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Ar-Ar Dating

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Geochemical Thermodynamics→
Ar-Ar K-Ar geochronology thermochronology step-heating

Core Idea

The 40Ar/39Ar method is a refined version of K-Ar dating where the sample is irradiated with neutrons to convert 39K to 39Ar, enabling measurement of both parent and daughter isotopes on the same aliquot by mass spectrometry. Step-heating (incrementally increasing temperature) releases argon from different crystallographic sites, producing an age spectrum that reveals the sample's thermal history. A flat (plateau) age spectrum indicates a single undisturbed cooling age. Disturbed spectra with young edges and old cores record partial argon loss during thermal events. The method dates cooling through the closure temperature of the mineral analyzed (K-feldspar ~150-350 C, biotite ~300 C, hornblende ~500 C, muscovite ~350 C), making it a thermochronometer that records when a rock cooled through specific temperatures.

Explainer

The Ar-Ar method improved upon K-Ar dating by measuring the parent (K, via proxy 39Ar) and daughter (40Ar) on the same aliquot, eliminating the need for separate K concentration analysis and the assumption of sample homogeneity. The neutron irradiation that converts a known fraction of 39K to 39Ar is the key innovation -- it turns a two-aliquot measurement into a single-aliquot isotope ratio measurement.

The step-heating technique extracts argon at progressively higher temperatures, exploiting the fact that argon in different crystallographic sites has different retentivity. Loosely held argon (from grain boundaries, fluid inclusions, or partially disturbed zones) is released at low temperatures; argon from the intact crystal lattice is released at high temperatures. Plotting apparent age versus cumulative 39Ar fraction produces an age spectrum. A plateau -- a series of contiguous steps with statistically indistinguishable ages comprising >50% of the total 39Ar -- provides a robust age estimate.

The concept of closure temperature (Tc) is central. As a mineral cools, it transitions from a state where argon diffuses freely out of the crystal (open system, no age accumulation) to a state where argon is quantitatively retained (closed system, age accumulates). The closure temperature depends on the mineral's crystal structure, grain size, and cooling rate. Hornblende (Tc ~500 C) closes at higher temperature than muscovite (~350 C) or biotite (~300 C) or K-feldspar (~150-350 C). Dating multiple minerals from the same sample provides a cooling history -- a series of time-temperature points that define the cooling path.

Applications span tectonic studies (timing of metamorphism, exhumation, faulting), volcanology (eruption ages), extraterrestrial chronology (ages of meteorites and lunar rocks), and paleomagnetic calibration (dating lava flows for the geomagnetic polarity time scale). The method works from ~100 ka (young volcanic rocks with very little radiogenic 40Ar) to the age of the solar system (~4.56 Ga), making it one of the most versatile geochronological tools available.

