Question

Aluminum is a face-centred cubic structure with a lattice constant of a = 4.05 ˚A. If incoming radiation has a wavelength of 1.5 ˚A, identify which reflections you will see and at which angles 2θ for a powder diffraction experiment. You may use Bragg’s Law along with the formula

d(hk`) = a √ h 2 + k 2 + ` 2 (1)

(the n in Bragg’s law is incorporated into the values for hk`) I recommend using a spread sheet or something similar for this problem. In fact these are the reflections for a simple-cubic lattice. The extra atoms at the fcc lattice points give rise to extra planes that cause destructive interference except when h, k, and ` are all odd numbers or all even. Which of the reflections are systematically absent?

Answer 1

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