Radiogenic IsotopesIn Igneous Petrology

Francis, 2013

Pro

ton

No.

Neutron No.

PP

N

N

Tin P = 50

Beta decay:

Beta Capture:(positron emission):

Alpha decay:

87Rb 87Sr + e- + + t1/2 = 5.2 1010 years = 1.42 10-11/ yr

147Sm 143Nd + 4He + t1/2 = 1.06 1010 years = 6.54 10-12/ yr

26Al 26Mg + e+ + + t1/2 = 0.72 106 years = 9.8 10-7/ yr

Conversion of protons to neutrons and vice versa – Weak Nuclear Force

Loss of alpha particles – residual Strong Nuclear Force

Radioactive Decay

+ ray

+ ray

ParentIsotope

+ ray

Radioactive Decay

P + → N o + e + +

e

Beta capture

Beta decay

P + + e - + e N o

4 He2+ + γ

Alp

ha de

cay

-δN / δt = λ × N

N = No × e-λt

-δN / N = λ × δt

ln(N) = -λ × t + No

D* = No - N

D* = N × (eλt – 1)

D = Do + D*

D = Do + N × (eλt – 1)

t1/2 = ln 2/λ

Law of RadioactivityRutherford and Soddy, 1902

Some Useful Radioactive Decay Schemes:

Beta decay:

182Hf 182W + e- + + t1/2 = 9 106 years = 7.7 10-8 /yr129I 129Xe + e- + + t1/2 = 16 106 years = 4.3 10-8/ yr176Lu 176Hf + e- + + t1/2 = 3.5 1010 years = 1.94 10-11/ yr187Re 187Os + e- + + t1/2 = 4.56 1010 years = 1.52 10-11/ yr

87Rb 87Sr + e- + + t1/2 = 5.2 1010 years = 1.42 10-11/ yr

Beta Capture (positron emission):

26Al 26Mg + e+ + + t1/2 = 0.72 106 years = 9.8 10-7/ yr

53Mn 53Cr + e+ + + t1/2 = 3.7 106 years = 1.9 10-7/ yr

40K 40Ar + e+ + + = 0.581 10-10/ yr

40K 40Ca + e- + + t1/2 = 1.250 109 years = 4.962 10-10/ yr

Alpha decay:

146Sm 142Nd + 4He + t1/2 = 103 106 years = 147Sm 143Nd + 4He + t1/2 = 1.06 1010 years = 6.54 10-12/ yr235U 207Pb + 7 4He + 4e- + t1/2 = 0.7038 109 years = 9.8485 10-10/ yr232Th 208Pb + 6 4He + 4e- + t1/2 = 14.010 109 years = 4.9475 10-11/ yr238U 206Pb + 8 4He + 6e- + t1/2 = 4.468 1010 years = 1.55125 10-10/ yr

combined

Summary Radioactive Decay Schemes:

Beta decay:

87Rb 87Sr + e- + + t1/2 = 5.2 1010 yrs = 1.42 10-11/ yr

Alpha decay:

147Sm 143Nd + 4He + t1/2 = 1.06 1010 yrs = 6.54 10-12/ yr

235U 207Pb + 7 4He + 4e- + t1/2 = 0.7038 109 yrs = 9.8485 10-10/ yr

232Th 208Pb + 6 4He + 4e- + t1/2 = 14.010 109 yrs = 4.9475 10-11/ yr

238U 206Pb + 8 4He + 6e- + t1/2 = 4.468 1010 yrs = 1.55125 10-10/ yr

Rb – Sr System

87Rb 87Sr + e- + +

t1/2 = 5.2 1010 years = 1.42 10-11/ yr

Rb+ substitutes for K+ in the large W site of phases such as feldspar, mica, and amphibole, whereas Sr2+ substitutes for Ca2+ in feldspars. In-grown 86Sr thus sits in a site that is not only too large for it, but which may have been damaged by the decay process. As a result, Rb-Sr isochrons are relatively easily disturbed. This situation is aggravated by the fact that both Rb and Sr are relatively soluble in aqueous solutions leading to the mobility of Rb and Sr during secondary processes such as weathering and metamorphism.

Not useful in old metamorphosed rocks.

