Structure and properties of condensed matter: crystal structure, unit cells, defects, band theory, semiconductors, and the amorphous/crystalline divide. Sits at the L1/L2 boundary between condensed-matter physics and solid-state chemistry.
materials-science
Crystal structure
Long-range periodic arrangement of atoms/ions in a solid described by a Bravais lattice plus a basis. The 14 Bravais lattices span 7…
Unit cell
Smallest repeating parallelepiped that, when tiled through space, reproduces the full crystal. Specified by six lattice parameters (a, b,…
Crystal defect
Deviation from the ideal periodic crystal: point defects (vacancies, interstitials, substitutions), line defects (dislocations), and planar…
Band theory of solids
Quantum-mechanical description of electrons in a periodic potential (Bloch's theorem): the discrete atomic levels broaden into continuous…
Semiconductor
Material with a small band gap (≲ 3 eV) such that thermal or optical excitation promotes electrons from the valence to the conduction band,…
Amorphous solid
Solid lacking long-range order but retaining short-range coordination. Includes glasses (SiO₂, metallic glasses), amorphous semiconductors…
Phonon
Quantised collective vibrational mode of a crystal lattice. Carries heat (thermal conductivity), couples to electrons (mediating…
X-ray diffraction pattern
Discrete Bragg-peak pattern produced when X-rays scatter off the periodic electron density of a crystal. The angular positions of the peaks…
Debye T³ law for specific heat
Low-temperature specific heat of a crystalline solid scales as C_V ∝ T³. Measurement yields the Debye temperature θ_D, which characterises…
Superconductor
Material with zero DC electrical resistance and complete Meissner-effect expulsion of magnetic flux below a critical temperature T_c.…
Ferromagnet
Material in which exchange coupling aligns atomic magnetic moments to give a spontaneous net magnetisation below the Curie temperature T_C.…
Piezoelectric material
Crystal without inversion symmetry in which mechanical strain produces a proportional electric polarisation (direct effect) and vice versa…
Ceramic materials
Inorganic non-metallic crystalline/amorphous solids: oxides (Al₂O₃, ZrO₂), carbides (SiC, B₄C), nitrides (Si₃N₄, BN). High Tm, hardness,…
Silicate glass
Amorphous SiO₂ network with Na⁺/Ca²⁺ modifiers (soda-lime glass). Zachariasen continuous random network. Chemical strengthening via…
Composite materials
Matrix (polymer/metal/ceramic) + reinforcement (fiber/particulate). CFRP (aerospace), GFRP (wind blades), concrete (largest by mass). Rule…
Metallic glasses (amorphous alloys)
Disordered metal alloys quenched past Tg; bulk metallic glasses (Vitreloy Zr-Ti-Cu-Ni-Be). High strength + elasticity; no grain boundaries.
2D materials (graphene, TMDs, hBN)
Atomically-thin layers: graphene (Dirac fermions, Geim-Novoselov Nobel 2010), MoS₂/WSe₂ (semiconducting), hBN (insulator). Van der Waals…
Grain boundaries & Hall–Petch
σ_y = σ₀ + k/√d; smaller grains → stronger material; inverse Hall-Petch below ~10 nm grain size.
Dislocations & Peierls–Nabarro stress
Edge, screw dislocations; Burgers vector b; Peierls stress τ = (2μ/(1-ν)) exp(-2πa/b(1-ν)); plastic deformation origin.
Martensitic transformation
Diffusionless shear transformation; steel Fe-C austenite→martensite on quench; shape-memory alloys (NiTi).
Shape memory & superelastic alloys
Martensitic transformation reversible thermally/mechanically; Nitinol 8% recoverable strain; medical stents, actuators.
Toughening of ceramics
Phase-transformation (Y-stabilized ZrO₂), microcracking, fiber pullout, layering; K_IC from 3 to 20 MPa·m^(1/2).
Composite rule of mixtures
E_c = V_f E_f + V_m E_m (parallel Voigt); 1/E_c = V_f/E_f + V_m/E_m (series Reuss); bounds on elastic modulus.
High-entropy alloys (HEAs)
≥5 principal elements in near-equiatomic; entropy stabilizes simple SS; exceptional strength/ductility combos; CrMnFeCoNi.
Metal-organic frameworks (MOFs)
Metal nodes + organic linkers; porous crystalline networks with SA up to 7000 m²/g; H₂/CO₂ storage, catalysis.
Covalent organic frameworks (COFs)
All-covalent porous crystalline networks via dynamic covalent chemistry; tunable bandgaps; organic MOF analogs.
Zeolites & molecular sieves
Aluminosilicate microporous crystals; acid sites, shape selectivity; ZSM-5 in petrochem; 200+ frameworks.
2D materials (TMDs, h-BN, phosphorene)
MoS₂, WSe₂ semiconducting; h-BN insulator; black phosphorus; heterostructures; Moiré physics in twisted bilayers.
Perovskite solar cells
ABX₃ hybrid (CH₃NH₃PbI₃) PCE >25%; tunable bandgap; tandem with Si; stability and lead-toxicity challenges.
Quantum dots (CdSe, PbS) & excitons
Size-tunable bandgap via quantum confinement; λ_emission ∝ R²; QLED displays, biomedical imaging; 2023 Nobel.
Thermoelectric figure of merit ZT
Thermoelectric figure of merit ZT = S^2 sigma T / kappa, where S is Seebeck coefficient, sigma electrical conductivity, T absolute…
Additive manufacturing (SLM/EBM)
Selective laser/electron-beam melting of metal powders; rapid solidification, residual stresses; aerospace alloys.