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Chapter 16 Stable and Radioactive Isotopes
Each atomic element (defined by its number of protons) comes in different flavors, depending on the number of neutrons. Most elements in the periodic table exist in more than one isotope. Some are stable and some are radioactive. Scientists have tallied more than 3600 isotopes, the majority are radioactive. The Isotopes Project at Lawrence Berkeley National Lab in California that gives detailed information about all the isotopes.
Stable and radioactive isotopes are the most useful class of tracers available to geochemists. In almost all cases the distributions of these isotopes have been used to study oceanographic processes controlling the distributions of the elements. Radioactive isotopes are especially useful because they provide a way to put time into geochemical models.
The chemical characteristic of an element is determined by the number of protons in its nucleus. Different elements can have different numbers of neutrons and thus atomic weights (the sum of protons plus neutrons). The atomic weight is equal to the sum of protons plus neutrons. The chart of the nuclides (protons versus neutrons) for elements 1 (Hydrogen) through 12 (Magnesium) is shown in Fig. 16-1. The Valley of Stability represents nuclides stable relative to decay.
Examples: Atomic Protons Neutrons % Abundance Weight (Atomic Number) Carbon 12C 6P 6N 98. 13C 6P 7N 1. 14C 6P 8N 10 - Oxygen 16O 8P 8N 99. 17O 8P 9N 0. 18O 8P 10N 0.
Several light elements such as H, C, N, O, and S have more than one stable isotope form, which show variable abundances in natural samples. This variability is caused by isotopic fractionation during chemical reactions. Heavier elements like Pb also have several stable isotopic forms but their distributions are controlled more by their different sources than by fractionation.
16-I.B. Oxygen Oxygen has three stable isotopes with the following average natural abundances. (^16) O 99.763% (^17) O 0.0375% (^18) O 0.1995%
The standards used for δ^18 O are either Standard Mean Ocean Water (SMOW) or the PDB standard. SMOW was originally a hypothetical seawater sample defined by Craig (1961) which is now provided to the community by the International Atomic Energy Agency (IAEA). The standard used for determination of paleotemperature was originally a Cretaceous belemnite shell from the PeeDee formation in South Carolina, thus PDB. The δ^18 O values of important oxygen containing materials (relative to SMOW) are shown in Fig 16-2 (from Hoefs, 1980). The first mass spectrometric studies of these isotopes in the sea was by Epstein and Mayeda (1953).
Most of the water in the atmosphere comes from the ocean and most of the evaporation occurs in the tropics. Net evaporation of water from the oceans produces vapor depleted in 18 O as the lighter isotope, 16 O, evaporates faster than (^18) O. Atmospheric circulation transports
this water vapor to higher latitudes. As temperature decreases water vapor condenses. Since 18 O is more likely to condense than 16 O the rain is always heavier than the vapor it originates from and the water vapor becomes progressively depleted in 18 O as rain removes water. In this way the δ^18 O of the rain is a function of the water vapor remaining in the atmosphere.
This process, in which the isotopic composition of the product varies as a result of the extent of reaction is called a Raleigh Distillation (see Appendix 16-A1 for the derivation). Its effect on the isotope composition of the remaining reactant is given by:
R (^) f / R (^) o = f (α-1)
Where f is the fraction of remaining reactant, Rf is the δ value of the reactant at some f and Ro is the δ value when f = 1 (i.e. the initial value)( Fig 16-3 ). In additional to fractional removal, temperature has a large effect. As temperature decreases the fractionation α increases ( Fig 16-4 ). This effect has been taken advantage of to calculate past variations in temperature in Greenland and Antarctic ice core records.
16-I.C. Carbon
Carbon has only two stable isotopes with the following natural abundances: (^12) C 98.89% (^13) C 1.11%
The values of δ^13 C for geologically important materials are shown in Fig 16-6 (Hoefs, 1980).
The standard used for carbon isotopes is the same PeeDee Belemnite shell used for oxygen isotopes. Below are some typical δ^13 C values on the PDB scale in %o.
Standard (CaCO 3 ; PDB) 0 Atmospheric CO 2 - Ocean ΣCO 2 +2 (surface) 0 (deep) Plankton CaCO 3 + Plankton organic carbon - Trees - Atmospheric CH4 - Coal and Oil -
Photosynthesis produces organic matter which is "depleted" in 13 C relative to the substrate CO 2. Compare the values for trees (-26) versus atmospheric CO 2 (-8) and marine plankton (-20) versus ΣCO 2 (+2)( Fig 16-7 ). Representative δ^13 C values are shown for living organisms ( Fig 16-8 ) and biochemical constituents ( Fig 16-9 ) (from Degens, 1968).
