BIOINORGANIC CHEMISTRY A Short Course Second Edition

86 INSTRUMENTAL METHODS

through lattice points, and these repeat regularly throughout the crystal. Paral-
lel planes are equidistant with distanced between them. Lattice planes cut the
x , y , and z axes into equal parts having whole numbers called indices. A set of
lattice planes is determined by three indicesh , k , and l if the planes cut the x
axis asa / h , the y axis as b / k , and the z axis as c / l. In Figure 3.5A , lattice planes
are shown in a two - dimensional lattice. In this fi gure, taken from Figure 3.5 of
reference 11 , h = 2 and k = 1. The lattice plane distance d is the projection of
a / h , b / k , and c / l on the line perpendicular to the corresponding lattice plane
(h k l ). If a set of planes is parallel to an axis, that particular index is 0 (the
plane intercepts the axis at infi nity). Therefore the unit cell is bounded by
planes (100), (010), and (001), with the parentheses indicating ( h k l ). Line
segments are given in brackets, that is, [100] is the line segment from the origin
of the unit cell to the end of thea axis and [111] is the body diagonal from
the origin to the opposite corner. These properties are illustrated in Figure
3.5B adapted from Figure 3.6 of reference 11.
The unit cell considered here is a primitive (P) unit cell; that is, each unit
cell has one lattice point. Nonprimitive cells contain two or more lattice points
per unit cell. If the unit cell is centered in the (010) planes, this cell becomes
a B unit cell; for the (100) planes, an A cell; for the (001) planes, a C cell.
Body - centered unit cells are designated I, and face - centered cells are called F.
Regular packing of molecules into a crystal lattice often leads to symmetry

Figure 3.5 (A) Lattice planes in a two - dimensional lattice as taken from Figure 3.5
of reference 11 ( h = 2 , k = 1). (B) Unit cell bounded by planes (100), (010), (001). Direc-
tions alonga , b , and c are indicated by [100], [010], and [001]. (Adapted with kind per-
mission of Springer Science and Business Media from Figure 3.6 of reference 11.
Copyright 1999, Springer - Verlag, New York.)

a

h

b

k

a

b

O
origin

y

x

d

AB

c

a

b

(010)β α

(100)

[010]

[001]

[100]

(001)

origin

γ