Igneous Petrology and Volcanology

Lava springs, Kilauea volcano, Hawaii

Lectures, H. C. Sheth, Dept. of Earth Sciences, IIT Bombay

• Earth is a planet ~4.5 billion years old and has an average radius of 6,371 km.

• Earth has threemain divisions orshells:

1. The core (mostlymetallic iron andnickel).

2. The mantle (mostlyFe-Mg silicaterocks).

3. The crust (varioussilicates, oxides,carbonates, etc.)

Seven elements that make up ~97% of the Earth by mass, and which make up various minerals and rocks

Granite

The main elements that make up the Earth’s Crust (by mass and by volume)

The Earth’s interior

Divisions of the Core and the Mantle are:

• The Inner Core (5150 km-6371 km)– Pressures are so great that iron is

solid, despite its high temperature.• The Outer Core (2900 km-5150 km):

Iron is molten.• The Lower Mantle (670 km-2900

km): Dense silicate rocks• The Upper Mantle (base of the crust

to 670 km): Dense silicate rocks – The temperature at the core-mantle

boundary is ~ 5000oC.

Heat sources in the Earth:1. Heat from the early accretion and differentiation of the

Earth2. Heat released by radioactive decay

Heat transfer is by:1. Radiation (heat from distant source via an intervening

medium)2. Conduction (hotter and colder bodies in physical

contact)3. Convection (hotter regions of a fluid upwell, colder

regions sink)

• Igneous rocks are formed through the cooling and solidification of magma.

• Magma is molten, mobile rock material existing within a planet, generated by natural processes.

• No magmas are made up of metallic Fe-Ni; liquid Outer Core cannot be the source.

• Most magmas are silicates, indicating silicate sources (Mantle, crust, or both).

• The unusual “carbonatites” are carbonates of Ca, Mg, Fe, etc., and also come from the Mantle.

• The science of igneous rocks is called igneous petrology

(Latin “ignis” = fire, compare Sanskrit “agni”; Greek “petra” = rock, “logia” = discourse).

Textbooks

• Best, M. G. Igneous and Metamorphic Petrology, 2nd Edn., Blackwell, 2003.• Cox, K. G., Bell, J. D. and Pankhurst, R. J. The Interpretation of Igneous Rocks. Unwin Hyman, 1979.• Hall, A. Igneous Petrology, 2nd Edn., Longman, 1996.• McBirney, A. R. Igneous Petrology, 3rd Edn., Jones & Bartlett, 2006.• Middlemost, E. A. K. Magmas and Magmatic Rocks. Longman, 1985.• Parfitt, E. and Wilson, L. Fundamentals of Physical Volcanology. Wiley-Blackwell, 2008.• Winter, J. D. Introduction to Igneous and Metamorphic Petrology. Prentice-Hall, 2001.

More textbooks

• Sen, G. Earth’s Materials: Minerals and Rocks. Prentice-Hall, 2001. •Ragland, P. C. Basic Analytical Petrology. 1989.• Middlemost, E. A. K. Magmas, Rocks and Planetary Development. Longman, 1997.•Wilson, M. Igneous Petrogenesis. Unwin Hyman, 1989.• Sigurdsson, H. and others, Encyclopedia of Volcanoes. Academic Press, 2000.• Faure, G. Origin of Igneous Rocks: The Isotopic Evidence. Springer, 2001.

• Magma, despite being the most important concept inigneous petrology, cannot be directly observed, collected,or experimented with.

• So we use the materials erupted by volcanoes (lava,pyroclastics, xenoliths of crustal and mantle rocks), aswell as magma bodies frozen at deeper levels andsubsequently exposed by erosion.

Lherzolite (two-pyroxene peridotite) xenolith in alkali basalt lava, San Carlos,

Arizona, U.S.A.

• “Geothermal gradient” or “Geotherm” is the rate ofincrease of temperature with depth in the Earth.• It is about 30oC/km in the crust.• The Geotherm is not linear but falls off with depth. If itdid not, the Earth would be molten inside.

• Pressure (force per unit area) prevents melting, despite high temperature. • Pressure within the Earth is referred to as “confining pressure” or “lithostatic pressure”. • This is similar to the “hydrostatic pressure” experienced by a diver entering a swimming pool. Water can flow and this equalizes the pressure in all directions. The same is true of rocks; rocks flow (“creep”) under high confining pressure and this equalizes the pressure in all directions. • The lithostatic pressure at any depth in the Earth is given by P = gh, where is density of overlying rocks, g the acceleration due to gravity, and h the height of the rock column.

• Pressure units:Pascal (Pa): This is the SI unit. 1 Pa = 1 N/m2 (a force of 1 N applied over an area of 1 m2).Because F = M.a (mass into acceleration), 1 N itself = 1 kg x ms-2.So 1 Pa = 1 kg.ms-2 x (1/m2) = 1 kg.m-1s-2

Pascal is an inconveniently small unit. So we useMegapascal (Mpa): 1 MPa = 106 Pa, andGigapascal (GPa): 1 GPa = 109 Pa.There are also bar and kilobar.1 bar = 0.987 atmosphere; 1 atmosphere = 1.013 bar. Kilobar (kb) = 1000 bars = 108Pa = 0.1 GPaSo, 1 GPa = 10 kb.

Q: Calculate the lithostatic pressure at the base of the average continental crust.A: (Using SI units)The lithostatic pressure at the base of the continental crust (35 km depth) is given by P = gh= 2800 kg/m3 x 9.8 m/s2 x 35000 m = 9.6 x 108 kgm-1s-2

= 9.6 x 108 Pa ~ 1 GPa (10 kb).Thus, 1 kb pressure corresponds to 3 to 3.5 km depth in the Earth.Work this out in c.g.s. units.

Big question: Convection in the mantle – whole mantle or layered?

Plate tectonics: Lithosphere is the outer strong shell of the Earth, consisting of the crust and the uppermost mantle, and divided into many plates, in perpetual relative motion.• Magma genesis in the Earth is intimately linked to tectonics.

