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Homework Help: X-rays: Distance between WZ [1 0 3/2]surf layers in InAs

  1. Aug 28, 2012 #1
    1. The problem statement, all variables and given/known data

    Hey

    I have a InAs wurtzite structure, and want to find the distance between the WZ [1 0 3/2] layers *surface coordinates*. I need it to find the angle of diffraction for the WZ [1 0 3/2] bragg peak, for a 15.32 keV beam. It is in fact a InAs nanowire, on a (111( Si substrate.


    2. Relevant equations
    The surface coordinates are given as, in cubic coordinates: a1=[1/2 0 -1/2]_c a2=[-1/2 1/2 0]_c a3=[1 1 1]_c

    the reciprocal lattice of the surface coordinates, is:
    b1=[2/3 2/3 -4/3]_c b2=[-2/3 4/3 -2/3]_c b3=[1/3 1/3 1/3]_c

    The wurtzite structure is, in cubic coordinates:
    a_1=[1/2 0 -1/2]_c a2=[-1/2 1/2 0]_c a3=[2/3 2/3 2/3]_c

    and reciprocal lattice, for the Wurtzite structure is:
    b_1 = [2/3 2/3 -4/3] b2= [-2/3 4/3 -2/3] b3=[1/2 1/2 1/2]_c

    the length for the in-plane vectors are a=4.308 Å, and c=7.028 Å for out-of-plane.

    Following basis vectors are described for such Wurtzite structure:
    r_1=1/3a1 + 2/3a2, r2=2/3a1+1/3a2+1/2a3, r3=1/3a1 + 2/3a2 + 3/8a3, r4=2/3a1+1/3a2+7/8a3

    3. The attempt at a solution

    The distance between the layers, are given as 2pi/G_hkl. So it is basicly finding the length of the shortest reciprocal vector perpendicular to the plane.

    From the above equations i know that the bragg peak [1 0 3/2]_surf, is the same as the bragg peak *7/6 7/6 -5/6]_c. and then i can calculate d as d=2pi/G_hkl = a_cubic/(sqrt(7/6^2+7/6^2+5/6^2)) = a_cubic/1.84
    I know from geometry that a_cubic = sqrt(2)*a, so d=3.32 Å.

    Is that right??? And then i can just use 2*d*sin(theta)=lambda
     
  2. jcsd
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