1、2019/5/28,材料科学基础,材料科学基础 Fundamental of Materials,Lesson six,2019/5/28,材料科学基础,2.7 Some Important Crystallographic Formulas,1. Zone and zone equationAll 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 hukvlw02. If hukvlw0，then u v
2、 w lies in (h k l)3. For cubic crystals, h k l (h k l),2019/5/28,材料科学基础,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,2019/5/28,材料科学基础,6. The distance between adjacent plane( interplanar distance )d(hkl)f(a,b,c
3、 , h,k,l)For orthorhombic:,For cubic:,For hexagonal crystals:,2019/5/28,材料科学基础,7. The length of u v w,For cubic:,8. The angle between (h1 k1 l1) and (h2 k2 l2),2019/5/28,材料科学基础,For orthorhombic:,For cubic:,2019/5/28,材料科学基础,For hexagonal:,9. The angle between u1 v1 w1 and u2 v2 w2,2019/5/28,材料科学基础,Fo
4、r orthorhombic:,For cubic:,2019/5/28,材料科学基础,For hexagonal:,2019/5/28,材料科学基础,10. The volume of unit cells V,2019/5/28,材料科学基础,2.8 Stacking Mode of Crystals,.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
5、(001) aaaa (110) abab,This sequence is called the stacking order,2019/5/28,材料科学基础,.Comparison of stacking mode of HCP and FCC,HCP stacking order:ABABABAB,1. HCP,2019/5/28,材料科学基础,2. FCC,Stacking order of (111)： ABCABCABC,2019/5/28,材料科学基础,2019/5/28,材料科学基础,.Stacking fault,For HCP: normal order: ABABABf
6、ault order: ABCABAB For FCC：normal order: ABCABCABCfault order: ABCACABCAABCACBCABC ABCABABAB ABCACBA ,2019/5/28,材料科学基础,.Transformation of hexagonal to rhombohedral indices and vice versa,2019/5/28,材料科学基础,2019/5/28,材料科学基础,Examples and Discussions,2019/5/28,材料科学基础,Exercise,2019/5/28,材料科学基础,Thank you !,6,
