Physics 871 (Solid State Physics)

Physics 871: Problem set 1

Calculate the total lattice energy of a two-dimensional ionic crystal with a square lattice. The Coulomb potential between the ions is ±q²/R. There is also a nearest neighbor repulsive potential A/Rⁿ.
M&A problem 20.1 (a) & (b).
(a) What is the number of atoms in a primitive unit cell of a diamond lattice?
(b) What is the number of atoms in the more conventional cubic unit cell of a diamond lattice?
(c) Find the angle between the tetrahedral bonds in this lattice.
(d) What is the packing fraction for hard spheres in such a lattice?
M&A problem 4.1
Primitive lattice vectors of a body-centered tetragonal lattice are: (a/2, a/2, -c/2); (-a/2, a/2, c/2); (a/2, -a/2, c/2). (The values a and c refer to the conventional tetragonal cell.) Initially c > a, but then the crystal is compressed along the c axis.
(a) At what value of c does it become a body-centered cubic lattice?
(b) At what value of c does it become a face-centered cubic lattice?