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Chapter 6
Aims & Objectives
The aim of this chapter is to provide a basic theory, with or without
mathematical proof, to diffraction in preparation for instruction on how to
calculate the intensity of powder diffraction peaks. Specific objectives and
points of counselling are:
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This chapter is the first of a two-part series: Diffraction Theory I (this
chapter) and Diffraction Theory II (which will follow later). There are strong
connections between these two: This week we go through the underlying theory of
diffraction and then subsequently you will be shown how to apply it with
specific examples.
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In Diffraction Theory I we start from a very basic point - the scattering of
radiation, such as X-rays, from a single electron - and then build up gradually
so that we eventually conclude with diffraction from a single crystal or
crystalline powder. During the development of the theory there is unavoidably
some considerable use made of mathematical tools such as exponentials,
calculus, imaginary numbers and so on. However it is absolutely crucial here to
emphasise that students who are not able to cope with this level of mathematics
need not despair. The theory is developed in a way that emphasises the
qualitative principles involved and then repeats the message in the appropriate
mathematical language. A student who cannot follow the mathematical part can
still remain in contact by making sure s/he at least understands the
qualitative principles; obviously an understanding of the principles and the
mathematics would be a bonus. Even for those who cannot follow the
mathematics, you can still appreciate that the formulae often display a shape
that reflects their qualitative meaning. In Diffraction II,
the method will be explained
in a prescriptive way that will enable all students to perform the necessary
intensity calculations irrespective of mathematical grasp.
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To help the non-mathematical students, many diagrams have been used. Some of
these diagrams are highly schematic and should not always be taken too
literally, but rather as an aid to qualitative understanding.
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Apart from possibly one section on the Reciprocal Lattice (see below)
Diffraction Theory I and II require that they be read sequentially and so links
to all the various topics are not given here. The student is strongly advised
to start at the beginning with
scattering of X-rays
by a single electron, and work linearly through the pages to the end.
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The idea of the reciprocal lattice falls naturally out from this theory. The
reciprocal lattice is an important concept in crystallography though it is not
vital in all aspects of powder diffraction.
However, in recognition of its use in
some of the later sections (e.g. unit-cell indexing)
a quick essential guide to the
reciprocal lattice
(and the Ewald sphere) is given,
together with pointers to its relevance for single crystals and
crystalline powders. The use of reciprocal space in studies of
amorphous/liquid materials is also briefly discussed.
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