Crystal chemistry and chemical order in ternary quasicrystals and approximants

In this work we review our current understanding of structure, stability and formation of icosahedral quasicrystals and approximants. The work has special emphasis on Cd–Yb type phases, but several concepts are generalized to other families of icosahedral quasicrystals and approximants. The paper handles topics such as chemical order and site preference at the cluster level for ternary phases, valence electron concentration and its influence on formation and composition, fundamental building blocks and cluster linkages, and the similarities and differences between different families of icosahedral quasicrystals and approximants.     

Al-Cu approximants and associated B2 chemical-twinning modes

The Al3Cu4 alloy, with an e/a ratio of 1.86 being close to ternary Al-Cu-TM (transition metal) quasicrystals, has been chosen for the search of Al-Cu approximants. Phase structures and compositions were studied using TEM, X-ray diffraction and EPMA techniques. Two new phases were found: face-centered orthorhombic oF-Al43.2Cu56.8 (a = 0.816(6), b = 1.414(9), c = 0.999(5) nm) and body-centered orthorhombic oI-Al41.3Cu58.7 (oI, a = 0.408(3), b = 0.707(4), c = 0.999(5) nm). Their e/a ratios are the same as that of the Al-Cu-Fe icosahedral quasicrystal. Both are B2 superstructures and their unit cell components can be expressed approximately as oF-Al36Cu48vacancies12 and oI-Al8Cu12vacancies4. They both exist in twinning variants of the types 120 degrees/[001] and 180 degrees/[310]. Such twinning modes indicate that these orthorhombic phases are the decomposition products of a high-temperature parent phase epsilon2-Al2Cu3, the atomic structure of which shows pentagonal atomic arrangements. Further analysis on the twinning modes of oF and oI leads to the recognition of the chemical-twinning mode of the basic B2 structure as 180 degrees/(111)B2. This kind of chemical twinning mode is responsible for the pentagonal atomic configuration in the Al-Cu approximants as well as for the pseudo-5-fold B2 twinning.     

落管中Al4Mn合金的形核研究

用1.2米长的落管对Al₄Mn合金进行了形核与过冷的研究.在落管底部收集到的样品中得到了正交Al₆Mn,β-Mn,两个十次准晶相关相、一个二十面体五次准晶相关相和十次准晶畴.发现这些相的含量与样品的尺寸大小有关,根据传统的形核理论对相含量与样品尺寸大小之间的关系作了定性的分析和讨论. 关键词：     

Quasicrystals and related approximant phases in Mg-Zn-Y

As-cast microstructure of Mg-rich Mg(68)Zn(28)Y(4) has been investigated by a detailed transmission electron microscopy study. The as-cast Mg(68)Zn(28)Y(4) alloy consisted of three different types of phases: 10-20 m size primary solidification phase, dendritic phase grown from the primary phase and a eutectic structure formed at the later stage of solidification. The primary solidification phase has an icosahedral structure with a large degree of phason strain. 1/1 rhombohedral approximant phase with lattice parameters a=27.2 A and =63.43 degrees is first observed in Mg-Zn-Y system. The rhombohedral structure can be obtained by introducing phason strain in the six-dimensional face centered hyper-cubic lattice. The decagonal phase nucleates with orientation relationship with the icosahedral phase, and Mg(4)Zn(7) nucleates with orientation relationship with the decagonal phase, indicating a close structural similarity between the three phases. Gradual depletion of Y during solidification plays an important role in heterogeneous nucleation of decagonal and Mg(4)Zn(7) phases from icosahedral and decagonal phases, respectively.     

Sign determination of the57Fe electric field gradient in Al-based crystals and icosahedral quasicrystals

The icosahedral quasicrystals i-AlMn isomorphically suostituted by 28 at.% Fe or by (CrFe) are studied for the first time by in-field Mössbauer spectroscopy (MS) in order to determine the sign and asymmetry parameter of the dominant EFG term. In addition, the orthorhombic o-Al(MnFe) and cubic α- and hexagonal β-Al(MnFe)Si phases are studied. We show that previous MS results are inadequate to determine if there are two sites in the i-AlMn structure in the ratio of the golden number. Our results for i-Al(MnFe) show that the dominant EFG is negative, with asymmetry parameter of about 0.6. For i-Al(CrFe), essentially no deviations are found from the model of Czjzek or the Gaussian isotropic model. The β phase is found to have a very similar quadrupole effect as that in i-Al(MnFe).     

