  Nanoscale single-crystals possess modified phonon dispersions due to the
truncation of the crystal. The introduction of surfaces alters the population
of phonons relative to the bulk and introduces anisotropy arising from the
breaking of translational symmetry. Such modifications exist throughout the
Brillouin zone, even in structures with dimensions of several nanometers,
posing a challenge to the characterization of vibrational properties and
leading to uncertainty in predicting the thermal, optical, and electronic
properties of nanomaterials. Synchrotron x-ray thermal diffuse scattering
studies find that freestanding Si nanomembranes with thicknesses as large as 21
nm exhibit a higher scattering intensity per unit thickness than bulk silicon.
In addition, the anisotropy arising from the finite thickness of these
membranes produces particularly intense scattering along reciprocal-space
directions normal to the membrane surface compared to corresponding in-plane
directions. These results reveal the dimensions at which calculations of
materials properties and device characteristics based on bulk phonon
dispersions require consideration of the nanoscale size of the crystal.
