Geochemistry
PUCP 2015
Isotope Geochemistry Isotope geochemistry Dr. Jochen Smuda
Part I Isotope Geochemistry Stabl e Iso to pes
Isotopes • Isotopes have different ## of neutrons, and thus a different mass • Affect on reactions in small, but real, and provides another measurement of reactions – affected by similar physicochemical parameters! • Also a critical tracer – the isotopes can be used to track molecules in a reaction!
Measuring Isotopes • While different, isotopes of the same element exist in certain fractions corresponding to their natural abundance (adjusted by Where Ra is the ratio of fractionation) a Ra α
b
=
heavy/light isotope and α is the fractionation factor
Rb
• We measure isotopes as a ratio of the isotope vs. a standard material (per mille ‰) δ
18
Rsample Rstandard × 103 Rstandard ‰
O =
3
10 ln
α
a b
δ
≈
a
δ
−
a b
= ∆b
Fractionation • A reaction or process which selects for one of the stable isotopes of a particular element 10 3 ln α a ≈ δ − δ = ∆a b
a
b
b
• If the process selects for the heavier isotope, the reaction product is ‘heavy’, the reactant remaining is ‘light’ • Isotope fractionation occurs for isotopic exchange reactions and mass-dependent differences in the rates of chemical reactions and physical processes
Temperature effects on fractionation • The fractionation factors, α, are affected by T (recall that this affects EA) and defined empirically: 10
3
a ln α b =
• Then,
A × 10 T
2
6
+
B
Where A and B are constants determined for particular reactions and T is temp. in Kelvins
103 ln α ba ≈ δ a − δ b = ∆ab
• As T increases, ∆ decreases – at high T ∆ goes to zero
Equilibrium vs. Kinetic fractionation •
•
Fractionation is a reaction, but one in which the free energy differences are on the order of 1000x smaller than other types of chemical reactions Just like other chemical reactions, we can describe the proportion of reactants and products as an equilibrium or as a kinetic function
FRACTIONATION DURING PHYSICAL PROCESSES • Mass differences also give rise to fractionation during physical processes (diffusion, evaporation, freezing, etc.). • Fractionation during in physical processofis a result of differences the velocities isotopic molecules of the same compound. • Consider molecules in a gas. All molecules have the same average kinetic energy, which is a function of temperature.
Ekinetic
= 12
mv 2
Because the kinetic energy for heavy and light isotopes is the same, we can write: vL vH
In the case of
12C16O
vL vH
=
=
mH mL
and 13C16O we have:
28.99827 27.994915
= 1.0177
Regardless of the temperature, the velocity of 12C16O is 1.0177 times that of 13C16O, so the lighter molecule will diffuse faster and evaporate faster.
Equilibrium Fractionation • For an exchange reaction: ½ C16O2 + H218O ↔ ½ C18O2 + H216O • Write the equilibrium:
1 18
(C O2 ) 2 ( H 16O2 )
K=
1 16
(C O2 ) 2 ( H 18O2 )
• Where activity coefficients effectively cancel out • For isotope reactions, K is always small, usually 1.0xx (this K is 1.047 for example)
WHY IS K DIFFERENT FROM 1.0? Because 18O forms a stronger covalent bond with C than does 16O. The vibrational energy of a molecule is given by the equations:
Evibrational = O H
H
1
2
hν
ν
1 =
2π
k m
F
= −
kx
Thus, the frequency of vibration depends on the mass of the atoms, so the energy of a molecule depends on its mass.
• The heavy isotope forms a lower energy bond; it does not vibrate as violently. Therefore, it forms a stronger bond in the compound. • The Rule of Bigeleisen (1965) - The heavy isotope goes preferentially into the compound with the strongest bonds.
Equilibrium Fractionation II • For a mass-dependent reaction: • Ca2+ + C18O32- CaC18O3 • Ca2+ + C16O32- CaC16O3 • Measure δ18O in calcite (δ18Occ) and water (δ18Osw) • Assumes 18O/16O between H2O and CO32- at some equilibrium T ºC = 16.998 - 4.52 (
18
Occ -
18
Osw) + 0.028 (
18
Occ-
18
Osw)2
Empirical Relationship between Temp. & Oxygen Isotope Ratios in Carbonates At lower temperatures, calcite crystallization tends to incorporate a relatively larger proportion of 18O because the energy level (vibration) of ions containing this heavier isotope decreases by a greater amount than ions containing 16O. As temperatures drop, the energy level of 18O declines progressively by an amount that this disproportionately greater than that of the lighter 16O.
