Trace ElementsFrancis, 2013

What is a trace element?

Cxyli / Cliq

i = Ki

For our purposes, a trace element is one which obeys Henry’s law:

Its partition coefficient is not a function of its concentration

Trace Elements

At equilibrium:

Coi = Cxyl

i × (1-F) + Cliqi × F

Coi = Ki × Cliq

i × (1-F) + Cliqi × F

Whole = ∑ Parts

F = fraction liquid

Ciliq = Ci

o / ((F + Ki(1-F))

Cixyl = Ki×Ci

o / ((F + Ki(1-F))

liquid

solid

Prediction of traceelement partitioning

Ideal mixing

Mixing of networkmodifiers

Ideally trace elements are those elements whose concentration is so low that they obey Henry’s law.

Cisolid / Ci

liq = K constant

In practice, many trace element partition coefficients vary with the composition of the silicate melt. Using a two lattice activity model one can sometimes reduce this dependence

Ni2+ substitutes for Mg2+ in olivine

KdNi = 3.346 × XNMMg - 3.665

GERM Website: earthref.org/GERM/index.html?main.htm

Trace Element PartitioningCpx M2 site

DI = conc. Isolid / conc. Iliquid

Partition coefficients for trace elements of the same valence are essentially a function of ionic radius versus the ideal size for the crystallographic site to be occupied.

Two Kinds of Trace Elements

Incompatible Compatible

Ki = Cxyli / Cliq

i < 1 Ki = Cxyli / Cliq

i > 1

Incompatible trace elements can not achieve satisfactory coordination in the crystallographic sites of the minerals that are present, commonly because they are too large or have too high a valence state.

Incompatible trace elements preferentially partition into the liquid phase.

Compatible trace elements can achieve satisfactory coordination in the mineral phases that are present by substituting for a major element with similar valence state and ionic radius.

Compatible trace elements preferentially partition into the solid phase.

La, Ce, Nb, Zr, Rb, Ba

Sc Ca in Cpx M2 siteCr Al in spinel in Y siteNi Mg in olivine in M1 & M2 sites

Rare Earth Elements - REE

First Inner Transition Series Elements (4f orbitals) :

La3+, Ce3-4+, Pr3+, Nd3+, Pm3+, Sm3+, Eu2-3+, Gd3+, Tb3+, Dy3+, Ho3+, Er3+, Tm3+, Yb3+, Lu3+

Ionic radius decreases and compatibility increases with atomic number for most minerals.

Although not officially a Rare Earth, Y3+ behaves vary similarly to Yb3+ and is usually considered with the REE

Typically presented in a spider-diagram in which actual abundances are normalized to the values for chondritic meteorite to eliminate the odd-even effect reflected in the Oddo-Harkins rule

Nd143 Sm147

[Xe] 4fn 6s2

Ciliq = Ci

o / ((F + Ki(1-F))

Cixyl = Ki×Ci

o / ((F + Ki(1-F))

Cixyl / Ci

liq = Ki

Coi = Ci

xyl × (1-F) + Ci

liq × F

The overall chemical similarity of the REE, but increasing compatiblity with increasing atomic number, makes them sensitive measures of partial melting. Furthermore, their relative insolubility in aqueous fluids (except Ce4+ ) makes them relatively immobile during metamorphism and alteration compared to major elements.

High field Strength Elements - HFSE

Field Strength = charge / ionic radius

Zr4+, Nb5+, Hf4+, Ta5+

Typically highly incompatible because of absence of suitable crystallographic sites in the common rock forming minerals. They become compatible only when sufficiently high levels are reached to stabilize their own phase – such as zircon in the case of Zr.

Typically insoluble, not transported by water, and thus they are resistant to alteration and metamorphic effects.

Characteristically high in alkaline and hot-spot magmas, but relatively depleted in calc-alkaline arc magmas.

Large Ion Lithophile Elements - LIL

Trace elements that have low field strengths; large size combined with low charge

Rb+, Sr2+, Cs+, Ba2+, & K+

These elements substitute for Na and K in feldspars, but are incompatible in mafic minerals that do not contain large 12-coordinated sites.

They are also relatively soluble in water, and thus very sensitive to alteration and metasomatic processes

Characteristically high in calc-alkaline lavas whose petrogenesis involves the dehydration of subducted slabs and metasomatic enrichment of the overlying mantle wedge.

LIL trace elements are also sensitive indicators of the involvement of mica or amphibole, which accept LIL elements substituting for K.

Increasing degree of melting ?

Compatible trace elements

Elements whose charge and ionic radius enables them to substitute for major elements in common minerals

Ni2+ substitutes for Mg2+ in olivine

KdNi = 3.346 × XNMMg - 3.665

Compatible trace elements – con’t

Cr3+ substitutes for Al3+ in spinel and clinopyroxene

In addition to being important sources of heat and isotopic tracers, Th and U, as well as their daughter Pb, are sensitive elemental tracers of crustal contamination. Their large size and charge make them incompatible in most common minerals and as a result they are highly concentrated in the Earth’s crust. For example, unlike OIB and MORB basalts, continental flood basalts are commonly characterized by positive Pb, U, and Th anomalies. U and Pb are relatively mobile and untrustworthy in altered or metamorphosed rocks. Th, however, appears more robust and is often used as a tracer of crustal contamination in old rocks.

