A thin section of a schist shows a garnet porphyroblast containing straight quartz inclusion trails that are continuous with the foliation of the matrix, and the matrix foliation is not deflected around the garnet. What does this show about the timing of garnet growth?

Garnet grew after the main deformation, because the earlier foliation is preserved straight inside it

Garnet grew before the foliation formed, because inclusions are always older than the matrix around them

Garnet grew during the deformation, because the crystal rotated and trapped curved inclusion trails

Garnet grew after the main deformation, because the earlier foliation is preserved straight inside it

Garnet grew before the deformation, because it behaved as a rigid object that the later foliation wrapped around

Which metabasite assemblage indicates metamorphism along a cold, high-pressure subduction-zone path?

glaucophane + lawsonite, the blueschist facies

hornblende + plagioclase, the amphibolite facies

chlorite + actinolite + albite + epidote, the greenschist facies

orthopyroxene + clinopyroxene + plagioclase, the granulite facies

Which of the following statements about paired metamorphic belts are correct?

In Miyashiro's pairs the high-P/low-T belt lies on the oceanward side of the margin

The landward high-T/low-P belt is heated by arc magmatism

In Miyashiro's pairs the high-P/low-T belt lies on the oceanward side of the margin

The landward high-T/low-P belt is heated by arc magmatism

The blueschist belt of a pair lies on the landward side, next to the volcanic arc

Both belts of a pair record the same geothermal gradient but different depths

Which observation would a petrologist take as the best evidence of ultrahigh-temperature metamorphism (above 900 °C) in an Mg–Al-rich granulite?

sapphirine together with quartz in textural equilibrium

coesite inclusions in garnet, which show burial of crust to more than 90 km

sapphirine together with quartz in textural equilibrium

glaucophane and lawsonite in the matrix, which show a very low geothermal gradient

andalusite and cordierite in a spotted schist, which show heating at low pressure

The reaction albite → jadeite + quartz has a negative volume change (ΔV < 0) and a negative entropy change (ΔS < 0). On a P–T diagram with P on the vertical axis, the equilibrium curve therefore

has a positive slope, so jadeite + quartz is the high-pressure assemblage

has a negative slope, because both ΔV and ΔS are negative

is horizontal, because the two changes cancel each other

is vertical, because a solid–solid reaction does not depend on pressure or on volume

has a positive slope, so jadeite + quartz is the high-pressure assemblage

A metapelite, projected from muscovite, quartz and H₂O into the three-component AFM system, shows five AFM minerals (garnet, chlorite, biotite, staurolite and kyanite) in apparent contact in one thin section, in a terrane where P and T change smoothly across the map. Under the mineralogical phase rule the best interpretation is that

the assemblage is not a single equilibrium one, or the rock sits exactly on an invariant condition

five phases are allowed because H₂O and the projection phases add extra degrees of freedom

the rock formed at exactly one invariant point, which is the normal state of pelites across a terrane

the assemblage is not a single equilibrium one, or the rock sits exactly on an invariant condition

kyanite and staurolite count as one phase because both are aluminous silicate minerals of similar density

Which of the following reactions are correctly balanced?

KAl₃Si₃O₁₀(OH)₂ + SiO₂ → KAlSi₃O₈ + Al₂SiO₅ + 2 H₂O (muscovite + quartz → K-feldspar + sillimanite)

NaAlSi₃O₈ → NaAlSi₂O₆ + 2 SiO₂ (albite → jadeite + quartz)

In Barrovian metamorphism of a pelite, the index minerals appear in which order with increasing grade?

chlorite, biotite, garnet, staurolite, kyanite, sillimanite

chlorite, garnet, biotite, staurolite, kyanite, sillimanite

chlorite, biotite, garnet, staurolite, kyanite, sillimanite

biotite, chlorite, garnet, kyanite, staurolite, sillimanite

chlorite, biotite, staurolite, garnet, sillimanite, kyanite

A siliceous marble contains calcite and quartz in contact with a CO₂-rich fluid at a temperature just below that at which wollastonite forms. Water-rich fluid from a cooling pluton then infiltrates the rock without changing T or P. What is the likely effect on the reaction calcite + quartz → wollastonite + CO₂?

It can now proceed at the same T, because diluting CO₂ in the fluid lowers the reaction T

It is driven backwards, because water is a product of the reaction and builds up in the fluid

It is unaffected, because T and P are unchanged and the reactants are both solids of fixed composition

It needs a higher T, because water stabilises calcite and quartz relative to wollastonite and CO₂

A granulite carries an anhydrous high-temperature assemblage to the surface, although hydrous minerals would be stable at the lower temperatures it later passed through. What is the best reason?

Retrograde hydration needs water, and the rock had lost its fluid and melt during prograde metamorphism

Hydrous minerals can never nucleate in a rock that has once reached the granulite facies

Granulites always cool faster than diffusion can act in any mineral, whatever the fluid supply, so no reaction is possible

Granulites have bulk compositions in which hydrous minerals are chemically impossible

Retrograde hydration needs water, and the rock had lost its fluid and melt during prograde metamorphism

Two calibrated reactions in one assemblage have the following changes at the P–T of interest. Reaction X: ΔV = +0.1 cm³/mol and ΔS = +20 J/(mol·K). Reaction Y: ΔV = −7 cm³/mol and ΔS = −35 J/(mol·K). Which statement is correct?

