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

[poul]

Homework Statement

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.

Homework 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

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

 

[mark726]

to find the angle of diffraction for the 15.32 keV beam.

Hello,

Yes, your approach is correct. The distance between layers can be calculated using the reciprocal lattice vectors as you have done. The final answer of 3.32 Å seems reasonable and can be used to find the angle of diffraction for the given beam energy. However, it would be helpful to provide more context and background information about the problem in order for others to understand and verify your solution. Additionally, it would be beneficial to include units in your final answer and show the calculations for finding the angle of diffraction. Overall, it seems like you have a good understanding of the problem and have approached it correctly. Keep up the good work!