Distillation • 2 varieties, Batch and Rayleigh distillation dependent on if the products stay in contact and re-equilibrate with the reactants • Batch Distillation: δf = δi – (1 – F) 103lnαCO2-Rock
where the isotope of the rock (δi) depends on it’s initial value (δf) and the fractionation factor • Rayleigh Distillation δf - δi =103(F(α – 1) – 1)
RAYLEIGH DISTILLATION Isotopic fractionation that occurs during condensation in a moist air mass can be described by Rayleigh Distillation. The equation governing this process is: α −1
Rv
=
Rvo f
where Rv = isotope ratio of remaining vapor, Rv° = isotope ratio in initial vapor, ƒ = the fraction of vapor remaining and a = the isotopic fractionation factor
Effect of Rayleigh distillation on the δ18O value of water vapor remaining in the air mass and of meteoric precipitation falling from it at a constant of 25°C. temperature Complications: 1) Re-evaporation 2) Temperature dependency of α
Using isotopes to get information on physical and chemical processes • Fractionation is due to some reaction, different isotopes can have different fractionation for thehave same reaction, and different reactions different fractionations, as well as being different at different temperatures and pressures • Use this to understand physical-chemical processes, mass transfer, temperature changes, and other things…
Volatilization • calcite + quartz = wollastonite + carbon dioxide CaCO3 + SiO2=
CaSiO
3
+
CO2
• As the CO 2 is produced, it is likely to be expelled
• Other volatilization reaction examples…
ISOTOPE FRACTIONATION IN THE HYDROSPHERE Evaporation of surface water in equatorial regions causes formation of air masses with H2O vapor depleted in 18O and D compared to seawater. This moist air is forced into more northerly, cooler air in the northern hemisphere, where water condenses, and this condensate is enriched in 18O and D compared to the remaining vapor. The relationship between the isotopic composition of liquid and vapor is: δ
18
Ol
=
l
αv δ
18
Ov
+ 10
3
− 10
3
Assuming that δ18Ov = -13.1‰ and αvl(O) = 1.0092 at 25°C, then δ
18
3
3
Ol = 1.0092 − 13.1 + 10 − 10 = −4.0 0 00 and assuming δDv = -94.8‰ and αvl(H) = 1.074 at 25°C, then 3 3 δD = 1.074 − 94.8 + 10 − 10 = −27.8 0 00 l
) composition These equations (give the isotopic of the first bit of precipitation. As 18O and D are removed from the vapor, the remaining vapor becomes more and more depleted. Thus, δ18O and δD values become increasingly negative with increasing geographic latititude (and altitude.
Map of North America showing contours of the approximate average δD values of meteoric surface waters.
Because both H and O occur together in water, δ18O and δD are highly correlated, yielding the meteoric water line (MWL): δD ≈ 8δ18O + 10
Deviation from MWL • Any additional fractionation process which affects O and D differently, or one to the exclusion of the other will skew a water away from the MWL plot • These effects include: – Elevation effects - (δD -8‰/1000m, -4‰/ºC) – Temperature (α different!) – Evapotranspiration and steam loss – Water/rock interaction (little H in most rocks)
Kinetic Fractionation • lighter isotopes form weaker bonds in compounds, so they are more easily broken and hence react faster. Thus, in reactions governed by kinetics, light isotopes are concentrated in thethe products. • Again, isotope reactions can be exchange reactions or mass-dependent chemical or physical reactions – kinetic factors may affect any of these!
