valence band of four compounds from the Al-Cr-Fe system, all being approximants of the decagonal quasicrystalline phase as probed by a combination of X-ray emission and X-ray photoemission spectroscopy techniques. Salient features are d-d and p-d hybridizations at the Fermi level and in its close vicinity as well as a repulsive interaction between the d states of the two transition elements. Within about 4 eV below the Fermi level Al states are suggested to be of more localized-like character in the Al-Cr-Fe samples than in Al-Cu-Fe ones.

The short-range order of stable and deeply undercooled liquids of Al13(Co,Fe)4 alloys forming polytetrahedral phases is investigated by combining the containerless processing technique of electromagnetic levitation with elastic neutron scattering. Partial structure factors were inferred from the diffraction data which allow an analysis of both, the topological and the chemical short-range order of these alloy melts as a function of the temperature.