Longitudinal sound in nickel travels at

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Lattice dynamics and thermal properties of solids · Lattice dynamics and thermal properties of solids

Condensed Matter Physics, Ch Elastic waves and the vibrating chain

Problem

Longitudinal sound in nickel travels at vs=6040 m s−1v_s=6040\,\mathrm{m\,s^{-1}}. Nickel is face-centred cubic with conventional cube edge 3.524 A˚3.524\,\mathrm{\mathring{A}}, giving a nearest-neighbour spacing a=3.524/2=2.492 A˚a=3.524/\sqrt2=2.492\,\mathrm{\mathring{A}}, and one nickel atom has mass M=9.746×10−26 kgM=9.746\times10^{-26}\,\mathrm{kg}. Following the same two steps as the copper worked example, find ((a)) nickel's bond stiffness KK and ((b)) the highest vibration frequency νmax\nu_{\rm max} its one-atom chain can carry.

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