Chapter 9: Trace Elements
Note
magnitude
of major
element
changes
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.
Chapter 9: Trace Elements
Now note
magnitude
of trace
element
changes
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.
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?
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. 6.10. Isobaric T-X phase
diagram at atmospheric
pressure After Bowen and
Shairer (1932), Amer. J. Sci. 5th
Ser., 24, 177-213. From Winter
(2001) An Introduction to
Igneous and Metamorphic
Petrology. Prentice Hall.
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
Chemical Fractionation

The uneven distribution of an ion between
two competing (equilibrium) phases
Exchange equilibrium of a component i between
two phases (solid and liquid)
i (liquid) = i (solid)
eq. 9.2
K=
a isolid
a iliquid
=
K = equilibrium constant
 X solid
i i
 X liquid
i
i


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

incompatible elements are concentrated in the
melt
(KD or D) « 1

compatible elements are concentrated in the
solid
KD or D » 1

For dilute solutions can substitute D for KD:
CS
D=
CL
Where CS = the concentration of some element in
the solid phase

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
Compatibility depends on minerals and melts involved.
Which are incompatible? Why?
Rb
Sr
Ba
Ni
Cr
La
Ce
Nd
Sm
Eu
Dy
Er
Yb
Lu
Rare Earth Elements
Table 9-1. Partition Coefficients (CS/CL) for Some Commonly Used Trace
Elements in Basaltic and Andesitic Rocks
Olivine
0.01
0.014
0.01
14.0
0.7
0.007
0.006
0.006
0.007
0.007
0.013
0.026
0.049
0.045
Opx
0.022
0.04
0.013
5.0
10.0
0.03
0.02
0.03
0.05
0.05
0.15
0.23
0.34
0.42
Data from Rollinson (1993).
Cpx
Garnet
0.031
0.042
0.06
0.012
0.026
0.023
7.0
0.955
34.0
1.345
0.056
0.001
0.092
0.007
0.23
0.026
0.445
0.102
0.474
0.243
0.582
3.17
0.583
6.56
0.542 11.5
0.506 11.9
Plag
Amph Magnetite
0.071
0.29
1.83
0.46
0.23
0.42
0.01
6.8
29.
0.01
2.0
7.4
0.148
0.544
2.
0.082
0.843
2.
0.055
1.34
2.
0.039
1.804
1.
0.1/1.5*
1.557
1.
0.023
2.024
1.
0.02
1.74
1.5
0.023
1.642
1.4
0.019
1.563
* Eu3+/Eu2+
Italics are estimated

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
A
WA = weight % of mineral A in the rock
Di = partition coefficient of element i in
A
mineral A
Rb
Sr
Ba
Ni
Cr
La
Ce
Nd
Sm
Eu
Dy
Er
Yb
Lu
Rare Earth Elements
Table 9-1. Partition Coefficients (CS/CL) for Some Commonly Used Trace
Elements in Basaltic and Andesitic Rocks
Olivine
0.010
0.014
0.010
14
0.70
0.007
0.006
0.006
0.007
0.007
0.013
0.026
0.049
0.045
Opx
0.022
0.040
0.013
5
10
0.03
0.02
0.03
0.05
0.05
0.15
0.23
0.34
0.42
Data from Rollinson (1993).
Cpx
Garnet
0.031
0.042
0.060
0.012
0.026
0.023
7
0.955
34
1.345
0.056
0.001
0.092
0.007
0.230
0.026
0.445
0.102
0.474
0.243
0.582
1.940
0.583
4.700
0.542
6.167
0.506
6.950
Plag
Amph Magnetite
0.071
0.29
1.830
0.46
0.23
0.42
0.01
6.8
29
0.01
2.00
7.4
0.148
0.544
2
0.082
0.843
2
0.055
1.340
2
0.039
1.804
1
0.1/1.5*
1.557
1
0.023
2.024
1
0.020
1.740
1.5
0.023
1.642
1.4
0.019
1.563
* Eu3+/Eu2+
Italics are estimated
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


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.


