1. Chapter 9: Trace Elements
Note magnitude of major element changes
Element Distribution...as a tool in the interpretation of the history of igneous rocks
Different elements have diff. affinities for environments to reside: Si later melts - Mg early xls.
Remember from Chapter 1: A. Goldschmidt:
some elements metals "Siderophile" Fe, Pt, Mo
some elements sulfides "Chalcophile" S,Cu,Zn
some elements silicates "Lithophile" Si,K,Ca,REE
SIMPLISTIC Xl Field Theory best results. Study of elec. envir. in lattice & melt...
Trace Elements: very low conc.
TE's don't govern the appearance of a phase (as K req. Ksp or Bi), but enter various phases by substitution.
Compare Harkers
Major E usually vary by < 101
Figure 8.2. Harker variation diagram for 310 analyzed volcanic rocks from Crater Lake (Mt. Mazama), Oregon Cascades. Data compiled by Rick Conrey (personal communication). From Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

2. Chapter 9: Trace Elements
Now note magnitude of trace element changes
TE often vary by > 103 very useful since so sensitive to distr. & fractionation
Figure 9.1. Harker Diagram for Crater Lake. From data compiled by Rick Conrey. From Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

3. Element Distribution Goldschmidt’s rules (simplistic, but useful)
1. 2 ions with the same valence and radius should exchange easily and enter a solid solution in amounts equal to their overall proportions
How does Rb behave? Ni?
therefore some TE's will follow similar major E
Periodic Table is next slide

4. Rb follows K & conc. in Ksp, mica, & late melt
Ni follows Mg & conc in olivine

5. Goldschmidt’s rules
2. If 2 ions have a similar radius and the same valence: the smaller ion is preferentially incorporated into the solid over the liquid
Fig Isobaric T-X phase diagram at atmospheric pressure After Bowen and Shairer (1932), Amer. J. Sci. 5th Ser., 24, From Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
smaller ion preferentially -> solid (Mg is smaller than Fe so more Mg in Ol than in melt)

6. 3. If 2 ions have a similar radius, but different valence: the ion with the higher charge is preferentially incorporated into the solid over the liquid
(Cr+3 and Ti+4 are always preferred in solids/liquids)

7. Chemical Fractionation
The uneven distribution of an ion between two competing (equilibrium) phases

8. K = equilibrium constant
Exchange equilibrium of a component i between two phases (solid and liquid)
i (liquid) = i (solid)
eq. 9.2 K = =
K = equilibrium constant
a solid
a liquid
 X solid
 X liquid i i i i i i

9. Thus if XNi in the system doubles the XNi in all phases will double
Trace element concentrations are in the Henry’s Law region of concentration, so their activity varies in direct relation to their concentration in the system
Thus if XNi in the system doubles the XNi in all phases will double
This does not mean that XNi in all phases is the same, since trace elements do fractionate. Rather the XNi within each phase will vary in proportion to the system concentration
For example: suppose C(Ni) = 20 ppm in a system
C(Ni) in olivine may be 100 ppm
C(Ni) in plagioclase may be 1 ppm
C(Ni) in liquid may be 10 ppm
Double C(Ni) in system to 40 ppm: Ol -> 200 ppm, Plag -> 2 ppm and liquid -> 20 ppm

10. incompatible elements are concentrated in the melt
(KD or D) « 1
compatible elements are concentrated in the solid
KD or D » 1

11. For dilute solutions can substitute D for KD: D =
Where CS = the concentration of some element in the solid phase CS CL
Since the concentration of a trace element (unlike major elements--note Fo-Fa) in any phase is proportional to the coverall concentration of that element, a more convenient constant is commonly used for them. It is commonly referred to as "D" for TE's (although some authors still use KD) and is called a partition coefficient:
D = C(S)/C(L)
Where CS and CL are the concentration of a trace element in the solid and liquid phases, respectively (the wt% or ppm value directly). As long as the element occurs in very dilute concentrations, D is a constant.

12. Incompatible elements commonly  two subgroups
Smaller, highly charged high field strength (HFS) elements (REE, Th, U, Ce, Pb4+, Zr, Hf, Ti, Nb, Ta)
Low field strength large ion lithophile (LIL) elements (K, Rb, Cs, Ba, Pb2+, Sr, Eu2+) are more mobile, particularly if a fluid phase is involved
Depends on the minerals involved!
Sr -> melt as ol & px separate -> plag (Ca) & not melt if plag is phenocryst phase
Commonly standardized to mantle compositions (olivine, pyroxenes, and perhaps garnet)
Thus the major elements Mg and Fe would usually be referred to as compatible, while K and Na as incompatible

13. Which are incompatible? Why?
Compatibility depends on minerals and melts involved.
Which are incompatible? Why?
Not exact, since D varies with the composition of mins & melt

