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Solid State: Diamond lattice and scatteringby barrinmw
Tags: crystal lattice, diamond, lattice, scattering, solid, solid state, spectroscopy, state 
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#1
Mar214, 12:14 PM

P: 6

I have the following homework question I am working on.
I am given three scattering angles: 42.8, 73.2, 89. (in degrees) without the wavelength of the light used. I am to show that these are consistent with a diamond lattice. I started with Laue's Law: delta(k) = G and according to the professor in this instance, I am only worried about magnitudes. By conservation of energy I know k = k' This led me to G = 2 k Sin[theta / 2] where k = 2 pi / lambda Now, if I take the ratios of G_1, G_2, G_3 I get: G_2 / G_1 = 1.63; G_3 / G_2 = 1.68 To get G, I started with the lattice vectors of the primitive cell of diamond which I believe are the same lattice vectors of the primitive cell of an FCC lattice. So a_1 = (1/2) a (yhat + zhat); a_2 = (1/2) a (xhat + zhat); a_3 = (1/2) a (xhat + yhat) I form the reciprocal lattice basis vectors from these. b_1 = (2 pi / a) (xhat + yhat + zhat); b_1 = (2 pi / a) (xhat + yhat  zhat); b_1 = (2 pi / a) (xhat  yhat + zhat) Now one problem is, that I don't know how to construct the G's from this since I don't know how to find the coefficients for the diamond lattice. I know that G = v_1 * b_1 + v_2 * b_2 + v_2 * b_2 but in the end I know that G should equal (2 pi / a) Sqrt( v_1^2 + v_2^2 + v_3^2) Any help would be appreciated, once I get this I can answer the next part of the question where he gives me the wavelength of the xrays and show that "a" is that for carbon diamond lattice. 


#2
Mar214, 02:22 PM

Sci Advisor
P: 3,554

Maybe this question is more apt for the advanced physics homework forum.



#3
Mar214, 02:30 PM

P: 6

I can try there, I figured here because this is from an Intro to Solid State course.



#4
Mar314, 09:26 AM

P: 660

Solid State: Diamond lattice and scattering
You are doing fine. I get the same value for G_1/G_2, but not for G_3/G_2.
Since you are using a primitive unit cell for the diamond lattice, your v_1, v_2 and v_3 can be any integer, 0,+/1, +/2,... Try using an Exel spreadsheet or python program to calculate the first few G and their ratios. 


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