Homework Set # 3 - Due February 21

  
   
1) Problem 3.1

100. What is the largest separation d between 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.

101. What is the largest separation d between 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.

102. 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.