X is a good geothermometer (slope about 200 MPa/K) and Y a good geobarometer (slope about 5 MPa/K)

X is a good geobarometer and Y a good geothermometer, because X has the smaller volume change

X is a good geothermometer (slope about 200 MPa/K) and Y a good geobarometer (slope about 5 MPa/K)

Both are good geobarometers, because both reactions have a nonzero volume change at these conditions

Both are good geothermometers, because both reactions have a nonzero entropy change at these conditions

A garnet in a staurolite–garnet schist has a bell-shaped Mn profile, highest in the core and falling smoothly to the lowest value at the rim, with no rise at the edge. What does this indicate?

Prograde growth zoning, with Mn strongly partitioned into growing garnet and depleted in the matrix

Retrograde resorption of garnet during cooling, which concentrates Mn in a rim around the crystal

Complete homogenisation of the crystal by diffusion at high temperature during peak metamorphism

Prograde growth zoning, with Mn strongly partitioned into growing garnet and depleted in the matrix

Contact metamorphism, because Mn zoning is found only around igneous intrusions and their aureoles

Which of the following statements about closure temperature and mineral ages are correct?

For the same mineral and system, faster cooling gives a higher closure temperature

For the same mineral and cooling rate, larger grains have a higher closure temperature

For the same mineral and system, faster cooling gives a higher closure temperature

For the same mineral and cooling rate, larger grains have a higher closure temperature

An Ar–Ar age of biotite always dates the time of peak metamorphism, whatever the cooling history

Zircon and monazite typically have lower closure temperatures for Pb than biotite has for Ar

Metamorphic Petrology: Textures, Facies and Grades, Reactions and Phase Equilibria, Protoliths, Thermobarometry and Timing

This chapter answers Part B1, “Metamorphic Petrology”, of the Geology and Geophysics (GG) paper: “Structures and textures of metamorphic rocks; Extreme metamorphism; Metamorphic facies and grades; Paired metamorphic belts; Mineral reactions and chemographic projections; Metamorphism of pelitic, mafic and impure carbonate rocks; role of bulk compositions and fluids in metamorphism; Thermobarometry; Timing of metamorphism.” It teaches foliations and textures, facies, grade and paired belts, extreme metamorphism, balanced reactions, the phase rule and chemographic diagrams, the pelite, metabasite and marble sequences, the role of fluids, thermobarometers and closure-temperature dating. The numericals are pressure and temperature from a stated geotherm, Clapeyron arithmetic, reaction volume change and exhumation rate from mineral ages.

1. Structures and textures of metamorphic rocks

Metamorphism is recrystallisation and reaction in the solid state, driven by changes in temperature, pressure and fluid, with the bulk chemistry almost unchanged except for volatiles (a change in bulk chemistry is metasomatism). Foliation is a planar fabric of aligned minerals made when rock is shortened: it forms perpendicular to the maximum compressive stress. With rising grade and grain size it passes from slaty cleavage (very fine mica, slate) to phyllitic sheen (phyllite), schistosity (visible aligned micas, schist) and gneissic banding (alternating light quartz–feldspar and dark mafic layers, gneiss). Lineation is a linear fabric (stretched grains, aligned amphibole). Rocks without foliation, such as hornfels, marble and quartzite, lacked directed stress or consist of equant minerals.

Metamorphic textures
Texture	Description	Typical occurrence
Granoblastic	Equant interlocking grains, no preferred orientation	Marble, quartzite, hornfels, granulite
Lepidoblastic	Aligned platy minerals (mica, chlorite)	Mica schist
Nematoblastic	Aligned prismatic minerals (hornblende, kyanite)	Amphibolite
Porphyroblastic	Large new crystals (garnet, staurolite) in a finer matrix	Garnet or staurolite schist
Corona, symplectite	Reaction rim or fine intergrowth where earlier phases broke down	Decompression or cooling in granulite and eclogite
Mylonitic	Fine-grained, strongly foliated, from ductile shear	Shear zones

The relation of a porphyroblast to the foliation dates its growth against deformation. Pre-tectonic: the matrix foliation wraps around the crystal, and inclusion trails are discordant or absent. Syn-tectonic: curved, spiral (S-shaped) inclusion trails, as in “snowball” garnet, with asymmetric pressure shadows, read as growth during rotation. Post-tectonic: straight inclusion trails continuous with the matrix foliation, which is not deflected around the crystal.

2. Grade, facies, paired belts and extreme metamorphism

Grade is the intensity of metamorphism (the temperature and pressure reached), shown by index minerals. An isograd is the map line where an index mineral first appears, in effect a reaction. In metapelites Barrow's zones, from low to high grade, are chlorite, biotite, garnet, staurolite, kyanite and sillimanite. A facies (Eskola) is the set of assemblages, over all bulk compositions, formed in one range of P–T; facies are named for metabasite assemblages.

