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Mineral Stability and Phase Diagrams

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Geochemical Thermodynamics→→Mantle Geochemistry Weathering and Soil Chemistry

Core Idea

Phase diagrams map the stability fields of minerals and mineral assemblages as functions of temperature, pressure, and composition. Each region of the diagram represents conditions where a specific mineral or assemblage has the lowest Gibbs free energy and is therefore thermodynamically stable. Boundaries between fields represent conditions where two assemblages coexist in equilibrium (univariant reactions). The Clausius-Clapeyron equation (dP/dT = delta-S/delta-V) governs the slope of these boundaries. Phase diagrams are the primary tool for interpreting metamorphic grade, predicting magmatic crystallization sequences, and understanding the mineralogical structure of Earth's interior.

Explainer

Phase diagrams are to geochemists what circuit diagrams are to electrical engineers -- they encode the fundamental constraints governing the system's behavior into a visual map. Reading a phase diagram means understanding what minerals exist under what conditions and what happens when conditions change.

The thermodynamic foundation is simple: at any given T-P-X condition, the stable assemblage is the one with the lowest total Gibbs free energy. Phase boundaries are the T-P loci where two assemblages have equal free energy. The Gibbs phase rule (F = C - P + 2) determines how many intensive variables (T, P, composition) can be independently varied while maintaining the observed assemblage. A divariant field (F=2) allows both T and P to change freely. A univariant line (F=1) constrains one variable once the other is fixed. An invariant point (F=0) fixes both T and P -- these are the diagnostic triple points or reaction intersections that calibrate geothermometers and geobarometers.

P-T diagrams are most commonly used for metamorphic petrology. A rock's mineral assemblage records the P-T conditions where it last equilibrated, and the sequence of mineral reactions (preserved as inclusion textures, reaction rims, and pseudomorphs) traces the rock's P-T path through time. Clockwise P-T paths (burial, heating, then exhumation) characterize collision zones; counterclockwise paths characterize contact metamorphism. These P-T paths, reconstructed from phase diagrams, constrain tectonic models.

T-X (temperature-composition) diagrams govern igneous crystallization. Binary and ternary phase diagrams predict the sequence of minerals that crystallize from a cooling magma: which mineral appears first, how compositions evolve with cooling (fractional crystallization), and what happens at eutectic and peritectic points. The lever rule quantifies the proportions of solid and liquid at any temperature. These diagrams explain why basalts and granites have characteristic mineral assemblages and why fractional crystallization produces compositional diversity in igneous suites.

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 → Mineral Stability and Phase Diagrams

Longest path: 185 steps · 1064 total prerequisite topics

Prerequisites (1)

Geochemical Thermodynamicshard

Leads To (2)

Mantle Geochemistrysoft Weathering and Soil Chemistrysoft