Structural And Physical Properties Of Quasicrystals

The discovery by Shechtman et al (1984) that certain Al-Mn alloys exhibit a phase with noncystallographic icosahedral symmetry challenged long-hold beliefs about the nature of translational order. Since that time the significant progress has been made in both experiment and theory. The researches extended from the structural and elastic properties of quasicrystals to their other properties which deepened our knowledge and understanding of quasicrystals. But many questions remain open and there is still long way to go towards a complete understanding of these materials.Quasicrystals possess both positional and orientational long-range order while lacking the periodicity of crystals. Thus quasicrystals can have five-, eight-, ten- and twelve-fold symmetries which are forbidden in crystallography. In addition, quasicrystals have two types of elastic hydrodynamic variables: one is the phonon variable and the other is the phason variable. It is worthwhile to propose a theoretical insight into what characteristic feature of physical properties in quasicrystals could follow from their symmetries alone and not from the details of atomic position and interatomic interactions. In this thesis, we use the group-theoretical method to investigate the relations between symmetries and physical properties and determine the independent components of physical property tensors in quasicrystals which is helpful in further research. In the case of crystals the method of direct verification is the most convenient method of derivation of the necessary conditions that are to be satisfied by a tensor invariant with respect to symmetries. This method has been adjust to fit in two-dimensional quasicrystals. By the new method, one who is not familiar with group theory can also determine all invariants of a physical property tensor of two-dimensional quasicrystals.The physical properties of quasicrystals we have explored in the thesis include nonlinear elastic properties, isotropic and anisotropic properties of elastic behavior, linear and nonlinear optical properties, pyroelectric, dielectric and piezoelectric properties, Hall effect and piezoresistance properties. The main results are:1. The independent components of nonlinear (third-order) elastic constants for tenfold quasicrystals are determined;2. Ordinary linear elastic properties of icosahedral quasicrystals are isotropic, whiletheir nonlinear elastic properties are anisotropic. Both ordinary linear and nonlinear elastic properties are all isotropic for all planar quasicrystals;3. All two-dimensional quasicrystals are uniaxial while some of them have nonlinear optical effect and icosahedral quasicrystals are optical isotropic and have no nonlinear optical effect;4. The icosahedral quasicrystals and two-dimensional quasicrystals with central symmetry have no piezoelectric effect, while the other two-dimensional quasicrystals could have piezoelectric effect due only to phonon field, only to phason field or to both.5. Quasicrystals can be divided into three classes according to their Hall effect. The First class consists of the icosahedral quasicrystals. The second class consists of two-dimensional quasicrystals with Albelian group. The third class consists of two-dimensional quasicrystals with non-Albelian group.6. The icosahedral quasicrystals and all two-dimensional quasicrystals but do-decagonal quasicrystals have piezoresistance effects due to both phonon and phason field. The dodecagonal quasicrystals have piezoresistance effect only due to phonon field.