The Foundations of Chemistry

EXAMPLE 13-7 Nearest Neighbors

In the simple cubic form of manganese there are Mn atoms at the corners of a simple cubic

unit cell that is 6.30 Å on edge. (a) What is the shortest distance between centers of neigh-

boring Mn atoms? (b) How many nearest neighbors does each atom have?

520 CHAPTER 13: Liquids and Solids

Problem-Solving Tip:The Locations of the Nearest Neighbors

in Cubic Crystals

The distance from an atom to one of its nearest neighbors in any crystal structure depends

on the arrangement of atoms and on the size of the unit cell. For structures (such as

metals) that contain only one kind of atom, the nearest neighbors of each atom can be

visualized as follows. (Recall that for a cubic structure, the unit cell edge is a). In a simple

cubic structure, the nearest neighbors are along the cell edge (i). In a face-centered cubic

structure, the nearest neighbors are along the face diagonal (ii). In a body-centered cubic

structure, they are along the body diagonal (iii).

The relationships just described hold only for structures composed of a single kind of

atom. For other structures, the relationships are more complex.

Cell

edge, a

Cell edge = a

= 2 atom radii

(i)

Cell

edge, a

Face diagonal = √ 2 a

= 4 atom radii

(ii)

Cell

edge, a

Body diagonal = √ 3 a

= 4 atom radii

(iii)