1. Solids and Modern Materials 熊同銘 tmhsiung@gmail.com
Chapter 12
Solids and
Modern Materials
熊同銘

2. Contents
Classification of Solids
Structures of Solids
Metallic Solids
Metallic Bonding
Ionic Solids
Molecular Solids
Covalent-Network Solids
Polymers
Nanomaterials

3. 1. Classification of Solids
Metallic solids: held together by a delocalized“sea”of collectively shared valence
electrons. This form of bonding allows metals to conduct electricity.
Ionic solids: held together by electrostatic attraction between cations and anions. Ionic solids do not conduct electricity.
Covalent-network solids: held together by an extended network of covalent bonds. result in materials that are extremely hard.
Molecular solids are held together by the intermolecular forces (dispersion forces,
dipole–dipole interactions, and hydrogen bonds). soft and low melting points.

4. Other Types of Solids
Polymers contain long chains of atoms connected by covalent bonds; the chains can be connected to other chains by weak forces. These molecules have different properties than small molecules or metallic or ionic compounds.
Nanomaterials are crystalline compounds with the crystals on the order of 1–100 nm; this gives them very different properties than larger crystalline materials.

5. Crystalline and Amorphous Solids
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2. Structures of Solids
Crystalline and Amorphous Solids
Crystalline solids: The solid have atoms/ions/molecules arranged in a regular pattern.
Amorphous solids: The solids have no significant long-range order.

6. Crystalline Solids: The Fundamental Types

7. Unit Cells and Crystal Lattices
Unit cell: The smallest portion of a crystal that reproduces the structure of the entire crystal when repeated in different directions in space. It is the repeating unit or building block of the crystal lattice.
Crystal lattice: An imaginary network of points on which the repeating motif of a solid may be imagined to be laid down so that the structure of the crystal is obtained. The motif may be a single atom or a group of atoms. Each lattice point represents an identical environment in the crystal.
Motif: 模體
Crystal lattice: 晶格

8. Structure of Crystals
There are 7 basic crystal structure systems (unit cells), and total 14 lattice types:
Cubic: Primitive, Body-centered, Face-centered
Tetragonal: Primitive, Body-centered
Monoclinic: Primitive, End-centered
Orthorhombic: Primitive, body-centered, face-centered, end-centered
Rhombohedral
Hexagonal
Triclinic
Unit cell: 單位晶胞

9. The seven three-dimensional primitive lattices
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The seven three-dimensional primitive lattices
Cubic:正立方，Tetragonal:四方，Orthorhombic:斜方，Rhombohedral:三方，Hexagonal:六方，Monoclinic:單斜，Triclinic:三斜

10. 3. Metallic Solids
The Structures of Metallic Solids

11. Atomic Radius (r) versus Edge length (a) for three Cubic Unit Cells
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Atomic Radius (r) versus Edge length (a) for three Cubic Unit Cells

12. Packing Efficiency
Packing efficiency: The percentage of the unit cell space occupied by the spheres (atoms), which can be calculated by:

13. Packing Efficiency of Cubic Cell
Primitive Body-centered Face-centered
Atom/Unit cell 1 2 4
a = 2r
Packing 52.36% 68.02% 74.04%
efficiency
Coordination
number
Coordination number: The number of atoms (or ions) surrounding and atom (or ions) in a crystal lattice.
The packing with 74.04% packing called close-packed.

14. Sample Exercise 12.1 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

15. Close-Packed Structure
Hexagonal Close-Pcked (HCP): The third layer covers the tetrahedral holes, produce two-layer repeating units.
Cubic Close-Packed (CCP): The third layer covers the octahedral holes, produce three-layer repeating units. (Crystal structure is identical to face-centered cubic unit cell)

16. Summary of Metal Crystal Structures
Type Packing efficiency
Primitive cubic 52%
Body-centered cubic 68%
Cubic Closest-Packed
(Unit cell: Face-Centered Cubic type) 74%
Hexagonal Closest-Packed
(Unit cell: Hexagonal type) 74%

17. Classify the Crystal Structure of Metals
Mn: primitive cubic, Ga: orthorhombic, In and Sn: tetragonal,
Hg: rhombohedral

18. Alloys
A substance that has the characteristic properties of a metal and contains more than one element. Often there is one principal metallic component, with other elements present in smaller amounts. Alloys may be homogeneous or heterogeneous.

