1. 2D Packing Examples hole Answer the following questions for both packing diagrams. 1.Find the smallest unit that, if repeated, would give you the entire structure. This is the unit cell. Draw a box on the diagram representing the unit cell. 2.How many total atoms are inside the unit cell? Remember that only fractions of some atoms lie inside the box you drew. 3.Accurately draw boxes exactly 3 atoms wide. How many total atoms are in each? Which displays the greater packing density ?

2. A TOP VIEW AA SIMPLE CUBIC PACKING A SCP 1SCP 1 | Flash Anim | Jmol 1Flash AnimJmol 1 unit cell: simple cubic

3. BODY CENTERED CUBIC PACKING - ABAB BCP 1BCP 1 | Flash Anim | Jmol 1Flash AnimJmol 1 Unit cell: body centered cubic A B Do not touch

4. A B HEXAGONAL CLOSEST PACKING - ABAB 120 0 Unit cell: hexagonal

5. A B C CUBIC CLOSEST PACKING

6. A B C A 6 6 A A B C CCP (FCC) 1CCP (FCC) 1 | Flash Anim | Jmol 1Flash AnimJmol 1 Unit cell: face centered cubic 3 3 6 6 4 4 1 1 7 7 2 2 5 5 8 8 1 2 3 4 5 7 8 FCC = CCP: Jmol

7. Counting atoms in a unit cell 1. What fraction of the white colored sphere is part of a unit cell in each of the lattices shown below. A corner atom? ________ A face atom? ________ An edge atom? ________ 2. From your answers above, how many spheres below to the unit cell shown. Simple Cubic ________ Body centered cubic ________ Face centered cubic ________

8. Now to some real structures. How do we know the arrangement of ions and atoms? X-Ray Crystallography: Na – bcc – what’s up with it’s 3s 1 electron Na – bcc NaCl NaCl Bragg’s Law and diffraction Xray diffraction (Laue transmission) from simple cubic, bcc and fcc lattices

9. NaCl Space fill 3 atoms e clouds in plane 109.5 0 TetrahedronTetrahedron – 4 identical equilateral triangles SF 6 5 atoms/ e clouds in plane OctahedronOctahedron – 8 identical triangles How do you describe salts with more than one atom type? By unit cells and holes Types of Holes What's a tetrahedrontetrahedron What's an octahedronoctahedron Holes: Cubic, tetrahedral, and Octahedral CCP and holes

10. Determining the empirical formula from unit cell data: A salt must be electrically neutral. If you know the charge on the cations and anions, you can determine M x N y. Alternatively, you can use crystal data to determine the structure of the unit cell and hence the empirical formula. Determine the number of each different ion in the following unit cells. Does it correspond to the formula from charge balance? 1.Copper (I) chlorideCopper (I) chloride 2. Barium Chloride 3. Rhenium oxide 4. Based on Cl - alone, what type of unit cell is this? What type of “hole” is occupied by Cu + ? Cu Cl 5. Based on just Cl - alone, what type of unit cell is NaCl? What type of “hole” is occupied by Na + ?NaCl

11. Top Side views 2r r Given Polonium Data density 9.23 g/cm 3 macroscopic meas. molar mass: 208.98 g Avogadro’s #: 6.022 x 10 23 atoms/mol Use 2 simple equations Solve for the following: V atom /V eff = V eff (from density data) and dimensional analysis V eff = V atom = r Po = Calculation of the atomic radius of a polonium atom, which forms a simple cubic cell, from macroscopic parameters. How many P atoms are in the unit cell? 2r

12. x 2 = a 2 + a 2 x = √2 a a 4r √2 a Body-Centered Cubic Unit Cell unit cell a a

13. Corner sphere Do how many unit cells does the yellow sphere belong? Face sphere Do how many unit cells does the yellow sphere belong? Edge sphere Do how many unit cells does the yellow sphere belong?

14. A B C CUBIC CLOSEST PACKING ABC

15. A B C A