1. Derive the relationship $|K_B| = 1/d$, in the following manner:
a. Sketch a cubic unit cell, shadowing the (010) type planes.
b. In a new sketch, show diffraction from the (010) planes by drawing a set of (010)
planes, showing the incident and diffracted wavevectors $k_i$ and $k_d$, and the scattering
angle $\theta$. Note that $|k_i| = |k_d| = 1/\lambda$.
c. In a new sketch, subtract $k_d$ from $k_i$, to show the diffraction vector K. Be sure to give
the angle between the two vectors.
d. Using geometry, show that $|K| = 2sin\theta/\lambda$.
e. Now, set $\theta$ to the Bragg angle $\theta_B$, where $\lambda = 2dsin\theta_B$, and substitute this expression for
$\lambda$ into the equation above.
f. Make a new sketch, as in c above, but now label K as g, and label the angle between
the two vectors $2\theta_B$.
1) The diffraction vector K gives the direction and magnitude of displacement of the
diffracted wave from the incident wave. What are they?
2) Does the relationship $|K| = 2sin\theta/\lambda$ apply just to the Bragg angle or to any angle?
3) What does $K = g$ signify?
4) May K take on other values besides g?
5) Draw the resulting diffraction pattern for when the Bragg condition is met for the
(010) planes, above.
