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For a hexagonal lattice with base vectors:
the lattice points are:
The positional vector for lattice geometries
Shown in figure 6.4 on the right is a hexagonal structure
which exhibits this property. However, one should note that there are
two ways of packing this layer as there are two positions in which the
first sphere can be placed. The two structures are called
hexagonal closepacked and facecentred cubic. The
hexagonal closepacked structure, or hcp, has the third layer
in having the same and coordinates as the first layer, the
second layer has the same and coordinates as the fourth layer
(ABABAB...) and so on (Kittel, 1996). The facecentred cubic
structure has an alternative arrangement of spheres in the third layer
where the spheres share the same coordinate with the first layer
but have different coordinates (ABCABC...). Although this
arrangement appears at the outset to be hexagonal, by rotating its
primitive cell the vectors can be shown to be a variant of a cubic
lattice.
Figure 6.4:
Two layers of spheres packed cubically (left) and hexagonally (right)

Figure 6.5:
600x600x150nm cut of simple cubic nickel antispheres in zero applied field. The colouring represents the angle between and in radians; the lower left inset shows an  cutplane through the centre of the sample, the lower right shows a cutplane through a lower part of the same sample

Next: Parameters of the antidot
Up: Introduction
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Richard Boardman
20061128