Chapter 9
Determination of Crystal Structure
Parameters
9.1 Steps in Crystal Structure Determinations
Crystal structure determinations in general are not easy and straightforward. They
are normally done by trial and error method and taking into account the following
three fundamental steps.
1. Indexing (or analysis) of diffraction pattern through the analytical or graphical
method to know the nature (shape and size) of the unit cell.
2. Determination of number of atoms in the unit cell from its shape and size,
chemical composition and density of the specimen.
3. Determination of atomic positions in the unit cell from suitable analysis of the
relative intensities obtained from diffraction experiments.
(a) Interpretation of X-ray Diffraction Data For Cubic Structures
One can use a simple method to identify whether the given (unknown) structure is
either bcc or fcc, when X-ray diffraction data is available. We can identify the
principal diffracting planes {hkl} and the corresponding 2h values as given in
Table 9.1. Further, for cubic structures the Bragg’s law gives us
sin
2
h ¼
k
2
4a 2 h
2
þ k
2
þ l
2
À
Á
where the lattice parameter, a and the wavelength of the X-ray beam, k are
constants. Eliminating these quantities by taking the ratio of two sin
2
h values, we
obtain
sin
2
h A
sin
2
h B
¼
h
2
A þ k
2
A þ l
2
A
h
2
B þ k
2
B þ l
2
B
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
M. A. Wahab, Numerical Problems in Crystallography,
https://doi.org/10.1007/978-981-15-9754-1_9
337