1. Trace Elements - Definitions
Elements that are not stoichiometric constituents in phases in the system of interest
For example, IG/MET systems would have different “trace elements” than aqueous systems
Do not affect chemical or physical properties of the system as a whole to any significant extent
Elements that obey Henry’s Law (i.e. has ideal solution behavior at very high dilution)

2. Graphical Representation of Elemental Abundance
In Bulk Silicate Earth (BSE)
Six elements make up 99.1% of BSE ->
The Big Six: O, Si, Al, Mg, Fe, and Ca
From W. M. White, 2001

3. Goldschmidt’s Geochemical Associations (1922)
Siderophile: elements with an affinity for a liquid metallic phase (usually iron), e.g. Earth’s core
Chalcophile: elements with an affinity for a liquid sulphide phase; depleted in BSE and are also likely partitioned in the core
Lithophile: elements with an affinity for silicate phases, concentrated in the Earth’s mantle and crust
Atmophile: elements that are extremely volatile and concentrated in the Earth’s hydrosphere and atmosphere

4. Trace Element Associations
From W.M. White, 2001

5. Trace Element Geochemistry
Electronic structure of lithophile elements is such that they can be modeled as approximately as hard spheres; bonding is primarily ionic
Geochemical behavior of lithophile trace elements is governed by how easily they substitute for other ions in crystal lattices
This substitution depends primarily by two factors:
Ionic radius
Ionic charge

6. Effect of Ionic Radius and Charge
Magnesium (Mg2+): 65 pm
Calcium (Ca2+): 99 pm
Strontium (Sr2+): 118 pm
Rubidium (Rb+): 152 pm
Ionic Radii
The greater the difference in charge or radius between the ion normally in the site and the ion being substituted, the more difficult the substitution.
Lattice sites available are principally those of Mg, Fe, and Ca, all of which have charge of 2+.
Some rare earths can substitute for Al3+.
Values depend on Coordination Number
1 pm = m
1 Å = m
1 pm = 10-2 Å

7. Classification of Based on Radii and Charge
Ionic Potential - charge/radius -
rough index for mobility
(solubility)in aqueous solutions:
<3 (low) & >12 (high) more
mobility
Low Field Strength (LFS)
Large Ion Lithophile (LIL)
2) High Field Strength (HFS)
REE’s
3) Platinum Group Elements
NB 1 Å = meters = 100 pm

8. More Definitions
Elements whose charge or size differs significantly from that of available lattice sites in mantle minerals will tend to partition (i.e. preferentially enter) into the melt phase during melting.
Such elements are termed incompatible
Examples: K, Rb, Sr, Ba, rare earth elements (REE), Ta, Hf, U, Pb
Elements readily accommodated in lattice sites of mantle minerals remain in solid phases during melting.
Such elements are termed compatible
Examples: Ni, Cr, Co, Os

9. Trace element substitutions

10. The (Lanthanide) Rare Earth Elements

11. Rare Earth Element Behavior
The lanthanide rare earths all have similar outer electron orbit configurations and an ionic charge of +3 (except Ce and Eu under certain conditions, which can be +4 and +2 respectively)
Ionic radius shrinks steadily from La (the lightest rare earth) to Lu (the heaviest rare earth); filling f-orbitals; called the “Lanthanide Contraction”
As a consequence, geochemical behavior varies smoothly from highly incompatible (La) to slightly incompatible (Lu)

12. Rare Earth Element Ionic Radii
NB that 1 pm = 10-6 microns = meters

13. Rare Earth Abundances in Chondrites
“Sawtooth” pattern of cosmic abundance reflects:
(1) the way the elements were created (greater abundances of lighter elements)
(2) greater stability of nuclei with even atomic numbers

14. Partition Coefficients for REEs

15. Partition Coefficients for REE in Melts
Amphibole-Melt
Dbulk = X1D1 + X2D2 + X3D3 + … + XnDn

16. Chondrite Normalized REE patterns
By “normalizing” (dividing by abundances in chondrites), the “sawtooth” pattern can be removed.