Kinetic fractionation I – SO42- reduction • SO42- + CH4 + 2 H+ H2S + CO2 + 2 H2O • This reaction is chemically slow at low T, bacteria utilize this for E in anoxic settings • Isotope fractionation of S in sulfide generated by microbes from this process generates some of the biggest fractionations in the environment (-120‰ for S) • THEN we need to think about exchange reactions with H2S or FeS(aq) as it may continue to interact with other S species
S isotopes and microbes • The fractionation of H 2S formed from bacterial sulfate reduction (BSR) is affected by several processes: – Recycling and physical differentiation yields excessively depleted H2S – Open systems – H2S loss removes
34S
– Limited sulfate – governed by Rayleigh process, enriching 34S – Different organisms and different organic substrates yield very different experimental δ34S
• Ends up as a poor indicator of BSR vs. TSR
Iron Isotopes Earth’s Oceans 3 Ga had no oxygen and lots of Fe2+, cyanobacteria evolved, produced O2 which oxidized the iron to form BIFs – in time the Fe2+ was more depleted and the oceans were stratified, then later become oxic as they are today
This interpretation is largely based on iron isotopes in iron oxides and sulfide minerals deposited at those times (Rouxel et al., 2005)
No one has yet bothered to measure how iron isotopes change when iron sulfide minerals precipitate …
Mass-independent fractionation •
•
•
Mass effects for 3 stable isotopes (such as 18O, 17O, and 16O) should have a mass-dependent relationship between each for any process Deviation from this is massindependent and thought to be indicative of nucleosynthetic, a nuclear process (radiogenic, spallation) as opposed to a physicochemical process Found mainly associated with atmospheric chemistry, effect can be preserved as many geochemical reactions in water and rock are massdependent
S-isotopic evidence of Archaen atmosphere • Farquar et al., 2001; Mojzsis et al., 2003 found MIF signal in S isotopes (32S, 33S, 34
S) preserved in archaen pyrites precipitated before 2.45 Ga • Interpreted to be signal from the photolysis of SO2 in that atmosphere – the reaction occurs at 190-220nm light, indicating low O2 and O3 (which very effficiently absorb that wavelength)
Part II GEOCHRONOLOGY Introduction to Radioactive Decay and Dating of Geological Materials
The Age of the Earth • The currently accepted age of the Earth is 4.54 Billion years, ie 4.54 x 109 years • How do we know this? • Let’s go back and look at what the early estimates of the age of the Earth were and why these ages under-estimated the age by quite a long way.
The Debate about the Age of the Earth • Prior to Geology becoming an accepted field of science, the age of the Earth was a matter for Theology. • Bishop Usher proclaimed in 1650 that the creation of the world took place in 4004 BC, a view that was unchallenged for over 100 years. • The official position of the church was that all the surface features of the Earth were related to catastrophic events such as the Great Flood which occurred intermittently.
Catastrophism versus Uniformitarianism • • • • •
So what changed? James Hutton arrived on the scene to shake up the establishment Hutton argued that very slow but continuously acting processes were what accounted for the surface features of the Earth He cemented this idea, which became known as uniformitarianism, in his book Theory of the Earth which was published in 1785. Although initially greeted with horror by many, his ideas gradually became accepted, including the conviction that very long periods of time are required for the deposition of sedimentary rocks
Early Estimates • Early estimates were based on the principle of superposition – In the late 1790’s early 1800’s, William Smith’s nephew calculated using this principle that the Earth was 96 million years old • Estimates where also based on the rate of cooling of the Earth – In 1779 the French naturalist Comte du Buffon did an experiment where he created a minature Earth and measured it’s rate of cooling. Doing this he estimated the Earth as being 75,000 years old.
William Thompson •
In 1862 the Scottish physicist William Thompson calculated that the Earth was between 24 and 400 million years old.
•
He assumed that the Earth had started life as a ball of molten rock and calculated the time it
•
would take to cool to its current temperature. However, Charles Darwin, who had published his theory of Evolution by Natural Selection did not feel that this was enough time to account for biological changes he had observed. Other biologists agreed
William Thompson •
However, Thompson’s ages were supported by independent calculations by others – The German Physicist Herman von Helmholtz in 1856 calculated an age of 22 million years – The Canadian astronomer Simon Newcomb in 1892 calculated an age of 18 million years – Charles Darwin’s theon astronomer George calculated an age of 56 million yearsson, based the amount of timeDarwin he thought was needed for Earth to develop a 24 hour day from tidal friction – In 1899-1900, John Joly, from the University of Dublin, calculated an age of 80 to 100 million years based on the amount of time needed to accumulate all the salt in the oceans from erosion – All these calculations tended to support William Thompson’s ideas and calculations. So where did William Thompson go from here?
