Solid State: Diamond lattice and scattering

  1. 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 x-rays and show that "a" is that for carbon diamond lattice.
  2. jcsd
  3. DrDu

    DrDu 4,636
    Science Advisor

    Maybe this question is more apt for the advanced physics homework forum.
  4. I can try there, I figured here because this is from an Intro to Solid State course.
  5. 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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