17. Trace Element Fractionation During Partial Melting
From:

18. Differentiation of the Earth
Melts extracted from the mantle rise to the crust, carrying with them their “enrichment” in incompatible elements
Continental crust becomes “incompatible element enriched”
Mantle becomes “incompatible element depleted”
From:

19. Uses of Isotopes in Petrology
Processes of magma generation and evolution - source region fingerprinting
Temperature of crystallization
Thermal history
Absolute age determination - geochronology
Indicators of other geological processes, such as advective migration of aqueous fluids around magmatic intrusions

20. Isotopic Systems and Definitions
Isotopes of an element are atoms whose nuclei contain the same number of protons but different number of neutrons.
Two basic types:
Stable Isotopes: H/D, 18O /16O, C, S, N (light) and Fe, Ag (heavy)
Radiogenic Isotopes: U/Pb, Rb/Sr, Hf/Lu, K/Ar

21. Stable Oxygen Isotopes
d18O‰ = [(Rsample - Rstandard)/Rstandard] x 1000
Three stable
isotopes of O
found in nature:
16O = %
17O = %
18O = %

22. Stable Oxygen Isotopes
d18O‰ = [(Rsample - Rstandard)/Rstandard] x 1000

23. Isotope Exchange Reactions
2Si16O2 + Fe318O4 = 2Si18O2 + Fe316O4
qtz mt qtz mt
This reaction is temperature dependent and therefore
can be used to formulate a geothermometer

24. Radioactive decay and radiogenic Isotopes
“Radiogenic” isotope ratios are functions of both time and parent/daughter ratios. They can help infer the chemical evolution of the Earth.
Radioactive decay schemes
87Rb-87Sr (half-life 48 Ga)
147Sm-143Nd (half-life 106 Ga)
238U-206Pb (half-life 4.5 Ga)
235U-207Pb (half-life 0.7 Ga)
232Th-208Pb (half-life 14 Ga)
“Extinct” radionuclides
“Extinct” radionuclides have half-lives too short to survive 4.55 Ga, but were present in the early solar system. b–
87Rb
87Sr

25. Half-life and exponential decay
Linear decay:
Eventually get to zero!
Exponential decay:
Never get to zero!

26. Rate Law for Radioactive Decay
Pt = Po exp - (to –t)
1st order rate law

27. Rb/Sr Age Dating Equation

28. Rb/Sr Isochron Systematics

29. Instruments and Techniques
Mass Spectrometry: measure different abundances of specific nuclides based on atomic mass.
Basic technique requires ionization of the atomic species of interest and acceleration through a strong magnetic field to cause separation between closely similar masses (e.g. 87Sr and 86Sr). Count individual particles using electronic detectors.
TIMS: thermal ionization mass spectrometry
SIMS: secondary ionization mass spectrometry - bombard target with heavy ions or use a laser
MC-ICP-MS: multicollector-inductively coupled plasma-ms
Sample Preparation: TIMS requires doing chemical separation using chromatographic columns.

30. Clean Lab - Chemical Preparation

31. Thermal Ionization Mass Spectrometer
From:

32. Schematic of Sector MS

33. Zircon Laser Ablation Pit

34. Mantle-Basalt Compatibility
Rb> Sr
Th> Pb
U> Pb
Nd>Sm
Hf>Lu
Parent->Daughter
Degree of compatibility

35. Radiogenic Isotope Ratios & Crust-Mantle Evolution
Eventually, parent-daughter ratios are reflected in radiogenic isotope ratios.
From:

36. Sr Isotope Evolution on Earth
87Sr/86Sr)0
Time before present (Ga)
87Sr/86Sr)0
Time before present (Ga)

37. Sr and Nd Isotope Correlations: The Mantle Array
147Sm->143Nd
(small->big)
87Rb->87Sr (big->small)