19. Categories of Alloys:
Substitutional alloys
Interstitial alloys
Heterogeneous alloys
Intermetallic compounds

20. Substitutional alloys
A homogeneous (solution) alloy in which atoms of different elements randomly occupy sites in the lattice.
Interstitial alloy
An alloy in which smaller atoms fit into spaces between larger atoms. The larger atoms are metallic elements and the smaller atoms are typically nonmetallic elements.

21. Heterogeneous alloys
An alloy in which the components are not distributed uniformly; instead, two or more distinct phases with characteristic compositions are present.
Microscopic view of the structure of the heterogeneous alloy pearlite.

22. Three examples of intermetallic compounds.
A homogeneous alloy with definite properties and a fixed composition. Intermetallic compounds are stoichiometric compounds that form between metallic elements.
Ni3Al: jet aircraft engines, strength at high temperature and its low density.
Cr3Pt, Razor blades coated, adds hardness, allowing the blade to stay sharp longer.
Nb3Sn, superconductor
Three examples of intermetallic compounds.

23. In the jewelry trade pure gold is termed 24 karat.
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Alloys of Gold
In the jewelry trade pure gold is termed 24 karat.
14 karat: 14/24 * 100 = 58% gold
18 karat: 18/24 * 100 = 75% gold

24. 4. Metallic Bonding Bonding in period 3 elements
Malleability:可塑性，Ductility: 延展性。

25. Electron-Sea Model
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.

26. Molecular–Orbital Model (Band Theory)
A model for bonding in atomic solids that comes from molecular orbital theory in which atomic orbitals combine and become delocalized over the entire crystal.
When two atomic orbitals combine they produce both a bonding and an antibonding molecular orbital.
When many atomic orbitals combine they produce a band of bonding molecular orbitals and a band of antibonding molecular orbitals.
The band of bonding molecular orbitals is called the valence band.
The band of antibonding molecular orbitals is called the conduction band.

27. Band Gaps and Conductivity
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Band Gaps and Conductivity
Band Gaps: The difference in energy between the valence band and conduction band is called the band gap. (The larger the band gap, the fewer electrons there are with enough energy to make the jump).
* The more electrons at any one time that a substance has in the conduction band, the better conductor of electricity it is.

28. Molecular Orbitals of Polylithium
* At absolute zero, all the electrons will occupy the valence band. As the temperature rises, some of the electrons may acquire enough energy to jump to the conduction band.

29. The electronic band structure of nickel

30. The melting points of metals from periods 4, 5, and 6.
Their MO diagrams lead to more bands that better explain conductivity and other properties of metals such as melting and boiling points, higher heats of fusion, hardness, and so forth.
The molecular–orbital model predicts that bonding first becomes
stronger as the number of valence electrons increases and the bonding orbitals are
increasingly populated.
Upon moving past the middle elements of the transition metal
series, the bonds grow weaker as electrons populate antibonding orbitals.
Strong bonds between atoms lead to metals with higher melting and boiling points,
higher heats of fusion, higher hardness, and so forth.

31. 5. Ionic Solids
The most favorable structure consideration:
The relative sizes (cation radius/anion radius).
The stoichiometry (number of cations per formula unit/number of anions per formula unit).
* Most favorable structures have cation–anion distances as close as possible, but the anion–anion and cation–cation distances are maximized.

32. Structure of Binary (1:1) Ionic Compounds
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Structure of Binary (1:1) Ionic Compounds
* The small size cations fill into the voids between the large size anions.

33. Coordination environments in CsCl, NaCl, and ZnS
Continued
Coordination environments in CsCl, NaCl, and ZnS

34. Structure Depend on Stoichiometry
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Structure Depend on Stoichiometry
Structure types (CsCl, NaCl, and ZnS) only for 1:1 ionic compounds.
NaF and NaCl have similar structure

35. 6. Molecular Solids
The solids whose composite units are molecules.
Held together by intermolecular attractive forces such as dispersion forces, dipole-dipole attractions, and H-bonds.
Tend to have low melting points, however, if hydrogen bonds present, the melting points increased.
highly symmetrical shape increase melting point

36. Nonbonding Atomic Solids
For those noble gases in solid form
Held together by dispersion forces, very low melting point
Tend to arrange atoms in closest-packed structure, either hexagonal closest-packed or cubic closest-packed

37. Covalent-Network Solids Diamond and Graphite
Each carbon bonded to three other carbons in the same plane using sp2 hybridization.
The delocalized p electrons between layers, make graphite a electricity conductor.
Diamond
Each carbon bonded to four other carbons in a tetrahedral arrangement using sp3 hybridization.
Network Covalent Atomic Solids: Solids forming by a network of covalent bonds throughout the solid.
Diamond and graphite, two allotropes (同素異形體) of carbon.

38. Quartz and Glass Quartz Glass
Crystalline array of SiO4 tetrahedral with shared oxygen atoms.
Glass
amorphous form of SiO2.

39. Semiconductors
The material that is neither a good conductor or a good insulator but that conducts more electricity when heat, light or voltage is added.
Elemental semiconductors: Group 4A element (Si, Ge etc.), all of which have 4 valence electrons.
Compound semiconductors: The average valence electron count as four per atom. For example: GaAs, ZnS, etc.

40. Band Structure of Semiconductors
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Band Structure of Semiconductors
* Energy band gap (Eg) over 3.5 eV lead to the material being an insulator.

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42. Semiconductor Doping
Doping: Adding impurities to the semiconductor’s crystal (Si, group 4A element for example) to increase its conductivity.
n-type semiconductors: Si doped with P (group 5A element), the additional electrons go into conduction band easily and can conduct electric current.
p-type semiconductors: Si doped with Al (group 3A element) resulting in electron “holes” in the valence band, thus electrons can move between holes, allowing conduction of electricity.
Doping: 摻雜

43. Diodes
When a p-type semiconductor adjoins an n-type semiconductor, the result is a p–n junction.
Electricity can flow across the p–n junction in only one direction; this is called a diode.
This also allows the for accumulation of electrical energy, called an amplifier.

44. Polymers
The macromolecules formed by the polymerization of monomers.
Nnatural polymers: wool, leather, silk, and natural rubber.
Synthetic polymers: by polymerizing monomers through controlled chemical reactions.

45. Addition polymerization
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Making Polymers
Addition polymerization
Polymerization of ethylene polyethylene for example:

46. Condensation polymerization
A monomer contains amine group (−NH2) and carboxylic acid group (−COOH) for example:

47. Copolymers
Polymers formed from two different monomers are called copolymers.
The formation of the copolymer nylon 6,6 for example:

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

49. The materials that have dimensions on the 1–100-nm scale.
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9. Nanomaterials
The materials that have dimensions on the 1–100-nm scale.
Semiconductors on the Nanoscale
* Reducing the size of a semiconductor crystal, the band gap energy gets larger.

50. Metals on Nanoscale
Physical and chemical properties of metallic nanoparticles are different from the properties of the bulk materials.
The solutions of colloidal gold nanoparticles.

51. Carbon on Nanoscale
Carbon nanotubes can be made with metallic or semiconducting properties without doping.
Graphene has been discovered: single layers with the structure of graphite.

52. End of Chapter 12