Igneous Petrology: Classification and Textures, Mantle Melting, Differentiation, Trace-Element Modelling and Volcanism

This chapter answers Part B1, “Igneous Petrology”, of the Geology and Geophysics (GG) paper: “Classification and textures of common igneous rocks; Mantle melting; Magmatic differentiation; Role of major, trace, and rare earth elements in igneous petrogenesis; Magma evolution, modeling crystallization and melting processes, plate margin volcanism; Intra-plate volcanism and large igneous provinces.” It teaches naming from mode (QAPF) and chemistry (TAS), textures, peridotite melting, differentiation, the use of major, trace and rare earth elements, the equations for batch and fractional melting, Rayleigh fractionation, mixing and AFC, and the volcanism of plate margins, hotspots and large igneous provinces. The numericals are batch-melting and Rayleigh concentrations, mass balance of fractionation, simple normative arithmetic and an AFC calculation.

1. Classification and textures of common igneous rocks

An igneous rock is named from two things: its mode (which minerals, in what proportions) and its texture (grain size and fabric, which record how it cooled). Plutonic rocks cool slowly at depth and are coarse (phaneritic), volcanic rocks cool quickly and are fine (aphanitic) or glassy, and hypabyssal dykes and sills lie between and are often porphyritic. Grain size reflects the balance of nucleation and growth: slow cooling gives few nuclei and large crystals, rapid cooling gives many tiny crystals or none at all (glass).

Textures of igneous rocks and what each records
TextureDescriptionWhat it records
PhaneriticCrystals visible to the eyeSlow cooling, plutonic (granite, gabbro)
AphaniticCrystals too small to seeFast cooling, volcanic (basalt, rhyolite)
PorphyriticLarge phenocrysts in a finer groundmassTwo stages: slow in a chamber, then fast
Vesicular, amygdaloidalGas bubbles, later filled by zeolite, calcite or quartzVolatile exsolution near the surface
OphiticPlagioclase laths enclosed in larger pyroxenePlagioclase crystallised first (dolerite, gabbro)
GraphicQuartz and alkali feldspar intergrown like cuneiform writingSimultaneous crystallisation near a eutectic
SpinifexLong skeletal olivine or pyroxene bladesVery rapid quenching of high-MgO komatiite lava

QAPF (IUGS) names plutonic rocks, and volcanic rocks with a countable mode. Q is quartz, A alkali feldspar (including albite An₀–₅), P plagioclase (An₅–₁₀₀) and F feldspathoids. It applies when mafic minerals (M) are below 90% of the rock: Q + A + P (or A + P + F) is recalculated to 100 and plotted on a double triangle (Q top, F bottom, A and P at the sides). Quartz and feldspathoids do not coexist. In the granitoid field (Q 20–60) the ratio P/(A + P) gives the name: alkali-feldspar granite (0–10%), syenogranite (10–35%), monzogranite (35–65%), granodiorite (65–90%), tonalite (90–100%). Lower lie syenite, monzonite and diorite/gabbro (plagioclase below An₅₀ is diorite, above is gabbro); anorthosite is over 90% plagioclase. Volcanic equivalents: granite–rhyolite, granodiorite–dacite, diorite–andesite, gabbro–basalt, syenite–trachyte. Ultramafic rocks (M above 90%) go on an olivine–orthopyroxene–clinopyroxene triangle: dunite (olivine over 90%), harzburgite (olivine and orthopyroxene), lherzolite (all three), wehrlite (olivine and clinopyroxene), and the pyroxenites.

TAS (total alkali–silica) classifies volcanic rocks that are too fine or glassy for a mode. Take a fresh analysis, recalculate it to 100% volatile-free, and plot Na₂O + K₂O against SiO₂ (wt%). SiO₂ separates ultrabasic (below 45), basic (45–52), intermediate (52–63) and acid (above 63) rocks; in the subalkaline part the boundaries between basalt, basaltic andesite, andesite, dacite and rhyolite fall near 52, 57, 63 and 69 wt% SiO₂. A line divides alkaline (trachyte, phonolite, tephrite) from subalkaline suites; subalkaline suites split into tholeiitic and calc-alkaline on an AFM plot, or by K₂O into low-, medium- and high-K.

⚠️ Colour is not composition
Obsidian is jet black yet acid (rhyolitic) in composition, because the colour comes from dissolved iron and tiny oxide dust in glass, not from mafic minerals. In altered or weathered rocks the alkalis are mobile, so TAS misleads; use immobile elements (Zr, Ti, Nb, Y).

