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Register a new userDiffusion and jump-length distribution in liquid and amorphous Cu$_{33}$Zr$_{67}$
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Using molecular dynamics simulation, we calculate the distribution of atomic jum ps in Cu$_{33}$Zr$_{67}$ in the liquid and glassy states. In both states the distribution of jump lengths can be described by a temperature independent exponential of the length and an effective activation energy plus a contribution of elastic displacements at short distances. Upon cooling the contribution of shorter jumps dominates. No indication of an enhanced probability to jump over a nearest neighbor distance was found. We find a smooth transition from flow in the liquid to jumps in the g lass. The correlation factor of the diffusion constant decreases with decreasing temperature, causing a drop of diffusion below the Arrhenius value, despite an apparent Arrhenius law for the jump probability.
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The Raman response of the metallic glass Ni$_{67}$Zr$_{33}$ is measured as a function of polarization and temperature and analyzed theoretically. Unexpectedly, the intensity in the range up to 300wn increases upon cooling, which is counterintuitive when the response originates from vibrations alone as in insulators. The increase finds a natural explanation if the conduction electrons are assumed to scatter on localized vibrations with a scattering probability proportional to the Debye-Waller factor. None of our assumptions is material specific, and the results are expected to be relevant for disordered systems in general.
We show that harmonic vibrations in amorphous silicon can be decomposed to transverse and longitudinal components in all frequency range even in the absence of the well defined wave vector ${bf q}$. For this purpose we define the transverse component of the eigenvector with given $omega$ as a component, which does not change the volumes of Voronoi cells around atoms. The longitudinal component is the remaining orthogonal component. We have found the longitudinal and transverse components of the vibrational density of states for numerical model of amorphous silicon. The vibrations are mostly transverse below 7 THz and above 15 THz. In the frequency interval in between the vibrations have a longitudinal nature. Just this sudden transformation of vibrations at 7 THz from almost transverse to almost longitudinal ones explains the prominent peak in the diffusivity of the amorphous silicon just above 7 THz.
The motion of the structure determining components is highly collective, both in amorphous solids and in undercooled liquids. This has been deduced from experimental low temperature data in the tunneling regime as well as from the vanishing isotope effect in diffusion in glasses and undercooled liquids. In molecular dynamics simulations of glasses one observes that both low frequency resonant vibrations and atomic jumps are centered on more than 10 atoms which, in densely packed materials, form chainlike structures. With increasing temperature the number of atoms jumping collectively increases. These chains of collectively jumping atoms are also seen in undercooled liquids. Collectivity only vanishes at higher temperatures. This collectivity is intimately related to the dynamic heterogeneity which causes a non-Gaussianity of the atomic displacements.
The atomic structure of the supercooled liquid has often been discussed as a key source of glass formation in metals. The presence of icosahedrally-coordinated clusters and their tendency to form networks have been identified as one possible structural trait leading to glass forming ability in the Cu-Zr binary system. In this work, we show that this theory is insufficient to explain glass formation at all compositions in that binary system. Instead, we propose that the formation of ideally-packed clusters at the expense of atomic arrangements with excess or deficient free volume can explain glass-forming by a similar mechanism. We show that this behavior is reflected in the structural relaxation of a metallic glass during constant pressure cooling and the time evolution of structure at a constant volume. We then demonstrate that this theory is sufficient to explain slowed diffusivity in compositions across the range of Cu-Zr metallic glasses.
In amorphous solids, a non-negligible part of thermal conductivity results from phonon scattering on the structural disorder. The conversion of acoustic energy into thermal energy is often measured by the Dynamical Structure Factor (DSF) thanks to inelastic neutron or X-Ray scattering. The DSF is used to quantify the dispersion relation of phonons, together with their damping. However, the connection of the dynamical structure factor with dynamical attenuation of wave packets in glasses is still a matter of debate. We focus here on the analysis of wave packets propagation in numerical models of amorphous silicon. We show that the DHO fits (Damped Harmonic Oscillator model) of the dynamical structure factors give a good estimate of the wave packets mean-free path, only below the Ioffe-Regel limit. Above the Ioffe-Regel limit and below the mobility edge, a pure diffusive regime without a definite mean free path is observed. The high-frequency mobility edge is characteristic of a transition to localized vibrations. Below the Ioffe-Regel criterion, a mixed regime is evidenced at intermediate frequencies, with a coexistence of propagative and diffusive wave fronts. The transition between these different regimes is analyzed in details and reveals a complex dynamics for energy transportation, thus raising the question of the correct modeling of thermal transport in amorphous materials.
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