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

Cubic Unit Cells havea = b = c

= 90 deg

a

cb

Three Types of Cubic Unit Cells

a

cb

Simple Cubic Body Centered Cubic

Face CenteredCubic

These Three Cubic Unit Cells are Structuresof most Metallic Elements(also hexagonal, hcp, to be seen later)

Cu, Ag, Au are all fccCr, Mo, W are all bccOnly Po is simple cubic (rare— why?)

Simple Cubic Body Centered Cubic

Face CenteredCubic

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

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 Cubic Body Centered Cubic Face Centered Cubic

Z = 1 atom/cell

Least Dense

Z = 4 atom/cell

Most Dense

Z = 2 atom/cell

How did we get Z???

To get Z, add ups the “bits” of atoms inside unit cell:

Simple Cubic Body Centered Cubic Face Centered Cubic

Simple Cubic Body Centered Cubic Face Centered Cubic

Z = 1 Z = 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 a3

Cell volume, V = a3 or l3, l is cell length

Cell mass, m = Z x at.wt. A

Simple Cubic Body Centered Cubic Face Centered Cubic

Z = 1 Z = 4Z = 2

Cell edge, a or cell length, lis related to the atomic radius but “how?” depends on which structure:

a or l = 2r

Simple Cubic Body Centered Cubic Face Centered Cubic

Z = 1 Z = 4Z = 2

Cell edge, a or cell length, lis related to the atomic radius but depends on which structure:

a or l = 2r a or l = 2√2 r

Diagonal4r = √2 a or √2 l

Solve for edge: 4r /√2 = a or l

Simple Cubic Body Centered Cubic Face Centered Cubic

Z = 1 Z = 4Z = 2

Cell edge, a or cell length, lis related to the atomic radius but depends on which structure:

a or l = 2r a = 2√2 ra = 2.8 r

Diagonal4r

4r = √3 aa = 4r /√3a = 2.3 r

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 a3

Find Z: defines if simple, bcc or fcc

This is a summary of the relationships

What do we need? ZWhat do we have? Nothing here, but can’t we look upDensity of Rh metal ?

Web Elements: at. weight = 102.91 g/molDensity = 12450 kg m-3Atomic radius = 173 pm

Packing a Square Lattice:

Makes a simple cubic cell

Can you pack spheres more densely?

The Rhomb is the Unit Cell Shapeof 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 layercovers the “up”triangles of thePink layer

The Yellow layercovers the “down”triangles of thePink layer

This packing sequence is A B C A B C,

Where B and C cover different “holes” in A

BC

A

BC

A

BC

A

BC

AP

acki

ng d

irec

tion

A C B A C B A

ccp CubicClosestPacking:A B C A B C …

Packing direction

Pac

king

dir

ecti

on

A C B A C B A

ccp CubicClosestPacking: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

AB

C

C

BA

ABABA . . . . Packed towards you

Packing direction

Pac

king

dire

ctio

n A B A B A B A

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 cellas 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-

2 x r-

r- + r+

The Simplest Ionic Solid is CsCl, simple cubic

Start withsimple cubicUnit cell of Cl- ions

Then add one Cs+ in center

Z =C. N. (Cs) =

How to draw this

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) =