结晶学 chap2_crystal lattices.pptVIP

Miller Indices：（h, k, l） * Diffraction pattern from one- and two- dimensional arrays Diffraction line is perpendicular to the array; Distance in diffraction lines is inversely proportional to the array distance: K/a; K/b; Real Space Reciprocal Space Relation of the Crystal lattice and Reciprocal lattice 3D- array a* ? to b and c vectors or bc plane a* // b x c b* ? to ac plane c* ? to ab plane ?a*? = K/ ?a? = ? b x c ? /a?(bxc) = ? bxc ? / V real space ( , , ) ? reciprocal space ( , , ) The non-coplanar vectors , ,and define a unit cell in the real lattice. The corresponding vectors for the unit cell of a reciprocal lattice, , and , will be defined by ； ； where the unit cell volume is given by Hence, the reciprocal lattice vectors , and are normal to the planes bc, ca,and ab respectively in the real space. By the way, the symmetry in the reciprocal space is the same as in the real space. Crystal Lattice cell ∴ a* in the direction of b ? c, i.e. a*?b ? a* ? c ? 0 ∴ a*, b*, c* are the three non-coplanar vectors of reciprocal lattice In direct space In reciprocal space Crystal Systems: Cubic Hexagonal Trigonal Tetragonal Orthorhombic Monoclinc Triclinic Lattice Centering—Pure Translation Symmetry Rhombohed-ral center Face center Base center Body center Primitive (0,0,0) ; (2/3, 1/3, 1/3); (1/3, 1/3, 2/3) 3 R (0, 0, 0); (1/2, 1/2, 0); (1/2, 0, 1/2); (1/2, 1/2, 0) 4 F (0, 0, 0); (1/2, 1/2, 0) 2 C (0, 0, 0); (1/2, 0, 1/2) 2 B (0, 0, 0); (0, 1/2, 1/2) 2 A (0, 0, 0); (1/2, 1/2, 1/2) 2 I (0,0,0) 1 P position type Take Orthorhombic for example Miller Indices (h, k, l) For any set of parallel planes with interplane distance d, the h, k, and l are integer numbers representing the reciprocal of the intercepts of the plane axes a, b, c. For example, （3, 2, 1） is the plane intercepting a, b, c at 1/3a, 1/2b, 1c respectively. Hexa