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Metamorphic Equilibrium and Phase Diagrams

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Gibbs Free EnergyMetamorphic Rocks+6 moreThermobarometry: Estimating Pressure and Temperature from Minerals
metamorphism phase-diagram equilibrium pressure-temperature

Core Idea

Mineral assemblages in metamorphic rocks reflect equilibrium at specific pressure-temperature (P-T) conditions. Phase diagrams show which minerals are stable at different P-T; mineral boundaries define metamorphic facies. Comparing observed minerals to phase diagrams reveals the P-T path rocks followed during metamorphism.

Explainer

From your study of metamorphic rocks, you know that pre-existing rocks transform when subjected to elevated temperature and pressure, producing new mineral assemblages and textures. From thermodynamics, you know that Gibbs free energy determines which phase is stable at given conditions, and from phase diagrams, you know how to read stability fields separated by reaction boundaries. Metamorphic phase diagrams bring these concepts together: they map out which mineral assemblages are thermodynamically stable at each combination of pressure and temperature, turning a metamorphic rock into a recorder of the conditions it experienced.

The fundamental principle is chemical equilibrium. At any given P-T condition, the mineral assemblage with the lowest total Gibbs free energy is the one that should form, given enough time and sufficient atomic mobility. A boundary line on a P-T diagram represents a reaction — say, the transformation of kyanite to sillimanite — where both phases have equal free energy. Cross that boundary, and one phase becomes unstable while the other becomes favored. In practice, metamorphic rocks contain multiple minerals whose mutual stability fields overlap, and identifying which combination of minerals coexists allows you to locate the rock's conditions within a specific region of P-T space. These regions are called metamorphic facies: greenschist facies (low-moderate T, low-moderate P), amphibolite facies (moderate-high T, moderate P), granulite facies (high T), blueschist facies (low T, high P), and so on. Each facies name tells an experienced geologist approximately where in P-T space the rock equilibrated.

The real power of this approach emerges when you consider that metamorphic rocks often preserve evidence of *changing* conditions — not just a single P-T point. As a rock is buried during mountain building, heated, and eventually exhumed, it passes through different stability fields. Early-formed minerals may be preserved as inclusions inside later-grown crystals, or reaction rims may develop around minerals that became unstable. By identifying these textural relationships and matching each mineral assemblage to its stability field on a phase diagram, petrologists reconstruct the rock's P-T path — the trajectory it followed through pressure-temperature space over millions of years. A path that shows increasing pressure followed by increasing temperature (a clockwise loop in P-T space) tells a story of burial followed by heating, characteristic of continental collision. A path showing high pressure at low temperature (upper-left region of the diagram) indicates subduction.

One important caveat: equilibrium is an idealization. Real metamorphic reactions require activation energy, fluid catalysts, and time. Some minerals persist metastably outside their stability fields because the reaction kinetics are too slow — this is why diamonds, which are only stable at mantle pressures, survive at Earth's surface. The art of metamorphic petrology lies in recognizing which minerals achieved equilibrium and which are metastable relics, and using that judgment to extract reliable P-T estimates from the phase diagram framework.