Metamorphic facies and diagnostic metabasite assemblages
Facies	Diagnostic assemblage	Setting
Zeolite, prehnite–pumpellyite	Zeolites; prehnite + pumpellyite + chlorite	Very low grade: burial, ocean floor
Greenschist	Chlorite + actinolite + albite + epidote	Low T, low to moderate P
Amphibolite	Hornblende + plagioclase (oligoclase–andesine)	Medium T and P
Granulite	Orthopyroxene + clinopyroxene + plagioclase (± garnet)	High T, mostly anhydrous
Blueschist	Glaucophane + lawsonite (or epidote)	Low T, high P: cold subduction
Eclogite	Omphacite + garnet, no plagioclase	Very high P
Hornfels	Fine, granoblastic, unfoliated	Low P, contact aureoles

The geothermal gradient sets the path. Low P/T (contact aureoles, rift or arc settings, Buchan-type belts) gives andalusite and cordierite; intermediate P/T (Barrovian, collisional thickening) gives kyanite then sillimanite; high P/T (cold subduction) gives blueschist and eclogite. The Al₂SiO₅ polymorphs are the key: andalusite is stable at low P, kyanite at high P and sillimanite at high T (kyanite is the densest at about 3.6 g/cm³, andalusite the least dense at about 3.15 g/cm³, which is why pressure favours kyanite).

Paired metamorphic belts (Miyashiro, 1961) are two contemporaneous belts of contrasting type along a convergent margin: an oceanward high-P/low-T belt (blueschist, as the Sanbagawa belt of Japan) and a landward high-T/low-P belt (the Ryoke belt, heated by arc magmatism). The cold subducting slab and the hot arc crust above it explain the contrast.

Extreme metamorphism lies beyond the normal range. Ultrahigh-temperature (UHT) metamorphism exceeds 900 °C at crustal pressure; in Mg–Al-rich rocks it is shown by sapphirine + quartz, orthopyroxene + sillimanite + quartz, or osumilite, and it needs an exceptional heat source such as extension with mantle upwelling or magmatic underplating. The Eastern Ghats Belt of India is a recognised UHT terrane. Ultrahigh-pressure (UHP) metamorphism exceeds about 2.7 GPa, the quartz–coesite transition, so crust was buried to roughly 90–100 km: coesite inclusions in garnet, zircon or omphacite, and eclogite, are the proof, as at Tso Morari (Ladakh) and Kaghan in the Himalaya. Shock metamorphism from impact is near-instantaneous at very high pressure, producing planar deformation features in quartz and high-pressure phases such as coesite; Lonar crater, in Deccan basalt, is an Indian example.

3. Mineral reactions, the phase rule and chemographic projections

Reaction types: polymorphic (andalusite ⇌ kyanite), net-transfer among solids (albite ⇌ jadeite + quartz), devolatilisation (muscovite + quartz ⇌ K-feldspar + Al₂SiO₅ + H₂O), exchange (Fe–Mg between garnet and biotite: compositions change, not modes) and continuous reactions in solid solutions. Balance a reaction by conserving every element, then check the oxygens. Examples: CaCO₃ + SiO₂ → CaSiO₃ + CO₂ (calcite + quartz → wollastonite); CaMg(CO₃)₂ + 2 SiO₂ → CaMgSi₂O₆ + 2 CO₂ (dolomite + quartz → diopside); Ca₂Mg₅Si₈O₂₂(OH)₂ + 3 CaCO₃ + 2 SiO₂ → 5 CaMgSi₂O₆ + 3 CO₂ + H₂O (tremolite + calcite + quartz → diopside); KAl₃Si₃O₁₀(OH)₂ + SiO₂ → KAlSi₃O₈ + Al₂SiO₅ + H₂O (muscovite + quartz → K-feldspar + sillimanite).

At equilibrium ΔG = 0, and the Clapeyron equation gives the slope of a reaction curve: dP/dT = ΔS/ΔV, with ΔS and ΔV the entropy and volume changes of the reaction as written (J/(mol·K) and m³/mol, so the slope is in Pa/K). High T favours the side of larger entropy and high P the side of smaller volume (Le Chatelier). Albite → jadeite + quartz has both ΔV and ΔS negative, so the slope is positive and jadeite + quartz is the high-P side. A devolatilisation reaction has a large positive ΔS; at low P the fluid is so voluminous that ΔV is large and the slope gentle, but as P rises the fluid is compressed, ΔV shrinks, the curve steepens and may turn back (dP/dT < 0) once the fluid volume falls below the solid volume lost.

⚠️ Two negatives give a positive slope

When ΔS and ΔV are both negative, dP/dT = ΔS/ΔV is positive: do not read “both negative” as a negative slope. The high-P, low-T side is the one with the smaller volume and the smaller entropy.

