Calculating LEED Spot Angles on Si(001) Surface with 100eV Electron Beam

[jonesj314]

Homework Statement

A 100eV electron beam is normally incident on an unreconstructed Si(001) surface. Calculate the angle from the surface normal to the (1, 0) and (1, 1) LEED spots (the spots are indexed using the surface unit cell)

Si cubic latice parameter is 5.43072 angstroms

Homework Equations

Can calculate the wavelength in angstroms of the electron beam using $λ = \frac{12.3}{√E}$ where E is in eV. And hence wave vector $k = \frac{2π}{λ}$

The Attempt at a Solution

I have used the Ewald sphere construction to calculate the angle, θ, to the (1, 0) LEED spot in terms of the wave vector, k , and the reciprocal lattice constant, b. $$b = \frac{2π}{5.43072} = 1.157$$ $$k = \frac{2π}{1.23} = 5.108$$

Hence $θ = arctan \frac{b}{k} = arctan \frac{1.157}{5.108} = 12.76°$

And then to the (1, 1) spot I used √2b instead of just b in the first part to find the angle = 17.76 degrees.

I'm very uncertain of my method and the answers. Are they correct? Thanks in advance

 

[jonesj314]

Bump. Would this be better moved to a different board?