87Sr = 87Sri + 87Rb × (eλt-1)

87Sr/86Sr = (87Sr/86Sr)i + (87Rb/86Sr) × (eλt-1)

Y = Yi + a × X

a = (eλt-1)

2 unknowns: t = Time

(87Sr/86Sr)i

i

D = Do + N × (eλt – 1)

The Effect of Metamorphism

Rb – Sr System

87Rb 87Sr + e- + +

KRb < KSr

Liquid (Rb / Sr) > Residue (Rb / Sr)

Small degrees partial melting fractionates the Parent / Daughter ratio Rb/Sr, such that liquids have higher parent / daughter ratios and residues have lower parent / daughter ratios.

During partial melting,

Sm - Nd System

147Sm 143Nd + 4He +

t1/2 = 1.06 1010 years = 6.54 10-12/ yr

Both Sm3+ and Nd3+ substitute for Al3+ in clinopyroxene, amphibole, and are also preferentially up taken by apatite. The Sm-Nd isotopic system is significantly more robust than the Rb/Sr system because both the parent and daughter are happy in similar crystallographic sites, and both are relatively insoluble and thus immobile.

The similar chemical properties of Sm and Nd, however, means that it is more difficult to find enough spread in the parent/daugther ratio to yield a good isochron.

143Nd = 143Ndi + 147Sm × (eλt-1)

143Nd /144Nd = 143Nd/144Ndi + (147Sm/144Nd) × (eλt-1)

D = Do + N × (eλt – 1)

Oldest Age on the Moon

Sm - Nd System

147Sm 143Nd + 4He +

Liquid (Sm / Nd) < Residue (Sm / Nd)

143Nd = 143Ndi + 147Sm × (eλt-1)

In contrast to the Rb/Sr system, in the Sm-Nd system partial melts have lower parent /daughter ratios and the solid residue of partial melting has higher parent daughter ratios.

Note: this is the reverse of the situation in the Rb/Sr isotopic system.

KSm > KNd

Sm - Nd:

147Sm 143Nd + 4He +

KSm > KNd

Liquid (Sm / Nd) < Residue (Sm / Nd)

143Nd = 143Ndi + 147Sm × (eλt-1)

During partial melting,

143Nd/144Nd = (143Nd/144Nd)i + (147Sm/144Nd) × (eλt-1)

Nd isotopic evolution

εNd(t) = ((143Nd/144NdSample(t)) / (143Nd/144NdChur(t)) - 1) × 104

MORB

εNd and Model Ages

Mantle Extraction Ages:

It is important to distinguish between crystallisation age and mantle extraction age of the continental crust. This problem has been addressed by DePaolo using a combination of zircon crystallization ages and Nd model mantle extraction ages. His results indicate that 80% of the Earth's continental crust was formed by 1.6 Ga. Many younger crustal rocks must thus represent reworked older crust.

εNd(t) = ((143Nd/144NdSample(t)) / (143Nd/144NdChur(t)) - 1) × 104

MORB

MantleArray

Long-term depleted source that has been recently enriched.

2 types of

Enrichment

The incompatible trace element enrichment of E-MORB is associated with elevated 87Sr/86Sr and 143Nd/144Nd isotopic ratios compared to N-MORB, opposite to the correlation observed at many hot spots, such as Hawaii.

Continental flood Basalts

Continental flood Basalts

Calc-Alkaline Arcs

U, Th, and Pb Isotopic Systems

235U 207Pb + 74He + 4e- + t1/2 = 0.7038 109 yrs = 9.8485 10-10/ yr

232Th 208Pb + 64He + 4e- + t1/2 = 14.010 109 yrs = 4.9475 10-11/ yr

238U 206Pb + 84He + 6e- + t1/2 = 4.468 1010 yrs = 1.55125 10-10/ yrU3-6+, Th4+, and Pb2-4+ are highly incompatible in most rock forming minerals (K << 1), with Th and U being more incompatible than Pb, leading to a crust with high U/Pb ratios. Furthermore, Th and U are lithophile and preferentially partition into large sites in accessory phases such as zircon, apatite, perovskite, and baddelyeite. Pb, on the other hand, is largely excluded from zircon and is significantly chalcophile, partitioning preferentially into sulfides. Both U and Pb are relatively easily mobilized and the use of these radiogenic isotopes as tracers is largely restricted to modern, unaltered igneous rocks. Th, on the other hand, is relatively immobile, and has been successfully used as a tracer in older metamorphosed rocks.