The Gibbs phase rule is F = C − P + 2: C components, P phases at equilibrium, F the intensive variables (P, T, compositions) that can change independently. On a P–T diagram a reaction curve is univariant (F = 1) and an invariant point (F = 0) has C + 2 phases. Goldschmidt's mineralogical phase rule: a rock equilibrated over a range of P–T (divariant, F = 2) holds at most P = C phases. More phases than components means the rock sits on a univariant or invariant condition or is not in equilibrium (relics, retrograde overprint). C is the minimum number of independent components, fewer than the oxides, since perfectly mobile components and phases in excess are removed.

Chemographic projections plot phase compositions in a triangle so that the assemblage can be read directly: vertices are components, each mineral is a point, tie-lines join minerals that coexist, and a rock plots in the triangle of its assemblage. For metapelites the AFM diagram (Thompson projection from muscovite, quartz and H₂O; A = Al₂O₃ − 3K₂O, F = FeO, M = MgO, in moles) shows garnet, biotite, chlorite, staurolite, kyanite and cordierite; for metabasites and calc-silicates the ACF diagram (Al₂O₃-based A, CaO, and FeO + MgO) does the same. A tie-line flip (continuous reaction) swaps which of two pairs coexists; a terminal (discontinuous) reaction removes a phase when a triangle collapses to a line.

4. Pelites, mafic rocks, impure carbonates, bulk composition and fluids

Pelites (clay-rich, Al- and K-rich) give the most informative sequence. At intermediate P/T (Barrovian) it runs slate (chlorite + muscovite + quartz) → phyllite → biotite schist → garnet schist → staurolite schist → kyanite schist → sillimanite schist and gneiss. At low P/T (Buchan, contact aureoles) andalusite and cordierite appear, as in spotted slate, then sillimanite. At high T muscovite + quartz break down to K-feldspar + sillimanite + water, and with a free fluid partial melting begins: migmatites have pale leucosome (crystallised melt), dark melanosome (residue) and unmelted mesosome. Granulite-facies pelites carry garnet, cordierite, sillimanite and K-feldspar, with biotite largely broken down.

Metabasites pass from zeolite and prehnite–pumpellyite through greenschist (chlorite + actinolite + albite + epidote) to amphibolite (hornblende + plagioclase) and granulite (pyroxenes + plagioclase ± garnet). On a cold subduction path they instead become blueschist (glaucophane + lawsonite) and eclogite (omphacite + garnet), where albite has broken down to a jadeite component plus quartz and plagioclase has vanished.

Impure carbonates. A pure limestone only recrystallises to calcite marble, since calcite is stable to high T. Silica- and clay-bearing carbonates react by devolatilisation to calc-silicates (balanced reactions above). The usual order with rising T is talc → tremolite → diopside → forsterite, with wollastonite (calcite + quartz) and periclase (from dolomite) at the highest T, and X_CO₂ moves every boundary. Because CO₂ is a product, diluting the fluid with water (lower X_CO₂ = CO₂/(CO₂ + H₂O)) lowers the reaction temperature, so infiltration of water-rich fluid drives reaction at constant T. This is how skarns form at igneous contacts with carbonate: Ca–Mg–Fe silicates such as grossular–andradite garnet, diopside–hedenbergite, wollastonite and epidote.

Bulk composition decides which minerals can form: at one P–T a pelite makes garnet, biotite and Al₂SiO₅, a basalt makes hornblende and plagioclase, and a limestone makes only calcite, so grade is read from the right rock type. Fluids (H₂O, CO₂, brines) catalyse reaction by dissolution and reprecipitation, carry mass and heat (metasomatism), set the activity of H₂O and CO₂, and lower melting temperatures: the water-saturated granite solidus lies far below mica dehydration melting. Prograde metamorphism releases fluid, so peak rocks are largely dry and retrogression needs fluid to be supplied; a dry granulite can reach the surface still anhydrous.

5. Thermobarometry and pressure–temperature from depth

Thermobarometry estimates the P and T of equilibration from mineral compositions, measured by electron microprobe, with a calibrated reaction and activity models. The slope dP/dT = ΔS/ΔV decides the use. A reaction with small ΔV and large ΔS plots nearly vertical on a P–T diagram, responds to T and makes a geothermometer: Fe–Mg exchange between garnet and biotite, whose K_D = (Fe/Mg)_garnet/(Fe/Mg)_biotite falls as T rises. A reaction with large ΔV and small ΔS plots nearly horizontal, responds to P and makes a geobarometer: GASP, 3 anorthite = grossular + 2 kyanite (Al₂SiO₅) + quartz; Al in hornblende, which rises with P in suitable granitoids; Si in phengite in HP rocks. A thermometer and a barometer on the same assemblage intersect at the P–T of equilibration; multi-equilibrium methods and computed pseudosections (phase diagrams for the actual bulk composition) refine it.

Retrograde resetting is the main hazard: on cooling, Fe–Mg diffusion between garnet and biotite lowers the apparent T below the peak, so use garnet cores and grains away from contacts, or inclusions shielded in garnet. Garnet growth zoning with Mn highest in the core and falling outward (bell-shaped) records prograde growth; Mn rising again at the rim shows retrograde resorption; a flat profile suggests homogenisation by diffusion at high T.