Practice Questions 3 questions

Prerequisite Chain

Understanding Zero → The Number Zero → Counting to Five → Counting to 10 → Counting to 20 → Counting a Set of Objects Up to 20 → Cardinality: The Last Number Counted → Matching Numerals to Quantities → Subitizing Small Quantities → Addition Within 10 → Number Bonds to 10 → Addition Within 20 → Doubles and Near Doubles → Doubles Facts Within 10 → Near Doubles Facts Within 20 → Mental Math Strategies for Addition → Mental Math: Adding and Subtracting Tens → Addition Within 100 → Repeated Addition as Multiplication → Multiplication as Equal Groups → Multiplication: Arrays → Basic Multiplication Facts (0s, 1s, 2s, 5s, 10s) → Multiplication Facts Within 100 → Division as Equal Sharing → Division as Grouping (Measurement Division) → Division: Grouping (Repeated Subtraction) Model → Division: Fair Sharing Model → Division as Equal Sharing → Division as Grouping → Basic Division Facts → Division Facts Within 100 → Multiplication and Division Fact Families → Relationship Between Multiplication and Division → Division Facts as Inverse of Multiplication → Remainders and Quotients in Division → Division Word Problems → Multi-Step Word Problems → Solving Multi-Step Word Problems → Multiplication Word Problems → Division Word Problems → Introduction to Long Division → Factors and Multiples → Prime and Composite Numbers → Equivalent Fractions → Relating Fractions and Decimals → Decimal Place Value → Integers and the Number Line → Comparing and Ordering Integers → Absolute Value → Adding Integers → Subtracting Integers → Multiplying Integers → Dividing Integers → Unit Rates → Proportions → Percent Concept → Converting Between Fractions, Decimals, and Percents → Operations with Rational Numbers → Two-Step Equations → Solving Multi-Step Equations → Equations with Variables on Both Sides → Angle Pairs: Complementary, Supplementary, and Vertical → Parallel Lines and Transversals → Corresponding Angles → Alternate Interior Angles → Triangle Angle Sum Theorem → Exterior Angle Theorem → Triangle Inequality Theorem → Similar Triangles: AA Similarity → Similar Triangles: SSS and SAS Similarity → Proportions in Similar Triangles → Right Triangle Trigonometry Introduction → Sine, Cosine, and Tangent Ratios → Trigonometric Ratios Review → Radian Measure → Converting Between Degrees and Radians → The Unit Circle → Graphing Sine and Cosine → Graphing Tangent and Reciprocal Trigonometric Functions → Derivatives of Trigonometric Functions → Antiderivatives → Indefinite Integrals → Basic Integration Rules → Riemann Sums → Definite Integral Definition → Double Integrals: Definition and Setup → Iterated Integrals and Fubini's Theorem → Double Integrals over Rectangular Regions → Double Integrals over General Regions → Applications of Double Integrals: Area, Mass, and Moments → Triple Integrals in Cartesian Coordinates → Triple Integrals in Cylindrical and Spherical Coordinates → Change of Variables and the Jacobian Determinant → Applications of Triple Integrals: Volume and Mass → Vector Fields and Their Representations → Line Integrals of Vector Fields → Work and Circulation → Line Integrals of Scalar and Vector Functions → Fundamental Theorem for Line Integrals → Conservative Vector Fields → Conservative Vector Fields and Potential Functions → Curl and Divergence of Vector Fields → Curl and Divergence → Divergence Theorem → Electric Flux and Divergence Theorem → Gauss's Law: Integral Form and Meaning → Solving Problems with Gauss's Law → Conductors in Electrostatic Equilibrium → Capacitance and Capacitors → Dielectrics → Dielectric Constant and Relative Permittivity → Electric Field Inside Dielectric Materials → Dielectric Materials and Polarization → Dielectric Susceptibility and Permittivity → Energy Density in Electric Fields → Electric Current and Current Density → Electrical Resistance and Resistivity → Ohm's Law and Circuit Elements → Electromotive Force (EMF) and Batteries → Kirchhoff's Circuit Laws: Voltage and Current → DC Circuit Network Analysis Methods → Transient Response in RC Circuits → RC Circuits → LC and RLC Circuits → AC Circuits: Fundamentals → Impedance and Reactance → AC Power and Resonance → Electromagnetic Waves → Postulates of Special Relativity → Time Dilation → Length Contraction → Lorentz Transformation → Relativistic Velocity Addition → Relativistic Momentum and Energy → Mass-Energy Equivalence and E=mc² → Photons as Particles with Energy and Momentum → Planck-Einstein Relation: Energy and Frequency → Photoelectric Effect → The Photon: Light as Quanta → Compton Scattering → Wave-Particle Duality → de Broglie Wavelength → The Schrödinger Equation → State Vectors and Wavefunctions → Quantum Superposition → Quantum Entanglement → Bell Theorem and Bell Inequalities → Postulates of Quantum Mechanics → Observables and Quantum Operators → Commutators and Commutation Relations → Quantum Angular Momentum → Quantum Mechanical Treatment of Hydrogen → Solving the Schrödinger Equation for Hydrogen Atom → Quantum Numbers → Electron Configuration → Periodic Trends → Covalent Bonding → Electronegativity and Bond Polarity → Ionic Bonding → Lewis Structures → VSEPR Theory and Molecular Geometry → Molecular Geometry and Electron Pair Geometry → Molecular Polarity and Dipole Moments → Intermolecular Forces → States of Matter and Phase Changes: Melting, Boiling, and Sublimation → Gas Laws and the Ideal Gas Equation → Gas Stoichiometry and Volume-Volume Calculations → Thermochemistry and Enthalpy → Heat Capacity and Calorimetry → Entropy and Molecular Disorder → Spontaneity and ΔG → Entropy and Gibbs Free Energy → Chemical Equilibrium → Statistical Mechanics: Ensembles and the Boltzmann Distribution → Partition Function: Definition and Properties → The Canonical Partition Function and Thermodynamic Derivation → Free Energy and Thermodynamic Relations from Partition Functions → Legendre Transformations and Thermodynamic Potentials → Chemical Potential and Partial Molar Properties → Phase Equilibrium and Coexistence Conditions → Clausius-Clapeyron Equation → Phase Diagrams and Clausius-Clapeyron Equation → Chemical Potential and Thermodynamic Equilibrium → Geochemical Thermodynamics → Ar-Ar Dating

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