# Electron Diffraction

Students use a Seargent-Welch electron diffraction apparatus to study electron diffraction from graphite and a randomly oriented metal target.

## Experiment Information

## Discussion Questions

- The diffraction condition in a lattice may be expressed as
**H⋅T**=*integer*, where the vector**H**=**n**/*d*, with**n**as the unit normal to the set of Bragg planes and*d*the spacing between them, and**T**is a translation vector in the lattice. For a simple cubic lattice, the translation vector is a linear combination of**a**_{1}= [*a*,0,0],**a**_{2}= [0,*a*,0], and**a**_{3}= [0,0,*a*], so that**T**= a[*p*], where_{x},p_{y},p_{z}*p*is an integer. Show that the vector_{i}**H**= [*h,k,l*]/*a*with*d*^{2}=*a*^{2}/(*h*^{2}+*k*^{2}+*l*^{2}) satisfies**H⋅T**=*integer*in a simple cubic lattice for all integers*h,k,l*, with the vector [*h,k,l*] perpendicular to the Bragg plane. - For the face-centered cubic (fcc) lattice, the translation vectors
**T**are linear combinations of**a**_{1}= (*a*/2)[0,1,1],**a**_{2}= (*a*/2)[1,0,1],**a**_{3}= (*a*/2)[1,1,0]. Show that the condition**H⋅T**=*integer*leads to the requirement that*h,k,l*be either all even or all odd. - Generate the ratio of the largest value of (
*d*/_{hkl}*a*) to the next 10 largest values of the same quantity for graphite and the three cubic lattices (all*hkl*for simple cubic,*hkl*all even or all odd for fcc and the sum*h*+*k*+*l*is even for bcc). Use this for your analysis in Part 2. (Hint: use a spreadsheet.) - In this experiment, you are basically finding a relationship between accelerating
potential
*V*and the ratio of the electron wavelength*λ*to the lattice parameter*d*. Can you use this apparatus to extract*λ*, the*d*value for aluminum and the*d*value for graphite without knowing one of them a priori? If so, how might you do this? If not, how might you alter the experiment and/or use other easily measured information to do so?