第5课材料化学全英文课件PPT课件.ppt

材料科学基础Fundamental of Materials Science Prof: Tian Min Bo Tel: E-mail: tmb@mail.tsinghua.edu.cn Department of Material Science and Engineering Tsinghua University. Beijing 100084 Lesson five 2.5 Indices of Crystal Planes and Directions 2.5.1 What’s crystal planes and directions? The atomic planes and directions passing through the crystal are called Crystal Planes and Crystal Directions 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). 2.5.2 Plane indices a c b x y z ? 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, . ? In some situation, 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. Total: 12 Total: 4×3！=24 3.5.3 Direction indices 1. Derivation for the crystallographic direction As the first above, set the origin on the direction to be indexed. Find the coordinates of another point on the direction in questions. Reduce to three smallest integers: u, v, w. Enclose in square brackets [u v w]. 2. The important direction in cubic crystals: 100 : crystal axes 110 : face diagonal 111 : body diagonal 112 : apices to opposite face-centers 3. Family of directions consists of crystallographically equivalent directions, denoted u v w 2.6 Hexagonal Axes for Hexagonal Crystals 2.6.1 Why choose four-axis system? Four indices has been devis