Effective elastic constants and phonon spectrum in metallic Ta/Al quasiperiodic superlattices.

Abstract

The propagation of acoustic waves in superlattices is investigated within the effective-medium model generalized to the quasiperiodic structure. The effective elastic constants are analytically obtained in closed form for superlattices with hexagonal symmetry. These results are used to interpret the observed low-frequency phonon spectra from Ta/Al superlattices with quasiperiodic Fibonacci ordering and the elastic constants ${\mathit{c}}_{11}$ and ${\mathit{c}}_{44}$ for the superlattices are determined by fitting the data with an acoustic model of supported hexagonal films. The relative Brillouin cross section is found to be accurately represented by a pure ripple effect without photoelastic contribution. We show that the measured and calculated ${\mathit{c}}_{11}$ demonstrates a reasonable agreement, but an appreciable discrepancy of \ensuremath{\sim}20% for ${\mathit{c}}_{44}$ is found. The implication of these results is discussed in detail.