An ordered arrangement of atom columnar clusters in a pentagonal quasiperiodic lattice of an Al-Ni-Co decagonal quasicrystal

The structure of an Al-Ni-Co decagonal quasicrystal (called the S1-type superstructure), which shows diffraction patterns with superlattice reflections, has been studied by atomic-scale observations of electron microscopy. The structure of the decagonal quasicrystal can be characterized as an ordered arrangement of two kinds of atom columnar cluster with different directions of pentagonal symmetry. A fundamental lattice, which is constructed by connecting all the atom clusters, shows a pentagonal quasiperiodic lattice with a bond length of about 2 nm. The pentagonal lattice is divided into two superlattices, which are constructed by connecting atom clusters with the same directions of pentagonal symmetry, with a bond length of 2     

Behaviour of helium in UO2 single crystals: a transmission electron microscopy investigation

We have found that the structure of an Al-Ni-Co decagonal quasicrystal, which shows a diffraction pattern with many superlattice reflections (called a 'type I superlattice'), can be described as an ordered arrangement of two kinds of atomic columnar cluster with different orientations of their pentagonal symmetry. The fundamental lattice, which is constructed by connecting the clusters, is a rhombic quasiperiodic lattice with a bond length of about 2nm. The two kinds of cluster are placed at the lattice points in a definite manner such that the two connected clusters have different orientations.     

Structural study of a superlattice Al-Ni-Ru decagonal quasicrystal using high-resolution electron microscopy and a high-angle annular dark-field technique

A high-quality superlattice Al-Ni-Ru decagonal quasicrystal with 0.4nm periodicity, formed in the conventionally solidified Al₇₀Ni₂₀Ru₁₀ alloy, has been studied by high-resolution electron microscopy and a high-angle annular dark-field (Z-contrast) technique. It has been clearly revealed that its structure is characterized as an aperiodically ordered arrangement of decagon-shaped atomic columnar clusters which have a diameter of 2nm and show pentagonal symmetry. On the basis of high-resolution electron microscopy structure images, and the atom-resolution Z-contrast observations which highlight the transition-metal sites, the arrangement of atoms in the superlattice decagonal quasicrystal are proposed.     

A new highly ordered Al-Ni-Ru decagonal quasicrystal with 1.6 nm periodicity

A new decagonal quasicrystal (the D phase) with a period of about 1.6 nm was found to form in conventionally solidified and heat-treated Al₇₅Ni₁₅Ru₁₀ alloys. The electron diffraction patterns of the Al-Ni-Ru D phase exhibit a large number of quite sharp diffraction spots located at precise decagonal symmetry positions, indicating a highly ordered decagonal quasicrystal with a long-range quasiperiodic correlation. The D phase is formed with a composition close to Al₇₄Ni₁₅Ru₁₁, as determined by energy-dispersive X-ray analysis. By means of high-resolution electron microscopy, the structural features of the Al-Ni-Ru D phase, which are obviously different from that of the Al-Pd D phase (a typical decagonal quasicrystal with 1.6 nm periodicity reported previously), have been revealed.     

Chemical effects on periodicity and structure of decagonal phases in Al-Ni- and Al-Co-based alloys

Abstract

The structures of decagonal phases in binary Al-Ni and Al-Co systems and ternary Al₇₀Ni _x TM_1?x(TM = Co, Rh or Ir) alloys have been studied by electron diffraction. In the Al-Co system, the periodicity of the decagonal phase is 1.6 nm in Al₈₀Co₂₀, and 0.8 nm in Al₇₆.₅Co_23.5 and Al₇₂Co₂₈, suggesting that the stacking rule between Al and Co atoms is different along the c axis for the three alloys. In the ternary systems, diffuse streaks and periodicity systematically vary with the atom substitution of Co for Ni and Ir for Ni, indicating that Ni, Co and Ir atoms play different roles in the decagonal phase and exhibit various sorts of chemical order with Al atoms.     

A new stacking motif in the decagonal approximant Mn3Ga5

The structure of the decagonal approximant Mn₃Ga₅     

Preparation of decagonal Zn-Mg-Y by melt spinning

It is shown, for the first time, how pure decagonal Zn-Mg-Y can be prepared by melt spinning and annealing. Study of the phase formation was performed by differential scanning calorimetry and the sample was further investigated by X-ray and electron diffraction. The lattice constants of the decagonal phase are a q =4.592Å and c =5.198Å calculated from a physical space model, or a q =4.485Å and c =5.193Å from a hyperspace model.     

