Download Types of Solids

Chapter 12
Solids and
Modern Materials
1
Types of Solids
• Four general types of
solids.
• Metallic solids share
a network of highly
delocalized electrons.
• Ionic solids are sets
of cations and anions
mutually attracted to
one another.
Modern
Materials
2
Bonding in Solids
• Covalent-network
solids are joined by an
extensive network of
covalent bonds.
• Molecular solids are
discrete molecules that
are linked to one
another only by van
der Waals forces.
Modern
Materials
3
Other Solids
• Polymers: long chains of atoms held
together by covalent bonds.
– The chains are often held to one another by
weaker intermolecular forces.
• Nanomaterials: solids whose crystals
have dimensions on the order of 1100nm.
Modern
Materials
4
Crystalline vs. Amorphous solids
• In crystalline solids
atoms are arranged in
a very regular pattern.
• Amorphous solids are
characterized by a
distinct lack of order in
the arrangement of
atoms.
Modern
Materials
5
Crystal Lattices
One can deduce the
pattern in a
crystalline solid by
thinking of the
substance as a
lattice of repeating
shapes formed by
the atoms in the
crystal.
Modern
Materials
6
Crystal Lattices (2 dimensions)
The individual
shapes of the lattice,
then, form "tiles," or
unit cells, that must
fill the entire space
of the substance.
– lattice point
– lattice vectors
Modern
Materials
7
Crystal Lattices(3-dimensions)
• There are seven
basic threedimensional lattices:
–
–
–
–
–
–
–
Cubic
Tetragonal
Orthorhombic
Rhombohedral
Hexagonal
Monoclinic
Triclinic
Modern
Materials
8
Three Types
of Cubic Lattice
Primitive lattice vs. Centered lattice
Within each major lattice type,
additional types are generated by
placing lattice points in the center
of the unit cell or on the faces of
the unit cell.
Modern
Materials
9
Filling the Unit Cell
Once one places atoms within a unit cell, the
structure of the compound can be seen by bonding
the atoms to one another across unit cells.
Modern
Materials
10
Metallic Solids
Metallic solids or metals consist solely of metal
atoms.
• Metallic bonding results from delocalization of
valence electrons throughout the solid.
– The metal nuclei are seen to exist in a “sea” of
delocalized valence electrons.
• Important physical properties of pure metals:
– malleable: can be hammered into thin sheets
– ductile: can be pulled into wires
– good electrical and thermal conductivity
Modern
Materials
11
Metallic Structure
The structures of many metals conform to
one of the cubic unit cells.
12
Modern
Materials
Cubic Structures
One can determine how many atoms
are within each unit cell which lattice
points the atoms occupy.
Modern
Materials
13
r
s
2r = s
14
4r = s √2
s=(r√8)=(r2√2)
4r = s(3)1/2
S=  4r 


 3
Modern
Materials
Volume of Unit Cells
Primitive:
Volume =  2r  = 8r 3
3
3
Bcc:
 4r 
Volume = 

3


Fcc:
 
Volume = r 8
3
Modern
Materials
15
Close
Packing
•Hexagonal close packing (hcp): The third
layer atoms are in the depressions that lie
directly over the first layer.
•Cubic close packing (ccp): The third layer
atoms do not sit directly above the spheres in
either of the first two layers.
•In both hcp and ccp each sphere has 12
equidistant nearest neighbors:
•6 in the same layer,
•3 from the layer above, and
•3 from the layer below.
•Each sphere has a coordination
number of 12.
•CN: the number of atoms
immediately surrounding a given
atom in the crystal structure. Modern
Materials
16
c.c.p
vs
Cubic close-packing
a-b-c
a
c
a cb
b
c
a
c
b
a
cc
b
b
a
cc
b
b
a
c
a
a
bb c bb c b
c
c
a
a
a
b
b
b c b
b
cc
c
c
a
a
b
b
b
c
c
ccp
h.c.p
Hexagonal close-packing
a-b-a
a
a
b
a
b
a
b
a
b
a
b
a
b
a
b
a
b
a
b
a
b
aa
b
aa
b
b
hcp
Modern
Materials
17
Close Packing
The atoms in a
crystal pack as
close together as
they can based on
the respective sizes
of the atoms.
