Dynamics of microscale granular crystals

In our study entitled “Complex Contact-Based Dynamics of Microsphere Monolayers Revealed by Resonant Attenuation of Surface Acoustic Waves,” recently published in Physical Review Letters, we utilized laser ultrasonic techniques to study the dynamics of microscale granular crystals.

The microscale granular crystal is composed of 2 μm diameter glass particles that are self-assembled into a two-dimensional hexagonally close packed structure on top of an aluminum-coated glass slide, as shown in the scanning electron microscope image below:


To characterize the dynamics of the crystal, we utilized the laser ultrasonic technique shown in the figure below.


In this technique, we focus a sub-nanosecond laser pulse into a line on the aluminum surface. The absorbed laser light causes a rapid thermoelastic expansion of the aluminum that launches acoustic waves. The vibrations of the sample due to the acoustic waves are measured via a knife-edge photo-deflection technique, where changes in intensity of a second laser beam caused by deflection of the sample surface are measured. To obtain spatial information, the sample is scanned with respect to the lasers.

After processing the data to obtain information about the vibrations in the frequency domain, we see the following picture, which shows three attenuation zones (blue regions) where the granular crystal interacts with the waves.


Using a theoretical model, we then identified each of these zones to be due to a specific type of vibrational mode. One type has vertical motion (N):


Then two others have both horizontal and rotation motion. One has mostly horizontal motion (HR):


The other has mostly rotational motion (RH):


We confirmed that these modes have the predicted type of motion in two ways. First, we used a measurement technique that is only sensitive to vertical motion to confirm that the middle mode is vertical mode. Second, we deposited a thin layer of aluminum on top of the granular crystal, which stiffens only the interparticle contacts. Our model predicts that this should only cause the rotational-horizontal modes (the highest and lowest frequency modes) to shift upwards in frequency. This change in frequency can be seen in panels in the earlier figure that shows the attenuation zones. Panel (b) shows the effect of 20 nm aluminum coating, and panel (c) shows the effect of 40 nm of aluminum.