2. Mantle melting

The upper mantle is peridotite: olivine (more than half), orthopyroxene, clinopyroxene and an aluminous phase that is plagioclase at the shallowest levels, spinel at moderate depth and garnet deeper. Partial melts of peridotite are basaltic. A rock melts when its temperature rises above the solidus, and there are only three ways to reach it: raise the temperature, lower the pressure, or lower the solidus by adding a volatile.

  • Decompression melting is the main route. Mantle upwelling beneath ridges, rifts and plumes rises almost adiabatically, losing little heat, so its temperature falls slowly while the solidus, which falls as pressure falls, drops faster. The two cross and melting begins, and more ascent gives more melt.
  • Flux melting operates above subducting slabs. The slab loses water as hydrous minerals break down; the water rises into the hot mantle wedge and lowers the peridotite solidus strongly. CO₂ also lowers the solidus at depth. The slab itself usually does not melt; the wedge does.
  • Thermal melting needs excess heat, from a hot plume or underplated magma. A hotter source melts more, which is how picrite and komatiite form.

Melting is non-modal. The first melts come from the low-melting minerals (clinopyroxene and the aluminous phase), so these are used up first and the residue becomes richer in olivine and orthopyroxene: harzburgite, then dunite. The degree of melting, F, controls the product. A few per cent, usually at greater depth, gives alkaline, incompatible-rich melts (alkali basalt, basanite, nephelinite); about 10–20% gives tholeiitic basalt of the MORB type; very high F in hot mantle gives picrite and komatiite. Melt leaves the residue at very small melt fractions. Depth of melting is read from heavy REE: garnet holds heavy REE (Yb, Lu) and Y, so melts formed with residual garnet have steep REE patterns (high Dy/Yb), while melts from the spinel field are flatter.

⚠️ Ridges are not hot
Normal-temperature mantle melts beneath a mid-ocean ridge simply because it rises: that is decompression, not extra heat.

3. Magmatic differentiation

Primary mantle melts, rich in MgO, Ni and Cr, rarely reach the surface unchanged. Differentiation turns one magma into a range of compositions through fractional crystallisation, assimilation of wall rock, magma mixing, liquid immiscibility (sulphide, or carbonate and silicate liquids) and partial melting of crust. Fractional crystallisation is the commonest and follows Bowen's reaction series: the discontinuous series olivine → pyroxene → amphibole → biotite, and the continuous series Ca-rich → Na-rich plagioclase, both ending in K-feldspar, muscovite and quartz. The residual liquid gains SiO₂, Na₂O, K₂O and incompatible elements and loses MgO, FeO, CaO, Ni and Cr: basalt → andesite → dacite → rhyolite.

On a Harker diagram (oxide against SiO₂), fractionation gives curved or kinked trends, and each kink marks a new phase joining: P₂O₅ turns down when apatite appears, FeO and TiO₂ fall when Fe–Ti oxides start, and CaO falls faster when clinopyroxene joins. Mixing of two magmas gives a straight line between the end members, so a straight line is a hint of mixing, not proof. Layered intrusions such as Skaergaard, Bushveld and Stillwater, and the Archaean Sittampundi anorthosite complex of Tamil Nadu, preserve cumulates, crystals piled on the chamber floor, as repeating layers.

Two classic differentiation trends
FeatureTholeiitic trendCalc-alkaline trend
Typical settingRidges, ocean-island shields, some arcsMature and continental arcs
Water and oxygen fugacityDry, relatively reducedHydrous, oxidised
Early phasesOlivine, plagioclase, clinopyroxene; Fe–Ti oxides lateMagnetite and amphibole early
Iron behaviourFeO*/MgO rises strongly (ferrobasalt, ferrogabbro)No iron enrichment; silica rises steadily
ExampleSkaergaard intrusionAndean andesite–dacite–rhyolite series

4. Major, trace and rare earth elements in petrogenesis

Major elements (Si, Ti, Al, Fe, Mn, Mg, Ca, Na, K, P: mostly above about 1 wt%, although Ti, Mn and P are often below it) are reported as oxides, fix the mineralogy and classification, and are summarised by Mg# = 100 × Mg/(Mg + Fe²⁺) in moles. A melt in equilibrium with mantle olivine has a high Mg# (about 70 or more), so a low Mg# shows that a magma has fractionated. Trace elements (below about 0.1 wt%) are too dilute to form their own minerals, so they follow Henry's law and divide between crystal and melt by the partition coefficient D = C_solid/C_liquid. Goldschmidt's rules decide the fit (similar radius and charge to the host site). Elements with D < 1 are incompatible and stay in the melt; D > 1 are compatible. Bulk D = Σ (mass fraction of mineral × D of that mineral), and D varies with temperature, pressure and melt composition.