14. For a rock, determine the bulk distribution coefficient D for an element by calculating the contribution for each mineral
eq. 9.4: Di =  WA Di
WA = weight % of mineral A in the rock
Di = partition coefficient of element i in mineral A A

15. Note that 85% Ol + Opx, but 5% Grt raises bulk D to 0.366
Example: hypothetical garnet lherzolite = 60% olivine, 25% orthopyroxene, 10% clinopyroxene, and 5% garnet (all by weight), using the data in Table 9.1, is:
DEr = (0.6 · 0.026) + (0.25 · 0.23) + (0.10 · 0.583) + (0.05 · 4.7) = 0.366

16. Trace elements strongly partitioned into a single mineral
Ni - olivine in Table 9.1 = 14
Figure 9.1a. Ni Harker Diagram for Crater Lake. From data compiled by Rick Conrey. From Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

17. Incompatible trace elements concentrate  liquid
Reflect the proportion of liquid at a given state of crystallization or melting
Figure 9.1b. Zr Harker Diagram for Crater Lake. From data compiled by Rick Conrey. From Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

18. Trace Element Behavior
The concentration of a major element in a phase is usually buffered by the system, so that it varies little in a phase as the system composition changes
At a given T we could vary Xbulk from 35  70 % Mg/Fe without changing the composition of the melt or the olivine

19. Trace element concentrations are in the Henry’s Law region of concentration, so their activity varies in direct relation to their concentration in the system

20. Trace element concentrations are in the Henry’s Law region of concentration, so their activity varies in direct relation to their concentration in the system
Thus if XNi in the system doubles the XNi in all phases will double

21. Trace element concentrations are in the Henry’s Law region of concentration, so their activity varies in direct relation to their concentration in the system
Thus if XNi in the system doubles the XNi in all phases will double
Because of this, the ratios of trace elements are often superior to the concentration of a single element in identifying the role of a specific mineral

22. K/Rb often used  the importance of amphibole in a source rock
K & Rb behave very similarly, so K/Rb should be ~ constant
If amphibole, almost all K and Rb reside in it
Amphibole has a D of about 1.0 for K and 0.3 for Rb
K/Rb for amphibole:
Usually behave similarly, so ~ constant ratio
Unless amphibole which has a D of about 1.0 for K and 0.3 for Rb
almost all K and Rb reside in it
Melt of amphibole-bearing rock will -> decrease K/Rb in the partial melt
Other factors being equal, a magma produced by partial melting of an amphibole-bearing source rock would have a lower K/Rb than one derived from amphibole-free source
High absolute K or Rb could also  an amphibole-bearing source, but may result from other causes (high phlogopite, or an alkali-enriched fluid)
The ratio is more indicative of amphibole due to the different D values
Fractional crystallization of amphibole would also -> low K/Rb ratio in the evolved liquid

23. Sr and Ba (also incompatible elements)
Sr is excluded from most common minerals except plagioclase
Ba similarly excluded except in alkali feldspar
Ba/Sr will help identify Kspar vs Plag
Both are incompatible -> first partial melts (or residual liquids of FX)
Effect depends on the mineral phases involved
Sr is excluded from most common minerals except plagioclase
Ba similarly excluded except in alkali feldspar
Thus the ratio Ba/Sr increases with crystallization of plagioclase, but may decrease when orthoclase begins to crystallize

24. Compatible example: Ni strongly fractionated  olivine > pyroxene
Cr and Sc  pyroxenes » olivine
Ni/Cr or Ni/Sc can distinguish the effects of olivine and augite in a partial melt or a suite of rocks produced by fractional crystallization
In all of the above cases using ratios, the idea is to find a mineral with a unique pair of elements for which it alone has a relatively high value of D for one element and a relatively low value of D for the other. The ratio of these elements is then sensitive only to liquid/crystal fractionation associated with that particular mineral

25. Models of Magma Evolution
Batch Melting
The melt remains resident until at some point it is released and moves upward
Equilibrium melting process with variable % melting

26. Models of Magma Evolution
Batch Melting
eq. 9.5
CL = trace element concentration in the liquid
CO = trace element concentration in the original rock before melting began
F = wt fraction of melt produced = melt/(melt + rock) C 1 Di (1 F) F L O = - +

27. A plot of CL/CO vs. F for various values of Di using eq. 9.5
Batch Melting
A plot of CL/CO vs. F for various values of Di using eq. 9.5
Di = 1.0
D = No fractionation so CL/CO = 1 for all values of F
Figure 9.2. 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 equation (9.5) for equilibrium batch melting. From Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

28. Di » 1.0 (compatible element) Very low concentration in melt
Especially for low % melting (low F)
Values of F > 0.4 unlikely for batch melting since greater amounts should separate and rise
Figure 9.2. 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 equation (9.5) for equilibrium batch melting. From Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