Modern
Materials
18
Sample Exercise 12.1 Calculating Packing Efficiency
It is not possible to pack spheres together without leaving some void spaces between the spheres. Packing efficiency
is the fraction of space in a crystal that is actually occupied by atoms. Determine the packing efficiency of a facecentered cubic (fcc) metal.
Solution
Volume of atoms =
Practice Exercise
Determine the packing efficiency by calculating the fraction of space occupied by atoms in a
body-centered cubic metal.
Modern
Materials
Answer: 0.68 or 68%
19
Alloys
• combinations of two or more elements, the
majority of which are metals.
• Addition of a second (or third) element
 change in the properties of the mixture
Modern
Materials
20
Alloys
• substitutional alloys: a metal atom replaced by
a second element
• interstitial alloys: a second element(nonmetals)
fills a space in the lattice of metal atoms.
Modern
Materials
21
• a second element in Substitutional alloys….
–
–
similar atomic radii.
similar bonding characteristics.
• a second element in Interstitial alloys….
– (nonmetal) significantly smaller radius
– much harder, stronger and less ductile than the pure metal
(increased bonding between nonmetal and metal).
– An example is steel (contains up to 3% carbon).
• mild steels (<0.2% carbon; useful for chains, nails, etc)
• medium steels (0.2-0.6% carbon; useful for girders, rails, etc.)
• high-carbon steels (0.6-1.5% carbon; used in cutlery, tools, springs)
– Other elements may also be added to make alloy steels.
• Addition of V and Cr increases the strength of the steel and improves
its resistance to stress and corrosion.
– The most important iron alloy is stainless steel. It contains C, Cr
(from ferrochrome, FeCr2), and Ni.
Modern
Materials
22
• Heterogeneous alloys: The components are not
dispersed uniformly (e.g., pearlite steel has two
phases: almost pure Fe and cementite, Fe3C).
• Intermetallic compounds: homogeneous alloys
with definite properties and compositions.
– Examples include:
• Ni3Al (a major component of jet aircraft engines).
• Cr3Pt (used to coat razor blades (to increase hardness and ability to
maintain a sharp edge),
• Co5Sm (used in permanent magnets in lightweight headsets).
• LaN5 (used as the anode in nickel-metal hydride batteries).
Modern
Materials
23
Metallic Bonding
• In elemental samples of nonmetals and metalloids,
atoms generally bond to each other covalently.
• Metals, however, have a lack of valence electrons;
instead, they form large groups of atoms that share
electrons among them.
Modern
Materials
24
Electron-Sea Model
• Metal: as a group of cations
suspended in a sea of
electrons.
• The electrical and thermal
conductivity, ductility, and
malleability of metals is
explained by this model.
Modern
Materials
25
Problems with the electronsea model
• As the number of
electrons increases, the
strength of bonding
should increase, and the
melting point should
increase.
• However, group 6B
metals (at the center of
the transition metals) have
the highest melting points
in their respective periods.
• cf) bp, strength, ∆Hfusion…
26
W
Mo
Cr
Modern
Materials
A Molecular-Orbital Approach
-band structureAs the number of
atoms in a chain
increases, the energy
gap between
molecular orbitals
(MOs) essentially
disappears, and
continuous bands of
energy states result.
– Bands
Modern
Materials
27
Band Structure of Nickel
Modern
Materials
28
Ionic Solids
• In ionic solids, the
lattice comprises
alternately charged
ions.
• Ionic solids have
very high melting
and boiling points
are quintessential
crystals.