Minerals as sinks for trace elements
MineralTakes up stronglySignature in the liquid or melt
OlivineNi, CoNi falls as olivine is removed
GarnetHeavy REE, Y, ScSteep REE pattern, high Dy/Yb in melt
PlagioclaseSr, Eu²⁺Sr falls; negative Eu anomaly

The REE (La to Lu) are trivalent except Ce and Eu, and their radius shrinks from La to Lu, so light REE are more incompatible in most mantle minerals while garnet holds heavy REE. REE are normalised to chondrite (divided by the chondritic value) to remove the even–odd zig-zag of natural abundance, and the slope is quoted as (La/Yb)_N. At magmatic oxygen fugacity Eu is partly 2+ and enters plagioclase like Sr, so the Eu anomaly Eu/Eu* = Eu_N/√(Sm_N × Gd_N) is below 1 in liquids from which plagioclase was removed (or melts from plagioclase-bearing residues) and above 1 in plagioclase cumulates. Ce can be 4+ in oxidised settings, giving Ce anomalies.

Normalised patterns and what they indicate
PatternReading
N-MORB: light-REE depleted, (La/Sm)_N below 1, no Nb troughDepleted source melted to a large degree beneath a ridge
OIB: strong light-REE enrichment, Nb and Ta peaksEnriched source, small melt fraction, often residual garnet
Arc basalt: Ba, K, Pb, Sr high relative to Nb, Ta, Ti (Nb–Ta trough)Slab fluid carried mobile LILE into the wedge, HFSE stayed behind (crustal contamination also makes an Nb–Ta trough, with high Th)

5. Modelling melting and crystallisation, mass balance and the norm

C_L is the melt concentration, C₀ the starting (source or parent) concentration, F the melt fraction (in crystallisation, the fraction remaining) and D the bulk partition coefficient.

  • Batch (equilibrium) melting: C_L/C₀ = 1/[D + F(1 − D)]. The residue holds C_S = D·C_L. For D ≈ 0, C_L ≈ C₀/F. The non-modal form is C_L/C₀ = 1/[D₀ + F(1 − P)], where D₀ comes from the source mode and P from the proportions in which the minerals enter the melt.
  • Fractional (Rayleigh) melting, each increment removed at once: C_L/C₀ = (1/D)(1 − F)^(1/D − 1) for the instantaneous melt.
  • Fractional (Rayleigh) crystallisation: C_L/C₀ = F^(D − 1), with F the melt fraction remaining. The crystals forming at that instant have C_S = D·C_L. Equilibrium crystallisation uses the batch form.
  • Mixing: C_mix = X·C_A + (1 − X)·C_B for concentrations; ratios mix along hyperbolae.
  • AFC (DePaolo): C_m/C_m0 = F^(−z) + [r/(r − 1)]·[C_a/(z·C_m0)]·(1 − F^(−z)), with z = (r + D − 1)/(r − 1) and r = rate of assimilation ÷ rate of crystallisation; C_a is the assimilant. At r = 0 it is Rayleigh crystallisation.
  • Mass balance: for parent P, daughter liquid D and extract E (the crystals removed), any oxide obeys C_P = x·C_E + (1 − x)·C_D, so the extract fraction is x = (C_P − C_D)/(C_E − C_D). With several oxides use least squares; a small residual supports the model.

Worked examples. Batch melting of a source with 2 ppm of an incompatible element, D = 0.02, at F = 0.05: C_L = 2/(0.02 + 0.05 × 0.98) = 2/0.069 ≈ 29 ppm, about fifteen times the source. Rayleigh crystallisation with D = 0.01 and F = 0.5: C_L/C₀ = 0.5^(−0.99) ≈ 1.99, so a highly incompatible element doubles, as the 1/F rule predicts. For D > 1 the exponent is positive and the liquid is depleted.

🧠 Melting or crystallisation?
In fractional crystallisation of a basalt, two highly incompatible elements (La and Th, say) rise together at a nearly constant ratio while Ni and Cr fall. In partial melting, the ratio of two incompatible elements of different D (La/Sm) changes strongly with F, because the more incompatible element is enriched faster at small F. A spread in such a ratio points to variable melting or source, not to crystallisation.

