Experimental Dispersion Curves for Phonons in Aluminum

A new multi‐scale dispersive gradient elasticity model with micro‐inertia: Formulation and ‐finite element implementation

“…Figure ). The presence of the γ term allows for a horizontal asymptote at non‐zero angular frequency for large wave numbers, which is confirmed by experimental findings on phonons for a number of engineering materials, see again . As an example, in Figure the experimental dispersion curve of aluminium for phonons propagating in the longitudinal direction is depicted (after Yarnel et al .…”

“…The dispersion curve shows a diagonal asymptote, the slope of which is governed by the ratio γ / α ; therefore, the case α = γ leads to a non‐dispersive medium (for which the dispersion curve is a straight line given by ω = c e k ). The case γ > α means that the higher wave numbers travel faster than the lower wave numbers, which is not realistic as compared with a discrete lattice or to several experiments performed on a range of engineering materials , the case α > γ results in a realistic behaviour in terms of phase velocities and angular frequency, in that the higher wave numbers travel slower than the lower wave numbers; α ≠ 0, β ≠ 0, γ = 0: this particular format of describes a model with two micro‐inertia contributions to capture wave dispersion more accurately than the ‘stable acceleration gradient’ model as described in (ii). The dispersion curve shows an inflexion (change of curvature), with a peak attained at , and tends to zero for infinitely large wave numbers. α ≠ 0, β ≠ 0, γ ≠ 0: the complete version of model represents an enhanced dynamically consistent model similar to that described in (iii) but with an additional micro‐inertia term to improve the dispersion behaviour.…”

“…It is worth noting that many real engineering materials (e.g. those described in ) do exhibit a change in the curvature of the ω ( k ) curve as predicted by Equation for non‐zero α , β and γ coefficients and for β > α γ (cf. Figure ).…”

Phonon excitations in quasicrystals

“…It is interesting here to re mind the reader of the early inelastic-neutron work of Stedman and Nilsson (1966) and of Yarnell (1965) oil pure aluminum. In Fig.…”

“…O ne of the m ain reasons for measuring the dispersion curves for lattice vibrations is to obtain inform ation on the forces betw een the atoms. In pure A l or in p u re Cu, such m easurem ents have shown that nearest-neighbor interactions are dom inant, but there is also a w eak longer-range force system with interactions extending to at least sixth-nearest neighbors (Yarnell, 1965). In lattice periodic crystals, modes are classified with the irreducible representations of the group of the wave vector.…”