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Structure matters |
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Packing
atoms |
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Solid matter is built up from the packing together of atoms which have the
shape |
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of
spheres. There is a direct correlation between the way that spheres pack
together |
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and
how polyhedra pack together to fill space. |
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For example, a layer of equal radius spheres (atoms) can be packed together
to |
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fill the plane in two characteristic ways.
Observe that the void spaces, or interstices, |
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Fig.
31 a |
click
image |
Fig.
31 b |
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to
enlarge |
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Fig.
31 Packing spheres to fill the plane |
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between the spheres in the triangular pattern are smaller than those in the
square |
pattern. This is because the spheres in the triangular pattern nestle
into the |
depressions formed between them. As a result the spheres in the
triangular array |
are
packed together closer than those in the square packing. Indeed this
is the |
closest packed arrangement of spheres possible in two dimensions. If
the center |
points of the spheres, representing the nuclei of atoms, are connected
together by |
lines, two dimensional grids, or lattices, are formed with the sphere
centers (nuclei) |
represented by the vertices of the lattice. Lattices, in turn, can be
modeled as nets, |
or
tessellations, of polygons which are linked together to fill the plane as
shown in |
Figure 31. |
Notice that the pattern of points surrounding every lattice point is
identical, or |
isometric. Such lattices have translational symmetry. That is, a
copy of one section |
of
the lattice can be superimposed on another section so that their points
coincide |
completely without changing the pattern. Hence they have utility in
modeling the |
structure of crystals since most solid matter is almost always spatially
periodic. |
Representing the arrangement of atoms in a substance by the vertices, edges, |
and faces of polygons is called the
topological model of matter because topology is |
concerned with the symmetry of these geometric elements. It enables
the geometry |
and
symmetry of atomic structures to be visualized more clearly. Therefore
the |
topological model of matter is the convention used throughout this lesson |
Back to
Knowhere |
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23 - Structure matters - Atom packing |
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