The CIPW norm recasts an analysis into a standard set of anhydrous minerals, working in molecular proportions (wt% ÷ molecular weight) and filling them in a fixed order: apatite, ilmenite, magnetite, then orthoclase, albite, anorthite, then pyroxene and olivine, with quartz or nepheline as the silica balance. For the feldspars: 1 K₂O takes 1 Al₂O₃ and 6 SiO₂ (orthoclase); 1 Na₂O takes 1 Al₂O₃ and 6 SiO₂ (albite); 1 CaO takes 1 Al₂O₃ and 2 SiO₂ (anorthite). Silica left over is normative quartz (silica-oversaturated); a deficit forces olivine and, in the extreme, nepheline (undersaturated, alkaline). The norm compares rocks on a common mineral basis.

6. Plate-margin and intra-plate volcanism, large igneous provinces

Volcanism by tectonic setting
SettingHow melting occursTypical magmas and chemistry
Mid-ocean ridgeDecompression of upwelling mantleN-MORB tholeiite, light-REE depleted; builds oceanic crust
Island and continental arcFlux melting of the mantle wedge by slab waterBasalt to rhyolite, mostly calc-alkaline; hydrous and explosive; high LILE, Nb–Ta trough
Continental riftDecompression under thinning lithosphereAlkali basalt, bimodal basalt–rhyolite, phonolite, carbonatite
Hotspot (ocean island)Hot plume rising and decompressingOIB: tholeiitic shield, then alkaline; light-REE enriched, Nb peak
Continental flood basalt (LIP)Melting of a plume head under thick lithosphereVoluminous tholeiitic basalt, some crustal contamination

At a Hawaiian-type volcano the magma type changes as the plate carries the volcano off the plume: a tholeiitic shield stage (most of the volume, high melt fraction), then alkali basalt in the post-shield stage, then rare strongly alkaline lavas (basanite, nephelinite) in a late rejuvenated stage, formed at the lowest melt fractions.

A large igneous province (LIP) is an outpouring of mainly mafic magma, typically from about 0.1 million to several million cubic kilometres, mostly erupted within a few million years or less. Types include continental flood basalts (Deccan, Siberian, Karoo, Columbia River, Paraná–Etendeka), oceanic plateaus (Ontong Java, Kerguelen) and giant dyke swarms. The usual model is a new plume whose broad hot head produces the LIP and whose narrow tail then leaves a hotspot track. LIPs are linked in time to mass extinctions: the Siberian Traps (about 252 Ma) to the end-Permian event and the Deccan (about 66 Ma) to the end-Cretaceous.

The Deccan Traps are tholeiitic flood basalts erupted about 66 Ma, close to the Cretaceous–Palaeogene boundary, by the Réunion plume; as India drifted north the hotspot track continues as the Laccadive–Chagos ridge to Réunion Island. The pile is made of many flows, each with a vesicular, amygdaloidal top, and red boles (fossil soils) between flows mark pauses. The Rajmahal Traps of eastern India are Early Cretaceous and are linked to the Kerguelen plume.

Key takeaways

  • Name plutonic rocks by QAPF (granitoid names from P/(A + P): 10, 35, 65, 90%), volcanic rocks by TAS (SiO₂ limits near 45, 52, 57, 63, 69). Textures record cooling: phaneritic slow, aphanitic fast, porphyritic two-stage, spinifex quenched komatiite.
  • Peridotite melts by decompression (ridges, plumes, rifts), slab-water flux (arcs) or extra heat (plumes). Low F gives alkaline melts, 10–20% gives MORB, high F gives picrite and komatiite; residual garnet gives steep heavy-REE patterns.
  • Fractional crystallisation follows Bowen's series: SiO₂ and alkalis rise, MgO, Ni and Cr fall. Dry tholeiitic magmas gain iron; hydrous, oxidised calc-alkaline ones lose Fe–Ti oxide early and do not. A Harker kink marks a new phase; mixing gives straight lines.
  • D = C_solid/C_liquid; incompatible elements have D < 1. A negative Eu anomaly means plagioclase was removed; arcs show high LILE and a Nb–Ta trough; N-MORB is light-REE depleted and OIB enriched.
  • Batch: C_L/C₀ = 1/[D + F(1 − D)]. Rayleigh crystallisation: C_L/C₀ = F^(D − 1). Mass balance: x = (C_P − C_D)/(C_E − C_D). In the norm, K₂O and Na₂O each take 1 Al₂O₃ and 6 SiO₂, CaO takes 1 Al₂O₃ and 2 SiO₂; leftover silica is normative quartz.
  • Ridges are decompression melts, arcs flux melts, hotspots plume melts. LIPs (Deccan about 66 Ma, Réunion plume; Siberian about 252 Ma) are huge, brief mafic outpourings linked to mass extinctions; a Hawaiian volcano passes from tholeiitic shield to alkaline stages.

