A lead nanowire runs along a close-packed direction and is long

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

A lead nanowire runs along a close-packed direction and is L=0.50 μmL=0.50\,\mathrm{\mu m} long. Lead is face-centred cubic with conventional cube edge 4.950 A˚4.950\,\mathrm{\mathring{A}}, so its nearest-neighbour spacing is a=4.950/2=3.500 A˚a=4.950/\sqrt2=3.500\,\mathrm{\mathring{A}}. Modelling the wire as a ring for counting purposes, as in Section 4.5, estimate ((a)) the number of atoms NN along the wire and ((b)) the total number of vibrational modes it carries, counting all three branches of Section 4.6.

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