GEOCHRONOLOGY HONOURS 2008 Lecture 02 The Rubidium – Strontium System

The Rb-Sr system  Strontium has four naturally occurring isotopes all of which are stable – 38 Sr 88, 38 Sr 87, 38 Sr 86, 38 Sr 84  Their isotopic abundances are approximately –82.53%, 7.04%, 9.87%, and 0.56%  However the isotopic abundances of strontium isotopes varies because of the formation of radiogenic Sr 87 from the decay of naturally occurring Rb 87  Therefore the precise isotopic composition of strontium in a rock or mineral depends on the age and Rb/Sr ratio of that rock or mineral.

Rb-Sr Isochrons  If we are trying to date a rock using the Rb/Sr system then the basic decay equation we derived earlier has the form Sr 87 = Sr 87 i + Rb 87 (e t –1)  In practice, it is a lot easier to measure the ratio of isotopes in a sample of rock or a mineral, rather than their absolute abundances. Therefore we can divide the above equation through by the number of Sr 86 atoms which is constant because this isotope is stable and not produced by decay of a naturally occurring isotope of another element.

Rb-Sr Isochrons  This gives us the equation 87 Sr/ 86 Sr = ( 87 Sr/ 86 Sr)i + 87 Rb/ 86 Sr(e t – 1)  To solve this equation, the concentrations of Rb and Sr and the 87 Sr/ 86 Sr ratio must be measured.  The Sr isotope ratio is measured on a mass spectrometer whilst the concentrations of Rb and Sr are normally determined by XRF or ICPMS.

Rb-Sr Isochrons  The concentrations of Rb and Sr are converted to the 87 Rb/ 86 Sr ratio by the following equation. 87 Rb/ 86 Sr = (Rb/Sr) x (Ab 87 Rb x WSr)/(Ab 86 Sr x WRb), where Ab is the isotopic abundance and W is the atomic weight.  The abundance of 86 Sr (Ab 86 Sr) and the atomic weight of Sr (WSr) depend on the abundance of 87 Sr and therefore must be calculated for each sample.

What can we learn from this? 1.After each period of time, the 87 Rb in each rock decays to 87 Sr producing a new line 2.This line is still linear but is steeper than the previous line. 3.We can use this to tell us two important things The age of the rock The initial 87 Sr/ 86 Sr isotope ratio

Determining the Age of a Rock

Let’s look now at the initial ratio

The Fitting of Isochrons  After the 87 Sr/ 86 Sr and 87 Rb/ 86 Sr ratios of the samples or minerals have been determined and have been plotted on an isochron, the problem arises of fitting the ‘best’ straight line to the data points.  The fit of data points to a straight line is complicated by the errors that are associated with each of the analyses

The Fitting of Isochrons

Equations for Calculating the Best Slope and Intercepts of a Straight Line

The initial ratio  How do we know if a series of rocks are co- genetic?  For rocks to be co-genetic, implies that they are derived from the same parent material.  This parent material would have had a single 87 Sr/ 86 Sr isotope value, ie the initial isotope ratio  Therefore, all samples derived from the same parent magma should all have the same 87 Sr/ 86 Sr isotope ratio  If they don’t, it implies that they are derived from a different parent source.

Errorchrons and MSWD Values – A brief view  A line fitted to a set of data that display a scatter about this line in excess of the experimental error is not an isochron.  The sum of the squares of miss-fits of each point to the regression line, may be divided by the number of degrees of freedom (number of data points minus two) to yield the Mean Squared Weighted Deviates (MSWD).  MSWD values give an indication of scatter and can therefore be used to indicate whether an errorchron or isochron is indicated by the data.  MSWD values should be near unity to be indicative of an isochron. Values over 2.5 are definitely errorchrons.