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.
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
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
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
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
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
Table 9-1. Partition Coefficients (CS/CL) for Some Commonly Used Trace
Elements in Basaltic and Andesitic Rocks
Rb
Sr
Ba
Ni
Cr
La
Ce
Nd
Sm
Eu
Dy
Er
Yb
Lu
Rare Earth Elements

Olivine
0.010
0.014
0.010
14
0.70
0.007
0.006
0.006
0.007
0.007
0.013
0.026
0.049
0.045
Opx
0.022
0.040
0.013
5
10
0.03
0.02
0.03
0.05
0.05
0.15
0.23
0.34
0.42
Data from Rollinson (1993).
Cpx
Garnet
0.031
0.042
0.060
0.012
0.026
0.023
7
0.955
34
1.345
0.056
0.001
0.092
0.007
0.230
0.026
0.445
0.102
0.474
0.243
0.582
1.940
0.583
4.700
0.542
6.167
0.506
6.950
Plag
Amph Magnetite
0.071
0.29
1.830
0.46
0.23
0.42
0.01
6.8
29
0.01
2.00
7.4
0.148
0.544
2
0.082
0.843
2
0.055
1.340
2
0.039
1.804
1
0.1/1.5*
1.557
1
0.023
2.024
1
0.020
1.740
1.5
0.023
1.642
1.4
0.019
1.563
* Eu3+/Eu2+
Italics are estimated
Sr and Ba (also incompatible elements)


Sr is excluded from most common minerals
except plagioclase
Ba similarly excluded except in alkali feldspar
Table 9-1. Partition Coefficients (CS/CL) for Some Commonly Used Trace
Elements in Basaltic and Andesitic Rocks
Rb
Sr
Ba
Ni
Cr
La
Ce
Nd
Sm
Eu
Dy
Er
Yb
Lu
Rare Earth Elements

Olivine
0.010
0.014
0.010
14
0.70
0.007
0.006
0.006
0.007
0.007
0.013
0.026
0.049
0.045
Opx
0.022
0.040
0.013
5
10
0.03
0.02
0.03
0.05
0.05
0.15
0.23
0.34
0.42
Data from Rollinson (1993).
Cpx
Garnet
0.031
0.042
0.060
0.012
0.026
0.023
7
0.955
34
1.345
0.056
0.001
0.092
0.007
0.230
0.026
0.445
0.102
0.474
0.243
0.582
1.940
0.583
4.700
0.542
6.167
0.506
6.950
Plag
Amph Magnetite
0.071
0.29
1.830
0.46
0.23
0.42
0.01
6.8
29
0.01
2.00
7.4
0.148
0.544
2
0.082
0.843
2
0.055
1.340
2
0.039
1.804
1
0.1/1.5*
1.557
1
0.023
2.024
1
0.020
1.740
1.5
0.023
1.642
1.4
0.019
1.563
* Eu3+/Eu2+
Italics are estimated
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
Table 9-1. Partition Coefficients (CS/CL) for Some Commonly Used Trace
Elements in Basaltic and Andesitic Rocks
Rb
Sr
Ba
Ni
Cr
La
Ce
nts

Olivine
0.010
0.014
0.010
14
0.70
0.007
0.006
Opx
0.022
0.040
0.013
5
10
0.03
0.02
Cpx
Garnet
0.031
0.042
0.060
0.012
0.026
0.023
7
0.955
34
1.345
0.056
0.001
0.092
0.007
Plag
Amph Magnetite
0.071
0.29
1.830
0.46
0.23
0.42
0.01
6.8
29
0.01
2.00
7.4
0.148
0.544
2
0.082
0.843
2
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

Models of Magma Evolution

Batch Melting
1
eq. 9.5 CL =
CO Di(1 - F)+ F
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)
Batch Melting
A plot of CL/CO vs. F for various
values of Di using eq. 9.5

Di = 1.0
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.
Di » 1.0 (compatible element)

Very low concentration in
melt

Especially for low %
melting (low 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.
Highly incompatible elements
 Greatly concentrated in
the initial small fraction
of melt produced by
partial melting

Subsequently 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.

