Electrostatic catastrophe

A priori, when the phonon relaxation is faster than the tunneling rates, thermodynamic equilibrium should hold at the temperature of the host reservoir. However, for the nano-junctions the local surface temperature may differ from the bulk equilibrium temperature. This is due to the Anderson orthogonality catastrophe (AOC)3 associated with interplay between the van der Waals and the electrostatic forces. The electron tunneling affects the overlap between differently shifted phonon ground states of the surface. The faster the tunneling rate, the closer is the phononic overlap to zero, and that hinders relaxation of the surface temperature. AOC presents the mechanism also affecting the thermal state of the electronic reservoir due to electron-phonon coupling. In Sec. 3, from comparison of our theoretical I-V curves at different electron-phonon temperatures and the experimental data [Park 2000] we infer that AOC exists. 

As shown in Fig. S.l, sterically stabilized dispersions often display an abrupt transition from long-term (indeed thermodynamic) stability to the onset catastrophic flocculation. Changing the temperature by only a few degrees kelvin is sufficient to transform a very stable dispersion into a flocculated coagulum. This dramatic temperature response contrasts sharply with the more sluggish response to temperature changes exhibited by electrostatically stabilized dispersions. Their stability is normally decreased by heating, as noted by Faraday (1857). 

Figure 1.1a is a typical stress-strain curve for a brittle ceramic having only elastic deformation up to the point of fracture. As indicated in the introduction, ceramics fail in a typically brittle manner, due to the ionic nature of the bonds, which prevent slip via dislocation motion. The fact that brittle catastrophic failure in ceramics is likely is an indication that very little energy is absorbed in the process of fracmre. Pure aluminum oxide behaves as indicated in Fig. 1.1b. The fracture strain of a ceramic is 0.0008-0.001. One can state that ceramics at room temperature are Hookean until fracture. In general, ceramic materials experience very little or no plastic deformation prior to fracture. Slip is difficult due to the structure and the strong local electrostatic potentials (a consequence of the ionic or covalent bonds).

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