HONOURS 2008
GEOCHRONOLOGY MODULE
Dr. Jodie Miller
Practical Exercise 01
Construction and Interpretation of Rb-Sr Isochrons
Date: 16th September 2008
Due Date: 16th September 2008, 5pm
YOU MUST HAND IN THIS EXERCISE SHOWING ALL WORKING AND WITH A PLOT DRAWN BY
HAND ON GRAPH PAPER.
In this practical exercise we will go through all the steps one-by-one to calculate the age of a rock
using the Rb-Sr system. These days, Rb-Sr is not really used to date rocks because of the better
precision, accuracy and resiliency of other decay systems notably U-Th-Pb. However, initial Sr-isotope
ratios are used extensively in tracer studies and the calculation of the initial Sr-isotope ratio uses the
same equations that would be used to calculate a Rb-Sr age. Moreover, in order to assess the quality
of an initial Sr-isotope dataset, an isochron would normally be constructed to check that none of the
samples have been significantly reset.
You know from the lecture that the radiogenic decay equation for the Rb-Sr system is as follows:
87Sr/86Sr
= (87Sr/86Sr)i + 87Rb/86Sr (et – 1)
[Eqn 1]
Let’s assume that you’ve prepared a rock and sent it off for analysis. The data comes back as follows:
Concentration of Rb = 472ppm, Concentration of Sr =12ppm
87Sr/86Sr
ratio = 2.74
In order to calculate t from equation [1] the 87Rb/86Sr ratio must be determined. To do this we use the
following equation, which was also given in the lecture, to calculate this ratio:
87Rb/86Sr
= Rb/Sr x (Ab87Rb x WSr)/(Ab86Sr x WRb)
[Eqn 2]
The abundance of 86Sr and the atomic weight of strontium depend on the abundance of
87Sr
and
therefore the value of these parameters must be calculated for each system.
Question 01
Calculate the abundances of the isotopes and atomic weight of Sr given the
sample and the following information:
88Sr
= 87.9056 amu;
87Sr
= 86.9088;
87Sr/86Sr
86Sr
ratio of your
= 85.9092 amu; 84Sr =
83.9134 amu; 86Sr/88Sr = 0.1190; 84Sr/88Sr = 0.006756. To get started, begin by casting all the ratios
as an XXSr/88Sr ratio.
Rb has only two isotopes, 85Rb and 87Rb. The Subcommision of Geochronology of the International
Union of Geological Sciences has adopted a constant value of 2.59265 for the ratio
means that the atomic abundance of the
87Rb
85Rb/87Rb,
which
isotope is 27.835% and the atomic weight of Rb is
85.46776.
Question 02
Using the information that you calculated at question 01 and the above information calculate the
87Rb/86Sr
ratio of your sample.
However, in order to calculate the age of our sample, we still need to know the value of the initial
87Sr/86Sr
ratio. In samples that are strongly enriched in radiogenic
87Sr
(ie contained little 87Sr initially),
the date calculated from equation 1 is insensitive to the value of the initial
87Sr/86Sr
isotope ratio.
In the case of our sample for the purposes of the calculation let’s assume that the initial
87Sr/86Sr
ratio
is 0.7082.
Question 03
Using all the above information that you have calculated and been given, calculate the age of your
sample using equation 1.
Remember that we can simplify equation 1 by assuming that 1+ t >> (t)2/2! + (t)3/3! + etc.
Therefore equation 1 becomes
87Sr/86Sr
= (87Sr/86Sr)i + 87Rb/86Sr x t
[Eqn 3]
Question 04
Recalculate the age of your sample using equation 3. Comment on how it differs from your answer to
question 03.
In the above calculations we assumed an initial Sr-isotope ratio. In reality we would plot an isochron to
determine the initial isotope value or else we would have a fairly good idea what the age should be
and use it to calculate the initial Sr isotope value.
Question 05
Assume that the age of your sample is 1040 Ma. What is the initial 87Sr/86Sr ratio of your sample? If
the age is 1045Ma or 1035Ma how does this affect the initial 87Sr/86Sr ratio?
An age difference of 5Ma is quite small for two estimates of an age. In fact just one age might have an
error on it of 5Ma. If this is the case we can see that it has an important impact on the calculation of
initial 87Sr/86Sr isotope ratios that are important in isotope studies of different reservoir systems. One
way of reducing the impact of such errors is to construct an isochron diagram from multiple analyses.
We have seen how this can be used in the lecture to construct an isochron diagram.
Isochron diagrams are constructed by fitting a line of best-fit through several points on a plot of
87Rb/86Sr
vs 87Sr/86Sr. In this plotting space, equation 1 has the form of a straight line, y = b + mx,
where b, the intercept is given by the initial ratio and the slope m is given by e t – 1.
The fitting of a line of best-fit through a set of data points can be problematic because of errors
associated with the analysis of the samples, which give rise to uncertainties in the estimate of the
slope and hence the calculated age. Most isochrons use a least squares regression procedure which
minimizes the deviations of either the x- or y-coordinate (or even better both) from the best fit line.
The equations for calculating the best slope and intercept of a straight line are:
m = [XY – ((X) x (Y) / N)] / [X2 – ((X)2/N)]
[Eqn 4]
b = [X x XY – Y x
[Eqn 5]
(X2)]
/
[(X)2
–Nx
(X)2]
where Y represents the 87Sr/86Sr ratios, X the 87Rb/86Sr ratios and N the number of data points.
Question 06
Using the above relations and given the following table of data, draw using a piece of graph paper an
isochron diagram for the four minerals. Use the equations above as you did in the first three questions
to calculate the age and initial 87Sr/86Sr value for each mineral. From the diagram and using equations
4 and 5 above what is the age and initial 87Sr/86Sr isotope value of the rock.
Mineral
Rb ppm
Sr ppm
87Sr/86Sr
Biotite
467
12
1.2146
Muscovite
217
4
1.4279
K-feldspar
273
4
0.7633
Plagioclase
184
76
0.7398