C-1. Primary Production (to be added)
C-2. Marine versus Terrestrial (use examples by Sackett, Hedges etc)
C-3. Methane Production (see Reeburgh, Martens, Quay for examples)
16-I.E. Sulfur
Sulfur has four stable isotopes with the following natural abundances: (^32) S 95.02% (^33) S 0.75% (^34) S 4.21% 36S 0.02% Sulfur isotope compositions are expressed as per mil differences relative to sulfur in an iron meteorite called Canyon Diablo Troilite (CDT) according to:
δ^34 S = [( 34 S/ 32 S)sample - (^34 S/ 32 S)CDT] / ( 34 S/ 32 S)CDT x 1000
Thode et al (1949) was one of the first to document wide variations in the abundances of sulfur isotopes.
The range of δ^34 S in geological materials is shown in Fig 16-14 (from Hoefs, 1980). It is interesting to note that δ^34 S of seawater sulfate is +20%o. This implies that some process is preferentially removing 32 S from the ocean. This process is probably sulfate reduction which produces 32 S enriched sulfide which can precipitate be removed from the ocean as iron sulfide minerals (pyrite, gregite etc). The δ^34 S of sedimentary sulfides over geological time are highly variable but trends exist which led Canfield (1998) to suggest that there was a sulfide-rich deep ocean in the middle- to late- Proterozoic.
E-1. Sulfate reduction
Sulfate reducing bacteria produce sulfide depleted in 34 S (enriched in 32 S) by 4 to 46 per mil compared with the starting sulfate. The depletions are variable because this is a kinetic fractionation that occurs during bacterial sulfate reduction. Based on this fractionation we expect sulfide to be depleted in 34 S by large but variable amounts. Field data show much larger fractionation suggesting that the real system even is more complicated. For example, the Black Sea is the classic marine anoxic basin where sulfate reduction is occurring. Enrichment cultures of sulfate-reducing bacteria produce sulfide depleted in 34 S by 26 to 29 per mil, yet water column sulfide is depleted by 62 per mil (Fry et al, 1991). Canfield and Thamdrup (1994) showed that these large fractionations in sulfide could be produced by a scheme where elemental sulfur (S°) is disproportionated to H 2 S and SO 4 2-^ by sulfur- disproportionating bacteria followed by oxidation of the sulfide to S° ( Fig 16-16 ).
E-2 Paleo variations in δ^34 S By comparison with sulfides, sulfur is removed to gypsum (CaSO 4. 2H 2 O) with little fractionation of sulfur isotopes. Thus the δ^34 S of gypsum in the geological record should reflect the isotopic composition of ambient seawater sulfate. Variations of δ^34 S in marine sulfate minerals from the Precambrain to the present are shown in Fig 16-17. The distribution of sulfur isotopes in seawater has clearly changed due to variations in the relative proportions of the oxidized and reduced reservoirs of sulfur (Holland, 1973). Variations in burial and weathering of pyrite are probably the key processes. The present
value of δ^34 S-SO 4 is about +20 %o but during the Permian the value was about +10 and at the Cambrian/Precambrian boundary it was greater than +30%o. Garrels and Lerman (1984) and Berner (1987) have modeled these variations (together with variations in δ^13 C) in terms of burial and weathering of 1) organic matter (as CH 2 O), 2) sedimentary carbonates (Ca,MgCO 3 ), 3) sedimentary pyrite (FeS 2 ) and 4) evaporitic gypsum (CaSO 4. H 2 O). The global redox reaction can be written as (Garrels and Perry, 1974):
4FeS 2 + 8 CaCO 3 + 7 MgCO 3 + 7 SiO 2 + 31 H 2 O = 8 CaSO 4. 2H 2 O + 2 Fe 2 O 3 + 15 CH 2 O + 7 MgSiO (^3)
The coupled records of δ^13 C and δ^34 S ( Fig 16-17 ) have been used to reconstruct the concentration of atmospheric oxygen over geological history. During the Paleozoic, the ocean became progressively enriched in 13 C and depleted in 34 S because of preferential removal of ocean carbon to organic matter rather than as CaCO 3 and of ocean sulfur to CaSO 4 rather than as FeS 2. There is little doubt that atmospheric O 2 has varied over Phanerozoic time and was higher during the mid-to-late Paleozoic due to increased organic carbon burial however accurate calculations of the atmospheric O 2 concentrations remain difficult (Berner, 1987; 1989).
