GEOL212
Due 11/14/16
Homework XI
General instructions: Although you are allowed to discuss homework questions with your classmates, your
work must be uniquely your own. Thus, please answer all questions in your own intelligible words. (When
in doubt, use complete sentences.) If calculations are involved, show all work (so that I will have some
basis for giving partial credit.) Be sure to use appropriate units and significant figures, where appropriate.
Stable isotope notation:
A major task of geochemists (regardless of where their samples come from) is finding
ways to present data on concentrations of elements and their isotopes that make it easy
to make comparisons. Previously we discussed one method – chondrite normalization
– in which the concentration of an element in a given sample is expressed in comparison
to its concentration in CI carbonaceous chondrites. A second geochemical convention
involves expressing proportions of stable isotopes of a particular element.
Fractionation: Recall that a given element may have several stable (i.e. non-radioactive)
isotopes. Although globally, there are typical ratios of these isotopes, natural processes
tend to sort or fractionate them in distinct ways. For example: Carbon has two natural
stable isotopes, 12C and 13C. (Forget 14C for now. It is radioactive, not stable.) On Earth,
much carbon is tied up in the biosphere. It gets there by way of photosynthesis,
however photosynthesizing organisms have a strong preference for 12C. Thus,
photosynthesis fractionates carbon, yielding “organic carbon” (i.e. carbon that has
passed through the biosphere) that is depleted in 13C.
1.) You are familiar with percent notation (%) which expresses parts per hundred. Per
mil notation (‰) expresses parts per thousand in a similar way. Now, after
analyzing a specimen with a mass-spectrometer, you determine that the
concentration of 13C is 0.0110000 g for every 1 g of 12C. Express this in parts per
mil (‰). (Watch significant figures!)
Rather than using absolute concentrations, it is customary to plot ratios of stable isotope
concentrations with respect to a reference with known, unchanging relative
concentrations. These tend to be arbitrary and based on convenience. For decades, the
standard reference for carbon was PDB - Pee Dee Belemnite (a fossil critter with a robust
CaCO3 skeleton recovered from the Pee Dee Formation of North America.) PDB has
0.0112372 g of 13C is for every 1 g of 12C.
Now we need a convenient way to express the ratio of 13C/12C we find in a sample with
respect to this standard. If a sample has a 13C/12C ratio of Rs and the reference (like PDB)
has a 13C/12C ratio of Rr, the sample ratio could be expressed as:
δ13C = (Rs /Rr -1) * 1000‰
This is called delta notation and the value δ13C would be pronounced "Del Carbon
thirteen."
Formulated differently:
Three things to note:
• The ratio is expressed as parts per mil (‰)
• If the sample ratio is identical to the reference standard, then δ13C = 0
• δ13C could be positive or negative. A sample with a positive value has more 13C than
the standard, a negative sample has less.
2.) Calculate δ13C for the sample discussed in Q 1 using the PDB standard.
If your answer isn't negative, you have made a mistake. What does the fact that the
result is negative mean about the amount of 13C?
Now for some applications:
From http://www.geo.arizona.edu/
There are two distinct photosynthetic chemical pathways used by different plants. Most
employ the C3 pathway, but some, including grasses, use the C4 pathway. As the figure
above indicates, these pathways fractionate carbon differently, yielding different values of
δ 13C.
3.) Based on the figure above, which plants exclude 13C more vigorously during
photosynthesis, C3 or C4 plants? (Hint: Pay attention the sign of the x axis.)
From http://www.geo.arizona.edu/
4.) The figure above tracks the concentration of 13C in Pakistan over the last fifteen
million years (oldest values on the left). During which interval does a major shift
in δ 13C values take place?
Given the information discussed in question 3, what change might have occurred in
the dominant plant types during that interval?
It’s not just carbon. Several isotope systems are useful to geochemists, including:
16
O, 17O, and 18O
32
S, 33S, 34S, 36S
84
Sr, 86Sr, 87Sr, 88Sr
In contrast to carbon, which is fractionated by biological effects, oxygen is fractionated by
changes in physical state. When sea water evaporates (see below), water molecules
containing 16O, the lightest isotope, are more likely to enter the vapor phase. Conversely,
in the vapor phase, molecules with heavier isotopes (especially 18O, which is more
common) are more likely to condense.
http://stableisotope.tamu.edu/research-and-education/stable-isotope-principles
5.) Normally, because water circulates constantly between reservoirs of the
hydrologic cycle, this is not important, but what would happen to the δ18O of sea
water over time if evaporating water were prevented from flowing back into the
ocean?
6.) The upper line of the graph below plots δ18O of ocean sediments over the last
500,000 years. (We care only about the y-axis scales on the left. Ignore the lower
curve. In this graph, the oldest values are on the right!)
From Yasuhara et al., 2009. http://www.pnas.org/content/106/51/21717
Describe the general pattern of change in marine 18O concentrations over time. (Be
sure to read the scale properly!)
To what major global environmental changes might these variations be related, and
how?
7.) The commonly used standard for δ18O is Standard Mean Ocean Water (SMOW).
In SMOW, 16O atoms make up 99.76% and 18O make up 0.20%. (The remaining
0.04% would be the rare isotope 17O.) An analyzed sample shows 99.756% of
16
O and 0.204% of 18O. Calculate the sample’s δ18O.
8.) Isotopes of strontium fractionate for yet again different reasons. Hydrothermal
processes in the deep ocean (associated with sea-floor spreading) tend to dissolve
86
Sr, adding it to ocean water, whereas the erosion of continental rocks results in
enriched 87Sr. Thus, the ratio of 87Sr / 86Sr reflects the relative contribution of
these processes. Periods of rapid sea-floor spreading have more 86Sr and therefore
lower values of 87Sr / 86Sr . Periods of rapid continental erosion are the opposite.
(Because Sr isotopes have similar concentrations, researchers typically just
calculate the ratio directly and don’t use δ notation.) The graph above shows this
ratio in marine sediments for the last 135 my. During which geologic period
would you conclude that sea-floor spreading was most active, the Neogene,
Paleogene, or Cretaceous?
9.) By odd coincidence, the ratio of 87Sr / 86Sr has increased in an almost linear
fashion over the last 50 my. This allows it to be used as a tool for geochronology.
For example, suppose you know nothing about a specimen of marine sediments
except that it has a 87Sr / 86Sr of 0.7089 and is definitely younger than 50 my.
Roughly how old is it?
Fractionation lines: Suppose we have a pristine sample substance that is so pure that if
we were to plot it in a graph with δ18O on one axis and δ17O on the other, all samples
would plot in essentially the same place. Then we allow it to be subjected to some
process that fractionates these stable isotopes. In nature, different parts of the sample
will become fractionated to different degrees depending on how intensely they are
exposed to the fractionating process. Nevertheless, the general trend of the fractionation
will be the same. Same direction but different rates. When different samples of the
substance are analyzed and plotted, their values will fall on a fractionation line. This is
because the fractionating process will have been working on both isotopes at the same
rate. Generally, when we see data points plotting along such lines, we can infer that the
samples have a common origin but have been subjected to different degrees of
fractionation.
From Horn et al., 2006. http://pubs.rsc.org/en/content/articlehtml/2006/ja/b504720j
10.) In the graph above, values for several classes of samples (identified by different
symbols) are plotted according to their δ57Fe and δ56Fe values. Which classes of samples
show evidence of a common origin?