Condensed Matter Physics

Structure, Vibration and Electrons in Real Materials in 14 chapters — from “What holds a solid together, and where its atoms sit” to “Soft matter: when entropy, not bonding, sets the structure”.

Chapters

  1. What holds a solid together, and where its atoms sit
    • Cohesive energy and bond types
    • The pair potential
    • Ionic crystals and the Madelung sum
    • Bravais lattice and basis
    • Primitive cells and conventional cells
    • Close packing and cubic crystal structures
    • Density from structure
    • Summary
    • Problems
  2. The reciprocal lattice and the Brillouin zone
    • Lattice-periodic functions
    • The reciprocal lattice
    • Miller indices and plane spacings
    • The first Brillouin zone
    • Zone equivalence of wavevectors
    • Scale in reciprocal space
    • Summary
    • Problems
  3. Diffraction: how a structure is actually measured
    • Scattering amplitude and the sum of phases
    • The Laue condition
    • Bragg's law is the same statement
    • Structure factor and missing reflections
    • Powder indexing to four figures
    • X-ray, neutron and electron diffraction
    • Summary
    • Problems
  4. Elastic waves and the vibrating chain
    • Bond stiffness and the harmonic chain
    • The dispersion relation of the chain
    • The long-wavelength limit and sound
    • Group velocity and the zone-boundary standing wave
    • Wavevectors beyond the zone and the mode count
    • Transverse branches and the measured dispersion curve
    • Summary
    • Problems
  5. Two atoms in the cell: acoustic and optical branches
    • The diatomic chain
    • Acoustic and optical branches
    • The zone-centre optical mode
    • The frequency gap at the zone boundary
    • Infrared absorption and the photon wavevector
    • The branch count of a real crystal
    • Summary
    • Problems
  6. Einstein, Debye and the heat capacity of solids
    • The Dulong-Petit law
    • Oscillator energy levels and the Boltzmann factor
    • Average energy of a quantised mode
    • The Einstein model
    • The density of modes and the Debye cut-off
    • The Debye heat capacity and the T3 law
    • Einstein and Debye models compared
    • Summary
    • Problems
  7. Thermal expansion and lattice thermal conductivity
    • No expansion in a harmonic crystal, infinite conductivity
    • Anharmonicity and thermal expansion
    • The Gruneisen relation
    • Low-temperature expansion
    • Lattice thermal conductivity
    • Temperature dependence of thermal conductivity
    • Summary
    • Problems
  8. The free-electron gas: what Drude gets right and what only Fermi fixes
    • Conduction electron density
    • The Drude conductivity
    • The Hall coefficient
    • Failures of the Drude model
    • The exclusion principle and the Fermi sphere
    • The Fermi function and electronic density of states
    • Electronic heat capacity
    • Mean free path at the Fermi surface
    • The Wiedemann-Franz law
    • Limits of the free-electron model
    • Summary
    • Problems
  9. Electrons in a periodic potential: Bloch's theorem and the opening of a gap
    • The periodic potential
    • Bragg reflection of electrons
    • Standing waves and the band gap
    • Bloch's theorem
    • Nearly-free-electron bands and zone schemes
    • The optical absorption edge
    • Validity of the weak-potential picture
    • Summary
    • Problems
  10. Tight binding, band filling and the three kinds of solid
    • Four solids and the atomic limit
    • The tight-binding band
    • Effective mass
    • Two routes to one band structure
    • Band filling per primitive cell
    • Metals, semiconductors and insulators
    • Holes and aluminium's Hall sign
    • The resistivity ladder
    • Summary
    • Problems
  11. Homogeneous semiconductors: counting carriers, doping and mobility
    • Band-edge density of states
    • Chemical potential and carrier densities
    • The law of mass action
    • Donors and acceptors
    • Doped carrier densities
    • Freeze-out, extrinsic and intrinsic regimes
    • Mobility
    • Semiconductor conductivity
    • Summary
    • Problems
  12. The junction: diodes, transistors, lamps and solar cells
    • The depletion region
    • The built-in voltage
    • Depletion width and field
    • The diode equation
    • The transistor as a controlled barrier
    • Light-emitting diodes
    • Photodiodes and solar cells
    • Summary
    • Problems
  13. Real crystals: vacancies, dislocations and the strength of metals
    • Point defects in a real crystal
    • The equilibrium vacancy concentration
    • Vacancy diffusion as a random walk
    • The theoretical shear strength
    • The edge dislocation
    • Hardening mechanisms in metals
    • Defect scattering of electrons
    • Summary
    • Problems
  14. Soft matter: when entropy, not bonding, sets the structure
    • Rubber bands and the thermal energy scale
    • A polymer chain as a random walk
    • The entropic spring
    • The rubber modulus
    • Brownian motion of colloids
    • Hard-sphere crystallisation
    • Liquid crystals and self-assembly
    • Summary
    • Problems