Renhui Wang

Symmetry groups, physical property tensors, elasticity and dislocations in quasicrystals

The first quasicrystal (QC) structure was observed in 1984. QCs possess long-range orientational and translational order while lacking the periodicity of crystals. An overview is given on some physical properties of QCs. It begins with group theory and symmetry. Then the thermodynamics of equilibrium properties and physical property tensors are discussed. Finally, the generalized elasticity theory of QCs and the elasticity theory of dislocations in QCs are presented.

Point and space groups and elastic behaviours of one-dimensional quasicrystals

A one-dimensional (1D) quasicrystal (QC) is defined as a three-dimensional body which is periodic in the x - y plane and quasiperiodic in the third dimension. Knowing that the possible symmetry operations for a 1D QC are 1, 2, 3, 4, 6, m, (inversion), (horizontal twofold rotation) and (horizontal mirror reflection), 31 possible point groups of 1D QCs have been deduced. These 31 point groups are divided into ten Laue classes and six systems. Considering screw (only ) and glide (only a, b and ) operations, 80 possible space groups of 1D QCs have also been obtained. According to our generalized elasticity theory of QCs, the elastic behaviours, including independent elastic constants and invariants, for each Laue class of 1D QCs have been discussed.

General expressions for the elastic displacement fields induced by dislocations in quasicrystals

The set of partial differential equations satisfied by the phonon and phason displacement fields u and w in quasicrystals has been solved by means of Fourier transform and eigenstrain methods, and general expressions of the elastic displacement fields induced by dislocations in quasicrystals have been given in terms of the Green function. The elastic Green tensor functions for every kind of quasicrystal are discussed in detail. Finally, as an example, the displacement fields induced by a straight dislocation line along the periodic tenfold axis of decagonal quasicrystals (three-dimensional) are calculated.

Point Groups and Elastic Properties of Two-Dimensional Quasicrystals

Possible point groups and elastic properties are discussed for a solid with two-dimensional quasiperiodic and one-dimensional periodic structures. The point groups and Laue classes are given for such structures with Fourier modulus of rank 5. The numbers of independent second-order elastic constants are calculated and all quadratic invariants are derived for all symmetries.

On some discrepancies in the literature about the formation of icosahedral quasi-crystal in Al-Cu-Fe alloys

To clarify some discrepancies in the literature about the formation of icosahedral quasi-crystal (IQC) in Al-Cu-Fe alloys, microstructures, and constituent phases of Al62.5Cu25Fe12.5 and Al65Cu20Fe15 alloys were studied, Each dendritic arm of the primarily solidified lambda -Al13Fe4 phase is a single crystal that possesses no definite orientation relationship with the IQC, formed by peritectic reaction (L + lambda + beta --> IQC) or a solid-state reaction (Cu-rich phases + lambda + beta --> IQC), This fact disproves an assumption that h-phase is an approximant of the IQC, Two types of cubic phase, beta -phase with CsCl structure containing more Fe and tau (3) phase, which is a superstructure and contains less Fe, were observed depending on the composition and thermal history of the samples.

Transmission electron microscopic analysis of stacking faults in a decagonal Al-Co-Ni alloy

Abstract The electron diffraction contrast of stacking faults in a decagonal Al70Co15Ni15 alloy has been analysed. The direction of the displacement vectors R of the stacking faults have been determined to be parallel to the and zone axes, respectively, for the first time in quasicrystalline structures. The corresponding fault planes are parallel to (1 0 0 0 0 0) and (0 1 0 0 0 0) lattice planes, respectively. The characteristics of the diffraction contrast fringes of the stacking faults in the decagonal Al-Co-Ni alloy are similar to those in conventional crystals.

Burgers vector determination of dislocations in an Al70Co15Ni15 decagonal quasicrystal

Abstract Not only the directions, but also the senses and magnitudes of the Burgers vectors b of dislocations in Al70Co15Ni15 decagonal quasicrystal have been determined for the first time by the large-angle convergent-beam electron diffraction technique. Right−hand screw dislocations with b = [3/400000] and [100000] have been determined.

Elasticity theory of straight dislocations in quasicrystals

The six-dimensional framework developed by Stroh to treat the elasticity theory of dislocations in crystals has been extended to a twelve-dimensional formalism in quasicrystals. The elastic fields induced by a straight dislocation line in quasicrystals are given in terms of integral representations, which may be suitable for numerical calculation.

Embedded-atom method study of the effect of the order degree on the lattice parameters of Cu-based shape memory alloys

Using the embedded-atom method, the variation in the total energies and lattice parameters with the degree of long-range order has been calculated for the parent and 18R1 martensite phases for several Cu-Zn-Al and Cu-Al-Ni shape memory alloys. It was found that the bond angle phi , i.e. the angle between lines connecting the nearest neighbours in the basal plane of the martensite, increases with increase in degree SB2 of B2-type order for both Cu-Zn-Al and Cu-Al-Ni alloys. When the degree SL2 of L21-type order increases, the bond angle phi increases for the Cu-Zn-Al shape memory alloys, but it decreases for the Cu-Al-Ni shape memory alloys. This result agrees well with experiment.

Elastic displacement fields induced by dislocations in dodecagonal quasicrystals

Abstract According to the general elastic model of defects in quasicrystals, the expressions of elastic displacement fields induced by infinite straight dislocations in dodecagonal quasicrystals are derived.