Crystalline Approximants Research Articles

Quasicrystal-like structure and its crystalline approximant in an Fe 48Cr 15Mo 14C 15B 6Tm 2 bulk metallic glass

Nanoscale quasicrystal-like structural states have been found in the course of crystallization in an Fe-based Fe 48Cr 15Mo 14C 15B 6Tm 2 bulk metallic glass. The quasicrystal-like structure is similar with the χ-FeCrMo structure exhibiting a deformed tenfold diffraction pattern due to projected pentagonal arrangements regarded as a Mo framework. We show the preliminary structural model for the quasicrystal-like structure and discuss the three-dimensional features based on the χ-FeCrMo crystalline approximant.

First-principles study for effect of lattice defects on the crystal structure of the Zn-Sc cubic crystalline approximant

Effects of impurity and vacancy introductions are investigated by the first-principles structural relaxation. Studied concentration of the lattice defects is 0.6 at%. As the impurity, a Cu atom is substituted for a Zn atom in Zn6Sc. For this concentration, the plausible candidate site of Cu substitution is the glue site distributing in the interstitial region between icosahedral clusters. The most stable vacancy site is the core of the icosahedral cluster. Some of the introduced vacancies migrate several angstrom and reach the core. A special site being outside the core plays an important role for the vacancy migration. The vacancy introduced near this site migrates to the core. Significant Zn-Zn bonds are found in the charge density map. The stability of the defect-introduced structure is discussed in terms of a breaking of this bond.

Structural stability of an icosahedral Cd-Yb quasicrystal and its crystalline approximant under high pressure

Synchrotron x-ray powder diffraction studies on an icosahedral Cd-Yb quasicrystal (iCd-Yb), its crystalline approximant of Cd6Yb (cCd-Yb) and the related Cd25Eu4 (cCd-Eu) material were performed under pressures of up to about 40 GPa at room temperature. The icosahedral lattice of the atomic cluster in iCd-Yb and the bcc lattices in cCd-Yb and cCd-Eu were found to be stable under pressure. Although the Tsai-type atomic cluster can possibly be distorted in various ways, low-symmetry distortion modes do not seem to develop even at high pressure. It is considered that the cluster structure of centrosymmetric dense atomic packing prevented low-symmetry distortions and consequently provided the cluster lattice stability. The bulk moduli were also determined to be B0(iCd-Yb) = 49.2(3) GPa, B0(cCd-Yb) = 46.1(7) GPa and B0(cCd-Eu) = 49.6(3) GPa, which were much lower than the typical reported values for other quasicrystalline alloys.

Exploratory Synthesis: The Fascinating and Diverse Chemistry of Polar Intermetallic Phases†This article is based on J. D. Corbett’s address upon receipt of the 2008 American Chemical Society’s F. Albert Cotton Award in Synthetic Inorganic Chemistry sponsored by the F. Albert Cotton Endowment Fund.

Exploratory synthetic adventures regarding the inorganic chemistry of polar intermetallic phases have proven to be especially productive of novel compositions, new and unprecedented structures, and unusual bonding regimes. Reactions of diverse elements with widely different electronegativities allow the definition of two opposed classes of products: polycationic or polyanionic clusters or networks of metals paired with the corresponding monatomic anions or cations. These can be usefully viewed as intermetallic "salts", redox products of simpler neutral intermetallic systems but with widely different factors governing their stabilities. Thus, combinations of rare-earth metals alone or with late transition metals form a novel variety of polymetal network structures with relatively isolated telluride (or halide) spacer anions. Similarly, extensions of traditional Zintl phases of the alkali or alkaline-earth metals from the later p elements to the earlier triels, Ga-Tl especially, yield many new and elegant polyanionic structures. The substitution or addition of still earlier p or late d metal components produces still electron-poorer and more condensed polar intermetallic phases with increasingly delocalized bonding, higher coordination numbers, and more unusual structures and bonding. These discoveries have also led to new approaches: electronic tuning via band calculations to generate new families of quasicrystals and their crystalline approximants with their characteristic structural regimes and regularities. Gold as a substituent generates particularly novel bonding in arrays of mixed metals or polygold anionic networks.