Modern
Materials
29
Modern
Materials
30
Structures of Ionic Solids
The different-sized ions in an ionic
compound minimize the distance between
oppositely charged ions while keeping likecharged ions away from each other.
Modern
Materials
31
Modern
Materials
32
Modern
Materials
33
Molecular Solids
• The physical properties of molecular solids are
governed by van der Waals forces.
– soft.
– gases or liquids at RT
• Molecular solids show poor thermal and electrical
conductivity.
– sucrose.
Modern
Materials
34
Covalent-Network Solids
Covalent-network solids consist of atoms held
together, in large networks or chains, with
covalent bonds.
• much higher melting points and much harder
than molecular solids.
– Due to the strong covalent bonds that connect the
atoms.
• Ex) diamond, graphite, quartz (SiO2), and
silicon carbide (SiC).
Modern
Materials
35
Covalent-Network and
Molecular Solids
• Diamonds are an
example of a
covalent-network
solid, in which
atoms are covalently
bonded to each
other.
– They tend to be hard
and have high
melting points.
Modern
Materials
36
Covalent-Network and
Molecular Solids
• Graphite is an
example of a
molecular solid, in
which atoms are
held together with
van der Waals
forces.
– They tend to be
softer and have
lower melting points.
Modern
Materials
37
Semiconductors
• Elemental semiconductors (made of only one type of
atom)
– Elemental semiconductors include silicon, germanium, and gray tin.
– These elements adopt the crystal structure of diamond.
– In this structure, four atoms in a tetrahedral coordination geometry
surround each atom.
– There are 4 valence electrons per atom thus, each hybrid orbital contains a
single electron.
– The result is that semiconductors are conductive but less so than metals due to the
presence of the band gap.
• Compound semiconductors (made up of two or more
elements)
– Compound semiconductors include GaAs, InP, and CdTe.
– These also maintain the average valence electron count as elemental
semiconductors (4 per atom)
Modern
Materials
38
Semiconductors
a gap between the occupied MOs (valence band) and the
unoccupied ones (conduction band)
: 0.08 to 3.05 eV (7 to 300 kJ/mol)
Modern
Materials
39
Semiconductors
Eg: C  Si  Ge  Sn (decrease)///Pb(a metal)
Due to the decrease in overlap
40
Modern
Materials
Doping
By introducing very
small amounts of
impurities that have
more (n-type) or fewer
(p-type) valence
electrons, one can
increase the
conductivity of a
semiconductor.
Modern
Materials
41
Sample Exercise 12.3 Qualitative Comparison of Semiconductor
Band Gaps
Will GaP have a larger or smaller band gap than ZnS? Will it have a larger or smaller band gap than GaN?
Solution
Eg(ZnS)>Eg(GaP) : The electronegativity difference to be larger for ZnS, which should result in ZnS having a larger
band gap than GaP.
Eg(GaN)>Eg(GaP) : P and N. Nitrogen is located above phosphorus in group 5A. Based on increased orbital
overlap,we would expect to GaN have a larger band gap than GaP.
Check External references show that the band gap of GaP is 2.26 eV, ZnS is 3.6 eV, and GaN is 3.4 eV.
Practice Exercise
Will ZnSe have a larger or smaller band gap than ZnS?
Answer: Because zinc is common to both compounds and selenium is below sulfur in the periodic table, the band gap of
ZnSe will be smaller than ZnS.
Modern
Materials
42
Sample Exercise 12.4 Identifying Types of Semiconductors
Which of the following elements, if doped into silicon, would yield an n-type semiconductor: Ga, As, or C?
Solution
As, if doped into silicon, would yield an n-type semiconductor.
Practice Exercise
Suggest an element that could be used to dope silicon to yield a p-type material.
Answer: Because Si is in group 4A, we need to pick an element in group 3A. Boron and aluminum are both
good choices—both are in group 3A. In the semiconductor industry boron and aluminum are commonly used
dopants for silicon.