Lord Kelvin • In 1869 William Thompson was involved in a very famous debate with a certain Thomas H Huxley… • In 1892 he was rasied to the peerage and became Lord Kelvin in recognition for his many scientific achievements. • In 1897 he delivered his famous lecture “The Age of the Earth as an Abode Fitted for Life” in which he reduced his previous estimate to between 20 and 40 million years. • But had he missed something…?
Mantle Currents •
Lord Kelvin has assumed that the cooling of the Earth was governed only by thermal gradients and did not take into account convective currents within the mantle which threw his age out
•
In 1895, John Perry produced an estimate for the age of Earth of 2 to 3 billions years old using a model of a convective mantle and thin crust Still a bit young but certainly better than 100 million years
• •
Refinement of this model would only be possible some 60 years later with the advent of plate tectonic theory
The next big thing.. •
•
In 1896, the French chemist Henri Becquerel discovered radioactivity. In 1898, two other French researchers, Marie and Pierre Curie, discovered the radioactive elements polonium and radium. In 1903 Pierre Curie and his associate Albert Laborde announced
•
that radium produces enough heat to melt its own weight in ice in less than an hour. What did this mean?
•
– The Earth produced it own internal heat – Calculations on the age of the Earth based on cooling underestimated the age of the Earth – Lot’s of scientists died of cancer
Radioactivity • •
•
•
In 1903 Marie and Pierre Curie and Henri Becquerel shared the Nobel Prize for Physics for the discovery of radioactivity By now scientists including JJ Thompson and Ernest Rutherford working at the Cavendish Laboratory at Cambridge University had started to unravel the internal structure of the atom. In 1898 Rutherford moved to MacGill University in Montreal as professor of physics where he reported that radiation consisted of three different components which he named alpha, beta and gamma. In 1900 Frederick Soddy came to MacGill as a demonstrator in Chemistry. Together, he and Rutherford formulated the theory of radioactive decay and growth which they expressed as –dN/dt = λN where λ is the decay constant, representing the probability that an atom will decay in unit time and N is the number of radioactive atoms present.
Radioactivity and Dating •
The postulation that radioactive decay could be measured opened the door to radioactive dating.
•
This possibility was recognised by Rutherford and Boltwood around 1905 and in a series of lectures at Yale University that year Rutherford proposed that the age of uranium minerals could be measured by the amount of helium that had accumulated in them, helium being the product of the radioactive decay. He carried out age determinations on several uranium minerals and obtained an age of 500 million years.
•
The state of radioactive dating was reviewed by Arthur Holmes in 1913 in his book “The Age of the Earth” which he wrote when he was just 23.
Radioactive Dating and Isotopes • • • • • •
Problems soon began to arise. The development of radioactivity and the formula for the rate of disintegration was based on assumed simple decay of one element to another. As decay systems began to be worked out it seemed that there were different types of radioactive elements and that the atomic weight of elements was not whole numbers but fractions. Soddy suggested a solution in which he proposed that the place occupied by an element in the periodic table could accommodate more than one kind of atom. A young scientist, F.W Aston, working at the Cavendish Laboratory at the time, set out to examine this and eventually identified 212 of the 287 naturally occurring isotopes. The presence of isotopes and their additional complication to the radioactive decay schemes lead many scientists to abandon the idea of radioactive dating.
