Phonon–phason coupling in a Mg–Ga–Al–Zn icosahedral quasicrystal

Abstract

Precise X-ray diffraction measurements have revealed that phonon (conventional) strain is introduced at the phase transition from an icosahedral quasicrystal to its orthorhombic crystal approximant in a Mg-Ga-Al-Zn alloy. From the magnitude of the measured phonon strain, the phonon-phason coupling constant has been evaluated. This constant is approximately À0:03 (: shear modulus) and it is in good agreement with the result of a theoretical calculation reported previously (W.-J. Zhu and C.L. Henley, Europhys. Lett. 46 748 (1999)). This is the first study that experimentally evaluates the phonon-phason coupling constant in any existing quasicrystalline phase.

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

“…Such a purpose can be fulfilled in view of the results available in the literature [32,[41][42][43][44][45][46]. 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.…”

Experimental evaluation of phonon–phason coupling in icosahedral quasicrystals

“…For the Mg-Ga-Al-Zn system, the details of the sample preparation and X-ray diffraction measurements were reported previously [30]. For the Al-Cu-Fe system, experimental details are given below.…”

“…It should be noted that the equations presented elsewhere [27,29,30] can be obtained from equation (5) by the substitution of w ij by w ji and the coordinate transformation (x ! y, y !…”

Comparative study on internal friction in an Al-Pd-Mn icosahedral quasicrystal and its crystal approximants

“…They showed that ͉K 3 ͉ is 0.02-0.1 for ͑Al,Cu͒-Li and 0.003-0.02 for Al-Mn. Edagawa and So 33,34 evaluated K 3 experimentally for the Mg-Ga-Al-Zn and Al-Cu-Fe i-phases, which belong to the Frank-Kasper and Al transition-metal classes, respectively, and reported ͉K 3 ͉ = 0.04 for the former and ͉K 3 ͉ = 0.004 for the latter. The Al-Pd-Mn i-phase studied in the present work belongs to the Al transition-metal class, and the evaluated value of ͉K 3 ͉ = 0.007 agrees roughly with those reported by Zhu and Henley, and by Edagawa and So.…”