Pressure from depth is lithostatic, P = ρgh. With ρ = 2800 kg/m³ and g = 9.8 m/s², each 10 km adds about 274 MPa, so 0.1 GPa (1 kbar) is about 3.6 km and 1 GPa about 36 km. With a linear geotherm T = T₀ + Gz, depth then fixes temperature: for T₀ = 20 °C and G = 25 °C/km, a rock at 30 km depth is at 770 °C and about 0.82 GPa.

6. Timing of metamorphism

Timing comes from radiometric ages of minerals. Growth ages date minerals that grew during metamorphism: Sm–Nd and Lu–Hf in garnet, U–Pb in metamorphic zircon rims (commonly low Th/U) and in monazite. Cooling ages date when a mineral cooled through its closure temperature: Ar–Ar in hornblende, muscovite and biotite. A mineral age therefore equals the age of metamorphism only if the mineral grew, or cooled, at that time.

The closure temperature T_c is the temperature at which a mineral–isotope system stopped exchanging the daughter isotope with its surroundings (Dodson, 1973). It is given implicitly by T_c = (E/R) / ln[A·R·T_c²·D₀ / (a²·E·(dT/dt))], where E is the activation energy, D₀ the pre-exponential diffusivity, a the diffusion dimension (grain radius), A a geometry factor and dT/dt the cooling rate. Faster cooling and larger grains therefore give a higher T_c. The rough order of T_c, highest first, is U–Pb in zircon and monazite, Sm–Nd in garnet (size dependent), Ar–Ar in hornblende, then muscovite, then biotite, and apatite fission tracks lowest.

Rates from ages. Cooling rate between two systems is (T_c1 − T_c2)/(t₁ − t₂), with ages t in Ma. Exhumation rate is the cooling rate divided by the geothermal gradient, and a rate in km/Myr equals mm/yr. Example: muscovite (T_c = 400 °C) at 60 Ma and biotite (T_c = 300 °C) at 50 Ma give 100/10 = 10 °C/Myr; with G = 25 °C/km that is 0.4 km/Myr, or 0.4 mm/yr.

A P–T–t path records the history. Clockwise paths (heating during burial and thickening, then near-isothermal decompression, then cooling) are typical of collisional orogens, with kyanite replaced by sillimanite and decompression coronas and symplectites. Anticlockwise paths (heating at low P before loading, then near-isobaric cooling) are typical of arcs or extensional settings with magmatic underplating. Reaction textures and garnet zoning are read to reconstruct the path.

⚠️ A mineral age is not always the metamorphic age

A biotite Ar–Ar age dates cooling through about 300 °C, which can be tens of millions of years after peak metamorphism. Compare the closure temperature of the system with the temperature of the event before calling an age “metamorphic”.

Key takeaways

Foliation grades from slaty cleavage through phyllitic sheen and schistosity to gneissic banding. A porphyroblast with wrapped foliation is pre-tectonic, with spiral inclusion trails syn-tectonic, with straight trails continuous with the matrix post-tectonic.
Facies are named for metabasite assemblages: greenschist, amphibolite, granulite, blueschist (glaucophane + lawsonite) and eclogite (omphacite + garnet). Paired belts are an oceanward high-P/low-T belt and a landward high-T/low-P belt. UHT exceeds 900 °C (sapphirine + quartz); UHP exceeds about 2.7 GPa (coesite).
Clapeyron: dP/dT = ΔS/ΔV; negative ΔS and ΔV give a positive slope. Phase rule: F = C − P + 2; a divariant rock holds at most C phases. In AFM (projection from muscovite) tie-lines show coexisting minerals and a flip is a continuous reaction.
Pelite: chlorite → biotite → garnet → staurolite → kyanite → sillimanite; mafic: greenschist → amphibolite → granulite, or blueschist → eclogite; carbonate: talc → tremolite → diopside → forsterite, with water-rich fluid lowering decarbonation temperature. Dry rocks resist retrogression.
Small ΔV, large ΔS gives a thermometer (Fe–Mg garnet–biotite); large ΔV, small ΔS gives a barometer (GASP). P = ρgh and T = T₀ + Gz fix a point on the geotherm. Retrograde diffusion lowers apparent T; bell-shaped Mn zoning in garnet records prograde growth.
Closure temperature rises with faster cooling and larger grains; cooling rate = ΔT_c/Δt and exhumation rate = cooling rate ÷ G. Zircon and monazite U–Pb are highest, then garnet, hornblende, muscovite, biotite. Clockwise P–T–t paths mean thickening then decompression; anticlockwise paths mean heating then isobaric cooling.

Practice questions (17)

Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.