Oceanic plateau, in contrast, have relatively flat, unfractionated trace element profiles, with relative depletions in LIL elements, and lack Nb and Pb anomalies.

U3-6+, Th4+, Pb2-4+Radiogenic Elements

Trace element Composition of the Continental Crust

The continental crust is highly enriched in incompatible trace elements compared to chondrite meteorites. Despite its small proportional mass (< 0.2 wt.%), the continental crust remains an important reservoir for the large ion lithophile elements, as well as the important heat producing elements U, Th, and K, but shows relative depletions in HFSE elements such as Nb, with respect to trace elements with similar degrees of incompatibility (e.g., K, Th, La). Although the lower crust is relatively poorly constrained, there appears to be an exponential decrease in the concentrations of heat producing elements, such as K, Th, and U, with depth, along with a change from granodioritic to gabbroic composition.

Extended Spider-Diagram

There is a remarkable similarity between the trace element profiles of the Earth’s continental crust and MORB source and that predicted for a 1 - 2% partial melt of the primitive mantle.

There is a systematic anti-correlation between degree of incompatible trace element enrichment and degree of Si saturation. Going from tholeiite to AOB to basanite and then olivine nephelinite corresponding to a systematic increase in the degree of enrichment in LREE, Nb, and Ta, with little change or a slight decrease in the levels of HREE.

olivine

Cxyli / Cliq

i = KiAt equilibrium:

Coi = Cxyl

i × (1-F) + Cliqi × F

Coi = Ki × Cliq

i × (1-F) + Cliqi × F

Whole = ∑ Parts

F = fraction liquid

Ciliq = Ci

o / ((F + Ki(1-F))

Cixyl = Ki×Ci

o / ((F + Ki(1-F))

liquid

solid

The fundamental equations:

Equilibrium Crystallization and/or Batch Melting

Ciliq = Ci

o / ((F + Ki(1-F))

Cixyl = Ki×Ci

o / ((F + Ki(1-F))

F = fraction liquid

If more than 1 mineral is involved, then the weighted-average partition coefficient can be calculated from the individual mineral partition coefficients and substituted for Ki:

∑n Xn = 1

Coi = Ci

xyl × (1-F) + Ci

liq × F

Cixyl / Ci

liq = Ki

Di = Xα× Kiα + Xβ × Ki

β + Xγ × Kiδ + ……..

Ciliq

Coi = Ci

xyl × (1-F) + Ci

liq × F

Cixyl / Ci

liq = KiFractional Crystallization

F × Ciliq1 = Ci

xyl × δF + (F-δF) × Ciliq2

δCiliq = Ci

liq2 × ((K-1) / F) × δF

F = fraction liquid

Ciliq = Ci

o × F(Ki -1)

Bulk Solid = Cio × (1-F)(Ki-1)

Liquid composition:

Ciliq1- Ci

liq2 = ((Cixyl –Ci

liq)/F)× δF

δCiliq / Ci

liq2 = ((K-1) / F) × δFCi

liq

Crystallization

Cieliq = Ci

o / ((F + Ki(1-F))

Cio

Ciliq

Cifliq = Ci

o × F(Ki -1)

The concentration of highly incompatible elements (K 0) in a residual liquid is:

Cio = Ciliq(1-f) + Cisolid(f)

Ciliq =Co / (1-f)when Cisolid =

0.0

As a result, plotting other elements against a highly incompatible element gives a good representation of the liquid line of descent produced by crystal fractionation.

Binary plots of 2 highly incompatible elements define straight lines passing through the origin

Highly Incompatible Trace Elements

Moderately Incompatible TraceElements

Compatible Trace Elements

Modal Fractional Melting

Cixyl = Ci

o × (1-F)(1-Ki)/Ki

Coi = Ci

xyl × (1-F) + Ci

liq × F

Cixyl / Ci

liq = Ki

δCixyl = ((Ci

liq – Cixy2) /(1-F)) × δF

Solid residue composition:

Instantaneous liquid composition:

δCixyl / Ci

xyl2 = (((1-Ki) / Ki) / (1-F))× δF

(1-F) × Cixyl1 = Ci

liq × δF + (1-F-δF) × Cixyl2

Cixyl1 – Ci

xyl2 = ((Ciliq - Ci

xyl2) / (1-F)) × δF

Ciiliq = (Ci

o / Ki) × (1-F)(1-Ki)/Ki

Cialiq = (Ci

o × (1 - (1-F)1/Ki) / F

Modal Fractional Melting – con’t

A more useful parameter than the instantaneous melt for fractional partial melting is the composition of the aggregate liquid that would be made by blending all the instantaneous melt fractions together over some interval of melting:

Aggregate Fractional Melt:

Modal Fractional Melting –con’t

CrystallizationPartial Melting

Plotting ratios of trace elements enhances the difference between partial melting and crystal fractionation and reduces the effects of changing K’s with pressure, temperature, and melt or mineral composition.

