Question

1. A powder diffraction pattern is recorded on a sample of an unknown elemental substance
known to have cubic symmetry. Cu K-alpha x-rays (wavelength of 0.154 nm) are used and the θ
values of the first 7 peaks are 14.22°, 23.64°, 28.05°, 34.55°, 38.17°, 43.99° and 47.45°.

(a) What are the lengths of the reciprocal lattice vectors (or change in x-ray wave-vector)
corresponding to these Bragg angles?

(b) For a cubic structure, these lengths should be equal to (2*Pi/a)(h 2 +k 2 +l 2 ) 1/2 , although depending
on the structure factor some hkl combinations may be missing. Try squaring the lengths and find
a common divisor, which converts the G 2 values into approximate integers. Which h,k,l
combinations give (h 2 +k 2 +l 2 ) that match this set?

(c) The missing reflections are a result of the structure factor and indicate that the cubic cell is
not primitive. Is the structure FCC, BCC or diamond? Consult the internet (e.g., the Wikipedia
article on structure factor) to find the allowed reflections for the diamond structure—which can
be described as two interpenetrating FCC lattices.

(d) What is the lattice constant a?

(e) Do a search for elements with this lattice constant and structure. What is the unknown
element?

Answer 1