Arthur Holmes • • • • • • •
Arthur Holmes work was generally ignored until the 1920s, though in 1917 Joseph Barrell, a professor of geology at Yale, redrew geological history as it was understood at the time to conform to Holmes's findings in radiometric dating. Barrell's research determined that the layers of strata had not all been laid down at the same rate, and so current rates of geological change could not be used to provide accurate timelines of the history of Earth. Holmes's persistence finally began to pay off in 1921, when the speakers at the yearly meeting of the British Association for the Advancement of Science came to a rough consensus that Earth was a few billion years old, and that radiometric dating was credible. Holmes published The Age of the Earth, an Introduction to Geological Ideas in 1927 in which he presented a range of 1.6 to 3.0 billion years, although this was still largely ignored by the geological community. The growing weight of evidence finally tilted the balance in 1931, when the National Research Council of the US National Academy of Sciences finally decided to resolve the question of the age of Earth by appointing a committee to investigate. Holmes, being one of the fe w people on Earth who was trained in radiometric dating techniques, was a committee member, and in fact wrote most of the final report. The age of the Earth as it is accepted today was determined by CC Patterson in 1956 (more about that later…)
Stable versus Unstable Nuclides • Not all combinations of N and Z result in stable nuclides. • Some combinations result in stable configurations – Relatively few combinations – Generally N ≈ Z – However, as A becomes larger, N > Z • For some combinations of N+Z a nucleus forms but is unstable with half lives of > 105 yrs to < 10-12 sec • These unstable nuclides transform to stable nuclides through radioactive decay
Radioactive Decay • •
•
Nuclear decay takes place at a rate that follows the law of radioactive decay Radioactive decay has three important features 1. The decay rate is dependent only on the energy state of the nuclide 2. The decay rate is independent of the history of the nucleus 3. The decay rate is independent of pressure, temperature and chemical composition The timing of radioactive decay is impossible to predict but we can predict the probability of its decay in a given time interval
Radioactive Decay • The probability of decay in some infinitesimally small time interval, dt, is λdt, where λ is the decay constant for the particular isotope • The rate of decay among some number, N, of nuclides is therefore dN / dt = -λN [eq. 1] • The minus sign indicates that N decreases over time. • Essentially all significant equations of radiogenic isotope geochronology can be derived from this expression.
Types of Radioactive Decay • Beta Decay • Positron Decay • Electron Capture Decay • Branched Decay • Alpha Decay
Beta Decay • Beta decay is essentially the transformation of a neutron into a proton and an electron and the subsequent expulsion of the electron from the nucleus as a negative beta particle. • Beta decay can be written as an equation of the form _ 19K
40
-> 20Ca40 + β- + ν + Q _
Where β- is the beta particle, ν is the antineutrino and Q stands for the maximum decay energy.
Positron Decay • Similar to Beta decay except that now a proton in the nucleus is transformed into a neutron, positron and neutrino. • Only possible when the mass of the parent is greater than that of the daughter by at least two electron masses. • Positron decay can be written as an equation of the form 9F
18
-> 8O18 + β+ + ν + Q
Where β+ is the positron, ν is the neutrino and Q stands for the maximum decay energy.
Positron VS Beta Decay The atomic number of the daught er isoto pe is decrea sed by 1 while the neutron number is inc reased by 1.
The atomic num ber of the daughte r iso tope is i ncrea sed by 1 while the neutron numb er is decreased by 1.
Therefore in bot h cases the pare nt and daugh ter iso top es ha ve the same ma ss n umb er and th erefor e sit on an is obar.
Electron Capture Decay • Electron capture decay occurs when a nucleus captures one of its extranuclear electrons and in the process decreases its proton number by one and increases its neutron number by one. • This results in the same relationship between the parent and the daughter isotope as in positron decay whereby they both occupy the same isobar.
Alpha Emission • Represents the spontaneous emission of alpha particles from the nuclei of radionuclides. • Only available to nuclides of atomic number of 58 (Cerium) or greater as well as a few of low atomic number including He, Li and Be. • Alpha emission can be written as: 238 -> 234 + He4 + Q 92U 90Th 2 Where 2He4 is the alpha particle and Q is the total alpha decay energy
Alpha Emission A daughter isotope produced by alpha emission will not necessarily be stable and can itself decay either alpha or emission, orby beta emission both.
Branched Decay • The difference in the atomic number of two stable isobars is greater than one, ie two adjacent isobars cannot both be stable. • Implication is that two stable isobars must be separated by a radioactive isobar that can decay by different mechanisms to produce either stable isobar. • Example 176 decays to 176 via negative beta decay 71Lu 72Hf 176 decays to 176 by positron decay or 72Hf 70Yb
electron capture.
