Geochemistry — IUPAC-VII applied chemistry at the rock/mineral/fluid grain. Foundations: radiometric decay N(t) = N_0·exp(−λt), half-life t_{1/2} = ln 2 / λ (Rutherford 1900, Holmes 1913) underwrites all isotope geochronology. U-Pb…
geochemistry
N(t) = N₀·exp(−λt); t_{1/2} = ln 2 / λ (universal isotope clock)
Radiometric decay (Rutherford 1900; Holmes 1913 applied it to zircon for the first radiometric geochronology). The number of un-decayed…
K_D = C_s / C_l; 2-phase mass-bal: C_l = X_tot/(F·K_D + 1−F)
Nernst partition coefficient: equilibrium solid/liquid distribution of a trace element between a mineral and its coexisting melt (or…
k = A·exp(−Ea/RT); ln(k₂/k₁) = (Ea/R)·(T₂−T₁)/(T₁T₂)
Arrhenius rate law (Arrhenius 1889): the temperature-dependence of a first-order rate constant k(T) = A·exp(−E_a/RT) where A is the…
N(t_{1/2})/N₀ = 1/2; with λ=ln 2, t=1 ⇒ ratio = 1/2 exactly
Sympy-exact witness of the half-life defining identity. Setup: N(t) = N₀·exp(−λt); at t = ln 2 / λ the exponent is −ln 2 exactly, giving…
R/R₀ = f^{α−1}: at f=1 ⇒ 1; at α=1 ⇒ 1 (no-fractionation limits)
Sympy-exact witness of the Rayleigh fractionation law at the two no-fractionation limits. Setup: R/R₀ = f^{α−1}, where R is the…
C_l = X_tot/(F·K_D + 1−F); at F=0 ⇒ X_tot; at F=1 ⇒ X_tot/K_D
Sympy-exact witness of the two-phase Nernst mass-balance formula at its all-liquid and all-solid limits. Setup: C_l(F, K_D) = X_tot /…
Rb-Sr isochron framework: (⁸⁷Sr/⁸⁶Sr) = (⁸⁷Sr/⁸⁶Sr)₀ + (⁸⁷Rb/⁸⁶Sr)·(e^{λt} − 1)
The Rb-Sr isochron dating framework — arguably the single most important geochronometric tool for Precambrian rocks and meteorites, derived…
δ-notation framework: δ = (R_sample/R_std − 1)·1000 ‰ (parts-per-mille isotope-ratio deviation)
The δ-notation — the universal convention for reporting light stable-isotope ratios in geochemistry, paleoclimate, and cosmochemistry. …
Goldschmidt framework: lithophile / siderophile / chalcophile / atmophile partitioning (silicate/metal/sulfide/gas affinity)
The Goldschmidt (1937) geochemical-classification framework — a periodic-table-wide empirical taxonomy assigning each element to one of…
Rb-Sr slope: m = e^{λt} − 1; m|_{λt small} ≈ λt; m|_{t = t_{1/2}} = 1
Sympy-exact witness of the Rb-Sr isochron slope formula and its two canonical regime limits. Setup: λ (decay constant) and t (age)…
δ = 1000·R_s/R_std − 1000; δ|_{R=R_std} = 0 ‰; δ|_{R=2R_std} = 1000 ‰
Sympy-exact witness of the δ-notation definition and its two calibration anchors. Setup: R_s (sample isotope ratio) and R_std (standard…
Goldschmidt flags: Na lithophile (1), Na siderophile (0), Fe siderophile (1), S chalcophile (1)
Sympy-exact (Integer-valued) witness of the Goldschmidt classification flags for four canonical textbook elements. Setup: each flag is…
Isotope fractionation (Urey 1947)
H Urey 1947 (Nobel 1934) isotope-fractionation factor alpha = (R_A/R_B)_eq; delta-notation 1000(R/R_std - 1); paleothermometry from…
Radiocarbon dating (Libby 1949)
W Libby 1949 (Nobel 1960) C-14 half-life 5730 yr; AMS 1980s 100x sensitivity; calibration via dendro + IntCal20; resolution ~50 yr in last…
REE patterns (McDonough-Sun 1995)
McDonough-Sun 1995 chondrite-normalized REE 'spider plots'; Eu anomaly = plagioclase fractionation; Ce anomaly = redox; basis of…
Bowen reaction series (1928)
N L Bowen 1928 reaction series: olivine -> pyroxene -> amphibole -> biotite (discontinuous); plagioclase Ca->Na (continuous); explains…
Clay CEC (Grim 1953)
R Grim 1953 clay-mineralogy: smectite CEC 80-150 vs kaolinite 3-15 meq/100g; tetrahedral + octahedral substitution; basis of soil-fertility…
Conservative tracers (Broecker 1974)
W Broecker 1974 Sr-86/87 + Nd-143/144 + delta-13C ocean tracers; thermohaline-circulation reconstruction; LGM AMOC slowdown documented via…
U-Pb zircon (Tilton 1955)
G Tilton 1955 U-Pb concordia; modern SHRIMP / LA-ICP-MS spot-dating + 4.4Ga oldest-zircon Wilde-2001 Jack-Hills.
Ar-Ar dating (Merrihue 1966)
C Merrihue-G Turner 1966 40Ar/39Ar; modern step-heating + furnace + laser-microprobe high-precision absolute ages.
Isotope fractionation (Urey detail)
H Urey 1947 (Nobel 1934) isotope-fractionation factor α; modern paleothermometry δ18O ocean-temperature reconstruction.
Clumped isotopes (Eiler 2007)
J Eiler 2007 Δ47 carbonate-clumped-isotope thermometry; modern paleoclimate + paleoaltimetry + diagenesis fingerprinting.
REE Eu-Ce anomaly (Goldschmidt 1937)
V Goldschmidt 1937 + Allegre 1968 Eu/Eu* + Ce/Ce* anomalies; modern oxidation-state proxy + crust-mantle differentiation.
Nd depleted-mantle (DePaolo 1981)
D DePaolo 1981 ε_Nd depleted-mantle reservoir; modern crust-mantle-recycling + Hf-Nd dual-isotope source-tracing.