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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” - PowerPoint PPT Presentation
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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
cb
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
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 = 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 depends on which structure:
a = 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 = l = 2r a = l = 2√2 r
Diagonal4r = √2 a = √2 l
Solve for edge: 4r /√2 = a = 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 = l = 2r a = l = 2√2 ra = 2.8 r
Diagonal4r
4r = √3 a = √3 la = l = 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 fccThis 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
APa
ckin
g di
rect
ion A
C B A C B A
ccp CubicClosestPacking:A B C A B C …
Packing direction
Pack
ing
dire
ctio
n 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
CBA
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 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