Solid-state chemistry — structural and electronic chemistry of bulk crystalline (and amorphous) materials, distinct from materials-science [L2] at the molecular-level grain. Foundations: crystallography applied at the chemical level — 14…
solid-state-chemistry
Bragg diffraction: n λ = 2 d sin θ (Bragg & Bragg 1913)
Foundational framework of solid-state chemistry: Bragg's law (Bragg & Bragg 1913, Nobel 1915) relates diffraction angles to crystal plane…
Madelung sum: M = Σ_shells (±n_k / r_k) for ionic-solid cohesive energy
Framework for ionic-solid cohesive-energy computation: the Madelung sum M (Madelung 1918) gives the per-ion-pair electrostatic energy of an…
Born-Haber cycle: Hess's law applied to ionic-solid formation enthalpies
Framework for ionic-solid lattice-energy determination: the Born-Haber cycle (Born & Haber 1919) applies Hess's law to the formation of an…
Bragg: n=1, λ=d ⇒ sin θ = 1/2, θ = π/6 (canonical first-order reflection)
Sympy-exact symbolic witness of Bragg's law evaluated at the canonical first-order reflection with λ = d — the textbook anchor for…
NaCl 4-shell partial Madelung sum: -8√3/3 - 3 + 6√2 (sympy canonical)
Sympy-exact symbolic witness of the first four coordination shells of the NaCl Madelung sum. Setup (Na⁺ at origin): Shell 1 — 6 Cl⁻ at…
Born-Haber NaCl: U_lattice = -787 kJ/mol (ΔH_f = -410 closure)
Sympy-exact symbolic witness of the Born-Haber-cycle closure for NaCl: solve for U_lattice from experimental step enthalpies. Inputs…
Brillouin zone & reciprocal lattice
Brillouin 1930: first Brillouin zone is the Wigner-Seitz cell of the reciprocal lattice; k-points within are the unique-momenta describing…
Tight-binding model
Slater-Koster 1954 / Mehl-Papaconstantopoulos 1996: linear combination of atomic orbitals (LCAO) with hopping-integral t between neighbours…
Defect chemistry (Kröger-Vink)
Kröger-Vink 1956 notation: V_M^x for vacancy at M-site with charge x; M_M for occupied; M_M• for charge-compensated. Defect-equilibria…
Ionic conductivity & superionic conductors
Faraday 1837 first ionic-conductors (Ag₂S); modern superionics (β-alumina Na+, AgI, Li₇La₃Zr₂O₁₂ garnet, Li₆PS₅Cl argyrodite). Arrhenius…
Perovskite Goldschmidt tolerance factor
Goldschmidt 1926: tolerance factor t = (r_A + r_O)/[√2(r_B + r_O)] predicts ABO₃ perovskite formability. t ≈ 1: cubic stable; 0.9 < t < 1:…
Reciprocal lattice & X-ray diffraction
Ewald 1913 reciprocal-lattice: lattice vectors b_i = 2π (a_j × a_k)/V form dual to direct lattice. Bragg condition Δk = G satisfied when…
Perovskite ABX3 (Goldschmidt 1926)
V M Goldschmidt 1926 tolerance factor t = (r_A + r_X)/sqrt(2)(r_B + r_X); 0.8 < t < 1.0 cubic perovskite; basis of CaTiO3 to MAPbI3 PSC…
Intercalation (Whittingham 1976)
M Whittingham 1976 + Goodenough 1980 LiCoO2 + Yoshino 1985 graphite anode (Nobel 2019); modern LiFePO4 + NMC811; basis of Li-ion battery…
Zeolite adsorption (Mobil ZSM-5)
Mobil 1975 ZSM-5 + Si/Al ratio + acid-site engineering; methanol-to-gasoline + FCC catalyst; modern hierarchical zeolite + chiral framework…
Solid-state Li/Na electrolyte
Yao-Kummer 1967 Na-beta-alumina; modern Li7La3Zr2O12 garnet (Murugan 2007); Li10GeP2S12 (Kanno 2011) sigma_Li ~ 10^-2 S/cm; basis of…
Bio-inspired layered (nacre)
Aksay-Sarikaya 1990s nacre-inspired aragonite-chitin; modern self-assembled Bouligand layered composites; record fracture-toughness 4-fold…
TI Bi2Se3 / Bi2Te3 (Zhang-Hasan 2009)
Zhang 2009 Bi2Se3 single-Dirac-cone surface state; Hasan 2009 ARPES validation; bulk-edge correspondence Z2 invariant; modern QSH device…
Hume-Rothery rules (1925)
W Hume-Rothery 1925 alloy-rules size + valence + electronegativity; modern Goldschmidt + perovskite-tolerance high-throughput.
Hägg interstitial (1935)
G Hägg 1935 interstitial-compounds; modern carbide / nitride-superhard / refractory-alloy + binary-superconductors HfNbCN.
Zintl-Klemm (1939)
E Zintl 1939 + W Klemm 1958 Zintl-electron-counting; modern thermoelectrics-Mg2Si + skutterudite + topological-insulator predictions.
CMR (Jonker-vanSanten 1950)
G Jonker-J van Santen 1950 + Wollan-Koehler 1955 colossal-magnetoresistance La1-xCax MnO3; modern double-exchange Zener.
HTSC (Bednorz-Müller 1986)
K Bednorz-A Müller 1986 (Nobel 1987) cuprate-30K Tc; modern YBa2Cu3O7 90K + Hg-cuprate 138K + room-T H3S 203K Drozdov 2015.
Graphene (Novoselov-Geim 2004)
K Novoselov-A Geim 2004 (Nobel 2010) mechanically-exfoliated graphene; modern twisted-bilayer Cao 2018 magic-angle SC.
Born-Lande equation U_lattice = -N_A M z+ z- e^2 / (4 pi eps_0 r_0) (1 - 1/n)
Born-Lande equation (Born-Lande 1918 *Verh Dtsch Phys Ges* 20, 210) is the closed-form prediction of the lattice energy U_latt of an ionic…