  Optical phonons in nanoparticles with the randomness of interatomic bonds are
considered both analytically and numerically. For weak dilute disorder two
qualitatively different regimes of separated and overlapped levels are
observed, resembling the case of random atomic masses investigated previously.
At stronger and/or more dense disorder, the particles become essentially
inhomogeneous, thus constituting the minimal model to describe an amorphous
phase, where the picture of vibrational modes becomes more subtle. We
concentrate here on the experimentally relevant case of strong disorder located
near the particle surface and formulate the core-shell model aimed to describe
the ubiquitous phenomenon of particle surface amorphization. We observe a
peculiar effect of volume optical phonons "repelling" from the disordered
shell. It results in the Raman spectrum in the form of a combination of narrow
well-resolved peaks stemming from the quantized modes of a pure particle core
(red-shifted due to its effective smaller size), and the noisy background
signal from the disordered shell placed primarily to the right from the main
Raman peak.