A thin section of a schist shows a garnet porphyroblast containing straight quartz inclusion trails that are continuous with the foliation of the matrix, and the matrix foliation is not deflected around the garnet. What does this show about the timing of garnet growth?
1. Garnet grew before the foliation formed, because inclusions are always older than the matrix around them
2. Garnet grew during the deformation, because the crystal rotated and trapped curved inclusion trails
3. Garnet grew after the main deformation, because the earlier foliation is preserved straight inside it
4. Garnet grew before the deformation, because it behaved as a rigid object that the later foliation wrapped around
Show answer
Answer: C — Garnet grew after the main deformation, because the earlier foliation is preserved straight inside it
Straight inclusion trails continuous with an undeflected matrix foliation mean that the foliation already existed when the garnet grew and that no later deformation wrapped it: growth was post-tectonic. Pre-tectonic crystals are wrapped by the matrix foliation, and syn-tectonic crystals, the tempting alternative, carry curved or spiral trails because they grew while rotating.
Which metabasite assemblage indicates metamorphism along a cold, high-pressure subduction-zone path?
1. glaucophane + lawsonite, the blueschist facies
2. hornblende + plagioclase, the amphibolite facies
3. chlorite + actinolite + albite + epidote, the greenschist facies
4. orthopyroxene + clinopyroxene + plagioclase, the granulite facies
Show answer
Answer: A — glaucophane + lawsonite, the blueschist facies
Glaucophane with lawsonite is the blueschist assemblage, formed at high pressure and low temperature, where the geotherm is depressed by a cold subducting slab. Hornblende + plagioclase is amphibolite (medium T and P), the greenschist assemblage is low P and T, and orthopyroxene + clinopyroxene + plagioclase is the hot, anhydrous granulite facies.
Which of the following statements about paired metamorphic belts are correct?
1. In Miyashiro's pairs the high-P/low-T belt lies on the oceanward side of the margin
2. The landward high-T/low-P belt is heated by arc magmatism
3. The blueschist belt of a pair lies on the landward side, next to the volcanic arc
4. Both belts of a pair record the same geothermal gradient but different depths
Show answer
Answer: A — In Miyashiro's pairs the high-P/low-T belt lies on the oceanward side of the margin; B — The landward high-T/low-P belt is heated by arc magmatism
A pair consists of an oceanward high-P/low-T (blueschist) belt, formed above the cold subducting slab, and a landward high-T/low-P belt, formed in the arc crust heated by magmatism, as with Sanbagawa and Ryoke in Japan. The blueschist belt is therefore not next to the arc, and the two belts differ in geothermal gradient, not only in depth.
Which observation would a petrologist take as the best evidence of ultrahigh-temperature metamorphism (above 900 °C) in an Mg–Al-rich granulite?
1. coesite inclusions in garnet, which show burial of crust to more than 90 km
2. sapphirine together with quartz in textural equilibrium
3. glaucophane and lawsonite in the matrix, which show a very low geothermal gradient
4. andalusite and cordierite in a spotted schist, which show heating at low pressure
Show answer
Answer: B — sapphirine together with quartz in textural equilibrium
Sapphirine + quartz is a classic diagnostic assemblage of UHT metamorphism in Mg–Al-rich compositions. Coesite is the UHP indicator, a pressure and not a temperature marker, and is the tempting answer because it is also called extreme metamorphism. Glaucophane + lawsonite marks cold, high-pressure conditions, and andalusite + cordierite marks low pressure and moderate temperature.
The reaction albite → jadeite + quartz has a negative volume change (ΔV < 0) and a negative entropy change (ΔS < 0). On a P–T diagram with P on the vertical axis, the equilibrium curve therefore
1. has a negative slope, because both ΔV and ΔS are negative
2. is horizontal, because the two changes cancel each other
3. is vertical, because a solid–solid reaction does not depend on pressure or on volume
4. has a positive slope, so jadeite + quartz is the high-pressure assemblage
Show answer
Answer: D — has a positive slope, so jadeite + quartz is the high-pressure assemblage
dP/dT = ΔS/ΔV, and a negative number divided by a negative number is positive, so the curve rises to the right and the side of smaller volume, jadeite + quartz, is stable at higher P. Reading “both negative” as a negative slope is the tempting error. The changes do not cancel, and every reaction with ΔV ≠ 0 depends on pressure.
A metapelite, projected from muscovite, quartz and H₂O into the three-component AFM system, shows five AFM minerals (garnet, chlorite, biotite, staurolite and kyanite) in apparent contact in one thin section, in a terrane where P and T change smoothly across the map. Under the mineralogical phase rule the best interpretation is that
1. five phases are allowed because H₂O and the projection phases add extra degrees of freedom
2. the rock formed at exactly one invariant point, which is the normal state of pelites across a terrane
3. the assemblage is not a single equilibrium one, or the rock sits exactly on an invariant condition
