The energy landscape of glassy dynamics on the amorphous hafnium diboride surface

Direct visualization of the dynamics of structural glasses and amorphous solids on the sub-nanometer scale provides rich information unavailable from bulk or conventional single molecule techniques. We study the surface of hafnium diboride, a conductive ultrahigh temperature ceramic material that can be grown in amorphous films. Our scanning tunneling movies have a second-to-hour dynamic range and single-point current measurements extend that to the millisecond-to-minute time scale. On the a-HfB2 glass surface, two-state hopping of 1-2 nm diameter cooperatively rearranging regions or "clusters" occurs from sub-milliseconds to hours. We characterize individual clusters in detail through high-resolution (<0.5 nm) imaging, scanning tunneling spectroscopy and voltage modulation, ruling out individual atoms, diffusing adsorbates, or pinned charges as the origin of the observed two-state hopping. Smaller clusters are more likely to hop, larger ones are more likely to be immobile. HfB2 has a very high bulk glass transition temperature Tg, and we observe no three-state hopping or sequential two-state hopping previously seen on lower Tg glass surfaces. The electronic density of states of clusters does not change when they hop up or down, allowing us to calibrate an accurate relative z-axis scale. By directly measuring and histogramming single cluster vertical displacements, we can reconstruct the local free energy landscape of individual clusters, complete with activation barrier height, a reaction coordinate in nanometers, and the shape of the free energy landscape basins between which hopping occurs. The experimental images are consistent with the compact shape of α-relaxors predicted by random first order transition theory, whereas the rapid hopping rate, even taking less confined motion at the surface into account, is consistent with β-relaxations. We make a proposal of how "mixed" features can show up in surface dynamics of glasses.