文档介绍：材料科学基础 Fundamental of Materials Lesson five Lesson five § Indices of crystal planes and directions ?Ⅰ.What ’s crystal planes and directions? The atomic planes and The atomic planes and directions passing directions passing through the crystal are through the crystal are called (crystal) planes called (crystal) planes and directions and directions respectively. respectively. 1. Steps to determinate the plane indices: ? Establish a set of coordinate axes ? Find the intercepts of the planes to be indexed on a, b and c axes ( x, y, z ). a cb x y z ??ⅡⅡ. Plane indices . Plane indices ? Take the reciprocals of the intercepts 1/ x , 1/ y , 1/z.? Clear fractions but do not reduce to lowest integers. ? Enclose them in parentheses, ( h k l ) Example: 1/2,1,2/3 2,1,3/2 (423) Plane indices referred to three axes a, b and c are also called Miller Indices. Several important aspects of the Miller indices for planes should be noted: ? Planes and their negatives are identical. Therefore . ? Planes and their multiples are not identical. ? In cubic systems, a direction that has the same indices as a plane is perpendicular to that plane. )020()020 (? 2. The important planes in cubic crystals (110) (110) (112) (112) (111) (111) (001) (001) 3. A family of planes consists of equivalent planes so far as the atom arrangement is concerned. )110() 011 ()110 ( )101 ()10 1() 110 (} 110 {?????? Total: 6 Total: 6 )1 11( )111() 11 1() 111 (} 111 {???? Total: 4 Total: 4 )121 ()112() 112() 211 ( )112 ()121()21 1()121 ( )2 11()211()12 1() 112 (} 112 {????????????)1 32 ()123() 21 3() 321 ( )2 31 ()213() 12 3() 312 ()3 21 ( )312() 13 2() 213 ()1 23 ()132( ) 31 2() 231 ()2 13 ()231() 32 1( ) 132 ()3 12 ()321() 23 1() 123 (} 123 {???????????????????????? Total: 12 Total: 12 Total: 4 Total: 4 × ×3 3! ! =24 =24 ?Ⅲ. Direction Indices 1. Derivation for the crystallographic direction ① As the first above, set the origin on the direction