1. Solids: Structures and Applications12
Solids: Structures and Applications

2. Chapter Outline 12.1 The Solid State 12.2 Structures of Metals
12.3 Alloys
12.4 Metallic Bonds and Conduction Bands
12.5 Semiconductors
12.6 Salt Crystals: Ionic Solids
12.7 Structures of Nonmetals
12.8 Ceramics: Insulators to Superconductors
12.9 X-ray Diffraction: How We Know Crystal Structures

3. The Solid State
Crystalline solid – a solid made of an ordered array of atoms, ion, or molecules.
Amorphous solids – a solid that lacks long- range order for the atoms, ions or molecules in its structure.
Molecular solids – a solid formed by neutral, covalently bonded molecules held together by intermolecular attractive forces
Ionic solids – a solid consisting of monatomic or polyatomic ions held together by ionic bonds.

4. Types of Solids

5. Chapter Outline 12.2 Structures of Metals Stacking Patterns
12.1 The Solid State
12.2 Structures of Metals
Stacking Patterns
Stacking Spheres and Unit Cells
Unit Cell Dimensions
12.3 Alloys
12.4 Metallic Bonds and Conduction Bands
12.5 Semiconductors
12.6 Salt Crystals: Ionic Solids
12.7 Structures of Nonmetals
12.8 Ceramics: Insulators to Superconductors
12.9 X-ray Diffraction: How We Know Crystal Structures

6. Stacking Patterns
Crystal lattice – Ordered three-dimensional array of particles in a crystalline solid.
Unit cell – basic repeating unit of the arrangement of particles in a crystalline solid.
Hexagonal closest-packed (hcp) – a crystal structure in which the layers of atoms or ions have an ababab… stacking pattern.
Cubic closest-packed (ccp) – a crystal structure in which the layers of atoms, ions, have an abcabcabc… stacking pattern.

7. Stacking Patterns (cont.)
Hexagonal closest-
packed (hcp)
Cubic closest-
packed (ccp)

8. Unit Cells
Hexagonal unit cell:

9. Cubic Unit Cells
Face-centered cubic (fcc) – closest packing unit cell in which atoms are located on the 8 corners and 6 faces of a cube.

10. Cubic Unit Cells (cont.)
Simple cubic (sc) – square-packing arrangement; particles located at 8 corners of cubic unit cell.

11. Cubic Unit Cells (cont.)
Body-centered cubic (bcc) – square packing arrangement in which particles are located at 8 corners and in center of cubic unit cell.

12. Crystal Structures of Metals

13. hcp and ccp: most efficient!

14. Unit Cell Dimensions Simple cubic (sc): Face-centered cubic (fcc):
Atoms touch along cell edge.
(radius) x 2 = ℓ
Face-centered cubic (fcc):
Atoms touch along face diagonal.
(radius) x 4 = ℓ x (2)1/2
Body-centered cubic (bcc):
Atoms touch along body diagonal.
(radius) x 4 = ℓ x (3)1/2

15. Shared Atoms in Unit Cells
Atoms on corners:
Shared by 8 cells; 1/8 in each cell.
(1/8 per corner) x 8 corners = 1 atom
Atoms on faces:
Shared by 2 cells; ½ in each cell.
(½ per face) x 6 faces = 3 atoms

16. Shared Atoms in Unit Cells (cont.)
Atoms in body:
Completely located in unit cell.
1 atom
Atoms on edges:
Shared by 4 cells; ¼ in each cell.
(¼ per edge) x 12 edges = 3 atoms

17. Number of Atoms in a Unit Cell
Simple cubic cell:
8 atoms on corners; 1/8 x 8 = 1 atom/cell
Body-centered cubic (bcc):
8 on corners + 1 in center
(1/8 x 8) + 1 = 2 atoms per unit cell
Face-centered cubic (fcc):
8 on corners + 6 on faces
(1/8 x 8) + (½ x 6) = 4 atoms per unit cell

19. Chapter Outline 12.3 Alloys 12.1 The Solid State
12.2 Structures of Metals
12.3 Alloys
Substitutional Alloys
Interstitial Alloys
12.4 Metallic Bonds and Conduction Bands
12.5 Semiconductors
12.6 Salt Crystals: Ionic Solids
12.7 Structures of Nonmetals
12.8 Ceramics: Insulators to Superconductors
12.9 X-ray Diffraction: How We Know Crystal Structures

20. Alloys
Alloy – a blend of a host metal and one or more other elements, which may or may not be metals, that are added to change the properties of the host metal.
Homogenous alloys – a solid solution in which atoms of host and added elements are randomly and uniformly distributed.
Heterogenous alloys – a matrix of host metal atoms with “islands” of atoms of added elements interspersed.

