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Solid-state theory has been formulated in the 20th century on the assumptions of regular crystalline lattices where linear dynamics holds at both classical and quantum levels, while dissipative effects are taken into account to perturbative order. While considerable success has been achieved in the further understanding of disorder effects on the electronic properties of solids, the same is not true for the thermal, vibrational and mechanical properties due to the difficulty of reformulating the whole body of lattice dynamics in a non-perturbative way for disordered systems. I will present a formulation of lattice dynamics extended (in a non-perturbative way) to disordered systems, called Nonaffine Lattice Dynamics (NALD), successfully tested on different systems [1-3]. I will then consider the effect of viscous dissipation on the lattice dynamics of crystalline solids and show how dissipation can lead, in perfectly ordered crystals, to effects very similar to disorder-induced effects in glasses. Theory can explain all these surprising effects in perfect crystals as a result of anharmonic damping inducing diffusive modes that compete with propagating modes [4], and also predicts similar effects resulting from low-lying soft optical phonons (experimentally confirmed). This framework may lead to a new quantitative connection between lattice/atomic parameters, electron-phonon coupling and the Tc of superconductors with the possibility, in future work, of rationalizing a variety of experimental data and to provide a more quantitative (less empirical) understanding of how Tc can be varied in conventional and perhaps also more exotic superconductors.
[1] A. Zaccone and E. Scossa-Romano, Phys. Rev. B 83, 184205 (2011). [2] R. Milkus and A. Zaccone, Phys. Rev. B 93, 094204 (2016). [3] V.V. Palyulin, C. Ness, R. Milkus, R.M. Elder, T.W. Sirk, A. Zaccone, Soft Matter 14, 8475 (2018). [4] M. Baggioli and A. Zaccone, arXiv:1810.09516v1 [cond-mat.soft].

Nanomechanical measurements allow us to determine mechanical characteristics of nano- and microobjects, which is required for further calculations of the mechanical parameters of the structures based on them. At the same time, in-situ measurements are carried out in the SEM and TEM chambers. Thus, it is possible to acquire graphic information that can supplement the indentation data.
In this work, indentation of titania microspheres with different phase composition was tested by MEMS-based Hysitron PI-95 at Zeiss Libra 200MC TEM. Evaluation of the mechanical properties of microspheres in the elastic region was made according to the Hertz model. It turned out that annealing of the amorphous titania leads to an increase in the Young modulus, whereas the hydrothermal treatment reduces it from 27 to 4 Gpa. The differences in the destruction process was demonstrated for these kinds of particles. It has been shown, that hydrothermal treatment of titania microspheres leads to the formation of a reticular internal structure, whereas annealing results in sintering of the internal structure of microspheres.
In the process of indentation, corresponding videos were also recorded, including the probe approach, indentation, and destruction of the microspheres. In order to process the videos we coded the program based on free Python packages. Using the Digital Image Correlation (DIC) algorithm, relative probe displacements were measured during indentation (Fig. 1a). The results obtained allowed us to clarify the calibration of the movement of the indenter in free sample tests, as well as to determine the drift function in real measurements. These results are important for long-term measurements, in particular creep tests.
Based on graphical data we were able to determine the evolution of the shape of indented microspheres. During the video processing, areas of individual objects were determined, sizes of contact areas were calculated, and changes in linear dimensions of the deformed objects were determined (Fig. 1b). Therefore, a large amount of quantitative data was obtained from electron microscopy images.


Fig.1 Illustration of probe displacement determination (a) and the shape evolution analysis