Page 33 - Principles and Applications of NanoMEMS Physics

1. NANOELECTROMECHANICAL SYSTEMS 19

The arrangement and orientation of atoms in a crystalline solid is
specified with reference to certain directions, see Figure 1-15. Thus, with
respect to the origin of a Cartesian set of coordinates, the position of an atom
may be described as being

Cr y sta l Dir ec tio n
Cr y sta l Dir ec tio n s s
[001]
[001]
[a b
[a b c ] c ]
[010]
[010] c c
[100
[100 ] ] a a
b b
Figure 1-15 Nomenclature of crystal directions.

s
[abc], that is, a unit along the direction [001], b units along the direction
[010], and c units along the direction [001]. Since a plane may be described
by a vector perpendicular to it (its normal), the direction [abc] also describes
a plane, which is denoted the plane (abc), shown in Figure 1-16(a).
CrystalPlane
[001]

l l (abc)
[010]
k
[100]
h
(a)

(100) (110) (111)

(b)

Figure 1-16. (a) Description of crystallographic plane by its normal (abc). (b) Description of
crystallographic planes of cubic (atoms occupy the corners and faces of a cube) crystal by
Miller indices.

Notice that, since a plane is described by three points common to it, the
points of intersection between a plane and the three coordinate axes may also
be used to denote it. In particular, see Figure 1-16(b), the points h, l, and k,
along the coordinate axes [100], [010], and [001], respectively, might be