Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

  1. Jan 10, 2019 #1
    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.
     
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?