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Register a new userAn atomic mechanism for the boson peak in metallic glasses
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The boson peak in metallic glasses is modeled in terms of local structural shear rearrangements. Using Eshelbys solution of the corresponding elasticity theory problem (J. D. Eshelby, Proc. Roy. Soc. A241, 376 (1957)), one can calculate the saddle point energy of such a structural rearrangement. The neighbourhood of the saddle point gives rise to soft resonant vibrational modes. One can calculate their density, their kinetic energy, their fourth order potential term and their coupling to longitudinal and transverse sound waves.
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The inelastic scattering intensities of glasses and amorphous materials has a maximum at a low frequency, the so called Boson peak. Under applied hydrostatic pressure, $P$, the Boson peak frequency, $omega_{rm b}$, is shifted upwards. We have shown previously that the Boson peak is created as a result of a vibrational instability due to the interaction of harmonic quasi localized vibrations (QLV). Applying pressure one exerts forces on the QLV. These shift the low frequency part of the excess spectrum to higher frequencies. For low pressures we find a shift of the Boson peak linear in $P$, whereas for high pressures the shift is $propto P^{1/3}$. Our analytics is supported by simulation. The results are in agreement with the existing experiments.
We show that a {em vibrational instability} of the spectrum of weakly interacting quasi-local harmonic modes creates the maximum in the inelastic scattering intensity in glasses, the Boson peak. The instability, limited by anharmonicity, causes a complete reconstruction of the vibrational density of states (DOS) below some frequency $omega_c$, proportional to the strength of interaction. The DOS of the new {em harmonic modes} is independent of the actual value of the anharmonicity. It is a universal function of frequency depending on a single parameter -- the Boson peak frequency, $omega_b$ which is a function of interaction strength. The excess of the DOS over the Debye value is $proptoomega^4$ at low frequencies and linear in $omega$ in the interval $omega_b ll omega ll omega_c$. Our results are in an excellent agreement with recent experimental studies.
Experimental results on the density of states and on the acoustic modes of glasses in the THz region are compared to the predictions of two categories of models. A recent one, solely based on an elastic instability, does not account for most observations. Good agreement without adjustable parameters is obtained with models including the existence of non-acoustic vibrational modes at THz frequency, providing in many cases a comprehensive picture for a range of glass anomalies.
The density of vibrational states $g(omega)$ of an amorphous system is studied by using the random-matrix theory. Taking into account the most important correlations between elements of the random matrix of the system, equations for the density of vibrational states $g(omega)$ are obtained. The analysis of these equations shows that in the low-frequency region the vibrational density of states has the Debye behavior $g(omega) sim omega^2$. In the higher frequency region, there is the boson peak as an additional contribution to the density of states. The obtained equations are in a good agreement with the numerical results and allow us to find an exact shape of the boson peak.
In glasses, atomic disorder combined with atomic connectivity makes understanding of the nature of the vibrations much more complex than in crystals or molecules. With a simple model, however, it is possible to show how disorder generates quasi-local modes on optic branches as well as on acoustic branches at low-frequency. The latter modes, possibly hybridizing with low-lying optic modes in real glasses, lead to the excess, low-frequency excitations known as {it boson-peak modes}, which are lacking in crystals. The spatially quasi-localized vibrations also explain anomalies in thermal conductivity and the end of the acoustic branches, two other specific features of glasses. Together with the quasi-localization of the modes at the nanometric scale, structural disorder lifts the crystalline or molecular spectroscopic selection rules and makes interpretation of experiments difficult. Nevertheless, vibrations in simple glasses such as vitreous silica or vitreous boron oxide are nowadays rather well described. But a comprehensive understanding of the boson peak modes remains a highly debated issue as illustrated by three archetypal glass systems, vitreous SiO$_2$ and B$_2$O$_3$ and amorphous silicon.
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