Branched decay scheme for A=38 isobar
Branched decay scheme for A=132 isobar
Decay of 238U to 206Pb
Radiogenic Isotope Geochemistry • Can be used in two important ways 1. Tracer Studies
Makes use of the differences in the ratio of the radiogenic daughter isotope to other isotopes of the element
Can make use of the differences in radiogenic isotopes to look at Earth Evolution and the interaction and differentiation of different reservoirs
Radiogenic Isotope Geochemistry 2. Geochronology
Makes use of the constancy of the rate of radioactive decay
Since a radioactive nuclide decays to its daughter at a rate independent of everything, it is possible to determine time simply by determining how much of the nuclide has decayed.
Radiogenic Isotope Systems • The radiogenic isotope systems that are of interest in geology include the following • K-Ar •• • • • • • •
Ar-Ar Fission Track Cosmogenic Isotopes Rb-Sr Sm-Nd Re-Os U-Th-Pb Lu-Hf
Table of the elements
Radiogenic Isotope Systems • The radiogenic isotope systems that are of interest in geology include the following • K-Ar •• • • • • • •
Ar-Ar Fission Track Cosmogenic Isotopes Rb-Sr Sm-Nd Re-Os U-Th-Pb Lu-Hf
Geochronology and Tracer Studies Isotopic variations between rocks and minerals due to 1. Daughters produced in varying proportions resulting from previous event of chemical fractionation •
40K
•
Basalt → rhyolite by FX (a chemical fractionation process)
•
Rhyolite has more K than basalt
•
40K
•
40Ar/39Ar
→
40Ar
by radioactive decay
→ more 40Ar over time in rhyolite than in basalt
ratio will be different in each 2. Time: the longer 40K → 40Ar decay takes place, the greater the difference between the basalt and rhyolite will be
The Decay Constant •
Over time the amount of the daughter (radiogenic) isotope in a system increases and the amount of the parent (radioactive) isotope decreases as it decays away. If the rate of radioactive decay is known we can use the increase in the amount of radiogenic isotopes to measure time.
•
The rate of decay of a radioactive (parent) isotope is directly proportional to the number of atoms of that isotope that are present in a system, ie Equation 1 that we have seen previously. – dN/dt = -λN, [eq. 1] – where N = the number of parent atoms and λ is the decay constant – The -ve sign means that the rate decreases over time
The Half Life •
The half life of a radioactive isotope is the time it takes for the number of parent isotopes to decay away to half their srcinal value. It is related to the decay constant by the expression
– T1/2 = ln2/λ •
For 87Rb, the decay constant is 1.42 x 10-11y-1, hence, t1/2 87Rb = 4.88 x 1010years. In other words after 4.88 x 1010years a system will contain half as many atoms of 87Rb as it started off with.
Geologically Important Isotopes and their Decay Constants
Using the Decay Constant The number of radiogenic daughter atoms (D*) produced from the decay of the parent since date of formation of the sample is given by D* = No- N
[eq. 2]
Where D* the number of daughter produced byisdecay of the parent atom atoms and N o is the number of srcinal parent atoms Therefore the total number of daughter atoms, D, in a sample is given by D = Do+ D*
[eq. 3]
Using the Decay Constant The two equations can be combined to give D = Do + N–o N
[eq. 4]
Generally, when rocks or minerals first form they contain a greater or lesser amount of the daughter atoms of a particular isotope system, i.e., not all the daughter atoms that we measure in a sample today were formed by decay of the parent isotope since the rock first formed.
Dating of Rocks from Radioactive Decay Recalling that -dN/dt = λN [eq. 1] Integration of the above yields -λt
N=Noe
[eq. 5]
We can substitute this into equation 4 to get D=Do + Neλt – N [eq. 6] which simplifies to D=Do + N(eλt – 1) [eq. 7]
The Radiogenic Decay Equation • Equation 7 is the basic decay equation and is used extensively in radiogenic isotope geochemistry. • In principle, D and N are measurable quantities, while Do is a constant whose value can be either assumed or calculated from data for cogenetic samples of the same age. • If these three variables are known then the above equation can be solved for t to give an “age” for the rock or mineral in question.
Plotting Geochron Data • There are two methods for graphically illustrating geochron data • 1. The Isochron Technique – Used when the decay scheme has one parent isotope decaying to a daughter isotope. – Results in a straight line plot • 2. The Concordia Diagram – Used when more than one decay scheme results in the formation of the daughter isotopes – Results in a curved diagram
Preguntas?
