513.001 Molecular and Solid State Physics

Return to
problem list

Wolfram Alpha

Physical
Constants

Periodic System
of Elements

      

MIT 8.231 Physics of Solids, 2.1

The figure below shows a primitive unit cell of one crystalline form of the element americium. The space lattice is hexagonal with $\vec{a}_1 = a\hat{x}, \vec{a}_2 =\frac{a}{2}\hat{x} +\frac{\sqrt{3}a}{2}\hat{y}, ~and~ \vec{a}_3 = c\hat{z}$. The basis is (0 0 0) , (2/3 2/3 1/4), (0 0 1/2) and (1/3 1/3 3/4).

a) Find the reciprocal lattice vectors G. Describe in words and sketch the reciprocal lattice.

b) Sketch the first Brillouin zone. Give values for the important dimensions.

c) Find the structure factors associated with the points (100), (001), and (120) of the reciprocal lattice.

d) What is the ratio of the scattering intensity corresponding to (120) to that corresponding to (100)?