Publications

"You have to learn the rules of the game. And then you have to play better than anyone else."

-Albert Einstain-

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Heating through the glass transition: A rigidity approach to the boson peakUsing molecular dynamics, we study the relationship between the excess of low-frequency vibrational modes (Boson peak, BP) and the glass transition for a bidispersive glass interacting through a truncated Lennard-Jones potential. The evolution of the BP with increasing temperature is correlated with the average coordination, as predicted by rigidity theory. This is due to a lack of atomic ``contacts,'' as is confirmed by taking a crystal with broken bonds. We show how the quadratic mean displacement $(⟨{u}^{2}⟩)$ is enhanced by the BP. When $⟨{u}^{2}⟩$ is obtained on short time scales or measured on inherent structures, the glass transition temperature ${T}_{g}$ is determined by the position and height of the BP. Between the melting temperature ${T}_{m}$ and ${T}_{g}$, the nature of the relaxation processes exhibit phase separation, where the backbone increases its rigidity while the smaller atoms diffuse away to form separate crystals.

Boson peak as a consequence of rigidity: A perturbation theory approachSome evidence is provided that the boson peak and floppy modes share a common origin. In the particular case of periodic systems, we show how a boson peak occurs as a consequence of a reduction of constraints in an overconstrained lattice, in contrast to floppy modes, which occur for a reduction of constraints in a flexible or isostatic lattice. In fact, the present approach allows us to follow the transformation of the boson peak into a floppy mode when a system goes from rigid to flexible. We use perturbation theory and Green's functions to see how resonances appear in the low-frequency region of the local vibrational density of states. For overconstrained lattices, we found that the boson peak frequency depends on the square root of the coordination of the lattice, and is at most 0.3 of the Debye frequency, a value close to the observed experimental ratio of 0.1. We also obtain the expected Rayleigh scattering for overconstrained networks, while we predict a different scattering for isostatic networks due to their critical nature. As an example, the effects of removing constraints are analyzed in a face-center-cubic lattice, and the same consequences are observed in a square network with and without diagonal links.

Effect of concentration in Ge-Te liquids: A combined density functional and neutron scattering studyThe structural properties of three compositions of Ge-Te liquids (${\mathrm{Ge}}_{10}{\mathrm{Te}}_{90}$, ${\mathrm{Ge}}_{15}{\mathrm{Te}}_{85}$, ${\mathrm{Ge}}_{20}{\mathrm{Te}}_{80}$) are studied from a combination of density functional based molecular dynamics simulations and neutron scattering experiments. We investigate structural properties including structure factors, pair distribution functions, angular distributions, coordination numbers, neighbor distributions and compare our results with experimental findings. Most noticeable is the good agreement found in the reproduction of the structure in real and reciprocal space, resulting from the incorporation of dispersion forces in the simulation. This leads to Ge and Te coordination numbers which are lower than in previous studies and which can now be followed with temperature, while also strongly depending on the chosen cutoff distance. Results show a gradual conversion of higher coordinated species (Te${}^{\text{IV}}$, Ge${}^{\text{V}}$) into lower coordinated ones at lower temperature, while leaving anticipated coordinations from the octet rule (Te${}^{\text{II}}$ and Ge${}^{\text{IV}}$) nearly unchanged. Structural correlations are characterized as a function of temperature and composition. The vibrational density of states is also measured from inelastic neutron scattering for different compositions and temperatures, and compared to the simulated counterpart which exhibits a reasonable agreement at low frequency.

Low-frequency vibrational mode anomalies and glass transition: Thermal stability, phonon scattering, and pressure effectsThe relationship between the excess of low-frequency vibrational modes observed in glasses and the stability against thermal fluctuations is explored. Such study is performed by calculating the correlation of atomic displacements inside the glass. As a result, it is proved that thermal stability requires that modes present in the boson or floppy peak (due to the flexibility or rigidity of the glass atomic network) should be localized or strongly scattered. The glass transition is thus determined by the size of the quadratic mean displacement. Also, the 2/3 relationship between melting and glass transition temperature is shown to have its origins in the differences between the mean-free path of phonons due to scattering. The size of this scattering is estimated using the Boson peak frequency and sound velocity. Finally, the change in the glass transition temperature with pressure is obtained from the displacement of low-frequency modes.

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