4. kyanite and staurolite count as one phase because both are aluminous silicate minerals of similar density
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Answer: C — the assemblage is not a single equilibrium one, or the rock sits exactly on an invariant condition
With three components a rock that equilibrated over a range of P–T (divariant) can hold at most three AFM phases; four need a univariant condition and five (C + 2, the most a three-component system can hold) only an invariant point. So the rock either records that rare invariant condition or, far more likely, contains relics and retrograde or overprinted phases that were never in equilibrium together. Phases in excess are already removed by the projection, so they add no freedom, and different minerals are different phases whatever their chemistry.
Which of the following reactions are correctly balanced?
1. CaCO₃ + SiO₂ → CaSiO₃ + CO₂ (calcite + quartz → wollastonite)
2. CaMg(CO₃)₂ + 2 SiO₂ → CaMgSi₂O₆ + 2 CO₂ (dolomite + quartz → diopside)
3. KAl₃Si₃O₁₀(OH)₂ + SiO₂ → KAlSi₃O₈ + Al₂SiO₅ + 2 H₂O (muscovite + quartz → K-feldspar + sillimanite)
4. NaAlSi₃O₈ → NaAlSi₂O₆ + 2 SiO₂ (albite → jadeite + quartz)
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Answer: A — CaCO₃ + SiO₂ → CaSiO₃ + CO₂ (calcite + quartz → wollastonite); B — CaMg(CO₃)₂ + 2 SiO₂ → CaMgSi₂O₆ + 2 CO₂ (dolomite + quartz → diopside)
Counting atoms: calcite + quartz gives wollastonite + CO₂ with Ca, Si, C and O all conserved; dolomite + 2 quartz gives diopside + 2 CO₂ (Ca 1, Mg 1, Si 2, C 2, O 10 on both sides). Muscovite + quartz releases one H₂O, not two, because muscovite carries only two H in its two OH groups. Albite loses only one SiO₂ in forming jadeite (NaAlSi₃O₈ minus NaAlSi₂O₆ leaves SiO₂), so 2 SiO₂ does not balance.
In Barrovian metamorphism of a pelite, the index minerals appear in which order with increasing grade?
1. chlorite, garnet, biotite, staurolite, kyanite, sillimanite
2. chlorite, biotite, garnet, staurolite, kyanite, sillimanite
3. biotite, chlorite, garnet, kyanite, staurolite, sillimanite
4. chlorite, biotite, staurolite, garnet, sillimanite, kyanite
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Answer: B — chlorite, biotite, garnet, staurolite, kyanite, sillimanite
Barrow's zones in a pelite run chlorite, biotite, garnet, staurolite, kyanite, sillimanite. The other orders swap neighbours: garnet appears after biotite, staurolite before kyanite, and sillimanite, the high-temperature polymorph, comes last.
A siliceous marble contains calcite and quartz in contact with a CO₂-rich fluid at a temperature just below that at which wollastonite forms. Water-rich fluid from a cooling pluton then infiltrates the rock without changing T or P. What is the likely effect on the reaction calcite + quartz → wollastonite + CO₂?
1. It can now proceed at the same T, because diluting CO₂ in the fluid lowers the reaction T
2. It is driven backwards, because water is a product of the reaction and builds up in the fluid
3. It is unaffected, because T and P are unchanged and the reactants are both solids of fixed composition
4. It needs a higher T, because water stabilises calcite and quartz relative to wollastonite and CO₂
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Answer: A — It can now proceed at the same T, because diluting CO₂ in the fluid lowers the reaction T
CO₂ is a product, so lowering its activity in the fluid, by diluting it with water, favours the products and lowers the reaction temperature; infiltration therefore drives decarbonation at constant T. Water is not a product of this reaction, so the claim that it is driven backwards is wrong, and the reaction depends on fluid composition even though the reactants are solids. Water does not stabilise calcite + quartz.
A granulite carries an anhydrous high-temperature assemblage to the surface, although hydrous minerals would be stable at the lower temperatures it later passed through. What is the best reason?
1. Hydrous minerals can never nucleate in a rock that has once reached the granulite facies
2. Granulites always cool faster than diffusion can act in any mineral, whatever the fluid supply, so no reaction is possible
3. Granulites have bulk compositions in which hydrous minerals are chemically impossible
4. Retrograde hydration needs water, and the rock had lost its fluid and melt during prograde metamorphism
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Answer: D — Retrograde hydration needs water, and the rock had lost its fluid and melt during prograde metamorphism
Prograde devolatilisation and melt loss leave granulites dry, and retrogression by hydration cannot proceed without water, so the high-T assemblage survives metastably. The same rock does retrogress where fluid is channelled in along shear zones, which refutes the claims that hydrous minerals can never form or are chemically impossible. Cooling-rate arguments cannot be universal, since retrogressed granulites exist.
Two calibrated reactions in one assemblage have the following changes at the P–T of interest. Reaction X: ΔV = +0.1 cm³/mol and ΔS = +20 J/(mol·K). Reaction Y: ΔV = −7 cm³/mol and ΔS = −35 J/(mol·K). Which statement is correct?
1. X is a good geobarometer and Y a good geothermometer, because X has the smaller volume change
