Twinning of quasicrystals and related structures

We consider for the first time twinning in quasicrystals and related structures in a systematic manner. The twinning operations are considered in the framework of six-dimensional crystallography. The number of twin variants and the symmetry of twinned aggregates are also discussed. It is shown that essentially two different types of interface can arise between any two twin variants.

An electron diffraction study of quasicrystals in Ti-37 at% Mn and Ti-24 at% Mn-13 at% Fe alloys

Electron diffraction studies were carried out to establish the icosahedral phase formation in rapidly quenched Ti-37 at% Mn and Ti-24 at% Mn-13 at% Fe alloys. Distortions in the diffraction spots and diffuse intensities in the diffraction patterns were investigated. The existence of a rational approximant structure and a decagonal like phase are also reported.

Quasicrystals:Indian research accomplishments and imperatives

: Within two months of the first report on quasicrystals in PRL in November 1984, Indian research which had a 'premature discovery' in 1978 in this area got under way, In the past nine years these efforts have led to original discoveries relating to new types of quasicrystalline phases as well as extensive investigations involving tiling theory, hyperspace, positron annihilation and electrical properties, These researches have been multi-institutional and multi-disciplinary. Enlightened and generous funding was extended by DST from 1986 by recognizing it as a thrust area in basic research via SERC and US-India Funds. International recognition, subjective though it is, in the form of citation of Indian papers, invited lectures and reviews, books as well as the membership of International Advisory Committee has followed and is among the highest in the fields of condensed matter science covered at the Bangalore meeting, Future directions pertaining to the exploration of mechanical and electronic properties as well as structures beyond the quasicrystalline order will be pointed out.

Indexing of decagonal quasicrystals .1. The T-8-phase

Indexing of a decagonal quasicrystal using the scheme utilizing five planar vectors and one perpendicular to them is examined in detail. A method for determining the indices of zone axes that a reciprocal vector would make in a decagonal phase of any periodicity has been proposed. By this method, the location of the zone axes made by any reciprocal vector can be predicted. The orthogonality condition has been simplified for the zone axes containing twofold vectors. The locations of zone axes have also been determined by an alternative method, utilizing spherical trigonometric calculations, which confirm the zone-axis locations given by the indices. The effect of one-dimensional periodicity on the indices and the accuracy of the zone-axis determination is discussed. Rules for the formation of zone axes between several reciprocal vectors and the prediction of all the reciprocal vectors in a zone are evolved.

Quasicrystals, crystals and multiple twins in rapidly solidified Al-Cr-Si, Al-Mn-Si and Al-Mn-Cr-Si alloys

The coexistence of quasicrystals and rational approximant structures (RAS) has been observed in melt-spun Al80Cr14Si6, Al80Mn14Si6 and Al75Mn10Cr5Si10 alloys. The presence of a b.c.c. alpha-AlMnSi phase in Al-Mn-Si and alpha-AlMnSi(Cr) phase in Al-Mn-Cr-Si has been seen. A multiple twinning around an irrational axis of the RAS has been reported in an aggregate of fine size cubic crystallites in all three alloys. Selected area diffraction patterns show that the crystalline aggregate symmetry is linked to the icosahedral point group symmetry (m35). Various ways of expressing the twin relationship in the cubic crystalline aggregates have been discussed. The thermal stability of the icosahedral phase at high temperatures reveals that the icosahedral phase in Al-Mn-Si and Al-Mn-Cr-Si alloys transforms to alpha-AlMnSi at temperatures of 690 and 670 K, respectively. In Al-Cr-Si alloy, heating to a high temperature (615 K) leads to the transformation of the icosahedral phase into a new metastable phase having an ordered cubic structure equivalent to alpha-AlMnSi. The occurrence of multiple twinning leading to icosahedral symmetry in the as-spun Al-Cr-Si alloy is presumably due to this metastable phase. Copyright (C) 1996 Acta Metallurgica Inc.

