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POINT LATTICES AND THE UNIT CELL
Let’s consider the three-dimensional arrangement of points in Fig.15.This arrangement is called a point lattice. If we take any point in the point lattice it has exactly the same number and arrangement of neighbors(i.e.,identical surroundings) as any other point in the lattice. This condition should be fairly obvious considering our description of long-range order in Sec. 2.1 We can also see from Fig. 15 that it is possible to divide the point lattice into much smaller untils such that when these units are stacked in three dimensions they reproduce the point lattice. This small repeating unit is known as the unit cell of the lattice and is shown in Fig.16
A unit cell may be described by the interrelationship between the lengths(a,b,c) of its sides and the interaxial angles (α,β,γ)between them. (α is the angle between the b and c, axes,β is the angle between the a and c axes, and γ is the angle between the a and b axes.)The actual values of a,b,and c, and α,β and γ are not important, but their interrelation is. The lengths are measured from one corner of the cell, which is taken as the origin. These lengths and angles are called the lattice parameters of the unit cell, or sometimes the lattice constants of the cell. But the latter term is not really appropriate because they are not necessarily constants; for example, they can vary with changes in temperature and pressure and with alloying. [Note: We use a,b and c to indicate the axes of the unit cell; a,b and c for the lattice parameters, and a,b and c for the vectors lying along the unit-cell axes.]
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