
Structure matters 
. 
. 
. 
Packing
atoms 
. 
Solid matter is built up from the packing together of atoms which have the
shape 
. 
of
spheres. There is a direct correlation between the way that spheres pack
together 
. 
and
how polyhedra pack together to fill space. 
. 
For example, a layer of equal radius spheres (atoms) can be packed together
to 
. 
fill the plane in two characteristic ways.
Observe that the void spaces, or interstices, 
. 
. 









Fig.
31 a 
click
image 
Fig.
31 b 

to
enlarge 





Fig.
31 Packing spheres to fill the plane 

. 





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 
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23  Structure matters  Atom packing 
