文档介绍：材料科学基础 Fundamental of Materials Science
Prof: Tian Min Bo
Tel: 62795426 ,62772851
E-mail: ******@.
Department of Material Science and Engineering
Tsinghua University. Beijing 100084
Lesson six
Some Important Crystallographic Formulas
Standard projection
Principle of stereographic projection
standard projection of cubic crystal system
Figure of standard projection
x=z line
x=y line
y=z line
x= 0
y= 0
z= 0
y= -z line
x= -y line
x= -z line
standard projection of HCP
1. Zone and zone equation
All planes parellel mon axis [u v w] constitute a (crystal) zone, the [u v w] zone.
If (h k l) belongs to zone [u v w], then hu+kv+lw=0
2. If hu+kv+lw=0,then [u v w] lies in (h k l)
3. For cubic crystals, [h k l] ⊥(h k l)
In another word,for cubic crystals, indices of plane’s normal direction equal to indices of plane.
4. The zone [u v w] contains two planes (h1 k1 l1) and (h2 k2 l2),then
5. The plane (h k l) belongs to two zones [u1 v1 w1] and [u2 v2 w2] if
h1 k1 l1 h1 k1 l1
h2 k2 l2 h2 k2 l2
k1l2-k2l1
l1h2-l2h1
h1k2-h2k1
1 0 0 1 0 0
1 1 0 1 1 0
[ 0 0 1 ]
( 1 0 0 )
( 1 1 0 )
[ 0 0 1 ]
6. The distance between adjacent plane
( interplanar distance )
d(hkl)= f (a,b,c ,α,β,γ, h,k,l)
For orthorhombic:
For cubic:
For hexagonal crystals: