1. 1 Unit 2 - Crystallography In most solids, atoms fit into a regular 3-dimensional pattern called a crystal In most solids, atoms fit into a regular 3-dimensional pattern called a crystal

2. 2 -Crystals are not small and simple like molecules are (e.g. H 2 0, C0 2 ) -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?

3. 3 -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

4. 4 The unit cell is repeated to form the crystal

5. 5

6. 6

7. 7 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

8. 8 There are seven common crystal geometries CubicHexagonal TetragonalRhombohedral Orthorhombic MonoclinicTriclinic

9. 9 Most metals have one of these 3 crystal geometries Face- centered cubic (FCC) Body- centered cubic (BCC) Hexagonal close-packed (HCP)

10. 10 Face-Centered Cubic (FCC) Unit Cell Reduced Sphere Representation Solid Sphere Representation

11. 11 Face-Centered Cubic (FCC) Lattice Structure Examples: Lead Copper Gold Silver Nickel

12. 12 If you know the atomic radius, you know the size of an FCC unit cell a 4R a 2 + a 2 = (4R) 2 a = 8 1/2 R Example: R gold =.144 nm a gold =.407 nm

13. 13 Body-Centered Cubic (BCC) Unit Cell Reduced Sphere Representation Solid Sphere Representation

14. 14 Body-Centered Cubic (BCC) Lattice Structure The most familiar example of BCC is room temperature iron Also tungsten and chromium

15. 15 The coordination number is the number of other atoms touched by each atom in a lattice This atom touches … 1 4 3 8 (atom opposite 5) 7 (opposite 6) 6 5 2 Plus 4 more atoms in the next unit cell over The coordination number for FCC atoms is 12

16. 16 Atoms per unit cell in FCC 6 x ½ = 3 8 x 1/8 = 1 Total = 4

17. 17 Atomic Packing Factor (APF) measures the fraction of the unit cell volume actually occupied by atoms Notice all the empty space Example for FCC APF = V atoms / V unit cell V atoms = 4 x 4/3 R 3 V unit cell = a 3 = 8 3/2 R 3 Do the arithmetic: APF = 0.74

18. 18 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). Also, how would you go about determining the APF (this is a homework problem).

19. 19 Density The concept of atomic packing factor allows us to relate atomic weight to macroscopically observed density The concept of atomic packing factor allows us to relate atomic weight to macroscopically observed density = nA V cell N A n = atoms/unit cell A = atomic weight V cell = volume of the unit cell N A = Avogadro’s number

20. 20 Hexagonal Close-packed (HCP) Unit Cell Reduced Sphere Representation HCP lattice structure