Structural and electrical transport properties of Al-Cu-Cr quasicrystals

Transport properties of quasicrystals in rapidly solidified as well as heat-treated Al65CU20Cr15 alloys were studied over a wide temperature range as a function of structure and microstructure. The characterization was done using x-ray diffraction, transmission electron microscopy and differential scanning calorimetry. Particular attention was paid to primitive to face-centered quasicrystalline transformation which occurs on annealing and the effect of microstructures on the transport behavior. The temperature dependence of resistivity is found to depend crucially on the microstructure of the alloy. Further, ordering enhances the negative temperature coefficient of resistivity. The low-temperature (T less than or equal to 25 K) resistivity of Al65Cu20Cr15 has been compared with that of Al63.5Cu24.5Fe12 alloy. In this region p(T) can be well described by a root T contribution arising from electron-electron interaction. We discuss our results in view of current theories.

Quasicrystals and their crystalline homologues in the Al–Mn–Cu ternary alloys

Electron diffraction and high-resolution electron microscopy have been employed to differentiate among icosahedral, decagonal and crystalline particles that occur in as-cast and rapidly solidified Al-Mn-Cu alloys. The resemblance between decagonal quasicrystals and crystals in their electron diffraction patterns is striking. The crystalline structure is based on the orthorhombic ‘Al3Mn’ structure, but also a new monoclinic phase called ‘X’ has been discovered and described here. The present observations are also closely related to the orthorhombic structures in Al60Mn11Ni4. The occurrence of fine-scale twinning and fragmentation into domains explains the complex diffraction effects.

Indexing of decagonal quasicrystals I. The T8-phase

Indexing of a decagonal quasicrystal using the scheme utilizing five planar vectors and one perpendicular to them is examined in detail. A method for determining the indices of zone axes that a reciprocal vector would make in a decagonal phase of any periodicity has been proposed. By this method, the location of the zone axes made by any reciprocal vector can be predicted. The orthogonality condition has been simplified for the zone axes containing twofold vectors. The locations of zone axes have also been determined by an alternative method, utilizing spherical trigonometric calculations, which confirm the zone-axis locations given by the indices. The effect of one-dimensional periodicity on the indices and the accuracy of the zone-axis determination is discussed. Rules for the formation of zone axes between several reciprocal vectors and the prediction of all the reciprocal vectors in a zone are evolved.

Observation of pseudo-gap and Kondo behaviour in Al70Pd30−xMnx quasicrystals

We report here the electrical and magnetic properties of Al70Pd30−xMnx quasicrystals (x=9 and 11), from resistivity and point contact spectroscopy measurements. Electrical resistivity shows a resistivity maximum for both of these compositions. The positive TCR at lower temperature is attributed to spin–orbit scattering. For x=11, we observe an upturn in the resistivity below 20 K, which follows a lnT dependence indicating Kondo-like behaviour. In the point contact spectroscopy studies we observe two regimes showing a V2 dependence at low bias voltages (for V<10 meV) crossing over to the V0.5 dependence at higher voltages. This is attributed to the signature of a pseudo-gap in the density of states at zero bias. We suggest that this V2 dependence can also arise due to magnetic scattering effects, which are signatures of the Kondo-like behaviour.

Wave propagation of phonon and phason displacement modes in quasicrystals: Determination of wave parameters

The paper presents the study of wave propagation in quasicrystals. Our interest is in the computation of the wavenumber (k(n)) and group speed (c(g)) of the phonon and phason displacement modes of one, two, and three dimensional quasicrystals. These wave parameter expressions are derived and computed using the elasto-hydrodynamic equations for quasicrystals. For the computation of the wavenumber and group speeds, we use Fourier transform approximation of the phonon and the phason displacement modes. The characteristic equations obtained are a polynomial equation of the wavenumber (k(n)), with frequency as a parameter. The corresponding group speeds (c(g)) for different frequencies are then computed from the wavenumber k(n). The variation of wavenumber and group speeds with frequency is plotted for the 1-D quasicrystal, 2-D decagonal Al-Ni-Co quasicrystals, and 3-D icosahedral Al-Pd-Mn and Zn-Mg-Sc quasicrystals. From the wavenumber and group speeds plots, we obtain the cut-off frequencies for different spatial wavenumber eta(m). The results show that for 1-D, 2-D, and 3-D quasicrystals, the phonon displacement modes are non-dispersive for low values of eta(m) and becomes dispersive for increasing values of eta(m). The cut-off frequencies are not observed for very low values of eta(m), whereas the cut-off frequency starts to appear with increasing eta(m). The group speeds of the phason displacement modes are orders of magnitude lower than that of the phonon displacement modes, showing that the phason modes do not propagate, and they are essentially the diffusive modes. The group speeds of the phason modes are also not influenced by eta(m). The group speeds for the 2-D quasicrystal at 35 kHz is also simulated numerically using Galerkin spectral finite element methods in frequency domain and is compared with the results obtained using wave propagation analysis. The effect of the phonon and phason elastic constants on the group speeds is studied using 3-D icosahedral Al-Pd-Mn and Zn-Mg-Sc quasicrystals. It is also shown that the phason elastic constants and the coupling coefficient do not affect the group speeds of the phonon displacement modes. (C) 2015 AIP Publishing LLC.

