材料科学基础 课件 15.ppt

材料科学基础 Fundamental of Materials Lesson fifteen Lesson fifteen § Twinning (I) —— Macroscopic Aspect ?Ⅰ. ?Ⅱ.Rules governing the change in length. 1. Change in shape of a hemisphere with unit radius. before twinning: bnlrlL ?????)(????? 11z 222???yx?? 2zz??????yyxx???? 1 into 2 substitute ellipsoid for equation 1z)( 222????????zryx 2. Undistorted planes and directions. ???????. . 1 1? K????? plane shear and of on intersecti the 2 2 2K K? Twin elements —— K 1、? 1,K 2、? 2 K K 1 1?? 1 1K K 2 2?? 2 2 FCC FCC BCC BCC HCP HCP ) 111 () 112 ( )111()2110 ()012 1( )211( ]211[]1 11[] 011 1[ ] 112 [] 111 []1110 [ FCC K 1, ? 1K 2, ? 2 BCC K 1, ? 1K 2, ? 2ca 1a 2a 3 HCP )2110 (] 011 1[) 012 1( ]1110 [ 3. 4. Rule for elongation or reduction of . All . in the region where K 1 and K 2 makes an obtuse ( acute ) angle will increase ( reduce ) its length after twinning. )2( ctg 2?????AAC D ?Ⅲ.Application: take HCP for example Suppose: , )2110 ( 1?K)012 1( 2