Structure of the surface layer of mercury and adhesion of Langmuir monolayers on it

A model crystalline approximant of the surface layer (SL) structure of liquid mercury is formed using the algorithm, previously applied to form a crystalline approximant of the SL structure of water, the experimental data on the SL structure of mercury, and the stereochemical data for Hg atoms in the α-Hg crystalline phase and bulk liquid mercury. The correspondence of the metrics of the crystalline approximant proposed for the SL structure of mercury and Langmuir monolayers composed of organic molecules with hydrocarbon tails and different hydrophilic groups on liquid mercury to the position of molecules along mercury SL is shown.

Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra

All hard, convex shapes are conjectured by Ulam to pack more densely than spheres, which have a maximum packing fraction of phi = pi/ radical18 approximately 0.7405. Simple lattice packings of many shapes easily surpass this packing fraction. For regular tetrahedra, this conjecture was shown to be true only very recently; an ordered arrangement was obtained via geometric construction with phi = 0.7786 (ref. 4), which was subsequently compressed numerically to phi = 0.7820 (ref. 5), while compressing with different initial conditions led to phi = 0.8230 (ref. 6). Here we show that tetrahedra pack even more densely, and in a completely unexpected way. Following a conceptually different approach, using thermodynamic computer simulations that allow the system to evolve naturally towards high-density states, we observe that a fluid of hard tetrahedra undergoes a first-order phase transition to a dodecagonal quasicrystal, which can be compressed to a packing fraction of phi = 0.8324. By compressing a crystalline approximant of the quasicrystal, the highest packing fraction we obtain is phi = 0.8503. If quasicrystal formation is suppressed, the system remains disordered, jams and compresses to phi = 0.7858. Jamming and crystallization are both preceded by an entropy-driven transition from a simple fluid of independent tetrahedra to a complex fluid characterized by tetrahedra arranged in densely packed local motifs of pentagonal dipyramids that form a percolating network at the transition. The quasicrystal that we report represents the first example of a quasicrystal formed from hard or non-spherical particles. Our results demonstrate that particle shape and entropy can produce highly complex, ordered structures.

Structural defects in Al–Ni–Rh and Al–Pd–Fe crystalline approximant phases

Abstract Structural defects of high density have been observed to exist in the as-cast crystalline approximants Al–Ni–Rh ξ and Al–Pd–Fe ε 16 which contain columnar atom clusters as the most fundamental building blocks. By means of high-resolution electron microscopy (HREM), the structural and distributional features of these defects have been revealed. It is clearly shown that, accommodating structural defects of high density in the Al–Ni–Rh ξ-phase can lead to the formation of a unique mixed structure in which nearly regular arrangement of structural defects can be established. On the basis of HREM observations, long-range structural features of the defective ξ- and ε 16-structures have been discussed in terms of the characteristic arrays of columnar atom clusters.

Synthesis and superstructure of Al—Ir, Al—Ir—Pd crystalline approximants and their electrical resistivities

Abstract Chemically ordered Al2.7Ir and Al64.5Ir22Pd13.5 1/0 approximants are prepared by two different methods and characterized by X-ray diffraction and transmission electron microscopy. Al2.7Ir possesses a primitive cubic lattice with a = 15.345(6), whereas Al64.5Ir22Pd13.5 has a face-centered cubic lattice with a = 15.497(9). Examination of the samples prepared by two different methods reveals that the texture of the samples prepared by spark plasma sintering is more homogeneous than those prepared by arc melting. Electrical resistivities of both the compounds exhibit metallic characters, i.e., a positive temperature coefficient of the resistivity (TCR) with a high resistivity value. The results suggest that the TCR may not always be negative for 1/0 approximants with 15 to 16 periodicity but the high residual resistivities are common to all the approximants, which is presumably attributed to the common structural unit, an icosahedral cluster of about 7.7.

