solid state pysics-1solid state physics-1solid state physics-1solid state physics-1.ppt

Crystal Structure * Each of the unit cells of the 14 Bravais lattices has one or more types of symmetry properties, such as inversion, reflection or rotation,etc. SYMMETRY INVERSION REFLECTION ROTATION ELEMENTS OF SYMMETRY Crystal Structure * Lattice goes into itself through Symmetry without translation Operation Element Inversion Point Reflection Plane Rotation Axis Rotoinversion Axes Crystal Structure * Inversion Center A center of symmetry: A point at the center of the molecule. (x,y,z) -- (-x,-y,-z) Center of inversion can only be in a molecule. It is not necessary to have an atom in the center (benzene, ethane). Tetrahedral, triangles, pentagons dont have a center of inversion symmetry. All Bravais lattices are inversion symmetric. Mo(CO)6 Crystal Structure * Reflection Plane A plane in a cell such that, when a mirror reflection in this plane is performed, the cell remains invariant. Crystal Structure * Examples Triclinic has no reflection plane. Monoclinic has one plane midway between and parallel to the bases, and so forth. Atomic Packing Factor Atomic Packing Factor (APF) is defined as the volume of atoms within the unit cell divided by the volume of the unit cell. Crystal Structure * 1-CUBIC CRYSTAL SYSTEM Simple Cubic has one lattice point so its primitive cell. In the unit cell on the left, the atoms at the corners are cut because only a portion (in this case 1/8) belongs to that cell. The rest of the atom belongs to neighboring cells. Coordinatination number of simple cubic is 6. a- Simple Cubic (SC) a b c Crystal Structure * Atomic Packing Factor of SC Crystal Structure * b-Body Centered Cubic (BCC) BCC has two lattice points so BCC is a non-primitive cell. BCC has eight nearest neighbors. Each atom is in contact with its neighbors only along the body-diagonal directions. Many metals (Fe,Li,Na..etc), including the alkalis and several transition elements choose the BCC structure. a b c Crystal Structure * 2 (0,433a) Atomic Packin