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

1. Aug 28, 2012

### poul

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