29. Highly incompatible elements
Greatly concentrated in the initial small fraction of melt produced by partial melting
Subsequently diluted as F increases
Highly incompatible elements are greatly concentrated in the initial small fraction of melt that is produced by partial melting, and subsequently get diluted as F increases
Figure 9.2. 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 equation (9.5) for equilibrium batch melting. From Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

30. As F  1 the concentration of every trace element in the liquid = the source rock (CL/CO  1)Di (1 F) F L O = - +
All -> 1.0 because all of the source is melted
Figure 9.2. 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 equation (9.5) for equilibrium batch melting. From Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

31. C 1 Di (1 F) F L O = - +
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 Di we can estimate the concentration of that element in the source region (CO)
If know (CL) for magma derived by a small degree of batch melting, and we know D, we can estimate the concentration of that element in the source region (CO).
This can provide very valuable information in constraining and characterizing the source region.
Figure 9.2. 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 equation (9.5) for equilibrium batch melting. From Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

32. For very incompatible elements as Di  0 equation 9.5 reduces to:1 Di (1 F) F L O = - + C 1 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

33. Worked Example of Batch Melting: Rb and Sr
Basalt with the mode:
1. Convert to weight % minerals (Wol Wcpx etc.)
Table 9.2
. Conversion from mode to
weight percent
Mineral
Mode
Density
Wt prop
Wt% ol 15
3.6 54
0.18
cpx 33
3.4
112.2
0.37
plag 51
2.7
137.7
0.45
Sum
303.9
1.00
Suppose that a source rock with a mode of 51% plagioclase, 33% clinopyroxene, and 18% olivine undergoes batch melting

34. Worked Example of Batch Melting: Rb and Sr
Basalt with the mode:
1. Convert to weight % minerals (Wol Wcpx etc.)
2. Use equation eq. 9.4: Di =  WA Di
and the table of D values for Rb and Sr in each mineral to calculate the bulk distribution coefficients: DRb = and DSr = 0.848
Table 9.2
. Conversion from mode to
weight percent
Mineral
Mode
Density
Wt prop
Wt% ol 15
3.6 54
0.18
cpx 33
3.4
112.2
0.37
plag 51
2.7
137.7
0.45
Sum
303.9
1.00
Rb is incompatible and Sr only slightly so, but near unity

35. 3. Use the batch melting equation (9.5)
to calculate CL/CO for various values of F C 1 Di (1 F) F L O = - +
Table 9.3
. Batch Fractionation Model for
Rb and Sr C L /C O
= 1/(D(1-F)+F) D Rb Sr F
0.045
0.848
Rb/Sr
0.05
9.35
1.14
8.19
0.1
6.49
1.13
5.73
0.15
4.98
1.12
4.43
0.2
4.03
3.61
0.3
2.92
1.10
2.66
0.4
2.29
1.08
2.11
0.5
1.89
1.07
1.76
0.6
1.60
1.05
1.52
0.7
1.39
1.04
1.34
0.8
1.23
1.03
1.20
0.9
1.01
1.09
From Winter (2010) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

36. 4. Plot CL/CO vs. F for each element
Figure 9.3. Change in the concentration of Rb and Sr in the melt derived by progressive batch melting of a basaltic rock consisting of plagioclase, augite, and olivine. From Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
Results:
Incompatible element Rb (no K minerals) strongly concentrated in the early small melt proportions (low F)
Thus  a sensitive measure of the progress of fractional crystallization (at least until rock half melted)
As melting proceeds, the incompatible element is gradually diluted by more compatible ones
Since D(Sr) is close to 1.0, the ratio Rb/Sr vs. F is nearly the same as Rb alone
Any ratio of incompatible to compatible element should then be sensitive to the degree of partial melting (at least in the initial stages).
Important for Rb/Sr isotopic systems
Note that can create a series of melts from a single source each with diff Rb/Sr

37. Incremental Batch Melting
Calculate batch melting for successive batches (same equation)
Must recalculate Di as solids change as minerals are selectively melted (computer)

38. Fractional Crystallization
1. Crystals remain in equilibrium with each melt increment
Incremental batch melting in reverse
Equation 9.5 would still apply
Batch FX: F = proportion of liquid remaining

39. Rayleigh fractionation
The other extreme: separation of each crystal as it formed = perfectly continuous fractional crystallization in a magma chamber
Rayleigh: Crystals form and accumulate -> isolated from reaction with the remaining liquid

40. Rayleigh fractionation
The other extreme: separation of each crystal as it formed = perfectly continuous fractional crystallization in a magma chamber
Concentration of some element in the residual liquid, CL is modeled by the Rayleigh equation:
eq. 9.8 CL/CO = F (D -1) Rayleigh Fractionation
Can also apply the Rayleigh equation to Rayleigh fractional melting

