# Powder sample crystal is analyzed using Debye-Scherrer method...

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1. Jan 10, 2019

### steroidjunkie

1. The problem statement, all variables and given/known data

Powder sample of monoatomic cubic lattice crystal is analyzed using Debye-Scherrer method. Primitive vetors of direct lattice are: a1 = (a, 0, 0), a2 = (0, a, 0) i a3 = (0, 0, a). Wavelength of x-ray radiation is 1 Å.
a) Find primitive vectors of reciprocal lattice.
b) Find the first four shortest vectors of reciprocal latitce.
c) First diffraction ring is observed at an angle $17,9^\circ$ with regard to incident radiation angle. Find lattice constant a.
d) Find angles for the next three difraction rings.

2. Relevant equations

a) $b_1 = \frac{2 \pi \cdot \vec{a_2} \times \vec{a_3}}{\vec{a_1} \cdot \vec{a_2} \times \vec{a_3}} = \frac{2 \pi}{a} \hat{x}$
$b_2 = \frac{2 \pi \cdot \vec{a_3} \times \vec{a_1}}{\vec{a_1} \cdot \vec{a_2} \times \vec{a_3}} = \frac{2 \pi}{a} \hat{y}$
$b_3 = \frac{2 \pi \cdot \vec{a_1} \times \vec{a_2}}{\vec{a_1} \cdot \vec{a_2} \times \vec{a_3}} = \frac{2 \pi}{a} \hat{z}$

b), c), d) ?

3. The attempt at a solution

I have no idea how to proceed. I've found the $\vec{k} = \frac{2 \pi}{d}$ on the internet, where $d=\lambda$, but I'm not sure if this equation can give me the shortest vector or how I'd find the other three shortest vectors.