Phonon-phason coupling in icosahedral quasicrystals

Abstract

received ; accepted ) PACS. 61.44Br -Quasicrystals. PACS. 62.20Dc -Elasticity, elastic constants. PACS. 61.10Dp -Theories of X-ray diffraction and scattering. PACS. 71.15Pd -Molecular dynamics calculations (Car-Parrinello) and other numerical simulations.Abstract. -From relaxation simulations of decoration-based quasicrystal structure models using microscopically based interatomic pair potentials, we have calculated the (usually neglected) phonon-phason coupling constant. Its sign is opposite for the two alloys studied, i-AlMn and i-(Al,Cu)Li; a dimensionless measure of its magnitude relative to the phonon and phason elastic constants is of order 1/10, suggesting its effects are small but detectable. We also give a criterion for when phonon-phason effects are noticeable in diffuse tails of Bragg peaks.( * ) Present address: IBM T.

Internal Friction of an Ag–In–Yb Icosahedral Quasicrystal

“…Zhu and Henley 21) calculated K 3 (À jj;? in their paper) for model icosahedral quasicrystals of Bergman-type (Al,Cu)Li and Mackay-type AlMn.…”

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

“…Such a mechanism implies that the phonon-phason coupling strength can be evaluated by measuring the magnitude of the phonon strain spontaneously introduced in crystal approximants to quasicrystals. By such a method, the phonon-phason coupling constants have been calculated for a model decagonal quasicrystal by Koschella et al [14] and for model icosahedral quasicrystals by Zhu and Henley [15]. In the present work, we have, for the first time, evaluated the coupling constant experimentally by applying this method to a Mg-Ga-Al-Zn system, in which a phase transformation from an i-phase to its crystal approximant has been reported [16].…”

“…Let us consider, in particular, an orthorhombic (pseudo-tetragonal) approximant with v 11 6 ¼ v 22 ¼ v 33 and all other v ij ¼ 0, as studied by Zhu and Henley [15]. Equations (1a) and (1c) predict that this type of phason strain induces a particular type of phonon shear strain as follows:…”

“…Zhu and Henly [15]. Then, the elastic free energy is no longer continuous against the magnitude of the phason strain, indicating the failure of the generalized elastic theory for quasicrystals.…”

“…Using % 46 GPa reported for a Mg-Zn-Y i-phase [22], we obtain K 3 % À1:4 GPa. Zhu and Henley [15] have calculated the phonon-phason coupling constant K 3 (À jj,? in their paper) for model quasicrystals of i-(Al,Cu)-Li and i-Al-Mn, representing the two important classes of the i-phase, namely, the Frank-Kasper and Al-transition metal classes.…”