ABSTRACT
GGGG ++= (39.1) where the numbers , andp q s are integers, so that the lattice is invariant under any translation that consists of multiples of the individual primitive vectors .,, cba GGG The primitive vectors may be omitted, and hence, the vectors (39.1) can be written by convention as [ ].pqs It follows that the primitive vectors themselves may be denoted by
, The lattice is generated by repeated arbitrary translation (39.1) of either a single lattice point or a primitive cell associated with it, as illustrated in Figure 39.1 for a two-dimensional lattice. A primitive cell always contains one lattice
[ ]100a =G [ ]010 ,b =G [ ]001 .c =G
point only. Either there are points at the corners of the cell only (a crystallographic cell) or one lattice point is in the centre of a cell which is defined by the planes bisecting the lines joining the central point with the adjacent lattice points (a Wigner-Seitz cell). Figure 39.1 shows that the sides of the Wigner-Seitz cell are determined by the equation
( )22 21 or 2 0 i.e.2r R R r R R r R r− ⋅ = ⋅ + = + =G G G G GG G G 2G (39.2) where rG is the position vector with respect to the central lattice point.
