Chapter 12 Homework The Unit Cell The Smallest Unit With

Chapter 12. Solids and Modern Materials

Media Resources

Figures and Tables in Transparency Pack: Section:

Figure 12.11 The Structures of (a) Primitive Cubic, 12.3 Metallic Solids

(b) Body-centered Cubic, and (c) Face-centered

Cubic Metals

Figure 12.12 A Space-filling View of Unit Cells for 12.3 Metallic Solids

Metals with a Cubic Structure

Activities: Section:

Close Packing 12.3 Metallic Solids

Metallic Bonding 12.4 Metallic Bonding

Band Structure 12.7 Covalent-Network Solids

Movies: Section:

Close Packing 12.3 Metallic Solids

Synthesis of Nylon 6,10 12.8 Polymeric Solids

3-D Models: Section:

Water 12.1 Classifications of Solids

Silicon Carbide 12.1 Classifications of Solids

Primitive Cubic 12.2 Structures of Solids

Simple Cubic 12.2 Structures of Solids

Body-Centered Cubic 12.2 Structures of Solids

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Phosphorus 12.7 Covalent-Network Solids

Polyethylene 12.8 Polymeric Solids

Buckminsterfullerene 12.9 Nanomaterials

Other Resources

Further Readings: Section:

Pictorial Analogies II: Types of Solids 12.1 Classifications of Solids

The Importance of Understanding Structure 12.2 Structures of Solids

Intelligent Materials 12.3 Metallic Solids

Nickel-Titanium Memory Metal: A “Smart” 12.3 Metallic Solids

Material Exhibiting a Solid-State Phase Change

and Superelasticity

Conducting Midshipmen–A Classroom Activity 12.4 Metallic Bonding

Modeling Extended Bonding in Solids

An Ionic Model for Metallic Bonding 12.4 Metallic Bonding

A Model to Illustrate the Brittleness of Ionic and 12.5 Ionic Solids

Metallic Crystals

The Origin of the Name ‘Nylon’ 12.8 Polymeric Solids

Dr. Baekeland’s Bakelite 12.8 Polymeric Solids

Thermosetting Resins 12.8 Polymeric Solids

Performance Polymers 12.8 Polymeric Solids

Elastomers I: Natural Rubber 12.8 Polymeric Solids

Rubber Reclamation 12.8 Polymeric Solids

Plastic Fantastic 12.8 Polymeric Solids

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Fishing for New Materials 12.9 Nanomaterials

Big Bucks from Small Science 12.9 Nanomaterials

The Smallest Revolution 12.9 Nanomaterials

Live Demonstrations: Section:

Kixium Monolayers: A Simple Alternative to the 12.2 Structures of Solids

Bubble Raft Model for Close-Packed Spheres

Paper-and-Glue Unit Cell Models 12.2 Structures of Solids

Close Packing of Identical Spheres 12.3 Metallic Solids

Memory Metal 12.3 Metallic Solids

Chapter 12

164

Chapter 12. Solids and Modern Materials

Common Student Misconceptions

• Students tend to have difficulty in “seeing” unit cells and crystal lattices; the use of models is often

helpful.

Teaching Tips

• It should be stressed that nanoscience is an interdisciplinary science and background knowledge in

physics, chemistry and biology is needed in order to understand how nanomaterials are designed,

made and applied.

Lecture Outline

12.1 Classifications of Solids

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• Solids are classified by the types of bonds that hold the atoms in place.

• Metallic solids: held together by a delocalized “sea” of shared valence electrons.

12.2 Structures of Solids

• Solids may be classified according to their level of order.

• Crystalline solids have atoms and ions arranged in an orderly repeating pattern.

• Examples: NaCl, quartz, diamond

• Amorphous solids lack the order of crystalline solids.

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Unit Cells and Crystal Lattices

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• Crystalline solids have an ordered, repeating structure.

• The smallest repeating unit in a crystal is a unit cell.

• The unit cell is the smallest unit with all the symmetry of the entire crystal.

• The three-dimensional stacking of unit cells is the crystal lattice.

• Each point in the lattice is a lattice point that represents an identical environment within the

• A square lattice: lattice vectors are equal in length and perpendicular to each other.

• A rectangular lattice: the lattice vectors are perpendicular but of different lengths.

• A hexagonal lattice: the lattice vectors are of the same length and the angle between them is 120˚.

• In three dimensions a lattice is defined by three lattice vectors: a, b, c.

• These define a parallelepiped: a 6-sided figure whose faces are all parallelograms.

• This figure is described by the length of the cell edges (a, b, c) and the angles between the edges

(  ).

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“Primitive Cubic” 3–D Model from Instructor’s Resource CD/DVD

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“Simple Cubic” 3–D Model from Instructor’s Resource CD/DVD

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“Body–Centered Cubic” 3–D Model from Instructor’s Resource CD/DVD

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“Face–Centered Cubic” 3–D Model from Instructor’s Resource CD/DVD

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“The Importance of Understanding Structure” from Further Readings

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• Example: A body-centered cubic lattice has one lattice point at each of the 8 corners plus

one at the center of the unit cell.