Practice questions (18)

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.

  1. A coarse-grained plutonic rock contains, by volume, quartz 25%, alkali feldspar 10%, plagioclase (An₃₀) 40% and biotite plus hornblende 25%. Recalculating Q + A + P to 100 and using the IUGS QAPF classification, the rock is a

    1. monzogranite, because quartz exceeds 20% and both feldspars are abundant
    2. granodiorite, because P/(A + P) is about 80% and quartz is between 20 and 60%
    3. tonalite, because plagioclase is the commoner feldspar and a mafic mineral is present
    4. quartz diorite, because plagioclase outweighs alkali feldspar in the rock
    Show answer

    Answer: B — granodiorite, because P/(A + P) is about 80% and quartz is between 20 and 60%

    Q + A + P = 25 + 10 + 40 = 75, so Q = 33.3%, A = 13.3%, P = 53.3% and P/(A + P) = 53.3/66.7 = 80%. In the granitoid field (Q 20–60) a ratio of 65–90% is granodiorite. Monzogranite needs 35–65%, which is the tempting choice because both feldspars are abundant; tonalite needs more than 90%, and quartz diorite plots at much lower quartz (5–20%).

  2. The upper part of a lava flow shows long, skeletal, blade-like olivine crystals arranged in sheaves (spinifex texture). What do the texture and the rock type indicate?

    1. A cumulate dunite, formed when olivine settled slowly on the floor of a magma chamber
    2. A rhyolite lava dome, formed when a viscous silicic melt crystallised at low temperature
    3. A komatiite lava, rich in MgO, quenched at the top so crystals grew as skeletal blades
    4. A granite pegmatite, formed when water-rich melt cooled slowly and allowed giant crystals to grow
    Show answer

    Answer: C — A komatiite lava, rich in MgO, quenched at the top so crystals grew as skeletal blades

    Spinifex is the signature of komatiite: a very hot, MgO-rich lava whose upper chilled zone grew skeletal olivine or pyroxene blades under strong undercooling. A cumulate dunite is the tempting alternative because it is olivine-rich, but cumulates form by slow settling and show blocky, not skeletal, crystals. A rhyolite is not olivine-bearing, and a pegmatite grows large crystals by slow cooling, not by quenching.

  3. Which of the following statements about the TAS (total alkali–silica) classification of volcanic rocks are correct?

    1. The analysis is recalculated to 100% on a volatile-free basis before Na₂O + K₂O is plotted against SiO₂
    2. Intermediate volcanic rocks lie between about 52 and 63 wt% SiO₂
    3. TAS can be applied without caution to strongly altered volcanic rocks because Na and K are immobile
    4. TAS requires the modal proportions of quartz, alkali feldspar and plagioclase
    Show answer

    Answer: A — The analysis is recalculated to 100% on a volatile-free basis before Na₂O + K₂O is plotted against SiO₂; B — Intermediate volcanic rocks lie between about 52 and 63 wt% SiO₂

    TAS works on the volatile-free recalculated chemical analysis, and the intermediate field spans about 52–63 wt% SiO₂. Na and K are mobile during alteration and weathering, so TAS misleads for altered rocks and immobile-element diagrams are used instead. The need for modal quartz, alkali feldspar and plagioclase describes QAPF, not TAS.

  4. What is the principal cause of melting beneath a mid-ocean ridge?

    1. Decompression of upwelling mantle, which crosses its solidus as it rises
    2. Addition of water released from a subducting slab that lies beneath the ridge axis
    3. Frictional heating on the transform faults that offset the ridge axis into segments
    4. Radioactive heating of the thin oceanic crust, which warms the mantle beneath it
    Show answer

    Answer: A — Decompression of upwelling mantle, which crosses its solidus as it rises

    Mantle of normal temperature rises beneath a spreading ridge almost adiabatically; its temperature falls slowly while the solidus falls faster with falling pressure, so melting starts. Water addition is the arc mechanism and is the tempting wrong answer; there is no slab beneath a ridge axis. Friction and crustal radioactivity supply far too little heat to melt the mantle.