Modern
Materials
43
Modern
Materials
44
Polymers
Polymers are molecules of high molecular
mass made by sequentially bonding
repeating units called monomers.
Modern
Materials
45
Plastics
Plastics are materials that can be formed into
various shapes, usually with heat and pressure.
• Thermoplastic materials can be reshaped.
– Recycling of polypropylene
• Thermosetting plastic materials are shaped by
an irreversible process.
– not readily reshaped.
• Elastomers are materials that exhibit elastic or
rubbery behavior.
– If a moderate amount of a deforming force is added,
Modern
the elastomer will return to its original shape.
Materials
46
Some Common Polymers
Modern
Materials
47
Addition Polymers
Addition polymers are made by coupling the
monomers by converting  bonds within each
monomer to  bonds between monomers.
Modern
Materials
48
Condensation Polymers
• Condensation polymers are made by
joining two subunits through a reaction in
which a smaller molecule (often water) is also
formed as a by-product.
• These are also called copolymers.
Modern
Materials
49
Synthesis of Nylon
Nylon is one example of a condensation
polymer.
Modern
Materials
50
Properties of Polymers
- Mw distribution
- Interactions between
chains of a polymer
lend elements of
order to the
structure of
polymers.
Modern
Materials
51
Properties of Polymers
Stretching the polymer chains as they form
can increase the amount of order, leading to
a degree of crystallinity of the polymer.
LDPE vs. HDPE
Modern
Materials
52
Plasticizers
• We can modify the polymeric properties
by the addition of substances with lower
molecular mass.
• Plasticizers are molecules that
interfere with interactions between
polymer chains.
– These make polymers more pliable.
Modern
Materials
53
Cross-Linking
Chemically bonding chains of
polymers to each other can
stiffen and strengthen the
substance.
Naturally occurring rubber is too soft and pliable
for many applications.
Modern
Materials
54
Cross-Linking
55
In vulcanization, chains are cross-linked by
short chains of sulfur atoms, making the
Modern
rubber stronger and less susceptible to
Materials
degradation.
12.9 Nanomaterials
• 1 – 100 nm
• Semiconductors on the Nanoscale
– Semiconductor particles with diameters in the
1 to 10 nm range are called quantum dots
– Semiconductor band gaps change
substantially with size in the 1-10 nm range
– By tuning the band gap, all colors of the
rainbow can be obtained from one material.
Modern
Materials
56
Nanoparticles
Different size particles
of a semiconductor
(like Cd3P2) can emit
different wavelengths
of light, depending on
the size of the energy
gap between bands.
….. Quantum well,
quantum wire
57
photoluminiscence
Modern
Materials
Metals on the Nanoscale
Finely divided metals
can have quite different
properties than larger
samples of metals.
mean free path of an
electron in a metal at room
temperature is on the 1-100
nm scale.
Modern
Materials
58
Fullerenes
• In 1985 molecules composed of 60 carbon
atoms, C60 molecules, were first described.
• C60 molecules are among a class of
molecules of carbon atoms known as
fullerenes.
• Buckyball or buckminsterfullerene may be
prepared by electrically evaporating graphite
in a helium atmosphere.
• Because fullerenes are composed of
individual molecules, they dissolve in various
organic solvents while diamond and graphite
do not.
Modern
Materials
59
Carbon Nanotubes
Carbon nanotubes
can be made with
metallic or
semiconducting
properties without
doping.
Modern
Materials
60
Graphene
• In 2004 sheets of carbon
atoms with a honeycomb
structure were isolated
and identified.
• Graphene has interesting
properties:
– It is very strong and has a high
thermal conductivity.
– Its electronic structure is like
that of a semiconductor with an
energy gap of zero.
– It can sustain very high
electrical current densities.
Modern
Materials
61
Problems
• 10, 26, 32, 46, 58, 64, 81, 101
Modern
Materials
62