skja_06 Crystallographic Formulas 材料科学基础（英文课件）.pptVIP

材料科学基础Fundamental of Materials §2.7 Some Important Crystallographic Formulas 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 (h2 k2 l2),then 6. The distance between adjacent plane ( interplanar distance ) d(hkl)＝f(a,b,c α,β,γ h,k,l) For orthorhombic: 7. The length of [u v w] For orthorhombic: For hexagonal: For orthorhombic: §2.8 Stacking Mode 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. Ⅱ.Comparison of stacking mode of HCP and FCC 2. FCC Ⅲ.Stacking fault For HCP: normal order: ABABAB…… fault order: ABCABAB…… For FCC： normal order: ABCABCABC…… fault order: ABCACABCA…… ABCACBCABC …… ABCABABAB …… ABCACBA …… Ⅳ.Transformation of hexagonal to rhombohedral indices and vice versa Examples and Discussions Exercise * * Prof: Tian Min Bo Tel: E-mail: tmb@ Department of Material Science and Engineering Tsinghua University. Beijing 100084 Lesson six 5. The plane (h k l) belongs to two zones [u1 v1 w1] and [u2 v2 w2] if For cubic: For hexagonal crystals: For cubic: 8. The angle Ф between (h1 k1 l1) and (h2 k2 l2) For cubic: 9. The angle between [u1 v1 w1] and [u2 v2 w2] For cubic: For hexagonal: 10. The volume of unit cells V For simple cubic (001) aaaa…… (110) abab…… This sequence is called the stacking order HCP stacking order: ABABABAB…… 1. HCP Sta