NoteTaking_B2: Crystal & Crystal Structures

CH2 LATTICES, PLANES AND DIRECTIONS

1. 14 Bravais Lattices

{cP, cF cI, tP, tI}, {oP, oI, oC, oF},{hR, hP}, {mP, mB, aP}
c: cubic
o: orthorhombic
h: hexagonal
m: monoclinic
a: triclinic
P: primitive
F: face-centered
I: body-centered
B/C: base-centered

2. Lattice planes and Miller indices

1) Miller indices, (hkl),  represent a set of identical parallel lattice planes.

2) "The values of h, k and l are the reciprocals of the fractions of a unit cell edge, a, b and c respectively intersected by an appropriate plane. "
3) "Negative intersections are written with a negative sign over the index (bar)"

How to determine Miller indices?

Trave along the axes in turn and then counting the number of spaces between planes encountered from one lattice point to the next.

4) Curly brakets, {hkl}, designate identical planes by virtue of the symmetry of the crystal.

5) Miller indices for hexagonal lattices : (hkil), where i=-(h+k)

3. Directions

Directions are generated written as [uvw]. The direction of [uvw] is simply the vector pointing from the origin to the lattice point with coordinates u, v,w.

4. Zone

A zone is a set of planes, all of which are parallel to a single direction. 

5. Useful Formula