Phonon expansion and dispersion for material diagnosis in condensed matter channels

Abstract

The “average acoustic pulse dispersion length in condensed matter channels” is expanded to show that propagating acoustic pulses may behave as phonons, which can be characterized and used to evaluate the channel through which they have travelled. Employing transducers, pulser/receivers and condensed matter channels, it is possible to generate and detect a ‘harmonic Gaussian’ pulse (i.e. a Gaussian pulse modulated by a phased carrier frequency). Propagating in the channel the pulse expands, its carrier frequency is diminished, but the harmonic Gaussian property stays. This parallels the quantum-mechanics ‘wave packet’ characterization, relating to such entities as ‘photons’ and ‘phonons’. Channel inhomogeneities affect travelling phonons. Application of nonlinear regression analysis to reflected echoes, at the front and back of the channel, uncovers intrinsic signal parameters. A theory provided relating the derived phonon profile change to average scattering length, mean domain size or defect spacing, g _s, a material property. Experimental and analytical results provide g _s estimates for diverse channels: a 10 mm column of glycerine, a 4.8 mm column of Elmer's glue and an 8 mm copper plate. The g _s values agree with length scales in the materials (nanometres to microns) determined by other experiments, e.g. electron microscopy.

Keywords:

• phonon
• harmonic Gaussian profile
• scattering
• grain size
• micro/nano structures
• in situ monitoring
• nonlinear regression analysis
• non-distorting filters

Acknowledgement

The work was supported in part by Pile Dynamics Inc.