21. Substitutional Alloy: Bronze
Substitutional alloy – atoms of nonhost metal replace host atoms in the crystal lattice
Bronze (substitutional, homogeneous):
Host = Cu; added element = Sn (up to 30%)
Close-packed Cu/Sn atoms
Possible unit cell for bronze

22. Interstitial Alloys
Interstitial alloy – atoms of added element occupy the spaces between atoms of the host.
Octahedral: larger; cluster of 6 host atoms.
Tetrahedral: smaller; cluster of 4 host atoms

23. Interstitial Alloy: Carbon Steel
Fe at high temperatures forms fcc lattice (austentite). Carbon atoms occupy octahedral spaces between Fe atoms in lattice structure.

24. Carbon atoms will occupy octahedral spaces, but not tetrahedral spaces in the austentite lattice.

25. Chapter Outline 12.1 The Solid State 12.2 Structures of Metals
12.3 Alloys
12.4 Metallic Bonds and Conduction Bands
12.5 Semiconductors
12.6 Salt Crystals: Ionic Solids
12.7 Structures of Nonmetals
12.8 Ceramics: Insulators to Superconductors
12.9 X-ray Diffraction: How We Know Crystal Structures

26. Metallic Bonds Metallic bonds:
Dense packing of metal atoms result in overlap of large number of valence orbitals.
Large number of interactions = strong overall
Limited sharing of electrons between any two atoms = weak bonds between individual atoms

27. Metallic Bonds (cont.) Band Theory: Valence band: Conduction band:
An extension of molecular orbital theory that describes bonding in solids.
Valence band:
A band of orbitals that are filled or partially filled by valence electrons.
Conduction band:
In metals, an unoccupied band higher in energy than a valence band, in which electrons are free to migrate.

28. Band Theory
Overlap of half-filled 4s orbitals of large number of Cu atoms results in a half-filled valence band.
Electrons move from partially occupied orbitals (purple) to the empty molecular orbitals (red), where they are free to migrate through delocalized empty orbital throughout the solid.

29. Conductors Overlap of valence, conduction bands
Electrons in empty orbitals of conduction band move freely.

30. Chapter Outline 12.1 The Solid State 12.2 Structures of Metals
12.3 Alloys
12.4 Metallic Bonds and Conduction Bands
12.5 Semiconductors
12.6 Salt Crystals: Ionic Solids
12.7 Structures of Nonmetals
12.8 Ceramics: Insulators to Superconductors
12.9 X-ray Diffraction: How We Know Crystal Structures

31. Band Gap
Band gap (Eg) – the energy gap between the valence and conduction bands.
Semiconductor – a semimetal (metalloid) with electrical conductivity between that of metals and insulators that can be chemically altered to increase its electrical conductivity.
n-type semiconductor – excess electrons contributed by electron-rich dopant atoms.
p-type semiconductor – “+” holes due to electron-poor dopant atoms.

32. Semiconductors

33. Chapter Outline 12.1 The Solid State 12.2 Structures of Metals
12.3 Alloys
12.4 Metallic Bonds and Conduction Bands
12.5 Semiconductors
12.6 Salt Crystals: Ionic Solids
12.7 Structures of Nonmetals
12.8 Ceramics: Insulators to Superconductors
12.9 X-ray Diffraction: How We Know Crystal Structures

34. Salt Crystals: Ionic Solids
Monoatomic or polyatomic ions held together by ionic bonds. (most are crystalline; e.g., NaCl)
Cubic closest packing (fcc) of Cl– ions with Na+ ions in octahedral holes. (rock salt structure)

35. Other Ionic Crystals
Sphalerite (ZnS):
fcc unit cell of S2– with Zn2+ in four of the eight tetrahedral holes

36. Practice: Lattice Structures
Sphalerite (ZnS) has S2– ions in a fcc structure with Zn2+ ions occupying four of the eight tetrahedral holes in the unit cell. Verify that the unit cell is neutral.
- Collect and Organize: We know the lattice structure and the formula unit for ZnS.

37. Practice: Lattice Structures
Sphalerite (ZnS) has S2– ions in a fcc structure with Zn2+ ions occupying four of the eight tetrahedral holes in the unit cell. Verify that the unit cell is neutral.
Analyze: From the lattice unit cell information we can calculate the number of each ion in the unit cell.

38. Practice: Lattice Structures
Sphalerite (ZnS) has S2– ions in a fcc structure with Zn2+ ions occupying four of the eight tetrahedral holes in the unit cell. Verify that the unit cell is neutral.
-Solve:
S2–: for the fcc lattice, there are 4 ions per unit cell = total –8 charge from sulfide ions.
Zn2+: four tetrahedral holes completely contained within the unit cell = 4 Zn2+ ions = total +8 charge from Zn ions.

