Lecture on CRYSTALLINE SOLIDS SPACE LATTCE AND 在晶体空间点阵讲座.pptVIP

CRYSTAL SYSTEMS AND BRAVAIS LATTICES??Seven crystal systems are each described by the shape of the unit cell which can be translated to fill space.Bravais lattices -- fourteen simple and complex lattices within the seven crystal systems. The complex lattices have atoms centered either in the center of a primitive unit cell or in the center of one of the unit cell faces.?  PRINCIPAL METALLIC CRYSTAL STRUCTURES?We will concentrate on three of the more densely packed crystal structures, BCC - body centered cubic, FCC - face centered cubic, and HCP - hexagonal close packed.?BCC - 2 atoms per unit cell CN = 8? EQUIVALENT SITES (ATOMIC POSITIONS) IN CUBIC UNIT CELLS?Simple Cubic, SC - one per unit cell - corner atoms only ?(0,0,0) (1,0,0) (1,1,0) (0,1,0) (0,0,1) (1,0,1) (1,1,1) (0,1,1)?Body Centered Cubic, BCC - two per unit cell - corner atoms as above, plus (1/2, 1/2, 1/2)?Face Centered Cubic, FCC - four per unit cell - corner atoms as above plus (1/2, 1/2, 0) (1/2, 0, 1/2) ( 0, 1/2, 1/2) (1, 1/2, 1/2) (1/2, 1, 1/2) (1/2, 1/2, 1)? DIRECTIONS IN CUBIC LATTICES 1 . Vector components of the direction are resolved along each of the coordinate axes and reduced to the smallest integers. 2. All parallel directions have the same direction indices. ?3. Equivalent directions have the same atom spacing.4. The cosine of the angle between two directions is given by? Indices of a Family or Form? MILLER INDICES FOR CRYSTALLOGRAPHIC PLANES?Definition: Miller Indices are the reciprocals of the fractional intercepts (with fractions cleared) which the plane makes with the crystallographic x,y,z axes of the three nonparallel edges of the cubic unit cell. ? Spacing between planes in a cubic crystal????where dhkl = interplanar spacing between planes with  Miller indices h,k,and l.a = lattice constant (edge of the cube)h, k, and l = Miller indices of cubic planes being consider