Transcript Lectures 11-13 - U of L Class Index

The Modern Periodic Table
name
& atomic
mass
numberweight
symbol
atomic number
Carbon
12.011
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C
Law of Periodicity
Group
Similar
chemical
properties
“The properties of the elements are
periodic functions of atomic number.”
Period
Repetition of properties
Nonmetals – insulators
not ductile
Metalloids - Semiconductors
Ductile ?
Metals – Conducting, Ductile
Crystalline Solids
Crystalline solids: Metals, ions, atoms, molecules
Constructed form crystal lattices.
Stabilized by electrostatic forces.
Identical building blocks : unit cells.
LATTICE:
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X-ray Diffraction
X-ray diffraction is used to study crystalline solids
The lattice of regularly repeating atoms with spacing acts as a diffraction grating for
the rays.
The diffraction pattern is used to establish the structure of the solid!
Amorphous Solids
Amorphous solids: disordered solids
Strongly resemble liquids in this lack of long-range order
Many amorphous solids can be thought of very accurately as frozen liquids.
Common examples of amorphous solid are glass, candy (sugar), plastics.
In all, there are then 5 categories of solids, 4 types of crystalline + amorphous
Summary of the Structures and Properties of Various
Types of Solid Substances
Type
Examples
Structural Units
Typical Properties
Ionic
NaCl, K2SO4,
CaCl2,
(NH4)3PO4
Positive and
negative ions
Hard; brittle; high melting point;
electric conductivity poor as solid &
good as liquid; often water-soluble
Metallic
Iron, silver,
copper, other
metals & alloys
Metal cations in a
sea of electrons
Malleable; ductile; wide range of
hardness and melting points; good
electric conductivity in solid & liquid;
good heat conductivity.
Molecular
H2, O2, I2, H2O,
CO2, CH4,
CH3OH,
CH3CO2H
Molecules
Soft; low to moderate melting points &
boiling
points;
poor
electric
conductivity in solid and liquid
Network
Graphite,
diamond, quartz,
feldspars, mica
Atoms
Wide range of hardnesses & melting
points (3-dimensional bonding > 2dimensional bonding > 1-dimensional
bonding); poor electric conductivity,
with some exceptions
Amorphous
(glassy)
Glass,
polyethylene,
nylon
Molecules, ions
No long range order
Soft, wide temperature range for
melting; poor electric conductivity, with
some exceptions
Semicrystalline Materials
Contain both amorphous and crystalline regions => strong and flexible.
Examples: Plastics (polymers), Steel, Wood (cellulose), collagen (tendon)
Example: Polyvinylidenedifluoride
…-CH2-CF2-CH2-CF2-…..
It has several different
crystal phases, which
can be modified by
processing methods.
The alpha phase
is non-polar
The beta phase is polar
PVDF can be
processed to contain
mostly the polar form,
by stretching the film to
several time its original
length
PVDF is semicrystalline - Similar to Teflon (-CF2-CF2-)
Electrical Properties of Semicrystalline Materials
Semicrystalline materials respond to heat, pressure and external fields.
They are used as heat and pressure sensors
Thin films can be prepared than have a permanent electric filed across them.
These are used as non-stick coatings, selective membranes, etc
Electropoled films are used by theelectronics industry, ex. speaker membranes
Lattices and Closest Packing
How do objects naturally arrange themselves?
OR
Non-closest
Closest
If a second layer is added how does that effect the arrangements?
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Lattices and Unit Cells
Mathematicians have shown that there are seven basic geometries in which unit cells
can be assembled that completely fill 3-D space.
These are called the seven crystal systems
We will focus only on the cubic and the hexagonal crystal systems
as they describe the vast majority of metallic elements.
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Unit Cells
LATTICE:
Identical building blocks : unit cells.
i) No “gaps” between them in the lattice.
ii) All have same orientation in the lattice.
iii) Cannot be arranged in a staggered fashion in the lattice.
NOT:
OR:
OR:
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Lattices and Unit Cells
Consider the smallest possible “unit cell” :
The smallest unit cell in a lattice is called the primitive unit cell.
In general one would have to consider three-dimensions.
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Closest Packing
The marbles adopted a “closest packing” as in most metals.
Two kinds:
cubic closest packed
hexagonal closest packed.
The difference arises when a third row is added:
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Hexagon Closest Packing
Orient the lattice so that the layers are more easily seen:
A
B
A
Note every second layer are superimposable, as shown in the
case of the red layers.
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Cubic Closest Packing
A
B
C
A
Every third layer is superimposible.
Note that, there is an atom at each corner of the cube
And, the center of each face.
It is also called face centered cubic (fcc).
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Cubic Lattices
There are three types of cubic unit cells:
Note in some cases only parts of an atoms is contained by the unit cell.
i.e. The unit cell only contains the fraction of each atom that is *inside* the
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cube!
Lattices and Unit Cells
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Co-ordination Number, Density and
Metallic Radii
The number of atoms an atom contacts in the lattice is referred to as
its co-ordination number.
Determine the coordination number of the following lattices:
Simple cubic (e.g. Po)
Face-centered cubic (e.g. Cu)
Body-centered cubic (e.g. Na)
Hexagonal closest packed (e.g. Mg)
Lattice type is related to density.
What is the relative order of density from most to least dense?
How would you measure the density of a metal?
How could you relate the lattice type and density to the atomic radius?
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EXERCISE
1. Aluminum has a density of 2.699 g· cm–3, and the atoms are packed into a
face-centered cubic unit cell. Use this information to find the radius of an
aluminum atom.
Count: there are 4 Al atoms per unit cell by counting rules
m
4  26.98 g mol
23
3
V 

6.6398

10
cm
23
d 2.699 g cm3  6.022 10 1mol
For any cube, a  3 V  3 6.6398 1023 cm3  4.049 108 cm  4.049 1010 m
By geometry, face diagonal d  4r  2a r 
2
 4.049 1010 m  143 pm
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Along the face diagonal, there are
two half and one whole sphere
The diagonal length is (a2 + a2)1/2
and corresponds to 4 atomic radii
(a  a) 2  a 2  a 2  2a 2  a 2
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EXERCISE
2) Lithium has a metallic radius of 152 pm and the atoms are packed into
a body-centered cubic unit cell. Calculate the density of lithium.
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Cubic Lattices
Lattice
simple cubic
body-centered cubic
face-centered cubic
Packing fraction
0.5236
0.6802
0.7405
Density (m/r3)
0.125
0.162
0.177
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Lattices, Density and Metallic Radii
Europium has a metallic radius of 198.4 pm and a density of 5.243 g/cm3.
Which cubic units cell is the likely for this crystal structure?
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