41. Other models are used to analyze
Mixing of magmas
Wall-rock assimilation
Zone refining
Combinations of processes

42. The Rare Earth Elements (REE)
Members of Group IIIA of the Periodic Table La -> to Lutetium (Z = 57  71)
All have very similar chemical and physical properties -> behave as a coherent series
All have a 3+ oxidation state
Ionic radius decreases steadily with increasing atomic number (lanthanide contraction)

43. Contrasts and similarities in the D values: All are incompatible
Also Note:
HREE are less incompatible
Especially in garnet
Eu can  2+ which conc. in plagioclase

44. La Ce Nd Sm Eu Tb Er Dy Yb Lu
REE Diagrams
Plots of concentration as the ordinate (y-axis) against increasing atomic number
Degree of compatibility increases from left to right across the diagram (“lanthanide contraction”)
Concentration
La Ce Nd Sm Eu Tb Er Dy Yb Lu

45. estimates of primordial mantle REE chondrite meteorite concentrations
Chondrite normalization:
Normalize to chondrite meteorites to:
1) avoid Oddo-Harkins (even Z more common)
2) think chondrite = primitive earth, so can compare to initial distribution
Eliminate Oddo-Harkins effect and make y-scale more functional by normalizing to a standard
estimates of primordial mantle REE
chondrite meteorite concentrations

46. What would an REE diagram look like for an analysis of a chondrite meteorite?
0.00
2.00
4.00
6.00
8.00
10.00 56 58 60 62 64 66 68 70 72
sample/chondrite L
La Ce Nd Sm Eu Tb Er Yb Lu ?

47. Divide each element in analysis by the concentration in a chondrite standard
0.00
2.00
4.00
6.00
8.00
10.00 56 58 60 62 64 66 68 70 72
sample/chondrite L
La Ce Nd Sm Eu Tb Er Yb Lu

48. REE diagrams using batch melting model of a garnet lherzolite for various values of F:
Figure 9.4. Rare Earth concentrations (normalized to chondrite) for melts produced at various values of F via melting of a hypothetical garnet lherzolite using the batch melting model (equation 9.5). From Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
Diagram created in similar way to Rb-Sr diagram in Example Problem
Calculate D(La) for lherzolite and model conc. in melt at F = 0.1 -> point on this diagram for La …
LREE are less compatible than HREE, so melts enriched in LREE -> (-) slopes
Slope is steeper for low values of F (low % partial melting)
As F  1 slope  0 at S/C = 1.0 since all of mantle sample is melted
Note again the use of RATIOS to -> slope on REE
La/Lu ratio -> REE slope
Tb/Lu for HREE only (garnet)
La/Sm -> LREE only

49. Europium anomaly when plagioclase is
a fractionating phenocryst or
a residual solid in source
Figure 9.5. REE diagram for 10% batch melting of a hypothetical lherzolite with 20% plagioclase, resulting in a pronounced negative Europium anomaly. From Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
Eu* is the value Eu “should” have if Eu+2 did not -> plagioclase
Another example of how RATIOS can help
Eu alone is inconclusive (low REE of low Eu)
Sm/Eu is slope or Eu anomaly trough (Use Eu*/Eu anyway)

50. Normalized Multielement (Spider) Diagrams
An extension of the normalized REE technique to a broader spectrum of elements
Chondrite-normalized spider diagrams are commonly organized by (the author’s estimate) of increasing incompatibility L  R
Different estimates  different ordering (poor standardization)
Order of elements based on estimates of increasing incompatibility from right to left in a "typical" mantle undergoing partial melting
Elements are all incompatible (D<1) during most partial melting and fractional crystallization processes. The main exceptions are
Sr, which may be compatible if plagioclase is involved,
Y and Yb with garnet
Ti with magnetite
Troughs at these elements would indicate respective mineral involvement
Oceanic basalts = large degrees of PM, their spider diagrams should reflect the trace element patterns of their source
Less incompatible elements on the right-hand side should be less enriched during PM (particularly for small degrees of it), tilting the curve up on the left -> (-) slope
Additionally, FX subsequent to magma segregation from the source should tip the pattern even further
Fig Spider diagram for an alkaline basalt from Gough Island, southern Atlantic. After Sun and MacDonough (1989). In A. D. Saunders and M. J. Norry (eds.), Magmatism in the Ocean Basins. Geol. Soc. London Spec. Publ., 42. pp

51. MORB-normalized Spider
Separates LIL and HFS
Figure 9.7. Ocean island basalt plotted on a mid-ocean ridge basalt (MORB) normalized spider diagram of the type used by Pearce (1983). Data from Sun and McDonough (1989). From Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
MORB-normalization
LIL on left and HFS on right. Incr. incompatibility toward center.
Coherent magma with enrichment has hump shape

