Di-hua Ding

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.

Atomic model of dislocations in Al-Pd-Mn icosahedral quasicrystals

Abstract Using the Greens function and eigenstrain method, we derived an analytical expression for the elastic displacement fields induced by a dislocation in an icosahedral quasicrystal. In this paper, we calculate the special case where the line direction of the dislocation is parallel to a fivefold axis. Combining this expression with a structure model of icosahedral Al-Pd-Mn (the model of Boudard et al.) the atomic structure of straight dislocations was calculated and the corresponding high-resolution electron microscopy images were simulated. These are the first simulations of dislocations in an icosahedral quasicrystal using a realistic structure model. As an example, series of images of dislocations are presented with different twofold Burgers vectors of type |b⊥|/|b∥| = τ3 and |b⊥|/|b∥| = τ7 respectively, which were both observed experimentally. An analysis of the fringe patterns, obtained by inverse Fourier transformation of the simulated images is presented.

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.

Analytical expressions of the elastic displacement fields induced by straight dislocations in decagonal, octagonal and dodecagonal quasicrystals

According to the generalized Eshelby et al (1953 Acta Metall. 1 251) method of a straight dislocation line in quasicrystals (QCs), the analytical expressions for elastic displacement fields induced by dislocations in decagonal, octagonal and dodecagonal QCs have been derived when the dislocation lines are parallel to some symmetry axes.

Diffuse scattering from octagonal quasicrystals

Explicit formulae for thermal diffuse scattering from octagonal quasicrystals have been derived in terms of elastic constants. Contours of constant diffuse scattering intensity are calculated. The anisotropic peak shapes vary greatly even for Bragg spots aligned with a given direction in reciprocal space. Diffuse scattering patterns in the plane perpendicular to a given zone axis are associated with corresponding specific elastic constants. Analysis of peak shapes can be used to acquire numerical values of elastic constants if diffuse scattering patterns can be measured precisely.

Evaluation of some useful integrals in the theory of dislocations in quasicrystals

Abstract A method based on mathematical induction and Greens functions is presented for the evaluation of some integrals used often in the elasticity theory of dislocations in quasicrystals.