Alfred Wegener

Intraplate volcanism: “Hotspots”

Tuzo Wilson Jason Morgan

Hotspots were explained by upwelling “mantle plumes”.

Structure and fabric of the Earth’s ocean floor, and the even more rugged topography of the continents, as revealed by satellites

The Hawaiian island-seamountchain

The modern mantle plume hypothesis: Plume “heads” and “tails”, plumes originating at the Core-Mantle Boundary

Ian Campbell

Plumes are the biggest debate in Solid Earth Sciences today.

Gillian Foulger

Don Anderson

Magmas in different tectonic settings often have distinctive petrological and geochemical characteristics.

• Pressure and temperature both increase within the Earth with depth. • Molten rock, “magma” or “lava”, thrown out of volcanoes on the Earth’s surface attests to great heat within the Earth. • However, the Earth is not molten inside, as evidenced by seismic data.

• Most of the mantle and crust are solid, not liquid. Thus magma must be specially made, in particular places.

Anak Krakatau, Sunda Strait, Indonesia

Igneous Petrology and VolcanologyPart 1: Magma Generation

Mantle minerals

Peridot (gem quality olivine)

Chemical composition of the

Upper Mantle

• The Upper Mantle is made up largely of peridotite = olivine + clinopyroxene + orthopyroxene + plagioclase/spinel/garnet (depending on the depth).

Olivine is the main constituent of peridotite.

Garnet peridotite (width of view 4 cm)

Pyrolite is a pyroxene-olivine material synthesized by Ringwood, who proposed it as the model mantle composition. It is a mixture of three parts peridotite and one part basalt.

A. E. Ringwood

• The upper mantle mayalso contain somepyroxenite or garnetpyroxenite and eclogite(garnet + omphaciteclinopyroxene).• Note that these rocksare mafic rocks (andhigh-pressure equivalentsof basalt), whereasperidotite is ultramafic.

Eclogite

Pyroxenite vein in peridotite

• Fertile mantle peridotite is either plagioclase, spinel, or garnet lherzolite, depending on depth (pressure).• The boundaries between these fields are boundaries of metamorphic reactions, mainly controlled by pressure. The slopes of the boundaries mean that pressure is more important than temperature.

The stability fields of plagioclase, spinel and garnet lherzolites.

•At <10 kb (~ 25-30 km depth), mantle peridotite consists of plagioclase, enstatite (orthopyroxene), clinopyroxene and olivine.

• Between 30-75 km depth, plagioclase transforms to spinel.

CaAl2Si2O8 + Mg2SiO4 = 2MgSiO3 + CaMgSi2O6 + MgAl2O4plag + ol = opx + cpx + sp

• At >75 km depth, spinel transforms to garnet.MgAl2O4 + 4MgSiO3 = Mg2SiO4 + Mg3Al2Si3O12

sp + opx = ol + gt• Plagioclase, spinel, and garnet are thus never found together in the same mantle rock sample. • Plagioclase lherzolites are found in ophiolites and layered mafic intrusions. Garnet lherzolites are restricted to kimberlite pipes.

Solid solutions

• When one or more ions substitute for other ions in a mineral’s atomic structure without seriously distorting the structure or by introducing chemical imbalances, a solid solution results.• Minerals that form a solid solution are called isomorphs.

They have similar atomic structure and crystal morphology.• Generally, ionic substitutions require the difference in ionic size of a substituting and substituted ion to be no more than 15%. • Also, the resultant atomic structure should not have any net electrical charge.• The mineral olivine, written (Mg,Fe)2SiO4, is a very good example of solid solution where Mg2+ and Fe2+ ions can substitute for each other.

• Mg2+ and Fe2+ ions have radii of 0.78 Å and 0.83 Å, resp. and identical charge. So the olivine structure is stable and electrically neutral. • Pure Mg2SiO4 is an end member called forsterite (Fo), and pure Fe2SiO4 is an end member called fayalite (Fa). • Natural olivines can be either, or usually anywhere in between, e.g., (Mg60Fe40)2SiO4, or Fo60Fa40. • Such complete substitution between two endmembers is called diadochy.

• Plagioclase feldspars (albite, NaAlSi3O8, to anorthite, CaAl2Si2O8) also exhibit extensive solid solution, but of a different type. • This type of solid solution involves coupled substitution of two or more ions by two or more other ions in the atomic structure.

• In terms of cation size, Na is the largest, followed by Ca. • Al and Si are much smaller and similar in size. • The Na+ ion has one positive charge, whereas Ca2+ has two positive charges. Therefore, when a Na+ ion is replaced by a Ca2+ ion, an excess positive charge is produced. •This extra positive charge must be cancelled by another ionic substitution in the structure: substitution of a Si4+ ion by an Al 3+ ion.

Mineral compositions: Mole % and weight %

• Many phase diagrams are plots of temperature (Y-axis) vs. composition (X-axis). • The composition can be represented in mole % or weight %. It is important to understand the distinction. • Forsterite (Fo) and enstatite (En) are both made up of MgO and SiO2. • Their molecular formulae are 2MgO.SiO2 and MgO.SiO2, i.e., the ratio of MgO to SiO2 moles is 2:1 in forsterite and 1:1 in enstatite.• So, in terms of mole percent, forsterite is composed of 67% MgO and 33% SiO2. Enstatite is composed of 50% MgO and 50% SiO2.What would be they composed of in terms of weight percent?

• Number of moles = Weight percent / molecular weight• Weight percentages of MgO and SiO2 in a mineral (say, forsterite) are different from mole percentages of MgO and SiO2 because MgO and SiO2 have different molecular weights. • Molecular weight of MgO is 40.3, of SiO2 60.1, and therefore wt.% composition of forsterite is different from the mole % composition of forsterite.• So, pure (100%) forsterite by weight will contain MgO = [2 x MgO MW / (2 x MgO MW + SiO2 MW)]= [(2 x 40.3) / (2 x 40.3 + 60.1)] x 100 % = 55.3 %.and it will contain (100 – 55.3) = 42.7% SiO2.

Similarly, 100% enstatite by weight will containMgO = [MgO MW / MgO MW + SiO2 MW)] x 100 = 40%.and it will contain (100 – 40) = 60% SiO2.

• For volatile-absent conditions, the melting of materials or rocks needs higher temperatures at higher pressures. • The solid state is favoured at higher pressures. Why?

Melting minerals and rocks

• This is because higher pressure makes a phase with lesser volume the preferred one, i.e., solid over liquid.• Higher temperature, on the other hand, favours randomness (increased entropy), i.e., liquid over solid.

Thus the slope of solid-liquid equilibrium should be positive, and increased pressure raises the melting point.

For volatile-absent conditions, the melting of materials or rocks needs higher temperatures at higher pressures.

Melting of a single mineral:

• A mineral (say, albite) has a fixed melting point for a given pressure. • The melting point increases with increasing pressure under normal (volatile-absent) conditions.

• Melting of a natural rock, which contains two or more minerals, is over a melting interval

at any pressure. • This is because of different degrees of melting of different minerals at that pressure.

• The solidus is the curve below which the rock is totally solid. • The liquidus is the curve above which the rock is totally liquid.• Between the two curves a mixture of unmelted rock and melt exists.• This is known as partial melting.

• So, partial melting does not mean melting a part of the source rock. • Most rocks have two or usually more than two minerals.• Partial melting means that the minerals in the source rock are variably melted, depending on their melting points. • Simply speaking, at the given pressure and temperature, minerals with lower melting points are melted out, leaving minerals with higher melting points in the solid residue.• However, it is not so simplistic in reality, because of solid solution.

Not partial melting

This is how partial melting looks.

• An olivine (Mg-Fe solid solution) produces an Fe-rich melt on partial melting, and the residual olivine becomes correspondingly Mg-rich.

• Most important mantle minerals – olivines, pyroxenes, and plagioclase (in shallow mantle) are solid solutions.

• A clinopyroxene or orthopyroxene crystal behaves similarly to olivine.• A plagioclase crystal produces a Na-rich melt on partial melting, and becomes correspondingly Ca-rich.• Thus, at a given temperature and pressure within the partial melting region, all of these minerals have variably melted and have all changed in composition. • The partial melt is a blend of melts from all these minerals (except some mineral which did not melt at all).• The residue is the unmelted crystals of all minerals, except some mineral that was completely melted out.

• Degree of melting

(also called melt

fraction)= Mass of melt produced / Mass of source rock• So if we start with 100 g of solid rock and partially melt it, 10% melting means 10 g of partial melt and 90 g of solid residue.

Locating the melting curve, or the solidus and liquidus with many experiments at various P and T

(melt will be represented by glass)

• The first melt droplets typically form at the junctions of several grains.

• Melt droplets get larger and larger with progressing melting and join together and form continuous films.

• The ability to form an interconnected film is dependent upon the dihedral angle (), a property of the melt.

For dihedral angle < 60, melt forms an interconnected network. For angles > 60, melt pockets remain isolated.

After sufficiently advanced melting, melt can collect in small pools and migrate upwards through pores, channels, and later, fractures (dykes).

• Most or all magmas form by partial melting in the Earth. • Why is melting always partial and never total? • This is because after a few degrees of melting, the melt cannot be retained. It escapes due to its buoyancy. • Melt rises relative to unmelted source rock due to its being liquid and buoyant. • The residue of melting also rises relative to unmelted source rock as the melt has a greater Fe/Mg ratio than the residue, making the residue lighter than the unmelted rock.

15

10

5

00.0 0.2 0.4 0.6 0.8

Wt.% TiO2

DuniteHarzburgite

Lherzolite

Tholeiitic basalt

Residuum

• Garnet lherzolite (ol + cpx + opx + gt) is fertile mantle.

• Harzburgite (ol + opx + gt) and dunite (ol) are refractory residuum left after basalt has been extracted by partial melting.

Partial melting is a major process of igneous

differentiation, with major geochemical effects.

Lherzolite: Two-pyroxene peridotitePeridotites by definition have 40% or more olivine

(IUGS)

Olivine

ClinopyroxeneOrthopyroxene

Lherzolite

Websterite

Orthopyroxenite

Clinopyroxenite

Olivine Websterite

Peridotites

Pyroxenites

90

40

10

10

Dunite

A simple ternary plotting scheme in which X, Y and Z together make up 100%

Under conditions of no melting, the geotherm is below the solidus of mantle peridotite at all pressures. Partial melting can be brought about by temperature increase, pressure reduction, or volatile influx.

Three mechanisms to produce partial melting

Mechanism 1: Adding heat at constant pressure: e.g., heat transfer into the continental crust by a mantle-derived magma. This process is unsatisfactory to explain large-volume volcanic provinces, however, because of several reasons.

Melting a rock by supplying heat and increasing its temperature is not efficient or significant.

Mechanism 1 is insignificant because:1. Heat conduction through rocks is extremely slow.2. Most magmas do not have superheat (excess temperature

above the liquidus).3. A magma trying to melt a country rock has to not only bring

the country rock to its solidus temperature (say to 900 oC from 600 oC) by using its own heat, but

4. The magma has to then supply the latent heat of melting to the country rock (heat consumed in solid to liquid conversion at constant temperature), which is very high.

5. So a magma supplying its heat to the country rock will itself quickly freeze.

6. Anatexis therefore occurs under special conditions, with long-term elevated heat flow, and produces granitic melts.

Consider heating ice to produce water. Phase Rule says P + F = C + 2.Here C = 1. If P = 2 (solid and liquid coexisting), F = 1. So, changing the pressure means having to change the temperature, along the phase boundary, as long as P = 2. But if pressure is constant, temperature must remain constant. Thus, adding heat does not raise the temperature, but gets used up in the phase change.

