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Final Report Summary - PLASTAMORPH (Complex mechanical response of silica-based amorphous materials: from the atomic to the mesoscopic scale)

Executive Summary:

This project has focused on the study of the mechanical response of model disordered materials, specifically amorphous silicon, at small length scales by numerical techniques.

In general, this project aims at obtaining an accurate theoretical description of the elastic and visco-plastic mechanical behaviour of amorphous materials at small length scales, which is a challenging task due to the lack of long-range crystalline order and to the impossibility to describe plasticity in terms of dislocations as in crystals.

A proper understanding of the atomic-scale mechanisms responsible for plasticity and for the rheological behaviour of these systems can result in improvements in current applications in the glass and nano/micro-electronic industry, ameliorating the performance of commonly used Si-based (nano-) devices by controlling plasticity and fatigue.

The project objectives that have been envisaged are manyfold and include:

- the understanding of the local mechanical response of Si-based amorphous material
- the connection between the local dynamics and the macroscopic rheological behaviour
- the characterization of the vibrational properties
- the study of the mechanical behaviour of Si nanopillars under compression

We have investigated in detail the small-scale mechanical response of amorphous silicon under shear by Molecular Dynamics (MD) simulations in the athermal quasi-static limit. In order to characterize the role of the bond directionality we have tuned the 3-body term in the interatomic interaction. We have seen that a systematic increase of the three-body interaction induces a monotonous change in the mechanical response of the system: increase of the yield stress and of the yield strain, decrease of the average size of the plastic events, decrease of the cumulative number of plastic event, increase of the energy dissipated at the yield stress with a strong localization of the plastic rearrangements and heterogeneous flow, systematic increase of the spatial correlation between local plastic rearrangements and structural defects. An analogous dependence can be seen by decreasing the quenching rate at which the amorphous sample is prepared. We have also seen that there is a formal analogy between shear bands in our amorphous system and the Peierls-Nabarro theory of dislocations in crystals, thus supporting the description of plasticity in amorphous solids as a dislocation-like mechanism.

As a next step we have studied the same system at finite shear rates, thus including an explicit time scale in the dynamics. The MD simulations have been performed at fixed imposed pressure and at very low temperatures in order to highlight the dynamical effects only due to geometrical conditions and to discard possible effects arising from thermal activation processes. In this way the local dynamics of the system can be analyzed with respect to the shear rate and the bond directionality. We have shown that this local dynamics is responsible for an anomalous viscous behaviour, characterized by a non-linear, power law dependence of the flow stress as a function of the shear rate (Herschel-Bulkley behaviour). The local dynamics has been studied in detail by probing the self-intermerdiate scattering function and the diffusion constants and we have shown evidence of two types of plastic rearrangements, namely the nucleation of isolated events and avalanche-like rearrangements, whose competition is shown to be responsible for the observed apparent viscosity. In fact, the non-linear rheological properties can be explained by a single relaxation time that we have related to the non-linear shear rate dependence of the avalanche properties of plastic rearrangements.

The vibrational properties of the amorphous Si model have also been quantified. We have calculated the vibrational density of states for different values of the prefactor of the 3-body term, by using two different methods : the Fourier transform of the velocity autocorrelation function and the Kernel Polynomial Method (KPM). These two methods yield comparable results, but the latter allows to reduce the noise and is computationally faster . The numerical results obtained also very well compare with the exact diagonalization of the dynamical matrix for low frequencies. The density of states rescaled by the square of the frequency shows a Boson peak that is more or less pronounced depending on the value of the prefactor of the 3-body term : in particular the relative difference between the position of the Boson peak and the Debye frequency decreases when the local order (or equivalently the bond rigidity) increases. Moreover, the calculation of the dynamical structure factor has been possible with the KPM. By looking at the diffusion of the energy in the system we have seen that for low frequencies the vibration modes are propagative, while for higher frequency the modes appear to diffuse in the system. This is a very important result, since it means that the classical description in terms of phonons fails in these systems.

Finally, we have studied the mechanical behaviour of Si nanopillars under compression. This study has been motivated by the observation that crystal silicon nanopillars of size larger than 400 nm under compression show a brittle behaviour, while for sizes smaller than 300 nm the behaviour is ductile. We have studied the behaviour of amorphous silicon nanopillars of sizes smaller than 10 nm, because larger sizes become computationally inaccessible for Molecular Dynamics simulations. The mechanical properties of the nanopillar have been investigated as a function of its size: we observe an increase of the mechanical properties, probed by the Young's modulus, the yield stress and the flow stress, as a function of the size. It has been seen that the size dependence is compatible with a variation of the inner pressure of the system with 1/R2, where R is the radius of the nanopillar. Furthermore, the "jumps" in the stress-strain curves have been linked to the importance of the non-affine displacements in the nanopillar, with two regimes: the first one dominated by surface effects, and the second one dominated by bulk plasticity.

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