Dynamics of a Monolayer of Microspheres on an Elastic Substrate

We present a model for wave propagation in a monolayer of spheres on an elastic substrate. The model, which considers sagittally polarized waves, includes: horizontal, vertical, and rotational degrees of freedom; normal and shear coupling between the spheres and substrate, as well as between adjacent spheres; and the effects of wave propagation in the elastic substrate. For a monolayer of interacting spheres, we find three contact resonances, whose frequencies are given by simple closed-form expressions. For a monolayer of isolated spheres, only two resonances are present. The contact resonances couple to surface acoustic waves in the substrate, leading to mode hybridization and "avoided crossing" phenomena. We present dispersion curves for a monolayer of silica microspheres on a silica substrate, assuming adhesive, Hertzian interactions, and compare calculations using an effective medium approximation to a discrete model of a monolayer on a rigid substrate. While the effective medium model does not account for discrete lattice effects at short wavelengths, we find that it is well suited for describing the interaction between the monolayer and substrate in the long wavelength limit. We suggest that a complete picture of the dynamics of a discrete monolayer adhered to an elastic substrate can be found using a combination of the results presented for the discrete and effective medium descriptions. This model is potentially scalable for use with both micro- and macroscale systems, and offers the prospect of experimentally extracting contact stiffnesses from measurements of acoustic dispersion

A Variational Approach to Extracting the Phonon Mean Free Path Distribution from the Spectral Boltzmann Transport Equation

The phonon Boltzmann transport equation (BTE) is a powerful tool for studying non-diffusive thermal transport. Here, we develop a new universal variational approach to solving the BTE that enables extraction of phonon mean free path (MFP) distributions from experiments exploring non-diffusive transport. By utilizing the known Fourier solution as a trial function, we present a direct approach to calculating the effective thermal conductivity from the BTE. We demonstrate this technique on the transient thermal grating (TTG) experiment, which is a useful tool for studying non-diffusive thermal transport and probing the mean free path (MFP) distribution of materials. We obtain a closed form expression for a suppression function that is materials dependent, successfully addressing the non-universality of the suppression function used in the past, while providing a general approach to studying thermal properties in the non-diffusive regime.Comment: 17 pages, 2 figure

Non-Contact Measurement of Thermal Diffusivity in Ion-Implanted Nuclear Materials

Knowledge of mechanical and physical property evolution due to irradiation damage is essential for the development of future fission and fusion reactors. Ion-irradiation provides an excellent proxy for studying irradiation damage, allowing high damage doses without sample activation. Limited ion-penetration-depth means that only few-micron-thick damaged layers are produced. Substantial effort has been devoted to probing the mechanical properties of these thin implanted layers. Yet, whilst key to reactor design, their thermal transport properties remain largely unexplored due to a lack of suitable measurement techniques. Here we demonstrate non-contact thermal diffusivity measurements in ion-implanted tungsten for nuclear fusion armour. Alloying with transmutation elements and the interaction of retained gas with implantation-induced defects both lead to dramatic reductions in thermal diffusivity. These changes are well captured by our modelling approaches. Our observations have important implications for the design of future fusion power plants.Comment: 15 pages, 3 figure

Unifying first principle theoretical predictions and experimental measurements of size effects on thermal transport in SiGe alloys

In this work, we demonstrate the correspondence between first principle calculations and experimental measurements of size effects on thermal transport in SiGe alloys. Transient thermal grating (TTG) is used to measure the effective thermal conductivity. The virtual crystal approximation under the density functional theory (DFT) framework combined with impurity scattering is used to determine the phonon properties for the exact alloy composition of the measured samples. With these properties, classical size effects are calculated for the experimental geometry of reflection mode TTG using the recently-developed variational solution to the phonon Boltzmann transport equation (BTE), which is verified against established Monte Carlo simulations. We find agreement between theoretical predictions and experimental measurements in the reduction of thermal conductivity (as much as $\sim$ 25\% of the bulk value) across grating periods spanning one order of magnitude. This work provides a framework for the tabletop study of size effects on thermal transport

Longitudinal Eigenvibration of Multilayer Colloidal Crystals and the Effect of Nanoscale Contact Bridges

Longitudinal contact-based vibrations of colloidal crystals with a controlled layer thickness are studied. These crystals consist of 390 nm diameter polystyrene spheres arranged into close packed, ordered lattices with a thickness of one to twelve layers. Using laser ultrasonics, eigenmodes of the crystals that have out-of-plane motion are excited. The particle-substrate and effective interlayer contact stiffnesses in the colloidal crystals are extracted using a discrete, coupled oscillator model. Extracted stiffnesses are correlated with scanning electron microscope images of the contacts and atomic force microscope characterization of the substrate surface topography after removal of the spheres. Solid bridges of nanometric thickness are found to drastically alter the stiffness of the contacts, and their presence is found to be dependent on the self-assembly process. Measurements of the eigenmode quality factors suggest that energy leakage into the substrate plays a role for low frequency modes but is overcome by disorder- or material-induced losses at higher frequencies. These findings help further the understanding of the contact mechanics, and the effects of disorder in three-dimensional micro- and nano-particulate systems, and open new avenues to engineer new types of micro- and nanostructured materials with wave tailoring functionalities via control of the adhesive contact properties

Complex Contact-Based Dynamics of Microsphere Monolayers Revealed by Resonant Attenuation of Surface Acoustic Waves

Contact-based vibrations play an essential role in the dynamics of granular materials. Significant insights into vibrational granular dynamics have previously been obtained with reduced-dimensional systems containing macroscale particles. We study contact-based vibrations of a two-dimensional monolayer of micron-sized spheres on a solid substrate that forms a microscale granular crystal. Measurements of the resonant attenuation of laser-generated surface acoustic waves reveal three collective vibrational modes that involve displacements and rotations of the microspheres, as well as interparticle and particle-substrate interactions. To identify the modes, we tune the interparticle stiffness, which shifts the frequency of the horizontal-rotational resonances while leaving the vertical resonance unaffected. From the measured contact resonance frequencies we determine both particle-substrate and interparticle contact stiffnesses and find that the former is an order of magnitude larger than the latter. This study paves the way for investigating complex contact-based dynamics of microscale granular crystals and yields a new approach to studying micro- to nanoscale contact mechanics in multiparticle networks.National Science Foundation (U.S.) (Grant CMMI-1333858)United States. Army Research Office (Grant W911NF-15-1-0030)University of Washington. Royalty Research FoundationNational Science Foundation (U.S.) (Grant CHE-1111557

Multi-frame Interferometric Imaging with a Femtosecond Stroboscopic Pulse Train for Observing Irreversible Phenomena

We describe a high-speed single-shot multi-frame interferometric imaging technique enabling multiple interferometric images with femtosecond exposure time over a 50 ns event window to be recorded following a single laser-induced excitation event. The stroboscopic illumination of a framing camera is made possible through the use of a doubling cavity which produces a femtosecond pulse train that is synchronized to the gated exposure windows of the individual frames of the camera. The imaging system utilizes a Michelson interferometer to extract phase and ultimately displacement information. We demonstrate the method by monitoring laser-induced deformation and the propagation of high-amplitude acoustic waves in a silicon nitride membrane. The method is applicable to a wide range of fast irreversible phenomena such as crack branching, shock-induced material damage, cavitation and dielectric breakdown