Wenge Yang

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.

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.

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.

Elastic strains induced by electric fields in quasicrystals

The classical formulae of piezoelectric and electrostriction effects in crystals are generalized to quasicrystals. Two types of strain (phonon strain and phason strain) induced by electric fields have been studied. According to group representation theory, the matrix forms of piezoelectric and electrostriction tensors of two-dimensional pentagonal, octagonal, decagonal, dodecagonal and three-dimensional icosahedral cubic quasicrystals are given. If one takes the external field as a magnetic field, these tensors can also be used to describe magnetoelastic effects in quasicrystals.

Group-theoretical derivation of quadratic elastic invariants of two-dimensional quasicrystals of rank five and rank seven

Transformation matrices of phonon and phason strains under symmetry groups of two-dimensional (2D) quasicrystals (QCs) which are three-dimensional solids periodically stacked by aperiodic planes have been derived by using group representation theory. Quadratic invariants have been calculated for all 2D QCs of rank 5 and rank 7.