Practice Questions 5 questions

Prerequisite Chain

Understanding ZeroThe Number ZeroCounting to FiveCounting to 10Counting to 20Counting a Set of Objects Up to 20Cardinality: The Last Number CountedMatching Numerals to QuantitiesSubitizing Small QuantitiesAddition Within 10Number Bonds to 10Addition Within 20Doubles and Near DoublesDoubles Facts Within 10Near Doubles Facts Within 20Mental Math Strategies for AdditionMental Math: Adding and Subtracting TensAddition Within 100Repeated Addition as MultiplicationMultiplication as Equal GroupsMultiplication: ArraysBasic Multiplication Facts (0s, 1s, 2s, 5s, 10s)Multiplication Facts Within 100Division as Equal SharingDivision as Grouping (Measurement Division)Division: Grouping (Repeated Subtraction) ModelDivision: Fair Sharing ModelDivision as Equal SharingDivision as GroupingBasic Division FactsDivision Facts Within 100Multiplication and Division Fact FamiliesRelationship Between Multiplication and DivisionDivision Facts as Inverse of MultiplicationRemainders and Quotients in DivisionDivision Word ProblemsMulti-Step Word ProblemsSolving Multi-Step Word ProblemsMultiplication Word ProblemsDivision Word ProblemsIntroduction to Long DivisionFactors and MultiplesPrime and Composite NumbersEquivalent FractionsRelating Fractions and DecimalsDecimal Place ValueIntegers and the Number LineComparing and Ordering IntegersAbsolute ValueAdding IntegersSubtracting IntegersMultiplying IntegersDividing IntegersUnit RatesProportionsPercent ConceptConverting Between Fractions, Decimals, and PercentsOperations with Rational NumbersTwo-Step EquationsSolving Multi-Step EquationsEquations with Variables on Both SidesAngle Pairs: Complementary, Supplementary, and VerticalParallel Lines and TransversalsCorresponding AnglesAlternate Interior AnglesTriangle Angle Sum TheoremExterior Angle TheoremTriangle Inequality TheoremSimilar Triangles: AA SimilaritySimilar Triangles: SSS and SAS SimilarityProportions in Similar TrianglesRight Triangle Trigonometry IntroductionSine, Cosine, and Tangent RatiosTrigonometric Ratios ReviewRadian MeasureConverting Between Degrees and RadiansThe Unit CircleGraphing Sine and CosineGraphing Tangent and Reciprocal Trigonometric FunctionsDerivatives of Trigonometric FunctionsAntiderivativesIndefinite IntegralsBasic Integration RulesRiemann SumsDefinite Integral DefinitionDouble Integrals: Definition and SetupIterated Integrals and Fubini's TheoremDouble Integrals over Rectangular RegionsDouble Integrals over General RegionsApplications of Double Integrals: Area, Mass, and MomentsTriple Integrals in Cartesian CoordinatesTriple Integrals in Cylindrical and Spherical CoordinatesChange of Variables and the Jacobian DeterminantApplications of Triple Integrals: Volume and MassVector Fields and Their RepresentationsLine Integrals of Vector FieldsWork and CirculationLine Integrals of Scalar and Vector FunctionsFundamental Theorem for Line IntegralsConservative Vector FieldsConservative Vector Fields and Potential FunctionsCurl and Divergence of Vector FieldsCurl and DivergenceDivergence TheoremElectric Flux and Divergence TheoremGauss's Law: Integral Form and MeaningSolving Problems with Gauss's LawConductors in Electrostatic EquilibriumCapacitance and CapacitorsDielectricsDielectric Constant and Relative PermittivityElectric Field Inside Dielectric MaterialsDielectric Materials and PolarizationDielectric Susceptibility and PermittivityEnergy Density in Electric FieldsElectric Current and Current DensityElectrical Resistance and ResistivityOhm's Law and Circuit ElementsElectromotive Force (EMF) and BatteriesKirchhoff's Circuit Laws: Voltage and CurrentDC Circuit Network Analysis MethodsTransient Response in RC CircuitsRC CircuitsLC and RLC CircuitsAC Circuits: FundamentalsImpedance and ReactanceAC Power and ResonanceElectromagnetic WavesPostulates of Special RelativityTime DilationLength ContractionLorentz TransformationRelativistic Velocity AdditionRelativistic Momentum and EnergyMass-Energy Equivalence and E=mc²Photons as Particles with Energy and MomentumPlanck-Einstein Relation: Energy and FrequencyPhotoelectric EffectThe Photon: Light as QuantaCompton ScatteringWave-Particle Dualityde Broglie WavelengthThe Schrödinger EquationState Vectors and WavefunctionsQuantum SuperpositionQuantum EntanglementBell Theorem and Bell InequalitiesPostulates of Quantum MechanicsObservables and Quantum OperatorsCommutators and Commutation RelationsQuantum Angular MomentumQuantum Mechanical Treatment of HydrogenSolving the Schrödinger Equation for Hydrogen AtomQuantum NumbersElectron ConfigurationPeriodic TrendsCovalent BondingElectronegativity and Bond PolarityIonic BondingLewis StructuresVSEPR Theory and Molecular GeometryMolecular Geometry and Electron Pair GeometryMolecular Polarity and Dipole MomentsIntermolecular ForcesStates of Matter and Phase Changes: Melting, Boiling, and SublimationGas Laws and the Ideal Gas EquationGas Stoichiometry and Volume-Volume CalculationsThermochemistry and EnthalpyHeat Capacity and CalorimetryEntropy and Molecular DisorderSpontaneity and ΔGEntropy and Gibbs Free EnergyChemical EquilibriumStatistical Mechanics: Ensembles and the Boltzmann DistributionPartition Function: Definition and PropertiesThe Canonical Partition Function and Thermodynamic DerivationFree Energy and Thermodynamic Relations from Partition FunctionsLegendre Transformations and Thermodynamic PotentialsChemical Potential and Partial Molar PropertiesPhase Equilibrium and Coexistence ConditionsClausius-Clapeyron EquationPhase Diagrams and Phase BoundariesIgneous RocksMetamorphic RocksMetamorphic Equilibrium and Phase Diagrams

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