材料学基础6.ppt
材料科学基础Fundamental of MaterialsProf:Tian Min Bo Tel:62795426，62772851 E-mail:Department of Material Science and EngineeringTsinghua University.Beijing 100084Lesson six2.7 Some Important Crystallographic Formulas1.Zone and zone equation1.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 hukvlw02.If 2.If huhukvkvlwlw0 0，then then u v wu v w lies in(lies in(h k lh k l)3.For 3.For cubic crystalscubic crystals,h k lh k l (h k lh k l)4.The zone 4.The zone u v wu v w contains two planes(contains two planes(h h1 1 k k1 1 l l1 1)and(and(h h2 2 k k2 2 l l2 2),then),then5.The plane(5.The plane(h k lh k l)belongs to two zones)belongs to two zones u u1 1 v v1 1 w w1 1 and and u u2 2 v v2 2 w w2 2 if if6.The distance between adjacent plane6.The distance between adjacent plane (interplanar distance)(interplanar distance)d(hkl)f(a,b,c ,h,k,l)For orthorhombic:For cubic:For hexagonal crystals:7.The length of 7.The length of u v wu v w For cubic:8.The angle 8.The angle between(between(h h1 1 k k1 1 l l1 1)and()and(h h2 2 k k2 2 l l2 2)For orthorhombic:For orthorhombic:For cubic:For cubic:For hexagonal:For hexagonal:9.The angle 9.The angle between between u u1 1 v v1 1 w w1 1 and and u u2 2 v v2 2 w w2 2 For orthorhombic:For orthorhombic:For cubic:For cubic:For hexagonal:For hexagonal:10.The volume of unit cells10.The volume of unit cells V V 2.8 Stacking Mode of Crystalsuu.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 cubicFor simple cubic(001)aaaa(001)aaaa(110)abab(110)ababThis sequence is called the stacking orderThis sequence is called the stacking orderuu.Comparison of stacking mode of HCP and FCCHCP stacking order:ABABABAB1.HCP1.HCP2.FCC2.FCCStacking order of(111)：ABCABCABCA AA AA AB BB BB BC CC CC Cuu.Stacking fault For HCP:For HCP:normal order:ABABAB fault order:ABCABAB For FCCFor FCC：normal order:ABCABCABC fault order:ABCACABCA ABCACBCABC ABCABABAB ABCACBA uu.Transformation of hexagonal to rhombohedral indices and vice versacHaHbHcRaRbRExamples and DiscussionsExerciseThank you!6