Phase diagram for H2O, to explain the latent heat concept:

Position of the H2O-saturated ternary eutectic in the albite-orthoclase-silica system at various pressures. The shaded portion represents the composition of most granites. Included are the compositions of the Tuolumne Intrusive Series (California, U.S.A.), with the arrow showing the direction of the trend from early to late magma batches.

Many granite magmas approach the Q-Ab-Or ternary eutectic. They are either residual liquids after advanced fractional crystallization, or minimum (eutectic) melts of crustal sources.

Mechanism 2: Melting a rock by decreasing its pressure,

without adding or removing heat, is very efficient and significant. This is known as adiabatic decompression, and produces partial melts even as the rising source rock is slightly cooling.

• Adiabat is the curve which shows heating of mantle materialdue to compression (or cooling of mantle because ofdecompression) alone.• Adiabatic means that no heat is supplied to or lost from theupwelling mass.• However, the upwelling mass cools (because it expands dueto decreasing pressure, and its internal heat gets distributedwithin an increasingly larger volume).• The rate of adiabatic cooling of upwelling mantle is ~0.3oC/km.• However, the solidus is reduced ~ 3 oC/km due todecompression.• The adiabat therefore intersects the solidus, and partialmelting starts.

• Potential temperature

(Tp) is the temperature a mantle rock would have if brought adiabatically to the surface without melting.• Mantle with higher Tpbegins to melt deeper than mantle with lower Tp.• Only Tp can strictly measure mantle temperature variations.

• Eclogite has a greatly lower solidus and liquidus than lherzolite at various pressures in the upper mantle. • Eclogite liquidus is not much above lherzolite solidus.• So, if the mantle contains substantial eclogite besides lherzolite, much more melt is produced for a given temperature and pressure.

Peter Wyllie

Dean Presnall

Adiabatic decompression melting of an upwelling, mixed pyroxenite-peridotite diapir

Adiabatic decompression melting is significant wherever the mantle upwells – under mid-ocean ridges, continental rifts, and hotspots.

East African Rift

Afar Triangle

Decompression melting is a major process involved in the production of flood basalts, many of which formed along rifting continental margins.

Mechanism 3: Depressing the mantle solidus by adding

volatiles

Higher pressure means higher melting point, if no volatiles present. Volatiles (H2O and CO2) depress the melting point of a mineral like albite (NaAlSi3O8).

Dry melting: solid liquidAdd water; water enters the melt.Reaction becomes:solid albite + water = albite liquid (aqueous)

The effect of H2O saturation on the melting of albite

At depth, during conditions of melting,PL = lithostatic pressure (depends essentially on depth)PF = fluid pressure (from H2O, CO2, SO2…)PL and PF can vary independently. PF depends on the amount of volatiles, their solubilities, P and T.If PF = 0, this is dry melting. If PH2O < Ptotal, the usual case, this is water-undersaturated melting.If PH2O = Ptotal, this is water-saturated melting.If PH2O > Ptotal, this is water-oversaturated conditions. Under these conditions, the walls of the source region must be strong enough to contain the excess water pressure (as in a pressure cooker), or an explosion would result.

Volatiles (H2O and CO2) lower the solidi of mantle and crustal rocks. H2O depresses melting points more than CO2 does. The solidus depression becomes more at greater pressures, because more H2O or CO2 can be dissolved in the melt at higher pressures.

• At atmospheric pressure, one cannot maintain a dissolved vapour phase, as vapour escapes. • The curves for vapour-saturated and dry conditions thus meet at a single point, close to 1118 oC for albite, its atmospheric pressure melting point.

The eutectic point (temperature at which the first melt is produced) for the diopside-anorthite binary system is much lower for 1 atm. than for for 1 GPa. The eutectic composition also is quite different. H2O greatly depresses the eutectic temperature, and favours diopside over anorthite.

Dry and water-saturated solidi for some common rock types

• The more mafic the rock the higher is the solidus. • All solidi are greatlylowered by water.

Liquidi of rocks are also correspondingly greatly lowered by water.

Dry and water-saturated solidi and liquidi for gabbro

Possible partial melting conditions under hotspots and ridges

The addition of H2O to a rock dramatically decreases the melting temperatures, and with increasing pressure, the melting point depression is more. After a while, however, the wet melting curve has the same slope as the dry melting curve. Why?

• The Clapeyron equation is dP/dT= S/V, where dP and dT are the change in pressure and temperature respectively, and S is the change in entropy, and V the change in volume. • If both S and V are positively correlated, then dP/dT is positive, i.e., the solid to liquid reaction boundary has a positive slope. • This is the situation under fluid-free conditions, where higher P requires higher T for melting.

In the Earth, under real conditions, one doesn’t have unlimited amounts of water available.

• If H2O is added to the system (say, albite), however, the equation isH2O (vapour) + albite = liquid (aq) • The reaction proceeds to the right because the product (liquid) has a greater ability to absorb the water than the reactant (albite). • At low pressures, the H2O vapour in the equation above has a very large volume compared to the solid or the liquid. Thus V is negative. • But S is positive. Thus, dP/dT, the melting reaction boundary, has a negative slope, of a small magnitude, because the denominator (V) has a much larger magnitude than the numerator (S).

• At higher pressures, however, the vapour being highly compressible, V becomes less and less negative, whereas S changes much less. • Note that more and more H2O gets dissolved with increasing P, but the rate of dissolution of H2O and therefore the amount of melting point reduction decrease. • The slope thus becomes steeper. • At very high pressures, the vapour phase occupies a very small volume, and V becomes positive again. • The slope thus returns to a positive value, similar to the curve for dry albite. • There is a temperature minimum on the liquidus.

Flux-induced melting is very important in subduction zones.

Island arcs and active continental margins

Structure of an island arc

The island arc of Japan, with volcanoes (dots) active in the past 1 million years

Mount Fuji, Japan’s famous volcano

Island arc magmatism results from subduction of one oceanic plate beneath another oceanic plate.

Barren Island, Andaman Sea: India’s only active volcano, a stratovolcano which is both effusive and explosive, part of the Indonesian arc.