52. Application of Trace Elements to Igneous Systems
1. Use like major elements on variation diagrams to document FX, assimilation, etc. in a suite of rocks
More sensitive  larger variations as process continues
Figure 9.1a. Ni Harker Diagram for Crater Lake. From data compiled by Rick Conrey. From Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

53. 2. Identification of the source rock or a particular mineral involved in either partial melting or fractional crystallization processes
Example: can use REE to distinguish between high pressure and low pressure sources of a mantle-derived magma
In the deep continental crust, and at depths over about 100 km in the mantle, garnet and clinopyroxene are important phases, which remain as residual solids during the generation of up to 15-20% partial melting

55. Garnet concentrates the HREE and fractionates among them
Thus if garnet is in equilibrium with the partial melt (a residual phase in the source left behind) expect a steep (-) slope in REE and HREE
Shallow (< 40 km) partial melting of the mantle will have plagioclase in the resuduum and a Eu anomaly will result

56. Garnet and Plagioclase effect on HREE
0.00
2.00
4.00
6.00
8.00
10.00 56 58 60 62 64 66 68 70 72
sample/chondrite
La Ce Nd Sm Eu Tb Er Yb Lu
67% Ol 17% Opx 17% Cpx
Garnet and Plagioclase effect on HREE
0.00
2.00
4.00
6.00
8.00
10.00
sample/chondrite
60% Ol 15% Opx 15% Cpx 10%Plag
La Ce Nd Sm Eu Tb Er Yb Lu
0.00
2.00
4.00
6.00
8.00
10.00 56 58 60 62 64 66 68 70 72
sample/chondrite
La Ce Nd Sm Eu Tb Er Yb Lu
57% Ol 14% Opx 14% Cpx 14% Grt

57. Figure 9.3. Change in the concentration of Rb and Sr in the melt derived by progressive batch melting of a basaltic rock consisting of plagioclase, augite, and olivine. From Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
Trace elements have much broader general application in petrology than indicating individual mineral involvement
They have been used to indicate mama mixing, assimilation, the degree of partial melting of fractional crystallization, etc.
We will see numerous examples in forthcoming chapters

58. Use as a Petrogenetic Indicator
Table 9.6  A Brief Summary of Some Particularly Useful Trace Elements in Igneous Petrology
Element
Use as a Petrogenetic Indicator
Ni, Co, Cr
Highly compatible elements. Ni and Co are concentrated in olivine, and Cr in spinel and clinopyroxene. High concentrations indicate a mantle source, limited fractionation, or crystal accumulation.
Zr, Hf
Very incompatible elements that do not substitute into major silicate phases (although they may replace Ti in titanite or rutile). High concentrations imply an enriched source or extensive liquid evolution.
Nb, Ta
High field-strength elements that partition into Ti-rich phases (titanite, Ti-amphibole, Fe-Ti oxides. Typically low concentrations in subduction-related melts.
Ru, Rh, Pd, Re, Os, Ir, Pd
Platinum group elements (PGEs) are siderophile and used mostly to study melting and crystallization in mafic-ultramafic systems in which PGEs are typically hosted by sulfides. The Re/Os isotopic system is controlled by initial PGE differentiation and is applied to mantle evolution and mafic melt processes. Sc
Concentrates in pyroxenes and may be used as an indicator of pyroxene fractionation. Sr
Substitutes for Ca in plagioclase (but not in pyroxene), and, to a lesser extent, for K in K-feldspar. Behaves as a compatible element at low pressure where plagioclase forms early, but as an incompatible element at higher pressure where plagioclase is no longer stable.
REE
Myriad uses in modeling source characteristics and liquid evolution. Garnet accommodates the HREE more than the LREE, and orthopyroxene and hornblende do so to a lesser degree. Titanite and plagioclase accommodates more LREE. Eu2+ is strongly partitioned into plagioclase. Y
Commonly incompatible. Strongly partitioned into garnet and amphibole. Titanite and apatite also concentrate Y, so the presence of these as accessories could have a significant effect.

59. Trace elements as a tool to determine paleotectonic environment
Useful for rocks in mobile belts that are no longer recognizably in their original setting
Can trace elements be discriminators of igneous environment?
Approach is empirical on modern occurrences
Concentrate on elements that are immobile during low/medium grade metamorphism
A bit ambiguous, since many variables (country rx, %PM, %FX)
Need immobile TE's, so met has no effect. Ti, Zr, Y, Hf
& apply to basic volc's to eliminate high %FX

60. Figure 9.8  Examples of discrimination diagrams used to infer tectonic setting of ancient (meta)volcanics. (a) after Pearce and Cann (1973), (b) after Pearce (1982), Coish et al. (1986). Reprinted by permission of the American Journal of Science, (c) after Mullen (1983) Copyright © with permission from Elsevier Science, (d) and (e) after Vermeesch (2005) © AGU with permission.