  5. Which of the following lower the temperature at which mantle peridotite begins to melt (its solidus temperature)?

    1. Addition of a small amount of water to the peridotite
    2. A decrease in confining pressure, with the composition unchanged
    3. Removal of an earlier basaltic melt, leaving a depleted residue
    4. An increase in confining pressure, with the composition unchanged
    Show answer

    Answer: A — Addition of a small amount of water to the peridotite; B — A decrease in confining pressure, with the composition unchanged

    Water lowers the solidus strongly, which is the basis of flux melting. The peridotite solidus falls as pressure falls, which is why decompression causes melting. A depleted residue has lost its low-melting components and is more refractory, so its solidus is higher, and raising the pressure at fixed composition raises the solidus.

  6. Basalts from an ocean island have (Dy/Yb) normalised to chondrite well above 1, with strongly fractionated heavy REE, whereas basalts of similar MgO from a mid-ocean ridge have flat heavy-REE patterns. Which interpretation fits best?

    1. The island basalts came from a spinel-peridotite source at shallower depth than the ridge basalts
    2. The island magmas fractionated much plagioclase, which takes Yb in preference to Dy
    3. The island magmas crystallised much olivine, which strongly retains Dy relative to Yb
    4. The island magmas formed with residual garnet, which retains Yb and keeps it out of the melt
    Show answer

    Answer: D — The island magmas formed with residual garnet, which retains Yb and keeps it out of the melt

    Garnet accepts Yb and Lu much more readily than Dy, so a melt formed while garnet remained in the residue is depleted in Yb and has a high Dy/Yb: the signature of melting at depth, in the garnet field. A spinel source gives flat heavy-REE patterns, so the shallower-source option would give the ridge pattern, not the island one. Neither plagioclase nor olivine has a strong preference between Dy and Yb.

  7. On a Harker diagram of a lava suite, P₂O₅ rises with SiO₂ from basalt to andesite and then falls sharply through dacite to rhyolite. What is the best explanation?

    1. Plagioclase began to crystallise at that stage and removed phosphorus by replacing calcium in its structure
    2. Apatite reached saturation and began to crystallise, so P₂O₅ turned from incompatible to compatible
    3. Olivine began to crystallise at that stage and took phosphorus into its structure
    4. Mixing with a hotter, more mafic liquid diluted the phosphorus at that stage
    Show answer

    Answer: B — Apatite reached saturation and began to crystallise, so P₂O₅ turned from incompatible to compatible

    P₂O₅ is incompatible until the melt is saturated in apatite; the rise followed by a sharp fall is the standard kink for the start of apatite fractionation. Plagioclase is the tempting wrong answer because it is the major early feldspar, but phosphorus does not substitute for calcium in it. Olivine does not hold phosphorus, and mixing with a hotter mafic liquid would not produce a sharp fall confined to the felsic part of the suite.

  8. Which of the following statements about differentiation trends are correct?

    1. Early magnetite crystallisation in a hydrous, oxidised arc magma suppresses iron enrichment and favours the calc-alkaline trend
    2. The marked iron enrichment of the Skaergaard intrusion reflects crystallisation from a dry magma at low oxygen fugacity
    3. In the calc-alkaline series FeO*/MgO rises strongly while the silica content stays almost constant throughout the suite
    4. Mixing of two magmas gives a curved trend on a Harker diagram, whereas fractionation always gives a single straight line
    Show answer

    Answer: A — Early magnetite crystallisation in a hydrous, oxidised arc magma suppresses iron enrichment and favours the calc-alkaline trend; B — The marked iron enrichment of the Skaergaard intrusion reflects crystallisation from a dry magma at low oxygen fugacity

    Oxidised, hydrous arc magmas crystallise magnetite early and so lose iron, giving the calc-alkaline trend, while the dry, reduced Skaergaard liquid kept its iron until Fe–Ti oxides appeared late and became strongly Fe-enriched. It is the tholeiitic trend, not the calc-alkaline one, in which FeO*/MgO rises strongly at nearly constant silica. Mixing gives a straight line between end-members, while fractionation gives curved or kinked trends.

  9. A rhyolite has Eu/Eu* = 0.3 and a low Sr content. Which process best explains these two features together?

    1. Removal of plagioclase, which takes up Eu²⁺ and Sr in place of Ca²⁺, from the parent magma
    2. Residual garnet in the source, which holds Eu together with the heavy REE during melting
    3. Fractionation of zircon, which takes Eu in preference to the neighbouring REE Sm and Gd
    4. Fractionation of olivine, which removes Eu together with Ni from the liquid as it crystallises
    Show answer

    Answer: A — Removal of plagioclase, which takes up Eu²⁺ and Sr in place of Ca²⁺, from the parent magma

    Eu²⁺ and Sr²⁺ are similar in size to Ca²⁺ and both enter plagioclase, so removing plagioclase depletes the liquid in Eu relative to its neighbours Sm and Gd (Eu/Eu* below 1) and lowers Sr. Residual garnet is the tempting alternative but it affects the heavy REE, not Eu specifically, and it does not explain low Sr. Zircon and olivine have no strong preference for Eu.