Partial melting is best at fractionating incompatible elements in silicate melts.

Fractional crystallization is best at fractionating compatible elements in silicate melts.

Cio/Ck

o = 1

Ci/Ckliq

Ciliq = Ci

o × F(Ki -1)

Cisoli = Ki × Cliq

i

For Fractional Crystallization:

Log – Log Diagrams

Modified after Cocherie, 1986

Cisol = Ci

o × (1-F)(1-Ki)/Ki

Ciiliq = (Ci

o / Ki) × (1-F)(1-Ki)/Ki

For Fractional Fusion:

Fractional crystallization is best at fractionating compatible elements, whereas fractional fusion is best at fractionating incompatible elements.

Log C1 versus log C2 is a straight line if K’sare constant

Slope = (K1-1) / (K2-1)

P

P

KNi ~ 5

KAl ~ 0.2

Compositional variation in solids

Oxidation State and Trace Element Partitioning

A number of trace elements have variable oxidation states that affect their partitioning between liquid and solid phases.

Ce3+ Ce4+

incompat ible soluble, mobile

Eu 2+ Eu3+

compatible in Feldspar relatively incompatible

Cr2+ Cr3+

incompatible on Moon compatible in Spinel & Cpx

V2+ V3+ V4+ V5+

compatible in silicates incompatible in silicates compatible in oxides

Reducing Oxidizing

Oxidation State of the Cordilleran Mantle

2×Fe2+Fe23+O4 + 6×FeSiO3 = 6×Fe2

2+SiO4 + O2

spinel opx oliv

Most likely oxygen buffer in the spinel lherzolite field:

P

Non-Modal Batch Melting

The previous trace element melting equations assumed that the proportion of phases going into the melt is the same as the proportion of minerals (mode) in the initial source. From our knowledge of the olivine-cliopyroxene-silica liquidus projection we know this is far from true.

The first melt is highly enriched in clinopyoxene (e1-P) compared to the mode of the mantle source. The accurate calculation of trace element behaviour requires a knowledge of both the starting mode of the source and the mode of the phases going into the melt.

Doi = Xα× Ki

α + Xβ × Kiβ + Xγ × Ki

δ + ……..

Pi = pα× Kiα + pβ × Ki

β + pγ × Kiδ + ……..

∑n Xn = 1

∑n pn = 1

The Batch Melting equation becomes:

Source Mode

Melt mode

Ciliq = Ci

o / (Doi + F × (1-Pi)) Ci

liq = Cio / ((F + Ki(1-F))

Modal melting

Non-Modal Fractional Melting

Cialiq = Ci

o × (1 - (1-(PiF / Doi))1/Pi) / F

Ciiliq = (Ci

o / Doi) × (1- (PiF) / Do

i)(1-Pi)/Pi

Instantaneous Liquid:

Aggregate Fractional Liquid:

The effects of incomplete melt extraction during partial melting or of the presence of interstitial melt in the crystal cumulates of crystal fractionation can be accounted for by including the melt as fictive mineral phase in the solid assemblage with a K i = 1 in the calculation of Do

i and Pi

Doi = Xα× Ki

α + Xβ × Kiβ + Xliq × 1

Pi = pα× Kiα + pβ × Ki

β + pliq × 1

∑n Xn = 1

∑n pn = 1

Cialiq = Ci

o × (1 - (1-F)1/Do) / F

modal fractional melting

There is typically de-coupling between major elements or compatible trace elements and incompatible trace elements, even in apparently co-magmatic suites. This can be attributed to at least two factors:

Element Decoupling

Mixing between liquids representing different melt fractions

Mixing during Crystal Fractionation

Increasing degree of melting ?

2 – component mixing ?

Increasing degree of melting ?

Mixing?

Mantle Sources for

Magmatic End-Members Hy-Norm

Basalt

Ol- Neph

Miller’s Ridge Transition

1mm

oliv

cpx

cpx

oliv

cpx cpxoliv

oliv

ankaramitic flows

ankaramitic flows

basaltic flows

basaltic flows

Ciliq1 = ΔF × Ci

xyl + (1-ΔF) × Ciliq2

Ciliq2 = (Ci

liq1× (1–ΔF × Ki)) / (1-ΔF)

Coi = Ci

xyl × (1-F) + Ci

liq × F

Cixyl / Ci

liq = Ki

Finite - Difference Computer Models

Mg

Mg

CpxFe

Olivine

Fe

Mg

Mg

Contrasting Olivine – Cpx Zoning

2 mm

cpx

oliv

oliv

cpx

M1 site

REECpx M2 site

Mg

Mg

CpxFe

Olivine

Fe

Mg

Mg

Contrasting Olivine – Cpx Zoning

2 mm

cpx

oliv

oliv

cpx