Atomic arrangement of Al–Co–Ni Co-rich quasicrystal and W(AlCoNi) crystalline approximant

Atomic arrangement of Al–Co–Ni Co-rich quasicrystal and W(AlCoNi) crystalline approximant

Successive phase transition of a Cd–Yb 1/1 crystalline approximant under high pressure

Successive phase transition of a Cd–Yb 1/1 crystalline approximant under high pressure

Approximant Phases and an Icosahedral Quasicrystal in the Ca−Au−Ga System: The Influence of Size of Gallium versus Indium

Two crystalline approximants (ACs) and their corresponding icosahedral quasicrystal (i-QC) are obtained in the Ca-Au-Ga system through conventional solid-state exploratory syntheses. Single crystal structural analyses reveal that the 1/1 AC, Ca 3Au x Ga 19- x ( x = approximately 9.3-12.1) [ Im3, a = 14.6941(6)-14.7594(6) A], has the empty cubes in the prototypic YCd 6 (= Y 3Cd 18) now fully occupied by Ga, resulting in a 3:19 stoichiometry. In parallel, the distorted cubes in the 2/1 AC, Ca 13Au 57.1Ga 23.4 [ Pa3, a = 23.9377(8) A] are fully or fractionally occupied by Ga. The valence electron count per atom ( e/ a) for the 2/1 AC (1.64) is smaller than that over the 1/1 AC composition range (1.76-2.02), and the e/ a of the Ca 15.2Au 50.3Ga 34.5 i-QC, 1.84, is somewhat distant from typical values for Tsai-type i-QCs ( approximately 2.0). Comparisons of the gallium results with the corresponding In phases suggest that the structural differences result mainly from size rather than electronic factors. The 1/1 and 2/1 appear to be thermodynamically stable on slow cooling, as usual, whereas the i-QC isolated by quenching decomposes on heating at approximately 660 degrees C, mainly into 2/1 AC and Ca 3(Au,Ga) 11. Calculations of the electronic structure of 1/1 AC suggest that the Fermi sphere-Brillouin zone interactions remain important for the Ca-Au-Ga i-QC.

A new orthorhombic approximant of the icosahedral Al–Cu–Fe quasicrystal

We report on the formation of a new crystalline approximant phase of the icosahedral (i-)Al–Cu–Fe quasicrystal. This phase is formed during sintering of Al-based composites reinforced with i-AlCuFeB quasicrystalline particles. The structure of this phase has been characterized by transmission electron microscopy (TEM) and high-resolution electron microscopy (HREM). TEM revealed that it is a B-centred orthorhombic phase with lattice parameters a = 1.166 nm, b = 1.195 nm and c = 3.44 nm. Its chemical composition, as determined by electron energy loss spectroscopy (EELS), is close to Al76.9Cu2.7Fe20.4, with an average number of valence electrons per atom e/a of 1.92, similar to the value in all other approximants of the i-phase discovered thus far. Initial results on local atomic arrangements along one of its pseudo-5-fold axes are also presented.

Defect Structures in Al-Ni-Rh Crystalline Approximants Studied by HREM and HAADF Techniques

By means of a combination of high-resolution electron microscopy (HREM) and high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) techniques, we have directly revealed that periodic arrangements in different manners for flattened hexagons constructed with atom columnar clusters can form two Al-Ni-Rh crystalline approximant phases. In contrast to periodic arrangements of flattened hexagons, configurations and distributions of various defects in these structurally-complicated alloy phases have been examined and their structural characteristics discussed. HREM observations clearly show that structural defects in Al-Ni-Rh crystalline approximants are of phason type and they are correlated with incorrect arrangements of atom columnar clusters. The distribution of high density planar defects can destroy the long-range periodicity in at least one direction in the pseudo decagonal symmetry plane. By means of the HAADF-STEM imaging technique, the existence of ill-formed atom columnar clusters in the core area of a linear defect, which is usually not visible in HREM observations, has been clearly revealed.

Structural Defects and Changes in Al-Pd-Fe Crystalline Approximant

Crystalline approximants structurally related to decagonal quasicrystal in the as-cast and heat-treated Al75Pd15Fe10 alloys and defect structures in them have been studied by means of high-resolution electron microscopy (HREM). Structural defects of linear and planar types were found to exist extensively in the orthorhombic ε16-phase formed in the as-cast Al75Pd15Fe10 alloy. In contrast with the distribution and configuration of the defects in the as-cast ε16-phase, we found that high-temperature heat treatment promotes the formation of a kind of regular network of structural defects in the ε16-phase. This suggests that rearrangements of atom clusters and as well as defects occurred due to the heat treatment. The relationship between the distribution of atom clusters and the configuration of defects will be discussed.