Barren Island in eruption, March 2009

Continental arc magmatism results from the subduction of an oceanic plate beneath a continental plate, e.g., Andes.

Cotopaxi

Chimborazo

The Cascades Range of western U.S.A.

Mount Saint Helens, Cascade Range: May 1980 eruption

Volcanoes in North America (Canada + U.S.A. + Mexico) and Central America, seen here, are part of the Pacific Ring of Fire.

Isotherms and mantle flow lines in subduction zones:1. Oceanic sediments. 2. Mantle wedge. 3. Arc crust.4. Lithospheric mantle of the subducting plate.5. Asthenosphere beneath the slab.

Schematic diagram to illustrate how a shallow dip of the subducting slab can pinch out the asthenosphere from the overlying mantle wedge.

The subducting Pacific slab under Japan dips steeply.The Andes overlie a shallow-dipping slab.Due to eastward mantle flow?

Schematic diagram illustrating (a) the formation of a gabbroic crustal underplate at an continental arc and (b) the remelting of the underplate to generate tonalitic plutons.

Left: the basalt tetrahedron. Right: the base of the basalt tetrahedron using cation normative minerals, with Hawaiian subalkaline and alkaline rocks, projected from cpx.

Yoder and Tilley (1962) proposed the Ne-Di-Fo-Qtz basalt

tetrahedron on which all basalts can be represented. This is cut by two planes.

Unlike CIPW norms, which express the normative minerals as weight percentages, and are in wide use in the U.S.A., molecular/cation norms express the normative minerals as molecular/atomic percentages. These were proposed by Niggli (1936) and Barth (1962) and are more popular in Europe.

By number of moles, 1Ne + 2Qz = 1AbNa2O.Al2O3.4SiO2 + 2SiO2 = Na2O.Al2O3.6SiO2And, also by moles, 1Fo + 1Qz = 2En2MgO.SiO2 + SiO2 = 2(MgO.SiO2)

The Di-Fo-Ab plane is called “plane of silica undersaturation”. Basalts which are undersaturated in silica plot on the nepheline side of this plane. The Di-En-Ab plane is called “plane of silica saturation”. Basalts which are oversaturated in silica plot on the quartz side of this plane.

Basalts that plot between the two planes can be considered simply saturated, with neither nepheline nor quartz in the norm.

• The alkaline and subalkaline rocks, when plotted on the base of the tetrahedron using the (cation) normative minerals ne, ol and q, are separated by the dividing line which is close to the plane of silica undersaturation. • Names for basalts based on normative composition: Oversaturated tholeiite: normative q + hySaturated tholeiite: normative hy, no q or olOlivine tholeiite: normative hy + olOlivine basalt: normative ol, no hyAlkali olivine basalt: normative ol + ne

Ne

Fo En

Ab

SiO2

Oversaturated(quartz-bearing)tholeiitic basalts

Highly undesaturated(nepheline-bearing)

alkali olivine

basalts

CO2

H2Odry

P = 2 GPa

Effect of water and CO2 on the positionof the eutectic in the basalt system:

Water moves the (2 Gpa) eutectictoward higher silica, while CO2moves it to more alkaline types

Melting experiments with depleted and enriched lherzolites

• Melts become more and more magnesian with increasing temperature (and degree of melting).

• Tholeiites favoured by shallower melting25% melting at <30 km tholeiite25% melting at 60 km olivine basalt

• Tholeiites favoured by greater degree of partial melting20 % melting at 60 km alkaline basalt

• incompatibles (alkalis) initial melts30 % melting at 60 km tholeiiteAlkaline melts are favoured by higher pressures and

lower degrees of melting.

(Previous page) Dashed lines are contours representing percent partial melt produced. Strongly curved lines are contours of the normative olivine content of the melt. “Opx out” and “Cpx out” represent the degree of melting at which these phases are completely consumed in the melt.

The significance of high-MgO volcanic rocks

• For a constant pressure (depth), and source composition, MgO-rich liquids indicate higher temperatures and degrees of mantle melting than MgO-poor liquids. • However, high-MgO picritic liquids are produced by peridotite melting at pressures > 2 GPa (basalts are only directly produced from peridotite at < 2 GPa). • Olivine is a phase very stable at low pressures, and is common in mafic lavas forming at shallow depths. •At > 25 kb, olivine in the peridotite melts out first, making melts highly magnesian (“picritic”).

• Very-high-MgO liquids (up to 30 wt.%) used to erupt as surface lavas in Archaean times. These are called komatiites

after the type locality Komati in South Africa. • They indicate that the Archaean mantle was much hotter than now.• They have a characteristic texture called spinifex, with long blades and feathers of quench olivine.

Komatiite with spinifex texture in thin section

How pressure affects the liquidus mineral

Phase diagram for the melting of a lunar basalt (above) and a Snake River (Idaho, U.S.A.) tholeiitic basalt under anhydrous conditions.

Pressure effects on binary eutecticsPressure changes the stability limits of minerals and thereby the sequence of minerals that crystallize or melt out.

A Di50An50 melt at 1 Gpa will precipitate clinopyroxene first, but if it rises to 1 atm., it will precipitate plagioclase, and the clinopyroxene will start to get resorbed.

Increased pressure moves the ternary eutectic (first melt) from silica-saturated to highly undersaturated alkaline basalts.

Change in the eutectic (first melt) composition with increasing pressure from 1 to 3 GPa projected onto the base of the basalt tetrahedron. Eutectic melts become silica-undersaturated with increasing pressure.