electron from a higher energy level. When the amount of energy available in a nucleus with a low neutron–proton ratio is at least 1.02 mev (twice the rest mass of an electron), a second process may compete with electron capture. In this situation a proton may transform into a positron (e+) , a neutron, and an antineutrino. The positron and the antineutrino are emitted, leaving the neutron in the nucleus. The resulting daughter has an atomic number one less than the parent. After any of the abovementioned nuclear transformations, the daughter nucleus may still possess more energy than is normal for the stable nucleus. This excess energy is emitted in the form of electromagnetic energy or gamma ( γγγγ ) radiation. All of these forms of energy that result from the decay process (with the exception of neutrinos) can be readily detected after suitable separation chemistry if necessary. The nature of radiation and its detection is discussed more fully in Overman and Clark (1960), Friedlander and Kennedy (1955), and Kruger (1971). In summary, the radioactive decay is:
- Independent of chemical or physical state.
- Independent of temperature and pressure.
- A property only of the nucleus.
2. Mathematical Formulation of Decay The decay rate of a collection of radioactive isotopes is proportional to the number of atoms present. The proportional constant is called the decay constant and the equation has the form of a typical first order reaction. This can be shown theoretically by assuming radioactive decay to be a random process and applying probability considerations. The incremental change in the number of atoms per incremental change in time is equal to the rate of radioactive decay.
dN / N dt
= λ (16.1)
The negative sign appears since the number of radioactive atoms decreases with time. This equation can be rewritten as:
dN dt
= – λN (16.2)
where N = the number of atoms of the radioactive substance present at time t λ = the first order decay constant (time-1^ ) The units of λ are reciprocal time. For example, the decay constant for 238U is 2.22 x 10-1 yr-1. This means that 22 percent of the atoms disintegrates per billion years. The number of parent atoms at any time t can be calculated as follows. Equation 16.2 can be rearranged and integrated over a time interval.
dN N (^) o N
N ∫ =^ –^ λ^0 dt
t ∫ (16.3)
where No is the number of parent atoms present at time zero. Integration leads to
ln
N
N (^) o
= (^) – λt (16.4)
or
N =^ N (^) o e − λt (^) (16.5)
Thus if we start with a fixed number of parent atoms that are not replenished with time, the number of atoms will decrease exponentially with time. The rate of decrease will depend on the magnitude of the decay constant. It is common practice in marine geochemistry to analyze for radioactive isotopes by determining the decay per unit time. This disintegration rate is referred to as the activity and is equivalent to the decay constant times the number of atoms present or:
A = N λ (16.6)
In many instances it is also more convenient to model oceanographic data in terms of activity. Equation (16.5) can be expressed in terms of activity.
N N (^) o
A
A (^) o
= e− λt^ (16.7)
or
ln
A
A (^) o
= − λt (16.8)
or
log
A
A (^) o
λt
The unit of absolute activity used as a reference is the Curie which by IUPAC convention (IUPAC, 1951) is defined as 3.700 x 1010 dps (decays per second). The units of activity used in the oceanographic and geochemical literature depend on the magnitude of the decay rate of interest. In addition, the activity is also commonly referenced to a unit of volume or weight such as dpm/kgsed or dpm/103l. The kilogram is normally preferred to liter in oceanographic measurements because it is independent of temperature and pressure.
3. Half Life The half life is defined as the time required for half of the atoms initially present to decay. After one half life:
N N (^) o
A
A (^) o
Thus
–ln
=^ λ^ t1/2^ (16.11)
5. Parent-Daughter Relationships
Example 16- An important oceanographic example of secular equilibrium is the decay of 226Ra with a half life of 1620 years to 222Rn with a half life of 3.824 days. The growth of 222Rn from 226Ra is shown graphically in Figure 16.18. The initial growth of 222Rn is a
function of the half life of 222Rn as can be seen from the general equation for in growth of the daughter (as derived from Equation 16.5):
A B =^ (A A,0) 1 −^ e
(− 0.693 t / t1/ 2,B)^
If necessary, the half life of the daughter can be determined from the rate of in growth of the daughter. No information about the half life of the long-lived parent can be obtained from the growth of the short lived daughter. However, there are frequently situations where the activity of a parent is conveniently measured by measuring the equilibrium activity of its daughter. An important example is 228Ra which emits a weak β– and is more conveniently analyzed by measuring the alpha decay of its daughter 228Th. At secular equilibrium the activities of 228 Ra and 228 Th are equal.