39. Practice: Lattice Structures
Sphalerite (ZnS) has S2– ions in a fcc structure with Zn2+ ions occupying four of the eight tetrahedral holes in the unit cell. Verify that the unit cell is neutral.
- Think About It: The total number of positive and negative charges in the lattice unit cell sums to zero, which would be expected for an ionic formula unit.

40. Other Ionic Crystals (cont.)
Fluorite (CaF2):
Ca2+ ions form an expanded fcc array to accommodate the larger F– ions, which occupy all eight tetrahedral holes.

41. Chapter Outline 12.1 The Solid State 12.2 Structures of Metals
12.3 Alloys
12.4 Metallic Bonds and Conduction Bands
12.5 Semiconductors
12.6 Salt Crystals: Ionic Solids
12.7 Structures of Nonmetals
12.8 Ceramics: Insulators to Superconductors
12.9 X-ray Diffraction: How We Know Crystal Structures

42. Crystalline Solids of Nonmetals
Covalent network solids:
Rigid, three-dimensional arrays of covalently bonded atoms.
Molecular solids:
Neutral, covalently bonded molecules held together by intermolecular attractive forces.
Clusters:
Ordered collections of atoms that are larger than typical molecular solids, smaller than network covalent solids.

43. Allotropes of Carbon
Allotropes – different molecular structures of an element.
Allotropes of carbon
Diamond:
Network covalent solid.
All carbon atoms sp3 hybridized; tetrahedral configuration.
Hard; nonconductive; high m.p.

44. Allotropes of Carbon (cont.)
Graphite:
Two-dimensional covalent network of sp2 hybridized carbon atoms in sheets of fused 6-membered rings.
Sheets held together by dispersion forces.
Soft; good lubricant; conductive

45. Allotropes of Carbon (cont.)
Carbon nanotubes:
Graphite sheet structure rolled into tubes
sp2 hybridized carbon atoms
Semiconductor behavior
Extreme strength!

46. Allotropes of Carbon (cont.)
Fullerene:
Three-dimensional network of sp2 hybridized carbon atoms in fused 5- and 6-membered rings to form molecular clusters of 60, 70, or more carbon atoms.

47. Chapter Outline 12.8 Ceramics: Insulators to Superconductors
12.1 The Solid State
12.2 Structures of Metals
12.3 Alloys
12.4 Metallic Bonds and Conduction Bands
12.5 Semiconductors
12.6 Salt Crystals: Ionic Solids
12.7 Structures of Nonmetals
12.8 Ceramics: Insulators to Superconductors
Polymorphs of Silica
Ionic Silicates
From Clay to Ceramics
Superconductors
X-ray Diffraction: How We Know Crystal Structures

48. Silica: SiO2
Silica – one of most abundant families of minerals in igneous rock.
Polymorphs:
Same empirical formulas but different crystal structures and properties
Amorphous solids:
Noncrystalline, disordered array of atoms, ions or particles in a solid state (e.g., glass).

49. Polymorphs of Silica
Quartz: crystalline
Obsidian: amorphous/glass

50. Ionic Silicates
Chrysotile – an ionic silicate, one of principle forms of asbestos; (Si2O52–)n.

51. Aluminosilicates Ionic silicates in which Al3+ is the cation Example:
Kaolinite
(clay mineral)

52. From Clay to Ceramics Ceramics:
Solid aluminosilicates with high melting points
Good thermal and electrical insulators
Formed by heating of clays (e.g., kaolinite)
(mullite)

53. Superconductors Superconductor: Critical temperature (Tc):
Material having zero resistance to flow of electric current.
Critical temperature (Tc):
Temperature below which a material becomes a superconductor.
Superconducting alloys, like Nb3Sn, must be cooled to 20 K to remain superconducting.

54. High-Temp. Superconductors
Yttrium-barium-copper (YBC) oxides:
YBa2Cu3O7 ceramic is superconducting at 77 K (just above liquid nitrogen’s b.p.).
Current superconducting ceramics with critical temperatures ~ 133 K.
Application:
“Meissner effect”

55. Chapter Outline 12.9 X-ray Diffraction: How We Know Crystal Structures
12.1 The Solid State
12.2 Structures of Metals
12.3 Alloys
12.4 Metallic Bonds and Conduction Bands
12.5 Semiconductors
12.6 Salt Crystals: Ionic Solids
12.7 Structures of Nonmetals
12.8 Ceramics: Insulators to Superconductors
12.9 X-ray Diffraction: How We Know Crystal Structures

56. X-ray Diffraction X-ray diffraction (XRD): Bragg equation: n2dsin
Technique for determining arrangement of atoms or ions in a crystal by analyzing the pattern that results when X-rays are scattered after bombarding the crystal.
Bragg equation: n2dsin
Where  = angle of diffraction of X-rays;
d = spacing between layers of ions/atoms in a crystal.

57. Structure Determination by XRD
X-ray diffraction for quartz

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