Liquids and residua of melted pyrolite

Identifying primary magmas

• Primary magmas – magmas that have not undergone any changes since formation (fractionation, assimilation…) –remain elusive. • Several characteristics have been proposed for primary magmas, but these are actually good at demonstrating that a particular magma is not primary. • Examples of criteria are1. High MgO content and high Mg Number (problem: olivine accumulation, use glasses or aphyric rocks)2. High Cr content (>1000 ppm) and Ni content (>400-500 ppm) (problem: olivine accumulation, as above)

3. Presence of mantle xenoliths (couldn’t have suffered crystal fractionation if brought xenoliths up) – what about wall-rock reaction?4. Olivine compositions that are highly forsteritic, Fo 90-91(this assumes a peridotite, not eclogite or pyroxenite, mantle, and is therefore model-dependent)5. High-pressure, alkalic compositions, steep REE patterns, mantle xenoliths, and so on…• No criterion can prove a magma to be primary.

Fractional melting vs. batch (equilibrium) melting

The simple

Fo-Di-Py

mantle rock

system

Fractional melting (Rayleigh melting): Small melt fractions produced and removed from the source immediately• In the Fo-Di-Py system, consider a starting rock composition X (Fo > Py > Di). • First melts have composition E (ternary eutectic melts), produced at 1670 oC, and can be erupted.• Residue moves from X to X’, X’ to X’’.• Melts still have composition E, because all three phases are contributing, until residue reaches R.

• R is the point where Di has disappeared (melted out).• Melt composition cannot remain at E now.• With two minerals now remaining, no melting occurs until the temperature reaches 1770 oC.• Now, melt of composition Bis produced as the binary eutectic melt of Py and Fo, and erupted.• B has much more Py than Fo components. Thus, residual composition shifts towards Fo.

• Finally, with Py melted out as well, the residue consists only of Fo. This is the rock dunite. • If the temperature ever reaches the melting point of Fo at this pressure, there will be a pure olivine melt.• Thus, during fractional

melting, melting shows gaps and compositional jumps (E, then B, then pure Fo).

• During batch melting, first melts are still the eutectic melts E. Let’s not separate them from the source, but let them equilibrate with the source further.• With more melting, Di is consumed first. With Di out, melt composition now moves towards B, because of contributions from Py and Fo alone.• At A, Py is also melted out. Melt A exists with residue Fo (only), and bulk composition X.

• At A, lever rule tells us that 46% melt has been produced (ratio of lengths XFo/AFo.• Because only Fo remains in the residue at A, melt composition must now turn directly towards Fo and X.• Total melting is achieved when the melt reaches the liquidus of the bulk composition X.• Thus, batch melting shows a smooth progression of melt compositions (E changing to A changing to X).

Geochemical data and petrogenetic models

Geochemical data are essential for understanding the petrogenesis of igneous rocks, and provide valuable information about the following:1. The nature of the source rocks.2. The nature of the melting processes (fractional, batch...) 3. Processes of magmatic evolution (e.g., crystal fractionation, contamination) Geochemical data can be divided into:• Major elements: > 1.0 wt.% of a rock• Minor elements: 0.1 – 1.0 wt.% of a rock• Trace elements: < 0.1 wt.% of a rock (i.e., < 1000 ppm) Isotopic ratios (e.g., 87Sr/86Sr).

A typical rock analysisWt. % Oxides to Atom % Conversion

Oxide Wt. % Mol Wt. Atom prop Atom %SiO 2 49.20 60.09 0.82 12.25TiO2 1.84 95.90 0.02 0.29Al2O3 15.74 101.96 0.31 4.62Fe 2O3 3.79 159.70 0.05 0.71FeO 7.13 71.85 0.10 1.48MnO 0.20 70.94 0.00 0.04MgO 6.73 40.31 0.17 2.50CaO 9.47 56.08 0.17 2.53Na2O 2.91 61.98 0.09 1.40K2O 1.10 94.20 0.02 0.35H2O+ 0.95 18.02 0.11 1.58(O) 4.83 72.26Total 99.06 6.69 100.00

Must multiply by # of cations in oxide

Peridotite Basalt Andesite Rhyolite PhonoliteSiO2 42.26 49.20 57.94 72.82 56.19TiO2 0.63 1.84 0.87 0.28 0.62Al2O3 4.23 15.74 17.02 13.27 19.04Fe2O3 3.61 3.79 3.27 1.48 2.79FeO 6.58 7.13 4.04 1.11 2.03MnO 0.41 0.20 0.14 0.06 0.17MgO 31.24 6.73 3.33 0.39 1.07CaO 5.05 9.47 6.79 1.14 2.72Na2O 0.49 2.91 3.48 3.55 7.79K2O 0.34 1.10 1.62 4.30 5.24H2O+ 3.91 0.95 0.83 1.10 1.57

Total 98.75 99.06 99.3 99.50 99.23

Some typical rock analyses

Note magnitude of trace element changes relative to major element changes.

Petrogenetic modelling:

Forward and inverse

Forward modelling:

Assume starting composition, calculate melts

Inverse modelling: Take melt compositions, work back to sources

Crater Lake (Oregon, U.S.A.) data

• Incompatible elements are concentrated in the melt relative to solid (during either melting or crystallization).

• For example, the alkali elements (Rb, Na, K) are highly incompatible.

• Compatible elements are concentrated in the solid relative to liquid (during melting or crystallization).

• We define partition coefficient or distribution

coefficient, Kd, as Kd = Cs/CL, where Cs = concentration of an element in the solid, and CL = its concentration in the liquid.

• For an incompatible element, Kd < 1• For a compatible element, Kd > 1

• A Kd value is specific to an element and a mineral, and also depends on temperature, melt composition, etc.

