  The morphology of nanoscopic Ag grains significantly affects the phonons.
Atomistic simulations show that realistic nanograin models display complex
vibrational properties. (1) Single-crystalline grains. Nearly-pure torsional
and radial phonons appear at low frequencies. For low-energy, faceted models,
the breathing mode and acoustic gap (lowest frequency) are about 10% lower than
predicted by elasticity theory (ET) for a continuum sphere of the same volume.
The sharp edges and the atomic lattice split the ET-acoustic-gap quintet into a
doublet and triplet. The surface protrusions associated with nearly spherical,
high-energy models produce a smaller acoustic gap and a higher vibrational
density of states (DOS) at frequencies \nu<2 THz. (2) Twined icosahedra. In
contrast to the single-crystal case, the inherent strain produce a larger
acoustic gap, while the core atoms yield a DOS tail extending beyond the
highest frequency of single-crystalline grains. (3) Mark's decahedra, in
contrast to (1) and (2), do not have a breathing mode; although twined and
strained, do not exhibit a high-frequency tail in the DOS. (4) Irregular
nanograins. Grain boundaries and surface disorder yield non-degenerate phonon
frequencies, and significantly smaller acoustic gap. Only these nanograins
exhibit a low-frequency \nu^2 DOS in the interval 1-2 THz.