61. Isotopes C Same Z, different A (variable # of neutrons)
General notation for a nuclide: 6 14 C
6 = Z = # of protons  element identity
14 = A = p + n

62. Isotopes C 12C 13C 14C Same Z, different A (variable # of neutrons)
General notation for a nuclide: 6 14 C
As n varies  different isotopes of an element
12C 13C 14C
May drop the subscript (redundant with symbol)

63. Stable Isotopes Stable: last ~ forever
Chemical fractionation is impossible
Mass fractionation is the only type possible
Mass differences « chemical differences, so mass fractionation is always small, but some fract may occur during reactions
If mass fractionation takes place, the light isotope -> vapor > liquid > solid
The efficiency of mass fractionation = f(mass difference/total mass)
204Pb - 205Pb will not fractionate
1H - 3H will fractionate appreciably
Stable isotope studies are usually limited to sulfur and lighter elements
Stable isotopes can give us information on:
-eqm T
-source indicators
-history of evolution

64. Example: Oxygen Isotopes
16O % of natural oxygen
17O % “
18O % “
Concentrations expressed by reference to a standard
International standard for O isotopes = standard mean ocean water (SMOW)

65. result expressed in per mille (‰)
18O and 16O are the commonly used isotopes and their ratio is expressed as d:
d (18O/16O) = eq 9.10
result expressed in per mille (‰) ( O/ O) x
1000 18 16
sample
SMOW -
What is d of SMOW??
What is d for meteoric water?

66. What is d for meteoric water?
Evaporation seawater  water vapor (clouds)
Light isotope enriched in vapor > liquid
Pretty efficient, since D mass = 1/8 total mass

67. What is d for meteoric water?
Evaporation seawater  water vapor (clouds)
Light isotope enriched in vapor > liquid
Pretty efficient, since D mass = 1/8 total mass
d =
therefore <
thus dclouds is (-) ( O/ O) x
1000 18 16
vapor
SMOW - ( O/ O) 18 16
Vapor ( O/ O) 18 16
SMOW

68. the value of d can vary from - 40 to almost 0
True, but:
the value of d can vary from - 40 to almost 0
d appears to be a function of temperature Why?
Hi T low % condensation, so fract vapor liquid is high and gets closer to SMOW.
Where T is lower and a higher % liq. the fract is less efficient and d is lower.
Paleothermometry of snow accumulation, carbonates
Greenland ice sheet cores paleoclimates?
Figure 9.9. Relationship between d(18O/16O) and mean annual temperature for meteoric precipitation, after Dansgaard (1964). Tellus, 16,

69. Stable isotopes useful in assessing relative contribution of various reservoirs, each with a distinctive isotopic signature
O and H isotopes - juvenile vs. meteoric vs. brine water
d18O for mantle rocks  surface-reworked sediments: evaluate contamination of mantle-derived magmas by crustal sediments
O and H isotopes used to evaluate juvenile vs. meteoric vs. brine characteristics of water and the type of water responsible for rock alteration
d18O is quite different for mantle rocks and surface-reworked sediments, so it may be used to evaluate the extent to which mantle-derived magmas are contaminated by crustal sediments
Thermometry of minerals?
Beware of re-equilibration and alteration!

70. Radioactive Isotopes Unstable isotopes decay to other nuclides
The rate of decay is constant, and not affected by P, T, X…
Parent nuclide = radioactive nuclide that decays
Daughter nuclide(s) are the radiogenic atomic products
Other products = subatomic products and energy

71. Isotopic variations between rocks, etc. due to:
1. Mass fractionation (as for stable isotopes)
Only effective for light isotopes: H He C O S

72. Isotopic variations between rocks, etc. due to:
1. Mass fractionation (as for stable isotopes)
2. Daughters produced in varying proportions resulting from previous event of chemical fractionation
40K  40Ar by radioactive decay
Basalt  rhyolite by FX (a chemical fractionation process)
Rhyolite has more K than basalt
40K  more 40Ar over time in rhyolite than in basalt
40Ar/39Ar ratio will be different in each
Last line: 39Ar is neither radiogenic nor radioactive - why use it??

73. Isotopic variations between rocks, etc. due to:
1. Mass fractionation (as for stable isotopes)
2. Daughters produced in varying proportions resulting from previous event of chemical fractionation
3. Time
The longer 40K  40Ar decay takes place, the greater
the difference between the basalt and rhyolite will be

74. Radioactive Decay The Law of Radioactive Decay eq. 9.11 - µ dN dt N or= N l 1
Note half-life is a constant (as is decay constant)
# parent atoms
time 

75. D = Nelt - N = N(elt -1) eq 9.14  age of a sample (t) if we know:
D the amount of the daughter nuclide produced
N the amount of the original parent nuclide remaining
l the decay constant for the system in question
Practical limitations on age range to which apply:
Very young rocks: cannot measure tiny amount of daughter accurately
Very old rocks: cannot measure tiny amounts of parent left accurately
Range depends on lambda
How can we distinguish radiogenic daughter isotopes from identical stable isotopes that were in a rock at its formation?