Positron annihilation spectroscopy in the study of quasicrystals and their related materials

AbstractRecent advances in the study of quasicrystals (QC's) and their related materials (crystalline approximants) by using positron annihilation spectroscopy are reviewed. We describe how a series of positron annihilation spectroscopy has been applied for the studies of aperiodic QC's. Positron lifetime measurements revealed the presence of high concentration of structural vacancies giving rise to saturation trapping for QC's and approximants studied. Chemical environments around the structural vacancies were successfully clarified by coincident Doppler broadening measurements. In addition, the concentrations of structural vacancies were estimated by analyzing the positron diffusion data obtained by a slow positron beam under the saturation trapping condition. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Development of the Ca−Au−In Icosahedral Quasicrystal and Two Crystalline Approximants: Practice via Pseudogap Electronic Tuning

Electronic tuning and syntheses to gain the icosahedral quasicrystal (i-QC) (Ca14.1(2)Au44.2(8)In41.7(7), e/a = 1.98) and two approximant crystals (ACs) are reported. The tuning was derived from Na2Au6In5, another cubic Mg2Zn11-type structure, for which the Fermi level (e/a = 1.77) should tune to a calculated pseudogap (e/a = 2.02) under a rigid band assumption. The 1/1 AC, Ca3Au12.2(1)In6.3(2) (e/a = 1.73), crystallizes in space group Im, with a = 15.152(2) A, Z = 8, and the 2/1 AC, Ca12.6(1)Au37.0(2)In39.6(6) (e/a = 2.01), in Pa, with a = 24.632(3) A , Z = 8. Both have substantially fixed compositions according to lattice dimensions. Structure analyses reveal that both ACs contain triacontahedral clusters as the basic building blocks at the body-centered and primitive cubic unit cell levels, respectively. Densities-of-states (DOS) analyses for the 1/1 AC structure reveal a pseudogap at e/a = 2.00, close to the point at which the i-QC was predicted and experimentally tuned. Phase relationships of the ACs and the i-QC are reported according to DTA, XRD, and temperature-dependent XRD measurements. The QC is thermodynamically metastable below approximately 500 degrees C.

準結晶研究の最近の展開 ４．準結晶のはたらき（準結晶の物性と応用）Ａｌ基準結晶と近似結晶の熱電物性

Al-based icosahedral quasicrystals and their corresponding approximants are characterized by large electrical resistivity, large thermoelectric power, and very small thermal conductivity. The factors leading to these characteristics were investigated by use of their crystalline approximants, which allow us to employ the structure analysis, band calculation, and phonon calculation well developed for crystalline materials. It is found that the quasiperiodic order does not play an exclusive role in providing the characteristic thermoelectric properties, while the icosahedral-symmetry and the characteristic quasi-Bllirouin-zone significantly contribute to these properties by deepening pseudogap at the Fermi level, reducing the mumber of acoustic phonons, and enhancing Umklapp scattering of phonons.

Defect-modulated structures in Al–Ni–Rh crystalline approximants

Defect-modulated Al–Ni–Rh crystalline approximants, which are structurally related to a decagonal quasicrystal with 1.6 nm periodicity, have been found to form in an as-solidified Al75Ni15Rh10 alloy. Their structural features were studied by a combination of high-resolution electron microscopy (HREM) and high-angle annular dark field scanning transmission electron microscopy (HAADF-STEM). The results show that the prefect structures of Al–Ni–Rh crystalline approximants are characterized by periodic arrangements of hexogen units (H) constructed from atom columnar clusters. Defect-modulated structures were formed due to ordered arrangement of one- or two-dimensional structural defects of high density. The basic structural defect is associated with incorrect arrangements of atom columnar clusters which appear as polygons different from the H units. These polygons of atom columnar clusters represent a type of linear defect extending along the columnar axis direction, and they can array to form a planar defect. By means of the HAADF-STEM imaging technique, the structural nature of the core area for the linear defect, which usually exhibits dark contrast in HREM observations, has been clearly revealed.

準結晶研究の最近の展開 ３．準結晶のかたち（準結晶の構造）Ｃｄ‐Ｙｂ近似結晶の低温高圧下で現れる多様な構造秩序

準結晶研究の最近の展開 ３．準結晶のかたち（準結晶の構造）Ｃｄ‐Ｙｂ近似結晶の低温高圧下で現れる多様な構造秩序

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.