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Anharmonicity, vibrational instability and Boson peak in glasses

V. L. Gurevich·D. A. Parshin·H. R. Schober
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Abstract

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 $ω_c$, 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, $ω_b$ which is a function of interaction strength. The excess of the DOS over the Debye value is $\proptoω^4$ at low frequencies and linear in $ω$ in the interval $ω_b \ll ω\ll ω_c$. Our results are in an excellent agreement with recent experimental studies.

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V. L. Gurevich, D. A. Parshin, H. R. Schober. 2003-01-13. Anharmonicity, vibrational instability and Boson peak in glasses. https://doi.org/10.1103/physrevb.67.094203

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