On the Ranges of Algebraic Functions on Lattices

We study ranges of algebraic functions in lattices and in algebras, such as Łukasiewicz-Moisil algebras which are obtained by extending standard lattice signatures with unary operations.We characterize algebraic functions in such lattices having intervals as their ranges and we show that in Artinian or Noetherian lattices the requirement that every algebraic function has an interval as its range implies the distributivity of the lattice. Presented by Daniele Mundici     

Transformation-induced elastic strain effect on the precipitation kinetics of ordered intermetallics

Abstract

A transformation-induced elastic strain effect on the decomposition kinetics of a disordered phase into a mixture of ordered and disordered phases was investigated for a prototype binary alloy in two dimensions (2-D) by using a computer simulation technique. The simulation technique not only described simultaneously different processes, such as atomic ordering, clustering, disordering and coarsening, but also produced automatically ordered structures and alloy morphologies. It was found that irrespective of the degree of the crystal lattice mismatch between precipitates and the matrix, the alloy morphologies, developed during the congruent ordering stage which preceded the decomposition, showed no alignment in any of the crystallographic directions. Alignment developed during subbequent decomposition of the congruently ordered single phase, which resulted in the appearance of an equilibrium disordered phase preferentially along the antiphase domain boundaries. It became increasingly pronounced as the time of alloy aging increased. The aligned morphology finally formed the modulated structure found in many alloys. This mechanism of modulated structure formation is new since almost all previous experimentally observed modulated structures were interpreted as a result of a homogeneous spinodal decomposition. The predicted kinetics was found to be in excellent agreement with recent experimental results in a Fe-Si system and should be expected in most two-phase alloys with an ordered intermetallic precipitate whose stress-free lattice constant is significantly different from that of the disordered matrix.     

Epitaxial decagonal thin films on crystalline substrates

Al-Cu-Fe-Cr quasicrystalline thin films were grown on atomically flat Al 2 O 3 sapphire (0001) substrates by single-target magnetron sputtering followed by annealing. A decagonal phase with the tenfold axis A 10 parallel to the substrate surface normal was observed. The epitaxial decagonal film had two different unique orientations: a twofold P axis A 2P and a twofold D axis A 2D parallel to of the substrate. These two configurations were explained using a coincidence reciprocal lattice planes model for the interface energy. We show that this classic approach for crystal-crystal epitaxy can be applied to quasicrystal-crystal systems.     

On Varieties of Biresiduation Algebras

A biresiduation algebra is a 〈/,\,1〉-subreduct of an integral residuated lattice. These algebras arise as algebraic models of the implicational fragment of the Full Lambek Calculus with weakening. We axiomatize the quasi-variety B of biresiduation algebras using a construction for integral residuated lattices. We define a filter of a biresiduation algebra and show that the lattice of filters is isomorphic to the lattice of B-congruences and that these lattices are distributive. We give a finite basis of terms for generating filters and use this to characterize the subvarieties of B with EDPC and also the discriminator varieties. A variety generated by a finite biresiduation algebra is shown to be a subvariety of B. The lattice of subvarieties of B is investigated; we show that there are precisely three finitely generated covers of the atom. Mathematics Subject Classification (2000): 03G25, 06F35, 06B10, 06B20 Dedicated to the memory of Willem Johannes Blok     

A three-dimensional model for the octagonal phase

Abstract

A three-dimensional model for the octagonal phase based on a cut-projection from the eight-dimensional hypercubic lattice is presented here. The phason-phonon coupling which leads the octagonal phase into 45° twinned cubic ones is also studied. Conclusions of this realistic model do not modify the previously stated conclusions from the standard but incomplete two-dimensional treatment.     

Transformation of the decagonal quasicrystalline phase to a B2 crystalline phase in the Al-Cu-Co system by high-energy ball milling

Samples of a decagonal quasicrystalline phase, located in the Al-Cu-Co system and synthesized by a slow cooling technique, have been mechanically milled in a high-energy planetary ball mill for 10, 20 and 30h. The milled powders, as well as powders that had been annealed (after milling) for times ranging from 30 to 150min at 600C, were characterized by X-ray diffraction, scanning electron microscopy and transmission electron microscopy. A phase transformation from the decagonal phase to a B2 crystalline phase during highenergy ball milling is reported here for the first time. Powders milled for more than 10h contained predominantly the B2-type crystalline phase with a lattice parameter of 0.29nm. This crystalline phase was found to be quite stable after milling for 30h and also on subsequent annealing at 600C. These experimental results lend support to an earlier suggestion that the decagonal phase in Al-Cu-Co is actually less stable than the B2 phase at low temperatures.     