Stable quasiperiodic icosahedral states

The discovery of icosahedral quasicrystals five years ago, has challenged the validity of the well-known conjecture that the ground state of a system of particles interacting via short-range forces is always crystalline at absolute zero. We have calculated the classical cohesive energies and pair distribution functions of a large class of monatomic icosahedral structures, interacting via the Lennard-Jones (LJ) and the Square-Well (SW) potentials. For the SW potential, we have found an icosahedral phase, with lower enthalpy than the BCC, FCC and HCP phases. The phase is robust with respect to small changes in the potential, pressure and even structure, and transforms to the BCC phase above a critical pressure. Our results suggest that icosahedral ground states may indeed be possible for a class of potentials with Friedel-like oscillations, whose extremal positions satisfy geometric constraints favoring icosahedral order.     

非晶Ni-P合金晶化过程中生成的六角亚稳相(Ⅲ)——六角多型体

利用电子显微镜旋转晶体法发现了非晶Ni-P合金晶化过程中生成的另外两个新的六角亚稳相(α₂相与α₃相)。它们与文献[3]报道的六角亚稳相(α₁)具有相同的α值(6.73?),但c值分别为α₁的3/2倍与4倍,表明这些相属于长周期多型体结构,α₂相具有六角密堆结构的消光规律。此外,还证实了α₁中的面心立方亚点阵(α=5.50?)实际上是一个单独的面心立方亚稳相,这些六角亚稳相就 关键词：     

Phonon-spectrum of an F-type icosahedral quasicrystal

We present calculations for the vibrational properties of F-type icosahedral quasicrystals. Two different approaches are compared, a cluster with complete icosahedral symmetry, and periodic approximants. Though no gaps in the spectra are observed, the well-known rescaling symmetry of ID systems is rediscovered in a generalized way.     

Continuous transformation from quasicrystals to approximants in Al–Cu–Fe alloys

Continuous transformation of icosahedral quasicrystals as observed in Al-Cu-Fe alloys proceeds through intermediate modulated structures towards rational approximants with a rhombohedral structure. Corresponding to the diffuse scattering in the electron diffraction during the transformation, a tweed contrast emerges throughout the icosahedral phase matrix. High-resolution electron microscopy reveals a complex modulated structure which tends to evolve into rhombohedral microdomains. The observed distortion of the reciprocal quasilattice due to the structural modulation has been simulated on a computer by introducing linear phason strains into the quasicrystals.     

A comparison of the57Fe EFG properties in the crystalline and quasicrystalline phases of the Al−Si−Mn system

We present here the determination of the distributionP(q) of the electric field gradient in Fe-doped Al?Si?Mn icosahedral and decagognal quasicrystals and in the related crystalline phases, using in-field Mössbauer effect spectroscopy. The distributionP(q) for the quasicrystalline compounds shows a bimodal, nearly symmetric form withP(0)?0 and equal averages over positive and negativeq=1/2eQV _zz :?〈q _? 〉～-〈q ₊ 〉 and equal standard derivations: σ_??σ₊. The results for the majority sign of the distributionP(q) will be compared to the results for the cubic, hexagonal and orthorhombic compounds. The results show that there are similarities in the local order between the icosahedral quasicrystalline phase and the hexagonal phase. No evidence is found for a two-site model which as recently been proposed by other authors.     

Metamagnetism of hexagonal iron

Summary We present the results of the fixed-spin-moment, self-consistent LMTO electronic structure calculations for hexagonal phase of iron. The relative stability of the nonmagnetic and ferromagnetic phases is discussed along with the magnetic and mechanical equations of state. It is shown that hexagonal Fe is metamagnetic with the nonmagnetic ground state, but at a sufficiently large atomic volume the system prefers a ferromagnetic solution at rather low internal magnetic pressure. These findings seem to be well correlated with the properties of the hexagonal Fe that has recently been grown epitaxially on the Ru substrate.     

Gold Nanoparticles Obtained by Bio-precipitation from Gold(III) Solutions

The use of metal nanoparticles has shown to be very important in recent industrial applications. Currently gold nanoparticles are being produced by physical methods such as evaporation. Biological processes may be an alternative to physical methods for the production of gold nanoparticles. Alfalfa biomass has shown to be effective at passively binding and reducing gold from solutions containing gold(III) ions and resulting in the formation of gold(0) nanoparticles. High resolution microscopy has shown that five different types of gold particles are present after reaction with gold(III) ions with alfalfa biomass. These particles include: fcc tetrahedral, hexagonal platelet, icosahedral multiple twinned, decahedral multiple twinned, and irregular shaped particles. Further analysis on the frequency of distribution has shown that icosahedral and irregular particles are more frequently formed. In addition, the larger particles observed may be formed through the coalescence of smaller particles. Through modification of the chemical parameters, more uniform particle size distribution may be obtained by the alfalfa bio-reduction of gold(III) from solution.     