Heat capacities of Al62.5Cu25Fe12.5 quasicrystals and B2 related crystals

The heat capacities of two Al62.5Cu25Fe12.5 samples containing icosahedral quasicrystals and B2 related crystals respectively were measured with a high-precision automatic adiabatic calorimeter over the temperature range of 75-385 K. The heat capacities of both samples increase with temperature. At the low temperature range, the heat capacity of the quasicrystalline sample is higher than that of the B2 approximate. However, the heat capacity of the B2 sample becomes higher above 254.987 K. (C) 1999 Elsevier Science B.V. All rights reserved.

SOLUTE-DERIVED THERMAL STABILITY OF NANOCRYSTALLINE ALUMINUM AND PROCESSING FACTOR INFLUENCE ON THE FORMATION OF AL6MN QUASICRYSTALS IN MELT-SPINNING

Thermal stability of nanograined metals can be difficult to attain due to the large driving force for grain growth that arises from the significant boundary area constituted by the nanostructure. Kinetic approaches for stabilization of the nanostructure effective at low homologous temperatures often fail at higher homologous temperatures. Thermodynamic approaches for thermal stabilization may offer higher temperature stability. In this research, modest alloying of aluminum with solute (1 at.% Sc, Yb, or Sr) was examined as a means to thermodynamically stabilize a bulk nanostructure at elevated temperatures. After using melt-spinning and ball-milling to create an extended solid-solution and nanostructure with average grain size on the order of 30-45 nm, 1 h annealing treatments at 673 K (0.72 Tm) , 773 K (0.83 Tm) , and 873 K (0.94 Tm) were applied. The alloys remain nanocrystalline (<100 nm) as measured by Warren-Averbach Fourier analysis of x-ray diffraction peaks and direct observation of TEM dark field micrographs, with the efficacy of stabilization: Sr>Yb>Sc. Disappearance of intermetallic phases in the Sr and Yb alloys in the x-ray diffraction spectra are observed to occur coincident with the stabilization after annealing, suggesting that precipitates dissolve and the boundaries are enriched with solute. Melt-spinning has also been shown to be an effective process to produce a class of ordered, but non-periodic crystals called quasicrystals. However, many of the factors related to the creation of the quasicrystals through melt-spinning are not optimized for specific chemistries and alloy systems. In a related but separate aspect of this research, meltspinning was utilized to create metastable quasicrystalline Al6Mn in an α-Al matrix through rapid solidification of Al-8Mn (by mol) and Al-10Mn (by mol) alloys. Wheel speed of the melt-spinning wheel and orifice diameter of the tube reservoir were varied to determine their effect on the resulting volume proportions of the resultant phases using integrated areas of collected x-ray diffraction spectra. The data were then used to extrapolate parameters for the Al-10Mn alloy which consistently produced Al6Mn quasicrystal with almost complete suppression of the equilibrium Al6Mn orthorhombic phase.

New perspectives on forbidden symmetries, quasicrystals, and Penrose tilings

Quasicrystals are solids with quasiperiodic atomic structures and symmetries forbidden to ordinary periodic crystals—e.g., 5-fold symmetry axes. A powerful model for understanding their structure and properties has been the two-dimensional Penrose tiling. Recently discovered properties of Penrose tilings suggest a simple picture of the structure of quasicrystals and shed new light on why they form. The results show that quasicrystals can be constructed from a single repeating cluster of atoms and that the rigid matching rules of Penrose tilings can be replaced by more physically plausible cluster energetics. The new concepts make the conditions for forming quasicrystals appear to be closely related to the conditions for forming periodic crystals.