• But, in general, olivine has a very high Kd for Ni, pyroxene for Sc, and so on. Elements which are incompatible in most minerals are Rb, Ba, Na, K, Ti, Zr, Hf, Nb, U, Th.Table 9-1. Partition Coefficients (CS/CL) for Some Commonly Used Trace

Elements in Basaltic and Andesitic Rocks

Olivine Opx Cpx Garnet Plag Amph Magnetite

Rb 0.010 0.022 0.031 0.042 0.071 0.29

Sr 0.014 0.040 0.060 0.012 1.830 0.46

Ba 0.010 0.013 0.026 0.023 0.23 0.42

Ni 14 5 7 0.955 0.01 6.8 29

Cr 0.70 10 34 1.345 0.01 2.00 7.4

La 0.007 0.03 0.056 0.001 0.148 0.544 2

Ce 0.006 0.02 0.092 0.007 0.082 0.843 2

Nd 0.006 0.03 0.230 0.026 0.055 1.340 2

Sm 0.007 0.05 0.445 0.102 0.039 1.804 1

Eu 0.007 0.05 0.474 0.243 0.1/1.5* 1.557 1

Dy 0.013 0.15 0.582 1.940 0.023 2.024 1

Er 0.026 0.23 0.583 4.700 0.020 1.740 1.5

Yb 0.049 0.34 0.542 6.167 0.023 1.642 1.4

Lu 0.045 0.42 0.506 6.950 0.019 1.563

Data from Rollinson (1993). * Eu3+/Eu2+ Italics are estimated

Rare

Eart

h E

lem

ents

What decides the partition coefficients: Some of the rules

1. If two ions have similar radii and the same valency, the smaller ion is preferentially incorporated into the solid over the liquid.

• If two ions have similar radii, but different valencies, the ion with the higher charge is preferentially incorporated into the solid over the liquid.

Victor Goldschmidt

• For a rock, determine the bulk distribution coefficient D

for an element by calculating the contribution for each mineral.

• Thus, for an element X, and a rock made up of minerals A, B and C with mass proportions WA, WB and WC in the rock, and individual partition coefficients for element X of KdA, KdB and KdC, respectively,

• DX = WAKdA + WBKdB + WAKdC• Be sure to use mass fractions of minerals, not volume

fractions (mode). Convert mode to wt.% as per example.Mineral Mode Sp. gravity Wt. prop. Wt.%Ol 15 3.6 54 17.57Cpx 34 3.4 115.6 37.62Plag 51 2.7 137.7 44.81Sum 100 307.3 100.00

Example: hypothetical garnet lherzolite = 60% olivine, 25% orthopyroxene, 10% clinopyroxene, and 5% garnet (all by weight), using the data in Table above,

DEr = (0.6 · 0.026) + (0.25 · 0.23) + (0.10 · 0.583) + (0.05 · 4.7) = 0.366

Table 9-1. Partition Coefficients (CS/CL) for Some Commonly Used Trace

Elements in Basaltic and Andesitic Rocks

Olivine Opx Cpx Garnet Plag Amph Magnetite

Rb 0.010 0.022 0.031 0.042 0.071 0.29

Sr 0.014 0.040 0.060 0.012 1.830 0.46

Ba 0.010 0.013 0.026 0.023 0.23 0.42

Ni 14 5 7 0.955 0.01 6.8 29

Cr 0.70 10 34 1.345 0.01 2.00 7.4

La 0.007 0.03 0.056 0.001 0.148 0.544 2

Ce 0.006 0.02 0.092 0.007 0.082 0.843 2

Nd 0.006 0.03 0.230 0.026 0.055 1.340 2

Sm 0.007 0.05 0.445 0.102 0.039 1.804 1

Eu 0.007 0.05 0.474 0.243 0.1/1.5* 1.557 1

Dy 0.013 0.15 0.582 1.940 0.023 2.024 1

Er 0.026 0.23 0.583 4.700 0.020 1.740 1.5

Yb 0.049 0.34 0.542 6.167 0.023 1.642 1.4

Lu 0.045 0.42 0.506 6.950 0.019 1.563

Data from Rollinson (1993). * Eu3+/Eu2+ Italics are estimated

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Eart

h E

lem

ents

Rayleigh fractional melting

• In Rayleigh fractional melting, each infinitesimally small melt fraction produced is immediately removed from the source. • The melting equation isCL = [CO (1 – F)(1/Do – 1)] / DOWhereCL = concentration of an element in the liquid; CO = concentration of the element in the original (unmelted) source rockF = melt fraction (weight fraction of produced melt); DO = bulk distribution coefficient prior to the onset of melting

Rayleigh fractional melting

• For the residuum (“restite”), CR = DO x CL• For a perfectly incompatible element, CL /CO is infinity.• When DO = 1, CL /CO = 1 (no change in concentration from source to melt).• For very low degrees of melting, highly incompatible elements are very strongly enriched in the melts, while the more compatible ones remain in the source (e.g., high La/Yb ratios in melts with residual garnet in the source).

Q: A garnet lherzolite mantle source contains 10 ppm Sr and 2000 ppm Ni. The mineralogical composition of the source is olivine (40%), clinopyroxene (30%), orthopyroxene (20%), and garnet (10%). The Kd’s for Sr are: 0.005 (ol), 0.1 (cpx), 0.01 (opx), 0.001 (gt). The Kd’s for Ni are: 12 (ol), 2 (cpx), 4 (opx), and 0 (gt). What will be the Sr and Ni concentrations in the basaltic melts and corresponding residues after (i) 5%, (ii) 10% fractional melting?

A: DOSr = (0.4 x 0.005) + (0.3 x 0.1) + (0.2 x 0.01) + (0.1 x 0.001) = 0.034.DONi = (0.4 x 12) + (0.3 x 2) + (0.2 x 4) + (0.1 x 0) = 6.2

Using CL = [CO (1 – F)(1/DO – 1)] / DO for 5% melting (F = 0.05),CL (Sr) = 10 x [(1 – 0.05)(1/0.034 – 1)] / 0.034 = 68 ppm; CR(Sr) = 0.034 x 68 = 2.31 ppmCL (Ni) = 2000 x [(1 – 0.05)(1/6.2 – 1)] / 6.2 = 337 ppm; CR(Ni) = 6.2 x 337 = 2089 ppmUsing the same relationship for 10% melting (F = 0.10),CL (Sr) = 10 x [(1 – 0.10)(1/0.034 – 1)] / 0.034 = 14.7 ppm; CR (Sr) = 0.034 x 14.7 = 0.50 ppmCL (Ni) = 2000 x [(1 – 0.10)(1/6.2 – 1)] / 6.2 = 352 ppm; CR(Ni) = 6.2 x 352 = 2182 ppmThus, for melts, greater degrees of melting mean dilution of incompatible elements like Sr, and enrichment of compatibleelements like Ni. For residues, progressive melting means depletion of incompatible elements like Sr, and enrichment of compatible elements like Ni.

