Transcript Lecture 6: Igneous classification, mid

Lecture 14: Stable Isotopes and Climate
• Questions
– How do different isotopes of the same element get
fractionated from one another?
– What can we learn about geology from measurements of
stable isotope ratios in rocks?
– What can we learn about the history of climate from such
measurements in ice, water, fossils, and sediments?
• Tools
– Thermodynamics and kinetics
• Reading:
– Albarède, Chapter 2 (again)
1
The stable isotopist’s periodic table
• We are interested here in elements that have more than one nonradiogenic isotope, for which the mass difference between
isotopes is a significant fraction of the atomic mass, and which
have enough interesting chemistry to fractionate the isotopes
IA
IIIA
IIA
IVA
VA
VIA VIIA VIIIA
1
2
H
1
4
3
Li
2
37
7
IIIB
38
22
21
Y
41
VIIIB
VIIB
24
25
26
27
IB
28
29
IIB
30
Al
104
43
74
105
N
15
Si
32
31
44
45
46
47
48
49
9
10
O
16
P
33
50
Zr Nb Mo Tc Ru Rh Pd Ag Cd In
73
C
8
F
Ne
17
S
34
18
Cl Ar
35
36
Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br
42
Hf Ta
Fr Ra
VIB
V
Ti
72
88
76
75
77
W Re Os
106
108
107
79
78
Ir
80
Tl
52
53
Sn Sb Te
82
81
Pt Au Hg
51
83
84
Kr
54
I
Xe
85
86
Pb Bi Po At
Rn
109
Rf Db Sg Bh Hs Mt
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
89
Actinides
VB
23
40
39
56
Lanthanides
IVB
7
14
13
Cs Ba
87
B
Limited or recent use only
Ca Sc
Rb Sr
55
6
20
K
4
5
Be
Na Mg
19
6
5
12
11
3
He
Standard Repertoire
90
91
Ac Th Pa
92
93
94
95
96
97
98
99
100
101
102
U Np Pu Am Cm Bk Cf Es Fm Md No
103
Lr
2
The stable isotopist’s periodic table
• Traditional stable isotope chemistry focuses entirely on the light
elements (H, Li, B, C, N, O)
• More recently analytical tools have become precise enough to
enable work on the small anomalies in heavier metals
Element
# isotopes
m/m
Abundances (%)
H
Li
B
C
N
O
Mg
Si
S
Cl
Fe
2
2
2
2
2
3
3
3
4
2
4
1
1/6
1/10
1/12
1/14
2/16
2/24
2/28
4/32
2/35
4/54
99.985, 0.015
7.5, 92.5
19.9, 80.1
98.89,1.11
99.634,0.366
99.762,0.038,0.2
78.99,10.0,11.01
92.23,4.67,3.10
95.02,0.75,4.21,0.02
75.77,24.23
5.85,91.75,2.12,0.28
3
Delta notation
• Stable isotope ratios are almost always expressed in d-notation:
Rsample-Rstandard
d
x1000
RStandard
=(
)
e.g.,
The x1000 implies that the units on d are parts per thousand, permil, or ‰
4
Theory of Isotope Fractionation
• Fractionation refers to the partial separation of two isotopes of the same
element, producing reservoirs with different ratios of the isotopes. These
differences are called isotopic anomalies.
• Two classes of basic mechanisms and two strange ones exist for
fractionating isotopes:
– The two basic mechanisms are:
• equilibrium isotope fractionation, which is due to differences in bond
energies of isotopes in compounds
• kinetic isotope fractionation, which is due to differences in average
velocity or reaction rates of different isotopes
• Both depend only on the mass of the isotope and are called mass
dependent fractionation; both will fractionate, say 18O/16O about
twice as much as 17O/16O
– The strange mechanisms are mass-independent fractionation; one
depends on quantum mechanical symmetry terms that occur for
molecules like O3 and SO2 and reflects only the identity (not mass) of
atoms, so fractionates 17O and 18O equally. The other depends on
isotope-specific wavelengths of photo-dissociation reactions and is
thought perhaps to have been relevant in the solar nebula.
5
Equilibrium Isotope Fractionation
• Equilibrium isotope fractionation controls the distribution of
isotopes in the case (obviously) that a system approaches
thermodynamic equilibrium.
– Tends to be most relevant for high temperature problems
• Igneous and (to a certain extent) metamorphic rocks
• Some meteoritic processes
• Hydrothermal interactions
– Tends to be less important in processes involving gas
phases, biological reactions, or transport
• Largest fractionations occur between states of a particular
element with very different chemical bonding environments
– Different oxidation states: N0 vs. N-3 vs. N+5...
– Different bonding partners: H2 vs. H2O vs. CH4...
