Scattering and diffraction. Optical
diffraction diagrams

In
the book Atlas of Optical Transforms
(G. Harburn, CA Taylor, TR Welberry, Ed G. Bell & Sons, London
1975) several optical analogues are shown which can help in order to
interpret X-ray diffraction patterns. Of the nearly
400
examples provided, we have selected a few which can help illustrate
what has been shown in this chapter.

In
each figure, the diagrams on the top row represent the system where the
light is diffracted, and the lower row shows the diffraction
produced. The exception is the final figure, which shows the
diffraction
patterns at the top and the objects obtained from the diffraction at
the bottom.

We
present here the simplest object (a circle) and the combination of two
simple circles, showing the effect of the distance (spacing) between
them. As this spacing increases, the number the diffraction fringes
also increases and they appear much closer (that is the
"reciprocal" effect. See the reciprocal lattice)

When
the object is combined into lines,
the corresponding diffraction fringes occur perpendicular to the
original line. If
the
object forms a 2-dimensional lattice
(figure on
the right), the diffraction pattern produces another lattice,
reciprocal of the original. The variations in intensity in the latter
are due to the finite size of the 2-dimensional object.

The
original object is getting slightly complicated. It can be
seen as
an idealized representation of several chemical molecules: benzene,
toluene and nitro-benzene.

The
same molecule can show polymorphic
structures, ie different crystal structures. The
diffraction diagrams apparently show
different
distributions of intensities, but in both cases one can discover how
the diffraction pattern reveals (somehow) the diffracting object, in
this case a molecule of benzene.

Distortions
of the periodicity in the direct lattice (figures at the top) are
transformed into the diffraction patterns as blurred lines.

If
the crystal is composed of a set of discontinuous mosaics (left), the
diffraction maxima on the diagrams become wider and diffuse. When the mosaics
also
change their orientation, the
diffraction
diagrams show emergent circles. Taken to the limit, this
would result in
a complete circle diagram, typical
of microcrystalline powder.

If
the sample contains two or more orientations in the
lattice (twins), the maxima on the diffraction pattern split,
and
if the size of the twin components are small, the split maxima can
appear as lines.

The
two figures in the lower row show the corresponding images of
a
molecule (rhodium - phthalocyanine) as obtained from their diffraction
patterns (upper row). The molecular image is more or less recognizable
depending
on the amount of information contained in the corresponding diffraction
patterns. The two
figures on
the
right column show the projection of the electron
density of this molecule, as well as a two-dimensional scheme
of it.

But let's go
back...