1. §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

2. 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 )

3. 4. The zone [ u v w ] contains two planes ( h 1 k 1 l 1 ) and ( h 2 k 2 l 2 ),then 5. The plane ( h k l ) belongs to two zones [ u 1 v 1 w 1 ] and [ u 2 v 2 w 2 ] if

4. 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:

5. 7. The length of [ u v w ] For cubic: 8. The angle Ф between ( h 1 k 1 l 1 ) and ( h 2 k 2 l 2 )

6. For orthorhombic: For cubic: 8. The angle between ( h 1 k 1 l 1 ) and ( h 2 k 2 l 2 )

7. For hexagonal:

8. For orthorhombic: For cubic: 9. The angle between [ u 1 v 1 w 1 ] and [ u 2 v 2 w 2 ] [ u 2 v 2 w 2 ]

9. For hexagonal:

10. 10. The volume of unit cells V

11. §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

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

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

14. A A A B B B C C C

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

16. Ⅳ.Transformation of hexagonal to rhombohedral indices and vice versa cHcH aHaH bHbH cRcR aRaR bRbR

18. Thanks !