1. Chapter 12 Solids and Modern Materials
Lecture Presentation
Chapter 12 Solids and Modern Materials
James F. Kirby
Quinnipiac University
Hamden, CT

2. Classifying Solids Based on Bonds
Metallic solids are held together by a “sea” of collectively shared electrons.
This type of bond allows metals to conduct electricity
Metals are relatively strong without being brittle
2) Ionic solids are sets of cations and anions mutually attracted to one another.
Do not conduct electricity well
They are brittle

3. Classifying Solids Based on Bonds
3) Covalent-network solids are joined by an extensive network of covalent bonds.
Some are extremely hard (diamonds)
Some are semiconductors
Examples: diamond, graphite, and silicon dioxide
4) Molecular solids are discrete molecules held together by intermolecular forces.
Tend to be soft with low melting points

4. Two Other Types of Solids
1) Polymers contain long chains of atoms connected by covalent bonds; the chains can be connected to other chains by weak forces.
Normally stronger and higher melting points than molecular solids
More flexible than metallic, ionic, and covalent-network solids

5. 2) Nanomaterials are crystalline compounds with the crystals on the order of 1–100 nm; this gives them very different properties than larger crystalline materials.
nanofibers, nanowires, nanotubes, etc

6. One Organization of Solids
Solids with a regular repeating pattern of atoms are crystalline.
Amorphous solids are characterized by a distinct lack of order in the arrangement of atoms.
Since crystalline solids have a regular pattern, they are of more interest to most chemists.

7. Unit Cell The basis of a repeating pattern is the unit cell.
The structure of a crystalline solid is defined by
the size and shape of the unit cell.
the locations of atoms within the unit cell.
lattice
point
At lattice points:
Atoms
Molecules
Ions

8. Lattice Points
Positions that define the overall structure of the crystalline compound are called lattice points.
Each lattice point has an identical environment.
Lattice vectors connect the points and define the unit cell.
The next slide shows how this works for five different two-dimensional lattices.

9. 2-D Lattices

10. 3-D Crystal Lattices
There are seven basic three-dimensional lattices: cubic, tetragonal, orthorhombic, rhombohedral, hexagonal, monoclinic, and triclinic.

11. Primitive vs. Centered Lattices
Primitive lattices have atoms only in the lattice points.
Centered lattices have atoms in another regular location, most commonly the body-center or the face-center.

12. Motifs
Sometimes, the atoms are not on the lattice points, but the overall structure follows a particular unit cell. The groups of atoms that define the overall structure is called a motif.

13. 12.3 Metallic Structure
The structures of many metals conform to one of the cubic unit cells: simple cubic, body-centered cubic, or face-centered cubic.

14. Coordination number = 6 Coordination number = 8 Coordination number = 12
Coordination Number: the number of atoms immediately surrounding a given atom in a crystal structure
11.4

15. Coordination number = 6
It is in contact with 6 other spheres, four in its own layer, one above and one below
11.4

16. Coordination number = 8
Each sphere is in contact with 4 spheres from the layer above and 4 spheres from the layer below
11.4

17. Shared by 8 unit cells
Shared by 2 unit cells
11.4

18. 1 atom/unit cell
2 atoms/unit cell
4 atoms/unit cell
(8 x 1/8 = 1)
(8 x 1/8 + 1 = 2)
(8 x 1/8 + 6 x 1/2 = 4)
11.4

19. Cubic Structures
Not every part of an atom on a lattice point is completely within that unit cell. One can determine how many atoms are within each unit cell.
Eight cubes meet at a corner, therefore only 1/8 of that corner atom is within any one unit cell meeting there.
Two cubes meet at a face, therefore only 1/2 of that face atom is within any one unit cell meeting there.
A body-centered atom is entirely within the unit cell.

20. Close Packing Nature does not like empty space!
The atoms in a crystal pack as close together as they can.
The two common types of packing seen are
cubic close-packed.
hexagonal close-packed.

21. Alloys
Alloys are materials that contain more than one element and have the characteristic properties of metals.
It is an important means employed to change the properties of certain metals.

22. Types of Alloys
Substitutional alloys: A second element takes the place of a metal atom.
Interstitial alloys: A second element fills a space in the lattice of metal atoms.
Heterogeneous alloys: components not dispersed uniformly

23. Intermetallic Compounds
compounds, not mixtures
distinct properties, definite composition (since they are compounds)
ordered, rather than randomly distributed
Better structural stability and higher melting points than the individual metals
More brittle than substitutional alloys
Examples:
Ni3Al: jet engines
Cr3Pt: razor blades
Nb3Sn: superconductor

24. 12.4 Metallic Bonding
One can think of a 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.