Equilibrium (batch) melting

• In equilibrium (batch) melting, melt continuously equilibrates with rock and is removed as a single batch.

• The equations for modal batch melting areCL = CO / [DO (1 – F) + F] and CR = DO x CL• For a perfectly incompatible element (DO = 0), CL /CO = 1/F• For F = 1.0 (complete melting), CL = CO for all elements, i.e., the melt has the same composition as the sourceFor DO = 1.0, CL = CO

Variation in the relative concentration of a trace element in a liquid vs. source rock as a fiunction of D and the fraction melted, using the equation for equilibrium batch melting.

Note how the highly incompatible elements are greatly enriched in the initial low-degree melt fractions, and get subsequently diluted as melt fraction increases.

• As F 1 the concentration of every trace element in the liquid = the source rock (CL/CO 1)

As F 1CL/CO 1C

C1

Di (1 F) FL

O=

- +

• Modal batch melting means that source minerals contribute to the melt in the same proportion as in the source (e.g., if a peridotite contains 65% ol, 24% opx, 6% cpx and 5% gt, then its modal batch melt will crystallize 65% ol, 24% opx, 6% cpx and 5% gt.) This is not a realistic process. • In non-modal batch melting, all the solid phases do not go into the melt equally. Garnet and clinopyroxene contribute more to the initial melts than olivine and orthopyroxene.The batch melting equation CL = CO / [DO (1 – F) + F] is for modal melting.The equation becomes CL = CO / [P (1 – F) + F] for non-modal melting.P = p1Kd1 + p2Kd2 + p3Kd3 + … where p is the normative weight fraction of a mineral in the melt.

•Non-Modal Batch Melting

Q: A mid-ocean-ridge-basalt (MORB) source contains 0.206 ppm La, 0.054 ppm Lu, and 13.2 ppm Sr. The mineralogical composition of this source is 65% ol, 24% opx, 6% cpx, and 5% gt. In case of modal batch melting of this source, what will be the bulk distribution coefficients for these three elements? Also, in case of non-modal batch melting and with the melt consisiting of 10% ol, 10% cpx, 40% cpx and 40% gt, what will be the bulk distribution coefficients for these elements? Use the following element/mineral Kds:

Ol Opx Cpx GtLa 0.00045 0.00125 0.037 0.007Lu 0.00315 0.049 0.235 5.6Sr 0.0015 0.016 0.100 0.008

A: For modal batch melting, melt contains the same proportions of the various minerals as the unmelted source (i.e., 65% ol, 24% opx, 6% cpx, 5% gt).

DO (La) = (0.65 x 0.00045 ) + (0.24 x 0.00125) + (0.06 x 0.037) + (0.05 x 0.007) = 0.0032DO (Lu) = (0.65 x 0.00315) + (0.24 x 0.049) + (0.06 x 0.235) + (0.05 x 5.6) = 0.3079DO (Sr) = (0.65 x 0.0015) + (0.24 x 0.016) + (0.06 x 0.100) + (0.05 x 0.008) = 0.0112

For non-modal batch melting, the specified melt composition is 10% ol, 10% opx, 40% cpx and 40% gt.

P (La) = (0.10 x 0.00045) + (0.10 x 0.00125) + (0.40 x 0.037) + (0.40 x 0.007) = 0.0178P (Lu) = (0.10 x 0.00315) + (0.10 x 0.049) + (0.40 x 0.235) + (0.40 x 5.6) = 2.3392P (Sr) = (0.10 x 0.0015) + (0.10 x 0.016) + (0.40 x 0.100) + (0.40 x 0.008) = 0.0449

Note the significant differences between the calculated distribution coefficients for assumed modal or non-modal melting.

Incremental batch melting:

• The total liquid is produced as a number of separate batches.• For a total of 30% melting, six batches of 5% each may separate successively. • Each is removed from the source without mixing with the next batch.• CR for the first melting event becomes CS for the next melting event.

Q: A garnet lherzolite underwent incremental batch melting (total of 15%, in three successive batches of 5% each). Calculate the Sr concentrations in the successive liquids and residues if the original rock contained 10 ppm Sr. DOSr = 0.034.A: CL = CO / [DO (1 – F) + F] and CR = DO x CLFor batch 1, CL = 10 / [0.034 (1 – 0.05) + 0.05] = 122 ppm; CR = 0.034 x 121.5 = 4.15 ppmFor batch 2,CL = 4.15 / [0.034 (1 – 0.05) + 0.05] = 50.4 ppm; CR = 0.034 x 50.4 = 1.71 ppmFor batch 3,CL = 1.71 / [0.034 (1 – 0.05) + 0.05] = 20.8 ppm; CR = 0.034 x 20.8 = 0.71 ppm

More complex cases:• Dynamic melting: A part of each batch remains behind in the source to mix with the next batch.• RTF magma chambers (M. J. O’Hara): A complex model involving magma chambers that are continuously replenished, tapped, and fractionated (RTF).• Concurrent assimilation – fractional crystallization (AFC) (D. J. DePaolo): heat required for assimilation of country rocks comes from heat of crystallization released by minerals.• Temperature-controlled assimilation: Hotter magmas assimilate more country rock than cooler magmas.

For very incompatible elements as Di 0

equation reduces to:

CC

1F

L

O

=

CC

1Di (1 F) F

L

O=

- +

If we know the concentration of a very incompatible element in both a magma and the source rock, we can determine the fraction of partial melt produced

As F 0 CL/CO 1/Di

If we know CL of a magma derived by a small degree of batch melting, and we know Diwe can estimate the concentration of that element in the source region (CO).

CC

1Di (1 F) F

L

O=

- +

This presentation last updated 04/01/2010, 14:30 hrs.