Electron spectrum and wave functions of icosahedral quasicrystals

Electron spectra and wave functions of icosahedral quasicrystals have been investigated in the tight-binding approximation using the two-fragment structural model (the Amman-MacKay network) with “central” decoration. A quasicrystal has been considered as a limiting structure in a set of optimal cubic approximants with increasing lattice constants. The method of level statistics indicates that the energy spectrum of an icosahedral quasicrystal contains a singular (nonsmooth) component. The density of electron states has been calculated for the first four optimal cubic approximants of the icosahedral quasicrystal, and the respective Lebesgue measures of energy spectra of these approximants have been obtained. Unlike the case of a one-dimensional quasiperiodic structure, the energy spectrum of an icosahedral quasicrystal does not contain a hierarchical gap structure typical of the Cantor set of measure zero in a one-dimensional quasicrystal. Localization of wave functions in an icosahedral quasicrystal has been studied, and their “critical” behavior has been detected. The effect of disorder due to substitutional impurities on electron properties of icosahedral quasicrystals has been investigated. This disorder makes the electron spectrum “smoother” and leads to a tendency to localization of wave functions. Zh. éksp. Teor. Fiz. 113, 1009–1025 (March 1998)     

Random cluster models for icosahedral phase alloys

We present results on computer generated random cluster models for icosahedral phase alloys. By the application of physically motivated constraints on the local atomic cluster configurations, the model achieves long range translational order comparable to, or greater than, that found in simple icosahedral alloys such asi-AlMnSi andi-AlLiCu. The parallel and perpendicular space structures are explored in some detail including a comparison with experimental powder diffraction patterns and an examination of the phason fluctuations. The latter are shown to decrease markedly with increased constraint on the local environment, but the remaining phason strain would seem finally not to vanish with increasing model size. Our model is compared with other cluster models for quasicrystalline materials and is shown to possess a density and connectivity very close to those of Elser's (best) model and those predicted by Henley for a canonical tiling. The relation of this model to recently discovered icosahedral phase alloys with resolution limited diffraction peak widths, which are essentially free of phason strain, is also discussed.     

Electronic properties of quasicrystals an experimental review

The electronic properties of a large number of icosahedral-crystal systems have been studied experimentally. These systems include alloys of the simple metals and those that contain transition metals. Some of the icosahedral phases (i-phases) are thermally stable while others are metastable; and their degree of structural order varies within each of the stability classes. The importance of sample quality to the exposition of intrinsic properties is emphasized, particularly for systems with high resistivities. As a result, experiments on single-phase samples from the diversity of systems studied have shed light on the physics of quasicrystalline alloys. Comparison made with the approximant and amorphous phases have provided important insights to the understanding of quasicrystallinity, randomness, and atomic-potential effects on electronic properties. Reduction in the electronic density of states (DOS) at the Fermi level relative to the free-electronic value is observed in the stable i-phase systems studied to date. Examples are the GaMgZn, AlCuLi, AlCuFe, and AlCuRu systems. Although the simple-metal i-alloys such as AlCu (Mg, Li) and (Al, Ga)MgZn within their metastable phase fields are found to have nearly free-electron DOS, the anomalies in their transport behaviour and compositional dependence of electronic properties have revealed the important role of the Fermi-surface-Jones-zone boundaries (FS-JZB) interaction in these measurements. Also, central to the FS-JZB interaction criterion of phase stability is the existence of a pseudogap in the DOS which is most evident in the stable i-phases. Unusual transport behaviour has been reported for the structurally ordered i-phases that contain transition metals. These materials exhibit semi-metallic transport behaviour characterized by a high resistivity (～4000–30000 μΩcm), a large resistivity ratio ρ(4·2 K)/ρ(300 K) ranging from 1·5 to 4 as well as a low carrier concentration of 10^?2 to 10^?3 electron per atom. Adding to the anomalous electron transport are the strong temperature dependences of the Hall coefficient and thermopower leading to a change of sign. Further understanding of the ordered i-phases has been advanced through studies of amorphous phases and crystalline counterparts of i-phases known as rational approximants. Based on these studies, the key findings are reported: (i) even for simple-metal systems in the weak scattering regime, differences in the electronic properties between the structural phases begin to emerge as the FS-JZB interaction increases in strength, (ii) semi-metallic conductivity and other anomalous transport properties are also observed in the approximant-crystals that contain transition metals (e.g. AlMnSi, AlFeCu), (iii) on the other hand, disordered i-phases and amorphous phases containing transition metals are found to possess metallic-glass-like properties. Experimental results reported indicate that the electronic properties of an ordered icosahedral quasicrystal are similar to those of a crystal in the presence of a strong FS-JZB interaction. Quite surprisingly, the elastic scattering time of electrons in the sp-d band ordered phases is found to be much longer than that in the nearly-free-electron i-phases. The propensity towards electron localization is ascribed to the realization of a potentially strong FS-JZB interaction in an ordered structure, particularly that with the icosahedral point group symmetry. The data have also provided evidence for the existence of rapidly varying electronic structures within the pseudogap of a semi-metallic i-crystal and its crystal analogue, despite the short electronic mean free path. The electron transport at low temperature can be described by the weak localization and electron-electron interaction effects. Contact with theories on quasiperiodic systems is also made. Finally, results from the stable decagonal crystals are discussed.     