25. A Molecular-Orbital Approach
As the number of atoms in a chain increases, the energy gap between the bonding orbitals and between the antibonding orbitals disappears, resulting in a continuous band of energy. The approach seen here only takes into account s-orbital population.

26. MO Approach with More Orbitals
Most metals have d and p orbitals to consider.
Their MO diagrams lead to more bands that better explain conductivity and other properties of metals.

27. 11.4

28. 4 atoms/unit cell in a face-centered cubic cell
When silver crystallizes, it forms face-centered cubic cells. The unit cell edge length is 409 pm. Calculate the density of silver in g/cm3.
1 pm = 10-12m
d = m V
V = a3
= (409 pm)3 = 6.83 x cm3
4 atoms/unit cell in a face-centered cubic cell
107.9 g
mole Ag x
1 mole Ag
6.022 x 1023 atoms x
m = 4 Ag atoms
= 7.17 x g
d = m V
7.17 x g
6.83 x cm3 =
= 10.5 g/cm3
11.4

29. Ionic Solids Ionic Crystals
Lattice points occupied by cations and anions
Held together by electrostatic attraction
Hard, brittle, high melting point
Poor conductor of heat and electricity

30. Ionic Solids
Most favorable structures have cation–anion distances as close as possible, but the anion–anion and cation–cation distances are maximized.
Three common structures for 1:1 salts:
CsCl structure
NaCl (rock salt) structure
zinc blende (ZnS) structure

31. Effect of Ion Size on Structure
The size of the cation compared to the anion (radius ratio) is the major factor in which structure is seen for ionic compounds.

32. 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 face-centered cubic metal.
Solution
Analyze We must determine the volume taken up by the atoms that reside in the unit cell and divide this number by the volume of the unit cell.
Plan We can calculate the volume taken up by atoms by multiplying the number of atoms per unit cell by the volume of a sphere, 4πr3/3. To determine the volume of the unit cell, we must find the edge length, a, of the cubic unit cell. Once we know the edge length, the cell volume is simply a3.
Solve
As shown in Figure 12.12, a face-centered cubic metal has four atoms per unit cell. Therefore, the volume occupied by the atoms is

33. Sample Exercise 12.1 Calculating Packing Efficiency
Continued
For a face-centered cubic metal, the edge length, a = 8 𝑟
Finally, we calculate the packing efficiency by dividing the volume occupied by atoms by the volume of the cubic unit cell, a3:
Packing efficiency = volume of atoms = ( 16 3 ) 𝜋r3 ÷ √8𝑟 = 0.74 or 74%
volume of unit cell

34. Sample Exercise 12.2 Calculating the Density of an Ionic Solid
Rubidium iodide crystallizes with the same structure as sodium chloride. (a) How many iodide ions are there per unit cell? (b) How many rubidium ions are there per unit cell? (c) Use the ionic radii and molar masses of Rb+ (1.66 Å , g/mol) and I– (2.06 Å, g/mol) to estimate the density of rubidium iodide in g/cm3.
Solution
Analyze and Plan
(a) We need to count the number of anions in the unit cell of the sodium chloride structure, remembering that ions on the corners, edges, and faces of the unit cell are only partially inside the unit cell.
(b) We can apply the same approach to determine the number of cations in the unit cell. We can double- check our answer by writing the empirical formula to make sure the charges of the cations and anions are balanced.
(c) Because density is an intensive property, the density of the unit cell is the same as the density of a bulk crystal. To calculate the density we must divide the mass of the atoms per unit cell by the volume of the unit cell. To determine the volume of the unit cell we need to estimate the length of the unit cell edge by first identifying the direction along which the ions touch and then using ionic radii to estimate the length. Once we have the length of the unit cell edge we can cube it to determine its volume.

35. Sample Exercise 12.2 Calculating the Density of an Ionic Solid
Continued
Solve
(a) The crystal structure of rubidium iodide looks just like NaCl with Rb+ ions replacing Na+ and I– ions replacing Cl–. From the views of the NaCl structure in Figures and we see that there is an anion at each corner of the unit cell and at the center of each face. From Table we see that the ions sitting on the corners are equally shared by eight unit cells (1/8 ion per unit cell), while those ions sitting on the faces are equally shared by two unit cells (1/2 ion per unit cell). A cube has eight corners and six faces, so the total number of I– ions is 8 (1/8) + 6 (1/2) = 4 per unit cell.

