A solution and solid state study of niobium complexes University of ...

Chapter 3
vibrations for shorter and stronger bonds generally occur at the higher energy end
(shorter wavelength) of the IR spectrum than the longer and weaker bonds. In
addition, bonds to lighter atoms also vibrate at a higher energy than bonds to heavier
atoms.
3.5 X-Ray Diffraction (XRD)
Most of the knowledge about crystal structures comes from X-ray diffraction.
Diffraction is the bending or scattering of a wave as it passes an obstacle. X-rays are
a form of electromagnetic radiation and are useful for probing crystalline solids as
their wavelengths are in the same range as that of atoms (10 -10 m). 8 When an X-ray
beam is focused on a crystal, the atoms within the crystal scatter the X-rays resulting
in a pattern of constructive and destructive interference. Constructive interference
results when waves are in phase and reinforce each other, while in destructive
interference the waves are out of phase and cancel each other. These scattered
beams create a diffraction pattern from which a three-dimensional picture of the
electronegativity of the electrons is obtained.
In a crystalline compound all the atoms are arranged in a regular pattern. The
repetition of the smallest volume element in three directions describes the crystal.
This smallest volume element is known as a unit cell. The dimensions of the unit cell
are described by three axes (a, b, c) and the angles between them; alpha, beta and
gamma. The directions and planes in a crystal lattice are known as Miller indices
(hkl). A given set of planes with indices h, k, l cut the a-axis of the unit cell in h
sections, the b axis in k sections and the c axis in l sections. A zero indicates that the
planes are parallel to the corresponding axis. 9
8 C. Suryanarayana, M. G. Norton, X-ray Diffraction: A Practical Approach, Springer, New York, 3, 1998.
9 B. E. Warren, X-ray Diffraction, Courier Dover Publications, New York, 1, 1990.
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