As F  1 the concentration of
every trace element in the
liquid = the source rock (CL/CO
 1)
As F  1
1
CL
=
C O Di (1 - F) + F CL/CO  1
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.
As F  0
CL/CO  1/Di
1
CL
=
C O Di (1 - F) + F
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)
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.

For very incompatible elements as Di  0
equation 9.5
1
CL
=
C O Di (1 - F) + F
reduces to:
CL 1
eq. 9.7
=
CO F
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
Worked Example of Batch Melting: Rb and Sr
Basalt with the mode:
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
1. Convert to weight % minerals (Wol Wcpx etc.)
Worked Example of Batch Melting: Rb and Sr
Basalt with the mode:
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
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 =
0.045 and DSr = 0.848
3. Use the batch melting equation
(9.5)
1
CL
=
C O Di (1 - F) + F
to calculate CL/CO for various values of F
Table 9.3 . Batch Fractionation Model for
Rb and Sr
F
0.05
0.1
0.15
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
C L/C O = 1/(D(1-F)+F)
D Rb
D Sr
0.045
0.848
9.35
1.14
6.49
1.13
4.98
1.12
4.03
1.12
2.92
1.10
2.29
1.08
1.89
1.07
1.60
1.05
1.39
1.04
1.23
1.03
1.10
1.01
Rb/Sr
8.19
5.73
4.43
3.61
2.66
2.11
1.76
1.52
1.34
1.20
1.09
From Winter (2010) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
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.
Incremental Batch Melting


Calculate batch melting for successive
batches (same equation)
Must recalculate Di as solids change as
minerals are selectively melted (computer)
Fractional Crystallization
1. Crystals remain in equilibrium with each
melt increment

Rayleigh fractionation
The other extreme: separation of each
crystal as it formed = perfectly continuous
fractional crystallization in a magma
chamber

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
Other models are used to analyze
 Mixing of magmas
 Wall-rock assimilation
 Zone refining
 Combinations of processes
The Rare Earth Elements (REE)
Contrasts and similarities in the D values:
All are incompatible
Table 9-1. Partition Coefficients (CS/CL) for Some Commonly Used Trace
Elements in Basaltic and Andesitic Rocks
HREE are less
incompatible
Especially in
garnet
Eu can  2+
which conc.
in plagioclase
Rb
Sr
Ba
Ni
Cr
La
Ce
Nd
Sm
Eu
Dy
Er
Yb
Lu
Rare Earth Elements
Also Note:
Olivine
0.01
0.014
0.01
14.0
0.7
0.007
0.006
0.006
0.007
0.007
0.013
0.026
0.049
0.045
Opx
0.022
0.04
0.013
5.0
10.0
0.03
0.02
0.03
0.05
0.05
0.15
0.23
0.34
0.42
Data from Rollinson (1993).
Cpx
Garnet
0.031
0.042
0.06
0.012
0.026
0.023
7.0
0.955
34.0
1.345
0.056
0.001
0.092
0.007
0.23
0.026
0.445
0.102
0.474
0.243
0.582
3.17
0.583
6.56
0.542 11.5
0.506 11.9
Plag
Amph Magnetite
0.071
0.29
1.83
0.46
0.23
0.42
0.01
6.8
29.
0.01
2.0
7.4
0.148
0.544
2.
0.082
0.843
2.
0.055
1.34
2.
0.039
1.804
1.
0.1/1.5*
1.557
1.
0.023
2.024
1.
0.02
1.74
1.5
0.023
1.642
1.4
0.019
1.563
* Eu3+/Eu2+
Italics are estimated
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
Log (Abundance in CI Chondritic Meteorite)
11
H
He
10
9
8
C
7
6
5
4
3
2
1
Li
O
Ne MgSi
Fe
N
S Ar
Ca Ni
Na
Ti
AlP
K
F Cl
V
B
Sc
Sn
Ba
Pt Pb
0
Be
-1
Th
-2
U
-3
0
10
20
30
40
50
60
70
80
90
Atomic Number (Z)