36. Sample Exercise 12.2 Calculating the Density of an Ionic Solid
Continued
(b) Using the same approach for the rubidium cations we see that there is a rubidium ion on each edge and one at the center of the unit cell. Using Table 12.1 again we see that the ions sitting on the edges are equally shared by four unit cells (1/4 ion per unit cell), whereas the cation at the center of the unit cell is not shared. A cube has 12 edges, so the total number of rubidium ions is 12 (1/4) + 1 = 4. This answer makes sense because the number of Rb+ ions must be the same as the number of I– ions to maintain charge balance.
(c) In ionic compounds cations and anions touch each other. In RbI the cations and anions touch along the edge of the unit cell as shown in the following figure.
The distance the unit cell edge is equal to r(I–) + 2r(Rb+) + r(I–) = 2r(I–) + 2r(Rb+). Plugging in the ionic radii we get 2(2.06 Å) + 2(1.66 Å) = 7.44 Å. The volume of a cubic unit cell is just the edge length cubed. Converting from Å to cm and cubing we get
Volume = (7.44 × 10–8 cm)3 = 4.12 × 10–22 cm3.

37. Sample Exercise 12.2 Calculating the Density of an Ionic Solid
Continued
From parts (a) and (b) we know that there are four rubidium and four iodide ions per unit cell. Using this result and the molar masses we can calculate the mass per unit cell
The density is the mass per unit cell divided by the volume of a unit cell
Check The densities of most solids fall between the density of lithium (0.5 g/cm3) and that of iridium (22.6 g/cm3), so this value is reasonable.

38. Molecular Solids
Consist of atoms or molecules held together by weaker forces (dispersion, dipole–dipole, or hydrogen bonds).
Shape (ability to stack) matters for some physical properties, like boiling point.

39. Covalent-Network Solids
Atoms are covalently bonded over large network distances with regular patterns of atoms.
Tend to have higher melting and boiling points.
Diamond, graphite, and quartz are examples.

40. Semiconductors
They have a gap between the occupied MOs (valence band) and the unoccupied ones (conduction band).
Electrons must enter the conduction band for electron transfer.
Group IVA elements have gaps between the bands of 0.08 to eV (7 to 300 kJ/mol).
Note: Band gaps over 3.5 eV lead to the material being an insulator.

41. What Forms a Semiconductor?
Among elements, only Group IVA, all of which have 4 valence electrons, are semiconductors.
Inorganic semiconductors (like GaAs) tend to have an average of 4 valence electrons (3 for Ga, 5 for As).

42. Doping
changing the conductivity of semiconductors by adding an element with more or fewer electrons
n-type semiconductors have more electrons, so the negative charge travels in the conductance band.
p-type semiconductors have fewer electrons, so the “hole” (positive charge) travels in the valence band.

43. Types of Crystals
11.6

44. Polymers
Polymers are molecules of high molecular weight made by joining smaller molecules, called monomers.
There are two primary types of polymers:
Addition polymers are formed when a bond breaks, and the electrons in that bond make two new bonds.
Condensation polymers are formed when a small molecule is removed between two large molecules.

45. Addition vs. Condensation Polymerization

46. Some Common Polymers

47. Bulk Properties of Polymers
The molecules are not straight lines—the longer the chain, the more twisting happens.
Chains can have a variety of lengths, and therefore a variety of molecular weights.
The material can be very flexible (plastics).
Short range order can lead to crystallinity in the solid.

48. Changing the Polymer’s Physical Properties
Chemically bonding chains of polymers to each other can stiffen and strengthen the substance.
In vulcanization, chains are cross-linked by short chains of sulfur atoms, making the rubber stronger.

49. Nanomaterials
Particles that have three dimensions on the 1–100 nm size
Their properties are the study of many labs around the world.

50. Semiconductors on the Nanoscale
Small molecules have discrete orbitals; macroscale materials have bands. Where does it switch over?
Theory tells us 1–10 nm (about 10–100 atoms).
Quantum dots are semiconductors this size.
Qua

51. Metals on the Nanoscale
Finely divided metals can have quite different properties than larger samples of metals.
Would you like “red gold” as in many old stained glass windows?

52. Carbon on the Nanoscale
Carbon nanotubes can be made with metallic or semiconducting properties without doping.
They are very strong materials.
Graphene has been discovered: single layers with the structure of graphite.