2. X is a good geothermometer (slope about 200 MPa/K) and Y a good geobarometer (slope about 5 MPa/K)
3. Both are good geobarometers, because both reactions have a nonzero volume change at these conditions
4. Both are good geothermometers, because both reactions have a nonzero entropy change at these conditions
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Answer: B — X is a good geothermometer (slope about 200 MPa/K) and Y a good geobarometer (slope about 5 MPa/K)
The Clapeyron slope dP/dT = ΔS/ΔV is (20)/(0.1 × 10⁻⁶) = 2 × 10⁸ Pa/K = 200 MPa/K for X and (−35)/(−7 × 10⁻⁶) = 5 × 10⁶ Pa/K = 5 MPa/K for Y. A very steep curve is almost vertical on a P–T diagram, so the equilibrium shifts mostly with T and X is a thermometer; a gentle curve shifts mostly with P and Y is a barometer. Assigning the roles the other way round is the tempting error.
A garnet in a staurolite–garnet schist has a bell-shaped Mn profile, highest in the core and falling smoothly to the lowest value at the rim, with no rise at the edge. What does this indicate?
1. Retrograde resorption of garnet during cooling, which concentrates Mn in a rim around the crystal
2. Complete homogenisation of the crystal by diffusion at high temperature during peak metamorphism
3. Prograde growth zoning, with Mn strongly partitioned into growing garnet and depleted in the matrix
4. Contact metamorphism, because Mn zoning is found only around igneous intrusions and their aureoles
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Answer: C — Prograde growth zoning, with Mn strongly partitioned into growing garnet and depleted in the matrix
Garnet takes Mn strongly, so early-grown cores are Mn-rich and the matrix is progressively depleted, giving a bell-shaped profile that preserves prograde growth. Retrograde resorption, the tempting reading, would raise Mn at the rim, and homogenisation by diffusion would give a flat profile. Growth zoning is not restricted to contact settings.
A metamorphic rock equilibrated at a pressure of 0.81 GPa. Take lithostatic pressure P = ρgh with ρ = 2750 kg/m³ and g = 9.8 m/s². The geotherm is linear, T = T₀ + Gz, with surface temperature T₀ = 20 °C and G = 20 °C/km. What was the temperature of equilibration in °C? Give the answer to the nearest whole number.
Numerical answer — type the value.
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Answer: 621
Depth h = P/(ρg) = 0.81 × 10⁹/(2750 × 9.8) = 0.81 × 10⁹/26 950 = 30 056 m = 30.06 km. Then T = 20 + 20 × 30.06 = 621 °C.
A dehydration reaction has ΔS = +90 J/(mol·K) and ΔV = +30 cm³/mol (1 cm³ = 10⁻⁶ m³). Using the Clapeyron equation and treating ΔS and ΔV as constant, by how many MPa must the pressure rise to keep the reaction at equilibrium when the temperature rises by 50 K?
Numerical answer — type the value.
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Answer: 150
dP/dT = ΔS/ΔV = 90/(30 × 10⁻⁶) = 3 × 10⁶ Pa/K = 3 MPa/K. For ΔT = 50 K the pressure must rise by 3 × 50 = 150 MPa.
The barometer GASP is 3 CaAl₂Si₂O₈ (anorthite) = Ca₃Al₂Si₃O₁₂ (grossular) + 2 Al₂SiO₅ (kyanite) + SiO₂ (quartz). Take molar volumes in cm³/mol: anorthite 100.8, grossular 125.3, kyanite 44.1, quartz 22.7. By how many cm³ does the volume of the solids decrease per mole of grossular formed? Give the answer to one decimal place.
Numerical answer — type the value.
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Answer: 66.2
Reactants: 3 × 100.8 = 302.4 cm³. Products: 125.3 + 2 × 44.1 + 22.7 = 125.3 + 88.2 + 22.7 = 236.2 cm³. ΔV = 236.2 − 302.4 = −66.2 cm³, so the volume decreases by 66.2 cm³. This large negative ΔV with a small ΔS makes GASP a sensitive geobarometer.
Hornblende (Ar–Ar, closure temperature 500 °C) in a gneiss gives an age of 520 Ma and biotite (closure temperature 300 °C) from the same rock gives 490 Ma. Assuming a constant cooling rate and a geothermal gradient of 25 °C/km, what exhumation rate does this imply, in mm/yr (equal to km/Myr)? Give the answer to two decimal places.
Numerical answer — type the value.
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Answer: 0.27
Cooling rate = (500 − 300)/(520 − 490) = 200/30 = 6.67 °C/Myr. Exhumation rate = cooling rate/G = 6.67/25 = 0.267 km/Myr, which rounds to 0.27 mm/yr.
Which of the following statements about closure temperature and mineral ages are correct?
1. For the same mineral and system, faster cooling gives a higher closure temperature
2. For the same mineral and cooling rate, larger grains have a higher closure temperature
3. An Ar–Ar age of biotite always dates the time of peak metamorphism, whatever the cooling history
4. Zircon and monazite typically have lower closure temperatures for Pb than biotite has for Ar
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Answer: A — For the same mineral and system, faster cooling gives a higher closure temperature; B — For the same mineral and cooling rate, larger grains have a higher closure temperature
In Dodson's equation T_c rises with the cooling rate dT/dt and with the diffusion dimension a (grain radius), so the faster-cooling and larger-grain statements are right. A biotite Ar–Ar age is a cooling age through about 300 °C and can postdate the metamorphic peak by tens of millions of years. Zircon and monazite retain Pb to very high temperatures, so their closure temperatures are far above that of biotite.