Directions and Planes in Crystals Directions (vector components:a single direction is expressed as [a set of 3 integers], equivalent directions(family)are expressed as a set of 3 integers> Planes:a single plane is expressed as(a set of 3 integers hk/=Miler indices)and equivalent planes are expressed as fa set of 3 integers Miler Indices:take x,y,z(multiple of basic vectors ex.x=4a,y=3a,z=2a) reciprocals(1/4,1/3,1/2)>common denominator(3/12,4/12,6/12)>the smallest numerators(3 4 6) [h k I]crystal direction is perpendicular lattice constant to (h k I)plane Z (100)plane a (110)plane [111] (111)plane [1001 XDirections and Planes in Cr ystals Directions (vector components: a single direction is expressed as [a set of 3 integers], equivalent directions (family) are expressed as < a set of 3 integers > y equivalent directions (family) are expressed as < a set of 3 integers > Planes: a single plane is expressed as (a set of 3 integers h k l = Miler indices) and equivalent planes are expressed as {a set of 3 integers} Miler Indices: take x, y, z (multiple of basic vectors ex. x=4 a, y=3 a, z=2 a) reciprocals (1/4, 1/3, 1/2) Æ common denominator (3/12, 4/12, 6/12) Æ the smallest ( ) lattice constant numerators (3 4 6) [h k l] crystal direction is perpendicular to (h k l) plane