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Close-packing of equal spheres can belong to the trigonal, hexagonal or cubic crystal systems. When the structure has the minimum symmetry discussed earlier it belongs to the trigonal system. When it has a 63 axis of symmetry it belongs to the hexagonal system. Structures belonging to the hexagonal system necessarily have a hexagonal lattice, i.e. a lattice in which we can choose a primitive unit cell with a = b c, = = 90, in Fig. 5. It should be noted that there are two spheres associated with each lattice point in the hcp structure, one at 000 and the other at . Structures belonging to the trigonal system can have either a hexagonal or a rhombohedral lattice. By a rhombohedral lattice is meant a lattice in which we can choose a primitive unit cell with a = b = c, = = 90. Both types of lattices can be referred to either hexagonal or rhombohedral axes, the unit cell being non-primitive when a hexagonal lattice is referred to rhombohedral axes or vice versa.
In close-packed structures, it is generally convenient to refer both hexagonal and rhombohedral lattices to hexagonal axes. The projection of the hexagonal lattice on the (001) plane is shown in Fig. 8. The axes, x, y define the smallest hexagonal unit cell, the z axis being normal to the plane of the paper; the hexagonal unit cell is primitive with all the lattice points at 000. Figure 9 depicts the projection of a rhombohedral lattice on the (00.1) plane. The full lines Oxh, Oyh represent the hexagonal axes and the three dotted lines represent rhombohedral axes. It is evident from the figure that the hexagonal unit cell of a rhombohedral lattice is non-primitive with lattice points at 000, and . If the lattice is rotated through 60 around , the hexagonal unit cell will then be centred at and . These two settings of the rhombohedral lattice are called `obverse` and `reverse` settings. They are indistinguishable by X-ray methods since the two are crystallographically equivalent: they represent twin arrangements when both of them occur in the same single crystal.
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