6
Theory of equilibrium isotopic fractionation
• Isotopes distribute themselves among compounds in a way that minimizes the
energy of the system. The sensitivity to mass comes in through the vibrational
modes of interatomic bonds
• Vibrations are quantized, E(vib) = hn(n+1/2) n=0,1,2,3
• 1/2•hn is called the Zero-Point Energy (ZPE)
• Vibrational frequency n depends on “spring constant” and reduced mass:
1
2
k

, 
Energy
H
Energy
Cl
n
n=1, E(vib)=3/2•h n
n=0, E(vib)=1/2•h n
Bond length
m1m2
m1  m2
isotopically light
molecule
isotopically heavy
molecule
Bond length
7
Theory of equilibrium isotopic fractionation: example
1HCl n = 8.97•1013 Hz
2HCl n = 6.43•1013 Hz
E(vib) = 1/2•hn
≈ 17,900 J/mol
1HF
n = 12.41•1013 Hz
E(vib) = 1/2•hn
≈ 24,800 J/mol
E(vib) = 1/2•hn
≈ 12,800 J/mol
2HF
n = 8.99•1013 Hz
E(vib) = 1/2•hn
≈ 17,900 J/mol
8
Theory of equilibrium isotopic fractionation, example
At Equilibrium, for H-isotope exchange between HF and HCl:
2HCl
+ 1HF
1HCl
+ 2HF
G0 ≈ E(vib) = E(vib)products – E(vib)reactants
E(vib) products = 17,900 J/mol (1HCl) + 17,900 J/mol (2HF)
E(vib) reactants = 12,800 J/mol (2HCl) + 24,800 J/mol (1HF)
E(vib) = –1,800 J/mol, driving the reaction to the right and
concentrating 2H in HF (by a factor of 2 at 25 ºC)!
• Need to consider all energy levels, not just ground state
(Boltzmann statistics), as well as entropy terms, both of which
give smaller fractionations at high temperature
9
Temperature dependence of
equilibrium isotope effects
RA
 A B 
RB
 AB  dA  dB  1000 ln  AB

10
Theory of kinetic isotope effects
• Kinetic isotope effects occur in fast, incomplete, or
unidirectional processes like evaporation, diffusion, and
biological reactions
• Consider an ideal gas. Every molecule has, on average, the
same kinetic energy E = 1/2 mv2
• The average velocities of two molecules with different masses
due to isotopic substitution therefore follow the relationship
v1
m2

v2
m1
• Hence the light isotopic species will diffuse faster in the gas
phase.
– e.g., this is one way to enrich 235U relative to 238U, but in the
form of the gas molecule UF6, the diffusivity ratio implies
only (352/349)1/2 = 4‰ separation per cycle
11
Theory of kinetic isotope effects
Kinetic fractionation effects
can be much larger than
equilibrium fractionations.
This is the result of two
factors:
• Equilibrium fractionation
factors depend on the
imbalance between forward
rate constants and reverse rate
constants for different
isotopes; kinetic factors
depend only on the forward
rates. Both rates are likely to
be faster for light isotopes, so
reverse reaction diminishes
the fractionation.
• The open-system effect,
whereby both the distillate
and the residue can become
very fractionated.
12
Theory of kinetic isotope effects
We can see kinetic isotope
effects resulting from
hydrothermal alteration of
igneous rocks initially in
equilibrium and in
metamorphic rocks as a result
of partial devolatilization
13
•
More on hydrothermal alteration
Hydrothermal alteration of rocks is
pervasive
– Any place that igneous rocks are
emplaced and cooled to the point where
fracture is possible, water is likely to
get in
– Resulting patterns depend on
composition of water (seawater vs.
meteoric, plus latitude dependence),
temperature, and water-rock ratio
– “Fresh” igneous rocks mostly acquire
odd isotope signatures by assimilating
altered ones
14
Stable isotope thermometry I
• Equilibrium fractionation
factors are temperature
dependent. Therefore
measurements of isotope
fractionation between
coexisting phases presumed to
have equilibrated with one
another define the
temperature at which they
equilibrated.
• Several common mineral
pairs have been calibrated by
laboratory exchange
experiments.
• The general problem is that
equilibrium is most readily
achieved at high temperature
but the isotope thermometers
are most sensitive at low
temperature!
15
Stable isotope thermometry II
A reversal
experiment
• In general minerals exchange more readily
with a free water phase than with each other:
– so it is easiest to calibrate
fractionation factors relative to water
and
– most reasonable to assume
equilibrium between mineral and
water in natural settings
Epstein et al (1953) produced the first useful
such calibration for biogenic calcite and
water and thereby founded the field of
isotope paleothermometry:
T(C) 16.9  4.2CaCO3  H2O  0.132CaCO3  H2O
16
Stable Isotope
thermometry III
Sediment-core records of the
isotopic composition of
biogenic calcite are available at
various resolutions and record
lengths covering the last 70 Ma.
Though there are vital effects
that modify the CaCO3-H2O
fractionation, these are small.
Problem: we have only the
calcite, not the H2O from which
it precipitated. So how much of
the d18O variation is due
directly to temperature (which
controls fractionation between
calcite and H2O) and how much
due to the change in d18O of
seawater?
Why does seawater d18O
change? Because of the growth
and decay of ice sheets…
But why is ice so light in 18O?
