Nanowires are high aspect ratio metal or semiconducting wires with diameters on the order of 1-100 nanometers and typical lengths of 1-100 microns. Nanowires will likely be used in the future to create high-density electronic circuits.
Nanowires can be fabricated from ZnO. ZnO has the wurzite structure. The wurzite structure is a hexagonal lattice with four atoms per lattice point at Zn (0,0,0), Zn (2/3,1/3,1/2), O (0,0,3/8), and O (2/3,1/3,7/8).
(a) How many atoms are there in the conventional unit cell?
(b) If the atoms were instead located at Zn (0,0,0), Zn (1/3,2/3,1/2), O (0,0,3/8), and O (1/3,2/3,7/8), would the structure be different? Please explain.
(c) For ZnO, the unit cell parameters are a=3.24A and c=5.19A. (Note: this is not the ideal HCP c/a ratio.) A typical ZnO nanowire is 20nm in diameter and 5 micrometers long. Assume that nanowires are cylindrical. Approximately how many atoms are there in a single ZnO nanowire?