76. The K-Ar System 40K  either 40Ca or 40Ar
40Ca is common. Cannot distinguish radiogenic
40Ca from non-radiogenic 40Ca
40Ar is an inert gas which can be trapped in
many solid phases as it forms in them
When a rock is hot all of the Ar escapes, “resetting the radiometric clock” - all of the daughter is removed
When a volcanic rock forms, the clock is reset, and 40Ar that accum. after must be daughter from 40K

77. The appropriate decay equation is: eq 9.16 40Ar = 40Aro + 40K(e-lt -1)
Where le = x a-1 (proton capture)
and l = x a-1 (whole process) l e æ è ç ö ø ÷
Normally 40Aro = 0 for igneous rocks
Thus can get an age from a single rock by measuring 40K and 40Ar in it (only unknowns)

78. Blocking temperatures for various minerals differ
40Ar-39Ar technique grew from this discovery
A recent discovery- blocking temperatures differ
Stepwise heating of sample releases Ar from different minerals -> several ages reflecting thermal history of rock
We can use it to -> uplift rates in eroded orogenic belts

79. Sr-Rb System 87Rb  87Sr + a beta particle (l = 1.42 x 10-11 a-1)
Rb behaves like K  micas and alkali feldspar
Sr behaves like Ca  plagioclase and apatite (but not clinopyroxene)
88Sr : 87Sr : 86Sr : 84Sr ave. sample = 10 : 0.7 : 1 : 0.07
86Sr is a stable isotope, and not created by breakdown of any other parent
Add to end:
87Sr is stable & non-radiogenic Sr is present in nearly any rock
The amount of 87Sr in any rock = original 87Sr + radiogenic 87Sr from 87Rb over time
Thus a rock cannot  an unambiguous age if you don’t know what % or 87Sr is radiogenic
Isochron technique use to solve this problem

80. Requires 3 or more cogenetic samples with a range of Rb/Sr
Isochron Technique
Requires 3 or more cogenetic samples with a range of Rb/Sr
Could be:
3 cogenetic rocks derived from a single source by partial melting, FX, etc.
Figure 9.3. Change in the concentration of Rb and Sr in the melt derived by progressive batch melting of a basaltic rock consisting of plagioclase, augite, and olivine. From Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

81. Requires 3 or more cogenetic samples with a range of Rb/Sr
Isochron Technique
Requires 3 or more cogenetic samples with a range of Rb/Sr
Could be:
3 cogenetic rocks derived from a single source by partial melting, FX, etc.
3 coexisting minerals with different K/Ca ratios in a single rock
Bt - Ms - Kfs

82. Recast age equation by dividing through by stable 86Sr
87Sr/86Sr = (87Sr/86Sr)o + (87Rb/86Sr)(elt -1) eq 9.17
l = 1.4 x a-1
For values of lt less than 0.1: elt-1  lt
Thus eq for t < 70 Ga (!!) reduces to:
eq Sr/86Sr = (87Sr/86Sr)o + (87Rb/86Sr)lt
y = b x m
= equation for a line in 87Sr/86Sr vs. 87Rb/86Sr plot

83. ( ) Begin with 3 rocks plotting at a b c at time to
86Sr
87Sr
86Sr
87Sr o ( )
Why have same value of 87Sr/86Sr?
(87Sr/86Sr)o = value at time to to a b c
86Sr
87Rb

84. After some time increment (t0 t1) each sample loses some 87Rb and gains an equivalent amount of 87Sr a b c a1 b1 c1 t1 to
86Sr
87Sr
87Rb o ( )
Result: a1 b1 and c1 are still colinear
Slope = f(t)
Intercept at zero 87Rb = (87Sr/86Sr)o

85. ( ) At time t2 each rock system has evolved  new line
Again still linear and steeper line a b c a1 b1 c1 a2 b2 c2 t1 to t2
86Sr
87Sr o ( )
86Sr
87Rb

86. Isochron technique produces 2 valuable things:
1. The age of the rocks (from the slope = lt)
2. (87Sr/86Sr)o = the initial value of 87Sr/86Sr
Isochron technique produces 2 valuable things:
The age of the rocks (from the slope = lambda t)
t = slope/lambda = /1.4 E-11 = 90.7 Ma
(87Sr/86Sr)o = the initial value of 87Sr/86Sr at the time of crystallization
WHY??
Figure Rb-Sr isochron for the Eagle Peak Pluton, central Sierra Nevada Batholith, California, USA. Filled circles are whole-rock analyses, open circles are hornblende separates. The regression equation for the data is also given. After Hill et al. (1988). Amer. J. Sci., 288-A,

