Page 19 - Modern physical chemistry

B Structure in Solids

(a) Triclinic (b) Monoclinic

z

Y, I
I
I , I Y,
c t. ___ _
, c /----
I'
I /
I '
,
I.
,b;toa
,
/b=a
, , / ,
a x , a FIGURE 1.6a-d Possible
(c) Orthorhombic (d) Tetragonal unit cells for filling space.
When the Miller indices for a set of planes are h, k, and l, the planes are called (hkl)
planes. A negative Miller index is indicated by a minus sign over the number. Thus, a
(liO) plane is parallel to a plane intersecting the x axis at a, the y axis at - b, and the z

axis at 00.
Example 1.3
If a (123) plane intersects the x axis at 6 a, what are its intercepts on the y and z axes?
The Miller indices h, k, l are proportional to reciprocals of the intercepts measured
in terms of a, b, and c, respectively. Here
1-1~ 3-1~
- OA' 2=1 ;B' - OC'

with
OA=6a.
Combining the first and fourth equations yields the constant of proportionality
1=6.