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1、材料科学基础 Fundamental of Materials Science,Prof: Tian Min Bo Tel: 62795426 ，62772851E-mail: Department of Material Science and Engineering Tsinghua University. Beijing 100084,Lesson six,2.7 Some Important Crystallographic Formulas,2.7.1 Standard projection,Principle of stereographic projection,standard
2、 projection of cubic crystal system,Figure of standard projection,x=z line,x=y line,standard projection of HCP,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-k2l1l1h2-l2h
3、1h1k2-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 , , h,k,l)For orthorhombic:,For cubic:,For hexagonal crystals:,7. The length of u v w,For cubic:,8. The angle between (h1 k1 l1) and (h2 k2 l2),For ort
4、horhombic:,For cubic:,For cubic the angle has no relation to lattice constant.,For hexagonal:,9. The angle between u1 v1 w1 and u2 v2 w2,For orthorhombic:,For cubic:,For hexagonal:,10. The volume V of unit cells,2.8 Stacking Mode of Crystals,2.8.1 A crystal can be considered as the result of stackin
5、g 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,2.8.2 Comparison of stacking mode of HCP and FCC,HCP stacking order:ABABABAB,1. HCP,2. FCC,Stacking order of (111)： ABCABCABC,2.8.3 Stacking f
6、ault,For HCP: normal order: ABABABfault order: ABCABAB For FCC：normal order: ABCABCABCfault order: ABCACABCAABCACBCABC ABCABABAB ABCACBA ,2.8.4 Transformation of hexagonal to rhombohedral indices and vice versa,aH,bH,Discussion,Interplanar distance.For example in FCC:Length of crystal directions.,Ex
7、ercise,1. Determine indices of directions in the figure by analysis.,2. In accordant with features of stacking in FCC and HCP, proof the size of octahedral interstitial equals to size of tetrahedral interstitial in these two crystals.,3. Take the three axis of hexagonal crystal a, b and c as base vector, determine the coordinate of octahedral interstitial and tetrahedral interstitial sites.,Thank you !,6,
