Transcript crystal
Unit 2 - Crystallography In most solids, atoms fit into a regular 3-dimensional pattern called a crystal 1 -Crystals are not small and simple like molecules are (e.g. H20, C02) -Theoretically a crystal can go on forever -Real crystals never do -However even the smallest crystal extends billions of atoms in all directions -Since crystals are so huge, how can we wrap our minds around the way crystals are structured? 2 -The conceptual tool we use for this is the unit cell -The unit cell is the smallest possible repeating pattern of atoms in the crystal Na+ Cl- Unit cell of NaCl 3 The unit cell is repeated to form the crystal 4 The unit cell is repeated to form the crystal 5 The unit cell is repeated to form the crystal 6 Lattice constants are numbers that characterize the size of the unit cell With a cubic geometry, only one lattice constant is needed. It is usually designed a With a hexagonal geometry, two lattice constants are needed, usually called a and c 7 There are seven common crystal geometries Cubic Orthorhombic Hexagonal Tetragonal Monoclinic Rhombohedral Triclinic 8 Most metals have one of these 3 crystal geometries Facecentered cubic (FCC) Bodycentered cubic (BCC) Hexagonal close-packed (HCP) 9 Face-Centered Cubic (FCC) Unit Cell Reduced Sphere Representation Solid Sphere Representation 10 Face-Centered Cubic (FCC) Lattice Structure Examples: Lead Copper Gold Silver Nickel 11 If you know the atomic radius, you know the size of an FCC unit cell a2 + a2 = (4R)2 a = 81/2R 4R a Example: Rgold = .144 nm agold = .407 nm 12 Body-Centered Cubic (BCC) Unit Cell Reduced Sphere Representation Solid Sphere Representation 13 Body-Centered Cubic (BCC) Lattice Structure The most familiar example of BCC is room temperature iron Also tungsten and chromium 14 The coordination number is the number of other atoms touched by each atom in a lattice The coordination number for FCC atoms is 12 5 2 1 7 (opposite 6) 6 This atom touches … 3 4 8 (atom opposite 5) 15 Plus 4 more atoms in the next unit cell over Atoms per unit cell in FCC 6x½= 3 8 x 1/8 = 1 Total = 4 16 Atomic Packing Factor (APF) measures the fraction of the unit cell volume actually occupied by atoms Example for FCC APF = Vatoms / Vunit cell Vatoms = 4 x 4/3 pR3 Vunit cell = a3 = 83/2 R3 Do the arithmetic: APF = 0.74 Notice all the empty space 17 Your turn: How many atoms are in a unit cell of BCC iron? Also, how would you go about determining the APF (this is a homework problem). 18 Density The concept of atomic packing factor allows us to relate atomic weight to macroscopically observed density r = nA VcellNA n = atoms/unit cell A = atomic weight Vcell = volume of the unit cell NA = Avogadro’s number 19 Hexagonal Close-packed (HCP) Unit Cell Reduced Sphere Representation HCP lattice structure 20