  10. A basalt from an intra-oceanic island arc, far from any continental crust, has high Ba, K and Pb but low Nb and Ta on a primitive-mantle-normalised diagram. The best explanation is that

    1. the source was plume mantle of the ocean-island type, which is enriched in every incompatible element equally
    2. olivine fractionation removed Nb and Ta from the liquid in preference to Ba, K and Pb
    3. the basalt assimilated large amounts of old continental crust on its way to the surface
    4. water-rich fluid from the subducting slab carried mobile Ba, K and Pb into the wedge, but not Nb and Ta
    Show answer

    Answer: D — water-rich fluid from the subducting slab carried mobile Ba, K and Pb into the wedge, but not Nb and Ta

    In subduction zones, aqueous fluids from the slab transport fluid-mobile LILE (Ba, K, Pb) into the wedge but not the high-field-strength elements Nb and Ta, which produces the arc signature. Ocean-island mantle would show Nb and Ta peaks. Olivine takes neither element in quantity. Crustal assimilation can also give an Nb–Ta trough, but the stem rules it out by placing the arc far from continental crust.

  11. Batch (equilibrium) melting follows C_L/C₀ = 1/[D + F(1 − D)]. A mantle source contains 0.50 ppm of an incompatible element and its bulk partition coefficient is D = 0.05. Find the concentration, in ppm, of the element in the melt at a melt fraction F = 0.10. Give the answer to two decimal places.

    Numerical answer — type the value.

    Show answer

    Answer: 3.45

    C_L = C₀/[D + F(1 − D)] = 0.50/[0.05 + 0.10 × 0.95] = 0.50/0.145 = 3.448, which rounds to 3.45 ppm. The element is enriched about seven times over the source, as expected for D far below 1.

  12. A basaltic magma contains 200 ppm Ni. It evolves by Rayleigh fractional crystallisation, C_L/C₀ = F^(D − 1), where F is the fraction of melt remaining, and the bulk partition coefficient of Ni is D = 6. After 30% of the original magma has crystallised (F = 0.70), what is the Ni content of the residual liquid in ppm? Give the answer to one decimal place.

    Numerical answer — type the value.

    Show answer

    Answer: 33.6

    C_L = 200 × 0.70^(6 − 1) = 200 × 0.70⁵ = 200 × 0.16807 = 33.6 ppm. A compatible element (D > 1) falls steeply in the liquid, from 200 to about 34 ppm after only 30% crystallisation.

  13. A parent magma contains 12.0 wt% MgO. It evolves by removal of olivine containing 46.0 wt% MgO, and the daughter liquid contains 7.0 wt% MgO. Assume the extract is pure olivine and use the mass balance C_P = x·C_E + (1 − x)·C_D. What percentage of the parent mass was removed as olivine? Give the answer to one decimal place.

    Numerical answer — type the value.

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    Answer: 12.8

    x = (C_P − C_D)/(C_E − C_D) = (12.0 − 7.0)/(46.0 − 7.0) = 5/39 = 0.1282, that is 12.8% of the parent. Check: 0.1282 × 46 + 0.8718 × 7 = 5.90 + 6.10 = 12.0.

  14. A rock contains, in moles per 100 g, SiO₂ 1.20, Al₂O₃ 0.13, K₂O 0.04, Na₂O 0.06 and CaO 0.03; ignore all other oxides. Use this simplified norm: K₂O forms orthoclase (1 K₂O : 1 Al₂O₃ : 6 SiO₂), Na₂O forms albite (1 : 1 : 6), the remaining Al₂O₃ combines with CaO to form anorthite (1 CaO : 1 Al₂O₃ : 2 SiO₂), and any SiO₂ left over is normative quartz. How many moles of normative quartz per 100 g are there? Give the answer to two decimal places.

    Numerical answer — type the value.

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    Answer: 0.54

    Orthoclase uses 0.04 Al₂O₃ and 6 × 0.04 = 0.24 SiO₂; albite uses 0.06 Al₂O₃ and 6 × 0.06 = 0.36 SiO₂. Al₂O₃ left = 0.13 − 0.10 = 0.03, which matches CaO 0.03, so anorthite uses 2 × 0.03 = 0.06 SiO₂. Silica consumed = 0.24 + 0.36 + 0.06 = 0.66, so normative quartz = 1.20 − 0.66 = 0.54 mol: the rock is silica-oversaturated.

