Previously in Chem 104: types of solids Unit Cell 3 types of cubic cells contents of unit cell Lecture 1 posted! TODAY Z quantify relationship between cell and density ionic solid unit cells solid stability thermodynamics and lattice energy “why doesn’t that solid exist” QUIZ later today

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

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

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

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 = l 3, l is cell length Cell mass, m = Z x at.wt. A

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 = l = 2r

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 = l = 2r a = l = 2 √ 2 r Diagonal 4r = √ 2 a = √ 2 l Solve for edge: 4r / √ 2 = a = l

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 = l = 2r a = l = 2 √ 2 r a = 2.8 r Diagonal 4r 4r = √ 3 a = √ 3 l a = l = 4r / √ 3 a = 2.3 r

Rh metal crystallizes in a cubic lattice where a = 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 = g/mol Density = kg m-3 Atomic radius = 173 pm

Packing a Square Lattice: Makes a simple cubic cell

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

Closest Packing: hexagonal layers build up 3D solid

Find the triangular gaps in the Pink layer

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

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

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

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

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

ABABA.... Packed towards you Packing direction

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

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

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+

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 make NaCl: start with fcc unit cell of Cl- ions

Add Na+ in between

Add Na+ in between, everywhere

Z = C. N. (Na) =

halite = face centered cubic = NaCl