Eliminate Oddo-Harkins effect and make y-scale
more functional by normalizing to a standard
 estimates of primordial mantle REE
 chondrite meteorite concentrations
100
What would an REE diagram look
like for an analysis of a chondrite
meteorite?
sample/chondrite
10.00
8.00
6.00
?
4.00
2.00
0.00
56 La58
Ce
L
60Nd 62Sm 64
Eu
66
Tb
68Er 70 Yb 72
Lu
Divide each element in analysis by the
concentration in a chondrite standard
sample/chondrite
10.00
8.00
6.00
4.00
2.00
0.00
56 La58
Ce
L
60Nd 62Sm 64
Eu
66
Tb
68Er 70 Yb 72
Lu
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.

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.
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)
Fig. 9.6. 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. 313-345.
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.
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.
2. Identification of the source rock or a particular
mineral involved in either partial melting or
fractional crystallization processes
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
Rb
Sr
Ba
Ni
Cr
La
Ce
Nd
Sm
Eu
Dy
Er
Yb
Lu
Rare Earth Elements
Table 9-1. Partition Coefficients (CS/CL) for Some Commonly Used Trace
Elements in Basaltic and Andesitic Rocks
Olivine
0.01
0.014
0.01
14.0
0.7
0.007
0.006
0.006
0.007
0.007
0.013
0.026
0.049
0.045
Opx
0.022
0.04
0.013
5.0
10.0
0.03
0.02
0.03
0.05
0.05
0.15
0.23
0.34
0.42
Data from Rollinson (1993).
Cpx
Garnet
0.031
0.042
0.06
0.012
0.026
0.023
7.0
0.955
34.0
1.345
0.056
0.001
0.092
0.007
0.23
0.026
0.445
0.102
0.474
0.243
0.582
3.17
0.583
6.56
0.542 11.5
0.506 11.9
Plag
Amph Magnetite
0.071
0.29
1.83
0.46
0.23
0.42
0.01
6.8
29.
0.01
2.0
7.4
0.148
0.544
2.
0.082
0.843
2.
0.055
1.34
2.
0.039
1.804
1.
0.1/1.5*
1.557
1.
0.023
2.024
1.
0.02
1.74
1.5
0.023
1.642
1.4
0.019
1.563
* Eu3+/Eu2+
Italics are estimated
10.00
67% Ol
sample/chondrite
8.00
17% Opx
17% Cpx
Garnet and Plagioclase
effect on HREE
6.00
4.00
2.00
0.00
56
58 Ce 60 Nd 62Sm Eu
64
La
Tb66
68
Er
70 Lu 72
Yb
10.00
10.00
60% Ol 15% Opx 15% Cpx 10%Plag
57% Ol
8.00
14% Opx
14% Cpx 14% Grt
sample/chondrite
sample/chondrite
8.00
6.00
4.00
6.00
4.00
2.00
2.00
0.00
0.00
La Ce Nd Sm Eu
Tb
Er
Yb Lu
56
58
La
64
Ce60 Nd 62Sm Eu
Tb66
68
Er
70 Lu
Yb
72
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.
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,
Platinum group elements (PGEs) are siderophile and used mostly to study melting and crystallization in mafic-ultramafic
Re, Os, Ir,
systems in which PGEs are typically hosted by sulfides. The Re/Os isotopic system is controlled by initial PGE
Pd
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.
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
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.
Isotopes
Same Z, different A (variable # of neutrons)
14
General notation for a nuclide:
6C
Isotopes
Same Z, different A (variable # of neutrons)
14
General notation for a nuclide: 6 C
As n varies  different isotopes of an element
12C 13C 14C
Stable Isotopes