87. If a modern melt is derived from partial melting of the mantle:
Primordial mantle ~ chondrite
Major melting event about 3 Ga ago  continental crust (hypothetical simplification)
Crust has high Rb/Sr so evolution curve is steep
Mantle is depleted in Rb, so lower Rb/Sr and shallower evolution curve
If a modern melt is derived from partial melting of the mantle:
(87Sr/86Sr)o < 0.706
If derived from old crust: (87Sr/86Sr)o > 0.706
Figure Estimated Rb and Sr isotopic evolution of the Earth’s upper mantle, assuming a large-scale melting event producing granitic-type continental rocks at 3.0 Ga b.p After Wilson (1989). Igneous Petrogenesis. Unwin Hyman/Kluwer.

88. The Sm-Nd System Both Sm and Nd are LREE
Incompatible elements fractionate  melts
Nd has lower Z  larger  liquids > does Sm
Sm/Nd lower in partial melts than source, and also lower in late FX liquids

89. Decay equation derived by reference to the non-radiogenic 144Nd
147Sm  143Nd by alpha decay
l = 6.54 x a-1 (half life 106 Ga)
Decay equation derived by reference to the non-radiogenic 144Nd
143Nd/144Nd = (143Nd/144Nd)o
+ (147Sm/144Nd)lt
Also requires the isochron technique to solve

90. Evolution curve is opposite to Rb - Sr
Partial melting selectively depletes the mantle in the daughter (Nd)
so Sm  Nd and radiogenic swamps original Nd
Basalt derived from the mantle will have a higher initial 143Nd/144Nd than a magma derived from the crust
Figure Estimated Nd isotopic evolution of the Earth’s upper mantle, assuming a large-scale melting or enrichment event at 3.0 Ga b.p. After Wilson (1989). Igneous Petrogenesis. Unwin Hyman/Kluwer.

91. The U-Pb-Th System Very complex system.
3 radioactive isotopes of U: 234U, 235U, 238U
3 radiogenic isotopes of Pb: 206Pb, 207Pb, and 208Pb
Only 204Pb is strictly non-radiogenic
U, Th, and Pb are incompatible elements, & concentrate in early melts
Isotopic composition of Pb in rocks = function of
238U  234U  206Pb (l = x a-1)
235U  207Pb (l = x a-1)
232Th  208Pb (l = x a-1)

92. The U-Pb-Th System
Concordia = Simultaneous co- evolution of 206Pb and 207Pb via:
238U  234U  206Pb
235U  207Pb
206Pb* means radiogenic 206Pb
The example shows 2.5 Ga of development of an isotopic system
Figure 9.16a. Concordia diagram illustrating the Pb isotopic development of a 3.5 Ga old rock with a single episode of Pb loss. After Faure (1986). Principles of Isotope Geology. 2nd, ed. John Wiley & Sons. New York.

93. The U-Pb-Th System Discordia = loss of both 206Pb and 207Pb
Discordia: loss of both 206Pb and 207Pb due to some thermal event (metamorphism)
All -> origin but not same amount
Suppose this occurs 2.5 Ga after original crystallization
Figure 9.16a. Concordia diagram illustrating the Pb isotopic development of a 3.5 Ga old rock with a single episode of Pb loss. After Faure (1986). Principles of Isotope Geology. 2nd, ed. John Wiley & Sons. New York.

94. The U-Pb-Th System Concordia diagram after 3.5 Ga total evolution
3.5 Ga = age of igneous crystallization
1.0 Ga = age of metamorphism
We will leave the details of this system until Chapter 14 when we will use it to distinguish crustal contamination of mantle magmas
Figure 9.16b. Concordia diagram illustrating the Pb isotopic development of a 3.5 Ga old rock with a single episode of Pb loss. After Faure (1986). Principles of Isotope Geology. 2nd, ed. John Wiley & Sons. New York.

95. The U-Pb-Th System 3.5 Ga = age of igneous crystallization
1.0 Ga = age of metamorphism
We will leave the details of this system until Chapter 14 when we will use it to distinguish crustal contamination of mantle magmas
Figure Concordia diagram for three discordant zircons separated from an Archean gneiss at Morton and Granite Falls, Minnesota. The discordia intersects the concordia at 3.55 Ga, yielding the U-Pb age of the gneiss, and at 1.85 Ga, yielding the U-Pb age of the depletion event. From Faure (1986). Copyright © reprinted by permission of John Wiley & Sons, Inc.