Elastic theory of icosahedral quasicrystals - application to straight dislocations

Abstract

In quasicrystals, there are not only conventional, but also phason displacement fields and associated Burgers vectors. We have calculated approximate solutions for the elastic fields induced by two-, three-and fivefold straight screw-and edge-dislocations in infinite icosahedral quasicrystals by means of a generalized perturbation method. Starting from the solution for elastic isotropy in phonon and phason spaces, corrections of higher order reflect the two-, three-and fivefold symmetry of the elastic fields surrounding screw dislocations. The fields of special edge dislocations display characteristic symmetries also, which can be seen from the contributions of all orders.

Fundamental solutions of penny-shaped and half-infinite plane cracks embedded in an infinite space of one-dimensional hexagonal quasi-crystal under thermal loading

“…It has been reported that the Lamé constants of AlPdMn, a special kind of icosahedral QC, are reported to be λ 0 = 85 GPa and μ 0 = 65 GPa [42], and that the ratio between the phonon-phason coupling coefficient and the shear modulus R i /μ 0 is approximately 0.03 [44]. Furthermore, Richer et al [42] also showed that the phason constants K 1 = 0.084 GPa and K 2 = 0.036 GPa. In addition, the coefficient of thermal conductivity is lower than those of conventional crystals [2,32].…”

Non-linear generalized elasticity of icosahedral quasicrystals

“…They refer to the same coordinate systems as in [15,19,22]. In Table A1, the icosahedral irreducible transformation matrices are given, which the irreducible strains and stresses transform after.…”

“…In Table A1, the icosahedral irreducible transformation matrices are given, which the irreducible strains and stresses transform after. Other coordinate systems in use are compared to our in some detail in [15].…”

“…The phason displacement gradient ∂w ∂a splits into a Γ 4 and a Γ 5 part (see (9)), and both are assumed to increase the elastic energy [2,15]. Therefore, we have a phason strain tensor η w with…”

Steady-state propagation of dislocations in quasi-crystals

“…Phonon and phason fields around a stationary dislocation have been explicitly evaluated as functions of elastic constants for several classes of quasi-crystals (e.g. Yang et al 1995;Ricker et al 2001). The investigation has been extended to moving dislocation in Zhu et al (2007) by using a displacement function and in Schaaf et al (2000) by a numerical approach.…”