U/Pb

U – Pb Concordia Diagrams

235U 207Pb + 74He + 4e- + t1/2 = 0.7038 109 years = 9.8485 10-10/ yr

238U 206Pb + 84He + 6e- + t1/2 = 4.468 1010 years = 1.55125 10-10/ yr

The difference in geochemical behaviour of Pb versus Th and U works to our advantage in using zircons for dating. The low levels of common Pb in zircon, combined with zircons high resistance to alteration make U-Pb isotopes in zircon an excellent geochronometer of the past.

U – Pb Concordia Diagrams

235U 207Pb + 74He + 4e- + t1/2 = 0.7038 109 years = 9.8485 10-10/ yr

238U 206Pb + 84He + 6e- + t1/2 = 4.468 1010 years = 1.55125 10-10/ yr

Mississippi River Zircons

Mackenzie River Zircons

Amazon River Zircons

Zircons in the Sands of Major Rivers

Pb Isochrons and the Age of the Solar System

Pb – Pb Isochron Diagrams

235U 207Pb + 74He + 4e- + t1/2 = 0.7038 109 years = 9.8485 10-10/ yr

238U 206Pb + 84He + 6e- + t1/2 = 4.468 1010 years = 1.55125 10-10/ yr

Future Ages, Mixing Lines, & Pseudo-Isochrons?

The apparent future ages of MORB and OIB can be explained by multi-stage fractionations, but the Pb paradox remains.

The first Pb Paradox: virtually all mantle reservoirs plot to the right of the Geochron, where are the complimentary reservoirs required for mass balance?

MORB

The lavas within many OIB suites define approximately linear arrays between two chemical and isotopic components, one relatively depleted and the other relatively enriched. Originally these were thought to correlate with the MORB source and primitive mantle respectively. However, it rapidly became apparent that these linear arrays were different in different OIB suites.

There are thus many "flavours" of OIB suites, and at least five different components are required to explain them. Furthermore, there are geographic correlations in the isotopic characteristics of OIB suites. For example, the DUPAL anomaly in the south Pacific is defined by the abundance of EM II OIB suites that appears to correlate with a lower mantle seismic tomography anomaly.

Mantle Components / Reservoirs

Bulk Silicate Earth (BSE) or Primitive Mantle (PM) 87Sr/86Sr = .7045, 143Nd/144Nd = .5126, chondrite-defined

Depleted MORB Mantle (DMM) lava characteristics: low 87Sr/86Sr <0.7025), high 143Nd/144Nd (>0.5130), low 206Pb/204Pb (~18) source time integrated: low Rb/Sr, high Sm/Nd, low U/Pb

nature: Primitive mantle minus continental crust or small degree melt.

Enriched Mantle I (EM 1): lava characteristics: moderate 87Sr/86Sr (~0.7050), lowest 143Nd/144Nd (~0.5124), Pitcairn Is., Tristan de Cunha low 206Pb/204Pb (< 17)Hawaii source time integrated: moderate Rb/Sr, low Sm/Nd, low U/Pb nature: subducted lower continental crust and/or lithospheric mantle, pelagic sediments?

Enriched Mantle II (EM 2): lava characteristics: highest 87Sr/86Sr (>0.7080), low 143Nd/144Nd (~.5125), 206Pb/204Pb (~19)Samoa, Society Islands source time integrated: high Rb/Sr, low Sm/Nd, low U/Pb Dupal anomaly nature: subducted upper continental crust and/or sediments, also similar to Group II kimberlites and some olivine lamproites

HIMU (high U/Pb): lava characteristics: low 87Sr/86Sr, (~ 0.7030), high 143Nd/144Nd (~0.5129), St. Helena Is., Austral Is., Azores highest 206Pb/204Pb (>20), high Ca source time integrated: low Rb/Sr, high Sm/Nd, high U/Pb nature: subducted oceanic crust that has lost Pb because of seawater alteration.

Focal Zone (FOZO:

The apparent point of convergence of the linear isotopic arrays of many OIB suites, thus possibly representing a mantle component that is common to all. It has a relatively depleted composition compared to primitive mantle in terms of Sr and Nd isotopes, but moderately radiogenic Pb isotopes. It is thus not the asthenospheric mantle (DMM), and not primitive mantle. It may be the figment of a fertile imagination.

