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