Autocorrelation Function Of Surface Roughness Research Articles

Boundary scattering of phonons: Specularity of a randomly rough surface in the small-perturbation limit

Scattering of normally incident longitudinal and transverse acoustic waves by a randomly rough surface of an elastically isotropic solid is analyzed within the small perturbation approach. In the limiting case of a large correlation length $L$ compared with the acoustic wavelength, the specularity reduction is given by $4\eta^2k^2$, where $\eta$ is the RMS roughness and $k$ is the acoustic wavevector, which is in agreement with the well-known Kirchhoff approximation result often referred to as Ziman's equation [J. M. Ziman, Electrons and Phonons (Clarendon Press, Oxford, 1960)]. In the opposite limiting case of a small correlation length, the specularity reduction is found to be proportional to $\eta^2k^4L^2$, with the fourth power dependence on frequency as in Rayleigh scattering. Numerical calculations for a Gaussian autocorrelation function of surface roughness connect these limiting cases and reveal a maximum of diffuse scattering at an intermediate value of $L$. This maximum becomes increasingly pronounced for the incident longitudinal wave as the Poisson's ratio of the medium approaches 1/2 as a result of increased scattering into transverse and Rayleigh surface waves. The results indicate that thermal transport models using Ziman's formula are likely to overestimate the heat flux dissipation due to boundary scattering, whereas modeling interface roughness as atomic disorder is likely to underestimate scattering.

Creep characteristics of combined bulk acoustic wave quartz resonator force sensors

Abstract This paper investigates the creep characteristics of a metal–quartz combined force sensor. The sensing quartz resonator is assembled with metal structures by epoxy adhesive to avoid direct-contact induced frequency instability. Creep of the sensor mainly attributes to the existence of epoxy, owing to its viscoelastic feature. In order to probe the factors that affect creep, theoretical and empirical models describing the relations between the creep and surface roughness and preload have been developed, based on the micro-peak model and the autocorrelation function of surface roughness. Experimental results show that with the decrease of the surface roughness or with the increase of the preload, as well as the elasticity of epoxy, the creep of the sensor can be reduced. A polishing method has been developed based on the experiments to reduce creep and improve the performance of the sensor.