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Partition Coefficients

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Geochemical Thermodynamics Trace Element Geochemistry→→Mantle Geochemistry REE Patterns in Geochemistry

partition-coefficients Kd crystal-melt-partitioning mineral-chemistry

Core Idea

The partition coefficient (D or Kd) quantifies how a trace element distributes between a mineral and a coexisting melt or fluid: D = C_mineral / C_melt. D depends on the element's ionic radius and charge (compatibility with the crystal site), the mineral's crystal structure, melt composition, temperature, and pressure. Elements whose ionic radius and charge match an available crystal site have high D (compatible); mismatches produce low D (incompatible). The bulk partition coefficient for a rock (D-bulk) is the weighted average of mineral D values, weighted by the modal abundance of each mineral. D-bulk controls whether an element is enriched or depleted during partial melting and fractional crystallization, making it the key parameter linking mantle mineralogy to magma composition.

Explainer

Partition coefficients are the quantitative link between crystal chemistry and magma geochemistry. They encode, in a single number per element-mineral pair, whether and how strongly an element is incorporated into a crystal structure during magmatic processes.

The physical basis is crystal-chemical. Each mineral has specific crystallographic sites with defined sizes and charges. An element with the right ionic radius and charge for a site enters readily (high D). The lattice strain model formalizes this: D for an element depends on the strain energy penalty for fitting a foreign ion into the site. Elements whose radius matches the site's ideal radius have the highest D; elements too large or too small have exponentially decreasing D. This produces the characteristic parabolic D pattern when plotted against ionic radius -- the basis for predicting D values for elements without experimental data.

In practice, D values are determined experimentally (equilibrating mineral and melt at controlled T-P-X and analyzing both) or empirically (from natural mineral-glass pairs in volcanic rocks). The most important datasets for igneous petrology cover olivine, clinopyroxene, orthopyroxene, garnet, plagioclase, spinel, and amphibole in basaltic to rhyolitic melts. These values populate the melting and crystallization models (batch melting, fractional melting, Rayleigh fractionation) that predict how trace element concentrations evolve during magma genesis and differentiation.

The sensitivity of melt composition to source mineralogy, through D-bulk, is what makes trace elements such powerful probes of mantle processes. The presence or absence of garnet in the mantle source (controlled by pressure/depth) completely changes the HREE behavior and produces diagnostic REE slope differences between shallow and deep-derived magmas. Similarly, the presence of residual amphibole, phlogopite, or accessory phases (rutile, apatite, zircon) selectively retains specific elements, creating the characteristic depletion patterns that fingerprint source mineralogy and tectonic setting.

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 → Trace Element Geochemistry → Partition Coefficients

Longest path: 186 steps · 1065 total prerequisite topics

Prerequisites (2)

Trace Element Geochemistryhard Geochemical Thermodynamicshard

Leads To (2)

Mantle Geochemistryhard REE Patterns in Geochemistryhard