Stable: last ~ forever
Chemical fractionation is impossible
Mass fractionation is the only type possible
Example: Oxygen Isotopes
16O
17O
18O
99.756% of natural oxygen
0.039%
“
0.205%
“
Concentrations expressed by reference to a standard
International standard for O isotopes = standard mean
ocean water (SMOW)
18O
and 16O are the commonly used isotopes
and their ratio is expressed as d:
d (18O/16O) =
eq 9.10
( 18 O/ 16 O) sample - ( 18 O/ 16 O) SMOW
18
16
( O/in per
O) mille
SMOW(‰)
result expressed
What is d of SMOW??
What is d for meteoric water?
x1000
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

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=
( 18 O/ 16 O) vapor - ( 18 O/ 16 O) SMOW
18
16
( O/ O) SMOW
x1000
therefore ( 18 O/ 16 O) Vapor < ( 18 O/ 16 O) SMOW
thus dclouds is (-)
Figure 9.9. Relationship between d(18O/16O) and mean annual temperature
for meteoric precipitation, after Dansgaard (1964). Tellus, 16, 436-468.
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 mantlederived magmas by crustal sediments

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
Isotopic variations between rocks, etc. due to:
1. Mass fractionation (as for stable isotopes)
Only effective for light isotopes: H He C O S
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
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
Radioactive Decay
The Law of Radioactive Decay
dN
N
eq. 9.11 dt
dN
or = lN
dt
1
½
¼
time 
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
The K-Ar System
40K
 either 40Ca or 40Ar
 40
Ca 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
The appropriate decay equation is:
eq 9.16
40Ar
=
40Ar
 le 

o+ 
 l
40K(e-lt -1)
Where le = 0.581 x 10-10 a-1 (proton capture)
and l = 5.543 x 10-10 a-1 (whole process)


Blocking temperatures for various minerals
differ
40Ar-39Ar technique grew from this discovery
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
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.
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
Recast age equation by dividing through by stable 86Sr
= (87Sr/86Sr)o + (87Rb/86Sr)(elt -1)
l = 1.4 x 10-11 a-1
87Sr/86Sr
eq 9.17
For values of lt less than 0.1: elt-1  lt
Thus eq. 9.15 for t < 70 Ga (!!) reduces to:
eq 9.18
87Sr/86Sr
y
= (87Sr/86Sr)o + (87Rb/86Sr)lt
=
b
+
x
= equation for a line in 87Sr/86Sr vs. 87Rb/86Sr plot
m
Begin with 3 rocks plotting at a b c at time to
87Sr
86Sr
( )
87Sr
86Sr
o
a
b
87Rb
86Sr
c
to
After some time increment (t0 t1) each sample loses
some 87Rb and gains an equivalent amount of 87Sr
87Sr
86Sr
t1
c1
()
b1
a1
87Sr
86Sr
o
a
b
87Rb
86Sr
c
to
At time t2 each rock system has evolved  new line
Again still linear and steeper line
t2
87Sr
c2
86Sr
b2
a2
()
t1
c1
b1
a1
87Sr
86Sr
o
a
b
c
to
87Rb
86Sr
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
Figure 9.12. 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, 213-241.
Figure 9.13. 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.
The Sm-Nd System

Both Sm and Nd are LREE
Incompatible elements fractionate  melts
 Nd has lower Z  larger  liquids > does Sm

147Sm
 143Nd by alpha decay
l = 6.54 x 10-13 a-1 (half life 106 Ga)

Decay equation derived by reference to
the non-radiogenic 144Nd
 143Nd/144Nd = (143Nd/144Nd)o
+ (147Sm/144Nd)lt
Evolution curve is opposite to Rb - Sr
Figure 9.15. 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.
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



 234U  206Pb
235U  207Pb
232Th  208Pb
238U
(l = 1.5512 x 10-10 a-1)
(l = 9.8485 x 10-10 a-1)
(l = 4.9475 x 10-11 a-1)
The U-Pb-Th System
Concordia = Simultaneous coevolution of 206Pb and 207Pb via:
 234U  206Pb
235U  207Pb
238U
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.
The U-Pb-Th System
Discordia = loss of both
206Pb
and 207Pb
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.
The U-Pb-Th System
Concordia diagram after 3.5 Ga total evolution
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.
The U-Pb-Th System
Figure 9.17. 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.