Using the equation given above, we can see that after five daughter half lives the activity of the daughter is within 3% of that of the parent.
t / t (^) 1/ 2 A (^) B / A (^) A,
Example 16- For decay chains involving several nuclides, all isotopes in the chain will be in secular equilibrium (AA = AB = AC = AD = etc.) if the parent has a long half life relative to all of the daughters. The total disintegration rate will be either λAA or λAA0 depending on whether the decay of the parent is negligible. The 238U decay chain is a prime example (Figure 16-19). The half life of the parent 238U is more than 104 greater than the second largest half life in the decay chain (234U: 2.5x105 yr). Within a few million years of the formation of the earth, the total activity from this decay chain was equal to 12 λ(238U). Now that about one half life of 238U has elapsed, the total radiation from this decay chain is about half what it was during the early days of the earth's history.
Example 16-4: 228Ra-228Th 228Ra with a half life of 6.7 years decays to 228Th which has a half life of 1.
years. 228Ac is an intermediate with a half life of 6.1 hours which we will ignore in this example. The in growth of 228Th and decay of both isotopes is shown in Figure 16- (not shown here). The equilibrium activity ratio of 228Th to 228Ra is 1.39.
Appendix 16-A1: Raleigh Fractionation
Any isotope reaction carried out so that the products are isolated from the reactants will exhibit a characteristic trend in isotopic composition called Raleigh Fractionation. For example consider the progressive formation and removal of raindrops from a cloud. The isotopic composition of the residual water vapor in the cloud is a function of the fractionation factor between vapor and water droplets.
The isotopic composition of the rain and cloud can be calculated as follows: Let A represent the amount of a species containing the major isotope and B the amount containing the trace isotope. The rate each species reacts is proportional to its amounts; thus
dA = kAA 16. and dB = kB B 16.
Since the isotopes react at slightly rates, kA ≠ k (^) B. We define the ratio of these two rate constants as kA/kB = α Thus dB /dA = α B/A 16.
If we rearrange and integrate from some initial values (A°, B°) to the present values (A, B) We obtain
∫ dB/B = α ∫ dA/A 16.
Integrating ln B/B° = α ln A/A° 16. or B/B° = (A/A°)α^ 16.
Dividing both sides by A/A° and rearranging gives
B/A = (A/A°)α-1^ 16. B°/A°
Since species B is only a trace fraction of the total A + B the fraction of residual material, f, is equal to A/A°. Hence
B/A = f α-1^ 16. B°/A°
Subtracting unity from both sides
B/A - B°/A° = f α-1^ - 1 16. B°/A°
The expression for the per mil change in isotopic composition, δ , is given by
(1000) x B/A - B°/A° 16. B°/A°
Thus δ = 1000 (fα-1^ - 1) 16.
The classic example of the Raleigh distillation is the fractionation of oxygen isotopes between water vapor in clouds and rain released from the cloud (Dansgaard, 1964) (Fig 16-3). (^18) O is enriched by 10 per mil in the rain drops. Hence the 18 O will be depleted at a rate
1.010 times faster than 16 O ( α = k18O/k16O = 1.010).
δ = - 1000 ( 1 - f0.10^ ) 16.
The resulting depletion of the 18 O/ 16 O ratio in the residual cloud water is given as a function of the fraction of the original vapor remaining in the cloud ( f ) (Fig A16-1). As f depends on cloud temperature, the relationship can also be given between isotopic composition and cloud temperature.
You can see that the initial drops will be rich in 18 O. As rain is removed the cloud is progressively depleted in 18 O. The 18 O in the rain drops decrease also but they are always enriched relative to the cloud vapor. So the fractionating of oxygen isotopes in rain will depend on cloud temperature but it could also be a function of the history of the air mass. In the studies of Greenland and Antarctic ice cores δ^18 O is usually used to indicate temperature. But the interpretation can be complicated when a site receives rain from air masses with different histories (e.g. Charles et al 199x).
The δ^18 O in average annual rainfall is a function of mean annual air temperature as shown in Figure 16-4.
