One-dimensional monatomic chain; square lattice; hcp close packed 2D lattice

lionellin

Given (i) a one-dimensional monatomic chain (ii) square lattice and (iii) hcp close packed 2D lattice with atomic distance a and using both the Free-electron and the Tight-Binding approximations to calculate

a. The density of states g(E)
b. Fermi energy Ef
c. Group velocity v
d. Effective mass of electrons
e. Plot the diagrams of E-k, V-k and m*-k
f. Discuss the orgin of the difference between the results derived from FE and TB approximations