Homework Set # 3 - Due February 20
1) Problem 3.1
What is the largest separation d between adjacent planes in a simple cubic lattice? Give your answer in terms of the lattice constant a and express the separation between these planes in terms of a vector of the reciprocal lattice.
What is the largest separation d between adjacent planes in a body centered cubic lattice? Give your answer in terms of the lattice constant a and express the separation between these planes in terms of a vector of the reciprocal lattice.
What can you say about the distance between the planes d1 in a family perpendicular to a vector of the reciprocal lattice K1compared with the distance between planes d2 in a family perpendicular to the reciprocal lattice vector K2 if K1<K2?
2) Problem 3.2
3) Problem 3.3
c) Provide the Miller indices of the planes indicated in Fig.3.2.
d) Provide the distance d between the planes.
4) Problem 3.4
5) Consider the diamond lattice as a simple cubic lattice with a basis, i.e., the primitive vectors are the ones for the sc lattice and there are 8 basis vectors:
a) Write down the 3 primitive vectors and the 8 basis vectors.
b) Find the modulation factor of this basis.
c) Find the zeroes of the modulation factor F.