• Example: A face-centered cubic lattice has one lattice point at each of the 8 corners plus

one at the center of each of the 6 faces of the unit cell.

Filling the Unit Cell

• A crystal structure is defined by the lattice as well as the location of the atoms relative to the lattice

points.

• Simplest case: a crystal structure made of identical atoms with each atom exactly coincident with

FORWARD REFERENCES

• Quartz – a crystalline solid, and glass – an amorphous solid, will be discussed in Chapter 22

(section 22.10).

12.3 Metallic Solids

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• Metallic solids or metals consist solely of metal atoms.

• Metallic bonding results from delocalization of valence electrons throughout the solid.

The Structures of Metallic Solids

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• The crystal structures of many metals correspond to one of three cubic lattices:

• Primitive cubic (examples: polonium); 1 atom per unit cell.

• Body-centered cubic (examples: sodium and chromium); 2 atoms per unit cell.

• Face-centered cubic (examples: silver, gold, copper, aluminum, lead); 4 atoms per unit cell.

Close Packing

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• The sharing of valence electrons makes it favorable for the atoms in a metal to pack closely together.

• Layers of atoms are efficiently packed by surrounding each atom by six neighbors.

• A three dimensional structure is formed by stacking additional layers on top of the base layer.

“Close Packing” Movie from Instructor’s Resource CD/DVD

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• There are two choices for the arrangement of the atoms in the third layer.

• Hexagonal close packing (hcp): The third layer atoms are in the depressions that lie directly

over the first layer.

Alloys

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• Alloys contain more than one element and have the characteristic properties of metals.

• Pure metals and alloys have different physical properties.

• An alloy of gold and copper is used in jewelry (the alloy is harder than the relatively soft pure 24

karat gold).

• 14 karat gold is an alloy containing 58% gold.

• Alloys can be divided into 4 categories:

• Substitutional alloys (the solute atoms take the positions normally occupied by a solvent atom)

• The atoms must have similar atomic radii.

• The elements must have similar bonding characteristics.

• The most important iron alloy is stainless steel. It contains C, Cr (from ferrochrome,

FeCr2), and Ni.

• 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).

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FORWARD REFERENCES

• Coordination numbers in the context of coordination transition metal compounds will be

discussed in detail throughout Chapter 23.

12.4 Metallic Bonding

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Electron-Sea Model

• A simple model that accounts for many properties of metals is the electron-sea model.

• An array of metal cations exist in a “sea” of valence electrons.

Molecular-Orbital Model

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• Problems with the electron-sea 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.

• We turn to molecular-orbital theory for a more general model.

• As the number of orbitals increases, their energy spacing decreases.

• As the chain length goes to infinity the allowed energy states become a continuous band.

• The complex electronic structure of a bulk solid is call a band structure.

• Many of the properties of metals can be understood in terms of its band structure.

• The available electrons do not completely fill the band of orbitals.

• Therefore, electrons can be promoted to unoccupied energy bands.

• Because the energy differences between orbitals are small the promotion of electrons

requires little energy.

FORWARD REFERENCES

• Molecular orbitals will be discussed in the context of the crystal field theory in Chapter 23

(Section 23.6).

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“Metallic Bonding” Activity from Instructor’s Resource CD/DVD

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12.5 Ionic Solids

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• Ionic solids are held together by ionic bonds: electrostatic attraction between cations and anions.

• The high melting and boiling points reflect the strength of ionic bonds.

Structures of Ionic Solids

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• Ionic solids tend to have close-packed arrangements of ions.

• The arrangement is different from that of metallic solids due to the different radii and different

charges of the cations and anions.

• Three common ionic structure types are commonly found for ionic solids:

• Structure based on a primitive cubic lattice: anions sit on the lattice points at the corners of

the unit cell and one cation sits inside each cell.

• Example: CsCl

• Coordination number: 4

• Tetrahedral coordination environment.

• The relative number of cations and anions determines the most stable structure type.

FORWARD REFERENCES

• Chemistry of nonmetals forming anions in ionic solids will be discussed in Chapter 22.

12.6 Molecular Solids

• Molecular solids consist of atoms or molecules held together by intermolecular forces.

• Weak intermolecular forces give rise to low melting points.

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“A Model to Illustrate Brittleness of Ionic and Metallic Crystals” from Further Readings

Chapter 12

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• Intermolecular forces include dipole-dipole, dispersion forces and H-bonds.

• Molecular solids are usually soft.

• They are often gases or liquids are room temperature.

• Efficient packing of molecules is important (because they are not regular spheres).

• Molecular solids show poor thermal and electrical conductivity.

