Question

Exercise 3: Reticular inter-spacing distance in hexagonal system 1-Establish the relation between hexagonal direct and reciprocal lattices, then establish the inter-spacing distance in hexagonal system 2- Give the equivalent reflections of the {100) family planes, then {1 -2 0; family planes.

Answer 1

The unit cell axes and angles of the direct cell are known by the letters a, b, c, d, B ands. The para- meters for reciprocal unit cell are nel represented with the symbols at btct , & B & 8" (just with addition of an asterisk) These reciprocal axes consespond to the vectors too, 2010 and sool respectively. Take = hat + lb* + ect The geometrical relationships b/w direct and reuprocal cells imply the following relations : is aut = bxc ; cos ole = cosp.cos y -cosy at is perpendicular (1) to B ande, Ves volume sog.smx üj b* -e xa ; cosß = can contacos 16 Est c and a stron a ce= bxa; cospe=coscoss-cost " ma imp c* is I to b and a Interlayer spacings can be calculated from Miller Indices Chike) and mit cell ares values. a hke a 2