17
Stable isotopes and the Hydrologic Cycle
• The ice-seawater difference reflects general aspects of the
fractionation of oxygen (and hydrogen) isotopes by the
hydrologic cycle
– These are mostly kinetic factors, since evaporation and
precipitation of water vapor, rain, and snow are nearly
Rayleigh processes
18
Stable isotopes and the
Hydrologic Cycle
• The more rain you pull out of a cloud, the
lighter the isotopes in the cloud become and
the lighter the next increment of rain gets
– Since low temperature lowers
solubility, air that reaches cold places
has become very dry and very light
– Since water vapor originates in the
ocean, by the time clouds get far inland
they become very light
– So there is a
continental effect
superimposed on a
latitudinal gradient
– Tests to distinguish
interaction with
seawater from
meteoric water are
much more
sensitive some
places than others!
19
d18O map
Stable isotopes and the Hydrologic Cycle
• Since hydrologic processes involve only mass fractionation, the
hydrogen isotopes and oxygen isotopes co-vary quite closely,
defining the meteoric water line dD = 8 * d18O + 10
dD map
20
Isotope Paleoclimatology
• First indication that climate variations in the Pleistocene are
cyclic and that there have been more ice ages than can be seen
in geological evidence came from deep sea sediment cores
measured by Emiliani (1966), but he had no timescale:
Calibration showed
that the major glacialinterglacial cycle has
a period of 100,000
years, modulated by
~20 ka and ~40 ka
oscillations
21
Isotope Paleoclimatology
• The marine isotope record can be deconvolved into temperature
(i.e., calcite-H2O) and ice volume (i.e. d18Owater) signals if we
know the variation of sea level, which directly measures how
much water is tied up ice sheets on land
Some data on this from 14C or U-Th
dating of coral terraces
22
Answer: about 1 ‰ from
each effect
23
Isotope Paleoclimatology
• Why are ice ages quasiperiodic? Because they are
driven by periodic
variations in solar forcing
resulting from quirks of the
Earth orbit, called
Milankovitch cycles
• These mostly affect the
seasonality of sunlight, not
the total amount received
Precessio
n
Isotope Paleoclimatology
• The so-called Milankovitch hypothesis (Hays, Imbrie, & Shackleton)
argues that ice ages are driven by summer insolation at 65°N.
• Why? Because ice sheets can only grow if snow that falls during
winter lasts through the summer without melting and the big highlatitude continental areas are in the northern hemisphere.
24
• The Milankovitch curve fits the
phases and relative power in the
20, 40, and 100 ka cycles well
but it has at least three
shortcomings:
– The forcing functions are
sinusoidal but the response is
sawtoothed (fast warmings),
which requires a nonlinear
coupling mechanism
– The amplitude of the climate
swings is much bigger than
one expects from fairly small
changes in forcing (another
nonlinear clue)
– And, ice-core data indicate
very high amplitude
variability at much higher
frequencies
Isotope
Paleoclimatology
25
Isotope Paleoclimatology
• Ice core records from Greenland provide annual time resolution(!)
but only constrain climate at high latitude and only go back one iceage cycle (4 in Antarctica but no annual bands there)
• Why is the time resolution so much better? Because sediment cores
suffer from bioturbation, slow sedimentation, and poor time control
26
•
•
•
•
Isotope Paleoclimatology
Ice core records record
extraordinary stability of
the Holocene and very
high-amplitude rapid
fluctuations during the late
Pleistocene
Are these fluctuations just
analytical noise? No, they
match up in both
Greenland summit cores
(GRIP and GISP)
Are they just a local
Greenland effect? No,
they correlate with
worldwide indicators
These are called Heinrich
events and their cause is
poorly understood
27
28
Mass-independent Effects
• Looking at three isotopes of the same element, all mass-dependent
fractionation (whether equilibrium or kinetic) should displace samples along
the same line (e.g., slope 1/2 in d17O-d18O space)
• Clayton and Mayeda (1974) demonstrated that different classes of meteorites
define different such lines, but that all objects from a given parent body (e.g.,
earth-moon system) share a common line
• But chondrites show a BIG depletion in 16O along a line with slope one,
originally interpreted as a nucleosynthetic effect, i.e. imperfect mixing into
solar system of some pure 16O material from a separate stellar source
Mass-independent Effects
29
• But Thiemens and coworkers discovered in the 1980’s that certain reactions
involving ozone (O3) can fractionate isotopes independent of mass due to a
quantum mechanical symmetry effect (there are more distinct states for
18O16O16O or 17O16O16O than for 16O16O16O; explained in detail by Gao and
Marcus (2001) in a prize-winning Caltech thesis)
• No real mechanism has been proposed, but the possibility of massindependent chemical effects casts doubt on the need for nucleosynthetic
explanation of the three O-isotope heterogeneity of the solar system/
• The symmetry mechanism also
works for SO2 and has been invoked
to explain anomalies in 33S ~ d33S–
d34S in Archaean rocks, when
presumably atmosphere was more
reducing and H2SO4 less dominant
O3
O2
O2+O=O3
O