  15. A suite of basalts from one volcano shows La varying about two-fold, La/Th and La/Sm almost constant, and Ni and Cr decreasing as La rises. Which process most likely generated the variation within the suite?

    1. Different degrees of partial melting of one common peridotite source, with melt fraction varying between samples
    2. Mixing between a mantle melt and a continental crustal melt rich in La and Th
    3. Fractional crystallisation of olivine and clinopyroxene from a common parental magma
    4. Melting in the garnet field for some samples and in the spinel field for others
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    Answer: C — Fractional crystallisation of olivine and clinopyroxene from a common parental magma

    Constant ratios of incompatible elements (La/Th, La/Sm) together with falling compatible elements (Ni, Cr) are the signature of fractional crystallisation: all incompatible elements are enriched by the same factor as the liquid shrinks, while olivine and clinopyroxene strip out Ni and Cr. Variable partial melting is the tempting alternative, but it would change La/Sm strongly because the two elements have different D. Crustal mixing would shift La/Th, and a garnet–spinel contrast would change Dy/Yb.

  16. The Deccan Traps, erupted about 66 Ma, are generally attributed to which mantle plume, whose hotspot track continues as the Laccadive–Chagos ridge?

    1. The Kerguelen plume, which produced the Rajmahal Traps of eastern India
    2. The Hawaiian plume, which lies beneath the central Pacific plate
    3. The Réunion plume, whose present position is beneath Réunion Island
    4. The Iceland plume, which lies beneath the North Atlantic ridge
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    Answer: C — The Réunion plume, whose present position is beneath Réunion Island

    The Deccan Traps are linked to the Réunion plume: as India drifted north the track was laid down as the Laccadive–Chagos ridge and the Mascarene plateau, ending at Réunion. Kerguelen is the tempting answer because it also affected India, but it is linked to the older Rajmahal Traps of the Early Cretaceous. Hawaii and Iceland are in other oceans.

  17. In a Hawaiian-type volcano, the voluminous shield stage is followed, as plate motion carries the volcano off the plume, by magmas that are

    1. ever more silica-rich and calc-alkaline, with andesite and dacite becoming dominant and rhyolite last
    2. alkali basalt in the post-shield stage, then small volumes of strongly alkaline basanite or nephelinite
    3. more tholeiitic, formed at ever higher degrees of melting as the volcano moves, ending in komatiite
    4. identical in type to the shield stage, because the plume source never changes in composition
    Show answer

    Answer: B — alkali basalt in the post-shield stage, then small volumes of strongly alkaline basanite or nephelinite

    As the volcano leaves the plume centre, melting degrees fall and the lithosphere thickens, so the magmas become alkaline (post-shield alkali basalt) and, in the late rejuvenated stage, strongly alkaline basanite and nephelinite at the lowest melt fractions. The shield stage itself is tholeiitic. Higher degrees of melting would be expected near the plume axis, not away from it, and calc-alkaline rhyolite is an arc, not an ocean-island, product.

  18. DePaolo's AFC equation is C_m/C_m0 = F^(−z) + [r/(r − 1)]·[C_a/(z·C_m0)]·(1 − F^(−z)), with z = (r + D − 1)/(r − 1), where r is the rate of assimilation divided by the rate of crystallisation, F is the fraction of melt remaining, C_m0 is the initial magma concentration and C_a the assimilant concentration. A basaltic magma contains 10 ppm of a perfectly incompatible element (D = 0) and assimilates crust containing 60 ppm of it while crystallising, with r = 0.2. What is its concentration in ppm when F = 0.5? Give the answer to the nearest whole number.

    Numerical answer — type the value.

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    Answer: 35

    z = (0.2 + 0 − 1)/(0.2 − 1) = 1, so F^(−z) = 2. Then C_m/C_m0 = 2 + [0.2/(−0.8)] × [60/(1 × 10)] × (1 − 2) = 2 + (−0.25)(6)(−1) = 2 + 1.5 = 3.5, so C_m = 35 ppm. Check by mass balance: crystallised mass = 0.5/0.8 = 0.625 and assimilated mass = 0.2 × 0.625 = 0.125 of the initial magma, so C_m = (10 + 0.125 × 60)/0.5 = 35 ppm. Pure Rayleigh crystallisation would give only 20 ppm.