Structural investigation of icosahedral Pd58.8U20.6Si20.6

The structure factors of the amorphous, icosahedral and crystalline Pd_58.8U_20.6Si_20.6 were measured with X-rays and neutrons. By comparing the radial distribution functions of the three phases, we find a similar short range order in the amorphous and icosahedral phase, but a different atomic arrangement in the crystalline phase. A magnetic long range order observed in the crystalline material is absent in the icosahedral phase.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

Quasicrystalline and rational approximant wave patterns in hydrodynamic and quantum nested wells

The eigenfunctions of nested wells with an incommensurate boundary geometry, in both the hydrodynamic shallow water regime and quantum cases, are systematically and exhaustively studied in this Letter. The boundary arrangement of the nested wells consists of polygonal ones, square or hexagonal, with a concentric immersed, similar but rotated, well or plateau. A rich taxonomy of wave patterns, such as quasicrystalline states, their crystalline rational approximants, and some other exotic but well known tilings, is found in these mimicked experiments. To the best of our knowledge, these hydrodynamic rational approximants are presented here for the first time in a hydrodynamic-quantum framework. The corresponding statistical nature of the energy level spacing distribution reflects this taxonomy by changing the spectral types.     

Formation of Tsai-type 1/1 approximants in In-Pd-RE (RE: rare earth metal) alloys

The formation of the 1/1 crystal approximant phase (1/1 phase) to the icosahedral phase (i phase) in In-Pd-RE (RE: rare earth metal) systems has been investigated. A new series of 1/1 phases were found in In₅₃Pd₃₃RE₁₄ (RE; Y, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, and Tm) alloys. For Y, Sm, Gd, Tb, Dy, and Ho, the 1/1 phases were found in annealed alloys, indicating that they are thermodynamically stable. The atomic structure of the 1/1 phases was directly observed by high-angle annular dark-field imaging performed via scanning transmission electron microscopy, revealing that the 1/1 phases consisted of a periodic arrangement of Tsai-type icosahedral clusters. Further, the atomic size effect on i phase formation, as well as formation conditions previously reported for other Tsai-type i and 1/1 phases were examined. It was found that the ratio of the atomic radius of base metals such as In and Pd affects i phase formation. Moreover, the appropriate range of the radius ratio for i phase formation was narrower than that for 1/1 phase formation.     

Specific heat and electrical resistivity of an icosahedral-structure Zr<Subscript>70</Subscript>Pd<Subscript>30</Subscript> alloy and of its amorphous and crystalline analogs

Binary icosahedral and crystalline phases of the Zr₇₀Pd₃₀ alloy were obtained in crystallization from the amorphous state during heat treatment. The specific heat and electrical resistivity of the icosahedral, amorphous, and crystalline phases were measured and compared. An increase in the electronic density of states on the Fermi surface, lattice softening, and an increase in the electron-phonon coupling constant were observed to occur with decreasing structural order. Despite the high valence electron density in the icosahedral phase, where the electronic densities of states are twice those in the crystal, the electrical resistivity of the icosahedral phase is ～50 times as high. Superconductivity was observed for the first time in the icosahedral phase of a binary system of transition metal atoms, Zr₇₀Pd₃₀.