§2.6 Some Important Crystallographic Formulas ＊

§2.6 Some Important Crystallographic Formulas＊ Lan Yu Faculty of Material Science and Engineering Kunming University of Science and technology

1. Zone and zone equation All Planes parellel to common 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)

4. The zone [u v w] contains two planes (h1 k1 l1) and (h2k2l2),then 5. The plane (h k l) belongs to two zones [u1v1w1] and [u2v2w2] if

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:

7. The length of [u v w] For cubic: 8. The angle Ф between (h1k1l1) and (h2k2 l2)

8. The angle between (h1k1l1) and (h2k2 l2) For cubic: For orthorhombic:

For hexagonal:

9. The angle between [u1v1w1] and [u2v2w2] For orthorhombic: For cubic:

For hexagonal:

10. The volume of unit cellsV

§2.7 Stacking Modes of Crystals Ⅰ. A crystal can be considered as the result of stacking the atomic layers, say (h k l ), one over another in a specific sequence. For simple cubic (001) aaaa…… (110) abab…… This sequence is called the stacking order

Ⅱ.Comparison of stacking mode of HCP and FCC 1. HCP HCP stacking order: ABABABAB……

2. FCC Stacking order of (111)： ABCABCABC……

A B A A C B B C C

Ⅲ. Stacking fault • For HCP: normal order: ABABAB…… fault order: ABCABAB…… • For FCC： normal order: ABCABCABC…… fault order: ABCACABCA…… ABCACBCABC …… ABCABABAB …… ABCACBA ……

cH cR bR aR bH aH Ⅳ.Transformation of hexagonal to rhombohedral indices and vice versa

Thanks !

§2.6 Some Important Crystallographic Formulas ＊