Previously in Chem 104: types of solids Unit Cell 3 types of cubic cells
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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
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Three Types of Cubic Unit Cells
a
cb
Simple Cubic Body Centered Cubic
Face CenteredCubic
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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
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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
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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
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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
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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
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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
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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
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Packing a Square Lattice:
Makes a simple cubic cell
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Can you pack spheres more densely?
The Rhomb is the Unit Cell Shapeof Hexagonal Lattices
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Closest Packing: hexagonal layers build up 3D solid
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Find the triangular gaps in the Pink layer
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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
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This packing sequence is A B C A B C,Where B and C cover different “holes” in A
BC
A
BC
A
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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
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Pack
ing
dire
ctio
n A C B A C B A
ccp CubicClosestPacking:A B C A B C …
Packing direction
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CCP viewed unit cell;
LOOK! It’s face centered cubic!!! CCP = FCC!!
….mmmMMM
CCP viewed as packing layers
AB
C
CBA
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ABABA . . . . Packed towards you
Packing direction
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Pac
king
dire
ctio
n A B A B A B A
hcp Hexagonal Closest Packing:A B A B …….mmmMMM
Packing direction
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From Metals to Ionic Solids
Will ionic solids pack exactly like metallic solids?
Na bcc unit cellas metal NaCl unit cell?
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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+
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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) =
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How to make NaCl: start with fcc unit cell of Cl- ions
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Add Na+ in between
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Add Na+ in between, everywhere
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Z =C. N. (Na) =
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halite = face centered cubic = NaCl
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