Solids: Structures and Applications 12 Solids: Structures and Applications

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

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.

Types of Solids

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

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.

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

Unit Cells Hexagonal unit cell:

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.

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

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.

Crystal Structures of Metals

hcp and ccp: most efficient!

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

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

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

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

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

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.

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

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

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

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

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

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

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.

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.

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

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

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.

Semiconductors

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

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)

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

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.

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.

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.

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.

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.

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

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.

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.

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

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

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.

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 12.9 X-ray Diffraction: How We Know Crystal Structures

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).

Polymorphs of Silica Quartz: crystalline Obsidian: amorphous/glass

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

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

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)

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.

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”

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

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.

Structure Determination by XRD X-ray diffraction for quartz

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