Solids and Modern Materials (Chapter 13)

13.1 Graphene

  • Thinnest, strongest known material; ~1 atom thick

  • Conducts heat and electricity; can be fully charged within 5 seconds

  • Transparent and completely impermeable to all substances

  • Potential applications: faster computers, foldable touchscreens, ultrathin light panels, super-strong light bulletproof vests

13.2 X-Ray Crystallography

  • X-ray diffraction determines atom arrangement in a crystal

  • X-rays of wavelength λ scatter from atomic planes to form diffraction patterns; measuring diffraction angles yields plane spacing and arrangement

  • Bragg’s Law: nλ=2dsin⁡θn\lambda=2d\sin\theta

    • n: order of diffraction

    • d: spacing between planes

    • θ: diffraction angle

    • λ: wavelength of X-rays

  • Example concepts relate wavelength, spacing, and angle to crystal structure

13.3 Unit Cells and Basic Structures

  • Unit cell: smallest repeating unit describing crystal arrangement

  • Commonly classified by symmetry into Simple Cubic (SC), Body-Centered Cubic (BCC), and Face-Centered Cubic (FCC)

  • Coordination number (CN): number of nearest neighbors for an atom/ion; depends on unit cell type

Simple Cubic (SC)

  • Atoms per unit cell: 1 (8 corners × 1/8)

  • Edge length: a=2ra=2r, where r is atomic/ionic radius

  • CN = 6

Body-Centered Cubic (BCC)

  • Atoms per unit cell: 2 (1 center + 8 corners × 1/8)

  • Edge length: a=43 ra=4\sqrt{3}\,r

  • CN = 8

Face-Centered Cubic (FCC)

  • Atoms per unit cell: 4 (8 corners × 1/8 + 6 faces × 1/2)

  • Edge length: a=22 ra=2\sqrt{2}\,r

  • CN = 12

13.4 Classifying Crystalline Solids

  • Crystalline solids classified by constituent particles: molecular, ionic, and atomic

13.5 Ionic Solids

  • Composed of cations and anions; charge neutrality

  • Held by strong electrostatic forces; high melting points

  • Coordination number depends on crystal structure and ion sizes; similar sizes allow higher CN and greater stability

  • Ion size ratio affects CN

  • Examples:

    • CsCl: CN = 8; simple cubic hole structure; 1:1 cation/anion

    • NaCl (rock-salt): CN = 6; FCC lattice with 1:1 ratio; CN 6

    • ZnS (zinc blende): CN = 4; large size difference reduces CN

13.6 Network Covalent Atomic Solids

  • Network covalent bonds: atoms connected by covalent bonds across a network

  • Very high melting points; covalent bonds stronger than intermolecular forces

  • Two broad families: carbon-based and silicates

Carbon forms

  • Graphite: mp ~3800°C; density ~2.2 g/cm³; planar sheets of SP2-hybridized C forming hexagonal rings; delocalized pi electrons conduct electricity; sheets held by dispersion forces; lubricating properties; used as electrical/thermal conductor and lubricants

  • Diamond: mp ~3800°C; density ~3.5 g/cm³; 3D network of SP3 C bonds; insulator (no free electrons); extremely rigid and hard

  • Buckminsterfullerene (C60): soccer-ball shaped; buckyballs; fullerene family (C60–C100)

  • Nanotubes: single-walled (SWNT) or multiwalled (MWNT); ultralight and very strong; used in nanoelectronics, displays, sensors, transistors, etc.

13.7 Ceramics, Cement, and Glass

  • Ceramics: silicate-based solids; used in buildings, electronics, pottery, kitchenware

  • Silicates: Si–O network (SiO2) with SiO4 tetrahedra; quartz is a common silicate; ~90% of Earth's crust

  • Cement: mixture of limestone (CaCO3) and silica (SiO2); hydrates to form Si–O–Si bridges; used with sand/pebbles to make concrete

  • Glass: amorphous solid from rapid cooling of molten silica

    • Soda-lime glass: ~70% SiO2 with Na2O and CaO; windows; inexpensive but vulnerable to thermal shock

    • Borosilicate glass (Pyrex): SiO2 with boric oxide; resists thermal cycling

    • Leaded glass (crystal): SiO2 with PbO; high refractive index; decorative but toxic; lead-free alternatives common

13.8 Semiconductors and Band Theory

  • Band theory: atomic orbitals form bands (valence band: bonding; conduction band: antibonding)

  • Band gap: energy difference between valence and conduction bands; governs conductivity

  • Conductors: negligible band gap; electrons move easily

  • Semiconductors: moderate band gap; conductivity can be controlled

  • Insulators: large band gap; poor conductivity

  • Group 4A elements (between metals and nonmetals):

    • Band gap decreases with increasing atomic radius down the group; affects overlap of orbitals

    • Si and Ge are semiconductors; C (diamond) is an insulator; Sn/ Pb trends toward metallic character

  • Doping: introduce impurities to control conductivity

    • n-type semiconductors: donor atoms with more valence electrons (e.g., Phosphorus) add free electrons

    • p-type semiconductors: acceptor atoms with fewer valence electrons (e.g., Gallium) create holes in the valence band

  • P–N junctions: essential for diodes and amplifiers (LEDs, displays, chargers, surge protectors; amplifiers in audio/video devices)

  • Diodes: components that allow flow of electricity in only one direction.

  • Amplifiers: components that amplify a small electrical current into a large one.

13.9 Polymers and Plastics

  • Polymers: long molecular chains made from monomers; natural (starch, proteins, DNA) or synthetic (plastics, PET, PVC, polyester)

  • Plastics: made of polymers, long molecular chains that define their properties

  • Polymerization: linking monomers to form larger molecules like polymers

    • Addition polymerization: monomers link without eliminating atoms (everything adds up to make the polymer)

    • Condensation polymerization: small molecules are eliminated (e.g., water)

  • Copolymers: polymers formed from two different monomers; dimers are two-monomer units

  • Addition polymers (examples):

    • Polyethylene (PE)

    • Polypropylene (PP)

    • Polystyrene (PS)

    • Polyvinyl chloride (PVC)

  • Condensation polymers (examples):

    • Polyurethane

    • Polyethylene terephthalate (PET)

    • Nylon 6,6

  • Uses span packaging, textiles, electronics, automotive, etc.