Twinning in the structure of the ‘decagonal’ phase Al65Cu20Co15

Abstract

The existence of twinning in the pseudo-decagonal phase Al₆₅Cu₂₀Co₁₅ has been established through TEM studies. From electron diffraction patterns, a rhombic crystalline lattice with a very large unit cell is easily identified. Diffraction patterns for microtwinned regions exhibit splitting and distortion of the reflections which is a result of the overlap of lattices which are rotated by 36° with respect to one another. While patterns from single components of the twins exhibit only pseudo-tenfold symmetry, those from the microtwinned regions exhibit nearly perfect tenfold symmetry.     

A new stable icosahedral quasicrystal in the Cd-Mg-Dy system

A new stable icosahedral quasicrystal has been found in annealed Cd-Mg-Dy alloys. The composition of the icosahedral phase was determined to be approximately Cd₆₆Mg₂₁Dy₁₃. Powder X-ray and electron diffraction patterns revealed that the phase has a primitive icosahedral lattice with a quasilattice parameter a_R = 0.5634 nm. The electron diffraction study confirmed that the phase has a well ordered primitive icosahedral structure.     

Stability and strain of decagonal Al-Ni-Co quasicrystal under high pressure up to 70GPa

The stability of high-quality decagonal Al72Ni20Co8 single quasicrystals has been investigated under high pressure up to 67 GPa by means of an in situ angular-dispersive X-ray powder diffraction method using synchrotron radiation and a diamond anvil cell. It is found that the compression behaviour is almost isotropic. On the other hand, the strain behaviour on compression is found to be fairly anisotropic. This means that the quasiperiodic structure in the decagonal Al72Ni20Co8 quasicrystal is much more easily distorted than is the periodic structure.     

Plastic deformation behaviour of decagonal Al70Ni15Co15 single quasicrystals

High-temperature deformation experiments have been performed on decagonal Al₇₀Ni₁₅Co₁₅ single quasicrystals at a constant strain rate of 10^-5s^-1 in the temperature range between 700 and 860°C. The samples were deformed in compression with the compression axis in different orientations, parallel to, inclined by 45° and perpendicular to the tenfold symmetry axis. Stress relaxation tests and temperature changes were carried out to determine thermodynamic activation parameters. The flow stress and the activation enthalpy were found to depend on the sample orientation whereas dependences of the activation volume and the stress exponent on the orientation were not observed. Additionally, deformation tests were performed on samples of the basic Co-rich modification of the decagonal phase at the temperature of 860°C in the same three orientations. The deformation behaviours of the two different modifications of the decagonal phase are discussed.     

Chemical ordering of Co and Ni in a W-(AlCoNi) crystalline approximant related to Al–Co–Ni decagonal quasicrystals studied by atomic resolution energy-dispersive X-ray spectroscopy

A W-(AlCoNi) crystalline approximant, which is closely related to Al–Co–Ni decagonal quasicrystals, in an Al_72.5Co₂₀Ni_7.5 alloy has been studied by atomic resolution energy-dispersive X-ray spectroscopy (EDS), in an instrument attached to a spherical aberration (Cs)-corrected scanning transmission electron microscope. On high-resolution EDS maps of Co and Ni elements, obtained by integrating many sets of EDS data taken from undamaged areas, chemical ordering of Co and Ni is clearly detected. In the structure of the W-(AlCoNi) phase, consisting of arrangements of transition-metal (TM) atoms located at vertices of pentagonal tilings and pentagonal arrangements of mixed sites (MSs) of TM and Al atoms, Co atoms occupy the TM atom positions with the pentagonal tiling and Ni is enriched in part of the pentagonal arrangements of MSs.     

Structural characteristics of a high-quality Al?Ni?Ru decagonal quasicrystal with 1.6nm periodicity,studied by atomic-scale electron microscopy observations

We report the structural characteristics of a high-quality stable decagonal quasicrystal (D phase) with 1.6nm periodicity, formed in Al₇₅Ni₁₅Ru₁₀ alloy annealed at 890°C for 24h. The tiling structure and the arrangement of transition-metal atoms (Ru and Ni) in this Al-Ni-Ru D phase have been clearly revealed by high-resolution electron microscopy (HREM) and by highangle annular detector dark-field (HAADF) scanning transmission electron microscopy (STM) respectively. On the basis of the HREM and HAADF STM observations, the relationship between the arrangement of local structural units and the formation of the long-range quasiperiodic tiling structure is discussed.