It is important to remember that not only is the identity of these different mantle components a matter of debate, there is little constraint on their physical location, They are typically hidden in the deep mantle

General Mixing Equation:

AX + BXY + CY + D = 0

A = a2b1Y2 – a1b2Y1

B = a1b2 – a2b1

C = a2b1X1 – a1b2X2

D = a1b2X2Y1 – a2b1X1Y2

ai = denominator of Yi

bi = denominator of Xi

r = a1b2 / a2b1

Open Systems: Bulk Contamination:

Two data points 1 and 2 may be related by a mixing curve between 2 end-members M and N provided the following relationship holds:

Mixing lines are hyperbolic curves whose curvature is proportional to r. The asymptotes of mixing curves with large or small r’s can be used to define some of the ratios of the unseen end-members.

Mixing in Ratio – Ratio Plots:

AX + BXY + CY + D = 0

A = a2b1Y2 – a1b2Y1

B = a1b2 – a2b1

C = a2b1X1 – a1b2X2

D = a1b2X2Y1 – a2b1X1Y2

ai = denominator of Yi

bi = denominator of Xi

R = a1b2 / a2b1

Mixing lines are hyperbolic curves

Two data points may be related by a mixing curve provided the following relationship holds:

Mixing lines are hyperbolic curves whose curvature is proportional to r

Contamination and

Assimilation

Assimilation Fractional Crystallization (AFC)

Ciliq = Ci

o × F-z + (r × Cia × (1-F-z)) / ((r-1) × z × Ci

o)

z = (r + Di - 1) / (r-1)DePaolo, 1981

r = assimilation rate / crystallization rate, ≤ 1 for closed system heat budget

Parent Liquid + Contaminant Daughter Liquid + Crystal Cumulates

Analytical solution for constant Di

Open Systems:

Open System: Compatible Elements

Daughter Liquid (1-X) × Parent Liquid - X × Crystal Cumulates + r ×X × Contaminant

Computer Models:

Open System: Incompatible Elements

Daughter Liquid (1-X) × Parent Liquid - X × Crystal Cumulates + r ×X × Contaminant

Computer Models:

87Sr/86Sr in

AOB & Hy-Norm Basalts

Armstrong’s

Granitoid Lines

> 0.707> 0.707

< 0.705< 0.705

HfHf

FSFS

RaRa

EdEd

CCCC OMBOMB

CPBCPB

IMBIMB

YTYT

Within the northern Canadian Cordillera,

there is a clear correlation between

isotopic composition and the tectonic

belt within which recent alkaline

magmas erupt that mirrors that observed

in Mesozoic granitoids and late

Cretaceous shoshonites. All the

alkaline basalts of the Omenica Belt are

have more radiogenic Sr and Pb isotopes

and less radiogenic Nd isotopes than

their equivalents in the Intermontane

Belt. This clearly indicates the

involvement of lithospheric mantle

and/or crust in their origin.

Mixing in Ratio - Element Plots:

AX + BXY + CY + D = 0

A = a2Y2 – a1Y1

B = a1 – a2 b = 1

C = a2X1 – a1X2

D = a1X2Y1 – a2X1Y2

ai = denominator of Yi

bi = denominator of Xi = 1

R = a1 / a2

Mixing lines are still hyperbolic curves

maybe

No

Mixing in Element -Element Plots:

AX + BXY + CY + D = 0

A = Y2 – Y1

B = 0

C = X1 – X2

D = X2Y1 – X1Y2

ai = denominator of Yi = 1

bi = denominator of Xi = 1

r = 1

Mixing lines are straight lines

EM1

EM2

HIM

U

PM

DMM

PMEM1

HIMU

EM2

EM2

EM2

The many "flavours" of OIB suites suggest the lower mantle is “blobby”

and contains at least 5 different components.

PM

DM

M

EM1

Fe-Ni Core

continent

ocea

n

There is typically a systematic increase in 143Nd/144Nd and decrease in 87Sr/86Sr

and Pb isotopes with decreasing Si, from Hy norm basalts through to

nephelinites. The values of nephelinites approach those of MORB.

Ol-Neph

Hy-Norm

EM1

EM2

HIM

U

PM

DMM

PMEM1

HIMU

EM2

EM2

EM2

The many "flavours" of OIB suites suggest the lower mantle is “blobby”

and contains at least 5 different components.

PM

DM

M

EM1

Fe-Ni Core

continent

ocea

n