1. Previously in Chem 104: types of solids Unit Cell TODAY 3 types of cubic cells contents of unit cell, Z quantify relationship between cell and density ionic solid unit cells solid stability

2. Cubic Unit Cells have a = b = c  = 90 deg a c b

3. Three Types of Cubic Unit Cells a c b Simple Cubic Body Centered Cubic Face Centered Cubic

4. These Three Cubic Unit Cells are Structures of most Metallic Elements (also hexagonal, hcp, to be seen later) Cu, Ag, Au are all fcc Cr, Mo, W are all bcc Only Po is simple cubic ( rare— why? ) Simple Cubic Body Centered Cubic Face Centered Cubic

5. What is one result of a metal’s “choice” to adopt a cubic, bcc or fcc lattice? Simple CubicBody Centered CubicFace Centered Cubic

6. What is one result of a metal’s “choice” to adopt a cubic, bcc or fcc lattice? Simple CubicBody Centered CubicFace Centered Cubic Z = 1 atom/cell Least Dense Z = 4 atom/cell Most Dense Z = 2 atom/cell How did we get Z???

7. To get Z, add ups the “bits” of atoms inside unit cell: Simple CubicBody Centered CubicFace Centered Cubic

8. Simple CubicBody Centered CubicFace Centered Cubic Z = 1Z = 4Z = 2 Knowing the unit cell structures can be used with other physical data and relationships: Cell Density = solid density = mass = Z x at.wt. volume A x a 3 Cell volume, V = a 3 or l 3, l is cell length Cell mass, m = Z x at.wt. A

9. Simple CubicBody Centered CubicFace Centered Cubic Z = 1Z = 4Z = 2 Cell edge, a or cell length, l is related to the atomic radius but “how?” depends on which structure: a or l = 2r

10. Simple CubicBody Centered CubicFace Centered Cubic Z = 1Z = 4Z = 2 Cell edge, a or cell length, l is related to the atomic radius but depends on which structure: a or l = 2r a or l = 2 √ 2 r Diagonal 4r = √ 2 a or √ 2 l Solve for edge: 4r / √ 2 = a or l

11. Simple CubicBody Centered CubicFace Centered Cubic Z = 1Z = 4Z = 2 Cell edge, a or cell length, l is related to the atomic radius but depends on which structure: a or l = 2r a = 2 √ 2 r a = 2.8 r Diagonal 4r 4r = √ 3 a a = 4r / √ 3 a = 2.3 r

12. Rh metal crystallizes in a cubic lattice where a = 380.34 pm. What is the crystal structure of Rh? Density = Z x at.wt. A x a 3 Find Z: defines if simple, bcc or fcc This is a summary of the relationships What do we need? Z What do we have? Nothing here, but can’t we look up Density of Rh metal ? Web Elements: at. weight = 102.91 g/mol Density = 12450 kg m-3 Atomic radius = 173 pm

14. Packing a Square Lattice: Makes a simple cubic cell

15. Can you pack spheres more densely? The Rhomb is the Unit Cell Shape of Hexagonal Lattices

16. Closest Packing: hexagonal layers build up 3D solid

17. Find the triangular gaps in the Pink layer

18. Note how layers “sit” on top of each other: The Cyan layer covers the “up” triangles of the Pink layer The Yellow layer covers the “down” triangles of the Pink layer

19. This packing sequence is A B C A B C, Where B and C cover different “holes” in A B C A B C A

20. B C A B C A Packing direction ACBACBAACBACBA ccp Cubic Closest Packing: A B C A B C … Packing direction

21. ACBACBAACBACBA ccp Cubic Closest Packing: A B C A B C … Packing direction

22. CCP viewed unit cell; LOOK! It’s face centered cubic!!! CCP = FCC!! ….mmmMMM CCP viewed as packing layers A B C C B A

23. ABABA.... Packed towards you Packing direction

24. ABABABAABABABA hcp Hexagonal Closest Packing: A B A B … ….mmmMMM Packing direction

25. From Metals to Ionic Solids Will ionic solids pack exactly like metallic solids? Na bcc unit cell as metal NaCl unit cell?

26. From Metals to Ionic Solids Build up Ionic Solids conceptually like this: assume Anions are larger than Cations, r- > r+ pack the Anions into a cubic lattice: ccp, simple or bcc add Cations to the interstitial spaces (“Mind the gap!”) 2 x r- r- + r+

27. The Simplest Ionic Solid is CsCl, simple cubic Start with simple cubic Unit cell of Cl- ions Then add one Cs+ in center Z = C. N. (Cs) = How to draw this

28. How to make NaCl: start with fcc unit cell of Cl- ions

29. Add Na+ in between

30. Add Na+ in between, everywhere

31. Z = C. N. (Na) =