• Examples: Ar(s), CH4(s), CO2(s), sucrose.

FORWARD REFERENCES

• Chapter 24 on organic chemistry will discuss formation and properties of many molecular

substances that are solids at room temperature.

12.7 Covalent-Network Solids

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• Covalent-network solids consist of atoms held together, in large networks or chains, with covalent

bonds.

• In graphite:

• each C atom is arranged in a planar hexagonal ring.

• layers of interconnected rings are placed on top of each other.

• the distance between adjacent C atoms in the same layer is close to that seen in benzene (1.42 Å

vs. 1.395 Å in benzene).

• electrons move in delocalized orbitals (good conductor).

• the distance between layers is large (3.41 Å).

• the layers are held together by weak dispersion forces.

• They slide easily past each other.

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Figure 12.30 from Transparency Pack

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“Diamond” 3–D Model from Instructor’s Resource CD/DVD

“Phosphorus” 3–D Model from Instructor’s Resource CD/DVD

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• The band gap is the energy gap between a filled valence band and an empty conduction

band.

• Valence band: forms from bonding molecular orbitals.

• Moving down a group, the band gap decreases.

• C → Si → Ge → Sn

• The band gap increases as the difference in group numbers of elements increases.

Semiconductor Doping

• Electrical conductivity may be influenced by doping.

FORWARD REFERENCES

• Network-covalent solids will be discussed further in Chapter 22.

• The chemistry of Si and Ge will be discussed in Chapter 22 (section 22.10).

12.8 Polymeric Solids

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• Polymers are molecules of high molecular weight that are made by polymerization (joining together)

of smaller molecules of low molecular mass.

• The building block small molecules for polymers are called monomers.

• Examples of polymers include plastics, DNA, proteins, and rubber.

• Plastics are materials that can be formed into various shapes, usually with heat and pressure.

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“Pictorial Analogies V: Polymers” from Further Readings

Chapter 12

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Making Polymers

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• Many synthetic polymers have a backbone of C–C bonds.

• Carbon atoms have the ability to form unusually strong stable bonds with each other.

• Example: Ethylene H2C=CH2.

• An amine (R–NH2) condenses with a carboxylic acid (R–COOH) to form water and an

amide.

• A biological example of this reaction is the linking of amino acids to form polymer chains–

proteins!

• A protein is an example of a copolymer–a polymer formed from different monomers.

• Another example of condensation polymerization is the formation of nylon 6,6.

• Diamine and adipic acid are joined to form nylon 6,6.

Structure and Physical Properties of Polymers

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• Synthetic and natural polymers commonly consist of a collection of macromolecules of different

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“Alkanes: Abundant, Pervasive, Important, and Essential” from Further Readings

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“Polyethylene” 3–D Model from Instructor’s Resource CD/DVD

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“Slime: Gelation of Poly(vinyl alcohol) with Borax” From Live Demonstrations

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“The Gelation of Polyvinyl Alcohol with Borax. A Novel Class Participation Experiment Involving the

Preparation and Properties of a ‘Slime’” from Live Demonstrations

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• The degree of crystallinity reflects the extent of the order.

• Stretching or extruding a polymer can increase crystallinity.

• The degree of crystallinity is also strongly influenced by average molecular mass:

• Low-density polyethylene (LDPE), which is used in plastic wrap, has an average molecular mass

of 104 amu.

• Rubber is cross-linked in a process employing short chains of sulfur atoms.

• Vulcanized rubber has more useful properties.

• It is more elastic and less susceptible to chemical reaction than natural rubber.

FORWARD REFERENCES

• Further mention of sulfur chemistry, including vulcanization of rubber, will be made in

12.9 Nanomaterials

• Nanomaterials have dimensions on the 1 – 100 nm scale.

Semiconductors on the Nanoscale

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• 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.

• The smaller the particle, the larger the band gap. Consider cadmium phosphide.

• On a macrolevel it looks black. The band gap is small and it absorbs most of the visible light.

• When the particle is made smaller, the color changes until it looks white.

• No visible light is absorbed.

• The band gap is so large that only UV light can excite electrons to the conduction band.

• By appropriately tuning the band gap of the quantum dots, all colors of the rainbow can be

obtained from one material.

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• Quantum wires have also been produced. A quantum wire is a semiconductor wire that may have a

very long length but a diameter that is only a few nanometers.

Metals on the Nanoscale

• The mean free path of an electron is the average distance it moves before bumping into something

Fullerenes, Carbon Nanotubes, and Graphene

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• 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.

• Carbon nanotubes are sheets of graphite rolled up and capped at one or both ends by half of a C60

molecule.

• It can sustain very high electrical current densities.

FORWARD REFERENCES

• The work of Michael Faraday will be discussed in Chapter 20 (section 20.5).

• Fullerenes will be further discussed in Chapter 22 (section 22.9).

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Figure 12.48 from Transparency Pack

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