Page 94 - Materials Science and Engineering An Introduction

66 • Chapter 3 / The Structure of Crystalline Solids

Point 1 is located at the origin of the coordinate system, and, z
therefore, its lattice position indices referenced to the x, y, and
z axes are 0a, 0b, and 0c, respectively. And from Equations 3.9a 6 9
through 3.9c,
7 8
lattice position referenced to the x axis 0a qa
5 4
lattice position referenced to the y axis 0b rb c y
1
lattice position referenced to the z axis 0c sc a
2 3
Solving the above three expressions for values of the q, r, and s b
indices leads to x

0a
q = = 0
a
0b
r = = 0
b
0c
s = = 0
c
Therefore this is the 0 0 0 point
Because point number 2, lies one unit cell edge length along the x axis, its lattice position
indices referenced to the x, y, and z axes are a, 0b, and 0c, and

lattice position index referenced to the x axis a qa
lattice position index referenced to the y axis 0b rb
lattice position index referenced to the z axis 0c sc

Thus we determine values for the q, r, and s indices as follows:
q = 1 r = 0 s = 0
Hence, point 2 is 1 0 0.
This same procedure is carried out for the remaining seven points in the unit cell. Point
indices for all nine points are listed in the following table.

Point Number q r s
1 0 0 0
2 1 0 0
3 1 1 0
4 0 1 0
5 1 2 1 2 1 2
6 0 0 1
7 1 0 1
8 1 1 1
9 0 1 1